United States

Environmental Protection

Agency

Office of Research and Development

Washington, DC 20460

EPA/600/R-99/030

March 1999

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of

Commerce

SCIENCE ALGORITHMS OF THE EPA MODELS-3

COMMUNITY MULTISCALE AIR QUALITY (CMAQ)

MODELING SYSTEM

Edited by:

D. W. BYUN*

 and J. K. S. CHING*

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711
EPA/600/R-99/030

DISCLAIMER

The information in this document has been funded wholly or in part by the United States

Environmental Protection Agency. It has been subjected to the Agency’s peer and

administrative review, and has been approved for publication as an EPA document. Mention of

trade names or commercial products does not constitute endorsement nor recommendation for

use.
EPA/600/R-99/030

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CONTENTS

FOREWORD ............................................................... iii

ACRONYMS .............................................................. xiii

ACKNOWLEDGMENTS .................................................... xvi

EXECUTIVE SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ES-1

1.0 INTRODUCTION TO THE MODELS-3 FRAMEWORK AND THE COMMUNITY

MULTISCALE AIR QUALITY MODEL (CMAQ) ........................ 1-1

 (J. Ching and D. Byun)

1.1 The Models-3 Emissions, Meteorology, and the CMAQ Modeling Systems . . . 1-3

1.2 CMAQ Interface Processors ....................................... 1-5

1.3 The CMAQ Chemical Transport Model (CCTM) ....................... 1-7

1.4 Analysis of CMAQ Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9

1.4.1 Process Analysis (Chapter 16) ................................ 1-9

1.4.2 Aggregation (Chapter 17) ................................... 1-10

1.5 Management of CMAQ Science Information Objects and Codes in Models-3 1-10

1.5.1 Program Control Processors (Chapter 15) ...................... 1-10

1.5.2 CMAQ Code Integration (Chapter 18) ........................ 1-11

1.6 Post Release Studies and Near-Future Plans . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11

1.6.1 CMAQ Evaluation Study ................................... 1-11

1.6.2 Testing Operational Configurations ........................... 1-11

1.6.3 Extensions and Science Additions ............................ 1-12

1.7 Opportunities and Encouragement for Long Term Extensions and Science

Community Involvement ......................................... 1-12

1.8 References .................................................... 1-14

2.0 MODELS-3 ARCHITECTURE: A UNIFYING FRAMEWORK FOR

ENVIRONMENTAL MODELING AND ASSESSMENT . . . . . . . . . . . . . . . . . . . . 2-1

(J. Novak and S. Leduc)

2.1 Introduction .................................................... 2-1

2.2 Overview of the Models-3 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

2.2.1 Dataset Manager .......................................... 2-1

2.2.2 Program Manager .......................................... 2-2

2.2.3 Study Planner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2

2.2.4 Strategy Manager .......................................... 2-3

2.2.5 Tool Manager ............................................. 2-3

2.2.6 Science Manager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5

2.2.7 Model Builder ............................................ 2-5

2.2.8 Source Code Manager ...................................... 2-6

2.2.9 Framework Administrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
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2.3 Models-3 System Architecture ...................................... 2-6

2.4. Schedule and Future Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9

2.5 References ..................................................... 2-9

3.0 DEVELOPING METEOROLOGICAL FIELDS ........................... 3-1

(T. Otte)

3.1 Credits and Disclaimers for Use of MM5 .............................. 3-1

3.2 Meteorology Model Pre-Processing .................................. 3-1

3.2.1 Defining the Simulation Domain (TERRAIN) . . . . . . . . . . . . . . . . . . . . 3-1

3.2.2 Processing the Meteorological Background Fields (DATAGRID) ..... 3-2

3.2.3 Objective Analysis (RAWINS) ................................ 3-2

3.2.4 Setting the Initial and Boundary Conditions (INTERP) . . . . . . . . . . . . . 3-3

3.3 The Meteorology Model (MM5) .................................... 3-3

3.3.1 Brief History .............................................. 3-3

3.3.2 Horizontal and Vertical Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4

3.3.3 Prognostic Equations ....................................... 3-4

3.3.4 Model Physics ............................................ 3-5

3.3.5 Nesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9

3.3.6 Four-Dimensional Data Assimilation ........................... 3-9

3.4 Meteorology Model Post-Processing ................................ 3-10

3.5 Changes to the MM5 System's Software for Models-3 .................. 3-10

3.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11

4.0 EMISSION SUBSYSTEM .............................................. 4-1

(B. Benjey, J. Godowitch, and G. Gipson)

4.1 Emission Inventory Processors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

4.1.1 Discussion ............................................... 4-1

4.1.2 General MEPPS Structure .................................. 4-10

4.2 The MEPPS Emission Processing System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11

4.2.1 The Inventory Data Analyzer (IDA) .......................... 4-13

4.2.2 The MEPPS Input Processor (INPRO) ........................ 4-15

4.2.3 Processing Procedure ...................................... 4-16

4.2.4 Modeled Emission Data .................................... 4-32

4.2.5 Chemical Speciation of Emission Data ........................ 4-77

4.2.6 Output Processor (OUTPRO) ............................... 4-91

4.3 Models-3 Emission Projection Processor (MEPRO) .................... 4-90

4.4 Emission Processing Interface ..................................... 4-93

4.4.1 Overview of Key Features of ECIP . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-93

4.4.2 Plume Rise of Point Source Emissions ......................... 4-95

4.4.3 Method for the Treatment of Initial Vertical Plume Spread ........ 4-98

4.4.4 Vertical Allocation of Plume Emissions ........................ 4-99

4.4.5 Generation of 3-D Emissions ................................ 4-99

4.5 Data Requirements .............................................. 4-99

4.6 Plans for Improvement ......................................... 4-101
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4.7 References ................................................... 4-102

5.0 FUNDAMENTALS OF ONE-ATMOSPHERE DYNAMICS FOR MULTISCALE

AIR QUALITY MODELING ...................................................................................... 5-1

(D. Byun)

5.1 Governing Equations and Approximations for the Atmosphere ........................ 5-1

5.1.1 Governing Equations in a Generalized Curvilinear Coordinate System 5-2

5.1.2 Assumptions of Atmospheric Dynamics ................................................ 5-5

5.2 Choice of Vertical Coordinate System for Air Quality Modeling .................... 5-10

5.3 Coupling of Meteorology and Air Quality ....................................................... 5-17

5.3.1 Meteorological Data for Air Quality Modeling .................................... 5-17

5.3.2 Off-line and On-line Modeling Paradigms ........................................... 5-17

5.4 Mass Conservation ........................................................................................... 5-21

5.4.1 Mass Consistency in Meteorological Data ........................................... 5-21

5.4.2 Techniques for Mass Conservation in Air Quality Models .................. 5-22

5.4.3 Temporal Interpolation of Meteorological Data .................................. 5-24

5.5 Conclusion ........................................................................................................ 5-25

5.6 References ........................................................................................................ 5-26

Appendix 5A. Tensor Primer and Derivation of the Continuity Equation in a 

Generalized Curvilinear Coordinate System ........................................ 5-29

6.0 GOVERNING EQUATIONS AND COMPUTATIONAL STRUCTURE OF THE

COMMUNITY MULTISCALE AIR QUALITY (CMAQ) CHEMICAL

TRANSPORT MODEL ............................................................................................... 6-1

(D. Byun, J. Young, and M.T. Odman)

6.1 Derivation of the Atmospheric Diffusion Equation ........................................... 6-2

6.2 Representation of Science Processes in CMAQ Modeling System .................... 6-8

6.2.1 Supporting Models and Interface Processors ......................................... 6-8

6.2.2 Modularity Concept of CMAQ .............................................................. 6-9

6.2.3 Description of Science Processes ......................................................... 6-14

6.3 Equivalent Model Formulations for Different Vertical Coordinates ................ 6-25

6.4 Nesting Techniques .......................................................................................... 6-27

6.5 Summary .......................................................................................................... 6-30

6.6 References ........................................................................................................ 6-30

Appendix 6A. Concentration Units Used for Air Quality Studies ............................... 6-33
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7.0 NUMERICAL TRANSPORT ALGORITHMS FOR THE COMMUNITY

MULTISCALE AIR QUALITY (CMAQ) CHEMICAL TRANSPORT MODEL 

IN GENERALIZED COORDINATES ....................................................................... 7-1

(D. Byun, J. Young, J. Pleim, M.T. Odman, and K. Alapaty)

7.1 Numerical Advection Algorithms ....................................................................... 7-2

7.1.1 Conservation Form Equation for Advection .......................................... 7-3

7.1.2 Classification of Advection Schemes ..................................................... 7-5

7.1.3 Description of Advection Schemes in CCTM ........................................ 7-5

7.1.4 Treatment of Boundary Conditions ...................................................... 7-10

7.1.5 Test of Algorithms with Idealized Linear Horizontal Flow Fields ....... 7-11

7.1.6 Vertical Advection ............................................................................... 7-14

7.1.7 Adjustment of Mass Conservation Error .............................................. 7-15

7.2 Vertical Mixing Algorithms .............................................................................. 7-17

7.2.1 Closure Problem ................................................................................... 7-18

7.2.2 Computing Vertical Mixing with the Eddy Diffusion Formulation: 

K-Theory .............................................................................................. 7-20

7.2.3 Flux Form Representation of Vertical Mixing ..................................... 7-30

7.3 Horizontal Mixing Algorithms .......................................................................... 7-42

7.4 Conclusions ...................................................................................................... 7-44

7.5 References ........................................................................................................ 7-45

Appendix 7A Numerical Solvers for Diffusion Equations .......................................... 7-50

8.0 GAS-PHASE CHEMISTRY ........................................................................................ 8-1

(G. Gipson and J. Young)

8.1 Background ........................................................................................................ 8-2

8.2 Chemical Mechanisms in the CMAQ System .................................................... 8-3

8.2.1 CB4 Mechanism ..................................................................................... 8-4

8.2.2 RADM2 Mechanism .............................................................................. 8-5

8.2.3 SAPRC-97 Mechanism .......................................................................... 8-6

8.2.4 Extended Mechanisms ........................................................................... 8-7

8.2.5 Changing or Adding Mechanisms in CMAQ ........................................ 8-10

8.3 Reaction Kinetics ............................................................................................. 8-11

8.3.1 Reaction Rates ..................................................................................... 8-11

8.3.2 Rate Constant Expressions ................................................................... 8-12

8.4 Mathematical Modeling ................................................................................... 8-14

8.4.1 Governing Equations ............................................................................ 8-15

8.4.2 SMVGEAR ........................................................................................... 8-17

8.4.3 QSSA Solver ......................................................................................... 8-21

8.4.4 Summary .............................................................................................. 8-24

8.5 References ........................................................................................................ 8-24

Appendix 8A Chemical Mechanisms Included in the CMAQ System ....................... 8-28
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9.0 PLUME-IN-GRID TREATMENT OF MAJOR POINT SOURCE 

EMISSIONS .................................................................................................................. 9-1

(N. Gillani and J. Godowitch)

9.1 Introduction ........................................................................................................ 9-1

9.2 Overview of the Conceptual Framework of the Plume-in-Grid Treatment .. 9-3

9.3 Formulation of the Plume-in-Grid Modeling Components ................................ 9-4

9.3.1 Description of the Plume Dynamics Model ........................................... 9-4

9.3.2 Formulation of the Plume-in-Grid Module .......................................... 9-11

9.4 Summary .......................................................................................................... 9-27

9.5 References ........................................................................................................ 9-27

10.0 THE AEROSOL PORTION OF MODELS-3 CMAQ ........................................... 10-1

(F. Binkowski)

10.1 Aerosol Dynamics ............................................................................................ 10-3

10.1.1 Modal Definitions ................................................................................. 10-3

10.1.2 New Particle Production by Nucleation ............................................... 10-4

10.1.3 Primary Emissions ................................................................................ 10-5

10.1.4 Numerical Solvers ................................................................................ 10-6

10.1.5 Mode Merging by Renaming ................................................................ 10-9

10.2 Aerosol Dry Deposition .................................................................................. 10-10

10.3 Cloud Processing of Aerosols ........................................................................ 10-10

10.4 Aerosol Chemistry .......................................................................................... 10-13

10.5 Visibility ......................................................................................................... 10-14

10.6 Summary ........................................................................................................ 10-16

10.7 References ...................................................................................................... 10-16

11.0 CLOUD DYNAMICS AND CHEMISTRY .............................................................. 11-1

(S. Roselle and F. Binkowski)

11.1 Background ...................................................................................................... 11-1

11.2 Model Description ............................................................................................ 11-1

11.2.1 Subgrid Convective Cloud Scheme ...................................................... 11-2

11.2.2 Resolved Cloud Scheme ....................................................................... 11-6

11.3 Conclusions ...................................................................................................... 11-7

11.4 References ........................................................................................................ 11-8

12.0 METEOROLOGY-CHEMISTRY INTERFACE PROCESSOR (MCIP) FOR

MODELS-3 COMMUNITY MULTISCALE AIR QUALITY (CMAQ) 

MODELING SYSTEM .............................................................................................. 12-1

(D. Byun, J. Pleim, R. Tang, and A. Bourgeois)

12.1 Introduction ...................................................................................................... 12-1

12.1.1 MCIP Functions ................................................................................... 12-3

12.1.2 MCIP’s Data Dependency ................................................................... 12-5

12.1.3 Computational Structure ...................................................................... 12-7

12.2 Data Types, Coordinates, and Grids ................................................................ 12-9
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12.2.1 Meteorological Data Types .................................................................. 12-9

12.2.2 Coordinates ........................................................................................ 12-13

12.2.3 Modification of Grid Structure ........................................................... 12-17

12.3 Estimation of Physical Parameters ................................................................. 12-22

12.3.1 PBL Parameters ................................................................................. 12-22

12.3.2 Dry Deposition Velocities .................................................................. 12-36

12.3.3 Cloud Parameters and Solar Radiation .............................................. 12-48

12.4 Meteorological Data for CCTM with Generalized Coordinate System ......... 12-51

12.4.1 Thermodynamic Variables: Pressure, Density and Entropy ............... 12-51

12.4.2 Vertical Jacobian and Layer Height ................................................... 12-53

12.4.3 Contravariant Velocity Components .................................................. 12-56

12.4.4 Mass Consistent Temporal Interpolation of Meteorological 

Parameters .......................................................................................... 12-59

12.4.5 Optional Conversion of Nonhydrostatic Data to Hydrostatic

Meteorological Data for MM5 ........................................................... 12-60

12.5 Operation of MCIP ........................................................................................ 12-62

12.5.1 MCIP Modules ................................................................................... 12-62

12.5.2 Building MCIP ................................................................................... 12-62

12.5.3 Executing MCIP ................................................................................. 12-64

12.5.4 Defining Grid and Domain for MCIP ................................................. 12-67

12.5.5 Extension of MCIP for Other Meteorological Models ....................... 12-71

12.6 Concluding Remarks ...................................................................................... 12-72

12.7 References ...................................................................................................... 12-73

Appendix 12A MCIP Output Data ............................................................................ 12-79

Appendix 12B Examples of Nest Domain Definitions for CMAQ system ............... 12-82

Appendix 12C Sample MCIP Configuration File ...................................................... 12-84

Appendix 12D Sample MCIP Run Script .................................................................. 12-86

13.0 THE INITIAL CONCENTRATION AND BOUNDARY CONDITION

PROCESSORS ........................................................................................................... 13-1

(G. Gipson)

13.1 Introduction ...................................................................................................... 13-1

13.2 Overview of the ICON and BCON Processors ................................................ 13-1

13.3 Input Sources .................................................................................................... 13-2

13.3.1 Time Invariant Concentration Profiles ................................................. 13-2

13.3.2 CCTM Concentration files ................................................................... 13-4

13.3.3 Tracer Species ...................................................................................... 13-4

13.4 Spatial Interpolation ......................................................................................... 13-6

13.4.1 Horizontal Interpolation ....................................................................... 13-6

13.4.2 Vertical Interpolation ........................................................................... 13-7

13.5 ICON/BCON Species Processing .................................................................... 13-8

13.6 Mechanism Conversions ................................................................................ 13-10

13.7 ICON/BCON Applications ............................................................................. 13-11
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13.8 References ...................................................................................................... 13-12

14.0 PHOTOLYSIS RATES FOR CMAQ ....................................................................... 14-1

(S. Roselle, K. Schere, J. Pleim, A. Hanna)

14.1 Background ...................................................................................................... 14-1

14.2 Preprocessor JPROC: Calculate Clear-sky Photolysis Rate Table .................. 14-2

14.3 Subroutine PHOT: Table Interpolation and Cloud Attenuation ....................... 14-3

14.4 Conclusions ...................................................................................................... 14-4

14.5 References ........................................................................................................ 14-5

15.0 PROGRAM CONTROL PROCESSING IN MODELS-3 ...................................... 15-1

(J. Young)

15.1 Domain Configuration ...................................................................................... 15-2

15.2 Input/Output Applications Programming Interface .......................................... 15-3

15.3 Other CCTM Configuration Control ................................................................ 15-3

15.3.1 CCTM Process Analysis ...................................................................... 15-3

15.3.2 CCTM Fixed Data ................................................................................ 15-4

15.4 Generalized Chemistry ..................................................................................... 15-5

15.4.1 Design ................................................................................................... 15-5

15.4.2 Operation .............................................................................................. 15-6

15.4.3 Supported Reaction Types ................................................................... 15-8

15.4.4 Mechanism Parsing Rules .................................................................... 15-9

15.4.5 Chemical Species Include Files ............................................................ 15-9

15.6 Conclusion ...................................................................................................... 15-15

15.7 References ...................................................................................................... 15-15

16.0 PROCESS ANALYSIS .............................................................................................. 16-1

(G. Gipson)

16.1 Integrated Process Rate Analysis .................................................................. 16-2

16.1.1 Computation of Integrated Process Rates ............................................ 16-2

16.1.2 Example IPR Analyses ......................................................................... 16-4

16.1.3 Implementation of IPR Analysis in the CMAQ System ....................... 16-5

16.1.4 Use of the PACP to set up an IPR Analysis ......................................... 16-6

16.2 Integrated Reaction Rate Analysis ................................................................... 16-8

16.2.1 Computation of Integrated Reaction Rates .......................................... 16-9

16.2.2 Example IRR Analyses ...................................................................... 16-10

16.2.3 Implementation of IRR Analysis the CMAQ system ........................ 16-12

16.2.4 Use of the PACP to set up an IRR Analysis ...................................... 16-13

16.3 Conclusion ...................................................................................................... 16-18

16.4 References ..................................................................................................... 16-19
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17.0 AN AGGREGATION AND EPISODE SELECTION SCHEME DESIGNED TO

SUPPORT MODELS-3 CMAQ ................................................................................ 17-1

(R. Cohn, B. Eder, and S. Leduc)

17.1 Introduction ...................................................................................................... 17-1

17.1.1 Background .......................................................................................... 17-1

17.1.2 Objectives ............................................................................................. 17-2

17.2 Summary of the Approach ............................................................................... 17-3

17.2.1 Basic Elements of the Methodology .................................................... 17-3

17.2.2 Rationale, Scope, and Limitations ........................................................ 17-4

17.2.3 Strategy ................................................................................................ 17-5

17.3 Cluster Analysis of Wind Fields ....................................................................... 17-7

17.3.1 Description of Wind Data .................................................................... 17-7

17.3.2 Basic Cluster Analysis Technique ........................................................ 17-7

17.3.3 Illustration of Cluster Analysis Results ................................................ 17-8

17.4 Evaluation of Alternative Aggregation Approaches ...................................... 17-10

17.4.1 Description of Alternative Approaches .............................................. 17-10

17.4.2 Description of Meteorological Data ................................................... 17-11

17.4.3 Analysis Methods ............................................................................... 17-11

17.4.4 Results ................................................................................................ 17-12

17.5 Refinement of the Sampling Approach .......................................................... 17-20

17.5.1 Determination of Appropriate Numbers of Strata and Events ........... 17-21

17.5.2 Selection of Stratified Sample of Events ............................................ 17-26

17.6 Application and Evaluation ............................................................................ 17-28

17.6.1 Application of the Aggregation Procedure ......................................... 17-28

17.6.2 Evaluation .......................................................................................... 17-30

17.7 Summary and Discussion ............................................................................... 17-31

17.8 References ...................................................................................................... 17-32

18.0 INTEGRATION OF SCIENCE CODES INTO MODELS-3 ................................. 18-1

(J. Young)

18.1 Introduction ...................................................................................................... 18-1

18.2 Classes and Modules ........................................................................................ 18-3

18.2.1 Operational Design ............................................................................... 18-3

18.2.2 CGRID ................................................................................................. 18-4

18.2.3 Class Driver .......................................................................................... 18-5

18.2.4 Synchronization Time Step ................................................................... 18-6

18.3 Input/Output Applications Programming Interface .......................................... 18-7

18.4 Code Configuration Management .................................................................... 18-9

18.4.1 The Need .............................................................................................. 18-9

18.4.2 The Tool ............................................................................................. 18-10

18.4.3 The Repository ................................................................................... 18-11

18.5 How a Model is Constructed .......................................................................... 18-13

18.5.1 Object Oriented Concepts .................................................................. 18-13

18.5.2 Global Name Table Data .................................................................... 18-13
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18.5.3 Build Template ................................................................................... 18-14

18.6 How a Model is Executed .............................................................................. 18-17

18.7 Using the Models-3 Framework ..................................................................... 18-17

18.8 Conformant Code ........................................................................................... 18-18

18.8.1 Thin Interface ..................................................................................... 18-18

18.8.2 Coding Rules ...................................................................................... 18-19

18.8.3 Science Process Code Template ........................................................ 18-20

18.8.4 Robustness and Computational Efficiency ........................................ 18-23

18.9 Conclusion ...................................................................................................... 18-24

18.10 References ...................................................................................................... 18-24
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FOREWORD

The Models-3 Community Multiscale Air Quality (CMAQ) modeling system has been developed

under the leadership of the Atmospheric Modeling Division of the EPA National Exposure

Research Laboratory in Research Triangle Park, NC. This new generation of modeling software

was under development for seven years and was made available in June 1998 without charge for

use by air quality regulators, policy makers, industry, and scientists to address multiscale,

multi-pollutant air quality concerns.

Models-3/CMAQ has a unique framework and science design that enables scientists and 

regulators to build their own modeling system to suit their needs. Users can access pre-installed

modeling systems provided by the EPA or can incorporate their own modeling systems to work

within the existing framework software.

This direct user involvement is key to the concept of a community modeling and analysis 

system. This approach to model development, application, and analysis leverages the

community's complementary talents and resources to set new standards for rapid incorporation of

better science into air quality model applications. The resulting comprehensive system forms the

foundation upon which the community, including governments, industry, academia, and other

stakeholders, can collaborate in the examination of issues and the subsequent development of

strategies that meet society challenges of environmental protection.

The release of Models-3/CMAQ is one of the many steps which we hope will unite the 

community under the common goal of advancing our knowledge and abilities to tackle critical

problems of the future in far more effective ways than have been attempted in the past. 

Scientifically sound modeling systems, developed and supported by the community, are one

method of achieving this goal.

The June 1998 release of the Models-3/CMAQ computer code was accompanied by a User

Manual [EPA-600/R-98/069(b)] to serve as a reference on how to use the software system. This

Science Document is the counterpart to the User Manual in that it presents the peer reviewed

scientific bases for the Models-3/CMAQ modeling systems. This document also includes

components such as interface processors, process analysis routines, and the present and planned

evaluation program. 

F. A. Schiermeier

March 1999
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ACKNOWLEDGMENTS

The development of the science components of the Models-3 Community Multiscale Air Quality

(CMAQ) system represents a major undertaking by a large team of dedicated atmospheric

scientists and a relatively long term effort beginning in the early 1990s, and covers a wide area of

subject material as embodied in each of the contributing chapters. Most of the EPA Models-3

CMAQ Science Team are from the Atmospheric Modeling Division (AMD) in the EPA Office of

Research And Development’s National Exposure Research Laboratory (NERL). With several

exceptions the contributing authors from this Division are on detail from the Air Resources

Laboratory of the National Oceanic and Atmospheric Administration (NOAA). The NOAAAMD effort is supported through Interagency Agreement (DW13937252) with the EPA. The

authors of each of the chapters of this document would like to collectively express their gratitude

to the other members of the NOAA Division. In particular we acknowledge the encouragement

and support of the Director of the Atmospheric Modeling Division, Francis Schiermeier. We are

indebted to Dr. Robin Dennis for his vision and role in ensuring the implementation of holisticone-atmosphere approach into CMAQ. We also recognize the technical help from our

colleagues Tom Pierce, Steven Howard, Alfreida Torian, and Gary Walter. 

We also want to recognize the contributions, helpful discussions, and assistance of many

members of the science community, either through formal agreements or through peer interest. 

For example, the work was supported by several cooperative agreements including:

• Atmospheric Modeling Research-Scientific and Computational (CR-822066: MCNC),

Principal Investigator (PI): Kenneth Galluppi Ed Bilicki, Steve Fine, Alison Eyth, and

Rohit Mathur;

• Research on Computational Framework in Generic Grids, Adaptive Grids, and Subgrid

Treatment of Air Quality Simulation (CR-822053: MCNC), PI: Talat Odman; with R.K.

Srivastava and D.S. McRae, North Carolina State University);

• Transport Algorithms for Air Quality Simulation Models (CR-822059, MCNC), PI: Talat

Odman;

• Emissions Modeling Research with High-Performance Computing (CR-822074: MCNC),

PI: Carlie Coats;

• Advanced Modeling of Meteorology in Support of Air Quality Models (CR-822628:

(MCNC), PI: Aijun Xiu, Kiran Alapaty, John N. McHenry, and Adel F. Hanna; with

Nelson L. Seaman and Aijun Deng, Pennsylvania State University; and John S. Kain,

National Severe Storms Laboratory);

• A Flexible and Efficient Methodology for Modeling Aerosol for Air Quality Models 

(CR-823634: MCNC), PI: Uma Shankar, Mark Read and Atanas Trayanov; with Anthony 

Wexler, University of Delaware; and John H. Seinfeld, California Institute of Technology;

• Develop Methods for Technology Transfer of Advanced Regional/Urban Air Quality 

Models (CR-822080: NCSU), PI: Alan Schula; and

• Plume-in-Grid development for a Multiscale Air Quality Modeling System (IAG

DW64937190, Tennessee Valley Authority (TVA)), PI’s: Robert E. Imhoff; with Noor

Gillani, Arastoo Biazar (now at Monash University, Australia), and Yu-Ling Lu,

University of Alabama, Huntsville).
EPA/600/R-99/030

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The following scientists also contributed under the formal contracts listed: Ruen Tang, Chris

Maxwell, and Hao Jin of the Technical Support Group, Dyntel Corp. (General Services

Administration IAG DW47937823); Tod Plessel, and Yan Ching Zhang of the Visualization

Laboratory, Lockheed Martin (EPA Contract 68-W7-0055); and Nick Moghari, Joe Susick, and

Dave Tivel of Science Applications International Corporation (SAIC) (EPA Contract 68-W1-

0055).

Significant contributions were made by: visiting scientists, including Sang-Mi Lee of the Seoul

National University, Korea, Chong Bum Lee of the KangWeon University, Korea, and Seiji

Sugata of the National Institute for Environmental Studies, Japan; UCAR’s post doctoral fellows

Yonghong Li, Qingyuan Song and Shoba Kondragunta; and Dr. Ingmar Akermann of Ford

Research in Aachen, Germany.

It is also a pleasure to thank the colleagues who engaged us in many seminal technical

discussions on various aspects of the CMAQ system. We recognize Professors Harvey Jeffries,

University of North Carolina at Chapel Hill; Ted Russell, Georgia Institute of Technology;

Nelson Seaman and Jack Kain, Pennsylvania State University; Dick McNider, University of

Alabama, Sonia Kreidenweis, Colorado State University, Panos Georgeopolus of Rutgers

University, and Itsushi Uno of Kyushu University, Japan. Many of our EPA colleagues provided

stimulating discussion or reviews of our effort including Gail Tonnesen, Deborah Luecken, Carey

Jang, John S. Irwin (NOAA) and Ed Edney. 

We are indebted to the following peer reviewers, who gave unselfishly of their time and whose

comments and suggestions were extremely valuable in improving the scientific aspects of the

report. Listed in alphabetical order, the reviewers are followed by the chapter(s) they reviewed: 

Jeff Brook, Atmospheric Environment Service, Canada (Ch. 17); David Chock, Ford Research

Laboratory (Ch. 2 and 7); Henry Hogo, Southern California Air Quality Modeling Division (Ch.

8 and 16); Sasha Madronich, National Center for Atmospheric Research (Ch. 14); Paulette

Middleton, RAND Environmental Science & Policy Center (Ch. 10); Ted Russell, Georgia

Institute of Technology (Ch. 18); Nelson Seaman, Pennsylvania State University (Ch. 3); 

Christian Seigneur, Atmospheric and Environmental Research, Inc. (Ch. 10 and 11); Trevor

Sholtz, ORTECH Corporation (Ch. 4); Saffet Tanrikulu, California Environmental Protection

Agency (Ch. 9 and 12); Robert Yarmartino, Earth Tech (Ch. 5 and 6); and Zion Wang (Ch. 13,

15, and 16).

Finally, the editors note with great appreciation, the efforts of Brian Eder, who facilitated many

of the activities and tasks involved in the preparation and completion of this document. We

thank the Raleigh, North Carolina, staff of SAIC, especially Alice Gilliland (now with NOAAAMD) and Andrea Verykoukis for their critical contributions in the area of technical editing,

assuring a high level of consistency and quality in all the chapters of this manuscript. We are

also grateful to Alice Gilliland for her invaluable work on the Executive Summary.
EPA/600/R-99/030

EXECUTIVE SUMMARY

THIS SCIENCE DOCUMENT PRESENTS THE PROCESSORS AND ALGORITHMS THAT

EMBODY THE INITIAL RELEASE OF THE MODELS-3 COMMUNITY MULTISCALE

AIR QUALITY (CMAQ) MODELING SYSTEM. CMAQ IS A MULTIPLE POLLUTANT

MODEL THAT CONTAINS NEW SCIENTIFIC APPROACHES TO AIR QUALITY

MODELING, WHICH REPRESENT THE CURRENT STATE OF SCIENCE. This CMAQ

Science Document is a living document that will be updated as the state of the science

progresses. The CMAQ Science Document provides a basis and point of reference for the state

of the science captured in the June1998 initial release of Models-3. Current and future efforts to

improve the Models-3 modeling system(s) will depart from the scientific reference points

presented in this document.

Models-3 is a flexible software system that provides a user-interface framework for CMAQ air

quality modeling applications and tools for analysis, management of model input/output, and

visualization of data. The Models-3 framework relies on two modeling systems to provide the

meteorological and emissions data needed for air quality modeling. With this data, the Models-3

CMAQ modeling system can be used for urban and regional scale air quality simulation of

tropospheric ozone, acid deposition, visibility, and particulate matter (PM2.5 and PM10). The

meteorological and emissions modeling systems that are provided with the current release of

Models-3 will be described in this document. However, CMAQ is designed as an open system

where alternative models can be used to generate the data.

This CMAQ Science Document contains chapters that address specific scientific and technical

issues involved in the development and application of the Models-3 CMAQ modeling system. 

The principal researchers for each model component or function authored the coinciding chapter

in this document. They serve as the points of contact for scientific questions regarding their

CMAQ air quality model components. For instructions on using the Models-3 framework and

using the MM5, MEPPS, and CMAQ modeling systems, refer to the Models-3 User Manual

(EPA/600/R-98/069b, National Exposure Research Laboratory, Research Triangle Park, NC)

and Tutorial (EPA/600/R-98/069c, National Exposure Research Laboratory, Research Triangle

Park, NC).

An overview of the MEPPS emissions, MM5 meteorology, and CMAQ air quality modeling

systems is provided in Chapter 1. Chapter 2 then introduces the Models-3 framework and

structure and explains how the framework’s user-interface is used with the MEPPS and CMAQ

modeling systems. More detailed discussions on the modeling systems are then discussed

separately in the following chapters. The amount of detail and the length of these discussions

vary depending on whether this information has already been provided elsewhere. Some

chapters provide a synopsis of the scientific components and refer to previously published

material on the subject, while other chapters provide extensive detail on new scientific

techniques that are not currently described in other publications.
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MM5 Meteorological data are essential for many processes simulated in the CMAQ chemical

transport model including transport, chemistry, and cloud processes. The Fifth-Generation Penn

State/NCAR Mesoscale Model (MM5) is the only meteorology model compatible with the initial

release of Models-3. MM5 is a complex, state-of-the-science community model, and it is

maintained by NCAR. MM5 is well documented by its primary developers in technical notes and

refereed journal articles. Chapter 3 briefly describes the scientific aspects of MM5, including

grid definitions, model physics, nesting, and four dimensional data assimilation. These

descriptions generally direct the user to more complete documentation about particular aspects of

MM5. To promote the flexibility of CMAQ, additional meteorology models will be compatible

with Models-3 future releases.

MEPPS Chapter 4 provides a description of the Models-3 Emission Processing and

Projection System (MEPPS) structure, its scientific approach, and the assumptions used in

modeling and processing emission data in the Models-3 framework. The chapter also discusses

data flow and quality control used with emission inventory and meteorological input data for

MEPPS. The description of the main Emission Processor addresses the basis of spatial and

temporal allocation procedures, and the methods and assumptions used in modeling mobile and

biogenic emissions and in the “lumping” of individual chemical species are also presented. This

chapter also explains the procedures used by the Models-3 Emission Projection Processor to

estimate emission data for use in modeling future air quality scenarios.

THE CMAQ CHEMICAL TRANSPORT MODEL (CCTM)

Fundamentals of One-Atmosphere Dynamics for Multiscale Air Quality Modeling

Chapter 5 provides information essential to the proper use of meteorological data in air

quality modeling systems. The chapter introduces a robust and fully compressible set of

governing equations for the atmosphere, which provides an integral view of atmospheric

modeling. The limitations of several simplifying assumptions on atmospheric dynamics

are presented, as are concepts of on-line and off-line coupling of meteorological and air

quality models. In addition, this chapter describes a procedure for conserving the mixing

ratio of trace species even in the case of meteorological data that are not mass consistent. 

In summary, Chapter 5 attempts to bridge the information gap between dynamic

meteorologists and air quality modelers by highlighting the implication of using different

meteorological coordinates and dynamic assumptions for air quality simulations.

Governing Equations and Computational Structure In Chapter 6, the governing

diffusion equation is derived in a generalized coordinate system, which is suitable for

multiscale atmospheric applications. CMAQ’s use of generalized coordinates for its

governing equations provides the flexibility to span multiple scales and to incorporate

meteorological data on different coordinates. The CMAQ system’s modularity concepts

and fractional time-step formulation, and CCTM’s key science processes are described. 

Chapter 6 also presents the dynamic formulations of several popular Eulerian air quality

models as emulated by the governing diffusion equations in the generalized coordinate

system.
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Numerical Transport Algorithms The transport processes in the atmosphere primarily

consist of advection and diffusion. In Chapter 7, CMAQ’s numerical algorithms for

advection and vertical and horizontal diffusion are discussed. To provide the CMAQ

system with multiscale capability, the transport processes, both advection and diffusion,

are formulated in conservation (i.e., flux) forms for the generalized coordinate system. 

Therefore, CMAQ’s numerical transport algorithms will function under a wide variety of

dynamical situations and concentration distribution characteristics. Users are encouraged

to experiment with their own algorithms to test different numerical schemes for air quality

simulations.

Gas Phase Chemistry Chapter 8 examines the way gas-phase chemistry is treated

in CMAQ. The CMAQ system currently includes two base chemical mechanisms,

RADM2 and CB4, while the incorporation of a third, the SAPRC97 mechanism, is

planned for the future. Chapter 8 describes each of these chemical mechanisms as well

as the manner in which the first two are linked to the aqueous chemistry and aerosol

formation processes. The chapter also discusses procedures for entering new chemical

mechanisms in the CMAQ system, the representation of reaction kinetics, the numerical

modeling of gas-phase chemistry, and the two numerical solvers included in CMAQ,

SMVGEAR and a variant of the QSSA method.

Plume-in-Grid Chapter 9 introduces the plume-in-grid (PinG) technique

developed for CMAQ. PinG is designed to treat more realistically the dynamic and

chemical processes impacting selected major point source pollutant plumes in CMAQ. 

The Plume Dynamics Model (PDM) simulates plume rise, horizontal and vertical plume

growth, and transport of each plume section during the subgrid scale phase. The PinG

module simulates the relevant physical and chemical processes during a subgrid scale

phase. This technique is in contrast to the traditional Eulerian grid modeling method of

instantly mixing the point source emissions into an entire grid cell volume. Chapter 9

describes the technical approach and model formulation of the relevant processes, and

discusses the capabilities and limitations of the initial version of the PinG approach.

The Aerosol Module One of CMAQ’s key strengths is that it is a multi-pollutant model

that fully addresses the criteria pollutants PM and ozone. Chapter 10 discusses the

aerosol module of CMAQ, which is designed to be an efficient and economical depiction

of aerosol dynamics in the atmosphere. This chapter discusses the techniques for

distributing particulates in three modes: coagulation, particle growth by the addition of

new mass, and particle formation. The aerosol module considers both PM2.5 and PM10

and includes estimates of the primary emissions of elemental and organic carbon, dust,

and other species not further specified. Secondary species considered are sulfate, nitrate,

ammonium, water and organic from precursors of anthropogenic and biogenic origin. 

Cloud Chemistry and Dynamics Chapter 11 discusses the role and functions of

clouds in CMAQ. Clouds are involved in aqueous chemical reactions, vertical mixing of

pollutants, and removal of aerosols by wet deposition, all of which affect the
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concentration of air pollutants. CMAQ’s cloud module performs several functions

related to cloud physics and chemistry, and it models three types of clouds: sub-grid

convective precipitating clouds, sub-grid non-precipitating clouds, and grid-resolved

clouds. The cloud module vertically redistributes pollutants for the sub-grid clouds,

calculates in-cloud and precipitation scavenging, performs aqueous chemistry, and

accumulates wet deposition amounts.

CMAQ INTERFACE PROCESSORS PREPARE INPUT DATA FROM SOURCES

INCLUDING THE EMISSION AND METEOROLOGICAL MODELING SYSTEMS FOR USE

IN THE CMAQ CTM. EACH OF THESE PROCESSORS, EACH OF WHICH HAVE

SPECIFIC FUNCTIONS, ARE DESCRIBED IN THE CHAPTERS MENTIONED BELOW. 

The interface processors that handle input data from the emissions and meteorological models are

essential because CMAQ is an open system in which meteorological and emissions data are

calculated separately (i.e., “off-line”), rather than during the chemical transport model

simulation. These interface processors also add extra quality control, so that inconsistencies

between input data and the CCTM are minimized.

ECIP In addition to describing the Models-3 MEPPS emission modeling system,

Chapter 4 discusses the Emission-Chemistry Interface Processor (ECIP). ECIP serves as

the key link between the MEPPS system and CCTM. ECIP’s primary function is to

generate hourly 3-D emission data files for CCTM from the individual emission file types

produced by the MEPPS. The key inputs for ECIP are the area emissions file, the stack

parameter and emission files for the point sources generated in MEPPS, and a set of

meteorological data files generated by the Meteorology-Chemistry Interface Processor

(MCIP) for the CCTM domain. All major point sources are subject to plume-rise and

initial vertical dispersion processes before being allocated to a particular vertical model

layer. 

MCIP Chapter 12 describes MCIP, which links meteorological models, such as MM5,

with the CCTM system to provide the complete set of meteorological data needed for air

quality simulation. To support CCTM’s multiscale generalized coordinate

implementation, MCIP provides appropriate dynamic meteorological parameters to allow

mass-consistent air quality computations. MCIP deals with issues related to data format

translation, conversion of parameter units, diagnostic estimations of parameters not

provided, extraction of data for appropriate window domains, and reconstruction of

meteorological data on different grid and layer structures. MCIP also relies on the

Landuse Processor (LUPROC) to provide landuse and vegetation information to define

surface characteristics to compute dry deposition and other PBL parameters. LUPROC

extracts information about landuse in the CMAQ domain from a landuse database and

converts it into the fractional landuse data used in MCIP. 

Initial and Boundary Conditions Initial conditions provide a simulation’s starting

point, while boundary conditions define influences from outside the domain.
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Chapter 13 describes the two interface processors that generate the concentration fields

for the initial and boundary conditions for CCTM. The chapter describes how the initial

condition (ICON) and boundary condition (BCON) processors can be used to generate

the concentration fields from either predefined default vertical profiles or from other

CMAQ simulation results when model nesting is being performed. This chapter also

discusses generating initial and boundary concentrations for special tracer species and

procedures for horizontal and vertical interpolation and conversions between chemical

mechanisms.

Photolysis Rate Processor Many chemical reactions in the atmosphere are initiated by

the photodissociation of numerous trace gases, including NO2, O3, and HCHO. Chapter

14 describes the photolysis rate processor (JPROC) that produces the photolysis rates

used in the CMAQ chemical transport simulation. JPROC predicts photolysis rates for

various altitudes, latitudes, and zenith angles. Currently, the radiative transfer algorithm

assumes clear-sky conditions (i.e., no clouds present), and CCTM then attenuates for

cloudiness.

As described above, each of the CMAQ interface processors incorporate raw data for CMAQ

and perform functions such as calculating parameters and interpolating or converting data. The

functions of the interface processors also include capabilities to handle raw data with various

resolutions or measurement units. Raw input data is currently specified in the source code for

JPROC, LUPROC, ICON, and BCON; however, the interface processors in future releases of

CMAQ will be modified to handle a more generalized set of input data.

PROGRAM CONTROL PROCESSORS, A SET OF PROGRAMS EMBEDDED IN THE

MODELS-3 FRAMEWORK, HANDLE SCIENCE INFORMATION OBJECTS SUCH AS GRID

AND LAYER SPECIFICATIONS, CHEMICAL MECHANISMS, AND MODEL

CONFIGURATIONS FOR REPEATED USE ACROSS SEVERAL PROCESS COMPONENTS

OF CMAQ.

Program Control Processing (PCP) Chapter 15 explains how PCP is used within

Models-3 to set up internal arrays, map species names, define global parameters, and

establish linkages among processors in the Models-3 CMAQ system. Specifications

needed for the CCTM simulation (e.g., grid and coordinate conditions and chemical

species names) are entered into the Models-3 system once by the graphical user

interfaces, and an object-oriented database accessible by all model components is

established. PCP utilizes this information in the object database and automatically

generates the required global FORTRAN include files. As a part of PCP, Models-3

CMAQ system employs a generalized chemistry mechanism processor (MP), also called

the “mechanism reader.” It greatly simplifies the task of implementing or altering gasphase chemistry mechanisms and provides the capability of easily and safely using

different mechanisms in the CMAQ system. 
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Integration of Science Codes into Models-3 One of the major objectives of the

Models-3 project was to develop a flexible, comprehensive air quality modeling system

with a modular coding structure that allows easy replacement of science process

components. Chapter 18 describes the modularity concepts, code management method,

and integration schemes of CMAQ science code with the Models-3 framework. The

CMAQ FORTRAN code was integrated into the Models-3 framework with the following

set of design, coding, and implementation standards: (1) modularity to allow easy

exchange of science process solvers, (2) a standard subroutine interface at the module

level, (3) restriction of coding practices, (4) the Models-3 I/O API

(http://www.iceis.mcnc.org/EDSS/ioapi/index.html/), which contains standardized file I/O

functions and a modeler-friendly interface built on top of self-describing netCDF

(http://www.unidata.ucar.edu/packages/netcdf/) files that are portable across most Unix

platforms.

MODELS-3 ALSO PROVIDES ANALYSIS ROUTINES FOR USE WITH CMAQ OUTPUT,

WHICH CAN BE USED TO PROVIDE PROCESS ANALYSIS RESULTS AND STATISTICAL

AGGREGATION TECHNIQUES.

Process Analysis Chapter 16 describes the implementation of process analysis

techniques in the CMAQ modeling system. These techniques can be used in CMAQ to

provide insights into how model predictions are obtained, which is particularly useful

when modeling nonlinear systems like atmospheric photochemistry. Two techniques are

available in the CMAQ system, integrated process rate (IPR) analysis and integrated

reaction rate (IRR) analysis. IPR analysis can be used to determine the relative

contributions of individual physical and chemical processes, and IRR analysis can help

elucidate important chemical pathways and identify key chemical characteristics.

Aggregation Chapter 17 discusses a statistical procedure called aggregation that is

applied to CMAQ’s outputs in order to derive the seasonal and annual estimates required

by assessment studies. Assessment studies require CMAQ-based distributional estimates

of ozone, acidic deposition, and PM2.5, as well as visibility, on seasonal and annual time

frames. Unfortunately, it is not financially feasible to execute CMAQ over such extended

time periods. Therefore, in practice CMAQ must be executed for a finite number of

episodes or “events,” which are selected to represent a variety of meteorological classes. 

The aggregation technique is used to incorporate these episode simulations into annual

and seasonal estimates. 

THE MODEL-3 CMAQ MODELING SYSTEM IS BEING FORMALLY EVALUATED TO

ASSESS THE PERFORMANCE OF CMAQ’S NEW DEVELOPMENTS IN AIR QUALITY

MODELING. THE EVALUATION WILL PROVIDE THE BASIS FOR UNDERSTANDING

THE STRENGTHS OR WEAKNESSES OF THE CURRENT STATE-OF-SCIENCE IN

CMAQ. With an evaluation of CMAQ simulations of 36, 12, and 4 km grid resolution,

CMAQ’s performance can be evaluated on both the regional and urban scales. This evaluation
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will include an initial comparison of relative performance against the RADM model and

diagnostic evaluation against databases from regional studies such as the 1995 Southern Oxidant

Study conducted in the vicinity of Nashville, TN and the 1995 NARSTO-NE study.

CMAQ can be configured for a wide range of applications, from scientific studies to regulatory

applications. While the scientific community can take advantage of CMAQ’s ability to create

alternative applications for research and development purposes, regulatory applications depend

upon a standardized, evaluated form of CMAQ for regulatory applications. The CMAQ

evaluation program will provide the scientific benchmark needed for this. 

FUTURE EXTENSIONS OF CMAQ INCLUDE NEAR-TERM EFFORTS TO PROVIDE A

NEW CHEMICAL MECHANISM AND EMISSION MODELING SYSTEM.

The SAPRC-97 gas phase mechanism will soon be incorporated into CMAQ, in addition

to the current CB-IV and RADM2 mechanisms available. The SAPRC mechanism will

be incorporated with a fixed subset of the approximately 100 organic species contained in

the semi-explicit version of the SAPRC mechanism.

The Sparse Matrix Operator Kernel Emissions modeling system (SMOKE)

(http://envpro.ncsc.org/products/) will also be incorporated into CMAQ in the near-term. 

The SMOKE model formulates emissions modeling in terms of sparse matrix operations

which require considerably less time to perform than current systems.

WE ENCOURAGE THE FULL PARTICIPATION AND INVOLVEMENT OF THE

SCIENTIFIC AND MODELING COMMUNITIES IN THE GROWTH AND USE OF MODELS3 CMAQ. THERE ARE MANY IDEAS AND PLANS FOR FUTURE DEVELOPMENTS OF

CMAQ, INCLUDING TOXIC POLLUTANT MODELING AND LINKAGES TO OTHER

MODELS.

Modeling atmospheric toxic pollutants A key opportunity for CMAQ is developing the

capability to model toxic pollutants. Models of airborne toxic pollutants are essential for

human exposure and risk assessments. They can also be used to assess the exchange of

toxic compounds between the atmosphere and sensitive ecosystems. With the ability to

simulate toxic pollutant processes in addition to the current photochemical oxidants and

particulates, it is planned to transport the CMAQ model to a finer than urban scale to link

with human exposure models. 

New linkages with global models It is hoped that information from the urban and

regional CMAQ applications and from global modeling applications can be bridged. 

CMAQ output, produced using state of the science techniques, can be used to benchmark

or examine the parametric basis of process formulations in global models. In addition,

global model output can be used to improve or enhance the initial and boundary

conditions for regional and urban scale CMAQ simulations. 
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Modeling ecosystems Efforts to combine environmental modeling techniques to

encompass an entire ecosystem is needed to address issues including (a) nutrient cycling

through the atmosphere, water bodies, and soil and (b) acidic wet and dry deposition into

sensitive ecosystems, including critical load analyses. With this ecosystem modeling

approach, air quality issues can be studied in combination with other aspects of

environmental health.

This is the Executive Summary of Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. 

Corresponding author address: Jason Ching, MD-80, Research Triangle Park, NC 27711. 

E-mail: Ching.Jason@epamail.epa.gov

**On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. 

Chapter 1

INTRODUCTION TO THE MODELS-3 FRAMEWORK AND 

THE COMMUNITY MULTISCALE AIR QUALITY MODEL (CMAQ)

Jason Ching*

 and Daewon Byun**

Atmospheric Modeling Division 

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

ABSTRACT

Models-3, a flexible software framework, and its Community Multiscale Air Quality (CMAQ)

modeling system form a powerful third generation air quality modeling and assessment tool

designed to support air quality modeling applications ranging from regulatory issues to science

inquiries on atmospheric science processes. The CMAQ system can address tropospheric ozone,

acid deposition, visibility, fine particulate and other air pollutant issues in the context of “one”

atmosphere perspective where complex interactions between atmospheric pollutants and regional

and urban scales are confronted. This CMAQ Science Document contains chapters that address

specific scientific and technical issues involved in the development and application of Models3/CMAQ system; collectively, it provides the scientific basis and point of reference for the state

of the science captured in the June 1998 initial release of the CMAQ. This chapter provides an

overview and context of each contributing chapter to the CMAQ system.
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1.0 INTRODUCTION TO THE MODELS-3 FRAMEWORK AND THE COMMUNITY

MULTISCALE AIR QUALITY MODEL (CMAQ)

Air quality simulation models are important tools for regulatory, policy, and environmental

research communities. In the United States, the Clean Air Act provides a societal mandate to

assess and manage air pollution levels to protect human health and the environment. The U.S.

Environmental Protection Agency (USEPA) has established National Ambient Air Quality

Standards (NAAQS), requiring the development of effective emissions control strategies for such

pollutants as ozone, particulate matter, and nitrogen species. National and regional policies are

needed for reducing and managing the amount and type of emissions that cause acid, nutrient and

toxic pollutant deposition to ecosystems at risk and for enhancing the visual quality of the

environment. Air quality models are used to develop emission control strategies to achieve these

objectives. Optimal control strategies should be both environmentally protective and cost

effective. Up to now, air quality model paradigms typically addressed individual pollutant issues

separately. However, it is becoming increasingly evident that when pollutant issues are treated in

isolation, the resulting control strategies may solve one set of problems but may lead to

unexpected aggravation of other related pollutant issues. Pollutants in the atmosphere are

subject to myriad transport processes and transformation pathways that control their composition

and levels. Also, pollutant concentration fields are sensitive to the type and history of the

atmospheric mixtures of different chemical compounds. Thus, modeled abatement strategies of

pollutant precursors, such as volatile organic compounds (VOC) and NOx, to reduce ozone levels

may under a variety of conditions, cause an exacerbation of other air pollutants such as

particulate matter or issues of acidic deposition.

The development of comprehensive air quality models started in the late seventies. The Urban

Airshed Model (UAM) (Morris and Meyers, 1990) followed by the Regional Oxidant Model

(ROM) (Lamb, 1983a, 1983b) provided Eulerian-based models for ozone, the former for urban

and the latter for regional scale. Strategies for State Implementation Plans (SIPs) used ROM to

provide boundary conditions for UAM simulations. Attention to acid deposition issues were

addressed in the eighties with the development and evaluation of regional acid deposition models

such as the Regional Acid Deposition Model (RADM) (Chang et al., 1987; Chang et al., 1990),

the Acid Deposition and Oxidant Model (ADOM) (Venkatram et al., 1988), and the Sulfur

Transport and Emissions Model (STEM) (Carmichael and Peters, 1984a, 1984b; Carmichael et

al., 1991). Other major modeling systems included the Regional Lagrangian Modeling of Air

Pollution model (RELMAP) (Eder et al., 1986), a Lagrangian framework system, and semiempirical and statistical models. The genre of models of this period were designed to address

specific air pollution issues such as ozone or acid deposition and to be applied under relatively

prescriptive implementation guidance strategies. Thus, flexibility to deal with other issues, such

as particulate matter or toxics, was very limited. Further, With the passage of the Clean Air Act

Amendments of 1990 (CAAA-90), a wide range of additional issues were identified including

visibility, fine and coarse particles, indirect exposure to toxic pollutants such as heavy metals,

semi-volatile organic species, and nutrient deposition to water bodies. The direct response

approach is to modify, adapt or extend current models to handle more complex implementations

and issues but is both cumbersome and limiting.
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Seeking a more strategic approach to handle the increased modeling requirements of the CAAA90, more comprehensive modeling approaches appear to be needed. With projections for the

increasing rapid pace of the development of computational capabilities at the start of the nineties,

the opportunity arose for a strategic review of modeling approaches leading to design of a system

that would both meet and keep pace with the increasing requirements on air quality modeling, of

incorporating advances in state-of-science descriptions of atmospheric processes, as well as

eliminate impediments of the current genre of models. The scope of such a system must be able

to process great and diverse information from complicated emissions mixtures and complex

distributions of sources, to modeling the complexities of atmospheric processes that transport and

transform these mixtures in a dynamic environment that operates on a large range of time scales

covering minutes to days and weeks. The corresponding spatial scales are commensurately large,

ranging from local to continental scales. On these temporal and spatial scales, emissions from

chemical manufacturing and other industrial activities, power generation, transportation, and

waste treatment activities contribute to a variety of air pollution issues including visibility, ozone,

particulate matter (PM), and acid, nutrient and toxic deposition. The residence times of

pollutants in the atmosphere can extend to multiple days, therefore transport must be considered

on at least a regional scale. NAAQS requirements and other goals for a cleaner environment

vary over a range of time scales, from peak hourly to annual averages. These challenges suggest

that more comprehensive approaches to air quality modeling are needed, and that assessments

and pollution mitigation are achieved more successfully when the problems are viewed in a “one

atmosphere” context that considers multiple pollutant issues. Further discussion of the needs for

the third-generation air quality modeling system can be found in Dennis et al. (1996) and Dennis

(1998). 

To meet both the challenges posed by the CAAA-90 and the need to address the complex

relationships between pollutants, the USEPA embarked upon the Models-3 project and

developed the Community Multiscale Air Quality (CMAQ) system, an advanced air quality

modeling system that addressed air quality from this “one atmosphere” multi-pollutant

perspective. Based on its conceptual design, the high performance computational Models-3

framework serves to manage and orchestrate air quality simulations, using the CMAQ modeling

system. The Models-3 framework is an advanced computational platform that provides a

sophisticated and powerful modeling environment for science and regulatory communities. The

framework provides tools used to develop and analyze emission control options, integrate related

science components into a state-of-the-art quality modeling system, and apply graphical and

analytical tools for facilitating model applications and evaluation. Descriptions of the Models-3

architecture are provided in Chapter 2 and in Novak et al. (1998). CMAQ is a multi-pollutant,

multiscale air quality model that contains state-of-science techniques for simulating all

atmospheric and land processes that affect the transport, transformation, and deposition of

atmospheric pollutants and/or their precursors on both regional and urban scales. It is designed

as a science-based modeling tool for handling all the major pollutant issues (including

photochemical oxidants, particulate matter, acidic, and nutrient deposition) holistically. 

More than six years of investment and commitment from Federal staff and from scientists and

model developers from the environmental and information communities were expended to
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develop the Models-3 framework and the CMAQ air quality modeling system. Models-3 CMAQ

was released to the public in June 1998. The science and model engineering concepts and

progress of the project have been described in two peer-reviewed AWMA Transaction papers

(Byun et al., 1995a; Coats et al., 1995) and others (Byun et al., 1995b, 1996, and 1998a; Ching

et al., 1995). This release version of the Model-3 software is supported by the following

documents under the overall heading “Third Generation Air Quality Modeling System”:

• System Installation and Operations Manual. EPA/600/R-98/069a, National Exposure

Research Laboratory, EPA, Research Triangle Park, NC

• Users Manual. EPA/600/R-98/069b, National Exposure Research Laboratory, Research

Triangle Park, NC

• Tutorial. EPA/600/R-98/069c, National Exposure Research Laboratory, EPA, Research

Triangle Park, NC

• Science Concepts of the Third Generation Air Quality Models: Project Report. In

preparation. Edited by D.W. Byun and A. Hanna. National Exposure Research

Laboratory, EPA, Research Triangle Park, NC

• Science Algorithms of the EPA Models-3 Community Multiscale Air Quality (CMAQ)

Modeling System, Edited by D.W. Byun and J.K.S. Ching. National Exposure Research

Laboratory, EPA, Research Triangle Park, NC (this document)

The project report “Science Concepts of the Third Generation Air Quality Models” summarizes

the basic atmospheric science concepts and mathematical principles pertinent to the development

of the third generation air quality modeling. This document discusses the key scientific features

and options incorporated into the Models-3 CMAQ modeling system. 

1.1 The Models-3 Emissions, Meteorology, and the CMAQ Modeling Systems

The structure of the Models-3/CMAQ system is shown in Figure 1-1. Orchestrated through the

Models-3 system framework, the Community Multiscale Air Quality (CMAQ) modeling system

incorporates output fields from emissions and meteorological modeling systems and several other

data source through special interface processors into the CMAQ Chemical Transport Model

(CCTM). CCTM then performs chemical transport modeling for multiple pollutants on multiple

scales. With this structure, CMAQ retains a flexibility to substitute other emissions processing

systems and meteorological models. One of the main objectives of this project was to provide an

air quality modeling system with a “one atmosphere” modeling capability based mainly on the

“first principles” description of the atmospheric system. CMAQ contains state-of-science

parameterizations of atmospheric processes affecting transport, transformation, and deposition of

such pollutants as ozone, particulate matter, airborne toxics, and acidic and nutrient pollutant

species. With science in a continuing state of advancement and review, the modeling structure

of CMAQ is designed to integrate and to test future formulations in an efficient manner, without

requiring the development of a completely new modeling system. Contents of the CMAQ in the
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June 1998 release version of Models-3 are summarized in Ching et al. (1998) and Byun et al.

(1998b). 

Currently, the Models-3 Emission Projection and Processing System (MEPPS) produces the

emissions and the Fifth Generation Penn State University/ National Center for Atmospheric

Research Mesoscale Model (MM5) provides the meteorological fields needed for the CCTM. 

They are considered to meet the present application needs for diverse air pollution problems in

urban and regional scales. However, given the CMAQ paradigm, and other considerations, the

emissions processing and meteorological modeling systems can be replaced with alternative

processors.

Each of these three modeling systems are described briefly below, where associated chapters of

this document are highlighted to provide directions to more in-depth discussions of these topics:

• The PSU/NCAR MM5 meteorological modeling system (Grell et al., 1994) generates the

meteorological fields for CMAQ. MM5 is a complex, state-of-the-science community

model, which is maintained by NCAR. MM5 is well-documented by its primary

developers in technical notes and referenced journal articles. Chapter 3 briefly describes

the scientific aspects of MM5, including grid definitions, model physics, nesting and fourdimensional data assimilation.

• The MEPPS emission modeling system is based on the Geocoded Emission Modeling and

Projection System (GEMAP) (Wilkinson et al., 1994) now known as the Emission

Modeling System-95 (EMS-95). MEPPS processes emission inventory data, performs

future projections (including control scenarios), and pre-processes data for use in the

CMAQ model (Chapter 4). It provides speciated emissions consistent with CB-IV or

RADM2 chemistry mechanisms. 

• The CMAQ chemical transport modeling system (CCTM) is then used to perform model

simulations for multiple pollutants and multiple scales with these input data (Chapters 6,

7, 8, 9, 10 and 11). The fundamental concepts used for the one-atmosphere dynamic

modeling is described in Chapter 5. The techniques used for the management of

CMAQ’s source code are discussed in Chapter 18.

The CMAQ modeling system also includes interface processors that process input data

for the emission and meteorological modeling systems, and other processors that calculate

photolysis rates, and develop initial and boundary conditions (Chapters 4, 12, 13, and

14). CMAQ also has an internal program control processor which is discussed in

Chapter 15.

Using the analysis routines provided in Models-3, the CMAQ output can be processed to

provide process analysis information (Chapter 16) and/or analyzed further to provide

aggregated statistical information (Chapter 17). 
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An important design requirements for CMAQ is that it addresses multiple scales and pollutants,

which requires that governing equations and computational algorithms among the different

systems should be consistent and compatible across the multiple scales. However, modeling

assumptions used in various modeling systems may not be valid across all scales. For example,

the atmospheric dynamics description in a meteorological model may have been optimized for

application of certain scale or limited range of scales (e.g., global vs mesoscale vs complex

terrain to urban). It is incumbent upon the user community to ensure the model component

formulations are applicable to the range of scales upon which CMAQ is applied. The current

version of MM5 and the CCTM is designed for regional to urban scales. Furthermore, when

using nesting procedures to scale down from regional to urban scales and for avoiding feedback

between the scales, one way nesting is recommended. In addition to the challenges of creating a

multiscale air quality model, CMAQ’s multi-pollutant capability cannot be achieved if the

emissions modeling system does not provide appropriate precursor or pollutant emissions to the

chemical transport model (CTM). The development of Models-3 and CMAQ overcome these

hurdles by providing the flexibility to modify specific requirements (e.g., chemical mechanisms,

model inputs, etc.), a generic coordinate system that ensures consistency across spatial scales,

and user interfaces that can integrate alternative emissions or meteorological modeling systems. 

1.2 CMAQ Interface Processors 

The CMAQ modeling system includes interface processors to incorporate the outputs of the

meteorology and emissions processors and to prepare the requisite input information for initial

and boundary conditions and photolysis rates to the CCTM. Figure 1-1 illustrates the

relationship and purpose of each of the CMAQ processors (and requisite interfaces) and their

relation to the chemical transport modeling system. The arrows show the flow of data through

the modeling system. Two additional functional features of the CMAQ system are included, one

for process analysis, which is primarily for model diagnostic analyses, and a second one that is an

aggregation methodology for estimating longer term averaged fields. Each of these processors is

described briefly below, and the associated chapter numbers are also listed to note where

detailed discussions can be found on the topics.
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Program Control

Processing

(Chapter 15)

Fundamentals of

Dynamics for CMAQ

Land use Processor (Chapter 5)

(Chapter 12)

Photolysis Rate 

Processor

(Chapter 14)

Initial and Boundary 

Condition Processors

(Chapter 13)

MM5

Meteorology Modeling System

(Chapter 3)

MEPPS

Emission Modeling System

(Chapter 4)

Emissions-Chemistry 

Interface Processor

(Chapter 4)

Meteorology-Chemistry 

Interface Processor

(Chapter 12)

CMAQ Chemical Transport Model (CTM)

Governing

Equations

(Chapter 6) Gas Phase 

Chemistry

(Chapter 8) Aerosol 

Chemistry and

Dynamics

(Chapter 10)

Cloud

Chemistry and

Dynamics

Transport (Chapter 11)

Algorithms

(Chapter 7)

Plume-in-Grid

Treatment

(Chapter 9)

Process Analysis

(Chapter 16)

Aggregation

(Chapter 17)

Integration of Science Code into Models-3 (Chapter 18)

JPROC

ICON and BCON

LUPROC

MCIP ECIP

Figure 1-1. Emissions and Meteorological modeling systems and the CMAQ

Chemical Transport Model and Interface Processor

& The Emission-Chemistry Interface Processor (ECIP) translates data from the MEPPS

emission model for use in the CCTM. ECIP generates hourly three-dimensional emission

data for CMAQ from the separate source type files produced by MEPPS, which include

mobile, area, and point sources (Chapter 4). ECIP calculates the plume rise and initial

vertical plume spread of point source emissions to determine the vertical level(s) of

CCTM into which point source emissions should be introduced. Since meteorological

conditions affect both point source plume rise and biogenic emissions, meteorological

data from MCIP is also used in ECIP. 

& The Meteorology-Chemistry Interface Processor (MCIP) translates and processes model

outputs from the meteorology model for the CCTM (Chapter 12). MCIP interpolates the

meteorological data if needed, converts between coordinate systems, computes cloud

parameters, and computes surface and planetary boundary layer (PBL) parameters for

the CCTM. MCIP uses landuse information from the landuse processor (LUPROC) to

calculate the PBL and surface parameters.

& Initial Conditions and Boundary Conditions (ICON and BCON) provide concentration

fields for individual chemical species for the beginning of a simulation and for the grids

surrounding the modeling domain, respectively. The ICON and BCON processors

(Chapter 13) use data provided from previous three-dimensional model simulations or
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from clean-troposphere vertical profiles. Both the vertical profiles and modeled

concentration fields have a specific chemical mechanisms associated with them, which

are a function of how these files were originally generated.

& The photolysis processor (JPROC) calculates temporally varying photolysis rates

(Chapter 14). JPROC requires vertical ozone profiles, temperature profiles, a profile of

the aerosol number density, and the earth’s surface albedo to produce the photolysis rates

for the CCTM. JPROC uses this information in radiative transfer models to calculate the

actinic flux needed for calculating photolysis rates. JPROC generates a lookup table of

photo-dissociation reaction rates.

Each of these CMAQ interface processors incorporates raw data into CMAQ and performs

functions such as calculating parameters and interpolating or converting data. Raw input data is

currently specified in the source code for JPROC, LUPROC, ICON, and BCON. However, the

interface processors in future releases of CMAQ will be modified to handle a more generalized

set of raw input data, so that alternative data sets with varying resolutions or measurement units

can be used.

1.3 The CMAQ Chemical Transport Model (CCTM)

The CCTM simulates the relevant and major atmospheric chemistry, transport and deposition

processes involved throughout the modeling domains. The fundamental basis for CMAQ’s oneatmosphere dynamics modeling is discussed in Chapter 5. Governing equations and model

structure, including definitions of CMAQ’s science process modules, are discussed in Chapter 6. 

The science options available to the user include the gas phase chemistry mechanisms, RADM2

and CB-IV, a set of numerical solvers for the mechanisms, options for horizontal and vertical

advection schemes, algorithms for fine and coarse particulate matter predictions, photolysis rates,

and a plume-in-grid approach. Through the Models-3 framework, CMAQ simulations can be

developed using these different options without modifying source code. A general overview of

these science process options is provided below along with a reference to the chapter(s) of this

document where more scientific detail can be found.

& Advection and Diffusion (Chapter 7): Several advection methods are implemented in the

CMAQ; these include a scheme by Bott (1989), a piecewise parabolic method (PPM)

(Collela and Woodward, 1984), and the Yamartino-Blackman cubic algorithm. Options

for computing subgrid vertical transport include eddy diffusion, and the Asymmetric

Convective Model (ACM) (Pleim and Chang, 1992) applicable to convective conditions. 

Horizontal diffusion is modeled using a constant eddy diffusion coefficient. Numerical

methods differ in the handling of advection of concentration fields. 

& Gas Phase Chemistry (Chapter 8): CMAQ includes both the RADM2 and CB4 gas-phase

chemical mechanisms. The CMAQ version of CB4 includes the most recent

representation of isoprene chemistry and two additional variants of the RADM2

mechanism also contain the newer isoprene chemistry at two levels of detail. In addition,

CMAQ provides the capability to edit these mechanisms or to import a completely new
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mechanism by means of a generalized chemical mechanism processor. CMAQ also

accounts for the formation of secondary aerosols and the reactions of pollutants in the

aqueous phase, and aqueous reactions are simulated by means of the aqueous chemical

mechanism incorporated in RADM. All CMAQ gas-phase mechanisms are linked to

these processes to provide the capability to simulate multi-phase interactions. 

Two chemistry solvers are available -- the Sparse Matrix Vectorized Gear (SMVGEAR)

algorithm developed by Jacobson and Turco (1994) and the Quasi-Steady State

Approximation (QSSA) method used in the Regional Oxidant Model. SMVGEAR is

generally recognized as the more accurate of the two, but it is much slower than QSSA on

non-vector computers.

& Plume-in-Grid (PinG) Modeling (Chapter 9): CMAQ includes algorithms to treat subgrid

scale physical and chemical processes impacting pollutant species in plumes released

from selected Major Elevated Point Source Emitters (MEPSEs). The PinG modules

simulate plume rise and growth, and the relevant dynamic and chemical reaction

processes of subgrid plumes. PinG can be used for the simulations at 36 km and 12 km

resolutions, PinG is not invoked at 4 km resolutions and the MEPSE emissions are

directly released into the CTM 3-D grid cells.

& Particle Modeling and Visibility (Chapter 10): One of the major advancements in CMAQ

is the modeling of fine and coarse mode particles, with the use of the fine particle model

described in Binkowski and Shankar (1995). CMAQ predicts hourly gridded

concentrations of fine particle mass whose size is equal to or less that 2.5 microns in

diameter (PM 2.5), speciated to sulfate, nitrate, ammonium, organics and aerosol water. 

Secondary sulfate is produced when hydroxyl radicals react with sulfur dioxide to

produce sulfuric acid that either condenses to existing particles or nucleates to form new

particles. CMAQ model output includes number densities for both fine and coarse

modes. The modeling of aerosols in CMAQ also provides the capability to handle

visibility, which is another CMAQ output. In another potential application, CMAQ can

provide the basis for modeling the atmospheric transport and deposition of semi-volatile

organic compounds (SVOC) with parameterizations for their rates of condensation to

and/or volatilization from the modeled particles.

& Cloud processes (Chapter 11 and 12): Proper descriptions of clouds are essential in air

quality modeling due to their critical role in atmospheric pollutant transport and chemistry

processes. Clouds have both direct and indirect effects on the pollutant concentrations:

they directly modify concentrations via aqueous chemical reactions, vertical mixing, and

wet deposition removal processes, and they indirectly affect concentrations by altering

radiative transmittances which affect photolysis rates and biogenic fluxes. CMAQ

models deep convective clouds (Walcek and Taylor, 1986) and shallow clouds using the

algorithms as implemented in RADM (Dennis et al., 1993) for 36 and 12 km resolutions. 

At 4 km resolution, the clouds are generally resolved, and explicit type cloud dominates.
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& Photolysis Rates (Chapter 14): The photochemistry of air pollutants is initiated by

photodissociation of smog precursors, which are driven by solar radiation. The amount of

solar radiation is dependent on sun angle (time of day), season, latitude, and land surface

characteristics, and is greatly affected by atmospheric scatterers and absorbers. 

Photolytic rates are also wavelength- and temperature-dependent. Within CCTM, 

temporally resolved 3-D gridded photolysis rates are interpolated from a lookup table

generated by JPROC processor and corrected for cloud coverage.

1.4 Analysis of CMAQ Output

Air quality modeling simulations arise from modeling of complex atmospheric processes. It is

important to assure and to understand the model results. Sensitivity tests are needed to detect

problems in model formulations and to determine if the model is credible for assessing emission

control strategies. A very powerful sensitivity analysis tool called process analysis is provided

with CMAQ. Also, an aggregation technique is provided with CMAQ. Aggregation can be used

to estimate seasonal or annual concentrations for pollutants from CMAQ simulations which are

usually performed for shorter time periods due to time and computational limitations.

1.4.1 Process Analysis (Chapter 16)

Sensitivity analyses are needed to detect errors and uncertainties introduced into a model by the

parameterization schemes and the input data. Results must also be analyzed to ensure that

realistic values are obtained for the right reasons rather than through compensating errors among

the science processes. Process Analysis techniques quantify the contributions of individual

physical and chemical atmospheric processes to the overall change in a pollutant’s concentration,

revealing the relative importance of each process. Process analysis is particularly useful for

understanding the effects from model or input changes. CMAQ provides the capability to

perform process analyses using two different pieces of information: Integrated Process Rates

(IPRs) and Integrated Reaction Rates (IRRs). 

& The IPRs are obtained during a model simulation by computing the change in

concentration of each species caused by physical processes (e.g., advection, diffusion,

emissions), chemical reaction, aerosol production, and aqueous chemistry. Values

provide only the net effect of each process. IPRs are particularly useful for identifying

unexpectedly low or high process contributions which could be indicative of model

errors. 

& The IRR analysis involves the details of the chemical transformations. For gas-phase

chemistry, the CCTM has been designed to compute not only the concentration of each

species, but also the integral of the individual chemical reaction rates. IRR analyses

have typically been used to understand the reasons for differences in model predictions

obtained with different chemical mechanisms. 
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1.4.2 Aggregation (Chapter 17)

In support of studies mandated by the CAAA-90, CMAQ can be used to estimate deposition and

air pollutant concentrations associated with specific levels of emissions. Assessment studies

require estimates of ozone, acidic deposition, particulate matter as well as visibility, on seasonal

and annual time frames. A statistical procedure called the “aggregation” has been developed and

is provided for the CMAQ to derive the required seasonal and annual estimates. This

methodology is an efficient technique and can be used instead of executing multiple CMAQ

model runs for the intended period of averaging. 

A typical CMAQ simulation provides hourly air quality fields for regional to urban scales for

multi-day episodes, typically up to five days in duration. The new PM2.5 standard includes an

annual average value, so utilization of CMAQ for PM2.5 will require the use aggregation

techniques in order to estimate annual average PM2.5 values. One such technique, initially

developed for RADM wet deposition applications, was recently modified and successfully

applied to PM2.5 by Eder and LeDuc (1996). The approach utilizes visibility data as a surrogate

for PM2.5, and it will be applied to CMAQ on a continental scale (i.e., contiguous United States,

southern Canada, and northern Mexico). Future efforts will be needed to validate this approach

when a network of PM2.5 samplers is deployed; also, aggregation approaches for mesoscale

domains will need to be developed perhaps utilizing the method by Eder and LeDuc (1994).

1.5 Management of CMAQ Science Information Objects and Codes in Models-3

The CMAQ source code is managed through the Models-3 framework to make the CMAQ

modeling system more efficient and easier to use by applying a program control processor,

management and integration of source code, and implementing a modularity concept. These

techniques also help users customize CMAQ for their own modeling applications without source

code modifications.

1.5.1 Program Control Processors (Chapter 15)

Certain science information, such as grid and layer definitions and dimensions, chemical

mechanisms, species list, model configurations, and episode (case) specification, is used

repeatedly across the several process components in Models-3 CMAQ modeling system. 

Program control processors are a set of programs embedded in the Models-3 framework to

handle these science information components and their codes. Program Control Processing

(PCP) refers to setting up internal arrays, mappings of species names in the input processors,

defining global parameters, and establishing linkages among processors in the CMAQ system. 

PCP allows users to define globally shared information on model components, and it uses that

information to generate the global FORTRAN include files required for building a model in

CMAQ. 
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1.5.2 CMAQ Code Integration (Chapter 18) 

CMAQ’s modularity facilitates efficient coordination of development work and management of

the science codes. Chapter 18 describes the modularity concepts, code management method,

and integration schemes of CMAQ science code with the Models-3 framework. Integrating the

CMAQ code into the Models-3 framework is achieved by following a set of design, coding, and

implementation standards that include: 

& A standard subroutine interface at the module level

& The restriction of coding practices to avoid practices that can conceal data dependencies,

hinder maintenance and foster hidden bugs

& The Models-3 Input/Output Applications Programming Interface (I/O API)

(http://www.iceis.mcnc.org/EDSS/ioapi/index.html/), which contains standardized file I/O

functions. The I/O API is an interface built on top of self-describing netCDF

(http://www.unidata.ucar.edu/packages/netcdf/) files that are portable across most Unix

platforms. 

1.6 Post Release Studies and Near-Future Plans

1.6.1 CMAQ Evaluation Study

It is important to conduct extensive evaluation of the CMAQ. Subsequent to the initial release of

the Models-3/CMAQ, the development team is engaged in a substantial program of evaluation.

The scope of the effort includes analyses of the performance and veracity of each individual

process module as well as the integrated air quality system. Findings from this evaluation can be

incorporated into future releases of the CMAQ modeling system. The degree and rigor of this

evaluation provides the basis for understanding the strengths or weaknesses of the current stateof-science in CMAQ. The evaluation of the initial release version of CMAQ is underway for

three nested grids with 36, 12, and 4 km grid resolutions. With these results, CMAQ’s

performance can be evaluated on both the regional and urban scales. This model evaluation

activity for CMAQ will be staged with the initial efforts to show relative performance against the

RADM model, which has undergone extensive model evaluation efforts. Diagnostic evaluation

will continue using databases from different regional studies such as the 1995 Southern Oxidant

Study conducted in the vicinity of Nashville, TN and the 1995 NARSTO-NE study. 

1.6.2 Testing Operational Configurations

CMAQ can be configured for a wide range of applications from science studies and

investigations to regulatory applications. While the scientific community can take advantage of

the CMAQ open system and flexibility to create alternative applications of CMAQ for research

and development purposes, regulatory applications depend upon a standardized, evaluated form

of CMAQ. The CMAQ evaluation program will provide the scientific benchmark needed for

this. As science advances in CMAQ, future configurations of a more operational nature can also
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be periodically re-benched as appropriate. As understanding of atmospheric processes improves,

it is a natural tendency for models to become more complex and have increased computational

demands. Efforts are underway to improve model computational efficiencies to compensate for

this.

1.6.3 Extensions and Science Additions

Two major extensions are planned for the CMAQ modeling 

& A version of the SAPRC-97 gas phase mechanism will be incorporated into CMAQ, in

addition to the current CB-IV and RADM2 mechanisms available. The initial

configuration of SAPRC will be in a fixed parameter mode, with a preset number of

organic species. Another possible future implementation of SAPRC will allow the user to

select from about 100 organic surrogate species in the semi-explicit SAPRC mechanism

to construct a user-defined, smaller SAPRC mechanism. Another approach for

representing gas-phase chemistry in CMAQ is also being developed. It will use a limited

number reactive entities termed “morphecules” to include in the chemical reactions while

using a much larger number of chemical species (singly or lumped) called allomorphs to

provide extra chemical detail. This latter approach provides a means for including a

much more detailed representation of atmospheric chemistry than conventional chemical

mechanisms without significantly increasing computational burden, albeit at the expense

of additional computer memory.

& A new emissions processor will be implemented which is called the Sparse Matrix

Operator Kernel Emissions modeling system (SMOKE)

(http://envpro.ncsc.org/products/). The linear operations used in emission processing can

be represented as multiplications by matrices. Since most entries in these matrices are

zeros, the SMOKE model formulates emissions modeling in terms of sparse matrix

operations that require considerably less time to perform than current systems. 

Efficiency is enhanced even further when considering variations in emissions projections

from base case scenarios by temporally modeling once per episode, calculating gridding

matrices only once per grid, and calculating speciation matrices only once per chemical

mechanism.

Development and testing of several science options is underway for incorporation into future

releases of the CMAQ. These include an advanced surface-PBL linked system (Pleim and Xiu,

1995), optional meteorological processors such as the Regional Atmospheric Modeling System,

RAMS, and an advanced 4-D Photolysis Rates Processor. 

1.7 Opportunities and Encouragement for Long Term Extensions and Science

Community Involvement

The Models-3/CMAQ concept is based on an open system design, we encourage the full

participation and involvement of the scientific and modeling communities in the growth and use

of Models-3 CMAQ. As described in this document, the Models-3 CMAQ system has flexibility
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for incorporating scientific and modeling advances into CMAQ processors, for testing of

alternative modeling techniques for science processes, and for extending its current capability to

handle multimedia environmental issues. Additionally, the community of users should be vigilant

in performing evaluations against improved databases and measurement technology to assess the

realism of model performance and to measure the strengths and weaknesses of the current state

of the-science as presented in the CMAQ modeling system. Some suggestions for extensions and

community involvement are provided below, but certainly not limited to:

(1) Modeling airborne and deposition of atmospheric toxic pollutants: A key opportunity for

CMAQ is the development of a modeling capability for toxic pollutants into the CMAQ chemical

transport modeling system. Models of airborne toxic pollutant provide an important tool for

understanding the transport and chemical pathways that are concerns to human exposure

assessments and for risk assessments and its management. It also provides a powerful means to

assess the exchange of toxic compounds between the atmosphere and sensitive ecosystems. 

However, developing such models is challenging. Air toxics arise from a wide variety of sources,

which may have a wide range of chemical lifetimes and reactivity. Consequently, their

toxicological impacts as well as their time-space distributions may be highly variable. These

complex mixtures of reactive compounds can exhibit wide range and variability in physical

properties and exist at various gas, liquid or particulate ambient metastates. Modeling paradigms

might evolve from introducing gas-particulate partitioning of the semi-volatile species (Ching et

al., 1997) to more fundamental modeling with detailed chemical mechanisms.

(2) Development of modeling capability to link with human exposure models: With the ability to

simulate toxic pollutant processes in addition to the current photochemical oxidants and

particulates, it is planned to transport the CMAQ model to a finer than urban scale to link with

human exposure models. International efforts to determine and understand the etiology of

adverse human effects of air pollutants, especially those that or associated with fine particles is

underway. Modeled concentrations of air pollutant constituents at neighborhood scales when

coupled with the limited numbers of sampling provide a powerful basis for driving human

exposure models. With this necessary data, human exposure models provide a basis for the

causality studies and for risk assessment research. Models have not yet been developed to

predict the spatial and temporal distributions of the various causal pollutant classes under current

consideration at the neighborhood scale. The downscaling requirements represent a great

challenge to the scientific basis in current meteorological processors. 

(3) Advanced data assimilation capability: As air quality modeling efforts extend to finer

horizontal resolutions and time scales, it becomes increasingly important to make use of higher

frequency asynoptic meteorological data such as satellite, radar wind profilers and NEXRAD. 

There is a need to develop and extend data assimilation techniques to these meteorological data

sources. Improved methods for introducing cloud information into the CMAQ should also be

investigated. Such fields have significant impact on chemical photolysis rates, the atmospheric

and surface energy budgets, the stability and dispersive power of the boundary layer, and

aqueous chemistry. 
EPA/600/R-99/030

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(4) Development of an air quality predictive mode: With further development of the emissions

and meteorological modeling systems, plans include developing a predictive capability in the

CMAQ modeling system. CMAQ is currently developed in retrospective mode for performing

assessments and for implementation of the National Ambient Air Quality Standards (NAAQS). 

In principle, CMAQ may be extended to a forecast mode in order to provide air quality

advisories for pollutants such as ozone and visibility and for operational support for issues such

as smoke and PM/haze from prescribed fires. These capabilities will require the development

and testing of day-specific emissions inventories and a real time data processing system for the

meteorological mode.

( 5) Up and downscale links to global scale models: New linkages with other areas of modeling,

including scale and media, are envisioned. It is hoped that information from the urban and

regional CMAQ applications and from global modeling applications can be bridged. Because

CMAQ offers the state of science to simulate atmospheric process as realistically as possible at

time scales commensurate with reality, CMAQ output can be used to benchmark or examine the

parametric basis of process formulations in global models. From a downscale perspective, global

model output can be used to improve or enhance the initial and boundary conditions in CMAQ

regional and urban scale simulations. 

(6) Ecosystem modeling: Efforts to combine environmental modeling techniques to encompass

an entire ecosystem is needed to address issues including: (a) nutrient cycle modeling, which

includes pathways through the atmosphere, water bodies, and soil; and (b) acidic wet and dry

deposition into sensitive ecosystems, including critical load analyses. With this ecosystem

modeling approach, air quality issues can be studied in combination with other aspects of

environmental health. For example, nitrogen deposition can cause adverse nutrient loadings to

ecosystems that can result in a reduction of water quality due to adverse biological responses. 

Further, toxic deposition can lead to adverse indirect human exposure from bioaccumulation

through the food chain.

1.8 References

Binkowski, F.S., and U. Shankar, 1995: The Regional Particulate Model: Part I. Models

description and preliminary results. J.Geophys. Res., 100(D12): 26191-26209.

Bott, A., 1989: A positive definite advection scheme obtained by nonlinear renormalization of

the advective fluxes, Mon. Wea. Rev. 117: 1006-1015.

Byun D. W., A. Hanna, C. J. Coats, and D. Hwang, 1995a: Models-3 air quality model prototype

science and computational concept development. Transactions of Air & Waste Management

Association Specialty Conference on Regional Photochemical Measurement and Modeling

Studies, Nov. 8-12, San Diego, CA. 1993, 197-212. 

Byun, D. W., C. J. Coats, D. Hwang, S. Fine, T. Odman, A. Hanna and K. J. Galluppi, 1995b:

Prototyping and implementation of multiscale air quality models for high performance

computing. Mission Earth Symposium, Phoenix, AZ, April 9-13, 1993. 527-532. 
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Byun, D.W., D. Dabdub, S. Fine, A. F. Hanna, R. Mathur, M. T. Odman, A. Russell, E. J.

Segall, J. H. Seinfeld, P. Steenkiste, and J. Young, 1996: Emerging Air Quality Modeling

Technologies for High Performance Computing and Communication Environments, Air Pollution

Modeling and Its Application XI, ed. S.E. Gryning and F. Schiermeier. 491-502. 

Byun, D.W., J.K.S. Ching, J. Novak, and J. Young, 1997: Development and Implementation of

the EPAís Models-3 Initial Operating Version: Community Multi-scale Air Quality (CMAQ)

Model, 1998a: Twenty-Second NATO/CCMS International Technical Meeting on Air Pollution

Modelling and Its Application, 2-6 June, 1997. Air Pollution Modeling and Its Application XII,

ed. S.E. Gryning and N. Chaumerliac, Plenum Publishing Coorp. 357-368. 

Byun, D.W., J. Young., G. Gipson., J. Godowitch., F. Binkowsk, S. Roselle, B. Benjey, J. Pleim,

J.K.S. Ching., J. Novak, C. Coats, T. Odman, A. Hanna, K. Alapaty, R. Mathur, J. McHenry, U.

Shankar, S. Fine, A. Xiu, and C. Jang, 1998b: Description of the Models-3 Community Multiscale

Air Quality (CMAQ) model. Proceedings of the American Meteorological Society 78th Annual

Meeting, Phoenix, AZ, Jan. 11-16, 1998: 264-268. 

Carmichael G.R. and L.K. Peters, 1984a: An Eulerian transport/transformation/removal model

for SO2 and sulfate-I. Model development, Atmos. Environ. 18: 937-952.

Carmichael G.R. and L.K. Peters, 1984b: An Eulerian transport/transformation/removal model

for SO2 and sulfate-II. Model calculation of SOx transport in the Eastern United States, Atmos.

Environ. 20: 173-188.

Carmichael G.R., L.K. Peters, and R.D. Saylor, 1991: The STEM-II regional scale acid

deposition and photochemical oxidant model-I. An overview of model development and

applications, Atmos. Environ. 25A: 2077-2090.

Chang, J.S., P.B. Middleton, W.R. Stockwell, C.J. Walcek, J.E. Pleim, H.H. Landsford, S.

Madronich, F.S. Binkowski, N.L. Seaman, and D.R. Stauffer, 1990: “The Regional Acid

Deposition Model and Engineering Model.” NAPAP SOS/T Report 4, in National Acid

Precipitation Assessment Program: State of Science and Technology, Volume 1. National Acid

Precipitation Assessment Program, 722 Jacksn Place, N.W., Washington, D.C., September 1990.

Chang, J.S., R.A. Brost, I.S.A. Isaksen, S. Madronich, P. Middleton, W.R. Stockwell, and C.J.

Walcek, 1987: A three-dimensional Eulerian acid deposition model: Physical concepts and

formulation.” J. Geophy. Res. 92: 14681-14700.

Ching, J.K.S., D.W. Byun, A. Hanna, T. Odman, R. Mathur, C. Jang, J. McHenry, K. Galluppi,

1995: Design requirements for multiscale air quality models. Mission Earth Symposium, Phoenix,

AZ, April 9-13 p532-538. 

Ching, J.K.S., D.W. Byun, J. Young, F. Binkowsk., J. Pleim, S. Roselle, J. Godowitch, W.

Benjey., and G. Gipson, 1998: Science features in Models-3 Community multiscale air quality
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system. Proceedings of the American Meteorological Society 78th Annual Meeting, Phoenix, AZ,

Jan. 11-16, 1998: 269-273

Ching, J.K.S., Francis S. Binkowski, and O. Russell Bullock, Jr., 1997: Deposition of semivolatile

toxic air pollutants to the Great Lakes: A regional modeling approach. In “ Atmospheric

Deposition of Contaminants to the Great Lakes and Coastal Waters, Ed by Joel Baker, SETAC

Press. pp 293-304.

Coats, C. J., A.H. Hanna, D. Hwang, and D.W. Byun, 1995: Model engineering concepts for air

quality models in an integrated environmental modeling system. Transactions of Air & Waste

Management Association Specialty Conference on Regional Photochemical Measurement and

Modeling Studies, Nov. 8-12, San Deigo, CA. 1993, 213-223. 

Colella, P., and P. L. Woodward, 1984: The Piecewise Parabolic Method (PPM) for gasdynamical simulations, J. Comput. Phys. 54: 174-201.

Dennis, R, 1998: The Environmental Protection Agency’s third generation air quality modeling

system: An overall perspective. Proceedings of the American Meteorological Society 78th

Annual Meeting, Phoenix, AZ, Jan. 11-16, 1998: 255-258.

Dennis, R.L., D.W. Byun, J.H. Novak, K.J. Galluppi, C.J. Coats, and M.A. Vouk, 1996: The

next generation of integrated air quality modeling: EPA's Models-3. Atmospheric Environment,

30, No. 12, 1925-1938. 

Eder, B.K., D.H. Coventry, C. Bollinger and T.L. Clark: RELMAP, 1986: A Regional

Lagrangian Model of Air Pollution User’s Guide. U.S. Environmental Protection Agency Report

EPA/600/8-86/013, Research Triangle park, NC 146 pp.

Eder, B.K., J.M. Davis and P. Bloomfeld, 1994: An automatic classification scheme designed to

better elucidate the dependence of ozone on meteorology. J. Appl. Meteor, 33: 1182-1199.

Eder, B.K. and S. LeDuc, 1996: Can selected RADM simulations be aggregated to estimate

annual concentrations of fine particulate matter? Reprint from the 11th Annual International

Symposium on the Measurement of Toxic and Related Pollutants, May 7-10, 1996, RTP, NC

732-739.

Gillani, N.V., A. Biazar, Y. Wu, J. Godowitch, J. Ching, R. Imhoff, 1998: The Plume-in-Grid

treatment of major elevated point source emissions in Models-3. 10th Joint Conference on

Applications of Air Pollution Meteorology with AWMA, January 11-16, 1998, Phoenix, AZ,

Amer. Meteorol. Soc., Boston, MA.

Grell, G.A., J. Dudhia, and D.R. Stauffer, 1993: A description of the Fifth-Generation Penn

State/NCAR Mesoscale Model(MM5). NCAR Technical Note, NCAR/TN-398+IA

Jacobson M. and R.P. Turco, 1994: SMVGEAR: A Sparse-Matrix, vectorized Gear code for

atmospheric models. Atmos. Environ. 28: 273-284.
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Jeffries, H. E. and S. Tonnesen, 1994: A comparison of two photochemical reaction mechanisms

using mass balance and process analysis, Atmos. Environ, 28(18): 2991-3003.

Lamb, R.G., 1983a: A Regional Scale (1000 km) Model of Photochemical Air Pollution, Part 1:

Theoretical Formulation. EPA-600/3-83-035, U.S. Environmental Protection Agency, Research

Triangle Park, NC.

Lamb, R.G., 1983b: A Regional Scale (1000 km) Model of Photochemical Air Pollution, Part 2:

Input Processor Network Design. EPA-600/3-84-085, U.S. Environmental Protection Agency,

Research Triangle Park, NC.

Morris, R.E. and T.C. Meyers, 1990: User’s Guide for the Urban Airshed Model, Volume 1:

User’s Manual for UAM(CB-IV). EPA-450/4-90-007A. U.S. Environmental Protection Agency,

Research Triangle Park, NC.

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Models-3: A unifying framework for environmental modeling and assessments. Preprint Volume,

10th Joint AMS and A&WMA Conference on the Applications of Air Pollution Meteorology,

Phoenix, AZ, Jan 11-16, 1998: 259-263.

Pleim J.E., and J.S. Chang, 1992: A non-local closure model in the convective boundary layer.

Atm Environ., 26A: 965-981.

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layer model for application in mesoscale models, J. Appl. Meteor., 34:16-32.

Wilkinson, J.G., C.F. Loomis, D.E. McNally, R.A. Emigh, and T.W. Tesche, 1994: Technical

Formulation Document: SARMAP/LMOS Emissions Modeling System (EMS-95), Final Report,

Lake Michigan Air Directors Consortium and the California Air Resources Board, AG-90/TS26

and AG-90/TS27, 120pp.

Venkatram, A.K. and P.K. Karamchandani, 1998: The ADOM II Scavenging Module. ENSR

Consulting and Engineering Report 0780-004-205. Camarillo, CA.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
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Chapter 3

DEVELOPING METEOROLOGICAL FIELDS

Tanya L. Otte*

Atmospheric Modeling Division

National Exposure Research Laboratory

U. S. Environmental Protection Agency

Research Triangle Park, NC 27711

ABSTRACT

Meteorological data are important in many of the processes simulated in the Community

Multiscale Air Quality (CMAQ) model included in the first release of the Models-3 framework.

The meteorology model that has been selected and evaluated with CMAQ is the Fifth-Generation

Pennsylvania State University/National Center for Atmospheric Research (NCAR) Mesoscale

Model (MM5). All software in the Penn State/NCAR mesoscale modeling system has been

dedicated to the public domain and is presently used for both research and operational purposes at

many organizations worldwide. Improvements to MM5 within the meteorological community are

ongoing, and these enhancements should be evaluated for their applicability to air quality

modeling. Other meteorological models are being considered for compatibility with CMAQ but

are not provided with the initial release. The application of MM5 with CMAQ is described in

Chapter 3.

 

*On assignment from the National Oceanic and Atmospheric Administration, U.S. Department. of Commerce.

Corresponding author address: Tanya L. Otte, MD-80, Research Triangle Park, NC 27711. Email:

tlotte@hpcc.epa.gov
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3.0 DEVELOPING METEOROLOGICAL FIELDS

3.1 Credits and Disclaimers for Use of MM5

The Fifth-Generation Pennsylvania State University/National Center for Atmospheric Research

(NCAR) Mesoscale Model (MM5) was developed in cooperation with Penn State and the

University Corporation for Atmospheric Research (UCAR). Penn State and UCAR make no

proprietary claims, either statutory or otherwise, to this version and release of MM5, and they

consider MM5 to be in the public domain for use by any person or entity without any fee or

charge. Penn State and UCAR shall be credited in any publications that result from the use of

MM5. The names “Penn State” and “UCAR” shall not be used or referenced in any advertising or

publicity that endorses or promotes any products or commercial entity associated with or using

MM5, or any derivative works thereof, without the written authorization of UCAR and Penn

State.

MM5 is provided to the public by Penn State and UCAR on an “as is” basis, and any warranties,

either express or implied, including but not limited to implied warranties of non-infringement,

originality, merchantability, and fitness for a particular purpose, are disclaimed. Neither UCAR

nor Penn State will be obligated to provide the user with any support, consulting, training, or

assistance of any kind regarding the use, operation, and performance of MM5, nor will they be

obligated to provide the user with any updates, revisions, new versions, error corrections, or

“bug” fixes. In no event will UCAR and Penn State be liable for any damages, whatsoever,

whether direct, indirect, consequential, or special, which may result from an action in contract,

negligence, or other claim that arises out of or about the access, use, or performance of MM5,

including infringement actions.

Data that are obtained from NCAR (e.g., global analyses and observations) are prepared and

maintained by the Data Support Section, Scientific Computing Division, NCAR. NCAR is

operated by UCAR and is sponsored by the National Science Foundation. Any published research

that uses data from the NCAR archive shall credit the maintainers of the archive. In addition, the

original source(s) of data shall be acknowledged.

3.2 Meteorology Model Pre-Processing

Before the meteorology model can be run, several smaller (“pre-processing”) programs must be

run to set up the domain for the simulation and to generate a set of initial and boundary conditions

for the meteorology model. The pre-processing programs are briefly described in this section.
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3.2.1 Defining the Simulation Domain (TERRAIN)

Domains for the meteorology simulations are defined by several primary parameters: number of

grid points in each horizontal dimension, grid spacing, center latitude, center longitude, map

projection (Mercator, Lambert conformal, or polar stereographic), and number of “nested”

domains and their horizontal dimensions. (Some other user-specific parameters are also defined

based on the primary parameters, as required.) These parameters are processed by a program that

is executed only when a new domain location is required. This program, TERRAIN, makes use of

high-resolution global terrain and land use data sets to create “static files” for the domain. The

static files currently include values for each grid point for terrain height and land use specification

(e.g., deciduous forest, desert, water). Future versions of TERRAIN may include additional

diurnal, seasonal, and location-specific information. The TERRAIN program is thoroughly

described by Guo and Chen (1994).

3.2.2 Processing the Meteorological Background Fields (DATAGRID)

After the simulation domain has been established, the program DATAGRID is run to process the

meteorological background fields. DATAGRID generates first-guess fields for the model

simulation by horizontally interpolating a larger-scale data set (global or regional coverage) to the

simulation domain. DATAGRID interpolates the background fields to the simulation domain for

times throughout the simulation period; these files are used ultimately to generate lateral boundary

conditions for the coarse-domain simulations. (Nested domains obtain lateral boundary

conditions from the coarse domain.) DATAGRID also processes the sea-surface temperature and

snow files by interpolating the analyses to the simulation domain. Lastly, DATAGRID calculates

map-scale factors and Coriolis parameters at each grid point to be used by MM5. The

DATAGRID program is thoroughly described by Manning and Haagenson (1992).

3.2.3 Objective Analysis (RAWINS)

The program RAWINS performs an objective analysis by blending the first-guess fields generated

by DATAGRID with upper-air and surface observations. There are four objective analysis

techniques available in RAWINS. The following descriptions are taken largely from Dudhia et al.

(1998).

• The Cressman scheme assigns a circular radius of influence to each observation. The

weights associated with the observations decrease radially from the observation to the

radius of influence. The first-guess (meteorological background) field at each grid point is

adjusted by taking into account all observations that influence that grid point. (See

Cressman, 1959.)
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• The Ellipse scheme alters the Cressman circles for analyses of wind and relative humidity

by elongating the circles along the wind flow. The eccentricity of the ellipses increases as

wind speed increases. This scheme reduces to the Cressman scheme under light wind

conditions. (See Benjamin and Seaman, 1985.)

• The Banana scheme alters the Cressman circles for analyses of wind and relative

humidity by elongating the circles in the direction of the flow and curving the influence

region along streamlines. The resulting influence region is banana-shaped. This scheme

reduces to the ellipse scheme under straight-flow conditions, and it further reduces to the

Cressman scheme under light wind conditions. (See Benjamin and Seaman, 1985.)

• The Multiquadric Interpolation scheme uses hyperboloid radial basis functions to

perform objective analysis. This scheme takes much more time and memory than the

Cressman-based schemes. This scheme must be used with caution in data-sparse regions

and when more than 25% of the domain is water-covered. (See Nuss and Titley, 1994.)

In addition, RAWINS performs some data quality control checks and buddy checks with userdefined thresholds. The objective analysis is performed for a user-defined number of pressure

surfaces (generally mandatory levels plus some additional surfaces). RAWINS is also used to

prepare the analyses for the analysis nudging in the simulation model. The RAWINS program is

thoroughly described by Manning and Haagenson (1992).

3.2.4 Setting the Initial and Boundary Conditions (INTERP)

The “standard” INTERP program sets the initial and boundary conditions for the meteorology

simulation. The analyses from RAWINS are interpolated to MM5’s staggered grid configuration

and from their native vertical coordinate (pressure) to MM5’s vertical coordinate (a terrainfollowing, pressure-based “sigma” coordinate). In addition, the state variables are converted as

necessary, e.g., relative humidity to specific humidity. The analyses from one time (generally the

first time analyzed by RAWINS) are interpolated by INTERP to provide MM5’s initial conditions,

while analyses from all times are interpolated to generate MM5’s lateral boundary conditions.

INTERP can also be used for “one-way nesting,” where the MM5 output from one model run is

interpolated to provide initial and boundary conditions for the nested run. This is a “nonstandard” use of the INTERP program, but it is commonly used to support air quality modeling.

3.3 The Meteorology Model (MM5)

The following subsections include brief summaries of the science and options that are available in

MM5. Thorough descriptions of the standard MM5 options are found in Grell et al. (1994) and

Dudhia et al. (1998). The source code for an early release of MM5 is documented in Haagenson
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et al. (1994). The Models-3 package does not include NCAR’s most current release of MM5.

MM5 user options have been tailored and expanded in the Models-3 release to support air quality

modeling. Some of these options have not yet been accepted into the official version that is

maintained by NCAR. Caution should be exercised when deviating from the version of MM5 that

is included with Models-3. Refer to Section 3.5 for a summary of changes to MM5 for CMAQ.

3.3.1 Brief History

MM5 is the Fifth-Generation Penn State/NCAR Mesoscale Model. It has evolved from the model

used by Anthes in the early 1970s, described by Anthes and Warner (1978). The improvements in

MM5 over the previous version (MM4) include the option for non-hydrostatic physics, as well as

more sophisticated explicit moisture, boundary layer processes, radiation, convective

parameterization, among other improvements. Dudhia (1993) documented the major changes

from MM4 to MM5. Starting with MM5 Version 2 (MM5v2), the software has been restructured

to run on various hardware platforms in addition to the Cray, with emphasis placed on

workstation-based MM5 simulations. The Cray version of MM5 provided on the Models-3

installation tape has been tested on the EPA’s Cray C90. A workstation-based version of MM5

may be used with subsequent releases of Models-3.

3.3.2 Horizontal and Vertical Grid

The coordinate system for MM5 is (x, y, sigma-p). The x and y dimensions are a regular lattice of

equally spaced points (delta-x = delta-y = horizontal grid spacing, in kilometers) forming rows

and columns. Sigma is a terrain-following vertical coordinate that is a function of the pressure at

the point on the grid (in hydrostatic runs) or the reference state pressure (in non-hydrostatic runs),

the surface pressure at the grid point, and the pressure at the top of the model. Sigma varies from

1 at the surface to 0 at the top of the model. The influence of the terrain on the sigma structure

diminishes with height, such that the sigma surfaces near the top of the model are nearly parallel.

The horizontal grid in MM5 has an Arakawa-B staggering of the velocity vectors with respect to

the scalars (Arakawa and Lamb, 1977). The momentum variables (u- and v-components of wind

and the Coriolis force) are on “dot” points, while all other variables (e.g., mass and moisture

variables) are on “cross” points. The dot points form the regular lattice for the simulation

domain, while the cross points are offset by 0.5 grid point in both the x and y directions. Note

that the interpolation of the variables to the staggered grid is done automatically within the

INTERP program.

3.3.3 Prognostic Equations

MM5 is based on primitive physical equations of momentum, thermodynamics, and moisture. The

state variables are temperature, specific humidity, grid-relative wind components, and pressure.
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In the prognostic equations, the state variables are mass-weighted with a modified surface

pressure. MM5 can be run as either a hydrostatic or non-hydrostatic model. In the hydrostatic

model, the state variables are explicitly forecast. In the non-hydrostatic model (Dudhia, 1993),

pressure, temperature, and density are defined in terms of a reference state and perturbations from

the reference state. MM5 is not mass-conserving in the non-hydrostatic mode. The vertical

(sigma) coordinate is defined as a function of pressure. The model’s prognostic equations are

thoroughly discussed in Grell et al. (1994) and Dudhia et al. (1998).

3.3.3.1 Time Differencing

The hydrostatic and non-hydrostatic versions of MM5 use different time differencing schemes to

filter the fast waves from the prognostic solutions in the model. In the non-hydrostatic model, a

semi-implicit scheme based on Klemp and Wilhelmson (1978) is used to control the acoustic

waves in the model solution. In the hydrostatic model, a split-explicit scheme based on Madala

(1981) is used to control gravity waves in the model solution. The time differencing in MM5 is

discussed at length in Grell et al. (1994) and Dudhia et al. (1998).

3.3.3.2 Lateral Boundary Conditions

There are five options for lateral boundary conditions in MM5: fixed, relaxation, time dependent,

time and inflow/outflow dependent, and sponge. The lateral boundaries in MM5 consist of either

the outer five grid points (relaxation and sponge options) or the outer grid point (all other

options) on the horizontal perimeter of the simulation domain. (The outer four grid points are

used for boundary conditions for “cross” point variables for the relaxation and sponge options.)

The lateral boundary conditions for the coarse domain are derived from the background fields

processed in DATAGRID and INTERP. When the one-way nest option is selected, the lateral

boundary conditions for nested domains are interpolated from the simulation on the parent

domain.

3.3.4 Model Physics

Several model physics options in MM5 are briefly noted below. The model physics options are

further discussed and compared in Dudhia et al. (1998). The descriptions of the model physics

options are largely taken from Dudhia et al. (1998), and other pertinent references are noted.

3.3.4.1 Radiation

There are five atmospheric radiation cooling schemes available in MM5.

• The “None” option applies no mean radiative tendency to the atmospheric temperature.

This scheme is unrealistic for long-term simulations.
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• The Simple Cooling scheme sets the atmospheric cooling rate strictly as a function of

temperature. There is no cloud interaction or diurnal cycle.

• The Surface Radiation scheme is used with the “none” and “simple cooling” schemes.

This scheme includes a diurnally varying shortwave and longwave flux at the surface for

use in the ground energy budget. These fluxes are calculated based on atmospheric

column-integrated water vapor and low/middle/high cloud fraction estimated from relative

humidity.

• The Dudhia Longwave and Shortwave Radiation scheme is sophisticated enough to

account for longwave and shortwave interactions with explicit cloud and clean air. This

scheme includes surface radiation fluxes and atmospheric temperature tendencies. This

scheme requires longer CPU time, but not much memory. (See Dudhia, 1989.)

• The CCM2 Radiation scheme includes multiple spectral bands in shortwave and

longwave, but the clouds are treated simply as functions of relative humidity. This scheme

is suitable for larger grid scales and probably more accurate for long time integration (e.g.,

climate modeling). It also provides radiative fluxes at the surface. (See Hack et al.,

1993.)

3.3.4.2 Convective Parameterization

There are currently six convective parameterization schemes in MM5. There is also the option for

no convective parameterization and an independent option for shallow convection. The

convective parameterization schemes have been designed for use at various simulation scales, and

they are not entirely interchangeable. For example, each scheme uses different assumptions for

convective coverage on the sub-grid-scale and for the convective trigger function. The

convective parameterization schemes also differ greatly in CPU usage and memory requirements.

• The Anthes-Kuo scheme is based on moisture convergence and is mostly applicable to

larger grid scales (i.e., greater than 30 km). This scheme tends to produce more

convective rainfall and less resolved-scale precipitation. This scheme uses a specified

heating profile where moistening is dependent on relative humidity. (See Anthes, 1977.)

• The Fritsch-Chappel scheme is based on relaxation to a profile due to updraft,

downdraft, and subsidence region properties. The convective mass flux removes 50% of

the available buoyant energy in the relaxation time. There is a fixed entrainment rate.

This scheme is suitable for 20-30 km scales due to the single cloud assumption and local

subsidence. (See Fritsch and Chappel, 1980.)
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• The Arakawa-Schubert scheme is a multi-cloud scheme that is otherwise similar to the

Grell scheme (described below). This scheme is based on a cloud population, and it

allows for entrainment into updrafts and the existence of downdrafts. This scheme is

suitable for larger grid scales (i.e., greater than 30 km). This scheme can be

computationally expensive compared to the other available schemes. (See Arakawa and

Schubert, 1974.)

• The Kain-Fritsch scheme is similar to the Fritsch-Chappel scheme, but it uses a

sophisticated cloud-mixing scheme to determine entrainment and detrainment. This

scheme also removes all available buoyant energy in the relaxation time. (See Kain and

Fritsch, 1990, 1993.)

• The Betts-Miller scheme is based on relaxation adjustment to a reference postconvective thermodynamic profile over a given period. This scheme is suitable for scales

larger than 30 km. However, there is no explicit downdraft, so this scheme may not be

suitable for severe convection. (See Betts, 1986; Betts and Miller, 1986, 1993; and Janjic,

1994.)

• The Grell scheme is based on rate of destabilization or quasi-equilibrium. This is a

single-cloud scheme with updraft and downdraft fluxes and compensating motion that

determines the heating and moistening profiles. This scheme is useful for smaller grid

scales (e.g., 10-30 km), and it tends to allow a balance between the resolved scale rainfall

and the convective rainfall. (See Grell et al., 1991; and Grell, 1993.)

• The “no convective parameterization” option (e.g., explicitly resolved convection on

the grid scale) is also available. This option is generally used for simulations on domains

with horizontal grid spacing smaller than 10 km.

• The Shallow Convection scheme is an independent option that handles non-precipitating

clouds that are assumed to be uniform and to have strong entrainment, a small radius, and

no downdrafts. This scheme is based on the Grell and Arakawa-Schubert schemes. There

is also an equilibrium assumption between cloud strength and sub-grid boundary layer

forcing.

3.3.4.3 Planetary Boundary Layer Processes

Four planetary boundary layer (PBL) parameterization schemes are available in MM5. These

parameterizations are most different in the turbulent closure assumptions that are used. The PBL

parameterization schemes also differ greatly in CPU usage.
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• The Bulk Formula scheme is suitable for coarse vertical resolution in the PBL (i.e.,

greater than 250 m vertical grid sizes). This scheme includes two stability regimes.

• The Blackadar scheme is suitable for “high-resolution” PBL (e.g., five layers in the

lowest kilometer and a surface layer less than 100 m thick). This scheme has four stability

regimes; three stable and neutral regimes are handled with a first-order closure, while a

free convective layer is treated with a non-local closure. (See Blackadar, 1979.)

• The Burk-Thompson scheme is suitable for coarse and high-resolution PBL. This

scheme explicitly predicts turbulent kinetic energy for use in vertical mixing, based on a

1.5-order closure derived from the Mellor-Yamada formulas. (See Burk and Thompson,

1989.)

• The Medium Range Forecast (MRF) model scheme is suitable for high-resolution PBL.

This scheme is computationally efficient. It is based on a Troen-Mahrt representation of

the counter-gradient term and a first-order eddy diffusivity (K) profile in the well-mixed

PBL. This scheme has been taken from the National Centers for Environmental

Prediction’s (NCEP’s) MRF model. (See Hong and Pan, 1996.)

3.3.4.4 Surface Layer Processes

The surface layer processes with the Blackadar and MRF PBL schemes have been parameterized

with fluxes of momentum, sensible heat, and latent heat, following Zhang and Anthes (1982). The

energy balance equation is used to predict the changes in ground temperature using a single slab

and a fixed-temperature substrate. The slab temperature is based on an energy budget, and the

depth is assumed to represent the depth of the diurnal temperature variation (~10-20 cm). The 13

land use categories are used to seasonally define the physical properties at each grid point (e.g.,

albedo, available moisture, emissivity, roughness length, and thermal inertia).

A five-layer soil temperature model (Dudhia, 1996) is also available as an option in MM5. In this

model, the soil temperature is predicted at layers of approximate depths of 1, 2, 4, 8, and 16 cm,

with a fixed substrate below using a vertical diffusion equation. This scheme vertically resolves

the diurnal temperature variation, allowing for more rapid response of surface temperature. This

model can only be used in conjunction with the Blackadar and MRF PBL schemes.

In a subsequent release of CMAQ, the Pleim-Xiu land-surface scheme (Pleim and Xiu, 1995) may

be included in MM5. The Pleim-Xiu scheme has been developed to address surface processes

that can significantly impact air quality modeling, including evapotranspiration and soil moisture.

Notable in the Pleim-Xiu scheme is the more careful treatment of the surface characteristics

(particularly vegetation parameters) that are currently assigned to grid points based on land use

specification, as well as a more detailed land use and soil type classification database.
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3.3.4.5 Resolvable-Scale Microphysics Schemes

There are six resolvable-scale (explicit grid-scale) microphysics schemes in MM5. There is also

an option for a “dry” model run. The microphysics schemes have been designed with varying

degrees of complexity for different applications of the model. In addition, there are new

prognostic output variables that are generated by the more sophisticated schemes. These

microphysics schemes also differ greatly in CPU usage and memory requirements.

• The Dry scheme has no moisture prediction. Water vapor is set to zero. This scheme is

generally used for sensitivity studies.

• The Stable Precipitation scheme generates non-convective precipitation. Large-scale

saturation is removed and rained out immediately. There is no evaporation of rain or

explicit cloud prediction.

• The Warm Rain scheme uses microphysical processes for explicit predictions of cloud

and rainwater fields. This scheme does not consider ice phase processes. (See Hsie and

Anthes, 1984.)

• The Simple Ice scheme adds ice phase processes to the warm rain scheme without adding

memory. This scheme does not have supercooled water, and snow is immediately melted

below the freezing level. (See Dudhia, 1989.)

• The Mixed-Phase scheme adds supercooled water to the simple ice scheme, and slow

melting of snow is allowed. Additional memory was added to accommodate the ice and

snow. This scheme does not include graupel or riming processes. (See Reisner et al.,

1993, 1998.)

• The Mixed-Phase with Graupel scheme adds graupel and ice number concentration

prediction equations to the mixed-phase scheme. This scheme is suitable for cloudresolving scales. (See Reisner et al., 1998.)

• The NASA/Goddard Microphysics scheme explicitly predicts ice, snow, graupel, and

hail. This scheme is suitable for cloud-resolving scales. (See Tao and Simpson, 1993.)

3.3.5 Nesting

MM5 can simulate nested domains of finer resolutions within the primary simulation domain. In

MM5, the software is configured to enable up to nine nests (ten domains) within a particular run.

However, due to current hardware resources, the state of the science, numerical stability, and

practicality, the number of domains in a simulation is generally limited to four or fewer.
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Nesting can be accomplished by either a “one-way” or a “two-way” method. In one-way nesting,

the coarse-resolution domain simulation is run independently of the nest. The coarse domain can

then provide the initial and boundary conditions for its nest. In one-way nesting, each domain can

be defined with independent terrain fields, and there are no feedbacks to the coarse domain from

its nest. Note that the simulated meteorology at the same grid point in the coarse-resolution

domain is likely to be different (if only slightly) from the nest in a one-way nest simulation.

Two-way interactive nesting (Zhang et al., 1986; Smolarkiewicz and Grell, 1992) allows for

feedback to occur between the coarse-resolution domain and the nest throughout the simulation.

The two domains are run simultaneously to enable this feedback, and terrain in the overlapping

regions must be compatible to avoid mass inconsistencies and generation of numerical noise. The

TERRAIN program automatically defines the terrain compatibility when the user specifies the

two-way nesting interaction. When two-way nesting is used, the portion of the coarse-resolution

domain that is simulated in the nest may reflect too much smaller-scale detail from the nest to be

useful for the CMAQ simulations.

The nesting ratio between domains in MM5 is generally 3:1. (Some other mesoscale meteorology

models allow for user-defined nest ratios.) For example, if the coarse domain is a 36-km

resolution domain, its nest will be a 12-km resolution domain. This is strictly true for a two-way

nest, but is largely held as a standard for the one-way nests in MM5. The nest ratio restricts the

number of grid points in each dimension of the nest domains to a multiple of 3, plus 1.

3.3.6 Four-Dimensional Data Assimilation

The four-dimensional data assimilation (FDDA) scheme included in MM5 is based on Newtonian

relaxation or “nudging”. Nudging is a continuous form of FDDA where artificial (non-physical)

forcing functions are added to the model’s prognostic equations to nudge the solutions toward

either a verifying analysis or toward observations. The artificial forcing terms are scaled by a

nudging coefficient that is selected so that the nudging term will not dominate the prognostic

equations. The nudging terms tend to be one order of magnitude smaller than the dominant terms

in the prognostic equations and represent the inverse of the e-folding time of the phenomena

captured by the observations.

There are two types of nudging in MM5: analysis nudging and observation nudging (“obs

nudging”). Analysis nudging gently forces the model solution toward gridded fields. Analysis

nudging can make use of three-dimensional analyses and some surface analyses. Analysis nudging

is generally used for scales where synoptic and mesoalpha forcing are dominant. Obs nudging

gently forces the model solution toward individual observations, with the influence of the

observations spread in space and time. Obs nudging is better suited for assimilating high

frequency, asynoptic data that may not otherwise be included in an analysis.
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Nudging in MM5 is extensively discussed in Stauffer and Seaman (1990, 1994) and Stauffer et al.

(1991). The data assimilation is generally used throughout the MM5 simulation period for air

quality simulations. Three-dimensional analyses of wind, temperature, and moisture are

assimilated, and only surface analyses of wind are assimilated, following Stauffer et al. (1991).

3.4 Meteorology Model Post-Processing

Since the output variables that are generated by an MM5 simulation are not always useful in their

raw form, those variables must be converted into fields that are required by the chemistry and

emission models. The conversion of MM5 output to useful fields for the other Models-3

programs is accomplished in the Meteorology Chemistry Interface Processor (MCIP), which is

discussed in Chapter 12. MCIP computes variables that are useful to the subsequent models in

Models-3, and it creates an output file written with the I/O API libraries in netCDF format that is

standard in the Models-3/CMAQ modeling system.

3.5 Changes to the MM5 System's Software for Models-3

The version of MM5 included with the initial release of Models-3 is MM5 Version 2, Release 6.

The system is complete with “bug fixes” included through October 1997. Only selected “bug

fixes” and upgrades have been included beyond October 1997. (Including all of the changes to

MM5 would have jeopardized testing and evaluation of CMAQ, which uses the MM5 output.)

The version of MM5 in the Models-3 release includes most of the science options in NCAR’s

current version. The omission of upgrades should not result in substandard or corrupted

meteorological simulations.

The following is a summary of EPA-initiated changes that were made to the NCAR release of

MM5 and its supporting software to support air quality modeling with CMAQ:

All Programs:

• Standardized the radius of the earth as 6370.997 km to be consistent with chemistry and

emission models.

TERRAIN:

• Set terrain height over ocean to zero when using the 1-minute terrain database.

• Improved representation of urban areas along coasts.

INTERP:

• Increased loop indices and parameter sizes to accommodate 120-hour simulation.
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MM5:

• Modified script and source code to enable analysis nudging on a one-way nested

simulation.

3.6 References

Anthes, R. A., 1977: A cumulus parameterization scheme utilizing a one-dimensional cloud

model. Mon. Wea. Rev., 106, 270–286.

Anthes, R. A., and T. T. Warner, 1978: Development of hydrodynamic models suitable for air

pollution and other mesometeorological studies. Mon. Wea. Rev., 106, 1045–1078.

Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical process of the

UCLA general circulation model. Methods in Computational Physics, 17, 173–265.

Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large

scale environment. Part I. J. Atmos. Sci., 31, 674–701.

Benjamin, S. G., and N. L. Seaman, 1985: A simple scheme for objective analysis in curved flow.

Mon. Wea. Rev., 113, 1184–1198.

Betts, A. K., 1986: A new convective adjustment scheme: Part I: Observational and theoretical

basis. Quart. J. Roy. Meteor. Soc., 112, 677–692.

Betts, A. K., and M. J. Miller, 1986: A new convective adjustment scheme. Part II: Single

column tests using GATE wave, BOMEX, ATEX and Arctic air-mass data sets. Quart. J. Roy.

Meteor. Soc., 112, 693–709.

Betts, A. K., and M. J. Miller, 1993: The Betts-Miller scheme. The representation of cumulus

convection in numerical models. K. A. Emanuel and D. J. Raymond, Eds., Amer. Meteor. Soc.,

246 pp.

Blackadar, A. K., 1979: High resolution models of the planetary boundary layer. Advances in

Environmental Science and Engineering, 1, No. 1, Pfafflin and Ziegler, Eds., Gordon and Briech

Sci. Publ., New York, 50–85.

Burk, S. D., and W. T. Thompson, 1989: A vertically nested regional numerical prediction model

with second-order closure physics. Mon. Wea. Rev., 117, 2305–2324.

Cressman, G. P., 1959: An operational objective analysis system. Mon. Wea. Rev., 87,

367–374.
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Dudhia, J., 1989: Numerical study of convection observed during the winter monsoon experiment

using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 3077–3107.

Dudhia, J., 1993: A nonhydrostatic version of the Penn State/NCAR mesoscale model:

Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121,

1493–1513.

Dudhia, J., 1996: A multi-layer soil temperature model for MM5. Preprints, The Sixth

PSU/NCAR Mesoscale Model Users' Workshop, Boulder, CO, Natl. Ctr. Atmos. Res.

Dudhia, J., D. Gill, Y.-R. Guo, D. Hansen, K. Manning, and W. Wang, 1998: PSU/NCAR

mesoscale modeling system tutorial class notes (MM5 modeling system version 2). [Available

from the National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307.]

Fritsch, J. M., and C. F. Chappel, 1980: Numerical prediction of convectively driven mesoscale

pressure systems. Part I: Convective parameterization. J. Atmos. Sci., 37, 1722–1733.

Grell, G. A., Y.-H. Kuo, and R. Pasch, 1991: Semi-prognostic tests of cumulus parameterization

schemes in the middle latitudes. Mon. Wea. Rev., 119, 5–31.

Grell, G. A., 1993: Prognostic evaluation of assumptions used by cumulus parameterizations.

Mon. Wea. Rev., 121, 764–787.

Grell, G. A., J. Dudhia, and D. R. Stauffer, 1994: A description of the fifth-generation Penn

State/NCAR mesoscale model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 117 pp.

[Available from the National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO

80307.]

Guo, Y.-R., and S. Chen, 1994: Terrain and land use for the fifth-generation Penn State/NCAR

mesoscale modeling system (MM5): Program TERRAIN. NCAR Tech. Note, NCAR/TN397+IA, 119 pp. [Available from the National Center for Atmospheric Research, P. O. Box

3000, Boulder, CO 80307.]

Haagenson, P., J. Dudhia, D. Stauffer, and G. Grell, 1994: The Penn State/NCAR mesoscale

model (MM5) source code documentation. NCAR Tech. Note, NCAR/TN-392+STR, 200 pp.

[Available from the National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO

80307.]

Hack, J. J., B. A. Boville, B. P. Briegleb, J. T. Kiehl, P. J. Rasch, and D. L. Williamson, 1993:

Description of the NCAR community climate model (CCM2). NCAR Tech. Note, NCAR/TN382+STR, 120 pp. [Available from the National Center for Atmospheric Research, P. O. Box

3000, Boulder, CO 80307.]
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Hong, S.-Y., and H.-L. Pan, 1996: Nonlocal boundary layer vertical diffusion in a medium-range

forecast model. Mon. Wea. Rev., 124, 2322–2339.

Hsie, E.-Y., and R. A. Anthes, 1984: Simulations of frontogenesis in a moist atmosphere using

alternative parameterizations of condensation and precipitation. J. Atmos. Sci., 41, 2701–2716.

Janjic, Z. I., 1994: The step-mountain eta coordinate model: Further development of the

convection, viscous sublayer, and turbulent closure schemes. Mon. Wea. Rev., 122, 927–945.

Kain, J. S., and J. M. Fritsch, 1990: A one-dimensional entraining/detraining plume model.

J. Atmos. Sci., 47, 2784–2802.

Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The

Kain-Fritsch scheme. The representation of cumulus in mesoscale models. K. A. Emanuel and

D. J. Raymond, Eds., Amer. Meteor. Soc., 246 pp.

Klemp, J. B., and R. B. Wilhelmson, 1978: Simulations of three-dimensional convective storm

dynamics. J. Atmos. Sci., 35, 1070–1096

Madala, R. V., 1981: Finite-difference techniques for vectorized fluid dynamics calculations.

Edited by D. L. Book, Springer Verlag, New York.

Manning, K., and P. Haagenson, 1992: Data ingest and objective analysis for the PSU/NCAR

modeling system: Programs DATAGRID and RAWINS. NCAR Tech. Note,

NCAR/TN-396+IA, 209 pp. [Available from the National Center for Atmospheric Research, P.

O. Box 3000, Boulder, CO 80307.]

Nuss, W. A., and D. W. Titley, 1994: Use of multiquadric interpolation in meteorological

objective analysis. Mon. Wea. Rev., 122, 1611–1631.

Pleim, J. E., and A. Xiu, 1995: Development and testing of a surface flux and planetary boundary

layer model for application in mesoscale models. J. Appl. Meteor., 34, 16–32.

Reisner, J., R. T. Bruintjes, and R. J. Rasmussen, 1993: Preliminary comparisons between MM5

NCAR/Penn State model generated icing forecasts and observations. Preprints, Fifth Intl. Conf.

on Aviation Weather Systems, Vienna, VA, Amer. Meteor. Soc., 65–69.

Reisner, J., R. J. Rasmussen, and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid

water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc., 124B,

1071–1107.
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Smolarkiewicz, P. K., and G. A. Grell, 1992: A class of monotone interpolation schemes.

J. Comp. Phys., 101, 431–440.

Stauffer, D. R., and N. L. Seaman, 1990: Use of four-dimensional data assimilation in a limitedarea mesoscale model. Part I: Experiments with synoptic-scale data. Mon. Wea. Rev., 118,

1250–1277.

Stauffer, D. R., N. L. Seaman, and F. S. Binkowski, 1991: Use of four-dimensional data

assimilation in a limited-area mesoscale model. Part II: Effects of data assimilation within the

planetary boundary layer. Mon. Wea. Rev., 119, 734–754.

Stauffer, D. R., and N. L. Seaman, 1994: Multiscale four-dimensional data assimilation. J. Appl.

Meteor., 33, 416–434.

Tao, W.-K., and J. Simpson, 1993: Goddard cumulus ensemble model. Part I: Model

description. Terr., Atmos., and Oc. Sci., 4, 35–72.

Zhang, D.-L., and R. A. Anthes, 1982: A high-resolution model of the planetary boundary layer --

Sensitivity tests and comparisons with SESAME-79 data. J. Appl. Meteor., 21, 1594–1609.

Zhang, D.-L., H.-R. Chang, N. L. Seaman, T. T. Warner, and J. M. Fritsch, 1986: A two-way

interactive nesting procedure with variable terrain resolution. Mon. Wea. Rev., 114, 1330–1339.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

__________________________________________________

*

 On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Daewon W. Byun, MD-80, Research Triangle Park, NC 27711. E-mail:

bdx@hpcc.epa.gov

Chapter 5

FUNDAMENTALS OF ONE-ATMOSPHERE DYNAMICS

FOR MULTISCALE AIR QUALITY MODELING

Daewon W. Byun*

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

ABSTRACT

This chapter provides essential information needed for the proper use of meteorological data in

air quality modeling systems. Sources of meteorological data are diverse and many difficulties

can arise while linking these with air quality models. To provide an integral view of atmospheric

modeling, a robust and fully compressible governing set of equations for the atmosphere is

introduced. Limitations of several simplifying assumptions on atmospheric dynamics are

presented. Also, concepts of on-line and off-line coupling of meteorological and air quality

models are discussed.

When the input meteorological data are recast with the proposed set of governing equations,

chemical transport models can follow the dynamic and thermodynamic descriptions of the

meteorological data closely. In addition, this chapter introduces a procedure to conserve mixing

ratio of trace species even in the case meteorological data are not mass consistent. In summary,

it attempts to bridge the information gap between dynamic meteorologists and air quality

modelers by highlighting the implication of using different meteorological coordinates and

dynamic assumptions for air quality simulations.
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5-1

5.0 FUNDAMENTALS FOR ONE-ATMOSPHERE MODELING FOR MULTISCALE

AIR QUALITY MODELING

To simulate weather and air quality phenomena realistically, adaptation of a one-atmosphere

perspective based mainly on “first principles” description of the atmospheric system (Dennis,

1998) is necessary. The perspective emphasizes that the influence of interactions at different

dynamic scales and among multi-pollutants cannot be ignored. For example, descriptions of

processes critical to producing oxidants, acid and nutrient depositions, and fine particles are too

closely related to treat separately. Proper modeling of these air pollutants requires that the broad

range of temporal and spatial scales of multi-pollutant interactions be considered simultaneously.

Several chapters (Chapters 4, 8, 9, 11 and 16) of this document present the one-atmosphere

modeling perspective related with the multi-pollutant chemical interactions. Another key aspect

of the one-atmosphere perspective is the dynamic description of the atmosphere. This is the

focus of the present chapter.

Air quality modeling should be viewed as an integral part of atmospheric modeling and the

governing equations and computational algorithms should be consistent and compatible.

Previously, many atmospheric models have been built with limited atmospheric dynamics

assumptions. To simplify the model development process, the governing equations were first

simplified to match with the target problems, then computer codes were implemented. This

approach enabled rapid development of models. However, we believe that dynamic assumptions

and choice of coordinates should not precede the computational structure of the modeling

system. To provide the scalability in describing dynamics, a fully compressible governing set of

equations in a generalized coordinate system is preferable. Once the system is based on the fully

compressible governing equations, simpler models can be built readily. The characteristics of

the vertical coordinates and other simplifying assumptions need to be considered as well. For

successful one-atmosphere simulations, it is imperative to have consistent algorithmic linkage

between meteorological and chemical transport models (CTMs).

The present chapter addresses the issue of consistent description of physical processes across

scales in meteorological and air quality modeling systems. It intends to provide appropriate

background information to properly link air quality and meteorological models at a fundamental

level. It deals with dynamic scalability issues, such as hydrostatic and nonhydrostatic modeling

covering wide range of both temporal and spatial scales. Some of the contents are extracts from

Byun (1999a and b) and others are complementary information to them. It includes mass

correction methods, mass conservative temporal interpolation method, and the coupling

paradigm for meteorology and chemical transport models.

5.1 Governing Equations and Approximations for the Atmosphere

In most weather prediction models, temperature and pressure, as well as moisture variables, are

used to represent thermodynamics of the system. Often these thermodynamic parameters are

represented with the advective form equations in meteorological models. Most of time, the
EPA/600/R-99/030

5-2

density is diagnosed as a byproduct of the simulation, usually through the ideal gas law. For

multiscale air quality applications where the strict mass conservation is required, prognostic

equations for the thermodynamic variables are preferably expressed in a conservative form

similar to the continuity equation. Recently, Ooyama (1990) has proposed the use of prognostic

equations for entropy and air density in atmospheric simulations by highlighting the

thermodynamic nature of pressure. Entropy is a well-defined state function of the

thermodynamic variables such as pressure, temperature, and density. Therefore, entropy is a

field variable that depends only on the state of the fluid. The principle he uses is the separation

of dynamic and thermodynamic parameters into their primary roles. An inevitable interaction

between dynamics and thermodynamics occurs in the form of the pressure gradient force.

In this section, a set of governing equations for fully compressible atmosphere is presented.

Here, density and entropy are used as the primary thermodynamic variables. For simplicity, a

dry adiabatic atmosphere is considered. Most of the discussions in this section should be

extensible for moist atmosphere if Ooyama’s approach is followed.

5.1.1 Governing Equations in a Generalized Curvilinear Coordinate System

Using tensor notation, the governing set of equations for the dry atmosphere in a generalized

curvilinear coordinate system can be written as:

∂

∂ ρ

∂

∂

∂

∂ ε ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ ˆ ;

v

t

vv g p

x x

v F

j

k

k

j jk

k k

jkl

k r

j ++ + l





 



 + =

1 2 Φ Ω (5-1)

∂ρ γ

∂

∂ρ γ

∂ γ ρ ρ

( ˆ ) ( ˆ ˆ )

ˆ ˆ ˆ t

v

x

Q Q

j

j + == (5-2)

∂ζ γ

∂

∂ζ γ

∂ γ ζ ζ

( ˆ ) ( ˆ ˆ )

ˆ ˆ ˆ t

v

x

Q Q

j

j + == (5-3)

∂φ γ

∂

∂φ γ

∂ γ φ φ

( ˆ ) ( ˆ ˆ )

ˆ ˆ ˆ i i

j

j t

v

x

Q Q i i + == (5-4)

where vˆj

 and vˆ k are contravariant and covariant wind components, respectively, ˆ

; v k

j

 represents

the covariant derivative of contravariant vector, εˆjkl is the Levi-Cevita symbol, Ωk is the angular

velocity of earth’s rotation, Fˆ

r

j

 represents frictional forcing terms, γˆ is the Jacobian of

coordinate transformation, Φ is geopotential height, ρ is air density, and gˆjk represents

components of gravity vector in tensor form. Refer to Appendix 5A for the tensor primer and the

derivation of the continuity equation in a generalized curvilinear coordinate system. φi

represents trace species concentration, and ζ is (dry air) entropy per unit volume (entropy

density), given as
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5-3

ζρ ρ ρ

ρ = − C TT vd R

oo

d

oo

ln( ) ln( ) (5-5)

where T is temperature, Too and ρoo are temperature and density of the reference atmosphere,

respectively, at pressure poo = 1000 mb = 105

 Pascal, Cvd is the specific heat capacity at

constant volume, and Rd is the gas constant for dry air. The Q-terms represent sources and sinks

of each conservative property. Although the source term for air density (Qρ ) should be zero in

an ideal case, it is retained here to capture the possible density error originating from numerical

procedures in meteorological models. It is important to understand how this error term

influences computations of other parameters such as vertical velocity component. Effects of the

error term on trace gas simulation are discussed later.

To close the system we need to utilize the ideal gas law and the thermodynamic relations for

temperature, entropy, pressure gradients, and density. Here, atmospheric pressure is treated as a

thermodynamic variable that is fully defined by the density and entropy of the atmosphere.

Then, pressure gradient terms can be computed using the thermodynamic relations with the

density and entropy (e.g., Batchelor, 1967; Ooyama, 1990; DeMaria, 1995) in terms of the

general vertical coordinate s x = ˆ 3, as:

p RT = ρ d (5-6a)

∇ = 



 



∇ + 



 

 sss p ∇ ∂p p

∂ρ ρ

∂

∂ζ ζ (5-6b)

∂

∂

∂

∂ρ

∂ρ

∂

∂

∂ζ

∂ζ

∂

p

s

p

s

p

s = 



 



 + 



 



 (5-6c)

∂

∂ρ

ζ

ρ

p C R T

C pd

d

vd

= − 



 



 (5-6d)

∂

∂ζ

p RT

C

d

vd

= , (5-6e)

where Cpd is the specific heat capacity at constant pressure for dry air, and

∇= + = = s s const s const x x ˆ / ˆ ˆ i j ∂∂ ∂∂/ ˆ 1 2 . For a conformal map projection, we can relate generalized

meteorological curvilinear coordinates ( ˆ , ˆ , ˆ ,ˆ xxxt) 123 to the reference rotated earth-tangential

coordinates (, ,,) xyzt as
EPA/600/R-99/030

5-4

ˆ

ˆ

ˆ

ˆ

x mx

x my

x s

t t

1

2

3

=

=

=

=















x mx

y mx

z hx x x t h x x x t z x x

t t

AGL sfc

=

=

== +

=















−

−

1 1

1 2

123 123 12

ˆ

ˆ

( ˆ , ˆ , ˆ ,ˆ) ( ˆ , ˆ , ˆ ,ˆ) ( ˆ , ˆ )

ˆ

(5-7a, b)

where m is the map scale factor, zsfc is the topographic height, and h is the geometric height, and

hAGL represents height above the ground (AGL). In the derivation of Equations 5-7a,b, we

neglected the first-order variations of the map scale factor in x- and y-directions. The

approximation establishes a quasi-orthogonality of the vertical coordinate to the horizontal plane

on the confomal map. The covariant metric tensor, for example, and its determinant are given as

ˆ

( ˆ ) ( ˆ )( ˆ ) ( ˆ )( )

( ˆ )( ˆ ) ( ˆ ) ( ˆ )( )

( ˆ )( ) ( ˆ )( ) (

γ

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

jk

m

h

x

h

x

h

x

h

x

h

s

h

x

h

x

m

h

x

h

x

h

s

h

x

h

s

h

x

h

s

h

s

=

+

+

−

−

2

1

2

12 1

1 2

2

2

2

2

1 2 )

2

































, (5-7c)

γ γ ∂∂ ˆ ˆ = = ( ) / jk mh s 1

4

2

. (5-7d)

With above relations, one can rewrite the governing momentum equation, Equation 5-1, into the

horizontal and vertical components of the curvilinear coordinates as (Byun, 1999a):

∂

∂

∂

∂ τ ˆ ( ˆ ) ˆ ˆ ˆ ˆ Vs V V V Vˆ s ss

s

s t

v

s

+ •∇ + + × f 3

3

+ ∇ +∇ − 



 

 mp m  + ∇= s

z

p

s s s s ss h 2 2 1 1 ( )( ) ˆρ

∂

∂ ρ

∂

∂

∂

∂

Φ Φ F (5-8)

∂

∂

∂

∂

∂

∂ ∂

∂

∂

ˆ ( ˆ )ˆ ˆ ˆ ˆ ˆ ˆ ˆ

v

t

v v

v

s

v v

h

x x

s

z s s

k j

k j

3

3 3

3 2

+ •∇ + + 



 

 V 

− ∇ +∇ •∇ + ∇ + = m

s

z

p hs p

s s ss sz F 2 2

3

∂ 1 1

∂ρ ρ

∂

∂

∂

∂ ( ) () Φ Φ ˆ (5-9)

where ˆVij ˆ ˆ s = + v v

1 2 , Φ( ˆ , ˆ , ˆ ,ˆ x x x t gz ) 123 = represents the geopotential height, Fˆ

s is the horizontal

forcing vector, τ 

ˆ 

3 is the vertical tangential basis vector and Fˆ

3 is the forcing term in the

momentum equation for x ˆ 3

 direction.

An alternative equation for the Cartesian vertical velocity component is given as:
EPA/600/R-99/030

5-5

∂ ρ

∂

ρ ∂ρ

∂

() ( J w ˆ )

t

m

J w

m

J wv

s

s

s

sz s + ∇• 





 + 2

3 V

+ + 



 









 



 = + 



 

 ρ  ρ

∂

∂

∂

∂

∂

∂ ρρ

ρ J m p

s s

s

z

J F wQ s s

Φ

3 (5-9’)

where V ij i j z = += + U V vm vm (ˆ / ) (ˆ / ) 1 2 is the horizontal wind vector represented in the

Cartesian coordinate system, w is the vertical velocity component, Js is the Jacobian for vertical

coordinate transformation ( J h

s gs s == = m

∂

∂

∂

∂ γ

1 Φ 2 ˆ ), and F3 is forcing term for the wcomponent. Note that the contravariant vertical velocity component is related to the Cartesian

vertical velocity as:

vˆ ds

dt

s

t

s w

s

z z z

3 = = + •∇ + 



 



 ∂

∂

∂

∂

V = + − •∇ + 



 



 ∂

∂

∂

∂

s

t g

w

s

z s s ( ˆ ) 1 V Φ , (5-10)

where ∇= + z z const z const = = x y ˆ / ˆ i j ∂∂ ∂∂/ .

The conservation equations for air density, entropy density, and tracer concentrations are found

to be:

∂ ρ

∂

ρ ∂ρ

∂ ρ

( ) ˆ J ( ˆ )

t

m

J

m

J v

s

J Q s

s

ss s + ∇• s











 + = 2

2

3 V (5-11)

∂ ζ

∂

ζ ∂ζ

∂ ζ

( ) ˆ J ( ˆ )

t

m

J

m

J v

s

J Q s

s

ss s + ∇• s











 + = 2

2

3 V (5-12)

∂ φ

∂

φ ∂φ

∂ φ

( ) ˆ ( ˆ ) i s

s

is s is

s

J

t

m

J

m

J v

s

J Q i + ∇• 









 + = 2

2

3 V (5-13)

5.1.2 Assumptions of Atmospheric Dynamics

In this subsection, several popular assumptions used in meteorological models are reviewed.

Here, the dynamic and thermodynamic assumptions are discussed separately because they have

been applied as independent approximations in many atmospheric models. However, readers

should be aware of the inseparable nature of the dynamics and thermodynamics of the

atmosphere. This study focuses on the impact of basic assumptions of the mass conservation

issues and limits of applications in air quality applications.

5.1.2.1 Boussinesq Approximation

The crux of the Boussinesq approximation is that variation in density is important only when it is

combined as a factor with the acceleration of gravity. Originally, it was applied for studying
EPA/600/R-99/030

5-6

shallow convection or boundary layer dynamics. Descriptions of the Boussinesq approximation

can be found in the literature (e.g., Arya, 1988; Pielke, 1984; Stull, 1988; and Thunis and

Bornstein, 1996). Although the Boussinesq approximation was originally developed for

incompressible fluid, Dutton and Fichtl (1969) expanded the concept for anelastic deep

convection applications. The results of the approximation lead to the following simplifications

of the equations of motions in the planetary boundary layer (PBL):

(1) Flows can be treated essentially as solenoidal either in velocity field (incompressible) or

in momentum field (anelastic).

(2) The equation of state for the fluctuating component is simplified because the ratio of

fluctuating density to total density can be approximated by the ratio of temperature

fluctuation to the reference temperature.

(3) Molecular properties including diffusivity are constant. These approximations are often

used in air quality modeling to simplify the equations of motions and trace gas

conservation equations. The effect of the Boussinesq approximation on mass continuity

is in the limitation of the flow characteristics, such as incompressible or anelastic. For

multiscale atmospheric studies, this approximation may be used only in the

parameterization of the surface fluxes where the density can be treated essentially

independent of height.

5.1.2.2 Nondivergent Flow Field Assumption

Essentially, this is an assumption about flow characteristics. The basis of this assumption is

purely dynamic although an incompressible assumption leads to the nondivergent flow

approximation. A priori, there is no connection with atmospheric thermodynamics. Therefore

this assumption does not provide any information about the state variables, such as density,

temperature, and pressure fields. For atmospheric applications, this approximation should be

viewed as a result of the incompressible atmosphere assumption linked through the continuity

equation of air. Because of the characteristics that the nondivergent velocity field can be

expressed as the curl of a vector stream function, the field is also called solenoidal. Implications

of this assumption on mass conservation of trace species are presented below in the description

of the incompressible atmosphere assumption. In the generalized coordinate system, the

nondivergent flow field is represented with following equation

1 0 ˆ

ˆ ˆ

γ ˆ

∂ γ

∂

v

x

j

j

( ) = , j = 123 , , (5-14)

This is somewhat different from the meteorological nondivergent flow field assumption in the

Cartesian coordinate system, ∇• = V 0. In the generalized meteorological coordinate system,

Equation 14 can be rewritten as
EPA/600/R-99/030

5-7

∂

∂

∂

∂

∂

∂

ˆ

ˆ ˆ ˆ ˆ lnˆ

v

x

mv

m

x

v

J

x

j

j

j

j

j s

j −+= 2 0 (5-14’)

The two additional terms represent essentially the effects of the map projection and the gradient

of the vertical Jacobian on the divergence of wind. For a small domain and for a coordinate

whose vertical Jacobian is constant with respect to height (e.g., σ z -coordinate), Equation 14’

becomes identical to the nondivergent wind flow assumption used in a meteorological model.

When the vertical Jacobian is a function of air density, the dependency of the wind on the density

distribution cannot be ignored.

5.1.2.3 Incompressible Atmosphere Assumption

This is an assumption about the thermodynamic characteristics of air. The equation of state

describes how density is affected by the changes in pressure and temperature fields. The

incompressibility of air can be assumed (Batchelor, 1967) if:

1

ρ

dρ

dt

<<

U

L , (5-15)

where U and L are the velocity and length scales, respectively, of the atmospheric motion.

As proposed in Byun (1999a), one can choose the density and the entropy as the two independent

parameters of state. The total derivative of pressure with respect to time can be expressed as:

dp

dt

p d

dt

p d

dt = 



 



 + 



 



 ∂

∂ρ

ρ ∂

∂ζ

ζ (5-16)

Then, Equation 5-15 becomes the relation:

1

2 ρ

∂

∂ζ

ζ

c

dp

dt

p d

dt

U

sound L − 



 



 << , (5-17)

where csound is the speed of sound in the atmosphere, i.e., c p sound = ∂ρ ∂/ . Batchelor (1967)

stated that for Equation 5-17 to be satisfied, not only the difference between the two terms in the

left hand side of Equation 5-17, but also the magnitude of each term should be small. When the

condition

1

2 ρc

dp

dt

U

sound L

<< (5-18)

is satisfied, the change in the density of a material element due to pressure variations are

negligible, that is, the fluid is behaving as if it were incompressible. By expanding the term dp

dt
EPA/600/R-99/030

5-8

in an Eulerian expression one can show that in order for the atmosphere to be treated as

incompressible, the following conditions must be satisfied:

U

csound

2

2 << 1;

U

c

p

sound

2

2 << 1; gL

csound

2 << 1, (5-19)

whereUp is the phase speed of dominant atmospheric waves. The first condition states that the

movement of air should have a Mach number much smaller than one, say 10%; the second

condition states that energy-carrying waves should not propagate as fast as 10% of the speed of

sound; and the last condition limits the vertical extent of motion to less than about one kilometer.

Similarly, Dutton and Fichtl (1969) showed that the nondivergent wind relation is generally

applicable up to half a kilometer above ground level through a scale analysis of the continuity

equation. Because of these limitations, a meteorological model with incompressible flow

approximation may not be suitable for multiscale air quality simulations that require descriptions

of atmospheric motions over a wide range of temporal and spatial scales. The second condition:

1

2 ρ

∂

∂ζ

ζ

c

p d

dt

U

sound L





 



 << (5-20)

means that variation of entropy due to internal heating or due to molecular conduction of heat

into the element must be small. For adiabatic or pseudo-adiabatic atmosphere, Equation 5-20 is

usually satisfied.

Basically, an incompressible atmosphere assumption is a shallow-water approximation for an

adiabatic atmosphere. With the incompressibility assumption, the distinction between the

continuity equation and its advective form becomes blurred. Consequently, concentrations in the

form of either density or mixing ratio are often used indiscriminately in atmospheric diffusion

equations. As presented above, the incompressible atmosphere assumption is a very restrictive

approximation that disassociates linkage between the thermodynamics and dynamics of

atmospheric motions. The incompressible atmosphere approximation simplifies the continuity

equation of the air to the nondivergent wind component relation regardless of the type of vertical

coordinates used. Compared with this, the atmosphere described with the hydrostatic pressure

coordinate is not necessarily incompressible even for the hydrostatic atmosphere. Because the

vertical layer is defined by the pressure surface, the hydrostatic approximation applied with the

hydrostatic pressure coordinate system limits only the vertical propagation of sound waves and

the atmosphere is not totally incompressible.

One might expect that as long as the wind field satisfies the nondivergent flow approximation, an

air quality model would satisfy the pollutant species mass conservation. In the following, it is

shown that this expectation is correct only when the air density field is perfectly mass consistent.

As will be shown later in Equation 5-24, the trace species mass conservation is affected by the

air density error term Qρ irrespective of whether or not the wind field is solenoidal. The

implication is that a nondivergent wind field does not guarantee the mass conservation of
EPA/600/R-99/030

5-9

pollutant species as long as there is inconsistency in air density and wind fields. It is not a

surprising statement, but in general this fact has not been actively addressed in air quality

modeling studies. Because the nondivergent relation simply disassociates density and wind

fields, it cannot be used to estimate the mass consistency error in the meteorological data set. On

the other hand, the diagnostic relations applicable for the family of hydrostatic pressure

coordinates based on total air density maintain the consistency in wind and air density fields.

5.1.2.4 Anelastic Atmosphere Assumption

Another popular limiting approximation applied in meteorological modeling is the anelastic

assumption. It simplifies the continuity equation as a diagnostic relation for the momentum

( ρoV, where ρo is density of reference atmosphere) components as follows:

∇• + = s os o s( ˆ v ˆ γ ρ ) ( ˆ ˆ ) ∂

∂

V γ ρ 3 0 (5-21)

Ogura and Phillips (1962) and Dutton and Fitchl (1969) found that for deep atmospheric

convection, if the characteristic vertical scale of motions is smaller than the atmospheric scale

height, the anelastic assumption is satisfied. For shallow convection, the Boussinesq

approximation allows us to treat the fluid as incompressible; for deep convection, the

approximate continuity equation requires the momentum field to be solenoidal, and the

expansion or contraction of parcels moving in the vertical is taken into account. Lipps and

Hemler (1982) also performed a scale analysis to propose a set of approximate equations of

motion which are anelastic when the time scale is larger than the inverse of Brunt-Väisäla

frequency. The anelastic approximation leads to a divergent wind field, i.e.:

∇ • + =− •∇ + s s sso o

v

s

v

s

( ˆ ˆ ) ( ˆ ˆ ) ˆ( ˆ γ ln ˆ ln ) ∂ γ

∂ γ ρ

∂

∂

V V ρ

3

3 (5-22)

Usually, the right hand side of Equation 5-22 does not vanish. Like the nondivergent wind field

approximation, this assumption provides a diagnostic relation among wind components although

it cannot be used to estimate the inconsistency in the total air density, ρ, and wind field data

provided by a meteorological model. However, unlike the incompressible atmosphere

assumption, the pressure, temperature and wind fields are not completely independent with the

anelastic assumption. The distribution of pressure must be such that the wind fields predicted by

the momentum equations continue to satisfy the anelastic relation (Gal-Chen and Somerville,

1975). For this reason, most anelastic meteorological models solve for the elliptic equation for

the pressure that is derived from Equation 5-22. Refer to Nance and Durran (1994) for a recent

review on the accuracy of anelastic meteorological modeling systems.

For air quality application, the anelastic approximation still requires use of a full continuity

equation for the perturbation density component. However, most anelastic meteorological

models do not solve for the perturbation air density directly. Therefore, one needs to infer it

from other thermodynamic fields. Also, because the trace gas concentration depends on the total
EPA/600/R-99/030

5-10

density of air, not on just the reference density, it does not simplify the pollutant continuity

equation and the concentration distribution represented in density units cannot be interchanged

with trace species mixing ratio.

5.1.2.5 Hydrostatic Atmosphere Approximation

Perhaps one of the most popular assumptions of atmospheric dynamics used in meteorological

models is the hydrostatic approximation. In the case of a hydrostatic atmosphere, the

acceleration and the frictional force terms in the z-direction of the earth-tangential Cartesian

coordinates are considered negligible. In earlier days of atmospheric modeling, the hydrostatic

approximation was usually applied with the pressure coordinate. It is well known that the

hydrostatic pressure coordinate applied to a hydrostatic atmosphere has a special property that

simplifies the continuity equation into a solenoidal form and provides a diagnostic equation for

the vertical velocity component. On the other hand, the geometric height coordinate was not

used extensively for studying a hydrostatic atmosphere. Recently, Ooyama (1990) and DeMaria

(1995) have presented a diagnostic vertical velocity equation. Extending this, a general

diagnostic equation for the vertical velocity component can be obtained with the hydrostatic

approximation for a coordinate whose Jacobian is independent of time (Byun, 1999a):

∂

∂ ρ

∂

∂

∂

∂

ρ

ρ s

c

v

s

sign s

z

g m

J

m

sound s J Q s s

s  ̃ ˆ ( )  ̃ ˆ 2

3

2

2





 



 =− ∇ • 









 − 















V

+ + − ∇• 









 − •∇

















∂

∂

∂

∂ρ

∂

∂ζ ρ ρ ζ s

p Q p Q mc

m

p sound s

s

s s (  ̃ )  ̃ ˆ 2 2 ˆ 2

V V (5-23)

The diagnostic Equation 5-23 can be used to maintain mass consistency in meteorological data

for air quality simulations.

It is worthwhile to note that the hydrostatic or nonhydrostatic atmospheric description, which is a

characterization of the vertical motion, is rather independent from either the

compressible/incompressible atmosphere or the anelastic atmosphere assumption, which is an

approximation of the mass continuity equation. Choices of the assumptions from the two distinct

groups have been used to simplify atmospheric motions, although some of the combinations,

such as compressible but hydrostatic atmosphere, are rarely used in atmospheric studies.

5.2 Choice of Vertical Coordinate System for Air Quality Modeling

Figure 5-1 provides a pedigree of vertical coordinates used in many atmospheric models.

Definitions of the coordinates are provided in Tables 5-1, 5-2 and 5-3. The hierarchy of

classification is: (1) temporal dependency of coordinates, (2) base physical characteristic of

coordinate variables, and (3) method of topography treatments. Application assumptions, such

as hydrostatic or nonhydrostatic atmosphere approximations, are not part of the classification

criteria. Isentropic coordinates are not included here because they are not suitable for the
EPA/600/R-99/030

5-11

regional and urban scale air quality simulation due to their inherent difficulties representing

planetary boundary layer (PBL) structure. For larger-scale simulations, an isentropic coordinate

system can serve as an interesting alternative (Arakawa et al., 1992). Also, there are new

developments of hybrid coordinates that combine isentropic coordinates with other coordinates

to mitigate the problem.

Many different types of vertical coordinates have been used for various meteorological

simulations. For example, the geometric height is used to study boundary layer phenomenon

because of its obvious advantage of relating near surface measurements with modeled results.

Pressure coordinates are natural choices for atmospheric studies because many upper

atmospheric measurements are made on pressure surfaces. Because most radiosonde

measurements are based on hydrostatic pressure, one may prefer use of the pressure coordinate

to study cloud dynamics. This idea of using the most appropriate vertical coordinate for

describing a physical process is referred to as a generic coordinate concept (Byun et al., 1995).

Several different generic coordinates can be used in a CTM for describing different atmospheric

processes while the underlying model structure should be based on a specific coordinate

consistent with the preprocessor meteorological model. The Models-3 Community Multiscale

Air Quality (CMAQ) modeling system allows users to choose a specific coordinate without

having to exchange science process modules (i.e., subroutines with physical parameterizations

for describing atmospheric processes) which are written in their generic coordinates. The

coordinate transformation is performed implicitly through the use of Jacobian within CMAQ.

Byun (1999a) discusses key science issues related to using a particular vertical coordinate for air

quality simulations. They include a governing set of equations for atmospheric dynamics and

thermodynamics, the vertical component of the Jacobian, the form of continuity equation for air,

the height of a model layer (expressed in terms of geopotential height), and other special

characteristics of a vertical coordinate for either hydrostatic or nonhydrostatic atmosphere

applications. Tables 5-1, 5-2 and 5-3 summarize properties of the popular time-independent

vertical coordinates (e.g., terrain-influenced height and the reference hydrostatic pressure

coordinate systems) and the time-dependent terrain-influenced coordinate systems, respectively.

Not only the assumptions on atmospheric dynamics, but also the choice of coordinate can affect

the characteristics of atmospheric simulations. For the time-independent vertical coordinates (z,

po, sigma-z, sigma-po), the vertical Jacobians are also time-independent. Especially with the

hydrostatic assumption, one can obtain a diagnostic equation for the vertical velocity component

, which includes soundwaves together with meteorological signals. Further assumptions on flow

characteristics, such as anelastic approximation, provide a simpler diagnostic equation for the

nonsolenoidal air flow. For such cases, with or without the anelastic approximation, one can

maintain trace species mass conservation in a CTM by using the vertical velocity field estimated

from the diagnostic relation. The scheme works whether the horizontal wind components,

temperature, and density field data are directly provided from a meteorological model or

interpolated from hourly data at the transport time step. This suggests that the mass error can be

estimated with the diagnostic relations that originate from one of the governing equations of the
EPA/600/R-99/030

5-12

preprocessor meteorological models. For a nonhydrostatic atmosphere, which does not have a

special diagnostic relation for time independent coordinates, one should rely on the methods

described below to account for the mass consistency errors.

For time dependent coordinates, the vertical Jacobians are also time dependent. In general, this

makes it more difficult to derive a diagnostic relation from the continuity equation. However,

for a coordinate with the Jacobian-weighted air density independent of height, a diagnostic

equation for the vertical velocity is available when appropriate top and bottom boundary

conditions are used. Vertical layers defined with this type of vertical coordinate are considered

as material surfaces because mass continuity can be satisfied in a diagnostic fashion. Air

particles are not expected to cross material surfaces during the advection process. An

atmospheric model based on this type of coordinate may not have a mass consistency problem

except for numerical reasons. The dynamic pressure coordinates based on true air density belong

to this category, which includes such coordinates as π -coordinate,σπ -coordinate, and the η -

coordinate defined in conjunction with σπ (See Table 5-3). A meteorological model using one

of these coordinates will conserve mass within the limits of numerical errors expected from finite

differencing and computer precision. For these coordinates, one can apply the same mass

conservation procedure for both hydrostatic and nonhydrostatic cases. Note that the diagnostic

relations obtained by appropriate choices of coordinates and assumptions on atmospheric

dynamics allow estimation of the density error term in the continuity equation. This information

can be used to reconstruct mass-consistent air density and wind fields that ensure mass

conservation of pollutant species in air quality models.
EPA/600/R-99/030

5-13

HYD

geometric

height

stephybrid

potential

temp.

base

pressure

mountain

hydrostatic

pressure

total

pressure

Time

Dependent Time Independent

T

T

T

T

(z) (po ) (π )

( ̃

p) (π )

(p)

σ( po

) σ( z )

terraininfluenced

(σ p ) (σ  ̃p ) (σ π )

(η

σ  ̃p )

terraininfluenced

terraininfluenced terrain- influenced terrain- influenced

NHY HYD

HYD HYD

HYD

HYD

HYD NHY

NHY

NHY

NHY

NHY NHY

NHY

NHY NHY

NHY

Figure 5-1. Pedigree of meteorological vertical coordinates. The encircled T symbol represents

that the associated coordinates are identical when temporal dependency is ignored. Dashedcircles show that all the coordinates can be used for hydrostatic (HYD) and nonhydrostatic

(NHY) application, regardless of the dynamic characteristics of the variables used to define

vertical coordinates.
EPA/600/R-99/030

5-14

Table 5-1. Summary of Characteristics of the Geometric Height and Pressure Coordinate

Systems. [Note: HYD and NHY stand for hydrostatic and nonhydrostatic applications,

respectively. D( ) and P( ) symbols are assigned for diagnostic and prognostic formulas with

equation numbers. ρo and ρ ̃ are the reference and dynamic (time-dependent) hydrostatic

pressure, respectively.]

Coordinate vertical velocity Vertical Jacobian Geopotential height

geometric height

( )z

NHY: w with P(5-9) or P(5-

9')

HYD: D(5-23)

Jz=1

constant in

(xxxt ˆ , ˆ , ˆ , ) 123

Φ = gz

reference

hydrostatic

pressure ( ) po

∂

∂ ρ pz z g o = − o ( )

NHY: P(5-9) or P(5-9')

HYD: D(5-23)

J g p o o = − ( ) ρ 1 constant

in (xxt ˆ , ˆ , ) 1 2

Φ Φ= − sfc ∫ o

o p

p dp

osfc

o '

ρ

dynamic

hydrostatic

pressure ( ) π , ∂π

∂ ρ z = − (, ,,) xyztg

ˆ  ̇ [ ˆ ] ' ' v m m

Q d

T

3 2

2 = =− ∇ • 









 − ∫ π ρ π π π ρ

π

π V

for both NHY & HYD

J g π = ρ − ( ) 1 but,

ρ π J g = 1/ constant

in (xxxt ˆ , ˆ , ˆ , ) 123

Φ Φ= − sfc ∫ d

sfc

π

π ρ

π '

large-scale

hydrostatic

pressure (p ̃), ∂

∂ ρ  ̃  ̃(, ,,) p

z = − xyztg

NHY: P(5-9) or P(5-9') for

perturbation component

HYD:

ˆ  ̃

 ̇ [

ˆ

 ̃ ]  ̃  ̃

 ̃

 ̃

 ̃

vp m m

Q dp p

p

p

p

T

3 2

2 = =− ∇ • 









 − ∫ V ρ

ρ

J g p ̃ = (  ̃ )

− ρ 1

Φ Φ= − sfc ∫p

p dp

sfc

 ̃'

 ̃  ̃

 ̃

ρ
EPA/600/R-99/030

5-15

Table 5-2. Summary of Time Independent Terrain-influenced Height and Reference Hydrostatic

Pressure Coordinate Systems. [Note: D( ) and P( ) symbols are assigned for diagnostic and

prognostic formulas with equation numbers, respectively, and ‘≠ ƒ( )’ represents that the

parameter is not dependent on the argument.]

Coordinate Application Vertical Momentum Vertical

Jacobian

Geopotential height

normalized

geometric

height ( ) σ z

hydrostatic D(5-23)

σ z

sfc

sfc

z z

H z = −−

generalized

hydrostatic P(5-9) or,

P(5-9') with Eq.(5-10)

J Hz z σ = − sfc

≠ ƒ (x t ˆ , ) 3

Φ = = gz

gz H z sfc z sfc [ ( )] + − σ

nonhydrostatic

terraininfluenced

reference

pressure

( ) σ po

hydrostatic D(5-23) J p

x g po

o

o

σ ρ =

*

( ˆ )

3

≠ ƒ( )t ,

p pz p o o sfc T

* = − ( ) Φ Φ= − sfc ∫ o

o

po

p d posfc

po

*

' ρ

σ σ

σ

σ po

o T

o sfc T

p p

pz p = −( ) − nonhydrostatic

P(5-9) or, P(5-9') with Eq.(5-

10) for perturbation

component
EPA/600/R-99/030

5-16

Table 5-3. Summary of Characteristics of the Time Dependent Terrain-influenced Coordinate

Systems.

Coordinate Applicatio

n

Vertical Momentum Vertical

Jacobian

Geopotential height

terraininfluenced

hydrostatic

pressure

hydrostatic π σπ σ

σ

π

* π

 ̇ T

= − ∇• ∫ [

ˆ

] ' *

*

π ρ

π σ ρ

σ

σ

σ

σ

π π

π

π

π Q m m d

T

2

2

V

 ̃  ̃

 ̃

*

ρ σ J p

g p

=

≠ ƒ(xˆ )

3

Φ Φ= − sfc ∫ p

p d psfc

p  ̃

 ̃ '

*

 ̃  ̃

 ̃

ρ σ σ

σ

( ) σπ

σ

π π

π π π = −−

T

sfc T

nonhydrostatic − − ( )

*

σ σ ∂π

∂ π πT t

ππ π * = − sfc T

ρ

π σ π J

g =

*

≠ ƒ(xˆ )

3

Φ Φ= − sfc ∫ sfcd π

ρ σ σ

σ

π π

π

*

 ̃ '

terraininfluenced

large-scale

hydrostatic

pressure ( ) σ

p ̃

nonhydrostaticP(5-9) or, P(5-9') with Eq.(5-10) for

perturbation component when p ̃

and ρ ̃ given

 ̃  ̃

 ̃

*

ρ σ J p

g p

=

≠ ƒ(xˆ )

3

Φ Φ= − sfc ∫ p

p d psfc

p  ̃

 ̃ '

*

 ̃  ̃

 ̃

ρ σ σ

σ

step-mountain

eta ( ) η with

σπ ,

η ση = π sfc ,

ηsfc =

pz p

p p

o sfc T

o T

( )

( )

−

0 −

hydrostatic ∂π

∂ η π ρ

η π

η

η ρ

η

η

η *

*

*

[

ˆ

] '

t

Q m m d

sfc

sfc

sfc

sfc

= − ∇• ∫ 1 2

2

0

V

πη η

∂π

∂

η *

*

 ̇

0 =− + t

[

ˆ

] ' *

*

π ρη π

η

η ρ

η

η

η Q m m d sfc

sfc

− ∇• ∫ 2

2

0

V

J p

g sfc

η ρ η =  ̃

 ̃

*

ρ ̃ η J ≠

ƒ(xˆ )

3

Φ Φ= − sfc ∫ sfc

p d sfc

 ̃

 ̃ '

*

ρη

η η

η

nonhydrostatic J

g sfc

η

π

ρ η =

*

ρ η J ≠

ƒ(xˆ )

3

Φ Φ= − sfc ∫

sfc sfc

d π

ρη

η η

η *

'

step-mountain

ETA (ησ p ̃ )

with σ

p ̃ ,

η ση σ  ̃  ̃ p= p sfc

nonhydrostaticP(5-9) or, P(5-9') with Eq.(5-10) for

perturbation component when  ̇  ̃ ησ p,

ρ ̃ provided

J p

g sfc

η ρ η =  ̃

 ̃

*

Φ Φ= − sfc ∫ sfc

p d sfc

 ̃

 ̃ '

*

ρη

η η

η
EPA/600/R-99/030

5-17

5.3 Coupling of Meteorology and Air Quality

Characteristics of air quality model simulations are heavily dependent on the quality of the

meteorological data. Meteorological data for air quality can be provided either by diagnostic

models, which analyze observations at surface sites and upper air soundings, or by dynamic

models with or without four-dimensional data assimilation (FDDA). Readers are referred to

Seaman (1999) for a state-of-science review on this topic. In the next section a dynamic

modeling with FDDA approach, which is used in the Models-3 CMAQ system, is described.

5.3.1 Meteorological Data for Air Quality Modeling

Meteorological simulations are applied to drive a CTM for solving atmospheric diffusion

equations for trace species. For regional scale simulations, whose problem size is continental

scale or somewhat smaller, hydrostatic meteorological models have been used, usually with

FDDA. For small scale simulations where topographic effects are important, nonhydrostatic or

compressible atmospheric models are used. These differences in the assumptions used for

atmospheric characterization affect air quality simulations greatly.

Meteorological data can be supplied by running dynamic models prognostically, or with the

archived reanalysis data routinely available as a part of numerical weather forecasting for air

quality simulations (Schulze and Turner, 1998). Currently, GCIP (GEWAX Continental-scale

International Project) provides an archive of the Eta model reanalysis of surface and upper air

fields at 48 km resolution (Leese, 1993; Kalany et al., 1996). Based on the success of GCIP, the

National Center for Environmental Prediction (NCEP), NOAA, is planning to archive regional

reanalysis at a higher resolution. Similarly, the Mesoscale Analysis and Prediction

System/Rapid Update Cycle (MAPS/RUC) of the Forecast Systems Laboratory (FSL), NOAA,

produces accurate and timely analyses and short-term forecasts at 40-60 km resolutions

(Benjamin et al., 1995, 1998). The output data are archived at 1-3 hour intervals on 25-34 levels.

These alternative data sources are promising because of the wealth of observation data used for

the reanalysis and the availability of long-term meteorological characterization data suitable for

seasonal or annual assessment studies.

5.3.2 Off-line and On-line Modeling Paradigms

Air quality models are run many times to understand the effects of emissions control strategies

on the pollutant concentrations using the same meteorological data. A non-coupled prognostic

model with FDDA can provide adequate meteorological data needed for such operational use.

This is the so-called off-line mode air quality simulation. However, a successful air quality

simulation requires that the key parameters in meteorological data be consistent. For example, to

ensure the mass conservation of trace species, the density and velocity component should satisfy

the continuity equation accurately. Details of this issue will be discussed below.

If air quality is solved as a part of the meteorology modeling, this data consistency problem

would be much less apparent. Dynamic and thermodynamic descriptions of operational
EPA/600/R-99/030

5-18

meteorological models should be self-consistent, and necessary meteorological parameters are

readily available at the finite time steps needed for the air quality process modules during the

numerical integration. The ultimate goal within atmospheric community is the development of a

fully integrated meteorological-chemical model (Seaman, 1995). This is the so-called on-line

mode air quality simulation. There have been a few successful examples of integrating

meteorology and atmospheric chemistry algorithms into a single computer program (e.g., Vogel

et al., 1995). For certain research purposes, such as studying two-way interactions of radiation

processes, the on-line modeling approach is needed. However, the conventional on-line

modeling approach, where chemistry-transport code is imbedded in one system, exhibits many

operational difficulties. For example, in addition to tremendously increasing the computer

resource requirements, differences in model dynamics and code structures hinder development

and maintenance of a fully coupled meteorological/chemical/emissions modeling system for use

in routine air quality management.

Figure 5-2 shows structures of the on-line and off-line air quality modeling systems,

respectively, commonly used at present time. Table 5-4 compares a few characteristics of online and off-line modeling paradigms. Each method has associated pros and cons. Therefore, in

the future versions of the Models-3 CMAQ system, we intend to realize both on-line and off-line

modes of operations through the use of an advanced input/output (I/O) applications programming

interface (API) (Coats, 1996). Figure 5-3 provides a schematic diagram of the implementation

idea. A proof-of-concept research effort using MM5 and a prototype version of CMAQ is

underway (Xiu et al., 1998). However, to accomplish the goals of multiscale on-line/off-line

modeling with one system, a full adaptation of the one-atmosphere concept is needed.

Development of the fully coupled chemistry-transport model to a meteorological modeling

system requires a fundamental rethinking of the atmospheric modeling approach in general.

Some of the suggested requirements for a next generation mesoscale meteorological model that

can be used as a host of the on-line/off-line modeling paradigms are:

• Scaleable dynamics and thermodynamics: Use fully compressible form of governing

set of equations and a flexible coordinate system that can deal with multiscale dynamics.

• Unified governing set of equations: Not only the weather forecasting, dynamics and

thermodynamics research but also the air quality studies should rely on the same general

governing set of equations describing the atmosphere.

• Cell-based mass conservation: As opposed to the simple conservation of domain total

mass, cell-based conservation of the scalar (conserving) quantities is needed. Use of

proper state variables, such as density and entropy, instead of pressure and temperature,

and representation of governing equations in the conservation form rather than in the

advective form are recommended.
EPA/600/R-99/030

5-19

• State-of-the-art data assimilation method: Not only the surface measurements and

upper air soundings, but also other observation data obtained through the remote sensing

and other in situ means must be included for the data assimilation.

• Multiscale physics descriptions: It has been known that certain parameterizations of

physical processes, including clouds, used in present weather forecasting models are

scale dependent. General parameterization schemes capable of dealing with a wide

spectrum of spatial and temporal scales are needed.

The Weather Research & Forecasting (WRF) Modeling System (Dudhia et al., 1998), which is

under development by scientists at NCAR and NOAA, could meet most of the above

requirements. Therefore, the WRF modeling system has the potential to be the future

meteorological model of the Models–3 CMAQ system to provide the multiscale on-line/off-line

air quality modeling capability simultaneously.

Table 5-4. Comparison of On-line and Off-line Modeling Paradigms

Off-line Modeling On-line Modeling

Dynamic

Consistency

• Need sophisticated interface

processors

• Need careful treatment of

meteorology data in AQM

• Easier to accomplish, but must have

proper governing equations.

• Meteorology data available as

computed

Process Interactions • No two-way interactions between

meteorology and air quality

• Two-way interaction

• Small error in meteorological data

will cause large problem in air

quality simulation (positive feedback

problem).

System

Characteristics

• Systems maintained at different

institutions

• Modular at system level. Different

algorithms can be mixed and tested

• Large and diverse user base

• Community Involvement

• Proprietary ownership

• Expensive in terms of computer

resource need (memory and CPU)

• Unnecessary repeat of

computations for control strategy

study

• Low flexibility

• Limited user base

• Legacy complex code, which

hinders new development

Application

Characteristics

• Easy to test new science concept

• Efficient for emissions control

study

• Good for independent air quality

process study

• Difficult to isolate individual

effects

• Excellent for studying feedback of

met. and air quality
EPA/600/R-99/030

5-20

Atmospheric

Modeling System

Emissions

Processing

MET.

Air Quality Modules

Environmental

Data

Meteorology

Modeling System

Emissions

Processor

Air Quality

Modeling System

Met., Landuse,

& Assimilation

Data

Surrogate &

Emisssions

Data

Chemistry

Data

Off-line Modeling On-line Modeling

Figure 5-2. Current On-line and Off-line Air Quality Modeling Paradigms
EPA/600/R-99/030

5-21

Meteorology

Modeling System

Emissions

Processor

Air Quality

Modeling System

Met., Landuse,

& Assimilation

Data

Surrogate &

Emisssions

Data

Chemistry

Data

I/O API

I/O API

I/O API

CPU/Network

Boundary

CPU/Network

Boundary

Computer-A

Computer-C

real-time I/O API

feedback on

file-based I/O API

feedback off

: On-line model

: Off-line model

Computer-B

Unified Governing

Set of Eqns !

+

Consistent Numerics

+

Figure 5-3. Proposed One-atmosphere Air Quality Modeling Paradigms. Double arrowhead

lines represent possibility of two-way coupling. The coupling of independent modeling

components is accomplished through the I/O API linking the cooperating executables.

5.4 Mass Conservation

For air quality simulations, mass conservation is the most important physical constraint. This is

because it is unrealistic to have injection of primary pollutant mass through any other means than

a real source emission process, and also because the little perturbations in the mass of both

primary and secondary pollutants will jeopardize the correct simulation of reactions among trace

species. Therefore, conserving mass of a passive primary trace species is a necessary property of

an air quality model.

5.4.1 Mass Consistency in Meteorological Data

The main objective of many meteorological models has been to predict synoptic or mesoscale

weather phenomena. Therefore, major design considerations are focused on such issues

important for energy conservation, resolving a spectrum of different wavelengths, and energy

cascade under nonlinear wave-wave interactions. Conservation of mass is not usually

emphasized as the other constraints listed. Also, the predictive quantities are generally

thermodynamic parameters, such as temperature and pressure. The conservation equation for air

density is rarely solved directly in meteorological models because of little operational use of air

density for weather forecasting and no direct measurements to compare. Usually it is estimated

from the equation for the state of ideal gas or from a hydrostatic relation when hydrostatic

assumptions are made. Even the predictive equations for the moisture variables are often written

in an advective form rather than a continuity equation form. On the other hand, air quality
EPA/600/R-99/030

5-22

simulation relies mostly on the continuity equation. The success of a simulation is heavily

dependent on the consistency of density and wind data (i.e., how well they satisfy the continuity

equation).

The mass inconsistency in density and wind fields from a meteorological model is most likely

caused by one or more of the following reasons:

1. Many meteorological models do not use the proposed ideal set of governing equations. A

continuity equation for air is not used as one of the prognostic equations and air density is

usually a diagnostic parameter in meteorological models.

2. The prognostic equation for temperature is often used to represent thermodynamics of the

atmosphere. It is well known that temperature is not a good conserving parameter.

3. Removal of hydrometeors due to condensation or sublimation may subtract and add mass

and heat to the moist atmosphere making the system nonadiabatic (thermodynamically

irreversible) and not mass-conserving.

4. Numerical schemes used in meteorological models are designed to conserve energy,

entropy, rather than the mass of air.

5. The FDDA and overall assimilation process, including the effects of Newtonian forcing

terms in the momentum and temperature equations, may cause inadvertent modification

of the energy balance and subsequent perturbation of air density resulting in mass

conservation problems.

6. Heat, moisture and momentum flux exchanges at the surface-atmosphere interface may

affect the air density distribution. Usually this effect is not significant as it is often

neglected with the Boussinesq approximation.

7. Flux exchanges at the nesting boundaries for nested runs affect mass balance.

8. Energy and mass balance characteristics of cloud modules used influence air and

moisture density fields.

9. Data output time steps are too large to capture the dynamic variations in the

meteorological models. If temporally averaged data are provided from the meteorology

model this problem can be minimized (Scamarock, 1998).

5.4.2 Techniques for Mass Conservation in Air Quality Models

As presented in Byun (1999b), species mixing ratios ( ci / ρ) is a useful conserved quantity for

photochemical Eulerian air quality modeling, in particular. In limited area atmospheric modeling

like an urban or a regional scale simulation, the total air mass in the simulation domain is subject

to the inflow conditions determined by large synoptic scale weather systems. In this situation,
EPA/600/R-99/030

5-23

the conservation of pollutant mass in the modeling domain can be difficult unless the density and

wind fields are perfectly mass consistent. When the mass inconsistency in the meteorological

fields is expected, the conservation equation for mixing ratio must be used as a necessary

condition to ensure exact conservation of pollutant mass. This is accomplished by replacing the

right-hand-side term of Equation 5-11 with Q c Q

c i i = ρ

ρ

. Then, the conservation equation for

pollutant species is rewritten as:

∂

∂

∂

∂ ρ

( ) ρ ˆ c J ( ˆ )

t

m

c J

m

cJv

s

c J Q i s

s

is s is + ∇• i s











 + = 2

2

3 V (5-24)

This adjustment alone is not sufficient to conserve pollutant mass when the density error term is

not small. Equation 5-24 shows that the correction term has the same form as a first-order

chemical reaction whose reaction rate is determined by the normalized air density error term.

Table 7-5 in Chapter 7 in this document summarizes correction methods discussed in Byun

(1999b). Among these, the method based on the two-step procedure (i.e., solving the lhs of

Equation 5-24 first followed by the mass correction step solving for rhs) is expected to be the

most accurate:

( ) ( )

( ) ( )int c J c JJ

J i s

cor i s

T

s

= T s ρρ , (5-25)

where superscripts cor, int, and T represent corrected, transported (advected), and interpolated

quantities, respectively. It should be noted that Js in Equation 5-25 must not be canceled out

even for a coordinate with time independent Js because the spatial variation of the Jacobian must

be taken into account for the numerical advection. In the event the total air mass in the

computational domain fluctuates, this correction procedure would affect air quality predictions.

In general, the air quality prediction can be as good as the density prediction of the

meteorological model. However, considering the nonlinear interactions of trace species in the

chemical production/loss calculations, one could expect serious effects on air quality simulations

when the quality of meteorology data is in doubt.

Byun (1999b) also provides an alternative method to deal with the mass inconsistency in

meteorological data through the modification of wind field, while keeping the density field

intact, before solving the species conservation equation. Assuming a modified wind field exists

that eliminates the source term in the continuity equation for air, the relationship between the

original and modified wind components is given as:

V V ˆ ˆ

s

M =+ ∇ s s

1

2 1

2 α

λ (5-26a)

v v ˆ ˆ s

3 3 M

3

2

1

2

= +

α

∂λ

∂ (5-26b)
EPA/600/R-99/030

5-24

where λ is the Lagrangian multiplier to be determined and α1 and α3 are the weights for the

horizontal and vertical wind components. λ must satisfy the Poisson equation

m

J

m s

J

s s J Q s

s

s

s

2

1

2 2

3

2 2 2

∇• ∇ 



 



 + = ρ

α

λ ∂

∂

ρ

α

∂λ

∂ ρ [ ] , (5-27)

with the associated boundary conditions:

λ= 0 for flow-through boundaries; and

∂λ ∂/ s = 0for impenetrable boundaries (i.e., at the topographic surface).

The modified wind components are subject to the same top and bottom boundary conditions

imposed by the given coordinate system and dynamic assumptions.

The main difference in the two proposed correction methods, correction after advection versus

correction of wind fields before advection, is practically philosophical. Should we process a

CTM using meteorological data as supplied, then correct possible errors in the species

concentrations, or should we modify the velocity field to be mass consistent before the

computation of trace gas concentrations in the CTM? The answer to this question lies in whether

the air quality modeling need is satisfied with simple mixing ratio conservation with the

adjustment process or not. In case the source-receptor relation is important, it is preferable to

maintain the linearity of transport process using the mass-consistent wind components, which

have been modified at the expense of truthfulness of meteorological fields. In practice, a

combination of both methods is needed. The mass consistency error in the meteorological data

must be corrected before air quality simulations with the wind-field adjustment method and the

mixing ratio correction method Equation 5-25 should be applied to compensate the numerical

differences in advection processes between meteorological and air quality models.

5.4.3 Temporal Interpolation of Meteorological Data

Byun (1999b) discusses a mass-conservative temporal interpolation method to complement the

mass inconsistency correction. Temporal interpolations of density and velocity data are often

required in a CTM because the meteorological model output has a coarser temporal resolution

than the transport time step (which is usually the synchronization time step for a CTM using a

fractional time-step method).

The Jacobian and density at a time t tt α =− + α α n n+ ( ) 1 1 between the two consecutive output time

steps, tn and tn+1, are interpolated with linearity assumed:

( ) ( )( ) ( ) J JJ s sn sn α =− + 1 α α +1 (5-28a)

( ) ( )( ) ( ) ρ α ρ αρ α J JJ s sn sn =− + 1 +1 (5-28b)
EPA/600/R-99/030

5-25

where 0 1 ≤ ≤ α . It is obvious that the functional form of the Jacobian (which depends on a

vertical coordinate) changes the characteristic of density interpolation. The premise used here is

that the Jacobian is a fundamental quantity that determines the coordinate system. When the

Jacobian is interpolated to define the vertical layers through linear interpolation, all other

components involved in the mass conservation equation need to be interpolated accordingly.

Wind components multiplied with the Jacobian-weighted density are interpolated linearly:

( ˆ ) ( )( ˆ ) ( ˆ ρ α ρ αρ ) α J JJ s s s sn s sn V VV =− + 1 +1 (5-29a)

(ρ α ρ αρ ˆ ) ( )( ˆ ) ( ˆ ) α Jv Jv Jv s sn sn

3 33 =− + 1 +1 (5-29b)

and interpolated wind components are derived with:

( ˆ ) ( ˆ )

( )

V V s

s s

s

J

J α

α

α

ρ

ρ = (5-30a)

(ˆ ) ( ˆ )

( )

v

J v

J

s

s

3

3

α

α

α

ρ

ρ = (5-30b)

However, the proposed scheme, Equation 5-28b, has a problem in such cases where the finite

difference value of ( ) ρJs cannot approximate the linear interpolation of the time rate change of

the quantity, ∂ ρ

∂

( ) J

t

s , adequately. Usually, this tendency term is not available with the

meteorological data. However, when the tendency is available or can be estimated with the

diagnostic relations for certain meteorological coordinate systems, a different interpolation rule

must be sought. Because the tendency term, not ( ) ρJs itself, is a component of the continuity

equation, linear interpolation of the tendency may be more appropriate. Then, ( ) ρJs at the

interpolation time step must be estimated in such a way that satisfies the continuity as well as the

tendency term (Byun 1999b).

5.5 Conclusion

In this chapter I attempted to bridge the information gap between dynamic meteorologists and air

quality modelers and to promote the proper use of meteorological information in air quality

modeling studies. It highlights the importance of dynamic consistency in meteorological and air

quality modeling systems. The effects of the common assumptions used for the atmospheric

study on the mass conservation for trace species have been reviewed. Although meteorological

data provided by operational meteorological models are usually self-consistent, air quality

modelers need to evaluate the data for exact consistency before they can be used in air quality

simulation. Minor adjustment of the meteorological data may be needed to assure mass

conservation of trace gas species in CTMs. Also, characteristics of vertical coordinates have

been discussed. Certain coordinates provide diagnostic relations that can be used to maintain

mass consistency in meteorological fields. When meteorological data are needed at sub-output
EPA/600/R-99/030

5-26

time steps within CTM, the interpolation of the data should be done in such a way that the mass

conservation and consistency in the thermodynamic variables are not compromised.

In addition, the on-line and off-line modeling concepts are discussed to provide design guidance

for fully integrated meteorological-chemical models. To realize the noble goal of implementing

the one-atmosphere modeling system, both the multi-pollutant chemistry and multiscale physics

capability in meteorology are needed. The following are the features that make the CMAQ air

quality model a suitable key component of an one-atmosphere modeling system:

• Flexible chemistry representations through a mechanism reader;

• Comprehensive list of atmospheric processes that are implemented;

• Modular coding structure and versatile data handling method;

• Capability to handle multiscale dynamics and thermodynamics;

• Fully compressible governing set of equations in generalized coordinates; and

• Robust mixing ratio conservation scheme, even with mass inconsistent meteorology data.

At present, we are encouraged by the efforts of the WRF meteorology model development

groups that focus on issues such as choice of coordinates, grid staggering method, state variables

in the governing equations (e.g., fully compressible), conservation properties (mass and energy)

both in the model equations and numerics, modularity of code, data communication methods,

and coding language. This entails continuous exchange of ideas between the Models-3 CMAQ

and WRF modeling groups.

To achieve the true one-atmosphere modeling system, we must address multi-pollutant and

multiscale processes that are typically broader than any one group (or institution) has expertise to

address. The need is well summarized in Dennis (1998):

Considering additional needs for emerging environmental problems such as

coastal eutrophication and ecological damage issues related with cross-media

purview, encompassing the one-atmosphere scope is needed. This means we have

to work with a more complete one-atmosphere description to facilitate

interactions within it as efficiently as broadly as possible. One potential answer is

to foster a community modeling perspective and model system framework that is

supported and used by a critical fraction of the scientific community.

5.6 References

Arakawa, A., C. R. Mechso, and C. S. Konor, 1992: An isentropic vertical coordinate model:

Design and application to atmospheric frontogenesis studies. Meteor. Atmos. Phys. 50, 31-45.
EPA/600/R-99/030

5-27

Arya, S. Pal, 1988: Introduction to Micrometeorology. Academic Press, Inc., 307 pp.

Batchelor, G. K., 1967: An Introduction to Fluid Mechanics. Cambridge University Press, 615

pp.

Benjamin, S.G., D. Kim, and T.W. Schlatter, 1995: The Rapid Update Cycle: A new mesoscale

assimilation system in hybrid-theta-sigma coordinates at the National Meteorological Center.

Second International Symposium on Assimilation of Observations in Meteorology and

Oceanography, Tokyo, Japan, 13-17 March, 337-342.

Benjamin, S.G., J.M. Brown, K.J. Brunge, B.E. Schwarts, T.G. Smirnova, and T.L. Smith, 1998:

The operational RUC-2. 16th Conference on Weather Analysis and Forecasting, Phoenix, AZ,

Amer. Meteor. Soc., 249-252.

Bishop, R. L. and S. I. Goldberg, 1968: Tensor Analysis on Manifolds. Dover Publications, Inc.

New York.

Byun, D. W., 1999a: Dynamically consistent formulations in meteorological and air quality

models for multiscale atmospheric applications: I. Governing equations in a generalized

coordinate system. J. Atmos. Sci., (in print)

Byun, D. W., 1999b: Dynamically consistent formulations in meteorological and air quality

models for multiscale atmospheric applications: II. Mass conservation issues. J. Atmos. Sci., (in

print)

Byun D. W. , A.. Hanna, C. J. Coats, and D. Hwang, 1995a: Models-3 Air Quality Model

Prototype Science and Computational Concept Development. Trans. TR-24 Regional

Photochemical Measurement and Modeling Studies, San Diego, CA, of Air & Waste

Management Association, 197-212.

Coats, C. J., cited 1996: The EDSS/Models-3 I/O Applications Programming Interface. MCNC

Environmental Programs, Research Triangle Park, NC. [Available on-line from

http://www.iceis.mcnc.org/EDSS/ioapi/H.AA.html.]

Defrise, P., 1964: Tensor Calculus in Atmospheric Mechanics. Advances in Geophysics 10, 261-

315.

DeMaria, M., 1995: Evaluation of a hydrostatic, height-coordinate formulation of the primitive

equations for atmospheric modeling. Mon. Wea. Rev., 123, 3576-3589.

Dennis, R.L., 1998: The environmental protection agency’s third generation air quality modeling

system: an overall perspective. Proceedings of the American Meteorological Society 78th

Annual Meeting, Phoenix, AZ, Jan. 11-16, 1998. 255-258.
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5-28

Dudhia, J., D. Gill, J. Klemp, and W. Skamarock, 1998: WRF: Cuurrent status of model

development and plans for the future. Preprints of the Eighth PSU/NCAR Mesoscale Model

User’s Workshop. Boulder, Colorado, 15-16 June, 1998.

Dutton, J. A., 1976: The Ceaseless Wind, an Introduction to the Theory of Atmospheric Motion.

McGraw-Hill, 579 pp.

Dutton, J. A., and G. H. Fichtl, 1969: Approximate equations of motion for gases and liquids. J.

Atmos. Sci., 26, 241-254.

Gal-Chen, T., and R. C. J. Somerville, 1975: On the use of coordinate transformations for the

solution of the Navier-Stokes equations. J. Comput. Phys., 17, 209-228.

Kalany, E., and Co-authors, 1996: The NCEP/NCAR 40-year Reanalysis Project. Bull. Amer.

Meteor. Soc., 77, 437-471.

Leese, J. A., 1993: Implementation Plan for the GEWEX Continental-Scale International Project

(GCIP). Int. GEWEX Project Office #6, 148 pp. [Available from IGPO, 1100 Wayne Ave., Suite

1225, Silver Springs, MD 20910].

Lipps, F. B., and R. S. Hemler, 1982: A scale analysis of deep moist convection and some related

numerical calculations. J. Atmos. Sci., 39, 2192-2210.

Nance, L. B., and D. R. Durran, 1994: A comparison of the accuracy of three anelastic systems

and the pseudo-incompressible system. J. Atmos. Sci., 51, 3549-3565.

Ogura, Y., and N. W. Phillips, 1962: Scale analysis of deep and shallow convection in the

atmosphere. J. Atmos. Sci., 19, 173-179.

Ooyama, K. V., 1990: A thermodynamic foundation for modeling the moist atmosphere. J.

Atmos. Sci., 47, 2580-2593.

Pielke, R. A., 1984: Mesoscale Meteorological Modeling. Academic Press, 612 pp.

Scamarock, W. 1998: Personal communication.

Schulze, R. H., and D. B. Turner, 1998: Potential use of NOAA-archived meteorological

observations to improve air dispersion model performance. EM, March 1998, 12-21.

Seaman, N. L, 1995: Status of meteorological pre-processors for air-quality modeling.

International Conf. on Particulate Matter, Pittsburgh, PA, Air & Waste Management

Association, 639-650.

Seaman, N.L., 1999: Meteorological modeling for air-quality assessments. (Submitted to Atmos.

Environ., 32, 87pp.)
EPA/600/R-99/030

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Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic

Publishers. 666 pp.

Thunis, P. and R. Bornstein, 1996: Hierarchy of mesoscale flow assumptions and equations. J.

Atmos. Sci., 53, 380-397.

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compounds emission in the state of Baden-Wurttemberg on ozone concentrations during

episodes of high air temperatures. J. Geophys. Res., 100, 22,907-22, 928.

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modeling system with integrated meteorology, chemistry, and emissions. Proceedings of the

International Symposium on Measurement of Toxic and Related Air Pollutants, Research

Triangle Park, North Carolina, 1-3 September, 1998. 144-152.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

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Appendix 5A.Tensor Primer and Derivation of the Continuity Equation in a Generalized

Curvilinear Coordinate System

The Appendix 5A summarizes essential information needed for understanding the governing

equations represented in tensor form. It includes tensor primer and derivation of the continuity

equation in a generalized coordinate system. Readers are referred to classic references such as

Dutton (1976), Defrise (1964), and Pielke (1984) for the details.

5A.1 Tensor Analysis in a Curvilinear Coordinate System

Cartesian coordinates are those curvilinear systems in which the positions of fluid elements are

determined by their distance from intersecting planes. Although the Cartesian coordinates with

orthogonal intersecting planes are specifically called rectangular, the adjective rectangular is

often dropped. To represent formulations governing atmospheric phenomena in a coordinate

system other than a rectangular Cartesian one, a tensor representation is often used. This

generally involves determination of the unit vectors in the new system, determination of the

components of a tensor with respect to theses unit vectors, and determination of the differential

derivatives (e.g., divergence, curl, and gradient) of a tensor. All these quantities depend

explicitly on the form of the new coordinate system and it is always convenient to express these

quantities in a rectangular Cartesian coordinate system for comparison purposes.

In atmospheric modeling one is frequently led to adopt a curvilinear coordinate system other than

the Cartesian coordinates depending on the problem under consideration. A general curvilinear

coordinate system can be defined relative to a Cartesian system x = (x1

,x2

, x3) represented by

three families of curved surfaces

x xxxt ˆ ( , , ,) i =ψ i

123 , i = 1,2,3 (5A-1)

Here, the symbols with carat (^) are used to denote a transformed curvilinear system. In vector

form, it is given as:

x x ˆ = ψ(,)t . (5A-2)

When the curvilinear system ψ is at rest relative to the rectangular Cartesian system, i.e.,

independent of time, x xxx ˆ (, , ) i =ψ i

123 , then the system is called a Euclidean system. Here we

assume that components of vector xˆ , (xxx ˆ , ˆ , ˆ ) 123 , are three independent, single-valued, and

differentiable scalar point functions such that to every point of some region Rˆ of threedimensional Euclidean space, there is a corresponding unique triple of values (x1

, x2, x3) in the

Cartesian space R. In other words, the function ψ prescribes one and only one value of x and is

such that the three coordinates are independent of each other. Also, we assume continuity of the

function ψ. Then the new coordinates xˆ are called curvilinear and the surfaces xˆ

1

 = ψ1 =

constant, xˆ 2

= ψ 2 = constant, xˆ 3= ψ 3 = constant are called coordinate surfaces. The curvilinear

coordinates (xxx ˆ , ˆ , ˆ ) 123 should be independent, single-valued, and differentiable. As shown in
EPA/600/R-99/030

5-31

Figure 5A-1, the vector OP pointing a parcel of air enclosed by the boundary ∂Ω can be

represented either in Cartesian or Euclidean curvilinear coordinate systems.

xˆ

1

xˆ 2

xˆ 3

k

i j

P

∂Ω

τˆ

1

τˆ

2

τˆ

3

x

1 = x

x

2 = y

x

3 = z

ˆ

R

R

O

Figure 5A-1. Coordinates of the Cartesian and Curvilinear Coordinates. R and Rˆ represent

Cartesian and Euclidean spaces, respectively.

Note that the transformation involves with not only the spatial variables but also time as an

independent variable. We need a tensor calculus in the four variables of space-time with regard

to the coordinate transformations. Defrise (1964) used the term ‘world tensor’ to distinguish it

from the time independent Euclidean tensor.

5A.2 Basis Vectors

In a rectangular coordinate system, directions of the basis vectors are constant in space.

However, in a general curvilinear coordinates, directions of the basis vectors will vary from point

to point and no one set of directions can be regarded as more natural than any other for the

directions of base vectors to define the local base vectors. Usually, an upper index denotes

contravariant, and a lower index denotes covariant tensors, respectively.

With the coordinates defined by Equation 5A-2, the chain rule provides the two expansions:

d

x

dx j

j x

x = ∂

∂ˆ ˆ (5A-3)
EPA/600/R-99/030

5-32

dx x

x

dx x d i

i

j

j i ˆ ˆ = =∇ • ( ˆ ) ∂

∂

x (5A-4)

Here, the Einstein summation convention (i.e., the repeated indices on two quantities that are

multiplied by each other are summed over) has been implied. The symbol (•) represents the

inner product. An inner product of two vectors yields a scalar that is invariant of the coordinate

system. An inner product of two tensors results in contraction of the rank in the resulting tensor.

From Equations 5A-3 and 5A-4, we can form two distinct sets of basis vectors. One is the

tangential vectors:

ˆ ˆ τi j x = ∂

∂

x (5A-5)

that reveals the variation of the position vector as it traces out a curve in which xˆj

 varies and the

other two coordinates are constant. Hence τˆ

i is tangent to the curve along which only xˆj

 varies.

The other set of basis vectors is the normal vectors of the surfaces where xˆi

 = constant:

ηˆ ˆ i = ∇x

i (5A-6)

While there could be many choices, the tangential ( τˆ

i) and normal (ηˆi

) vectors are considered as

a natural choice for the local basis vectors for the curvilinear coordinate system. Using

Equations 5A-5 and 5A-6, one can show that:

τηδ ˆ ˆ i

j

i

j i j

i j

⊗== =

≠







1

0 (5A-7)

where δi

j

 is the Kronecker delta and the symbol ⊗ represents the outer product. Outer product

of two tensors with rank r1 and r2 yields a tensor with rank (r1+r2 ).

A curvilinear system is not orthogonal when not all the off-diagonal components of η η ˆ ˆ i j ⊗ and

τ τ ˆ ˆ i j ⊗ vanish. The orthogonal curvilinear coordinate system is often used for interesting

engineering problems that can be described with simple geometric orthogonal coordinates, such

as spherical, cylindrical coordinate systems. Usually, meteorological coordinates are not

orthogonal and therefore, the vector calculus specific for the orthogonal curvilinear coordinates

must not be used.

5A.3 Distance and Metric Tensor in a Curvilinear Coordinate System

The differential element of distance ds can be expressed in terms of the curvilinear coordinates

as:

( ) ˆ ˆ ˆ ˆ ˆ ˆ ds dx dx ˆ ˆ ˆ ˆ ˆ x

x

dx x

x

dx x

x

x

x

dx dx dx dx i

i

i

j

j

i

k

k

i

j

i

k

j k

jk

2 j k == = = ∂

∂

∂

∂

∂

∂

∂

∂ γ (5A-8)
EPA/600/R-99/030

5-33

ˆ ˆ ˆ γ ˆ ˆ ∂

∂

∂

∂ jk

i

j

i

k j k

x

x

x

x

= =⊗ τ τ (5A-9)

Because of its obvious role in the measurement of distance, the quantity γˆik is called the metric

tensor. It is a symmetric tensor. As such, it has an inverse matrix γˆik , which will satisfy

following condition:

ˆ ˆ ˆ γ ˆ ˆ ∂

∂

∂

∂

ik

i

l

k

l

x

x

x

x

= =⊗ η η i k (5A-10)

γγ δ ˆ ˆ ij

ik

j

k j k

j k = = =≠







1

0 (5A-11)

The Levi-Cevita symbol ε used in Equation 5-1 is an antisymmetric tensor defined as

ε

ijk

if i j j k or i k

if i j k are an even permutation of

if i j k are an odd permutation of

=

−











0 == =

1

1

123

123

 

 , , 

 ,, ,,

 ,, ,,

(5A-12)

Using the Levi-Cevita symbol, the cross vector product A BC = × can be written as

A BC i ijk = j k ε .

One of the uses of the metric tensor and its inverse is for converting a covariant tensor to a

contravariant tensor, and vice versa. Another important usage of the metric tensor is the

estimation of the Jacobian determinant of the transformation, which is defined as:

J = γ γ ˆ = det( ˆ )ij [det( = ˆ )]− γ ij 1 (5A-13)

where J J xxx

xxx x

x = = { } (, , )

( ˆ , ˆ , ˆ )

ˆ ∂

∂

123

123

. Note that the Jacobian matrix and the metric tensor are related

as:

ˆ { }{ } ˆ ˆ γ ij x

x T

x

x = J J (5A-14)

A necessary and sufficient condition that (xxx ˆ , ˆ , ˆ ) 123 be orthogonal at every point in R is that the

components of the metric tensor vanish for i ≠ j.

5A.4 Covariant Tensor and Contravariant Tensor

In this section, the covariant and contravariant tensor concepts are presented using a vector,

which is a simple form of a tensor (i.e., a tensor of rank one). A distance in a Euclidean space

can be represented in two corresponding sets of tangential basis vectors:
EPA/600/R-99/030

5-34

ds dx dx j

j

l = = l ˆ τ τ ˆ (5A-15)

where

ˆ ˆ τ

∂

∂ τ j

l

j l

x

x = (5A-16)

Any vector that transforms similarly to the tangential basis vector τˆj is called as a covariant

vector. On the other hand, when a vector transforms like the local normal basis vectors ηˆi, we

call it a contravariant vector:

ˆ ˆ v

x

x

v

k

k

j

j = ∂

∂ , (5A-17)

where vj

 is the components of V with respect to the normal base vectors.

Since a vector A is invariant between coordinate systems, we can express it using either

contravariant components (i.e., with the tangential basis vectors) or covariant components (i.e.,

with the normal basis vectors):

A = = A A j

j l

l η τ ˆ ˆ (5A-18)

Using Equation 5A-7, one can readily find the covariant and contravariant components with:

Aj j = • A τˆ (5A-19a)

Ai i = • A ηˆ (5A-19b)

5A.5 Derivatives, Total Derivative, and Divergence in Euclidean Coordinate

Covariant derivative of a contravariant vector is defined as:

ˆ ˆ

ˆ ˆ ˆ V;

V

x

k V i

i

k kj

i j = +

∂

∂

Γ , ˆ ˆ

ˆ ˆ Γkj

i

i

l

l

k j

x

x

x

x x = ∂∂

∂

∂ ∂

2

. (5A-20)

Similarly, covariant derivative of a covariant vector is defined as:

 ̃  ̃

 ̃  ̃  ̃ A;

A

x

i k A

i

k ki

l l = − ∂

∂

Γ ,  ̃  ̃

 ̃  ̃ Γki

l

l

r

r

k i

x

x

x

x x = ∂∂

∂

∂ ∂

2

. (5A-21)

The Christoffel symbol Γ ˆ 

kj

i is not a tensor but it is an important quantity relating the derivatives

in the curvilinear coordinate system with those in the original Cartesian coordinate system. Its

relation with the metric tensor is:
EPA/600/R-99/030

5-35

ˆ ˆ ( ˆˆˆ Γ ) kj

i jl il

k

kl

i

ik

l

xxx

= +−

1

2

γ ∂γ

∂

∂γ

∂

∂γ

∂ (5A-22)

Divergence of a contravariant vectorW ˆ , wind for example, can be expressed as:

ˆ ˆ

ˆ ˆ ˆ ˆˆ

ˆ

ˆ

ˆ

ˆ W;

W

x

W W

x

W

x

i

i

i

i ij

i j

i

i

j

j =+ =+

∂

∂

∂

∂ γ

∂ γ

∂

Γ

 = +=

1 1

ˆ

{ ˆ ˆ

ˆ ˆ ˆˆ } ˆ

( ˆ ˆ )

γ ˆ γ

∂

∂

∂ γ

∂ γ

∂ γ

∂

W

x

W

x

W

x

i

i

j

j

i

i (5A-23)

The total derivative of a covariant vector A is represented in a Cartesian coordinate as

d

dt t

A A = + •∇ v A ∂

∂

= +

∂

∂

∂

∂

A

t

v

A

x

i j i

j ˆ ˆ (5A-24)

where v •∇= = = v

x

v

x

x x

v

x

l

l

j

l

j l

j

j

∂

∂

∂

∂

∂

∂

∂

∂ ˆ ˆ ˆ ˆ was used. This expression is correct in any holonomic

coordinate system where the covariant component Ai, metric tensor, velocity, and xk

 all refer to

the same system whether or not the coordinate system is time dependent.

5A.6 Continuity Equation in Generalized Curvilinear Coordinate System

Many practical coordinate systems used for atmospheric studies are time dependent. Consider

the case when a volume element that confines the fluid moves with the fluid. Then, this is also

the velocity of the fluid in the respective coordinate system. A direct conversion from the

continuity equation expressed in a Cartesian coordinate system does not work because the

divergence term should take into account for the time rate change of volume element as well the

same for the time dependent curvilinear coordinates. In this situation, the Lie derivative concept

(e.g., Bishop and Goldberg, 1968) becomes appropriate. A Lie derivative is obtained by

differentiating a function with respect to the parameters along the moving frame of reference.

Following Defrise (1964), one can show that a Lie derivative of a mass volume integral along the

moving frame vanishes:

 

L( ) δM = 0 (5A-25)

where δ ρδ ρ γ δ MV V = = ˆ ˆ, δ δδδ V xxx = 123 , andδ δδδ ˆ

V xxx = ˆˆˆ

123 . Therefore:

 

δ ργ δ ∂ρ γ

∂ ρ γ

∂

∂

μ

μ

μ

μ

ˆ ( ˆ ) ˆ(ˆ ˆ

ˆ ˆ ˆˆ V Vv )

x

v

x

L = +

= = δ ∂ρ γ

∂

μ

μ

ˆ ( ˆ ˆ )

ˆ V v

x

0 (5A-26)
EPA/600/R-99/030

5-36

where, index μ = 1,4; x t ˆ 4 = and vˆ4 = 1. Using the same notation convention, the contravariant

velocity is defined as for the coordinates that moves with fluid:

ˆ ˆ v

x

x

v μ

μ

α

∂ α

∂ = ; α, μ = 1,4 (5A-27)

Note that one cannot derive the same result by directly replacing the divergence term in the

continuity equation for a Cartesian coordinate system because the volume element is dependent

on time as well.

Alternatively, one can obtain Equation 5A-26 by a method based on the finite derivative of a

volume integral with the application of the Leibnitz rule. This method of derivation helps to

visualize the meaning of terms in the equation more clearly than the procedure based on the Lie

derivative. Volume integral in a Cartesian coordinates is defined as:

F fx x x V = ∫∫∫ (, , )

∂

δ

Ω

123 (5A-28)

where f is a conservative quantity, such as density or total kinetic energy. Equation 5A-28 can

be rewritten in the curvilinear coordinate as:

F fx x x V = ∫∫∫ (ˆ , ˆ , ˆ ) ˆ ˆ

∂

γ δ

Ω

123 (5A-29)

For example, if f =1:

F VV V V = == = ∫∫∫ ∫∫∫

∂

∂

∂

∂ δ γδ γ

Ω

Ω

Ω

Ω ˆ ˆ ˆ ˆ (5A-30)

The meaning of the metric becomes very clear–it is a measure of volume correction for the

transformed coordinates.

F f x x x V hx x x x x x = = ∫∫∫ ∫∫∫ ( ˆ , ˆ , ˆ ) ˆ ˆ ( ˆ , ˆ , ˆ ) ˆˆˆ 123 123 123

∂ ∂

γδ δ δ δ

Ω Ω

(5A-31)

where hx x x f x x x ( ˆ , ˆ , ˆ ) ( ˆ , ˆ , ˆ ) ˆ 123 123 = γ was used.

Consider a time derivative following the control volume. Applying a three-dimensional version

of Leibnitz rule for the time differential of the integral, we get:

δ

δ

δ

δ

δδδ

∂

F

t t

hx x x x x x

following

volume

= ∫∫∫ ( ˆ , ˆ , ˆ ) ˆˆˆ 123 123

Ω

 = ∫∫∫( ) ˆˆˆ ˆ , ˆ , ˆ

∂

∂ δδδ

∂

h

t

xxx xxx 123

123

Ω
EPA/600/R-99/030

5-37

 + −





 

 ∫ ∫  ˆ

ˆ

ˆ

ˆ

( ˆ , ˆ , ˆ ) ˆ ( ˆ , ˆ , ˆ ) ˆ ˆ ˆ

x

x

b

b

a

a

x

x

a

b

a

b

hx x x dx

dt

hx x x dx

dt

x x 2

2

3

3

123

1

123

1

3 2 δ δ

 + −





 

 ∫ ∫  ˆ

ˆ

ˆ

ˆ

( ˆ , ˆ , ˆ ) ˆ ( ˆ , ˆ , ˆ ) ˆ ˆ ˆ

x

x

b

b

a

a

x

x

a

b

a

b

hx x x dx

dt

hx x x dx

dt

x x 1

1

2

2

123

3

123

3

2 1 δ δ

 + −





 

 ∫ ∫  ˆ

ˆ

ˆ

ˆ

( ˆ , ˆ , ˆ ) ˆ ( ˆ , ˆ , ˆ ) ˆ ˆ ˆ

x

x

b

b

a

a

x

x

a

b

a

b

hx x x dx

dt

hx x x dx

dt

x x 3

3

1

1

123

2

123

2

1 3 δ δ (5A-32)

Then, using the following relation with the aid of Figure 5A-2:

∂

∂ δ ˆ

ˆ ˆ ( ˆ ) ˆ ( ˆ ) ˆ

ˆ

ˆ

x

h dx

dt

x hx dx

dt

h x dx

dt x

x

bd

b

b

a

a

a

b

2

2

2 2

2

2

2

2

2

∫ 









 = − (5A-33)

we obtain an integral equation:

δ

δ

∂

∂

∂

∂

∂

∂

∂

∂ δδδ Ft

h

t x

h

dx

dt x

h

dx

dt x

h

dx

dt

xxx

following

volume bd bd bd

= + 









 + 









 + 



























 ∂  ∫∫∫ ˆ

ˆ

ˆ

ˆ

ˆ

ˆ ˆˆˆ 1

1

2

2

3

3

123

Ω

 (5A-34)

xˆ

1

xˆ 2

xˆ 3

dxˆb

2

dt

δt

xˆb

2 xˆa

2

xˆb

3

xˆa

3

xˆa

1

xˆb

1 ηˆ 2

ηˆ 3

Figure 5A-2. Volume Element in a Curvilinear Coordinate System

When f = ρ (density) , then F xxx xxx M = = ∫∫∫ ρ δδδ

∂

(, , ) 123 123

Ω

 = mass of the volume element.

Therefore, the conservation law states:
EPA/600/R-99/030

5-38

δ

δ

δ

δ

F

t

M

t following

volume

following

volume

= = 0 (5A-35)

Here, for example, dx

dt bd

ˆ 2

is the velocity of the boundary of the volume element in the curvilinear

coordinate xˆ 2. Because the volume element confines the fluid and moves with the fluid, this is

velocity component of the fluid in the curvilinear coordinate xˆ 2. Then, we have

∂ρ γ

∂

∂ρ γ

∂ δ

∂

( ˆ ) ( ˆ ˆ )

ˆ ˆ

t

v

x

V

j

j +















 = ∫∫∫

Ω

0 (5A-36)

Since above integral should be satisfied for an arbitrarily infinitesimal volume element, we

obtain the continuity equation in differential equation form for the time-dependent curvilinear

coordinate as follows:

∂ρ γ

∂

∂ρ γ

∂

( ˆ ) ( ˆ ˆ )

t ˆ

v

x

j

j + = 0 (5A-37)
EPA/600/R-99/030

Chapter 6

GOVERNING EQUATIONS AND COMPUTATIONAL STRUCTURE OF THE

COMMUNITY MULTISCALE AIR QUALITY (CMAQ) CHEMICAL TRANSPORT

MODEL

Daewon W. Byun* and Jeffrey Young**

Atmospheric Modeling Division,

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

M. Talat Odman***

MCNC-Environmental Programs

P.O. Box 12889, 3021 Cornwallis Road

Research Triangle Park, NC 27709-2889, USA

ABSTRACT

The chemical transport model (CTM) of the Models-3/CMAQ (Community Multiscale Air

Quality) modeling system can be configured to follow the dynamics of the preprocessor

meteorological model. A science process module in the CMAQ CTM is not specific to a

coordinate system. The generality is accomplished through the use of the coordinate

transformation Jacobian within the CMAQ CTM. In this chapter, we derive the governing

diffusion equation in a generalized coordinate system, which is suitable for multiscale

atmospheric applications. We describe the CMAQ system’s modularity concepts, fractional

time-step formulation, and key science processes implemented in the current version of the

CMAQ CTM. We examine dynamic formulations of several popular Eulerian air quality models

as emulated by the governing diffusion equations in the generalized coordinate system. Also, a

nesting technique for the CMAQ CTM is introduced. Finally, because the amount of a

substance in the atmosphere can be expressed in many different ways, we summarize the most

popular expressions for concentration and their transformation relations.

 

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Daewon W. Byun, MD-80, Research Triangle Park, NC 27711.

E-mail: bdx@hpcc.epa.gov

** On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

*** Present Affiliation: Georgia Institute of Technology, Atlanta, GA.
EPA/600/R-99/030

6-1

6.0 GOVERNING EQUATIONS AND COMPUTATIONAL STRUCTURE OF THE

COMMUNITY MULTISCALE AIR QUALITY (CMAQ) CHEMICAL TRANSPORT

MODEL

In Chapter 5, “Fundamentals of Atmospheric Modeling ...” we discussed the fundamental set of

equations for atmospheric dynamics and thermodynamics in a generalized coordinate system. In

this Chapter, we investigate the diffusion equation for the trace species in the atmosphere in the

generalized coordinate system and the computational structure of the Community Multiscale Air

Quality chemical transport model (CMAQ CTM or, hereafter, CCTM).

One requirement of the CMAQ modeling system is to maintain a consistent description of the

atmosphere for different meteorological and chemical transport models. This is a feature that is

essential for spatial scalability. Various coordinate systems are used in atmospheric models.

Selection of a suitable coordinate system is an important step of model formulation. There are

numerous criteria to be considered in selecting a coordinate system, such as the dynamic

characteristics it can handle and how well it can deal with curvature of the earth’s surface and

features of the terrain. Formulation of the models may vary substantially for different coordinate

systems. If a CTM can be formulated and coded using a generalized coordinate system, it would

be easy to switch from one coordinate to another depending on the application. The generalized

coordinate concept is useful because a single CTM formulation can adapt to any of the

coordinates commonly used in meteorological models. It is also desirable to compare the benefits

of various coordinate systems and to be able to link the CTMs to meteorological models and

databases in different coordinates.

Conformity of the coordinates to the physics of the problem is very important. Unlike a model

with a fixed coordinate system, a generalized coordinate system allows use of generic coordinates

for the specific science processes within a model. Although the model’s overall structure is

determined by the choice of a coordinate system, the individual science modules can still use their

own generic coordinates that best suit the physical processes they model. This means that each

science process can utilize the parameterizations based on the best coordinate to represent the

problem. For example, the planetary boundary layer (PBL) parameterizations can be expressed

in terms of geometric height, or dimensionless height scaled with PBL height, while for cloud

physics, they can be represented in terms of pressure. The linkages between the generic

coordinate parameterizations in the science processes and the governing conservation equation in

the generalized coordinates are established through the application of appropriate coordinate

transformation rules.

Here, we intend to provide a comprehensive and rational development of the governing

conservation equation in generalized coordinates, which can be readily implemented in an Eulerian

model. The operating assumptions used for the derivations are listed below (see Srivastava et al.,

1995).

• Assumption 1: Pollutant concentrations are sufficiently small, such that their presence

would not affect the meteorology to any detectable extent. Hence, the species
EPA/600/R-99/030

6-2

conservation equations can be solved independently of the Navier-Stokes and energy

equations. The conditions which could invalidate this assumption are for cases where

sufficient heat is generated by chemical reactions to influence the temperature of the

medium or where an atmospheric layer become so concentrated with pollutants that

absorption, reflection, and scattering of radiation alter the air flow (Seinfeld, 1986).

• Assumption 2: The velocities and concentrations of the various species in atmospheric

flow are turbulent quantities and undergo turbulent diffusion. Because turbulent diffusion

is much greater than molecular diffusion for most trace species, the latter can be ignored.

• Assumption 3: The metric tensor that defines the coordinate transformation rules is not a

turbulent variable. This means that we can define the coordinates based on the Reynolds

averaged quantities. The vertical grids will be defined incrementally between time steps

when a time-dependent vertical coordinate is used.

• Assumption 4: The ergodic hypothesis holds for the ensemble averaging process. This

means that the ensemble average of a property can be substituted with the time average of

that property.

• Assumption 5: The turbulence is assumed stationary for the averaging time period of

interest (say 30 minutes to one hour for atmospheic applications).

• Assumption 6: The source function (i.e., emissions of pollutants) is deterministic for all

practical purposes and there is no turbulent component.

• Assumption 7: The effect of concentration fluctuation on the rate of chemical reaction is

negligible, i.e., contributions of covariance effects among tracer species are neglected.

• Assumption 8: Because the large-scale motions of the atmosphere are quasi-horizontal

with respect to the earth's surface, science processes can be separately represented in

horizontal and vertical directions (i.e., quasi-orthogonal in transformed coordinates).

6.1 Derivation of the Atmospheric Diffusion Equation

In Chapter 5, we derived the species continuity equation in generalized coordinates. It is given

as:

∂ φ

∂

φ ∂φ

∂ φ

( ) ˆ (  ̇) i s

s

is s is

s

J

t

m

J

m

J s

s

J Q i + ∇• 









 + = 2

2

V (6-1)

where φi is the trace species concentration in density units (e.g., kg m-3), Js is the vertical

Jacobian of the terrain-influenced coordinate s, m is the map scale factor, V ˆ 

s and s& are horizontal

and vertical wind components in the generalized coordinates, and i

Qφ is the source or sink term.
EPA/600/R-99/030

6-3

To make the instantaneous species continuity equation useful for air quality simulation, we need

to derive the governing diffusion equation. This is done by decomposing the variables in

Equation 6-1, except for the Jacobian and map scale factor, in terms of mean and turbulent

components. The Reynolds decompositions of species concentration and mixing ratio are

expressed as:

φφφ i ii = + " (6-2a)

qqq i ii = + " (6-2b)

φφ ρ ρ ρ ρ ii i i i i += + + + " " " "" qq qq (6-2c)

where qi

i = φ

ρ

 is the species mass mixing ratio and a stochastic quantity is decomposed into

mean ,( ), and turbulent, ("), components. Stationary turbulence assumption 5 implies that a

turbulent component has a zero mean for the averaging period. Following Venkatram (1993), we

can estimate the mean and turbulent components of species and air concentrations as

φ ρ i i ≈ q (6-3a)

φ ρρ ρ ii i i " " " "" = ++ q qq (6-3b)

q

q

i

i

"" "

( )

ρ

ρ

ρ

ρ

≈ <<

2

2 1 (6-3c)

Without loss of generality, we redefine the terrain-influenced vertical coordinate s with a

coordinate x ˆ 3

, whose value is increasing monotonically with height, as:

ˆ ( )

( )

x

s if s increases with height

s if s decreases with height

3

1 = = −





 ξ (6-4)

The choice of a generalized vertical coordinate which increases monotonically with height

simplifies the derivation of the governing equation and thus reduces the likelihood of making sign

errors in the formulas and in computer codes. The transformation does not change the horizontal

wind components or the Jacobian, which is always defined to be a positive quantity. Hereafter,

the subscript s is replaced with ξ to reflect modification of the vertical coordinate. Subsequently,

the vertical velocity is represented with ˆ /  ̇ v d dt 3 = = ξ ξ , which is positive for upward motion.

Application of decomposition of velocity components in Equation 6-1 and ensemble averaging

produces Reynolds flux terms in the mass conservation equation as:
EPA/600/R-99/030

6-4

∂ φ

∂

ξ φ φ

ξ

ξ ξξ ( ) ( ")( ˆ ˆ ") i ii J

t

m

J

m

+ ∇•

+ + 















2

2

V V

+ ++ 

  = ∂

∂ φ φ ξ ξ φ ˆ ( ")(ˆ ˆ ")x

i i v v J JQ 3 i

3 3 (6-5)

where we used J J ξ ξ = and Q Q φ φ i i = based on Assumption 3 and Assumption 6, respectively.

The Reynolds flux terms in Equation 6-5 can be approximated in terms of the mixing ratio as:

φ ρ ρρ i ii i ξ ξξ ξ " qq q ˆ " " ˆ " " ˆ " " ˆ VVVV ≈+≈ " (6-6a)

φ ρ ρρ i ii i "v qv q v qv ˆ " " ˆ " " ˆ " " ˆ " 3 33 3 ≈+≈ (6-6b)

qi ρ ξ " ˆV " << 1 (6-6c)

q v i ρ" ˆ "

3 << 1 (6-6d)

in which we have neglected the second order perturbation terms based on the scale analysis of the

equations. Equation 6-5 can be rewritten using Equations 6-3a-c and 6-6a-c to give:

∂ φ

∂

φ ∂φ

∂

ξ

ξ

ξξ ξ ( ) ˆ ( ˆ )

ˆ

i ii J

t

m

J

m

v J

x

+ ∇•















 + 2

2

3

3

V

+ ∇•















 m + =

q J

m

qvJ

x

J Q i i

i

2

2

3

ξ 3

ξξ ξ ρ ξ φ

∂ ρ

∂

" ˆ " (" ˆ " )

ˆ

V

(6-7)

The turbulence flux terms can be parameterized using a simple closure scheme such as the eddy

diffusion concept (K-theory):

qu K q

x

i

l i

l " ˆ " ˆ ˆ ξ

∂

∂ = − 1 ; qv K q

x

i

l i

l " ˆ " ˆ ˆ ξ

∂

∂ = − 2 ; qv K q

x

i

l i

l " ˆ " ˆ ˆ

3 3 = − ∂

∂ (6-8)

where Kˆ jl denotes the eddy diffusivity tensor in the transformed coordinate. The eddy

diffusivity tensor for the generalized meteorological coordinates is related to the diffusivity

tensor in Cartesian coordinates as:

ˆ ˆ ˆ K x

x

x

x

K kl

k

i

l

j

ij = ∂

∂

∂

∂ (6-9)
EPA/600/R-99/030

6-5

If we postulate that the diffusivity tensor in Cartesian coordinates is diagonal (i.e., all the offdiagonal components vanish), then the eddy diffusivity tensor in the generalized meteorological

coordinates becomes:

ˆ

ˆ

ˆ

ˆ ˆ ( ˆ ) ( ˆ ) ( ˆ )

K =

+ +

































mK m x

x

K

mK m x

y

K

m

x

x

K m x

y

K x

x

K x

y

K x

z

K

xx xx

yy yy

xx yy xx yy zz

2

3

2

3

3 33

2

3

2

3

2

0

0

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

(6-10)

where K K xx = 11 , K K yy = 22 , and K K zz = 33 are the diagonal components of eddy

diffusivity tensor in the Cartesian coordinate. To match with the computational grid, the gradient

terms in Equation 6-10 must be rewritten in terms of the generalized coordinates xˆ 3 (defined

based on height above ground h hz AGL = − sfc , where zsfc represents the height of topography)

using the appropriate chain rules, for example, 1

1 31 m 3 3

A

x

A

x

A

z

A

x

h

x zx x

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂





 



 = 



 



 − 



 









 



 ˆ ˆˆ ˆ ˆ

. When A

= xˆ 3

, we get

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ ( ˆ ) ˆ ˆ

K =

−

−

− − 



 



 + 





mK m x

z

h

x

K

mK m x

z

h

x

K

m

x

z

h

x

K m x

z

h

x

K x

z

m

h

x

K m h

x

xx xx

yy yy

xx yy xx

2 2

3

1

2 2

3

2

2

3

1

2

3

2

3

2

1

2

2

0

0

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂





 +





 









































2

K K yy zz

(6-11).

 Then the non-zero diffusion terms in Equation 6-7 can be parameterized with the eddy diffusion

theory as follows:

m

q J

m

m

x

J

m

K q

x

K q

x

i 2 i i

2

2

1 2

11

1

13 ∇ • 3















 =− +





 

 ξ  ξξ ξ ρ

∂

∂

ρ ∂

∂

∂

∂

" ˆ "

ˆ ( ˆ ˆ ˆ ˆ )

V

+− +





 



m  x

J

m

K q

x

K q

x

2 i i

2 2

22

2

23

3

∂

∂

ρ ∂

∂

∂

∂

ξ

ˆ ( ˆ ˆ ˆ ˆ ) (6-12)

and

∂ ρ

∂

∂

∂ ρ

∂

∂

∂

∂

∂

∂

ξ

ξ

( " ˆ " )

ˆ ˆ ( ˆ ˆ ˆ ˆ ˆ ˆ ) qvJ

x x

J K q

x

K q

x

K q

x

i iii

3

3 3

31

1

32

2

33

3 =− + + 



 



 (6-13)
EPA/600/R-99/030

6-6

Rewriting Equation 6-7 with Equations 6-12 and 6-13, and separating the diagonal and offdiagonal diffusion terms with an explicit description of the source terms, one can obtain the

governing atmospheric diffusion equation in the generalized coordinates where the turbulent flux

terms are expressed with the eddy diffusion theory:

∂ φ

∂

φ ∂φ

∂

ξ

ξ

ξξ ξ ( ) ˆ ( ˆ )

ˆ

i ii J

t

m

J

m

v J

x

+ ∇•















 + 2

2

3

3

V

 (a) (b) (c)

− 



 



 − 



 



m  x

J

m

K q

x

m

x

J

m

K q

x

2 i i

1 2

11

1

2

2 2

22

2

∂

∂

ρ ∂

∂

∂

∂

ρ ∂

∂

ξ ξ

ˆ ( ˆ ˆ ) ˆ ( ˆ ˆ ) − 



 





∂

∂ ρ

∂

∂ ξ ˆ ( ˆ ˆ )

x

J K q

x

i

3

33

3

 (d) (e)

− 



 



 − 



 



m  x

J

m

K q

x

m

x

J

m

K q

x

2 i i

1 2

13

3

2

2 2

23

3

∂

∂

ρ ∂

∂

∂

∂

ρ ∂

∂

ξ ξ

ˆ ( ˆ ˆ ) ˆ ( ˆ ˆ )

 (f)

− + 



 





∂

∂ ρ

∂

∂

∂

∂ ξ ˆ ( ˆ ˆ ˆ ˆ )

x

J K q

x

K q

x

i i

3

31

1

32

2

 (g)

= ++ + + JR JQ

J

t

J

t

J

t i i N

i

cld

i

aero

i

ping

ξ φ ξ φ

ξξ ξ φ φ

∂ φ

∂

∂ φ

∂

∂ φ

∂ ( ,..., ) () () ()

1 (6-14)

(h) (i) (j) (k) (l)

The terms in Equation 6-14 are summarized as follows:

(a) time rate of change of pollutant concentration;

(b) horizontal advection;

(c) vertical advection;

(d) horizontal eddy diffusion (diagonal term);

(e) vertical eddy diffusion (diagonal term);

(f) off-diagonal horizontal diffusion;

(g) off-diagonal vertical diffusion;

(h) production or loss from chemical reactions;

(i) emissions;

(j) cloud mixing and aqueous-phase chemical production or loss;

(k) aerosol process; and
EPA/600/R-99/030

6-7

(l) plume-in-grid process.

Note that the dry deposition process can be included in the vertical diffusion process as a flux

boundary condition at the bottom of the model layer.

Alternatively, we can express the turbulent flux terms in Equation 6-7 using the Reynolds flux

terms defined as:

qu F i qi " ˆ " ˆ ξ = 1 , qv F i qi " ˆ " ˆ ξ = 2 , qv F i qi " ˆ " ˆ 3 3 = (6-15)

and the turbulent flux terms are related with the Cartesian counterpart using ˆ ˆ F x

x q F k

k

j q

j

i i = ∂

∂

:

F mF ˆ

q q

x

i i

1 = , F mF ˆ

q q

y

i i

2 = , ˆ ( ˆ ) ( ˆ ) ( ˆ F ) x

x

F x

y

F x

z q q F x

q

y

q

z

i iii

3

333

=++

∂

∂

∂

∂

∂

∂ (6-16)

In comparison with Equation 6-14, the Reynolds flux terms shown in Equation 6-15 include the

off-diagonal components. One can now rewrite the governing conservation equation for trace

species equivalently to Equation 6-14 in terms of the Reynolds flux terms:

∂ φ

∂

φ ∂φ

∂

ξ

ξ

ξξ ξ ( ) ˆ ( ˆ )

ˆ

i ii J

t

m

J

m

v J

x

+ ∇•















 + 2

2

3

3

V

+





 



 +





 



 m + [ ] x

J

m

F m

x

J

m

F

x q qq J F i ii

2

1 2

1 2

2 2

2

3

∂ 3

∂

ρ ∂

∂

ρ ∂

∂ ρ ξ ξ

ξ ˆ ˆ ˆ ˆ ˆ ˆ

= ++ + + JR JQ

J

t

J

t

J

t i i N

i

cld

i

aero

i

ping

ξ φ ξ φ

ξξ ξ φ φ

∂ φ

∂

∂ φ

∂

∂ φ

∂ ( ,..., ) () () ()

1 (6-17)

The governing equation can be simplified for a domain with gentle topography for which one may

ignore all the terms involved with the horizontal gradients of the surface normal to the vertical

coordinate. This forces the vertical diffusion terms in the curvilinear coordinate system to be

identical to those of the orthogonal Cartesian coordinate system. Then the trace species

conservation equation can be written in a simpler form:

∂φ

∂ φ ∂ φ∂ ρ γ

∂ρ γ

∂ ξξ ξ

i

i

i

q

q

t

v

x

F

x i

i

*

*

*

ˆ ˆ ( ˆ )

ˆ

ˆ ˆ ˆ ( ˆ ˆ )

ˆ +∇ •[ ] + +∇ • V F [ ] +

3

3

3

3

= ++ + + ˆ ( ,..., ) ˆ () () () ** *γ φφ γ ∂ φ

∂

∂ φ

∂

∂ φ

∂ R S φ φ tt t i i N

i

cld

i

ping

i

aero

1 (6-18)
EPA/600/R-99/030

6-8

whereφ γφ φ ii i ξ J m * = = ˆ (/ ) 2 . In writing Equation 6-18, we have explicitly identified terms to

directly relate to science process modules implemented in the CMAQ. Equation 6-18 is similar

to the conservation equation in the generalized coordinates as suggested by Toon et al. (1988).

6.2 Representation of Science Processes in CMAQ Modeling System

This section describes how the CMAQ modeling system is structured to accommodate many

different science process modules that provide a one-atmosphere, multiscale and multi-pollutant

modeling capability to the CMAQ system. First, we describe the modularity concepts and key

science processes implemented in the current version of CMAQ. Then the governing fractional

time-step formulation for each science process is presented.

6.2.1 Supporting Models and Interface Processors

Key supporting models for the current version of the CMAQ modeling system are the

Mesoscale Model Version 5 (MM5) (Seaman et al., 1995)and Models-3 Emissions Processing

and Projection System (MEPPS). The CMAQ modeling system is comprised of the main

CMAQ chemical transport model (CCTM) and several interface processors that link other model

input data to the CCTM. The Meteorology-Chemistry Interface Processor (MCIP) processes

MM5 output to provide a complete set of meteorological data required for CCTM. MCIP is

designed in such a way that other meteorological models can be linked with minimal effort. Initial

and boundary conditions are generated with the ICON and BCON processors, respectively, and

the Emissions-Chemistry Interface Processor (ECIP) combines area and point source emissions

to generate three-dimensional gridded emissions data for CCTM. In addition, a plume dynamics

model (PDM) is used to provide dimensions and positions of plumes from major elevated pointsources. The PDM data are used for driving the plume-in-grid processing in CCTM. A

photolytic rate constant processor (JPROC) which is based on the RADM (Chang et al., 1987)

approach, computes species specific photolysis rates for a set of predefined zenith angles,

latitude, and altitudes. An alternative detailed-science version adopts state-of-the-science

radiative transfer models that can take into account the total ozone column (TOMS data) and

turbidity. Refer to Table 6-1 for the list of the interface processors in CMAQ and Figure 6-1 for

the data linkage among these interface processors.

By assembling appropriate science modules available in the CMAQ system, users can build a

specific CCTM’s that may include all or some of the critical science processes, such as

atmospheric transport, deposition, cloud mixing, emissions, gas- and aqueous-phase chemical

transformations, and aerosol dynamics and chemistry. One of the features of CMAQ that

distinguishes it from other air quality models is the hierarchical functional modularity of the

science processor codes. We define the levels of modularity in the science model based on the

granularity of the modeling components. The coarsest level of modularity is the distinction

between the system framework and science models. The second level is the division of science

sub-models (MM5, MEPPS, and CMAQ). The third level of modularity involves a driver

module, processor modules, data provider modules, and a utility module (a collection of assisting
EPA/600/R-99/030

6-9

subroutines) in a CTM. While the emissions processing and the meteorology model are modular

at the second level, the CCTM achieves the third-level of modularity by employing the operator

splitting, or fractional time step, concept in the science processes. The next level of modularity

is based on the computational functionality in a processor module, e.g., science parameterization,

numerical solver, processor analysis, and input/output routines. The lowest meaningful

modularization level is the isolation of sections of code that can benefit from machine dependent

optimization.

6.2.2 Modularity Concept of CMAQ

To allow for both the continuous improvement of science and for the addition of new capabilities

in a unified fashion, it is critical to have efficient modular schemes in the CMAQ design.

Currently, the modularity within CMAQ is based mostly on the fractional time-step

implementation of the science processes. This level of modularity involves the distinction of a

driver, processor modules, data provider modules, and utility subroutines in CMAQ. We have

chosen this method because it provides a natural disciplinary distinction for different science

processes through which developments in specific research areas can readily be incorporated

(Refer to Figure 6-2).

In some of the process modules, such as the aqueous-phase chemistry module, the science

algorithms and numerical solvers are tightly linked. For other types of modules, the science

parameterization components and numerical solvers have a looser association. In such cases the

modularity can be defined either at the parameterization level, the numerical algorithm level, or

both. For example, the module definition for the advection process is based on the numerical

advection algorithm used. For the gas-phase chemistry process, the modularity is based on the

ordinary differential equation numerical solvers. The chemistry mechanism description is

generalized and the Models-3/CMAQ framework provides a straightforward method to link

model species surrogate names with the species names in the data set. See Chapter 15 for details.

The use of different chemical mechanisms is accommodated through the mechanism reader and

generalized codes for setting up the production and loss terms of the chemistry reactions.

Therefore, the CCTM does not require different gas-phase chemistry modules for different

mechanisms.

The vertical diffusion process can be formulated using either local- or non-local-mixing

parameterization schemes. The current classification of vertical diffusion modules is based on the

process parameterization methods. The modularity of this process can be enhanced if we

distinguish the method used for computing the vertical diffusivities for local-mixing. In this case,

the modularity is defined at the level of data provider modules. The modularity level can be

deepened further if we identify different numerical solution methods for the diffusion.

With the current version of CMAQ, the level of science modularity is subordinated by the way

the science process codes are archived in the system. Here, we define a class as a collection of

different modules for a given science process. The science classes are identified with the grouping
EPA/600/R-99/030

6-10

of the terms in the governing conservation equation, Equation 6-18. Currently, nine science

process classes are defined in CCTM:

• DRIVER controls model data flows and synchronizes fractional time steps;

• HADV computes the effects of horizontal advection;

• VADV computes the effects of vertical advection;

• ADJCON adjusts mixing ratio conservation property of advection processes;

• HDIFF computes the effects of horizontal diffusion;

• VDIFF computes the effects of vertical diffusion and deposition;

• CHEM computes the effects of gas-phase chemical reactions;

• CLOUD computes the effects of aqueous-phase reactions and cloud mixing;

• AERO computes aerosol dynamics and size distributions; and

• PING computes the effects of plume chemistry.

 CCTM does not have emissions as a separate science process because it can be either a part of

the vertical diffusion or the gas-phase chemical reaction process. It is worthwhile to mention

here that the current modular paradigm does not prevent establishment of combination of

processes in a larger single module. For example, one can develop a module describing the vertical

transport, chemistry, and emissions simultaneously when time scales of those processes become

comparable. Users could experiment with the combination of modules to best fit to their

problems at hand.

 In addition to nine science process modules, CCTM includes two science process classes. The

PHOT computes photolysis rates, and AERO_DEPV computes particle size-dependent dry

deposition velocities. These are typical “data-provider” science process classes, which do not

involve updating concentrations directly. There are some other classes that do not fall in any of

the above definitions. We have grouped these auxiliary routines as the UTIL class, which is a

collection of utility subroutines. As one can see, the current modularity of the CCTM is

implemented more on a practical basis rather than by strictly following a design paradigm. One

can also see that the present modularity definition of CMAQ is somewhat subjective. In the

future we intend to allow definition of the modularity at the user-defined granularity level.

 Figure 6-1 describes the key science process modules in CCTM and their data linkage with

CMAQ’s preprocessors, whose descriptions are available in other chapters. The only data

dependencies among the CCTM science modules are the trace species concentration field as seen

in the diagram and the model integration time step. Figure 6-2 shows the distinct data
EPA/600/R-99/030

6-11

dependencies within the CCTM. To facilitate modularity and to minimize data dependency in

CCTM, we store concentrations in global memory while the environmental input data are

obtained from random-access files and interpolated to the appropriate computational

(synchronization) time step. This realizes the recommended “thin-interface” structure of the

model:

• Common timing data are managed through the science process main subroutine’s call

arguments;

• Concentrations are the object of all process operations;

• Environmental data are provided through a standard I/O interface;

• Model structure data are provided through shared include files; and

• Standard physical constants are obtained from shared include files.

See Chapter 18 for further details on how the science codes are integrated in the Models-3

CMAQ system.
EPA/600/R-99/030

6-12

CMAQ

Driver Couple/

Decouple

Vert.

Diffusion

Horiz.

Diffusion

Gas-Phase

Chemistry

Aerosol

Aqueous

Chemistry &

Cloud

Dynamics

Plume

in Grid

Init

Meteorology Concentration

Emissions

ICON

PDM

JPROC

MCIP

ECIP

BCON

Horiz.

Advection

Vert.

Advection

Photolitic

rates

Plume Dynamics

Boundary

Conditions

Initial

Conditions

Output Files

CMAQ Science Processors

Figure 6-1. Science Process Modules in CMAQ. Interface processes are shown with rectangular

boxes. Typical science process modules are updating the concentration field directly and the dataprovider modules include routines to feed appropriate environmental input data to the science

process modules. Driver module orchestrates the synchronization of numerical integration across

the science processes. Concentrations are linked with solid lines and other environmental data with

broken lines. (From Byun et al., 1998.)
EPA/600/R-99/030

6-13

Table 6-1. Interface Processors for the CMAQ Modeling System

Interface

Processor

Description Reference

ICON Provides initial three-dimensional fields of trace species

concentrations for modeling domain

Chapter 13

BCON Provides concentrations of trace species for the boundary

cells

Chapter 13

ECIP Incorporates emissions from separate area and major

point sources to generate hourly 3-D emissions input file

Chapter 3

MCIP Processes the output of a meteorological model to

provide the necessary meteorological data for CMAQ

models

Chapter 12

JPROC Computes photolysis rates for various altitudes,

latitudes, and sun zenith angle

Chapter 14

PDM Generates plume information needed to apply plume-ingrid (PinG) processing in CCTMChapter 9
EPA/600/R-99/030

6-14

6.2.3 Description of Science Processes

In this section we describe individual science processes, shown in Figure 6-1, associated with the

groups of individual terms in the governing diffusion equation. Note that different concentration

units are used for different science processes in CMAQ CTMs. Appendix 6A provides the

relationships among the concentration units and their conversion factors from one unit to another.

P Output N P

1 ••••• Input

(once)

P

2 P3

Sk S

k Sk Sk

 Random-Access Disk File

Global Memory

(Concentration)

Local

Memor

y

CMAQ CTM 's Data Flow

IC

Data

 Environmental Data (Meteorology, Emissions, BC)

Figure 6-2. Data Dependencies Among Modules in CCTM. P and Sk represent a science process

module and the related subroutines for the module, respectively. (From Byun et al., 1995.)

6.2.3.1 Driver Class for CCTM

The key function of the driver class module is hosting the science processors. It is responsible

for coordinating model integration time (synchronizing fractional-time steps of science process

call) and some input/output sequences. The driver structure of the current CCTM is given in

Figure 6-3. A synchronization time step is used to ensure the global stability of the CCTM’s

numerical integration at the advection time step, which is based on a Courant number limit.

Nesting requires finer synchronization time steps for the fine grid domain. The CCTM’s process

synchronization time steps are represented as integer seconds because the Models-3 I/O API can

only handle integer seconds for I/O data. All the needed data are appropriately interpolated

based on the synchronization time step. For maintaining numerical stability and for other

reasons, an individual process module may have its own internal time steps. In general, each

science process module uses the synchronization time step ( ∆tsync ) as the input time step of

required environmental data. The global output time steps can be set differently from the
EPA/600/R-99/030

6-15

synchronization time step. Usually, the output time step ( ∆tout) is set as one hour, but subhourly output down to the synchronization time step is possible.

Table 6-2. List of Science Process Subroutines Called by the CMAQ Driver

Subroutine Science Class Description

CGRID_MAP UTIL Sets up pointers for different concentration species: gas

chemistry, aerosol, non-reactive, and tracer species

INITSCEN INIT* Initializes simulation time period, time stepping constants, and

concentration arrays for the driver

ADVSTEP DRIVER Computes the model synchronization time step and number of

repetitions for the output time step

COUPLE/

DECOUPLE

COUPLE* Converts units and couples or de-couples concentration values

with the density and Jacobian for transport

SCIPROC DRIVER Controls all of the physical and chemical processes for a grid

(currently, two versions are available: symmetric and

asymmetric around the chemistry processes)

XADV,

YADV

HADV Computes advection in horizontal plane (x- and y-directions)

ZADV VADV Computes advection in the vertical direction in the generalized

coordinate system

ADJADV ADJCON Adjusts concentration fields to ensure mixing ratio

conservation given mass consistency error in meteorology data

HDIFF HDIFF Computes horizontal diffusion

VDIFF VDIFF Computes vertical diffusion and deposition

CHEM CHEM Solves gas-phase chemistry

PING PING Computes effects of plume-in-grid process

AERO AERO Computes aerosol dynamics, particle formation, and

deposition

CLDPRC CLOUD Computes cloud mixing and aqueous chemistry

*

represents a process class that is part of DRIVER function.
EPA/600/R-99/030

6-16

XADV

YADV

ZADV

ADJCON

HDIFF

VDIFF

CHEM

AERO

CLDPRC

COUPLE

VDIFF

PING

HDIFF

ZADV

YADV

XADV

ADJCON

Symmetric SCIPROC

DECOUPLE

∆t

sync

∆t

sync / 2

DECOUPLE

XADV*

YADV*

ZADV

ADJCON

HDIFF

DECOUPLE

VDIFF

CHEM

AERO

CLDPRC

COUPLE

PING

Asymmetric SCIPROC

* Alternating

XADV and YADV calls

for each asymmetric

SCIPROC call

CGRID_MAP

INITSCEN

ADVSTEP

COUPLE

SCIPROC

Synchronization

Time Step

Output

Time Step

CMAQ-DRIVER

∆t

sync

∆t

sync

∆t

sync

∆t

out

Figure 6-3. Driver Module and Its Science Process Call Sequence.

Both asymmetric and symmetric call sequences in SCIPROC are presented. ∆tsync and ∆tout are

model synchronization and output time steps, respectively. Refer to Table 6-2 for the description

of the subroutines.

The DRIVER program calls initialization routines to set up CCTM runs. It initializes the

concentration field and checks if the input files, run time, and grid/coordinate information are

consistent for a given scenario. Subroutines used for the initialization process are grouped into

the INIT class. Usually, initial concentrations for gaseous species are in molar mixing ratio units

(ppm) and aerosol species in density units (μg m-3), the same as the output units of CMAQ.

Also, DRIVER calls couple/decouple subroutines to convert concentration units for appropriate

data processing. The pair of couple/decouple calls, which are available in the class COUPLE,

limit the interchange of process modules between two different concentration units, such as

density versus mixing ratio. The classes INIT and COUPLE are introduced just for the
EPA/600/R-99/030

6-17

convenience of code management from the point of view of science process modularity, and they

should be considered as part of the DRIVER class modules.

6.2.3.2 Advection Processes for CCTM: HADV, VADV and ADJCON

For convenience, the advection process is divided into horizontal and vertical components. This

distinction is possible because the mean atmospheric motion is mostly in horizontal planes.

Usually the vertical motion is related with the interaction of dynamics and thermodynamics. The

advection process relies on the mass conservation characteristics of the continuity equation:

∂ γφ

∂ γ φ ∂ γφ∂ ξ ξ

( ˆ ) ˆ ˆ ( ˆ ˆ )

ˆ

i

i

i

t

v

x

= −∇ • ( ) V −

3

3 (6-19)

Using the dynamically and thermodynamically consistent meteorology data from MCIP, we can

maintain data consistency for air quality simulations at the synchronization time step. In case

the meteorological data provided and the numerical advection algorithms are not exactly mass

consistent, we need to solve a modified advection equation:

∂ γφ

∂ γ φ ∂ γφ∂ φ γρ ξ ξ

ρ ( ˆ ) ˆ ˆ ( ˆ ˆ )

ˆ ˆ i

i

i

i t

v

x

Q = −∇ • ( ) V − +

3

3 (6-20)

where Qρ is mass consistency error term (Byun, 1999). Equation 6-20 ensures conservation of

mixing ratio, which is a necessary (though not sufficient) condition for preserving total tracer

mass given significant fluctuations of density field in space and time. The equation shows that

the correction term has the same form as a first-order chemical reaction whose reaction rate is

determined by the mass consistency error (normalized with air density) in the meteorology data.

Modules in HADV class solve for the horizontal advection:

∂ γφ

∂ ξ ξ γ φ ( ˆ ) ˆ i ˆ

i t

= −∇ • ( ) V (6-21)

and modules in VADV class solve for the vertical advection with boundary conditions vˆ

3 = 0 at

the bottom and top of the model.

∂ γφ

∂

∂ γφ

∂

( ˆ ) ( ˆ ˆ )

ˆ

i i

t

v

x = −

3

3 (6-22)

In simulating air quality, one of fundamental characteristic of the model application should be

conservation of mass. Therefore, the modules in the ADJCON class solve for the mass

correction term:

∂ γφ

∂ φ γρ

ρ ( ˆ ) ˆ i

i t

Q = (6-23)
EPA/600/R-99/030

6-18

We wish to emphasize that the artificial distinction of advection modules between horizontal and

vertical processes is not adequate and that all three modules (HADV, VADV, and ADJCON)

should be considered as an integral unit for solving the physical advection process of trace

species. The advection and mass adjustment algorithms are described in detail in Chapter 7.

6.2.3.3 Diffusion Process Classes for CCTM: HDIFF and VDIFF

For convenience the atmospheric diffusion process is divided into horizontal and vertical

components. This distinction is needed because the vertical diffusion mostly represents the

thermodynamic influence on the atmospheric turbulence by the air-surface energy exchange

processes while the horizontal diffusion represents subgrid scale mixing due to the unresolved

wind fluctuations. To handle the atmospheric diffusion processes in the generalized coordinates,

we need to carefully examine the governing equation to properly set up the diffusion solver.

We start from the atmospheric diffusion equation in the same concentration units as used in

advection:

∂φ

∂

∂ γρ

∂ γ ρ

∂ γρ

∂ γ ρρ

i φ

diff

i

diff

s q

q

t

q

t

F

x

Q

i

i i

* ˆ ˆ ˆ ˆ ( ˆ ˆ )

ˆ = ˆ ( ) = −∇ •[ ] − + 



 

 F 

3

3 (6-24)

where φ γφ i i

* = ˆ , and the term (Qφi / ρ ) is the time rate change of mass mixing ratio due to

emissions of species i. Initially, it is assumed that we can decompose the diffusion into the

horizontal and vertical components with respect to the curvilinear coordinates:

∂φ

∂

∂ γρ

∂ γ ρ ξ

i

hdiff

i

hdiff

q t

q

t i

* ˆ ˆ ˆ ˆ = ( ) = −∇ •[ ] F (6-25)

∂φ

∂

∂ γρ

∂

∂ γρ

∂ γ ρρ

i φ

vdiff

i

vdiff

q

t

q

t

F

x

Q i i

* ˆ ( ˆ ˆ )

ˆ = ˆ ( ) =− + 



 





3

3 (6-26)

Emissions can be included either in vertical diffusion or gas-phase chemistry module. If we can

parameterize the turbulent fluxes directly in the curvilinear coordinates, we can implement

HDIFF and VDIFF modules following Equations 6-25 and 6-26. When the turbulent fluxes are

parameterized with eddy diffusion theory, the contributions of the off-diagonal (crossdirectional) diffusion terms show up explicitly as shown in Equation 6-14:

∂φ

∂

∂

∂ γ ρ

∂

∂

∂

∂ γ ρ

∂

∂

i

cdiff

i i

t x

K q

x x

K q

x

*

ˆ ˆ ( ˆ ˆ ) ˆ ˆ ( ˆ ˆ = ) 



 



 + 



 

 1  13

3 2

23

3
EPA/600/R-99/030

6-19

+ + 



 





∂

∂ γ ρ

∂

∂

∂

ˆ ∂ ˆ ( ˆ ˆ ˆ ˆ )

x

K q

x

K q

x

i i

3

31

1

32

2 (6-27)

For a domain with a significant topographic feature, the module CDIFF must be implemented.

However, the current CMAQ version does not include CDIFF module as the off-diagonal terms

are often neglected in operational air quality models. In such a case, the HDIFF and VDIFF

modules solve for diagonal terms (with respect to the curvilinear coordinates) as follows:

∂φ

∂

∂

∂ γ ρ

∂

∂

∂

∂ γ ρ

∂

∂

i

hdiff

i i

t x

K q

x x

K q

x

*

ˆ ˆ ( ˆ ˆ ) ˆ ˆ ( ˆ ˆ = ) 



 



 + 



 

 1  11

1 2

22

2 (6-25’)

∂φ

∂

∂

∂ γ ρ

∂

∂

i

vdiff

i

t x

K q

x

*

ˆ ˆ ( ˆ ˆ = ) 



 

 3  33

3 (6-26’)

Compared with above formulations, let’s consider the case that we approximate the quantity

γ ρˆ , which defines the computational grid, to be constant for the duration of synchronization

time step for integrating the diffusion process with the fractional time-step method. Then, the

problem becomes equivalent to solving for the diffusion equations in terms of the mass mixing

ratio instead of density:

∂

∂

∂

∂ ρ ξ

q φ

t

F

x

Q i

diff

q

q

i

i i = −∇ •[ ] − + 



 



 ˆ ˆ ( ˆ )

ˆ F

3

3 − •∇ [ ] − [ ] ˆ ˆ ln( ˆ ) ˆ ln( ˆ )

ˆ Fq q i i F

x ξ γ ρ

∂ γρ

∂

3

3 (6-28)

If we rely on Equation 6-28 for representing the atmospheric diffusion process, the concentration

must first be decoupled to obtain mass mixing ratio, qi. Once the new mixing ratio is computed, it

needs to be coupled with γ ρˆ to give the updated concentration in terms of φi

*

. This means

that the operator for the horizontal diffusion process should compute:

∂

∂ γ ρ ξ ξ

q

t

i

hdiff

q q i i = −∇ •[ ] − •∇ [ ] ˆ ˆ ˆ ˆ F F ln( ˆ ) (6-29)

and the vertical diffusion process should solve for:

∂

∂

∂

∂ ρ

∂ γρ

∂

q φ

t

F

x

Q F

x

i

vdiff

q

q

i i

i =− + 



 



 − ( [ ] ˆ )

ˆ ˆ ln( ˆ )ˆ

3

3

3

3 (6-30)

This approach is more convenient in numerically solving the flux-form turbulence mixing

representation because most of the flux-based closure algorithms use parameterizations of

turbulent fluxes in terms of conserving quantities, such as the mass mixing ratio, qi. A

considerable amount of meteorological and air quality literature on turbulence diffusion fails to

clarify this important point. Especially for the case of multiscale applications, the representation

of diffusion in terms of a conserving quantity is critical as shown by Venkatram (1993).
EPA/600/R-99/030

6-20

The effects of turbulence flux caused by the divergence of the grid boxes in the coordinate system

need to be included in order to describe the turbulence exchange processes precisely. One can

readily show that the coordinate-divergence term in Equation 6-30 vanishes for a mass conserving

vertical coordinate. Similarly, when topographical features vary significantly and horizontal

variations of the quantity γ ρˆ are large, one cannot neglect the last term in Equation 6-29.

Chapter 7 of this document describes physical parameterization schemes and numerical

algorithms for the horizontal and vertical diffusion processes in the CCTM.

One may wonder how deposition should be represented in the generalized coordinate system. In

Eulerian air quality models, the deposition process affects the concentration in the lowest layer

as a boundary flux condition. Considering the deposition process as the diffusion flux at the

bottom of the model, we can relate the boundary condition in the generalized coordinate system

to that of the Cartesian coordinate system as:

ˆ ( ˆ ) ( ˆ ) ( ˆ F ) x

x

F x

y

F x

z q q F x

q

y

q

z

i dep i dep i dep i dep

3

333

=++

∂

∂

∂

∂

∂

∂ = ( ˆ ) ∂∂

x

z

Fq

z

i dep

3

(6-31)

because Fq

x

i dep

 and Fq

y

i dep do not exist. Then, the effects of dry deposition on the species

concentration is accounted for by the following relationship:

∂φ

∂

∂ γρ

∂

∂ γρ

∂

∂

∂ γ ρ

∂

∂

i

dep

i

dep

q

dep

q

z

dep t

q

t

F

x x

x

z

F i

i

* ˆ ( ˆ ˆ )

ˆ ˆ ˆ ( ˆ = ) ( ) =− =− 



 





3

3 3

3

≈ −

− ( ) =− =−( ˆ ) ( ˆ )

( ˆ ) ( ˆ ) *

∂

∂ γ ρ

γρ φ

x

z

F

x

v

h q

v

h

dep i dep

dep dep

layer

dep

layer

q

z

d

i

d

i

3

3 1 1 ∆ (6-32)

where h z

x

x dep

dep

= dep





 



 ∂

∂ˆ ( ˆ ) 3

3 ∆ is the thickness of the lowest model layer in the geometric height

coordinate. In the derivation of Equation 6-32, we assume that the deposition flux is constant in

the lower part of the surface layer (i.e., a constant flux layer). Thus, the deposition velocities are

computed at the middle (in terms of the generalized coordinate, ξ) of the lowest model layer at

which the concentrations are represented. For the case in which the mass mixing ratio is used as

the concentration variable for solving the diffusion equation, the deposition should be

implemented as a boundary condition for the vertical diffusion (VDIFF) in the following manner:

∂

∂

∂

∂

∂

∂

∂

∂

q

t

F

x x

x

z

F i

dep

q

dep

q

z

dep

i

i =− =− 



 



 ( ˆ )

ˆ ˆ ( ˆ )

3

3 3

3

(6-33)

Therefore, the bottom boundary condition for the VDIFF module is given as:
EPA/600/R-99/030

6-21

∂

∂

∂

∂

∂

∂

q

t x

x

z

F i

q

z

dep

i

dep

= − 



 



 ˆ ( ˆ ) 3

3

≈ −

−





 



 ( ) = ( ) = −

∂

∂

ˆ

( ˆ )

x

z

F

x

F

h

v

h q bottom

i dep

dep

i dep

dep dep

layer

q

z

q

z

d

i

3

3 1

∆ (6-33’)

Equations 6-32 and 6-33 show that we do not need to estimate contravariant deposition

velocities if the deposition process is implemented as a bottom boundary condition in the

generalized coordinate formulation.

In the current CCTM implementation, the concentration units for horizontal and vertical

diffusion processes are density (coupled with Jacobian) and molar mixing ratio, mi = qi

Mair

Mi

,

respectively. We have chosen mi as the generic concentration unit for the vertical diffusion to

coordinate with the emissions units in the data. Subsection 6.2.3.6 provides a detailed

explanation for this. Therefore, HDIFF is placed outside and VDIFF is placed in between the

pair of couple/decouple calls. Because the ratio of molecular weights are constant, equations for

the vertical diffusion in terms of molar mixing ratio are equivalent to those in terms of mass

mixing ratio, qi . Refer to Chapter 7 for details of the computational algorithms for HDIFF and

VDIFF.

6.2.3.4 Gas-phase Chemistry Process for CCTM

Instead of directly computing the time rate of change of φi

*

, as is given by:

∂ φ

∂ γ φφ γ φ φ

( ) ˆ ( ,..., ) ˆ *

i

chem

N t

R Q i i = + 1 (6-34),

we need to decouple the Jacobian and air density in γ φˆ i

 before computing gas-phase chemistry.

This is useful because we can approximate that the computational grid remains constant for the

duration of a synchronization time step, which is set by the Courant conditions for the fractional

time step numerical integration schemes. Because the concentration unit required in the gasphase chemistry is the volumetric mixing ratio, we rewrite the concentration φi

*

 as follows:

φ γφ γρ γρ ii i

air

i

i

air

i

air

i

i

air

q

M

M

M

M q

M

M

M

M

* == = ˆˆ ˆ 



 





 = 



 



m  M

M i

i

air

γ ρˆ (6-35)

where m q

M

M i i

air

i

= is used as the definition of the volumetric or molar mixing ratio. The time rate

of change of the volumetric mixing ratio due to the gas-phase chemistry is evaluated with the

following equation:
EPA/600/R-99/030

6-22

∂

∂

m

t

Rm m Qm i

chem

m N mi i i = + ˆ ( ,..., ) ˆ ( ) 1 (6-36)

where Rˆ

mi

 and Qˆ

mi

represent chemistry reactions and source terms in molar mixing ratio units,

respectively.

CMAQ employs generalized chemistry solvers, such as QSSA (Young et al., 1993) and

SMVGEAR (Jacobson and Turco, 1994), which are designed to solve the nonlinear set of stiff

ordinary equations presented in Equation 6-36. They can be applied independent of the

coordinate and grid descriptions. To accommodate the need for modified or new chemical

mechanisms, the CMAQ system is equipped with a generalized chemical mechanism processor.

Refer to Chapter 8 for detailed description of numerical solvers used for gas-phase chemistry.

The Models-3 framework provides a mapping table to link chemistry mechanism species with

surrogate species names in the initial and boundary condition files and emissions files. See

Chapter 15 for details. When a new mechanism is used, appropriate emissions data must be

supplied. It is possible to include emissions either in the gas-phase chemistry or in the vertical

diffusion process. It is preferable that the emissions are interpolated with the same temporal

interpolation schemes used in the transport processes.

6.2.3.5 Aerosol Process Class for CCTM

The fractional time step implementation solves for the effects of aerosol chemistry and dynamics

on trace gas and aerosol species concentrations with:

∂φ

∂ γ φφ γ ∂φ∂ξ

i

aero

aero N aero g

i

t

R Qv i i

* *

= +− ˆ ( ,..., ) ˆ ˆ 1 (6-37)

where Raeroirepresents processes such as new particle formation and growth and depletion of

existing particles. Qaeroi stands for all the external sink and source terms, and vˆg is the

contravariant sedimentation velocity. The generic concentration units for the aerosol process are

[ μg m−3] (density) for aerosol mass and [ number m−3] for aerosol particle number density.

Because the aerosol process is called within the pair of couple/decouple calls, the input

concentration is already decoupled and the following set of governing equations are solved in the

aerosol process module:

∂φ

∂ φ φ ∂φ∂ξ

i

aero

aero N aero g

i

t

R Qv i i = +− ( ,..., ) ˆ 1 (6-38)

The present implementation of the aerosol module in CCTM is derived from the Regional

Particulate Model (Binkowski and Shankar, 1995). Here, primary particles are divided into two

groups: fine particles and coarse particles. The fine particles result from combustion and

secondary production processes and the coarse group is composed of materials such as wind-
EPA/600/R-99/030

6-23

blown dust and marine particles. The key scientific algorithms simulating aerosol processes for

the CCTM are: (1) aerosol removal by size-dependent dry deposition; (2) aerosol-cloud droplet

interaction and removal by precipitation; (3) new particle formation by binary homogeneous

nucleation in a sulfuric acid/water vapor system; (4) the production of an organic aerosol

component from gas-phase precursors; and (5) particle coagulation and condensation growth.

Refer to Chapter 10 for details on aerosol process implemented in CCTM.

6.2.3.6 Emissions Process for CCTM

As mentioned earlier, the emissions process does not have its own science process class. Instead,

it is included either in vertical diffusion or in the gas-phase chemistry process. In the governing

conservation equations for the trace gases, the emissions process is represented simply as source

terms.

If emissions data are given in the unit of time rate of change of mass, for example for particulate

species, such as PM2.5 and PM10 in [g s-1], they are expressed as:

Q E

V V

V

t V

q V

t i

i i

emis

i

emis

φ δ δ

∂ φδ

∂ δ

∂ρ δ

∂ == = 1 1 () ( ) (6-39)

where δV is volume of the cell and E V

t i

i

emis

= ∂ φδ

∂

( ) represents the emissions rate into the cell. If

the mass of air in the cell does not change for each time step (usually one hour), the concentration

expression, either as the time rate of change of density or as the mass mixing ratio can be used.

Otherwise, when the volume and density of a cell change substantially with time, the effect of

change in air mass must be accounted for in determining the emissions rates.

For gaseous species, the time rate of change of EI for each hour and each grid cell are provided in

the three-dimensional emissions data files in molar units, ( i.e., mole s−1):

E M

M

Q

i V air

i

i = 



 



 φ

ρ

δ (6-40)

Emissions for gaseous species in molar units are preferred to those in mass units because molar

units are the natural units for chemistry and mass units must be transformed into [ mole s−1]

eventually for the gas-phase chemistry process. For gaseous species the molar mixing ratio and

mass mixing ratio differ only by a simple multiplication factor, the ratio of molecular weights.

However, for lumped species, the molecular weights are variable depending on the fractional

compositions of the categorized hydrocarbon species in the emissions data. Therefore,

transformation of emissions in mass units into the molar units for the lumped species can

introduce misrepresentation of emissions amount. The data for the fractional compositions of

the categorized hydrocarbon species are available in the emissions processor, Models-3

Emissions Projection and Processing System (MEPPS) (See Chapter 4). Thus, when emissions
EPA/600/R-99/030

6-24

data are processed in [ mole s−1] units, we do not have this conversion problem. Then the

emissions process is represented as:

∂

∂ ρ

m φ

t

M

M

Q i

emiss

air

i

i ≈ (6-41)

An additional benefit is that the same transformation rule can be applied when emissions are

included either in the vertical diffusion or in the chemistry.

6.2.3.7 Cloud Mixing and Aqueous-phase Chemistry (CLOUD) for CCTM

The rate of change in pollutant concentrations due to cloud processes is given by:

∂

∂

∂

∂

∂

∂

m

t

m

t

m

t

i

cld

i

subcld

i

rescld

= + (6-42)

where subscripts cld, subcld, and rescld represent cloud, subgrid scale cloud, and resolved cloud,

respectively. Although calls to the CLOUD module are made at every synchronization time

step, the subgrid cloud effects are accounted for once an hour while the resolved cloud effects are

impacted at each call. This is equivalent to assuming that the cloud life time of all sub-grid clouds

is one hour. The effects of subgrid cloud processes, such as mixing (mix), scavenging (scav),

aqueous-phase chemistry (aqchem), and wet deposition (wdep) on grid-average concentrations

are parameterized with a “representative cloud” within the grid cell:

∂

∂

m

t

f mix scav aqchem wdep i

subcld

~ ( , , , ) (6-43)

where f represents a function of its arguments. We chose this expression because of the implicit

nature of the algorithm representing the processes. For the resolved cloud, no additional cloud

dynamics are considered in CMAQ and only effects of the scavenging and aqueous-phase

chemistry are considered:

∂

∂

∂

∂

∂

∂

m

t

m

t

m

t

i

rescld

i

scav

i

aqchem

= + (6-44)

See Chapter 11 for details of the cloud process descriptions.

6.2.3.8 Plume-in-Grid Process (PING) for CCTM

Anthropogenic precursors of the tropospheric loading of ozone, aerosols, and acidic species are

largely emitted from major point sources, mobile sources, and urban-industrial area sources. In

particular, inadequate spatial resolution of the major point source emissions can cause inaccurate

predictions of air quality in regional and urban Eulerian air quality models. A plume-in-grid
EPA/600/R-99/030

6-25

(PinG) approach in CCTM provides a more realistic treatment of the subgrid scale physical and

chemical processes for major elevated point source emitters (MEPSEs).

The PING module solves for:

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

m

t

m

t

m

t

m

t

m

t

p p

disp

p

emis

p

chem

p

dep

=++ + (6-45)

where mp is concentration of the subgrid plume (in molar mixing ratio) and the time-rate of

change terms with subscripts disp, emis, chem, and dep represent effects of plume dispersion,

point source emissions, plume chemistry, and dry deposition in the plume, respectively. The

location and shape of plumes are determined by the PDM and plume chemistry is computed in

the CCTM within plume subsections. When the subgrid scale phase of the plume simulation has

been completed, the PING module updates grid scale concentrations with:

∂

∂

δ

δ

∂

∂

m

t

V

V

m m

t

i

ping

p p ibg = ( ) − (6-46)

where mibg is the back ground concentration and δVp is the volume of plume in a grid cell with

volume δV. Currently, only gaseous species are treated with the PING module. Readers are

referred to Chapter 9 for the details. The work for the inclusion of particulates in the PING

process has been started.

6.3 Equivalent Model Formulations for Different Vertical Coordinates

Because the CCTM is based on a generalized coordinate system, it is possible to emulate the

governing equations of other popular Eulerian air quality models. For most urban and regional

applications, the choice of horizontal map projection is handled with the map scale factors at the

individual grid points. Therefore, there are no real differences in formulations in horizontal

directions. One caveat is that the current CMAQ version is not tested with anholonomic

coordinates, such as spherical coordinates. A few implementation details must be taken into

account to accommodate the spherical coordinates. Most of the distinction of the dynamics is

attributed to the choice of the vertical coordinate of the system.

The generalized governing conservation equation for trace species, written in the Reynolds flux

form, is given in Equation 6-18. The same equation in eddy-diffusion form, in which the

components of the eddy diffusivity tensor are represented in terms of those in Cartesian

coordinates, is given below:

∂

∂ φ

φ ∂φ

∂ξ ξ ξ

ξ

ξ

ξ

t

J m

J

m

J v

i

i i ( ) ˆ ˆ ( ˆ ) + ∇• 



 



 + 2

2

3

V
EPA/600/R-99/030

6-26

− 



 



 − 



 



 m

x

J K q

x

m

x

J K q

x xx

i

yy

2 i

1 1

2

2 2

∂

∂ ρ

∂

∂

∂

∂ ρ

∂

∂ ξ ξ ˆ ( ˆ ) ˆ ( ˆ )

− ++

















∂

∂ξ

ρ ∂

∂

∂

∂

∂

∂ξ ξ J

z

x

K z

x

K K sfc sfc q

xx yy zz

i [( ˆ ) ( ˆ ) ]) 1

2

2

2

= + JR Q [ ] ++ +

J

t

J

t

J

t i i N

i

cld

i

ping

i

aero

ξ φ φ

ξξ ξ φ φ

∂ φ

∂

∂ φ

∂

∂ φ

∂ ( ,..., ) () () ()

1 (6-47)

In most popular air quality models, including the present implementation of the CCTM, the

cross-terms from the off-diagonal components of the diffusivity tensor are neglected. Note that

some models use wind components defined in Cartesian coordinates. The mass conservation

characteristic of Equation 6-47 is heavily dependent on the quality of the wind data provided. In

particular, depending on the dynamic assumptions used in atmospheric models, methods for

estimating the contravariant vertical velocity component vary considerably. Refer to Chapter 5

for the details.

Formulations of other air quality models with popular meteorological vertical coordinates, such

as z,σ z , σ po, and σ

p ̃ ; and the step-mountain eta coordinate, η, can be obtained by substituting

the appropriate vertical Jacobian in Equation 6-47. Refer to Table 6-3 for the coordinate

definitions, associated Jacobians and contravariant vertical velocity components. Occasionally,

one may find discrepancies in the governing equation between the one represented by Equation 6-

47 and the one presented in the documentation of a specific model with the same vertical

coordinates. Some of these can be attributed to the explicit representation of the dynamic

characteristics and other idiosyncratic implementation practices used in those models. In the

CCTM, the vertical coordinate is defined to increase with geometric height as given in Equation

6-4. This restriction simplifies interpretation of terms in the governing equations and eventually

the computer coding of the algorithms. For example, the sign of the contravariant vertical

velocity component is kept the same (i.e., positive value represents upward motion) across the

different coordinate systems.

The terrain-influenced height coordinate σ z has been used often for studying air quality

especially with some simplifying conditions such as the Boussinesq approximation and anelastic

assumption. For urban air quality simulations, there are a few examples of applying the σ z

coordinate defined with time and space dependent H (thickness of model), which is often related

with the boundary layer height. The σ z coordinate is used in air quality models, such as the

Urban Airshed Model (UAM) (Scheffe and Morris, 1993), STEM-II (Carmichael et al., 1991),

CIT (Harley et al., 1993), CALGRID (Yamartino et al., 1992), and others. The terrain-influenced

reference pressure coordinate is used in SAQM (Chang et al., 1997), which is designed to be

consistent with the nonhydrostatic MM5 meteorological model. The terrain-influenced time

dependent hydrostatic pressure coordinate is used in RADM (Chang et al., 1987). It is the same

coordinate used for MM4 or MM5 hydrostatic applications. Step-mountain eta coordinate is
EPA/600/R-99/030

6-27

used for NCEP’s Eta meteorological model (Black, 1994, and Mesinger et al., 1988), but no

operational air quality model using the eta coordinate is available.

Table 6-3. Vertical Coordinates and Associated Characteristics

CMAQ

Coordinate

xˆ 3 = ξ

Definition Contravariant

Vertical

Velocity

vˆ

3

Vertical

Jacobian

Jξ

Remarks

Z w = dz

dt

1 Geometric height

σz σ z

sfc

sfc

H

z z

H z = −−

d

dt

σ z H z

H

− sfc H is the thickness of

model and σ z is the

scaled height

σz σ z

sfc

sfc

z z

H z = −−

d

dt

σ z H z − sfc Nondimensional height,

terrain-influenced

1− σ po

σ po

o T

os T

p p

p p = −− − d

dt

σ po p p

g

os T

o

−

ρ

Nondimensional

reference pressure

1− σ

p ̃ σ  ̃

 ̃

 ̃ p

T

s T

p p

p p = −− − d

dt

σ

p ̃  ̃

 ̃

p p

g

s T −

ρ

Nondimensional

geostrophic pressure

1 −η η

π π

π π = η −−





 



 T

s T

sfc

− d

dt

η π π

ρ η

s T

sfc g

−

 ̃

Step-mountain ETA

ηsfc

o sfc T

o T

pz p

p p = −−





 



 ( )

( ) 0

6.4 Nesting Techniques

The nested grid CTM is needed to provide the required high resolution simulations. At present,

Models-3 CMAQ allows only static grid nesting. In static grid nesting, finer grids (FGs) are

placed (i.e., nested) inside coarser grids (CGs). The resolution and the extent of each grid are

determined a priori and remain fixed throughout the CTM simulation. Static grid nesting

conserves mass and preserves transport characteristics at the interfaces of grids with different

resolutions (Odman et al., 1995). It allows for effective interaction between different scales with

efficient use of computing resources. On the other hand, the nest domain is redefined during a

simulation with the dynamic nesting. Both static and dynamic nesting techniques allow one-way

or two-way exchange of information among FGs and the CG and periodically by independently

simulating CTMs at each grid (coarse or nested) with its own time step. The dynamic nesting

procedure is not implemented in the CMAQ system.

In one-way nesting, the primary concern is the mass conservation at the grid interface where

boundary conditions are input to the FG using the CG solution. The advective flux at the inflow
EPA/600/R-99/030

6-28

boundaries of the FG is the flux as determined by the CG solution that passes through this

interface. We also allow for time variation of the flux during the CG time step. This is

performed by computing the departure point of the last particle passing through the interface for

each FG time step. In the Lagrangian description, the mass crossing the interface is equal to the

spatial integral of the concentration distribution between the departure point and the interface.

Most flux-conserving advection schemes use the same Lagrangian concept to calculate the mass

transfer between grid cells (e.g., Bott, 1989). During each FG time step, we meter into the FG

the exact amount of mass that would have crossed the interface on the CG (Byun et al., 1996).

In two-way nesting, the concentrations are updated in each CG cell by averaging the

concentrations of all the FG cells overlapping with the CG cell. Special care is required to assure

strict mass conservation at the grid interface. The mass of some species (e.g., radicals) may no

longer be conserved because, when advancing the FG solution, we perform nonlinear chemical

transformations in addition to transport. However, the mass of the basic chemical elements such

as sulfur, nitrogen, and carbon must be conserved. The FG solution is used to compute the flux

of each element at the grid interface. When conservation principles are applied to the grid

interface, as described above, the CG concentrations near the interface must be corrected (when

the Courant stability limit is applied, only the first row of CG cells immediately outside the

interface need correction). This is done by renormalizing the concentration of each species based

on the assumption that the ratio of the species mass to element mass will remain the same before

and after the correction. This method is similar to the renormalization procedure used to make

slightly non-conservative chemical solvers strictly conservative. Alapaty et al. (1998) compares

different spatial interpolation schemes used for the two-way nesting. INPUT FEEDBACK INPUT INPUT

∆t

∆T

∆t ∆t

cCG

cFG

Figure 6-5. Static Grid Nesting Used in CMAQ System

The CCTM provides a static nesting (see Figure 6-5) capability while maintaining a high level of

modularity by separately processing object codes for different grid domains and by enforcing the

protocol that each module reads its required input data independently from others. The scheme
EPA/600/R-99/030

6-29

is also applicable for multiple and multi-level grid nesting. Multi-level nesting is a natural

extension of the single static grid nesting. Figure 6-6 presents a schema for multi-level nesting,

where three-levels are illustrated. The feedback processes update coarser grid concentrations at

each synchronization time steps of the nest grids. The information about the grid is

communicated to each process module through a set of FORTRAN include files specific to each

grid domain during compilation time. This allows use of the same process modules for different

grids. Customizing a nested model is as simple as preparing include files with grid dimensions for

each grid and a driver with the appropriate process calling sequence.

As seen in Figure 6-6, the only difference between the one-way and two-way nesting is whether

concentrations in coarser grid simulations are updated with the finer grid simulations through the

feedback processors or not. Depending on the computer hardware and software configurations,

one could build a nested CTM model with one executable collectively simulating all the FGs and

CG, or with independent CTM executables for different grids that run simultaneously on

multiple CPUs accessing common data through appropriate I/O API. The latter approach relies

on the cooperating processors concept in a UNIX environment. As mentioned before, the

current CMAQ version lacks a feedback module, which is necessary for the two-way nesting.

cGrid

Driver

fGrid_1

Driver

BC

Proc

Feedback

Proc

fGrid_2

Driver

BC

Proc

Feedback

Proc

cGrid

J file

cGrid

IC file

cGrid

BC file

cGrid

Emis

cGrid

Met Coarse_Conc

fGrid_1

J file

fGrid_1

IC file

fGrid_1

Emis

fGrid_1

Met fGrid_1_Conc

fGrid_2

J file

fGrid_2

IC file

fGrid_2

Emis

fGrid_2

Met fGrid_2_Conc

∆t_sync_cGrid

∆t_Sync_fGrid1

interpolate

conc

Update

Coarse

interpolate

Conc

Update

fGrid_1

Legend

cGrid: coarse grid domain

fGrid: fine grid domain

Emis: emissions file

Met: meteorology files

J: photo lysis rat e

IC: initial condit ions

BC: boundary condit ions

Conc: concentr ati on

Sync: synchronizat ion

Proc: processor

Figure 6-6. Schematics for Multi-level Nesting (three levels illustrated)
EPA/600/R-99/030

6-30

6.5 Summary

The CMAQ system achieves multi-pollutant and multiscale capabilities by combining several

distinct modeling techniques. The generalized governing conservation equations of the CCTM

allow transformation among various vertical coordinates (e.g., terrain-influenced geometric height,

or pressure) and transformation among various horizontal coordinates, especially map

projections (e.g., rectangular, Mercator, Lambert, and polar stereographic) by simple changes in a

few scaling parameters defining the boundary domain, map origin, and orientation. Therefore,

CMAQ can be configured to match the dynamic characteristics of the preprocessor

meteorological models. The CMAQ system uses a nesting technique and a plume-in-grid

approach to handle small scale air quality problems and subgrid scale plume dispersion and

chemical reactions, respectively. The multi-pollutant capability is provided by a generalized

mechanism reader and generalized chemistry solvers, linked cloud mixing and aqueous reaction

processes, and aerosol modules. The CCTM code uses a modular structure that allows for the

continuing improvement of the science and addition of new capabilities in a unified fashion. It

provides a natural disciplinary distinction among different science processes through which

developments in specific research areas can be readily incorporated.

As mentioned above, there remain a few implementation tasks, such as development of feed-back

modules for two-way nesting and adaptation of anholonomic coordinates (e.g., latitudelongitude), which will provide additional functionalities in CCTM.

6.6 References

Alapaty, K., R. Mathur, and T. Odman, 1998: Intercomparison of spatial interpolation schemes

for use in nested grid models. Mon. Wea. Rev. 126, 243-249.

Binkowski, F. and U. Shankar, 1995: The regional particulate model, Part I: Model description

and preliminary results. J. Geophys. Res., 100: 26191-26209.

Black, T., 1994: The new NMC mesoscale Eta model: Description and forecast examples. Wea.

Forecasting, 9, 265-278.

Bott, A., 1989: A positive definite advection scheme obtained by nonlinear renormalization of

the advective fluxes. Mon. Wea. Rev. 117, 1006-1015.

Byun D. W. , A. Hanna, C. J. Coats, and D. Hwang, 1995: Models-3 Air Quality Model

Prototype Science and Computational Concept Development. Trans. TR-24 Regional

Photochemical Measurement and Modeling Studies, 8-12 November 1993, San Diego, CA, Air &

Waste Management Association. Pittsburgh, PA., 197-212.

Byun, D.W., D. Dabdub, S. Fine, A. F. Hanna, R. Mathur, M. T. Odman, A. Russell, E. J.

Segall, J. H. Seinfeld, P. Steenkiste, and J. Young, 1996: Emerging Air Quality Modeling

Technologies for High Performance Computing and Communication Environments, Air Pollution

Modeling and Its Application XI, ed. S.E. Gryning and F. Schiermeier, 491-502.
EPA/600/R-99/030

6-31

Byun, D.W., J. Young., G. Gipson., J. Godowitch., F. Binkowsk, S. Roselle, B. Benjey, J. Pleim,

J. Ching., J. Novak, C. Coats, T. Odman, A. Hanna, K. Alapaty, R. Mathur, J. McHenry, U.

Shankar, S. Fine, A. Xiu, and C. Jang, 1998: Description of the Models-3 Community Multiscale

Air Quality (CMAQ) model. Proceedings of the American Meteorological Society 78th Annual

Meeting, Phoenix, AZ, Jan. 11-16, 1998. 264-268.

Byun, D. W., 1999: Dynamically consistent formulations in meteorological and air quality

models for multi-scale atmospheric applications: II. Mass conservation issues. J. Atmos. Sci., (in

print).

Carmichael, G.R., L.K. Peters, and R.D. Saylor, 1991: The STEM-II regional scale acid

deposition and photochemical oxidant model-I. An overview of model development and

applications. Atmos. Environ. 25, 2077-2090.

Chang, J.S., R.A. Brost, I.S.A. Isaksen, S. Madronich, P. Middleton, W.R. Stockwell, and C.J.

Walcek, 1987: A three-dimensional Eulerian acid deposition model: Physical concepts and

formulation, J. of Geophys. Res., 92, 14,681-700.

Chang J. S., S. Jin, Y. Li, M. Beauharnois, C.-H. Lu, H.-C. Huang, S. Tanrikulu, and J. DaMassa,

1997: The SARMAP air quality model. Final Report, SJVAQS/AUSPEX Regional Modeling

Adaptation Project, 53 pp. [Available from California Air Resources Board, 2020 L Street,

Sacramento, California 95814.]

Coats, C.J., cited 1996: The EDSS/Models-3 I/O Applications Programming Interface. MCNC

Environmental Programs, Research Triangle Park, NC. [Available on-line from

http://www.iceis.mcnc.org/EDSS/ioapi/H.AA.html.]

Harley, R.A., A.G. Russell, G.J. McRae, G.R. Cass, and J.H. Seinfeld. 1993: Photochemical

modeling of the Southern California air quality study. Envir. Sci. Technol. 27, 378-388.

Jacobson, M.Z. and R.P. Turco, 1994: SMVGEAR: A sparse-matrix vectorized Gear code for

atmospheric models. Atmos. Environ. 20, 3369-3385.

Mesinger, F., Z. I. Janjic, S. Nickovic, D. Gavrilov, and D. G. Deaven, 1988: The step-mountain

coordinate: model description and performance for cases of Alpine lee cyclogenesis and for a case

of Appalachian redevelopment. Mon. Wea. Rev., 116, 1493-1518.

Odman, M.T., R. Mathur, K. Alapaty, R.K. Srivastava, D.S. McRae, and R.J. Yamartino, 1995:

Nested and adaptive grids for multiscale air quality modeling. U.S. EPA Workshop on Next

Generation Models Computational Algorithms (NGEMCOM), Bay City, MI, June 1995.

Seaman, N. L., D. R. Stauffer, and A. M. Lario-Gibbs, 1995: A multiscale four-dimensional data

assimilation system applied in the San Joaquin Valley during SARMAP. Part I: Modeling design

and basic performance characteristics. J. Appl. Meteor., 34, 1739-1761.
EPA/600/R-99/030

6-32

Seinfeld, J.H., 1986: Atmospheric Chemistry and Physics of Air Pollution. Wiley-Interscience,

New York.

Scheffe, R. D., and R. E. Morris, 1993: A review of the development and application of the

Urban Airshed Model. Atmos. Environ., 27B, 23-39.

Srivastava, R.K., D.S. McRae, M.T. Odman, 1995: Governing Equations of Atmospheric

Diffusion. Technical Report, MCNC [Available from MCNC-North Carolina Supercomputing

Center, P.O. Box 12889, 3021 Cornwallis Rd. Research Triangle Park, NC 27709-2889.]

Schwartz, E. S. and P. Warneck, 1995: Units for use in atmospheric chemistry. Pure & Appl.

Chem. 67, Nos 8/9, 1377-1406.

Toon, O.B., R.P. Turco, D. Westphal, R. Malone, and M.S. Liu, 1988: A multidimensional

model for aerosols: Description of computational analogs. J. Atmos. Sci., 45, 2123-2143.

Venkatram, A., 1993: The parameterization of the vertical dispersion of a scalar in the

atmospheric boundary layer. Atmos. Environ. 27A, 1963-1966.

Yamartino, R.J., J.S. Scire, G.R. Carmichael, and Y.S. Chang, 1992: The CALGRID mesoscale

photochemical grid model - Part I. Model formulation, Atmos. Environ. 26A, 1493-1512.

Young, J.O., E. Sills, D. Jorge, 1993: Optimization of the Regional Oxidant Model for the Cray YMP, EPA/600/R-94/065. [Available from U.S. Environmental Protection Agency, Research

Triangle Park, NC 27711.]

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

6-33

Appendix 6A. Concentration Units Used for Air Quality Studies

As we have seen above, many different concentration units are used for air quality studies. In

this section we summarize the relations among the concentration units and their conversion

factors from one unit to another. For Models-3/CMAQ system we follow the International

System of Units (Système International, SI) as a framework for units in the formulations. The

fundamental assumption used here is that air and trace gases follow the ideal gas law, i.e.,

pV R T = ν g , (6A-1)

where Rg is the universal gas constant = 8.314510 [ J mol K /( ) • ],

ν is molar number,

V is volume of the gas [m3],

p is pressure [Pa], and

T is temperature [K].

There are many different ways to express the amount of substance in the atmosphere. We

introduce most popular quantities and transformation relations among them are presented below.

Number Density, n

One way to express trace gas quantities is to count number of molecules in the unit volume. For

example, number of molecules of air in the unit volume, nair, is expressed as:

n

N

V air

air A = ν (6A-2)

where νair is number of moles of air,

NA is the Avogadro’s number = 6 0221367 1023 . × , and

Similarly, number of molecules of trace gas per volume, i.e., number density of species ni, is

defined as:

n

N

V

N

RT p

p

k T i

iA iA

ig i

i

B

== = ν ν

ν / [molecules m−3

] (6A-3)

where νi is number of moles of trace gas i in a given volume, and

k RN B gA = / is Bolzmann’s constant

pi is the partial pressure of species i.

Molar Density, ci

The number of moles of air (cair) and trace gas (ci) normalized for a unit volume of air are simply

defined as:
EPA/600/R-99/030

6-34

c

V air

air = ν (6A-4a)

c

V i

i = ν (6A-4b)

with the unit [ mole m−3

]. Because the SI unit for the amount of substance is mol, this quantity

can be used conveniently for expressing chemical relationships.

Partial Pressure, pi

Although not used widely in atmospheric chemistry, the partial pressure has been playing an

important role specifying thermodynamic properties of the atmosphere, especially for water

vapor in the air. The Dalton’s law states that the total pressure exerted by a mixture of gases is

equal to the sum of the partial pressure exerted by each constituent at the given temperature and

volume. Because we assume that each trace gas follows the ideal gas law, the partial pressure

can be used to express the trace gas quantity. The partial pressure of atmospheric constituent

gas is related to the number of moles per volume as:

p

R T

V i cRT i g = = i g

ν

(6A-5)

and the standard SI unit for the partial pressure is Pascal [Pa].

Molar Mixing Ratio, mi

Often, the molar mixing ratio is used as a synonym for the volume mixing ratio, or the mole

fraction of a substance in air. Basically it is a unitless quantity. However, it is customary to

identify in terms of molar unit as [ mole mole / ]. Because the volume occupied by a mole of ideal

gas at given pressure is the same regardless of the constituent, the mole fraction is essentially

equal to the volume fraction. However, mole fraction is preferred because it does not require the

implicit assumption of the ideality of the gases, and more importantly because it is applicable

also to condensed-phase species (Schwartz and Warneck, 1995). For a given volume, the volume

mixing ratio of a trace species is expressed in terms of concentration units defined above as:

m

c

c c

p

p

i

i

air i

i

air i

i = + = + = ν

ν ν

, (6A-6)

where p is the total pressure.

Because ν ν i air << for trace gases, Equation 6A-6 can be approximated as:

m

c

c

p

p

i

i

air

i

air

i

air

≈== ν

ν
EPA/600/R-99/030

6-35

When dealing with trace gases in the real atmosphere, the contribution of moisture can be used in

the definition of mixing ratio. Therefore, pair represents total pressure of the atmosphere which

includes vapor pressure of water while the contribution of other trace gases are neglected.

Because the variation caused by the moisture can amount to several percent, some researchers

prefer to use dry air when expressing trace gas mixing ratios. However, in the Models-3/CMAQ

system, we use the trace gas mixing ratio with respect to the moist air because we rely on the

continuity equation for the total air density to represent atmospheric mass conservation.

Mass Mixing Ratio, qi

Mass mixing ratio is used often for describing transport process and is simply related with the

volume mixing ratio as:

q m

M

M i i

i

air

= (6A-7)

Density, φi

Concentrations of substances in air can be expressed in terms of amount of substance mass per

volume of air, i.e. density. Density is a most popular unit for dynamic representation of

atmospheric concentration because it is the operating units of the mass continuity equation.

Density can be expressed in terms of other concentration units as:

φ

ν

i

i i

i i

i

air

air i

M

V

c M c

c = == c M

 ≈ = ( )( ) m

M

M

i cM q i

air

air air i air ρ (6A-8)

Table 6A-1 provides cross-reference relationships among the concentration variables described.

However, the individual process science area prefers to use certain specific units of decimal

multiples of the SI unit suggested. We included the conversion factors among the concentration

variables actually implemented in science process modules. Because it is convenient to express

the conversion factors in terms of the dry air quantities, the virtual temperature is used in Table

6A-1.
EPA/600/R-99/030

6-36

number density, Ni

[molecules/m3]

molar density, ci

[mol/m3]

partial pressure, pi

[Pascal]

molar mixing ratio,

mi [ppmV]

mass mixing ratio,

qi [ppm]

density, φi [μg/m3]

number density,Ni[molecules/m3]

1 Ni = (NA )ci Ni = (kBT )−1 pi Ni = 10−3 • NA ρair Mair   mi Ni = 10−3 • NA ρ air Mi   qi Ni =10 −6 • NA M i  φi

molar density, ci[mol/m3] ci = (NA )−1Ni 1 ci = (RgT)−1 pi ci = 10 −3 • ρair Mair  mi ci =10 −3 • ρair Mi   qi ci =10 −6 • Mi ( )−1φipartial pressure,pi [Pascal] pi = kBT ( )Ni pi = RgT ( )ci 1 pi = 10−6 • ( p)mi pi =10 −6 • Mair Mi p   qi pi = 10−6 • R Tg Mi  φimolar mixingratio, mi [ppmV] mi = 103 • Mair ρair NA   Ni mi = 103 • Mair ρair   ci mi = 106 • (p)−1 pi 1 mi = Mair Mi   qi mi = 10−3 • Mair ρair Mi  φimass mixingratio, qi [ppm] qi = 103 • Mi NAρair  Ni qi = 103 • Mi ρair   ci qi = 106 • Mi pMair   pi qi = Mi Mair  mi 1 qi = 10−3 • ρ air ( )−1φidensity, φi[μg/m3] φi =106 • Mi NA   Ni φi =106 • Mi ( )ci φi =106 • M i R Tg   pi φi =103 • ρairMi Mair   mi φi =103 • ρair ( )qi 1

Table 6A.1. Conversion formula among various trace gas concentration units used in the CMAQ system

Note: Values for the Avogadro’s constant (NA)) is 6.0221367x1023 [number/mol], the universal gas constant (Rg) is 8.314510 [J/mol-K], and the Boltzmann’s

constant (kB) is defined with Rg/ NA. Molar mixing ratio is equivalent to volume mixing ratio and their units [ppmV], [ppb], and [ppt] are short hand notations for

[ ], [ ], and [ ], respectively. The unit for mass mixing ratio, [ppm], is a short hand for [ ]. Both and may represent values for dry air or moisture air dependingon applications. However, in one processing system, their usage should be consistent. and (molecular weight of species i) are in [g mol-1] and is in [kg m-3].
EPA/600/R-99/030

Chapter 7

NUMERICAL TRANSPORT ALGORITHMS FOR THE COMMUNITY MULTISCALE

AIR QUALITY (CMAQ) CHEMICAL TRANSPORT MODEL IN GENERALIZED

COORDINATES

Daewon W. Byun,*

 Jeffrey Young,** and Jonathan Pleim**

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

M. Talat Odman+

 and Kiran Alapaty

MCNC-Environmental Programs

P.O. Box 12889, 3021 Cornwallis Road

Research Triangle Park, NC 27709-2889

ABSTRACT

The transport processes in the atmosphere primarily consist of advection and diffusion, except

for the mixing of pollutants by the parameterized subgrid-scale clouds. In this chapter, numerical

algorithms for advection, vertical diffusion, and horizontal diffusion implemented in the

Community Multiscale Air Quality (CMAQ) chemical transport models are discussed. To

provide the CMAQ system with multiscale capability, we have formulated the transport

processes, both advection and diffusion, in conservation (i.e., flux) forms for the generalized

coordinate system. Therefore the numerical transport algorithms implemented in CMAQ will

function under a wide variety of dynamical situations and concentration distribution

characteristics. Users can not only choose transport algorithms from optional modules available

in CMAQ, but also are encouraged to experiment with their own algorithms to test different

numerical schemes for air quality simulations.

 

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Daewon W. Byun, MD-80, Research Triangle Park, NC 27711.

E-mail: bdx@hpcc.epa.gov

**On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

+

Present Affiliation: Georgia Institute of Technology, Atlanta, GA.
EPA/600/R-99/030

7-1

7.0 NUMERICAL TRANSPORT ALGORITHMS FOR THE COMMUNITY

MULTISCALE AIR QUALITY (CMAQ) CHEMICAL TRANSPORT MODEL IN

GENERALIZED COORDINATES

In this chapter, we study numerical algorithms for the transport processes in a turbulent

atmosphere. Many of the contents provided here are the results of a collaborative research

project, the EPA’s Cooperative Agreement CR822053-01 with MCNC-Environmental Programs

(Exploratory Research on Air Quality Modeling Techniques: Research on Numerical Transport

Algorithms for Air Quality Simulation Models), and other related in-house projects at EPA.

Readers are referred to Alapaty et al. (1997), Byun (1999a, b), Byun and Lee (1999), and Odman

(1998) for additional information.

In principal, the transport process consists of advection and diffusion that cause the movement

and dispersion of pollutants in space and time. Transport of pollutants by the parameterized

subgrid-scale cloud modules is not considered here. We have assumed that the transport of

pollutants in the atmospheric turbulent flow field can be described by means of differential

equations with appropriate initial and boundary conditions. In Eulerian air quality models, the

transport process is modeled using numerical algorithms. These numerical algorithms for the

advection and diffusion processes must satisfy several properties that are essential for making

useful air quality simulations. As with all numerical methods, the numerical schemes for solving

the transport equations must meet convergence conditions and correctly model the conservation,

dissipation, and dispersion properties of the governing equations. A numerical scheme is said to

be convergent if the solution approaches the true solution of the corresponding partial differential

equation as the grid spacing and time-step size become infinitesimally small. Thus, a convergent

numerical scheme can provide a numerical solution of any desired accuracy within finite precision

bounds by reducing the grid spacing and the time-step size. For linear equations, consistency and

stability are both necessary and sufficient conditions for convergence (Lax’s equivalence

theorem). In practice, machine precision and the computational resource availability limit the

reduction of grid spacing and time-step size. Therefore, numerical errors associated with using

limited grid spacing and time-step sizes must be of concern.

There have been many studies on the numerical advection algorithms used in air quality models.

The reason it attracted so much attention is that the equation is hyperbolic in nature and spatial

discretization of the solution generates a finite number of Fourier modes that travel at different

speeds and leads to constructive and destructive interference. If the high wave-number Fourier

modes are damped significantly, then numerical diffusion becomes prevalent. Solving the

diffusion equation, on the other hand, is a lot safer because the stiffness matrix is diagonally

dominant and the discretized solution is stable and sign preserving for a relatively wide range of

conditions (Chock, 1999).
EPA/600/R-99/030

7-2

Transport processes are of central importance in turbulent flow studies, and in the literature there

are numerous transport algorithms that have different numerical characteristics and varying

degrees of accuracy and computational complexity. The skill needed here is to select appropriate

numerical schemes that provide solutions with the desired accuracy at reasonable computational

cost. This document does not intend to provide an extensive review of the transport algorithms

used in air quality modeling. Instead, we describe several popular numerical schemes

implemented in the Community Multiscale Air Quality Chemical Transport Model (CMAQ

CTM or, hereafter, CCTM), expecting users to choose the algorithms appropriate to their own

study objectives. We offer a few examples of good transport algorithms and present some key

numerical characteristics users should look for. With this information, users can find the best

algorithms through evaluation processes, and may even bring in their own algorithms to build a

transport model for their applications. To provide the CMAQ system with the multiscale and

multi-pollutant capabilities, we strive to incorporate schemes that can function under a wide

variety of dynamic situations and distribution characteristics (e.g., distributions of different

primary species and secondary species are quite distinct). Also, the schemes should be efficient

in the use of computer time and storage. Selected numerical transport algorithms for horizontal

and vertical advection and for vertical and horizontal diffusion are described below.

7.1 Numerical Advection Algorithms

Numerical advection algorithms for air quality models should satisfy several computational

requirements.

• They should be free of mass conservation errors to accurately account for pollutant

sources and sinks.

• They should have small numerical diffusion to minimize the spread of a signal in every

direction and the smoothing of spatial gradients.

• They should also have small phase errors since disturbances that propagate at different

speeds produce spurious oscillations.

• Given initial positive concentrations, the schemes should be positive-definite (i.e., they

should not produce negative concentrations.

• They should be monotonic (i.e., they should not produce new extrema).

While it is essential that the schemes be positive-definite, this alone may not be sufficient

because the monotonic property, for example, is just as desirable for air quality modeling.
EPA/600/R-99/030

7-3

Numerical algorithms have not been able to satisfy all the requirements listed above, and they are

imperfect, with varying degrees of accuracy. Advection schemes with different properties

introduce different errors, all of which are sources of uncertainty in air quality model predictions.

Before recommending its use, it is critical to identify which of the computational properties a

scheme possesses. Because an advection scheme with all the desired properties is not currently

available, a user needs to select a scheme with the most desirable properties and greatest

efficiency to meet the needs of the application.

7.1.1 Conservation Form Equation for Advection

The atmospheric advection process is expressed in conservation (flux) form as:

∂φ

∂ φ ∂ φ∂ ξ ξ

i

adv

i

i

t

v

x

*

*

*

ˆ ( ˆ )

ˆ = −∇ • ( ) V −

3

3 (7-1)

where * φi is the concentration of trace species i coupled with the coordinate Jacobian. Refer to

Chapters 5 and 6 for the definition of symbols used in Equation 7-1. For convenience, the

advection process is decomposed into horizontal and vertical advection processes, with the

fractional time-step implementation:

∂φ

∂ φ ∂ φ∂

∂ φ

∂ ξ ξ

i

hadv

i

i i

t

v

x

v

x

*

*

* *

ˆ ( ˆ )

ˆ

( ˆ )

ˆ = −∇ • ( ) V =− −

1

1

2

2 (7-2)

∂φ

∂

∂ φ

∂

i

vadv

i

t

v

x

* * ( ˆ )

ˆ = −

3

3 (7-3)

where vˆ

1

, vˆ2 and vˆ

3

 are contravariant components of wind velocity. Splitting of the threedimensional (3-D) advection into the horizontal and vertical components will lead some

difficulties, such as the representativeness of the mass continuity and setting up of proper

boundary conditions for non-orthogonal horizontal and vertical directions when simulating a

region with complex topography.

Many models further split the horizontal advection equation in two directions and solve for two

one-dimensional equations, one in each direction, using the solution of one as the initial condition

of the other. We refer to this scheme as a one-dimensional (1-D) algorithm. Others solve the

two-dimensional (2-D) form directly. Although using 1-D schemes is very common, it has been

found that problems can arise due to this additional splitting (Flatoy, 1993, and Odman and

Russell, 1993). Although 2-D schemes may be more desirable in this regard, fewer have been

tested and they are often more difficult to implement and less computationally efficient than 1-D

schemes. Also, there are general conditions in which the splitting scheme is actually more stable
EPA/600/R-99/030

7-4

and accurate than the non-splitting case for higher-order approximations because the splitting

scheme intrinsically contains cross-spatial derivatives whereas the non-splitting scheme would

not (Leith, 1965). Yanenko (1971) has shown that time-splitting is second-order accurate if the

one-component advection operators commute. Alternating the sequence of operations would be

quasi-second-order accurate in the case of non-commutativity (Chock, 1999). Here, only 1-D

schemes will be discussed. When using appropriately interpolated contravariant wind

components, the 1-D advection in the generalized coordinate system is equivalent to the 1-D

equation in the Cartesian coordinate system. Therefore, it is sufficient here to discuss advection

algorithms in Cartesian coordinates.

The 1-D advection equation written in the Cartesian coordinate system is:

∂φ

∂

∂ φ

t ∂

u

x

+ = ( ) 0 (7-4)

Equation 7-4 is the flux (or conservation) form and the quantity Fx = uφ is defined as the onedimensional constituent flux. The flux form is a natural choice here because it is based on the

continuity equation without any assumptions on the atmospheric dynamics. Maintaining the

advection equation in flux form is key to providing transport schemes with multiscale and multipollutant capabilities. A flux-form discretization of Equation 7-4 with first-order accuracy in

time results in:

φ φ j

n

j

n

j

j

n

j

n t

x

F F + =− − ( ) + −

1

12 12

∆

∆ / / (7-5)

where Fj

n

+1 2/ and Fj

n

−1 2/ denote the advective fluxes through the faces of cell j, ∆t is the time-step

and ∆xx x jj j = − +12 12 / / − is the horizontal grid spacing. To maintain numerical stability, and to

accommodate other physical changes such as emissions input in a synchronized way, the timestep of 1-D advection should satisfy the Courant-Friedrich-Lewy (CFL) condition for hyperbolic

equations:

j

max j ( ) β +1 2/ ≤ 1 (7-6)

where β j j

j

u

t

x + + 12 12 / / = ∆

∆

 is the Courant number for advection. This condition should be viewed

as a method defining a reference time scale for accommodating different physical processes in

AQMs. If we do not consider the synchronization of mass injection to the cell through other

physical processes, the CFL condition can be determined separately for individual advection

schemes. For certain schemes the restriction can be significantly less than one. And for
EPA/600/R-99/030

7-5

advection alone, an implicit scheme may not have the Courant number restriction for stability

(Chock, 1999).

7.1.2 Classification of Advection Schemes

Numerical advection schemes in the literature were developed using several different approaches

(e.g., Chock and Dunker, 1983, and Chock, 1985, 1991). Following Rood (1987), we classify

these schemes based on the methods used in their formulations. However, reviews in the

literature may not capture the most recent developments in advection research. Depending on

the methods used, the schemes may be classified as:

• Finite difference schemes;

• Finite volume schemes;

• Flux corrected schemes;

• Lagrangian Schemes;

• Finite element schemes; or

• Spectral schemes.

The distinction is somewhat arbitrary and only meant to convey the key intrinsic features of the

scheme. Current trends in advection scheme development show a merging of the methods to take

advantage of the most desirable properties of several schemes. For example, the CharacteristicGalerkin method (Childs and Morton, 1990) combines the best of the finite element and

Lagrangian methods. Flux corrections are being used in the framework of finite element and

spectral schemes (Löhner et al., 1987). Also, the classical finite difference schemes are being

abandoned in favor of modern finite volume schemes. Refer to Odman (1998) for details of the

classification.

7.1.3 Description of Advection Schemes in CCTM

In this section we describe the schemes that are available with the first release of the CCTM

codes in the following order: the piecewise parabolic method (PPM), the Bott scheme (BOT),

and the Yamartino-Blackman Cubic scheme (YAM).

Odman (1998) provides additional descriptions of the Smolarkiewicz scheme (SMO), the

accurate space derivative scheme (ASD) (Chock,1991, and Dabdub and Seinfeld,1994), the fluxcorrected transport, the semi-Lagrangian method, and the chapeau function scheme with Forester

filter. These codes are not integrated into the CMAQ system yet, but along with other advection

modules, will be added to the system in the near future.
EPA/600/R-99/030

7-6

To simplify the discussion, we will consider a uniform (i.e., constant j ∆x = ∆x ) and staggered

grid (φj represents the grid cell average of the concentration, while uj+1/2 is the advection velocity

defined at grid cell interfaces). While discussing the finite-volume schemes (the piecewise

parabolic method, the Bott scheme and the Yamartino scheme) below, we use the explicit flux

formula presented in Equation 7-5. Further, a nondimensional coordinate η is defined as η =(x -

xj-1/2)/∆x, so that, in grid cell j, 0 ≤ η ≤ 1. Now, suppose that the concentration has a certain

distribution φj(η) in each grid cell. Depending on the direction of the velocity, the flux Fj+1/2 can

be expressed as:

F

x

t

d u

x

t

d u

j

j j

j j

j

+ j

−

+

+ +

=

≥

<















+

+

∫

∫

1 2

1

1

1 2

1

0

1 2

1 2

1 2

0

0

/

/

/

() ,

() ,

/

/

∆

∆

∆

∆

φη η

φ ηη

β

β (7-7)

where βj+1/2 is the Courant number at the right boundary of grid cell j.

The conditions of high-order accuracy and freedom from spurious oscillations are difficult to be

achieved simultaneously. The usual way to satisfy one of these conditions without significant

violation of the other is to introduce a correction mechanism. Typically, this mechanism is

provided by nonlinear flux-corrections, or by nonlinear filtering. In advection schemes, such

adjustments are either applied implicitly through the solution or explicitly as a subsequent step

to the linear solution. There is extensive literature on both solution algorithms (linear and

nonlinear) and explicit nonlinear mechanisms.

7.1.3.1 Piecewise Parabolic Method (PPM)

In the piecewise parabolic method (Colella and Woodward, 1984) the concentration distribution

is assumed to be parabolic in any given grid cell. In terms of the grid cell average concentration φj

and the predicted values of the parabola at the left and right boundaries of the cell φL,j and φR,j,

this distribution can be written as:

φη φ ηφ φ φ φ φ

j Lj Rj Lj j η n Lj Rj ( ) =+ − ( ) + −  +



 



( ) − 



 

 , ,,  , , 6

2

1 (7-8)

Since the initial cell average is known, the construction of the parabola involves the determination

of the edge values. First, an approximation to φ at xj+1/2 is computed subject to the constraint
EPA/600/R-99/030

7-7

that its value is within the range of the values at the neighboring cells. For the uniform ∆xj , a

first guess for φj+1/2 is estimated with:

c cc c c j j

n

j

n

j

n

j

n

+ + +− 12 1 2 1 = +− +

7

12

1

12 / ( )( ) (7-9)

In smooth parts of the solution away from extrema, φL,j+1 = φR,j = φj+1/2 so that the distribution

is continuous at xj+1/2. In other parts, the cell boundary values are further modified so that φ is

monotonic on each grid cell. This step introduces discontinuities at cell edges and yields a

piecewise continuous global distribution for concentration. There are two cases where the edge

values are modified. First, if φj is a local extremum, then the distribution is assumed to be

constant instead of parabolic. The second case is when φj is between φL,j and φR,j, but

sufficiently close to one of the values so that the parabola may take on values outside the range,

and lead to overshoots or undershoots. In this case, to make the distribution monotonic, one of

the edge values is reset so that the derivative of φ (η) is zero at the opposite edge.

The most distinctive feature of this monotonic scheme is that the nonlinear adjustments are

purely geometric. The numerical diffusion introduced by this scheme may be slightly higher than

in some other schemes discussed here, but its monotonic property is desirable for photochemical

modeling purposes. The scheme has been used in meteorological modeling (e.g., Carpenter et al.,

1990) and in air quality models (Odman et al., 1993) including the CCTM. The scheme can be

modified so that, in the neighborhood of a discontinuity, it produces a narrower profile. This

feature, known as steepening, avoids the smearing of sharp gradients. Though Carpenter et al.

(1990) did not recommend steepening for meteorological modeling, this feature may be beneficial

in air quality modeling practice, where steep gradients may occur in the vertical direction.

However, it should be noted that steepening is of no value and the PPM reverts to a lower order

method in the case of sharp spikes or extreme values in a single cell such as emissions from point

sources.

7.1.3.2 Bott Scheme (BOT)

The numerical scheme introduced in Bott (1989) is a positive definite scheme with small

numerical diffusion. The distribution of the concentration within the cell is represented by a

polynomial of order l as:

φη η j j k

k

k

l

( ) a = ,

=

∑

0

(7-10)

The polynomial can be made area-preserving by requiring:
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7-8

φ ηη j i j k

k

k

l

i

i

+ a d

=

+

= ∫ ∑ ,

0

1

, i l = ±± ± 012

2 , , ,..., (7-11)

over a stencil of l+1 grid cells by varying the value of i. The solution to this linear system yields

the coefficients aj,k. The coefficients obtained this way for a quadratic (l=2) and quartic (l=4)

together with those of the donor cell (or upwind) scheme, and Tremback’s scheme with secondorder polynomials (Tremback et al., 1987), are listed in Table 7-1.

Using Equation 7-7, integrating the polynomial of Equation 7-10 between appropriate limits, we

arrive at a first estimate of the fluxes. Finally, to make the scheme positive-definite, the total

outflux from cell j is limited by requiring that it should be positive and less than what the

available mass in the cell would allow:

0 ≤ ≤ F x

t

c j j

out ∆

∆ (7-12)

The outflux Fj

out is a combination of the boundary fluxes and its expression depends on the sign

of the velocities. In the CCTM implementation, we used fourth-order polynomials as

recommended by Bott (1989) except for the boundary cells. The scheme is receiving increasing

attention in current air quality models because of its high accuracy and low computational cost.

Recently, a monotonic version of the scheme was also developed (Bott, 1992) and the timesplitting errors associated with the use of one-dimensional operators in multidimensional

applications were reduced (Bott, 1993). Monotonicity is obtained by directly replacing the

positive-definite flux limiter of the original approach by new monotone flux limiters as:

min , max ,

min , max ,

φφ φ φφ

φφ φ φφ

j

n

j

n

j

n

j

n

j

n

j

n

j

n

j

n

j

n

j

n

u

u

−

+

−

+

+

+

( ) ≤ ≤ ( ) ≥

( ) ≤ ≤ ( ) <

1

1

1

1

1

1

0

0

 , if 

 , if 

(7-13)

Although the new flux limited Bott scheme yields monotonic results, there is an inherent mass

conservation problem. This problem is directly related to the flux limiting that takes place. Near

the leading edge of a sharp wave the use of second or higher order polynomials causes an

underestimation of a certain advective flux, Fk-1/2. When this flux is not corrected it is less than

Fk+1/2, and an undershoot occurs in cell k, as experienced with the original algorithm (Bott, 1989).

The motivation for the monotone flux limitation is to avoid such undershoots. However, there

are cases when the monotone flux limiter leaves the underestimated flux intact. Instead of

increasing the underestimated flux, the limiter reduces the advective flux downwind, Fk+1/2, in

order to avoid an undershoot in cell k. This eventually reduces the net flux out of the domain

resulting in an accumulation of mass in the domain.
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Table 7-1. Coefficients of the Polynomials Used in Each Scheme

Donor

Cell

Tremback-2 Bott-2 Bott-4

a0

φ j φ j − −− ( ) + −

1

24 φ φφ j jj 1 1 26 1

1920

9 116 2134 116 9 ( ) φ φ φ φφ j j j jj + + −− 2 1 12 −+−+

a1

— 1

2 ( ) φ φ j j + − 1 1 − 12 ( ) φ φ j j + − 1 1 − 148 ( ) −+ − + 5 34 34 5 φ φ φφ j j jj + + −− 2 1 12

a2

— 1

2

2 ( ) φ φφ j jj + − 1 1 − +

1

2

2 ( ) φ φφ j jj + − 1 1 − +

1

16 ( ) −+ − + − φ φ φ φφ j j j jj + + −− 2 1 12 12 22 12

a3

—— — 1

12 ( ) φφφφ j jjj + +−− 2112 −+− 229

a4

—— — 1

24 ( ) φ φ φφφ j j jj j + + −− 2 1 12 − +− + 4 64

7.1.3.3 Yamartino-Blackman Cubic Scheme (YAM)

Yamartino (1993) presents another finite volume scheme where the interpolating polynomial is a

cubic spline:

φη η η η j( ) =+ + + aa a a 01 2

2

3

3 (7-14)

where a0 = φ j

a dx 1 = j ∆

a

x

2 1 1 11 j jj j j d d 1

4

2 3

8

=− − + ( ) φ φφ + − +− + − ( ) ∆ (7-15)

a

x

3 11 1 1 j j j jj d dd

6 = − ( ) φ φ +− + − − ++ ( ) 10 ∆

The spline derivatives, dj , are obtained from the tridiagonal system:

α αα

φ φ d dd

x j jj

j j

− +

+ − + − ( ) + = − 1 11 1 1 2

2∆ (7-16)

with α=0.22826. Note that a value of α=0 would correspond to explicit expressions of dj .
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The positivity of φ ηj( ) is ensured by various mechanisms. First, when φj is a local minimum, a

donor-cell scheme is used instead of the cubic spline. Second, the spline is spectrally limited by

the relation:

a

a k

k k

k

0

≤ = 123 π

!

, , , . (7-17)

Third, a mass conservative flux renormalization is applied, where the fluxes are normalized with

the ratio for the upwind cell of the cell concentration (i.e., concentration at η=0) divided by the

average concentration. Finally, a mildly diffusive filter is applied in an attempt to block the

depletion of donor cells. Yamartino’s scheme is not monotonic and can generate new maxima.

7.1.4 Treatment of Boundary Conditions

Mathematically, the advection equation is a first-order hyperbolic partial differential equation, so

it accepts only inflow boundary conditions. Physically, the solution is not affected by the

downwind concentrations, so no outflow boundary conditions should be imposed. In practice,

however, some outflow boundary conditions have to be imposed. Often, the characteristics of a

numerical advection scheme are affected by the boundary condition used.

In the CCTM, a positive-definite zero-flux outflow boundary condition with appropriate flow

divergence restriction is used. The zero-flux divergence condition at the boundary (flux gradient

out of the boundary cell is set equal to the flux gradient into the cell, i.e.,

u xu x 11 0 2 2 1 ( )/ ( )/ φφ φφ − =− ∆ ∆ ) gives:

φ φ φφ 0 1

2

1

2 1 = −− 0













max , ( ) u

u

(7-18)

where φ0, φ1, and φ2 represent concentrations outside the computational domain, at the boundary

cell, and first cell of the inner domain, respectively. u1 is wind at the outer boundary flux point

and u2 is wind at the inner boundary flux point. Refer to Figure 7-1 for the cell subscript

definitions at the outflow boundary. To prevent spurious boundary flux situations that are often

associated with the zero-flux divergence boundary condition, the following constraints are

applied. When u1 is sufficiently small (for example smaller than 10-3 m/s), or when the wind is

divergent at the boundary cell (i.e., u1• u2 < 0), a zero concentration gradient at the outflow

boundary (i.e., φ φ 0 1 = ) is imposed. This boundary scheme can be used with any of the

numerical advection algorithms implemented in CCTM.
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On the other hand, Odman (1998) introduced a “no condition at outflow boundary” [sic], for

Bott’s scheme where the scheme is modified to remove the need for the concentration φ 0 at the

downwind cell. A first-order polynomial (derived from φ 1 and φ 2) is used in Cell 1 to compute

the flux out of the domain. A second-order polynomial (derived from φ 1, φ 2 and φ 3 is used in

Cell 2 and a fourth-order polynomial is used in Cell 3. Mathematically, this condition is more

correct than the others. However, the order of the polynomial is reduced to one at the boundary

while the other conditions use a second-order polynomial to compute the flux out of the domain.

Because of the lack of generality of this approach, we have not implemented Odman’s boundary

scheme in the CCTM. The improved positive-definite zero-flux outflow boundary condition

scheme essentially reproduces his results without having to rely on the modified advection

algorithms near boundary.

u1 u2

φ0 φ1

0 12 3

Figure 7-1. Outflow boundary condition. Cell 0 is outside the domain. Vertical solid line

denotes the domain boundary and the vertical dotted lines denote the cell interfaces. The

advection scheme computes concentrations for Cells 1, 2, 3, and so on.

7.1.5 Test of Algorithms with Idealized Linear Horizontal Flow Fields

Typically, the performances of advection schemes are measured and compared with each other

using test cases with idealized flow fields. These ideal flow tests have analytic solutions and

may be very useful for determining certain properties of the schemes. Odman (1998) provides

some evaluation results identifying schemes with desirable properties. Here we summarize the

results of the one-dimensional tests and rotating cone test. The evaluation and comparison of the

schemes are based on the performance measures listed in Table 7-2. Again, readers are referred to

Odman (1998) for the details of the analysis.
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Table 7-2. Summary of Performance Measures Used to Test the Effects of Numerical

Advection. φi

*

 and φi

*e

 methods and exact concentrations.+

Performance Measure Formula Description

peak ratio&

max( )

max( )

*

*

φ

φ

i

i

e

Measure of peak preservation (best when 1.0)

Background to peak ratio min( )

max( )

*

*

φ

φ

i

i

e

Measure of ripples introduced by a nonmonotonic scheme

mass ratio ( )

( )

*

*

φ

φ

i

i

e

∑

∑

Measure of mass conservation characteristic

(best when 1.0)

Distribution ratio ( )

( )

*

*

φ

φ

i

i

e

2

2

∑

∑

Measure of shape retention (best when 1.0)

Average absolute error 1

N i i

e | | * * ∑ φ φ− Measure of absolute difference (best when 0.0)

root-mean square error 1

2

N

i i

i

e

e

φ φ

φ

* *

*

 −



 

 ∑ 

Measure of distribution error (best when 0.0)

 + To account for the total mass correctly, the concentration should be coupled with the Jacobian of the grid system

 & Peak ratio alone is not a meaningful criteria unless the positions of the computed and actual peaks are also given.

7.1.5.1 Advection of One-Dimensional Pulses

Various tests have been conducted in the literature with pulses of different shapes advected with

uniform velocity. We conducted tests using a Gaussian signal of exactly 8∆x width with 100

ppm peak advected from cell 25 to cell 75 in a 100-cell uniform grid domain. Background values

were set at 5 ppm. Table 7-3 summarizes the value of various performance measures after

advected the signal for a distance of 50∆x at a Courant number of 0.25 (i.e., after 200 time-steps).

The Accurate Space Derivative (ASD) and Yamartino’s schemes (YAM) preserved the peak

height very well. However, the distribution ratio has a lower value for YAM, indicating

distortions of the pulse’s shape. For the same reason, the average and RMS errors are larger than

those of the ASD. On all accounts, these two schemes perform much better than the other

schemes in this test. Bott’s scheme (BOT) ranks third overall, but large ripples are observed at

leading and trailing edges of the pulse as indicated by the values below the background (as much

as 4% of the peak height). When the monotonic limiter is used (BOT-M), the ripples are

eliminated but the peak retention performance deteriorates. Also, a 2% increase in mass is

observed. PPM is somewhat more diffusive than BOT-M. However, PPM performed better

than BOT-M in minimizing the average absolute error and root mean square error and because it

is intrinsically monotonic, did better in regard to shape retention as measured by the distribution

ratio. Smolarkiewicz’s scheme (SMO) displays poorer performance than the other schemes.
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SMO produces ripples upwind from the pulse and leads to average and RMS errors larger than

other schemes.

Table 7-3. Gaussian signal test (Abridged from Odman, 1998)

Scheme ASD BOT BOT-M PPM SMO YAM

Peak Ratio 0.99 0.87 0.74 0.69 0.61 0.98

Background 0.05 0.01 0.05 0.05 0.02 0.05

Mass Ratio 1.00 1.00 1.02 1.00 1.00 1.00

Distribution 0.99 0.93 0.83 0.79 0.66 0.92

Average Error 0.08 0.87 1.38 1.16 2.21 0.51

RMS Error 0.01 0.18 0.27 0.17 0.50 0.12

7.1.5.2 Rotating Cone Test

In this test, a cone-shaped puff is introduced into a rotational flow field and followed for a certain

number of revolutions. The exact solution is a rigid-body rotation of the puff without any change

to its original shape. Various errors can be revealed in this test. For example, numerical diffusion

(or dissipation) manifests itself in the drop of the peak height during rotation. Also, by

observing the location of the peak, one can determine the leading or lagging phase-speed errors.

A 32x32 grid is used for this test (i.e., −16∆x ≤ x ≤ +16∆x; −16∆y ≤ y ≤ +16∆y ∆x= ∆y ). A

cone-shaped puff with peak concentration equal to 100 ppm and a base radius of 4∆x is

initialized such that its peak is located at [+8∆x , 0]. Note that the peak is not initially at a gridcell center but a cell corner (i.e., there are four cells around the peak with the same average

concentration). The background concentration is set to 5 ppm. To obtain a counterclockwise

rotation around an axis passing through the center of the domain, the wind field is defined

as u y = −ω and v x = ω . The angular velocity, ω, is adjusted so that the Courant number of

approximately 0.28 at the location of the peak of the puff.

Table 7-4. Rotating Cone Test (Abridged from Odman, 1998)

Scheme ASD BOT BOT-M BOT2D PPM SMO YAM

Peak Ratio 0.99 0.87 0.65 0.65 0.61 0.49 0.99

Background 0.06 0.03 0.06 0.06 0.06 0.02 0.06

Mass Ratio 1.00 1.00 1.02 1.02 1.00 1.00 1.00

Distribution 0.96 0.93 0.83 0.83 0.78 0.64 0.91

Average Error 0.18 0.46 0.76 0.76 0.54 1.60 0.33

RMS Error 0.05 0.16 0.30 0.30 0.18 0.51 0.13

ASD and YAM maintain the peak height and the overall shape of the cone better than the others.

BOT performs third best in this test, but it yields non-monotonicity, which results in values

below the background (as seen in a ring-shaped valley at the base of the cone). BOT-M and
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PPM predict similar peak heights (65% and 61%, respectively), but the shape distortions look

very different in each case. PPM has the worst peak clipping effect but the resulting shape has

the smallest base span among the three schemes. SMO is clearly the most diffusive scheme; it

also introduces a ripple upwind from the cone. Table 7-4 summarizes the performance measures

at the end of two rotations. Since there is no shear in the flow field, BOT-M and the twodimensional version of Bott’s scheme (BOT2D) (Bott, 1993) produce identical results. Again,

the mass conservation problem is revealed with BOT-M. BOT preserves 87% of the peak height

(third best after ASD and YAM), but it leads to ripples with an amplitude of 3% of the original

peak height. Performances of BOT-M and PPM are comparable in predicting the peak. But

PPM produces the lower distribution ratio, smaller absolute average and RMS errors. Notice

that the comparison results obtained from this test are very similar to those of the Gaussian

signal test. Additional test results such as skew advection of a point-source plume and advection

with shear flow are available in Odman (1998). Also, effects of density distribution on the

numerical advection are studied with a set of linear flows in Byun and Lee (1999). The solvers

integrated into the CCTM are BOT, PPM and YAM. Although ASD has very high accuracy

except for the 2 ∆x wavelengths, ASD is neither strictly mass conservative nor monotonic. It is

also the most CPU-intensive scheme (taking about 4-5 times longer than BOT). In addition to

BOT’s overall performance, results reported in Odman (1998) for a broad series of tests showed

that BOT had the best computational performance of all the schemes tested. However, because

of the concerns over the non-monotonicity about BOT and the mass conservation problem and

diffusive nature of BOT-M, we chose PPM for a number of demonstration executions (Byun et

al., 1998). Similar testing with BOT and YAM is underway. We intend to integrate other

methods into the CCTM at a later time.

7.1.6 Vertical Advection

Algorithms in the CCTM for vertical advection are essentially the same as those for the onedimensional horizontal algorithms. However, the vertical advection is performed in terms of the

generalized vertical coordinate in CMAQ. The contravariant vertical velocity component is used

as the transport wind for the irregular vertical grid spacing (usually expanding with altitude)

represented in the generalized coordinate. For the irregular grid, the computational time-step

should satisfy the CFL condition:

∆ ∆ ∆ ∆∆t

k vvvv

k k kk

kkkk

≤ − +

−−++

min{

ˆ ,ˆ ,ˆ ,ˆ } ////

ξ ξ ξξ 1

333

1

3 12 12 12 12

(7-19)

As in the case of Cartesian representation, we assume there is no mass exchange by advection

(i.e., vˆ

3 = 0) at the top and bottom boundaries of the model. Therefore, there is no need to apply

special algorithms for the boundary process. Because vertical grid spacing is usually irregular in
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most air quality models, a scheme that can accommodate irregular spacing must be used for

vertical advection. This means that numerical algorithms used to represent the vertical advection

may be different from that used for horizontal advection. For example, when the ASD algorithm,

which requires equal spacing in the computational domain, is used for horizontal advection, a

numerical algorithm that allows irregular spacing (e.g., BOT and PPM) would need to be used for

vertical advection.

7.1.7 Adjustment of Mass Conservation Error

Recently, Byun (1999a, b) has highlighted the importance of dynamic consistency in

meteorological and air quality modeling for multiscale atmospheric applications. Mass

consistency quantifies how well the density and wind fields satisfy the continuity equation for

air. One of the fundamental requirements for the numerical transport algorithms used in air

quality models is the conservation of trace species in the domain. Ideally, the input

meteorological data for air quality simulations should be mass consistent. However, using

numerical models with highly parameterized physical and cloud algorithms, inappropriate set of

governing equations, misapplication of four-dimensional data assimilation (FDDA) schemes, or

using incomplete objective analysis methods to characterize the atmosphere for a CTM could

result in meteorological conditions that are not mass consistent. In this situation, even precisely

mass conserving numerical algorithms may fail to conserve trace species mass in the domain.

Preferably, the mass inconsistency must be minimized before air quality simulation using a

suitable diagnostic relation or a variational wind field adjustment scheme as discussed in Byun

(1999b) and in Chapter 5. For certain vertical coordinates with appropriate dynamic

assumptions, the diagnostic methods can be used within the CTM to provide mass consistent

wind data. This is accomplished usually by adjusting the vertical wind component for the

advection process. However, the variational methods are applied during the meteorological data

preparation stage, instead of inside CTMs, mostly due to the computational efficiency reasons.

Whether the meteorological data are mass consistent or not, Byun (1999b) has shown that the

tracer mixing ratio must be conserved as a precondition for the tracer mass conservation. He has

reported several adjustment schemes used in current air quality models and proposed a two-step

time splitting numerical algorithm that satisfies the mixing ratio conservation equation. In the

event the meteorological data are not mass consistent, the mixing-ratio conservation scheme is

demonstrated to be useful for photochemical air quality models where chemical production and

loss terms are computed using molar mixing ratio. For this purpose, Equation 7-1 should be

modified as follows to conserve trace species:

∂φ

∂

∂ φ

∂

∂ φ

∂

∂ φ

∂ φρ

ii ii ρ

i t

u

x

v

x

v

x

** ** ( ˆ) * Q

ˆ

( ˆ)

ˆ

( ˆ )

ˆ =− − − + 1 2

3

3 (7-20)
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where Qρ is the density error term for the meteorological data. This is a necessary condition for

the tracer mass conservation. The total tracer mass of the domain is conserved only when the

additional condition that total air mass of the domain is conserved, i.e.:

J

m

Q dV s

2 ρ 0

∂Ω

∫∫∫ = (7-21)

where ∂Ω represents the boundary of a computational domain. However, even this condition

does not guarantee the cell base conservation of tracer mass except for the case of uniform mixing

ratio, because φ

ρ

ρ

∂

ρ

∂

ρ

∂

i i

s

i

s Q dV q J

m

Q dV q J

m

Q dV *

ΩΩ Ω

∫∫∫ ∫∫∫ ∫∫∫ = ≠ 2 2 in general. Because of this, the

correction methods should only be used for improving mass conservation characteristics of the

numerical advection algorithms after the mass inconsistency is minimized . Nevertheless, if the

objective is to maintain the property of cell-based mixing ratio conservation, the mass

conservation error caused by the inconsistency in meteorology data (φ

ρ

ρ

i

* Q ) can be corrected

with:

( ) ( ) exp[ ] * * φ φ

ρ

ρ

i

cor

i

T Q = dt ∫ (7-22)

where superscripts ‘T’ and ‘cor’ represent values after transport (advection) and after correction,

respectively. Table 7-5 summarizes several adjustment methods reported in Byun (1999b). An

adequate correction scheme for photochemical Eulerian AQMs should conserve the tracer mixing

ratio at least even if wind and density fields are not mass consistent. The correction scheme

proposed and labeled A5 in Table 7-5 is expected to maintain conservation of mixing ratio up to

machine precision. Correction schemes A1 and A2 ignore the effects of coordinate/grid structures

during the advection process. For Cartesian coordinates where the Jacobian is uniform and

constant with time, the scheme A2 is equivalent to A5. For a steady-state flow, schemes A3, A4,

and A5 become identical. Note that all the correction algorithms in Table 7-5 become the same for

a steady state flow with uniform density distribution in Cartesian coordinates.
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Table 7-5. Trace Gas Mass Correction Schemes

Symbol Correction Method Mass correction algorithm

A0 No correction

A1 Advection of unity φ φ

φ i φ cor i

T

r

= T r

, φr = 1 0.

A2 Advection of air density φ φ

ρ i ρ cor i

T

T = int

A3 Advection of ρ ξ J m/ 2

 with

anelastic approximation

( / ) ( / ) exp ( /)( /)

( /) φ

ρ ρ

ρ ξ ξ

ξ ξ

ξ

i

cor

i

T n

T

n

J m cJ m

Jm Jm

J m

2 2

2 2

2 =  −















A4 Advection of ρ ξ J m/ 2

 with

finite differencing of tendency term

( / ) ( / ) exp ( /) ( /)

( /)

int

int φ φ

ρ ρ

ρ ξ ξ

ξ ξ

ξ

i

cor

i

T

T

Jm Jm

Jm Jm

J m

2 2

2 2

2 =  −















A5 Advection of ρ ξ J m/ 2

 with twostep time splitting

( /) ( /)

( /) ( /)int φ

φ

ρ

ρ ξ

ξ

ξ

i ξ

cor i

T

T J m

J m

J m

J m 2

2

2

2 =

(Note: Superscripts cor, int, and T represent corrected, interpolated, and advected quantities, respectively.)

Byun and Lee (1999) compared the performance of the correction algorithms under several

idealized two-dimensional linear flows and different density fields. In addition, the linearity of

the advection processes was studied to show how well the different precursors from same

sources can be advected without losing their integrity. The characteristics of the correction

procedures can be summarized as follows:

• The correction scheme fixes mass conservation errors due to the time splitting and

numerical algorithms as well as the mass inconsistent meteorological data input.

• The correction scheme does not, however, improve inherent properties of the numerical

advection scheme such as monotonicity, or numerical diffusion.

• In a budget study, such as in process analysis, the adjustment process must be considered

as an integral part of the three-dimensional advection. Horizontal advection, vertical

advection, and the mass correction step all together simulate the atmospheric advection

process.

7.2 Vertical Mixing Algorithms

In this section, we describe turbulence closure schemes for the CCTM. We describe numerical

algorithms for vertical mixing and dry deposition, and discuss the details of the mathematical

representations, integration time-steps and solvers. Unless stated otherwise, the vertical

structures of meteorological and chemical transport models are assumed to be the same. This is
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desirable because the interpolation of meteorological quantities in vertical direction would alter

the original turbulent flux exchange characteristics.

7.2.1 Closure Problem

Because of the stochastic nature of atmospheric motion, the primitive equations in the set

describing the atmosphere are averaged to form a set of deterministic equations before they can be

solved numerically. The decomposition of velocity components and concentrations into mean

and turbulent terms and the application of ensemble averaging produces Reynolds flux terms in

the species mass continuity equation. Introduction of the Reynolds flux terms generates a new

problem set in which the number of unknowns is larger than the number of equations. This

closure problem is caused by the attempt to represent nonlinear processes such as momentum

advection using a linear decomposition such as the Reynolds decomposition. We describe some

approaches on the closure of the Reynolds flux terms below.

7.2.1.1 Local Closure

Local closure assumes that turbulence is analogous to molecular diffusion, i.e., that an unknown

turbulence flux at any point in space is parameterized by values of known quantities at the same

point (Stull, 1988). First order closure retains the prognostic equations for only the mean

variables such as wind, temperature, humidity, and trace gas concentrations while the secondorder moments (Reynolds fluxes) are approximated. An example of a local closure scheme is the

approximation of Reynolds flux terms using a gradient transport theory, or a mixing length theory

resulting in an eddy diffusion method. One of the problems with the gradient transport theory is

finding a rational basis for parameterizing the eddy diffusivity. Also, the theory fails when

eddies larger than the grid size are present, like they are in a convective boundary layer.

The so-called one-and-a-half order closure retains the prognostic equations for the mean variables

and adds equations for the variances of those variables. The set of one-and-a-half order equations

is obtained by simplifying the full second-order turbulence equations. Instead of the velocity

component variance equations, the turbulent kinetic energy (TKE) equation is often used. By

including the variance equations, we have increased the number of unknowns that need to be

parameterized compared to the first-order closure approach. However, the benefit is that the

eddy diffusivity can be parameterized not only with the mean quantities but also with the TKE

and the temperature variance which characterize turbulence intensity. However, if an air quality

model is based on one-and-a-half order closure in a true sense, the prognostic equations of the

variances for the tracer concentrations should be included explicitly. In practical Eulerian air

quality models that deal with photochemical problems, additional prognostic variance equations

for the tracer species are very expensive computationally. Also, the additional closure problem
EPA/600/R-99/030

7-19

must be dealt with by parameterizing the Reynolds average terms involved with the variances for

tracer species. Therefore, the one-and-a-half order closure for an air quality model often actually

means that the diffusion equations for the tracer species are formulated with first order closure,

while eddy diffusivities (if gradient theory is applied for the closure) or turbulent fluxes (if nonlocal flux-based closure is used) are estimated with the TKE information from a meteorological

model with one-and-a-half order schemes for wind, temperature, and humidity.

The set of second-order turbulence equations includes all the second moment terms. To derive

these terms, parameterizations on a full set of third-order moments are required. Similar to the

first-order case, the second-order closure approximates terms involving third moments. Several

basic closure assumptions such as down-gradient diffusion, return to isotropy, and turbulent

dissipation in the inertial subrange are used in the parameterization of the third moment terms.

These parameterizations must be valid, especially, for the scales of the energy-containing eddies

that are sensitive to atmospheric stability. Measurements of high-order moments in the real

atmosphere are difficult because of large scatter in the direct flux measurements and because a

long averaging time or a very large sample size of data is required because the events with a much

lower probability of occurrence must be gathered to estimate higher-order moments using eddycorrelation methods. For air quality applications, especially for a complex chemical reaction

system, the technique requires too many ad-hoc assumptions that cannot be confirmed by

observations or other theoretical reasoning. In addition the second-order closure incurs a

prohibitively high computational cost. As before, we can solve the first-order tracer diffusion

equations with the variances and covariances for wind components, temperature, and humidity

from the second-order meteorological models. For air quality applications, the true second-order

closure formulation solves for the cross-species covariances explicitly. Some researchers have

attempted second-order closure for simple chemical mechanisms with a limited number of

photochemically reactive species. The introduction of additional parameterizations for the thirdorder moment terms among the tracer species themselves and wind components (about which we

lack sufficient knowledge) and the added cost of solving for a large number of covariance terms

make this scheme impractical and prohibitively costly for operational Eulerian photochemical

models.

7.2.1.2 Non-local Closure

Non-local closure recognizes that larger-size eddies can transport fluid across finite distances

before the smaller eddies have a chance to cause mixing. This advection-like concept is supported

by observations of thermals rising with undiluted cores, finite size swirls of leaves or snow, and

the organized circulation patterns sometimes visible from cloud photographs.
EPA/600/R-99/030

7-20

Two main approaches of non-local closure methods are the transilient turbulence theory and the

spectral diffusion theory. Both allow a range of eddy sizes to contribute to the turbulent mixing

process. The spectral diffusion theory attempts to simulate mixing process by transforming

signals into a spectral space. For example, a spectral diffusion model of Otte and Wyngaard

(1996) represents the mean variables within the planetary boundary layer (PBL) by a truncated

series of Legendre polynomials. The first Legendre mode represents the layer average, and

additional modes add structure to the vertical profiles. Only a few modes are necessary to

resolve vertical profiles comparable to high resolution diffusion models. However, the need to fit

a different number of spectral modes for each trace species makes the scheme less attractive for

air quality application and thus it have not been considered here. The transilient turbulence

theory (e.g., Stull, 1988) is a general representation of the turbulent flux exchange process. The

Latin word transilient, meaning to jump over, is used since turbulent eddies that exist in the PBL

can transport mass and momentum directly across several grid layers. A variety of mixing

processes can be modeled with the transilient scheme depending on the form of the transilient

matrix. Examples include complete mixing, top-down/bottom-up mixing, asymmetric convection

mixing, small-eddy mixing, cloud top entrainment, a detraining updraft core, patchy turbulence,

no turbulence, or eddies triggered by the surface layer. Non-local closure is most suitable for

describing vertical turbulence mixing process, which should represent turbulent diffusion and

atmospheric transport by eddies of different sizes simultaneously.

In the following, we describe only the first-order turbulent mixing schemes. The true one-and-ahalf and the second-order closure schemes are not discussed here. We organize the description of

vertical mixing algorithms based on the details of the turbulence parameterization; the eddydiffusion form or the Reynolds-flux form. Both the eddy-diffusion and the Reynolds-flux forms

are capable of accommodating information from higher order turbulence closure for momentum

and other meteorological parameters such as potential temperature and humidity. The vertical

diffusion modules in CMAQ will include two different ways of parameterizing the eddy

diffusivity (using PBL similarity theory and using TKE) and three flux form non-local algorithms

(Blackadar, ACM, and Transilient Turbulence).

7.2.2 Computing Vertical Mixing with the Eddy Diffusion Formulation: K-Theory

The eddy diffusion algorithm in the CCTM computes the following:

∂φ

∂

∂

∂ γ ρ

∂

∂

i

vdiff

i

t x

K q

x

*

ˆ ˆ ˆ ˆ = 



 



 



 

 3  33

3 (7-23)
EPA/600/R-99/030

7-21

where Kˆ 33 is the contravariant vertical component of eddy diffusivity in the generalized

coordinates. The contravariant eddy diffusivity is related to the diffusivities in Cartesian

coordinates as:

ˆ ˆˆˆ K x

x

K x

y

K x

z xx yy zz K 33

3 2 3 2 3 2

= 



 



 + 



 



 + 



 



 ∂

∂

∂

∂

∂

∂

= + 



 



 +





 



 − J m h

x

m

h

x ξ K K H zz

∂

∂

∂

∂

2

1

2

2

2 ( ˆ ) ( ˆ ) (7-24)

where J x

z ξ

∂

∂

− =1

3 ˆ . Here we focus on the parameterization of the eddy diffusivity, Kzz, in a

generic Cartesian vertical coordinate z (geometric height h). Parameterizations of the horizontal

eddy diffusivity are described later. However, in the current CMAQ implementation, the term

involving horizontal diffusivity KH in Equation 7-24 for the estimation of Kˆ 33 is neglected.

Evaluation of the effects of this simplification is left for future work.

7.2.2.1 Parameterization of Vertical Eddy Diffusivity Kzz with PBL Similarity Theory

There are several eddy diffusivity parameterizations using different similarity theories. Since

these are somewhat similar, we consider the formulations suggested by Businger et al. (1971) and

Hass et al. (1991) to represent the turbulent process in the surface layer and mixed layer.

Previous studies (Chang et al., 1987, and Hass et al., 1991) indicated that this type of

formulation can represent turbulent mixing in air quality models adequately. With K-theory, we

assume that trace species have non-dimensional profile characteristics similar to potential

temperature,Θ, i.e., Kzz = Kh. We briefly describe the surface and boundary layer similarity

theory used for the parameterization of eddy diffusivity for different stability regimes of the

PBL below. The stability regime is defined with a nondimensional number z/L, where z is the

height above the ground and L is the Monin-Obukhov length.

For the surface layer, the non-dimensional profile functions of the vertical gradient of Θ are

expressed as:

φ β h o h

z

L

= + Pr ( ) 1 for moderately stable conditions (1 ≥ z/L ≥ 0) (7-25a)

φ γ h h

z

L = − −

( ) /1 1 2 for unstable conditions (z/L < 0) (7-25b)

where Pro is the Prandtl number for neutral stability and βh and γ h are coefficients of the profile

functions determined through field experiments. In addition, following Holtslag et al. (1990) we
EPA/600/R-99/030

7-22

add a function for the very stable condition (z/L ≥ 1) to extend the applicability of the surface

layer similarity:

φ β h o h

z

L

= + Pr ( ) (7-25c)

Parameterizations for eddy diffusivity for the surface layer can be shown as:

(z / L )

ku z

K

h

*

h

φ = (7-26a)

where u* is the surface friction velocity.

For the PBL (above the surface layer), eddy diffusivity is parameterized with:

K ku z z h

z L h

h

= * − / ( /)

(/ )

1 3 2

φ

for z

L

> 0 (stable) (7-26b)

K kw z z h h = − * ( /) 1 for z

L

< 0 (unstable) (7-26c)

In the above expressions, h is the depth of the boundary layer, k the Von Karman constant, and

w* the convective velocity. Refer to Chapter 12 for the method used to estimate the PBL height

in the CMAQ modeling system.

These parameterizations for Kh are sensitive to the boundary-layer height (h) and surface-layer

height. Therefore, when the vertical resolution is too coarse in the boundary layer, using a

"representative" eddy diffusivity together with the mean-concentration gradient at the interface

seems to be more appropriate for the estimation of the diffusive flux. In fact, the diffusive flux

across the interface can be estimated more accurately with the mean diffusivity and mean

concentration gradient than with local diffusivity and mean concentration gradient; the former has

an error of Ο ∆[( ) ] ξ 2 (at best) while the latter has an error of Ο ∆[ ] ξ . To estimate the

"representative" eddy diffusivity at the layer interface, integrated eddy diffusivity formulas are

used as in RADM and CMAQ. They are summarized in the following equations (Byun and

Dennis, 1995)

• Surface Layer

(a) Stable conditions:
EPA/600/R-99/030

7-23

 

K

z z

ku z

z L

dz ku

z z

z z z

z

h

z o h

z

o

= 1

1

1 1

21 21 1

2 1

1 1

2

1 1

2

− + = −

− − +

+





 









 

 ∫  * *

Pr ( / ) Pr ( ) β ββ

β

β

ln 1

1

 (7-27a)

where β β

1 = h

Pro L .

(b) Unstable conditions:

K

z z

ku z

z L

dz h

z o h

z

= 1

2 1 1 1

2

− − ∫ *Pr ( / ) γ

= ( ) −

( ) − ( ) + − ( ) − ( ) + 















ku

z z

z zzz

o

*

Pr 2 1

2 2

3

2

2

1 1

3

2

2

23 2 1

15

23 2 1

15

α α

α

α α

α

(7-27b)

where α = - γ h /L.

• Planetary Boundary Layer

(a) Stable conditions:

 

K ku

z z

z zh

z L

dz

r a

r a ar

r a

r a ar

a a

a

a

h

z o h

z

= −

−

+

= + − + − ( ) 



 



 − + − + − ( ) 



 





= − ( ) ( ) +

∫ *

/ ( /)

Pr ( / ) 2 1

3 2

2

5 2

2

3 42

2

1

5 2

1

3 42

1

6 4

1

1

5

1

3 5

1

3

1

2

1

2

β

ln 2 a r −

+ + ( )





 





r

a r

1

1 a r2

(7-27c)

where r zh 1 1

1 2 = − ( /) 1 / , r zh 2 21 2 = − ( /) 1 / , a

2 = + ( )/ 1 δ δ , andδ β = h

o

h

Pr L .

(b) Unstable conditions:

K kw

z z

z

z

h

dz h

z

z

 = * ( )

2 1

2

1

2

− − ∫ = + − + + kw z z z zz zh *[ 21 2

2

21 1

2

2 3 ] (7-28)

In the free atmosphere above the mixed layer, turbulent mixing is parameterized using the

formulation as implemented in RADM (Chang et al., 1987), in which vertical eddy diffusivities

are represented as functions of the bulk Richardson number and wind shear in the vertical. This

formulation can be written as:
EPA/600/R-99/030

7-24

KKS Ri Ri

Ri h o

c B

c

= + 2 − (7-29)

where the Richardson number is defined as

k

k

o

B

S z

g Ri

∆

∆Θ

Θ = 2 , Ko is the background value set at

1 m2 s-1, and S is the vertical wind shear. Effects of the parameterization, Equation 7-29, on air

quality simulation will be evaluated in near future. Furthermore, not much is known of the eddy

diffusivity formulas for strong stable condition (i.e., z/L > 1) and therefore require further

research in this area.

7.2.2.2 Estimation of Vertical Eddy Diffusivity Using Turbulent Kinetic Energy

Various forms of higher order closure schemes are becoming common in mesoscale meteorology

models. Typically, such models are referred to as TKE models. The simplest form of a TKE

model, which Mellor and Yamada (1974) referred to as level 2.5, has only one second order

prognostic equation, for TKE itself. The next level up in complication is the true one-and-a-half

order closure model, level 3 in Mellor and Yamada (1974) nomenclature, which in addition to

TKE includes prognostic equations for the turbulent variances of other relevant quantities such as

temperature and humidity. The TKE scheme in the latest version of MM5 can be run as either

level 2.5 or level 3 where prognostic equations for temperature variance, moisture variance, and

temperature-moisture covariance are added to the TKE equation (Burk and Thompson, 1989).

Another similar form of a higher order closure model is known as TKE-ε, which has prognostic

equations for TKE and the turbulent dissipation rate (ε). An example of this type of model is

described by Alapaty et al (1996).

A common feature of TKE models, for level 2.5 or 3 or TKE-ε, is that the turbulent fluxes of

momentum, heat, and moisture are represented as local gradient diffusion similar to Equation 7-

23. It is this characteristic that distinguishes 1.5 order closure from true 2nd order closure where

the flux covariances are explicitly represented by prognostic equations. Therefore, adaptation of

a CTM to a meteorology model that includes TKE closure is essentially simple if the TKE fields

are available to the CTM. Only a small part of the TKE model need be reproduced in the CTM,

namely the parameterization of eddy diffusion coefficients based on quantities already produced

in the meteorology model. For example, in the TKE-ε model of Alapaty et al. (1996), the

governing TKE equations in Cartesian coordinates are:

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

E

t

u

E

x

v

E

y

w

E

z

u w

u

z

v w

v

z = −− − − − "" ""
EPA/600/R-99/030

7-25

+− + 



 



 − g w

z

wE pw Θθ ∂

∂ ρ "" "" "" ε

1 (7-30a)

∂ε

∂

∂ε

∂

∂ε

∂

∂ε

∂

ε ∂

∂

∂

∂

θ

t

u

x

v

y

w

z

c

E

u w

u

z

v w

v

z

g = −− − + − − + w 



 



 1 "" "" "" Θ

− − ( ) c

E

c

z

w 2

2

3

ε ∂

∂ " "ε , (7-30b)

where u, v are horizontal wind components;

E is the turbulent kinetic energy per unit mass;

z is height;

Θv

 is the virtual potential temperature;

ε is the rate of TKE dissipation;

u w" ", v w" ", and g w

Θ

θ" " are turbulence fluxes of momentum components and heat flux;

ρ is the density; and

p" is the fluctuating pressure.

The constants c1, c2, and c3 can be estimated following Detering and Etling (1985). The first

three terms on the right-hand-side of the first equation represent advection of turbulent kinetic

energy, and the other terms, shear production, buoyancy production, turbulence transport and

the dissipation, respectively. Similarly, the first three terms on the right-hand-side of the second

equation represent advection of ε. The rest of the terms represent the net rate change of ε due to

shear and buoyancy production, the rate change of ε related to the time-scale of turbulence, and

the vertical transport, respectively. The coefficients of eddy viscosity for momentum and heat

can be written as:

K c E m = 2

2

ε

 (7-31a)

K K z L

z L h m

m

h

= φ

φ

(/ )

(/ ) (7-31b)

where Km and Kh are the eddy exchange coefficients for momentum and heat, respectively. E

and ε need to be provided by meteorological models in their native coordinates, thus the

parameterization does not depend on the grid spacing explicitly. Obviously, we are assuming

here that the vertical layer structure in the CTM is compatible with that used in the preprocessor

meteorological model. Once Kh is computed, chemical fluxes can be modeled assuming similarity
EPA/600/R-99/030

7-26

with heat flux using the same eddy diffusion numerical algorithm described below (section

7.2.3.1). The derivation of eddy coefficients in the Burk and Thompson (1989) model is

algebraically more complex (see Mellor and Yamada, 1974, 1982) but based only on mean

quantities plus TKE. Therefore, given the TKE fields, which are output automatically from

MM5 when the Burk and Thompson (1989) option is invoked, Kh can be re-diagnosed within

the CTM.

7.2.2.3 Numerical Algorithm for Vertical Eddy Diffusion Modules

As described in Chapter 5, the vertical eddy diffusion module must solve the following equation

in terms of mixing ratio q :

∂

∂

∂

∂

∂

∂

∂ γρ

∂

∂

∂

q

t x

K q

x

K

x

q

x

i

vdiff

i i = + ˆ ( ˆ ˆ ) ˆ ln( ˆ )

ˆ ˆ 3

33

3

33

3 3 , (7-32)

where the vertical mixing is represented with the pure diffusion term and the turbulent flux

exchange term, respectively.

Numerical algorithm for the diffusion kernel

In its generic form, the diffusion kernel solves for:

∂

∂

∂

∂ξ

∂

∂ξ

q

t

K q = ( ) (7-33)

where ξ is the generic vertical coordinate which increases with geometric height. To account for

the loss process due to deposition in the lowest model layer (j=1), dry deposition flux is

considered as the flux boundary condition at the surface, i.e.:

∂

∂

q

t

v

h q

dep

d

dep

1 = − 1 (7-34)

where the geometric thickness of the lowest model layer is used for hdep.

The diffusion equation can be discretized for level j (1 < <j N) in a N-layer model and timesteps t

n

 and t

n+1

 as:
EPA/600/R-99/030

7-27

q q

t K

j q q qq nj

n

j

j

j

j

n

j

n

j

n

j

+ ++ n = + − +− − ( ) 







+

+

+ +

1 11 1 2

1 2

1 1 1 ∆

∆ ∆ ξ ξ θ θ /

/

( ) ( )( )

− − +− − ( )







−

−

+ +

− − ( ) ( )( ) /

/

K

q q qq j

j

j

n

j

n

j

n

j

1 2 n

1 2

1 1

1 1 1 ∆ξ θ θ , (7-35a)

where θ is a time-step weighting factor and

ξ ξξ j jj + + 12 1 / = + ( )/ 2 ; ∆ξ ξ ξ j jj + + 12 12 12 /// = − − ; ∆ξ ξ ξ j jj + + 1 1 = −

For the lowest model layer, we need to account for the loss due to deposition process:

q q

t K

q q qq n n n n nn

1

1

1

1

1 1 1 1

2

1 1

2

2 1 21 1 + ++ = + − +− − ( )

















+

+

∆

∆ ∆ ξ ξ θ θ ( ) ( )( )

− +− [ ] + ∆t

v

h q q d n n

dep

θ θ 1 1

1 ( ) 1 (7-35b)

and for the top layer we have zero flux through the top boundary:

q q

t K N q q qq n

N

n

N

N

N

N

n

N

n

N

n

N

+ + n

−

+

= − − +− − ( ) −

−

−

1 1 2

1 2

1

1

1

1 1

∆

∆ ∆ ξ ξ θ θ /

/

( ) ( )( ) (7-35c)

Depending on θ , the finite difference scheme is explicit (θ =0), semi-implicit (θ =1/2), or fully

implicit (θ =1). In the current version of CMAQ, the semi-implicit (Crank-Nicholson) algorithm

is implemented. Equations 7-35a-c can be rearranged to yield a matrix equation:

Aq b = (7-36)

where A is tridiagonal whose coefficients (sub-diagonal component aj , diagonal component dj ,

and super-diagonal component cj) when j=1 are given as:

d t Kt

v

h

d

dep

1

1

1 1

1

2

1

1

2

=+ +

θ

ξ ξ θ ∆∆ ∆

∆

c

t K

1

1

1

1

1

2

1

2

= −θ

ξ ξ

∆

∆ ∆ (7-37a)
EPA/600/R-99/030

7-28

and for j=N:

a

t K

N

N

N

N

= − −

−

θ

ξ ξ

∆

∆ ∆

1

2

1

2

d t K

N

N

N

N

= + −

−

1 1

2

1

2

θ

ξ ξ

∆

∆ ∆ (7-37b)

and for 2 1 ≤≤ − j N :

a

t K

j

j

j

j

= − −

−

θ

ξ ξ

∆

∆ ∆

1

2

1

2

d t

K K

j

j

j

j

j

j

=+ +





















+

+

−

−

1

1

2

1

2

1

2

1

2

θ

ξξ ξ

∆

∆∆ ∆

c

t K

j

j

j

j

= − +

+

θ

ξ ξ

∆

∆ ∆

1

2

1

2

(7-37c)

Coefficients of vector b are, for j=1 and N:

b t

K

t

h q

t

K

q

b t

d

dep

n n

N

N

1

1

1

1

2

1

1

2

1

1

1

1

2

1

1

2

1 2

1 1 1

1 1

= − ( ) − 



















− − ( )





















+ ( ) − 







































= − ( ) −

θ

ξ ξ θ ν θξ ξ

θ

ξ

∆

∆ ∆

∆ ∆

∆ ∆

∆

∆

K

q

t

K

q

N

N

N

n

N

N

N

N

n −

−

−

−

−









































+ ( ) − 







































1

2

1

2

1

2

1

2

1

1

∆

∆

ξ ∆ ∆

θ

ξ ξ

(7-37d)

and for 2 1 ≤≤ − j N :
EPA/600/R-99/030

7-29

b t K K

j q

j

j

n j

j

j

j

= − − +

































+

+

−

−

1 1 1

2

1

2

1

2

1

2

( ) θ

ξξξ

∆

∆∆∆

+ − 





























 + − 































+

+

+

−

−

−

() () 1 1 1

2

1

2

1

1

2

1

2

1

θ

ξ ξ

θ

ξ ξ

∆

∆ ∆

∆

∆ ∆

t K

q

t K

q

j

n

j

n j

j

j

j

j

j (7-37e)

The numerical algorithm solving the tridiagonal system is based on the Thomas algorithm. Refer

to Appendix 7A.1 for details of the algorithm and stability characteristics.

Numerical algorithm for the coordinate divergence kernel

The coordinate divergence kernel solves for

∂

∂

∂ γρ

∂ξ

∂

∂ξ

∂

∂ξ

q

t

K q V q = = mix

ln( ˆ ) (7-38)

where V K mix = ∂ γρ

∂ξ

ln( ˆ )

. The differential equation is in advective from with the effective mass

transfer velocity Vmix . It can be solved with a vertical advection code. Because most operational

meteorological models rely on logarithmically spaced vertical layering based on sigma-p type

coordinates, Vmix is expected to be small. Currently, this component is not implemented in

CMAQ. However, a quantitative study is needed to assess the importance of this term.

Integration time-steps

According to Oran and Boris (1987), any numerical algorithm for the diffusion equation (with

equal grid spacing) should produce the following quantitative properties:

• the total integral of q t (,) ξ should be conserved;

• the amplitude q t (,) ξ should decay monotonically;

• there should be no phase errors introduced by the algorithm (for equal grid spacing); and

• positivity should be preserved.

Although the numerical solver algorithm for the semi-implicit scheme is stable in the sense that

the amplitude of the signal either decays or stays the same, the positivity condition may not be

satisfied if we choose a large time-step for the integration, especially for signals with small

wavelengths. For example, with equal grid spacing, we can use the Von Neuman stability

analysis technique to demonstrate that some part of the short-wavelength spectrum shows a
EPA/600/R-99/030

7-30

negative amplitude when the time-step is too long. The semi-implicit scheme is positive definite

given the rather stringent CFL condition, for a uniform vertical grid spacing:

β ξ ≡ <

2 1 0 2

∆

∆

tK

( ) . (7-39a)

For non-uniform grid spacing, we use the CFL condition:

max{ } max . /

/

/

/

β ξξ ξ j

t K K

j

j

j

j

j

≡ + 































< −

−

+

+

∆

∆∆ ∆

1 2

1 2

1 2

1 2

1 0 (7-39b)

to ensure positive definiteness of the semi-implicit solution. The internal time-step for vertical

diffusion is thus determined in CMAQ with the following equation:

∆ ∆ t t vdiff = min{ }j (7-40)

where ∆ ∆

∆ ∆

t

K K

j j

j

j

j

j

= + 









 −

−

+

+

−

ξ ξ ξ

1 2

1 2

1 2

1 2

1

/

/

/

/

7.2.3 Flux Form Representation of Vertical Mixing

Vertical mixing can be represented in flux form as:

∂

∂

∂

∂ξ

∂ γρ

∂ξ

ξ q ξ

t

F =− − F [ ] ln( ˆ )

, (7-41)

where F Fqi

ξ = ˆ 3

 is the turbulent flux represented in the generalized vertical coordinate ξ , whose

value increases monotonically with geometric height. Here, the flux should be parameterized in ξ

coordinate instead of the generic height coordinate. The cross directional (w.r.t. generalized

coordinate) diffusion terms, as well as the flux divergence due to grid spacing (second term in

Equation 7-41), are neglected.

Thus, the numerical solver kernel for the flux form vertical diffusion should solve for:

∂

∂

∂

∂ξ

ξ q

t

F = − (7-42)

when the source term is zero. The flux form representation is extremely useful in describing the

algorithms based on non-local closure. Non-local closure recognizes that larger-size eddies can
EPA/600/R-99/030

7-31

transport fluid across distances longer than the grid increment before the smaller eddies have a

chance to cause mixing (Stull, 1988).

To represent the turbulent mass exchange with the transilient parameterization, the boundary

layer height must coincide with the height of layer interfaces of the vertical grid. For most

situations, the index for the boundary layer top (Lp) is less than the total number of model layers

(i.e., L N p < ). With the transilient turbulence formulation, the new values of the trace species

mixing ratio q due to turbulent mixing for a layer j at a future time ( ) t t + ∆ can be written as:

q t t c t tq t j jk

k

L

k

p

( ) (, ) () + = =∆ ∆ ∑

1

(7-43)

where cjk are the components of a transilient matrix and subscripts j and k are indices of two

different grid boxes (vertical layers) below boundary layer top in a column of atmosphere. If we

consider turbulent mixing between grid boxes j and k, cjk represents fraction of air mass ending in

the grid box j that came from grid box k. The grid box j is considered as the “destination” box

while grid box k is considered as the “source” box. Thus, the change in the tracer concentration

due to turbulent mixing for grid box j at a time interval ∆t is a simple matrix multiplication with

concentration from the source cell. The transilient matrix representation is in fact applicable for

any physical process that involves mass exchange among grid boxes in a column. For example,

convective cloud mixing can be represented by a transilient matrix as well, similar to how mixing

in a convective boundary layer is handled.

The mass conservation requirements provide constraints for the coefficients of the transilient

matrix. The conservation of air mass requires that the sum over k of all mixing fractions be unity:

ctt jk

k

Lp

(, ) ∆ =

∑ = 1

1 (7-44)

and the conservation of trace gas amount requires that the sum over j of all mass-ratio weighted

transilient coefficients be unity as well:

∆

∆

∆ ξ

ξ

j

k

jk

k

L

ctt

p

(, ) =

∑ = 1

1 (7-45)

where ∆ ∆ ξ ξ j k / represents the mass ratio (i.e., ratio of layer thicknesses for mixing ratio q)

between the source and destination boxes. In order that transilient turbulence theory be useful,

the coefficients should be determined using appropriate turbulent flux parameterizations.
EPA/600/R-99/030

7-32

Consider how the mixing coefficients are related with the turbulent flux representations. Because

the transilient matrix describes the exchange of mass between grid boxes, the kinematic turbulent

fluxes across the j-th level can be expressed, for a vertical layering with non-uniform grid spacing

(Stull, 1993), for 2 ≤ ≤j Lp as:

Ft t F t t

t

c t tqt qt j j

j

jk

k

L

j k

p

( , ) ( , ) ( , )[ ( ) ( )] ∆ ∆

∆

∆

=+ − − ∆ =

1 ∑

1

ξ (7-46a)

and for j=1 as:

Ft t

t

c tqt qt k

k

L

k

p

1

1

1

1

1 ( , ) ( )[ ( ) ( )] ∆ ∆

∆ = − =

∑ξ (7-46b)

The concentration (mixing ratio) of the lowest model layer, taking into account the deposition

flux, is:

∂

∂ ξ

q

t

FF v

h q

ctt

t

qt qt s d

dep

k

k

L

k

p

1 1

1

1

1

1

= − 1

− =− − − =

∑ ∆

∆

∆

(, )[ ( ) ( )] (7-47)

where Fs is the flux at the surface.

The transilient turbulent representation, as shown in Equation 7-43, is an explicit expression in

which the magnitudes of mixing coefficients depend on the numerical integration time-step. To

use the transilient matrix representation as a general expression for the non-local turbulent closure

methods, we need to relate Equation 7-43 with the semi-implicit representations of simple nonlocal closure algorithms such as in Blackadar (1978) and the Asymmetric Convection Model

(Pleim and Chang, 1992). Using Blackadar’s definition of mjk , which is the fraction of mass

exchange between two levels j and k per unit time, the turbulent fluxes at a given time t can be

rewritten as:

Ft F t m t q t q t jj j jk

k

L

j k

p

( ) ( ) ( )[ ( ) ( )] =+ − −

=

1 ∑

1

∆ξ (7-48)

Note that mc t jk jk = / ∆ for an explicit method. Substituting Equation 7-43 into the semi-implicit

method, as in Equation 7-46, we get:

q q

t

j F F FF nj

n

j

j

n

j

n

j

n

j

+ + n

−

+ = − − +− − [ ] −

1 1

1

1 1 1

∆

∆ξ θ θ ( ) ( )( ) (7-49)
EPA/600/R-99/030

7-33

resulting in a general matrix equation:

Pq Rq n n + =1 (7-50)

where the coefficients of P and R are given as:

p tm jj jk

k

k j

Lp

= + =

≠

1 ∑

1

θ∆ ; p tm jk

j k

jk

≠

= −θ∆

r tm jj jk

k

k j

Lp

=− − =

≠

1 1 ∑

1

( ) θ ∆ ; r tm jk

j k

jk

≠

= − ( ) 1 θ ∆

If the matrix P is nonsingular, we have a general expression for the transilient turbulence:

q P Rq Cq n nn + − = = 1 1 (7-51)

where C=P-1R.

The relationship between the coefficients of the transilient matrix and the mass exchange ratio

among the grid boxes are somewhat complicated for the semi-implicit scheme. However, the

semi-implicit scheme becomes attractive for the closure algorithms with sparse P matrix (i.e.,

when the matrix inversion is not so expensive) because it allows longer integration time-steps

than the explicit method. In the following, we describe non-local flux-form atmospheric

turbulence algorithms as a subset of the generalized transilient turbulence representations.

7.2.3.1 Blackadar Non-local Scheme

This scheme, first introduced by Blackadar (1978), has long been used as one of the PBL schemes

in the Mesoscale Meteorology model generation 4 (MM4) and generation 5 (MM5). The

Blackadar model is a simple non-local closure scheme designed to simulate vertical transport by

large convective eddies during conditions of free convection. Therefore, this scheme is used only

in the convective boundary layer and must be coupled with another scheme for non-convective

conditions and above the boundary layer, such as K-theory. In general, the flux-form diffusion

algorithm can be written for the lowest layer as:

∂

∂

q

t

v

h q m tqt qt d

k

k

L

k

dep

p

1

1 1

1

=− − − 1

=

∑ ( )[ ( ) ( )] (7-52a)

and for 2 ≤ ≤j Lp as:
EPA/600/R-99/030

7-34

∂

∂

q

t

m tqt qt j

jk

k

L

j k

p

=− − =

∑ ( )[ ( ) ( )]

1

(7-52b)

where mjk is the rate of mass exchange between two grid boxes in a column of the atmosphere

(below boundary layer top) per unit time. The convective mixing is assumed to be dominated by

eddies of varying sizes but all having roots in the surface layer, each eddy exchanging a certain

amount of its mass with the air around it as it ascends. The rate of change of mean potential

temperature caused by the mass exchange in the mixed layer can be expressed as:

∂

∂ ξ Θ Θ Θ

t = − M wu sfc ( )( ) (7-53)

where w(ξ) is a weight function that accounts for the variation of exchange rate with height.

The mass exchange rate, Mu , can be estimated from conservation of energy, which requires the

heat flux at any level to satisfy the equation:

H H M C w Jd sfc u pd sfc

sfc

=− − ∫ ρ ξξ

ξ

ξ

ξ ( ) ( ') ' Θ Θ (7-54)

where Hsfc is the sensible heat flux leaving the surface layer and Cpd is the specific heat at

constant pressure. When the integration limit is extended to the top of the boundary layer, where

H is assumed to be zero, we can estimate Mu with:

M H C w Jd u sfc pd sfc

sfc

h

= − ∫ / ( ) () ρ ξ ξ

ξ

ξ

Θ Θ ξ (7-55)

Usually the weight function w is approximated to be unity in the mixed layer. With the

Blackadar scheme, the mixing algorithm is represented for the lowest model layer by:

∂

∂

ξ

ξ

q

t

v

h q M qt qt d

u

k

k

L

k

dep

p

1

1

1 1

=− − − 1

=

∑ ∆

∆ [ ( ) ( )] (7-56a)

and for 2 ≤ ≤j Lp by:

∂

∂

ξ

ξ

q

t

M qt qt j

u

j

=− − j

∆

∆

1

1 [ ( ) ( )] (7-56b)
EPA/600/R-99/030

7-35

where we used m M k u

k

1

1

= ∆

∆

ξ

ξ , m M j u

j

1

1 = ∆

∆

ξ

ξ , and all other components of mjk are zero.

Finite difference representations of the above equations are:

q q

t

v

h q q

n n

d

dep

1 n n

1

1

1

1

1 1

+ − + =− + −

∆ [ ( )] θ θ − −− 



 



 +

=

+ θ ∑ ξ ξξ ξ M

q q u

h

n

k

k

L

k

n

p

∆

∆ ∆

1

1 1

1

2

1 ( )

−− − − 



 



 =

() ( ) 1 ∑

1

1 1

2

θ ξ ξξ ξ M

q q u

h

n

k

k

L

k

n

p

∆

∆ ∆ (7-57a)

where we used ξ ξ h k

k

Lp

= =

∑∆

1

, and for 2 ≤ ≤j Lp :

q q

t

M q q M qq j

n

j

n

u

j

j

n n

u

j

j

n n

+

+ + − =− − − − −

1

1 1

1

1 1

1 1

∆

∆

∆

∆

∆

θ ξ

ξ θ ξξ ( )( ) ( ) (7-57b)

After rearrangement, we obtain the following matrix equation:

 

df f f

e d

e d

e d

q

q

q

q

b

b

b

k L

j j

L L

n

n

j

n

L

n

j

p

p p p

1 2

2 2

1

1

2

1

1

1

1

2 00 0

0 0

000 0

000

L L

L

M OLL

MM MM

M O

L

M

M

M

M









































































=

+

+

+

+ bLp





































(7-58)

where the elements are defined with:

d v t

h

d tM

dep

u

1 h

1

=+ + − 1 θ θ 1 ξ ξ ξ ∆ ∆

∆ ( ) ∆

=

∆ξ ∆ξ

∆ ξ − ∆ξ + − θ

∆ξ

∆ − − θ ∆ = − − θ

p L

k

n

k k

n u

h

u

dep

d q

tM ( ) q ( ) tM ( ) h

v t b ( )

1 2

1 1

1

1 1 1 1 1

and for 2 ≤ ≤j Lp :

f tM

j

u

j

= − 









 θ ξ ξ ∆

∆

∆ 1
EPA/600/R-99/030

7-36

e

tM

j

u = − j





 

 θ  ξ ξ ∆

∆

∆

1

d tM

j

u

j

= + 









 1 θ 1 ξ ξ ∆

∆

∆

b tMq

tM

j q u

j

j

n u

j

n = −− 



























+ − 









 11 1 1 11 () () θ ξ ξ θ ξ ξ ∆

∆

∆ ∆

∆

∆

The numerical algorithm to solve the sparse matrix system is similar to the Thomas algorithm for

the tridiagonal system. For the details of the numerical algorithm, refer to Appendix 7A.2.

(a) (b)

Figure 7-2. Schematics of the Blackadar Scheme (a) and the Asymmetric Convective Model (b)

7.2.3.2 Asymmetric Convective Mixing

The Asymmetric Convective Model (ACM), developed by Pleim and Chang (1992), is based on

Blackadar’s non-local closure scheme (Blackadar, 1978) but with a different scheme for
EPA/600/R-99/030

7-37

downward mixing in the convective boundary layer (CBL). Blackadar’s scheme is based on the

assumption that the turbulent mixing is isotropic (i.e., symmetric) in the CBL. However,

observational evidence and large-eddy simulation modeling studies indicate that mixing processes

in a convective boundary layer are essentially asymmetric (i.e., turbulence is anisotropic;

Schumann, 1989) with fast upward buoyant plumes and slow broad compensatory subsidence.

Therefore the direct, non-local downward transport of the Blackadar scheme is replaced with

layer by layer subsidence which increases in mass flux as it descends, like a cascading waterfall

(Figure 7-2). As with the Blackadar model, the ACM can only be used during convective

conditions in the PBL. For other stability regimes, one needs to rely on other schemes such as

K-theory.

Turbulent mixing in the PBL for any dynamic, or thermodynamic variables, or trace gas species

concentrations can be represented in essentially the same way as in the above transilient

parameterization. Also, the conceptual design of the ACM allows for considerable

simplification. Because the mass influx to the lowest model layer is from the second layer only

in ACM (refer to Figure 7-2), we can write the time rate change of mixing ratio as follows:

∂

∂ ξ ξξ ξ qt

v

h q M qt M qt d

u h d

dep

1

1

1

1 1 2 2 2

1 =− − − − ∆ [ ( ) ( ) ( )] ∆ (7-59a)

For 2 ≤ ≤j Lp :

∂

∂

ξ

ξ

q

t

Mq M q M q j

u dj j dj

j

j

=− + + j

+

1 1 +

1

1

∆

∆ (7-59b)

where Mu represents upward mixing rate. Mdj represents downward mixing rate at layer j and is

defined as:

M M dj u

h j

j

= − − ξ ξ

ξ

1

∆ (7-60)

The scheme can be represented in terms of transilient mixing rates (mjk), as shown in general form

in Equation 7-48:

∂

∂

q

t

mq q m q q j =− − − − j j jj j j 11 1 1 + + () ( ) , (7-61)

Therefore, by equating Equations 7-59b and 7-61, we see that m Mm j uj 1 1 = ≠ , which shows that

the transfer coefficients are asymmetric as expected, and mm M j jj 1 1 + = , + dj , which demonstrates

a recursive relationship for Mdj:
EPA/600/R-99/030

7-38

M MM dj u dj

j

j

−

+

1 = +

∆ 1

∆

ξ

ξ (7-62)

Finally, we rewrite the prediction equation in terms of the upward mixing rate:

∂

∂

ξ ξ

ξ

q

t

M qq v

h u q h d

dep

1 1

1

= − 12 1

− − − ∆ ( ) (7-63a)

and for 2 ≤ ≤j Lp :

∂

∂

ξ ξ

ξ

ξ ξ

ξ

q

t

Mq q q j

u

h j

j

j

h j

j

= − j

 −









 +

 −



























−

+

1 +

1

1

1 ∆ ∆ (7-63b)

Note that this scheme does include the effects of vertical wind shear in generating turbulent

mixing. The magnitude of the mixing rates of the transilient matrix is based on the conservation of

sensible heat flux in the vertical direction:

MHc J u = −− sfc /( ) [ ] pρθ θ ξ ξ sfc h ( ) 2 1 ξ

(7-64)

Finite difference representations of the above equations are:

q q

t

v

h Mq q

n n

d

dep

u

1 h n n

1

1 1

1

1

1

1 1

+ − + =− +  −









 + −

∆ ∆

ξ ξ

ξ [ ( )] θ θ

+ − + − + Mq q u

ξ ξ h n n

ξ θ θ 1

1

2

1 1 2 ∆ [ ( )] (7-65a)

and for 2 ≤ ≤j Lp :

q q

t

Mq q j

n

j

n

u

n n

+

+ − = +−

1

1

1

1 1

∆ [ ( )] θ θ

−

 −









 +− +  −









 + − − +

+

+

+

+

ξ ξ

ξ θ θ ξ ξξ θ θ h j

j

j

n

j

n h j

j

j

n

j

n qq qq

1 1

1

1

1

1 1 1

∆ ∆ [ ( )] [ ( ) ] (7-65b)

This results in a sparse matrix of the form:
EPA/600/R-99/030

7-39

 

d c

edc

e dc

c

e d

q

q

q

q

b

b

j jj

L

L L

n

n

j

n

L

n

p

p p p

1 1

2 22

1

1

1

2

1

1

1

1

2

0 0

0 0

0 0

000

000

L L

L

M OOL

MM M

M O

L

M

M

M

−

+

+

+

+









































































= b

b

j

Lp

M





































, (7-66)

where:

d v

h

M t d

dep

u

h

1

1

1

=+ + 1 − ( ) ξ ξ

ξ θ∆

∆ ;

cM t u

h

1

1

1

= − ξ ξ −

ξ θ∆

∆ ;

b v

h M tq d

dep

u

h n

1

1

1

=− + 1 1 1

− [ ( )( ) ] − ξ ξ

ξ θ∆

∆ + − M tq u − ξ ξ h n

ξ θ 1

1

2 1

∆ ( )∆ ;

e Mt j u = − θ∆ ;

dM t j u

h j

j

= + −

+

1

1

( )

ξ ξ

ξ θ∆

∆ ;

cM t j u

h j

j

= − − ( )

ξ ξ

ξ θ∆

∆ ; and

b M tq j u

h j

j

j

n = − − − − [ )( ) ] 1 1 1 ξ ξ

ξ θ∆

∆ + − − +−

+

M tq M tq u +

h j

j

j

n

u

n ξ ξ

ξ θ θ∆

∆ ∆

1

1 1 1 1 () () .

The numerical algorithm solving the sparse matrix system is presented in Appendix 7A.3.

7.2.3.3 Transilient Turbulence Parameterization

The general computational paradigm for the transilient turbulence parameterization has been

presented above. In order to use the transilient turbulence concept for mixing trace gases, one

needs to know the mass exchange coefficient matrix. This is the closure problem with this

parameterization. A couple of methods have been presented in the literature. One method is

based on the TKE equation (Stull and Driedonks, 1987, and Raymond and Stull, 1990) and the

other is the one based on non-local Richardson number (Zhang and Stull, 1992). In the following

we describe briefly the TKE based scheme and discuss its associated difficulties.

The horizontally homogeneous form of the TKE equation, Equation 7-30a is given as:
EPA/600/R-99/030

7-40

∂

∂

∂

∂

∂

∂ θ ε Et

u w

u

z

v w

v

z

g w

o

=− − + − "" "" "" Θ . (7-67)

Note that the pressure and turbulent transport terms have been ignored. After normalizing with

E, the non-local analogy of the finite difference form of Equation 7-67 can be written as:

∆ ∆

∆

∆

∆ Θ

∆ t jk

jk

jk

jk jk

jk

jk jk j

jk

jk

jk

jk

t

E

E

u w

E

u

z

v w

E

v

z

g w

E E = t ( ) − 





 +

( ) − 





 + ( ) −

















"" "" θ" " ε

, (7-68)

where the symbol ∆t represents temporal change while ∆ represents spatial gradient. To close

the system, the unknown parameters are written in terms of known parameters by introducing

three scaling parameters To, Ric, and D, which are the time scale of turbulence, the critical

Richardson number, and dissipation factor, respectively. Thus, weighted kinematic fluxes can be

written as:

( ) − = 







u w

E

T u

z

jk

jk

o

jk

" " ∆

∆ , (7-69a)

( ) − = 







v w

E

T v

z

jk

jk

o

jk

" " ∆

∆ , (7-69b)

( ) − = 







θ" " w

E

T

Ri z

jk

jk

o

c jk

∆Θ

∆ . (7-69c)

Then Equation 7-68 can be rewritten as:

Y

E

E

T t

z

u v g

Ri

z

t

E jk

t jk

jk

o t

jk

jk jk

c j

jk jk

jk t

jk

= = ( ) ( ) + ( ) − ( )( ) 















− ∆ ∆

∆

∆ ∆

Θ

∆Θ ∆

∆

2

2 2 ε

. (7-70)

To use Equation 7-70 for the generalized coordinate ξ, the corresponding layer heights ( )jk ∆z

should be computed for ( ) ∆ξ jk .

Since we are dealing with fraction of masses that are coming from and going to different layers

(i.e., j ≠ k), Yjk in the above equation is for off-diagonal elements only. Diagonal elements in

Equation 7-70, Yjj , represent mass of air that remain in each layer without interaction with other

layers. Observations during convective conditions (Ebert et al., 1989) indicated that turbulent

eddies cause a well-mixed rather than convectively overturned boundary layer. This requires
EPA/600/R-99/030

7-41

that the values of the mixing potential elements (Yjk) should increase monotonically from the

upper right-most element towards the main diagonal. Further, to account for the subgrid scale

mixing in each layer, an independent parameter Yref was introduced. Thus, the diagonal elements

can be written as:

Y MAX Y Y Y jj = + jj jj − + ref (,) , , 1 1 (7-71)

given values for To, Ric, and D. Usually, Yref is estimated based on observations (Stull, 1988).

Finally, the off-diagonal elements of the transilient matrix are estimated with:

×

= Y

jk

jk

Y

c (7-72)

where × Y is the infinite norm of matrix Y, max{ } Y . The formulation presented in Raymond

and Stull (1990) and Alapaty et al. (1997) includes the additional weighting based on the mass in

the layer for irregularly spaced grids. However, we believe that Equation 7-72 should be valid

even for irregularly spaced grids when the constraint Equation 7-45 is satisfied. Also, Stull

(1993) states that the formulation Equation 7-72 causes too much mixing near the surface and

inclusion of the mass weighting in the formulation exacerbates the problem further. The diagonal

elements of the transilient matrix can be computed by rewriting Equation 7-44 as:

c c jj jk

k

k j

Lp

= − =

≠

1 ∑1(7-73)

Once the transilient matrix is determined, the concentration due to turbulent processes in the

boundary layer can be estimated from Equation 7-43. The difficulties associated with this

parameterization are:

• The scheme still depends on many free parameters (To, Ric, D, and Yref) and they control

the behavior of the mixing algorithm; and

• The time-steps should be such that the trace species mixing ratio cannot be negative

because Equation 7-43 is written in explicit form. Although explicit methods do not

require matrix inversion, the time-step must be small enough to ensure positivity and

numerical stability of the solution.
EPA/600/R-99/030

7-42

7.3 Horizontal Mixing Algorithms

Unfortunately, our understanding of horizontal turbulence is limited due to the lack of adequate

turbulence measurements as well as the scale dependency of the problem. In earlier days of

atmospheric modeling, the horizontal diffusion process was often ignored because the numerical

diffusion associated with the advection algorithms used was large. For problems with large scales,

such as regional to global transport studies, the coarse grid resolutions did not require an explicit

implementation of horizontal diffusion. However, with the advent of very accurate (i.e., less

diffusive) numerical advection schemes and the emerging need for high resolution grids for urban

scale problems, a good algorithm for horizontal diffusion is required. The skill needed is

balancing numerical diffusion associated with the advection schemes with the added explicit

diffusion to model horizontal diffusion in the atmosphere. A fundamental problem is that we do

not know much about the expected magnitude of the actual horizontal diffusion. In this section

we will describe the numerical algorithm for the horizontal diffusion implemented in the CMAQ

system.

The horizontal diffusion process in the curvilinear coordinate system (See Equation 6-25’ in

Chapter 6) is given as:

∂

∂

∂ γρ

∂ γ ρ

c

t

q

t

i

hdiff

i

hdiff

s qi

* ˆ ˆ ˆ ˆ = ( ) = −∇ •[ ] F (7-74)

There are not many choices for the horizontal diffusion parameterizations. Frequently, the

horizontal turbulent fluxes are parameterized using eddy diffusion theory. The contributions of

the off-diagonal diffusion terms show up explicitly as in Equation 6-14 in Chapter 6. Often,

these off-diagonal terms are neglected in air quality simulations, and in the CMAQ

implementation, we solve for diagonal terms only:

∂

∂

∂

∂ γ ρ

∂

∂

∂

∂ γ ρ

∂

∂

c

t x

K q

x x

K q

x

i

hdiff

i i

*

ˆ ˆ ( ˆ ˆ ) ˆ ˆ ( ˆ ˆ = ) 



 



 + 



 

 1  11

1 2

22

2 . (7-75)

The contravariant eddy diffusivity components are related to the Cartesian counterparts as

K mK ˆ xx

11

= and K mK ˆ yy

22

= . In practice, for Eulerian air quality modeling, we do not distinguish

between eddy diffusivities in two different horizontal directions (i.e., KKK xx yy H = = ). For a

Lagrangian simulation of atmospheric turbulence, the longitudinal (following the plume

movement) and lateral (perpendicular to the plume movement) dispersion are treated differently

according to characteristics from the isotropic turbulence analysis. Often the horizontal eddy

diffusivity in the Cartesian coordinates is parameterized with the magnitude of the deformation in
EPA/600/R-99/030

7-43

the gridded wind field. For that case, one must be careful whether the wind data are represented

in Cartesian coordinates or in the transformed coordinates.

Unlike the vertical diffusion case, we do not separate the grid divergence term from the diffusion

equation. An explicit solution method for Equation 7-75 is:

() () * * ρ ρ l m,, ,,

n

l m

n

l m

n

l m

n

q q + += 1 1 + −− − [ ] ++ + −

∆

∆

t

x l m K q q Kq q n

lm lm

n

l m

n

l m

n

lm lm

n

l m

n

( ˆ ) ( ) ˆ ( )() ˆ ( ) * *

1 1 1 , , , , ,, , ,

11

1

11

2 ρ ρ 1

+ −− − [ ] ++ + −

∆

∆

t

x l m K q q Kq q n

lm lm

n

l m

n

l m

n

lm lm

n

l m

n

( ˆ ) ( ) ˆ ( )() ˆ ( ) * *

2 , , , , ,, , , 1 1

22

1

22

2 ρ ρ 1 , (7-76)

where ˆ ( ˆ ˆ ) K KK lm lm lm , ,,

11

1

1 11 11

2

= + + and ˆ ( ˆ ˆ ) K KK lm l m lm , ,,

22

1

1 22 22

2

= + + . At the boundary cells, a zero-gradient

boundary condition (Neumann) is applied. Because Equation 7-76 is an explicit scheme, the

time-step should be chosen to prevent numerical instability and to maintain positivity. With an

appropriate Courant number for horizontal diffusion, βhdiff , the time-step can be determined

with:

∆ ∆t

x

K K hdiff hdiff

l m

lm lm

=

∀

β ( )

max( ˆ ˆ )

( , )

, , ,

2

11 22 . (7-77)

At present βhdiff = 0.3 and a uniform eddy diffusivity KH ∆x km =4 = 2000 m2

/s is used for the 4-km

grid resolution. To compensate for larger grid sizes for coarser grids, the eddy diffusivity is

modified to give:

K

x

H K ∆ ∆ x H x km ∆ = =

( )

( )

4000 2

2 4 (7-78)

where ∆x is in meters.

Obviously, the above parameterization is too simple to be realistic in a variety of atmospheric

conditions. Also, depending on the numerical advection algorithms chosen, the artificial

diffusivity can be quite different. This calls for several in-depth studies on following two major

issues:

(1) Quantification of realistic horizontal sub-grid scale diffusion.

The simplest approach is to assume a space independent diffusivity (e.g., Kh = 50 m2/s).

Smagorinsky (1963) formulated a horizontal diffusivity that accounts for diffusion due to
EPA/600/R-99/030

7-44

distortion or stress in the horizontal wind field. For plumes which are several kilometers or more

across, the Briggs (1973) parameterizations of horizontal diffusion define the diffusivity as a

constant times the transport wind speed. The constant is usually based on the landuse (i.e.,

urban or rural) and the stability class (i.e., stable through unstable). However, it is difficult to

quantify what the horizontal eddy diffusivity should be appropriate for a variety of atmospheric

conditions without more detailed wind field and turbulence information.

(2) Maintaining appropriate horizontal diffusion in the presence of numerical diffusion.

Most methods for simulating advective transport in current models yield an effective numerical

diffusivity much larger than physical horizontal diffusivities (Yamartino et al., 1992). Thus, the

physical process may be outweighed by the numerical errors in the model. A re-assessment of

this issue is required when the resolution of the model changes or when the method for simulating

advection is updated. For idealized concentrations and wind fields distributions, we may be able

to quantify the magnitude of the numerical diffusion in an advection scheme. However, for the

more general applications, estimating the magnitude of numerical diffusion with a specific

advection scheme is almost impossible. Refer to Odman (1997) for methodologies that quantify

numerical diffusion errors associated with advection algorithms.

7.4 Conclusions

In this chapter, we have described numerical advection and diffusion algorithms. It has two

purposes: to provide a description of the algorithms currently implemented in CCTM, and to

describe the fundamental formulations that would guide future implementation of advection and

diffusion modules. We encourage the development of algorithms in conservation (i.e., flux) forms

to ensure compatibility of new modules with existing ones.

Because of the concerns over the non-monotonicity of BOT and YAM schemes and the mass

conservation problem and diffusive nature of BOT-M, we have used PPM for a number of

demonstration executions (Byun et al., 1998). Similar testing with BOT and YAM is underway.

We intend to integrate other methods into the CCTM at a later time.

Also, we have identified several aspects in vertical and horizontal diffusion algorithms that

require additional quantitative studies:

• Effects of the parameterization for the free troposphere;

• Importance of coordinate divergence term for vertical diffusion, in particular for the

height-based constant coordinates;

• Characteristics among competing algorithms for the vertical diffusion, such as TKE and

transilient turbulence schemes; and
EPA/600/R-99/030

7-45

• Practical and theoretical concerns with the horizontal diffusion algorithms.

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This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
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Appendix 7A Numerical Solvers for Diffusion Equations

In this appendix we describe numerical procedures for eddy diffusion, the Blackadar mixing

scheme, and the asymmetric convective model.

7A.1 Stability of Tridiagonal Solver

The eddy diffusion formulation requires the solution of the linear equation

Aq b = (7A-1)

where:

 

A =



































 −−−

d c

adc

adc

adc

a d

nnn

n n

1 1

222

333

111

00 0

0 0

0 0

0 0

0 00

L

L

L

MMMMMM

L

L

;

 

q = ( ) qqq qn

T

123 L ; and

 

b = ( ) bbb bn

T

123 L .

The system Equation 7A-1 can be solved by the Thomas algorithm (Gaussian elimination of a

tridiagonal matrix without pivoting) followed by back substitution. Assume that the following

stage of the elimination has been reached:

α β jj jj j −− − − 11 1 1 q cq + = (7A-2a)

aq dq cq b jj jj jj j − + 1 1 ++ = (7A-2b)

where α1 1 = d and β1 1 = b .

For j=2,3,···n-1, eliminating qj −1 from Equations 7A-2a,b leads to:

α β jj jj j q cq + = +1 (7A-3a)

where

α

α j j

j j

j

d

a c = − −

−

1

1

(7A-3b)
EPA/600/R-99/030

7-51

β β

α j j

j j

j

b

a = − −

−

1

1

(7A-3c)

The last pair of simultaneous equations are:

α β n n nn n −− − 11 1 q cq + = (7A-4a)

aq dq b nn nn n −1 + = (7A-4b)

Eliminating qn−1 gives:

α β nn n q = (7A-5a)

and with Equation 7A-3a, we can obtain the solution by back substitution, i.e., j = n-1, n-2,···,1:

q

c q

j

j jj

j

= β + +

α

1 (7A-5b)

The algorithm described above is stable for the tridiagonal system if:

(i) dj > 0 , aj < 0, and cj < 0 ;

(ii) d ac j jj >− + + − ( ) 1 1 for j=1,2, ,···n-1, defining c a o n = = 0 ; and

(iii) d ac j jj >− + ( ) for j=1,2, ,···n-1, defining a c 1 1 = = n− 0.

The first two conditions ensure that the forward elimination is stable and the first and third

conditions ensure that the back substitution is stable.

To prove that the forward elimination procedure is stable, it is necessary to show that the moduli

of the multipliers m a j jj = − − /α 1 used to eliminate q1, q2, ... are positive and less than or equal to

one. From Equation 7A-2, we get:

α j j jj = + d mc −1 (7A-6a)

and

m

a a

d mc j

j

j

j

j jj

+

+ +

−

=− = −

+ 1

1 1

α 1

(7A-6b)

Then, since da c 1 2 >− > = 0 o:

0 1 2

2

1

< <− < m

a

d (7A-7a)
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7-52

Similarly, we have:

0 1 3

3

2 21

3

2 1

3

31 1

< < −

+

< −

+

< −

−++

m = a

d mc

a

d c

a

( ) ac c

(7A-7b)

since d ac 2 31 >− + ( ). In this way, we can show that 0 1 < < mj for j=1, 2, ···n-1.

For back substitution, we can write:

q cq p q j

j

j jj j j

j

j

=−= + + ++

1

1 11

α

β β

α

( ) (7A-8)

with a c 1 1 = = n− 0 for j=1, 2, ···n-1.

There will be no build-up of errors in the back substitution process if pj +1 < 1, where:

p

c c

d ap j

j

j

j

j jj

+ = − = −

+ 1α

(7A-9a)

Now, 0 1 < =− < p cd 2 11 / , since a1 = 0 and d c 1 1 > − by hypothesis. Then:

p

c

d ap 3

2

2 22

= −

+

(7A-9b)

As − > c2 0, 0 1 < < p2 , and d a 2 2 >− > 0, it follows that:

0 1 3

2

2 2

2

22 2

< < −

+

< −

−+−

p = c

d a

c

( ) ac a

(7A-10)

Similarly, we can show that 0 1 < < pj for j=1, 2,···n-1.

7A.2 Solver for Blackadar Scheme

The Blackadar scheme requires solving the sparse linear matrix equation Aq=b of the form
EPA/600/R-99/030

7-53

 

A =





































−

− −

dff f f

e d

e d

e d

e d

n n

n n

n n

123 1

2 2

3 3

1 1

00 0

000

00 0

000

L

L

L

MMMMMM

L

L

(7A-11)

The solver for this system uses a similar numerical procedure as for the tridiagonal system. The

elements of the linear set of equations are related as follows:

dq fq b j j

j

n

1 1

2

+ = 1

=

∑ (7A-12a)

and for 2 ≤ ≤j n:

eq dq b j jj j 1 + = (7A-12b)

By substituting qj with q1 for each j, we get:

q

b bf d

d ef d

jj j

j

n

jj j

j

1 n

1

2

1

2

=

−

−

=

=

∑

∑

/

/

(7A-13a)

and for 2 ≤ ≤j n:

q b eq d j jj j = − ( )/ 1 (7A-13b)

Note that Equation 7A-13b involves neither a forward nor a backward substitution loop.

7A.3 Solver for Asymmetric Convective Model (ACM)

The Asymmetric Convective Model requires solving the linear matrix equation Aq=b with a

sparse matrix of the form:
EPA/600/R-99/030

7-54

 

A =



































 − −−

d c

edc

e dc

e dc

e d

n nn

n n

1 2

2 22

3 33

1 11

0 00

0 0

0 0

0 0

000

L

L

L

MMMMMM

L

L

(7A-14)

The solver for this system is based on a numerical procedure similar to the tridiagonal solver.

The relation among the variables qi are given as:

dq cq b 11 12 1 + = (7A-15a)

eq dq b n nn n 1 + = (7A-15b)

and for 2 1 ≤≤− j n :

eq dq cq b j jj jj j 1 1 ++ = + (7A-15c)

Assume that the following stage of the elimination has been reached for 1 1 ≤≤− j n :

α β j jj j q cq 1 1 + = + (7A-16a)

where:

α α j j

j

j

j e

d

c = −

−

−

1

1 (7A-16b)

β β j j

j

j

b j

d

c = −

−

−

1

1 (7A-16c)

with α1 1 = d and β1 1 = b . From Equation 7A-16a for j n = −1 and Equation 7A-15b, q1 is found

to be:

q

d bc

d ec

n n nn

n n nn

1

1 1

1 1

= −

−

− −

− −

β

α

(7A-17a)

and all other qis are computed with:

q

q

c j

j j

j

+ = − 1

β α 1 (7A-17b)
EPA/600/R-99/030

7-55

for 1 1 ≤≤− j n . The final substitution stage can be implemented either in a forward or backward

sweep.
EPA/600/R-99/030

*

Corresponding author address: Gerald L. Gipson, MD-80, Research Triangle Park, NC 27711. E-mail:

ggb@hpcc.epa.gov

**On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. 

Chapter 8

GAS-PHASE CHEMISTRY

Gerald L. Gipson*

Human Exposure and Atmospheric Sciences Division

National Exposure Research Laboratory

U. S. Environmental Protection Agency

Research Triangle Park, NC 27711, USA

Jeffrey O. Young**

Atmospheric Modeling Division

National Exposure Research Laboratory 

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711, USA

ABSTRACT

This chapter describes the manner in which gas-phase chemistry is treated in the Models-3

Community Multiscale Air Quality (CMAQ) modeling system. The CMAQ system currently

includes two chemical mechanisms -- RADM2 and CB4 -- with plans to incorporate a third -- the

SAPRC97 mechanism -- in the near future. Each of these mechanisms is described, and the

manner in which the first two are linked to the aqueous chemistry and aerosol formation

processes is discussed. Enhanced isoprene chemistry that has been included in the RADM2

mechanism is also described, and procedures for entering new chemical mechanisms in the

CMAQ system are addressed. The representation of reaction kinetics in the CMAQ system and

the numerical modeling of gas-phase chemistry are also presented. The CMAQ system currently

employs two numerical solvers, SMVGEAR and a variant of the QSSA method. The numerical

procedures used in each are presented, and the relative computational efficiencies of each on

different computing platforms are noted.
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8-1

8.0 GAS-PHASE CHEMISTRY

Since atmospheric chemistry plays a major role in many air pollution problems, the

representation of chemical interactions among atmospheric constituents is often an essential

element of an air quality model. All important chemical transformations relevant to the problem

being studied must be included to make accurate predictions of ambient pollutant concentrations. 

Many atmospheric pollutants or their precursors are emitted as gases and interact primarily in the

gaseous phase. However, some important atmospheric processes such as acid deposition and the

formation of aerosols involve the interaction of constituents in the gas, liquid, and solid phases,

so transformations taking place in all three phases often need to be represented. For

computational efficiency, these processes are usually modeled separately. This approach has

been adopted in the Chemical Transport Model (CTM) that is part of the Community Multiscale

Air Quality (CMAQ) modeling system (hereafter referred to as the CCTM). This section

addresses the modeling of gas-phase transformations alone in the CCTM. Descriptions of the

linkages of gas-phase constituents with aerosols and with aqueous chemistry are discussed below

and in Chapters 10 and 11, respectively. A potential future improvement to the CCTM would

involve more closely coupling the chemical interactions taking place in all three phases. 

Nevertheless, the current formulation still enables the investigation and assessment of

environmental problems using a multi-pollutant, one-atmosphere modeling concept.

Interactions in the gas-phase are represented in air quality models by means of chemical 

mechanisms. The CMAQ system currently includes two base chemical mechanisms that have

been developed primarily to address issues associated with urban and regional scale ozone

formation and acid deposition -- the CB4 (Gery et al., 1989) and RADM2 (Stockwell et al.,

1990) mechanisms. Variants of these two mechanisms have been developed for the CMAQ

system to provide the necessary linkages to the aerosol and aqueous chemistry processes. 

Current plans also call for adding a third mechanism -- the SAPRC-97 mechanism (Carter, 1997). 

Although these mechanisms should be adequate for many air pollution applications, it may be

necessary to modify or even replace these mechanisms to address some issues. To facilitate

changing mechanisms and adding new ones, the CMAQ system has been equipped with a

generalized chemical mechanism processor. It must be emphasized, however, that supplemental

data for other CMAQ processors may be required when one of the predefined mechanisms is

modified or replaced. This is addressed in more detail section 8.2.5.

The remainder of this chapter addresses different aspects of the representation of gas-phase

chemistry in the CMAQ system. The first section includes background information on chemical

mechanisms and provides the rationale for including the predefined chemical mechanisms in the

CMAQ system. The subsequent section describes the predefined chemical mechanisms as

implemented in the CMAQ system and addresses adding new mechanisms or changing existing

ones. This is followed by a description of reaction kinetics as it relates to the CCTM

representation, and the final section describes the mathematical procedures used internally in the

CCTM to solve the equations that arise from the mathematical representation of gas-phase

chemistry.
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8-2

8.1 Background

A chemical mechanism is a collection of reactions that transforms reactants into products,

including all important intermediates. Chemical mechanisms developed for air quality modeling

are highly condensed, parameterized representations of a true chemical mechanism. They include

artificial species and operators, and many of the mechanism reactions are parameterizations of a

large set of true atmospheric reactions. In some cases, mechanism reactions may include

elements which have no physical significance (e.g., products with negative stoichiometry). While

it would be difficult to design a generalized mechanism processor to handle all possible

parameterizations used in various condensed mechanisms, some degree of generalization in the

CMAQ system is achieved by using special conventions for entering chemical mechanisms. 

First, all reactions in the mechanism are treated as if they are elementary, and the stoichiometric

coefficients for all reactants must be one. Since all reactions are assumed to be elementary, a

reaction can have no more than three reactants. These conventions permit the reaction rate to be

derived directly from the stoichiometric equation, thereby simplifying the mathematical

representation of the reactions. Other conventions adopted for the CMAQ generalized

mechanism processor are included in Section 8.3 and in Chapter 15.

Mechanism species can be divided into two categories: inorganic and organic. The number of

important inorganic species is relatively small, and they are almost always represented explicitly

in chemical mechanisms. The important inorganic species included in these mechanisms are

ozone, nitric oxide, nitrogen dioxide, nitric acid, nitrous acid, hydrogen peroxide, sulfur dioxide,

and several radicals formed through their interactions with other species. Although most of the

chemical reactions involving these species are common to all mechanisms, some differences do

exist. For example, some of the mechanisms omit a few reactions because they are normally

minor pathways and thus do not affect modeling results significantly. Also, different rate

constants may be used for some reactions, especially those that are photolytic. The

representation of organic species usually differs more substantially, however. Some species in

the mechanism represent real organic compounds, but others represent a mixture of several

different compounds. The manner in which the grouping of organic compounds is carried out

typically distinguishes one mechanism from another, and that is described next. In this chapter,

the phrase mechanism species is used to refer to any species in the gas-phase mechanism,

regardless of whether it is an explicit species or not. 

Although explicit mechanisms have been developed for many organic compounds, the resultant

number of reactions and species needed to represent their atmospheric chemistry is too large to

model efficiently in photochemical grid models such as the CCTM. In addition, explicit

mechanisms have not yet been developed for most organic compounds, thereby requiring that

some reaction pathways be postulated. Thus, both compression and generalization are necessary

when depicting organic reactions. Although chemical mechanisms differ in the manner in which

organic species are represented, the mechanism developer usually chooses some distinguishable

organic property to group similar organics into classes that reduce both the number of mechanism

species and reactions. The three most common representations include the lumped structure

technique, the surrogate species approach, and the lumped species method. In the lumped
EPA/600/R-99/030

8-3

structure approach, organic compounds are apportioned to one or more mechanism species on

the basis of chemical bond type associated with individual carbon atoms (Whitten et al., 1980). 

In the surrogate species method, the chemistry of a single species is used to represent compounds

of the same class (e.g., Lurmann et al., 1987). Generalized reactions are then written based on

the hypothetical model species. The lumped species method is very similar to the surrogate

species approach, but various mechanism parameters associated with a particular surrogate are

adjusted to account for variations in the composition of the compounds being represented by the

surrogate species (e.g., Carter, 1990, and Stockwell et al., 1990). 

The construction of a compact chemical mechanism necessarily introduces varying levels of

distortion, generalization, and omission in the representation of atmospheric chemistry (Jeffries,

1995). Although mechanisms are routinely tested using results obtained from environmental

chamber experiments, the data are often insufficient to resolve uncertainties associated with

some of the chemical representations. For example, Carter (1990) noted that much is unknown

about several important reaction types, and that their representations “... continue to be largely

speculative or are based on empirical models derived from fits to environmental chamber data.” 

Further, rate constants for some reactions are either unknown completely, or significant

disagreement exists as to their accuracy. Several studies have been conducted to compare

different chemical mechanisms (e.g., Leone and Seinfeld, 1985; Hough, 1988; and Dodge, 1989). 

These comparisons revealed that the mechanisms often yield results that are similar for some

species. This could indicate that the fundamental atmospheric chemistry is fairly well understood

for these species, or that the mechanisms were derived from the same experimental kinetic or

mechanistic data, which may or may not be accurate. Larger differences tend to occur for those

species for which the atmospheric chemistry is more uncertain. Thus, it is often difficult to

assess the relative merits of different mechanisms when applied to any one situation. Therefore,

the CMAQ system includes the capability to use more than just one chemical mechanism.

Given the inherent uncertainties in existing chemical mechanisms, alternate approaches for

representing gas-phase chemistry are needed. One approach being explored involves decreasing

uncertainties associated with the simplifications that are introduced to reduce mechanism size. 

This approach is based on the concept that much of the information needed for an expanded

chemical representation does not necessarily have to be included in the mechanism explicitly, but

rather can be maintained in auxiliary variables linked to a relatively small number of core species

that are included in the mechanism (Jeffries et al., 1993). Thus, it may be possible to expand

chemical representations without greatly increasing the size of the basic mechanism, and this

could be a future enhancement to the treatment of gas-phase chemistry in the CMAQ system. 

8.2 Chemical Mechanisms in the CMAQ System

This section includes summary descriptions of the two basic chemical mechanisms included in

the CMAQ system -- the CB4 (Gery et al., 1989) and the RADM2 (Stockwell et al., 1990). Since

the SAPRC-97 mechanism (Carter, 1997) is to be added in the near future, some discussion of it

is also included. These mechanisms require that information be supplied to the CCTM in a form

that is unique for each mechanism, and this is carried out in several sub-systems incorporated in
EPA/600/R-99/030

8-4

the CMAQ system. These include the emissions processing system which generates emissions

for key mechanism species; the initial conditions/boundary conditions processor that generates

ambient starting and boundary concentrations for mechanism species; and the photolysis rate

processor that produces mechanism specific photolysis rates. The reader is referred to the

chapters describing those sub-systems for a description of the treatment of mechanistic data, and

to the mechanism references for a more detailed description of each chemical mechanism.

In addition the base mechanisms, both the base CB4 and RADM2 mechanisms have been

modified in the CMAQ system to provide necessary linkages for aerosol and aqueous chemistry

processes, and the RADM2 mechanism has also been modified to create two new mechanism

variants that include enhanced isoprene chemistry representations. Note that the existing subsystems provide all of the necessary information for the extensions to the base mechanism. The

modifications to the base mechanisms are discussed below in the section on mechanism

extensions. Complete listings of all mechanisms currently available in the CMAQ system are

included in Appendix 8A. The last portion of this section briefly discusses changing the base

mechanism or their variants or adding new mechanisms to the CMAQ system.

8.2.1 CB4 Mechanism

The CB4 mechanism is a lumped structure type that is the fourth in a series of carbon-bond

mechanisms, and differs from its predecessors notably in the detail of the organic compound

representation. It has been used in models such as EPA's Empirical Kinetic Modeling Approach

(EPA, 1989) and Regional Oxidant Model (Lamb, 1983), and in versions IV and V of the Urban

Airshed Model (EPA, 1991 and SAI, 1993). The CMAQ implementation of the basic CB4

mechanism includes 36 species and 93 reactions, including 11 photolytic reactions.

The CB4 uses nine primary organic species (i.e., species emitted directly to the atmosphere as

opposed to secondary organic species formed by chemical reaction in the atmosphere). Most of

the organic species in the mechanism represent carbon-carbon bond types, but ethene (ETH),

isoprene (ISOP) and formaldehyde (FORM) are represented explicitly. The carbon-bond types

include carbon atoms that contain only single bonds (PAR), double-bonded carbon atoms (OLE),

7-carbon ring structures represented by toluene (TOL), 8-carbon ring structures represented by

xylene (XYL), the carbonyl group and adjacent carbon atom in acetaldehyde and higher

molecular weight aldehydes represented by acetaldehyde (ALD2), and non-reactive carbon

atoms (NR). Many organic compounds are apportioned to the carbon-bond species based simply

on the basis of molecular structure. For example, propane is represented by three PARs since all

three carbon atoms have only single bonds, and propene is represented as one OLE (for the one

carbon-carbon double bond) and one PAR (for the carbon atom with all single bonds). Some

apportionments are based on reactivity considerations, however. For example, olefins with

internal double bonds are represented as ALD2s and PARs rather than OLEs and PARs. 

Further, the reactivity of some compounds may be lowered by apportioning some of the carbon

atoms to the non-reactive class NR (e.g., ethane is represented as 0.4 PAR and 1.6 NR). 

Apportioning rules have been established for hundreds of organic compounds, and are built into
EPA/600/R-99/030

8-5

the emissions processing sub-systems to produce the appropriate emission rates for the CB4

mechanism species.

The CB4 mechanism described by Gery et al. (1989) has undergone several changes since its

publication. In 1991, the PAN rate constants were changed and a termination reaction between

the XO2 operator and the HO2 radical were added. Subsequently, terminal reactions for the

XO2N operator were also added. An updated CB4 isoprene chemistry mechanism based on the

work of Carter (1996) was developed in 1996. All of these changes have been incorporated in

the CMAQ version. It should also be noted that the original CB4 mechanism incorporated simple

Arrhenius type rate constant expressions that were derived from more complex expressions for

temperature and pressure dependent rate constants. Since the top of the CCTM domain may

extend to heights that makes pressure dependencies important, the CMAQ version incorporates

the original expressions rather than the derived ones. 

8.2.2 RADM2 Mechanism

The RADM2 mechanism is a lumped species type that uses a reactivity based weighting scheme

to adjust for lumping (Stockwell et al., 1990). It has evolved from the original RADM1

mechanism (Stockwell, 1986), and is employed in version 2 of the Regional Acid Deposition

Model (Chang et al., 1987). The base mechanism as implemented in the CMAQ system contains

57 model species and 158 reactions, of which 21 are photolytic. 

In RADM2, the primary organics are represented by 15 mechanism species, five of which are 

explicit because of their high emission rates or because of special reactivity considerations

(methane, ethane, ethene, isoprene, and formaldehyde ). The other ten represent groups of

organic compounds aggregated on the basis of their reactivity with the hydroxyl radical (HO)

and/or their molecular weights. To account for varying reactivities of the different organics that

are lumped into a single group, emissions of each organic within a group are weighted by a

reactivity factor (F) that is computed as the ratio of the fraction of emitted organic compound

that reacts to the fraction of the mechanism species that reacts:

F 


1 	 exp(	kHO Emiss P

[HO] dt)

1 	 exp(	kHO Mech P[HO] dt)

. (8-1)

The integral term is estimated from a daily average integrated HO radical concentration of 110

ppt min that was derived from RADM simulations (Stockwell et al., 1990). Note that F

approaches unity if the reactivity of the emitted organic nearly equals that of the mechanism

species or if the reactivities of both are very large. As with CB4, the RADM2 lumping and

weighting rules have been built into the CMAQ emission processing system.

The implementation of the RADM2 mechanism in the CMAQ system is almost identical to that

described by Stockwell et al. (1990), with only two minor modifications. First, the reaction of HO
EPA/600/R-99/030

8-6

with cresol (CSL) was reformulated as follows to eliminate negative stoichiometry in the

mechanism:

From: HO + CSL  0.1 HO2 + 0.9 XO2 + 0.9 TCO3 - 0.9 HO kHO+CSL;

To: HO + CSL  0.1 HO2 + 0.9 XO2 + 0.9 TCO3 kHO+CSL;

HO + CSL  CSL 0.9 kHO+CSL.

(Note that negative stoichiometry is permitted in the CMAQ system, but was removed here for

consistency with previous implementations of RADM2.) Second, the concentration of methane

in the CCTM is assumed to be constant at 4.5x1013 molecules/cc. Thus, methane was removed

as a reactant in the reaction of OH with methane and the corresponding rate constant changed

from second-order to pseudo first-order using the assumed CCTM methane concentration. 

8.2.3 SAPRC-97 Mechanism

The SAPRC-97 mechanism (Carter, 1997) employs the lumped surrogate species approach, but

offers the capability to incorporate semi-explicit chemistry of selected organics. The SAPRC

series of mechanisms evolved from the “ALW” mechanism of Atkinson et al. (1982). SAPRC97 is similar to its predecessors SAPRC-90 and SAPRC-93, but incorporates improvements to

aromatic chemistry and updates to reactions of many individual organic compounds. Although

many of the reactions for organic compounds are generalized and incorporate non-explicit

species, product yield coefficients and rate constants are tabulated for over 100 individual

organic compounds. Thus, each of these organics can be modeled individually by including their

semi-explicit chemistry in the mechanism. Due to computational constraints, however, the full

set of organic compounds cannot be incorporated in an Eulerian model. For this situation, the

mechanism is condensed by lumping individual organic compounds into groups with

corresponding rate constants and product yield coefficients that have been weighted by mole

fractions of the individual organics. The mole fractions are typically derived from emission

inventory data used in the model simulation. Thus, unlike the previous mechanisms, the SAPRC97 mechanism can potentially change with each application since new rate constants and product

yield coefficients can be computed for each application.

The SAPRC-97 mechanism has been developed with supplemental software to facilitate

constructing mechanisms of varying levels of condensation. Documentation of the procedures

include three distinct levels of detail, differing primarily in the number of organic species that are

included in the mechanism (Carter, 1988). Since no decisions have made on the form of the

mechanism that will be added to the CMAQ system, listings for this mechanism are not included

in Appendix 8A. Documentation will be provided when the CMAQ version is made available

however.

8.2.4 Extended Mechanisms
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8-7

Each gas-phase chemical mechanism has been linked to aqueous chemistry and to aerosol

formation processes. Since these linkages required some modifications to the original gas-phase

mechanisms, different versions of the same mechanism were created for modeling gas-phase

chemistry alone or for modeling gas-phase chemistry with or without aerosols and/or aqueous

chemistry. Different versions of the mechanisms are distinguished by means of a special naming

convention. Gas-phase mechanisms that have not been modified are referred to by their base

name (e.g., CB4, RADM2, and SAPRC when the latter is available). Mechanisms that have been

modified to account for aerosol production have their names appended with “_AE”, mechanisms

modified for aqueous chemistry are appended with “_AQ”, and mechanisms modified for both

are appended with “_AE_AQ”. Thus, CB4_AE_AQ refers to the CB4 gas-phase mechanism

that has been modified to include linkages to both aerosols and aqueous chemistry. A second set

of RADM2 gas-phase mechanisms that incorporates new isoprene chemistry has also been

included in the CMAQ system. These mechanisms include either “_CIS1” or “_CIS4” in their

names to denote that the mechanism incorporates enhanced isoprene chemistry. Methods used

to develop the extended mechanisms are described below according to the three types of

extensions: aerosol, aqueous chemistry, and isoprene chemistry.

8.2.4.1 Aerosol Extensions

A major pathway leading to the formation of aerosols is the oxidation of sulfur dioxide (SO2) to

sulfate, primarily by the gas-phase reaction of SO2 with the hydroxyl radical (OH). All

mechanisms in the CMAQ system incorporate this reaction. Because organics are represented

differently in the base mechanisms, however, aerosol formed from the reactions of organic

compounds must be handled somewhat differently. In the CCTM, organic aerosol formation is

quantified using aerosol yields, i.e., μgm-3 of aerosol produced per ppm of organic reacted with

OH, ozone or nitrate radical (NO3). The yields used in the CCTM are those reported by Bowman

et al. (1995) that were derived from the work of Pandis et al. (1992). These yields are given in

terms of the SAPRC-90 chemical mechanism species, so some adjustments were required to

adapt them to the CMAQ mechanisms. In the CMAQ system, aerosol production is assumed to

occur from reactions involving five different generic organic groupings. Individual mechanism

species are then mapped to these general groupings to obtain the aerosol yields. The five generic

groups are defined as: 1) long-chain alkanes; 2) alkyl-substituted benzenes such as toluene and

xylene; 3) cresol and phenols; 4) long-chain olefins; and 5) monoterpenes. Note that the aerosol

yields vary significantly among these five groups, so it is important to map the organic species in

each mechanism to the proper aerosol production group. The remainder of this section describes

the mapping that is used for the CMAQ base mechanisms and how the aerosol production rates

are determined from the gas-phase reactions. The derivation of the yields used in the CCTM and

the manner in which they are used in the aerosol module are described in Chapter 10. 

To apply the aerosol yields, the amount of reactant consumed by reaction must be determined for

several mechanism species. In the CMAQ system, this is accomplished by using “counter”

species that have been added as products to those reactions involving the mechanism species of

interest (e.g., Bowman et al., 1995). These counter species are essentially “dummy” species with

no physical significance, and are not subjected to any other model process such as advection or
EPA/600/R-99/030

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diffusion. Thus, changes in their concentrations reflect the effect of chemical reaction alone. 

Also, their inclusion in the mechanisms does not affect basic gas-phase chemistry since they do

not interact with any of the other species in the mechanism. 

Special procedures are used in the CCTM to determine aerosol production from monoterpenes

since their aerosol yields are relatively large and they are either lumped with other organic

compounds into a single mechanism species or are apportioned among several mechanism

species. The approach involves tracking the rate of reaction of monoterpenes separately from

the rates of their mechanistic representation. The CMAQ emission processor generates emissions

for monoterpenes as a unique species in addition to lumping or apportioning the emissions into

the appropriate mechanism species. Whenever aerosols are being modeled, the unique

monoterpene species is included in the mechanisms and is modeled as a separate species. As

with the counter species, however, the monoterpene species is incorporated in the mechanisms

such that it does not affect the basic gas-phase chemistry. This is described in more detail below. 

A potential future modification to the CMAQ system would involve incorporating a more explicit

representation of monoterpenes in the base mechanisms that would eliminate the need for this

special treatment and would also improve the chemical representation of these species in the gasphase mechanisms (e.g., Stockwell et al., 1997).

& RADM2_AE. Much of the linkage between the RADM2 mechanism and aerosol

formation is relatively straightforward. Aerosol production from SO2 and long-chain

alkanes is derived from the amount of SO2 and HC8 reacted with OH, respectively. 

Similarly, aerosol production from alkyl-substituted benzenes is derived from the sum of

the TOL and XYL reactions with OH. The production from phenols and cresols is based

upon the sum of the CSL reactions with OH and NO3. Thus, special counter species

named SULAER, HC8AER, TOLAER, XYLAER, and CSLAER have been added to

track these reactions.

In the RADM2 mechanism, both monoterpenes and other olefinic compounds are lumped

into the mechanism species OLI. As noted above, however, monoterpenes are modeled

separately whenever aerosols are modeled. The monoterpenes are represented in the

RADM2 mechanism by the species TERP, and the following reactions are added:

TERP + HO  TERPAER + HO

TERP + NO3  TERPAER + NO3

TERP + O3  TERPAER + O3

These reactions use the same rate constants as the reaction of OLI with these species, and

have the TERPAER counter species added to track the throughput of this reaction. Note

that concentrations of the reactants OH, NO3 and ozone are unaffected by these reactions

since their production equals their loss. 
EPA/600/R-99/030

8-9

The final pathway for aerosol production in the RADM2 mechanism is via reaction of

long-chain olefins with OH, NO3 and ozone. The RADM2 mechanism species OLI is

used as the surrogate for long-chain olefins, and thus a counter species product named

OLIAER is added to each of the reactions of OLI with OH, NO3 and ozone. Since OLI 

includes both monoterpenes and other olefins, however, OLIAER tracks the reaction rate

of both. The amount of long-chain olefins reacted is determined by subtracting the

concentration of the counter species TERPAER from that of OLIAER. The yield of

aerosols from long-chain olefins is then applied to this difference to obtain aerosol

production by this pathway. 

& CB4_AE. Since the CB4 gas-phase mechanism is structure-based, individual organic

molecules are often disaggregated and assigned to more than one mechanism species. For

example, long-chain alkenes are apportioned to both the PAR and OLE mechanism

species. Thus, many of the organic mechanism species contain fragments of molecules,

and the identity of the original contributing organic compound is lost. As a result, it is not

possible to ascertain with certainty the amount of long-chain alkanes and alkenes reacting

in the CB4 mechanism, and thus aerosol production via these pathways is omitted. The

production of aerosols from the reactions of toluene, xylene, and cresol is included,

however, by tracking the amounts of TOL, XYL, and CRES that react using the counter

species TOLAER, XYLAER, and CSLAER. The manner in which aerosol production

from monoterpenes is modeled is identical to that used in the RADM2 mechanism.

Monoterpenes are modeled independently as the mechanism species TERP, with rate

constants for the reactions of TERP with OH, O3, and NO3 set to the same values as those

used in the RADM2 mechanism extension.

8.2.4.2 Isoprene Extensions

Over the past few years, the importance of isoprene in ozone formation has become a major

concern. Its representation in the original gas-phase mechanisms was substantially condensed,

partially because of computational resource considerations and partially due to significant

uncertainties about the pathways of its reaction products. Recent mechanistic and environmental

chamber studies have led to a greater understanding of its atmospheric chemistry and thus

improved mechanistic representations (Carter and Atkinson, 1996). In the CMAQ system, two

different levels of more detailed isoprene chemistry have been included in the RADM2

mechanism, and these are referred to as the one-product and the four-product Carter isoprene

mechanisms (Carter, 1996). Both are condensed forms of the more detailed mechanism

developed by Carter and Atkinson (1996). Since this detailed mechanism may be too large to use

in full-scale Eulerian modeling studies, Carter condensed the detailed mechanism to two levels of

detail: one in which isoprene products are represented by four products, and one in which only

one product is used. The four-product mechanism is the lesser condensed of the two, and

includes the explicit representation of many of the isoprene’s unique products (e.g.,

methacrolein, methyl vinyl ketone, and methacrolein’s PAN analogue). The one-product form

lumps the major products into a single species, thereby yielding a more compact albeit less

explicit mechanism. As noted above, these two mechanisms are named RADM2_CIS4 and
EPA/600/R-99/030

8-10

RADM2_CIS1, and both have been linked to aerosols and aqueous chemistry as well. It should

also be noted that the isoprene chemistry incorporated in the CMAQ CB4 mechanism

corresponds to the Carter 1-product form, but the 4-product form is not available for the CB4

mechanism in the CMAQ system

8.2.4.3 Aqueous Chemistry Extensions

The base RADM2 mechanism does not have to be modified to link it to the aqueous chemistry

processes since the aqueous processes in the CMAQ system are similar to those incorporated in

the original RADM model. As described in Chapter 15, other aspects of the linkages require a

separate mechanism with a unique name. The linkages to aqueous chemistry do require some

minor changes to the CB4 mechanism however. These changes were based on a variant of the

CB4 mechanism developed for acid deposition modeling by Gery et al. (1987). In this version, 

the following product species that were omitted in the base CB4 mechanism are included: formic

acid, acetic acid, peroxyacetic acid, and methylhydroperoxide (MHP). Since these species are

products only, their inclusion in the mechanism does not affect the concentrations of any of the

other mechanism species. It should be noted, however, that the concentration of MHP in this

modified mechanism represents an upper limit for two reasons. First, known decomposition

pathways for it are not included in the mechanism. Second, the production of MHP will be

overstated since it is produced by an operator that includes radicals other than the methylperoxy

radical (Gery et al., 1987).

8.2.5 Changing or Adding Mechanisms in CMAQ

As noted in the introduction to this chapter, the CMAQ system has been instrumented with a

generalized chemical mechanism processor to facilitate making changes to existing mechanisms

or adding new mechanisms. The procedures for altering or adding a new mechanism are

described in EPA (1998), and will not be repeated here. It should be emphasized, however, that

the addition of a new mechanism will likely require modifications to the previously mentioned

subsystems that provide key mechanism-specific information, i.e., emissions, initial/boundary

condition, and photolytic rate processors. Changes to an existing mechanism would also likely

require modifications to these processing subsystems if new organic species are added or if an

alternative organic grouping scheme is implemented. If changes are limited such that they affect

only the reactions of intermediate and/or product species, however, these subsystems may not

need to be changed at all, and the modifications can then be implemented solely within the

generalized chemical mechanism processor. For example, the modifications to the base

mechanisms to provide linkages to aerosol and aqueous chemistry and to expand isoprene

chemistry that were described previously did not require any major changes to the other

processors except to add a photolysis rate for acrolein in the photolytic rate processor for the

CIS1 and CIS4 versions of RADM2. 

Although the CMAQ system provides a convenient tool for making mechanism changes, some

caution should be exercised in modifying existing CMAQ mechanisms. The mechanisms

currently in the CMAQ system have been evaluated outside of the CMAQ system using
EPA/600/R-99/030

8-11

environmental chamber data and/or more detailed chemical mechanism representations. Any

proposed changes to reactions or reactions rates that significantly affect model predictions should

normally be subjected to similar independent testing before being introduced into the CMAQ

system and subsequently used in modeling applications. Thus, it would be expected that the

introduction of most changes to a mechanism in the CMAQ system would only be performed by

a researcher who is experienced in atmospheric chemistry and is familiar with the base

mechanism.. Finally, it should be noted that the existing CMAQ mechanisms are fully specified. 

In most instances, it will only be necessary for a user to choose one of the existing mechanisms

for their application, and it will not be necessary to make any changes to that mechanism.

8.3 Reaction Kinetics

The rates of chemical reaction determine whether a species is formed or destroyed by gas-phase

chemistry. Since the CMAQ system treats all reactions as if they are elementary, the laws of

reaction kinetics can be used directly to develop mathematical expressions for the rates of each

chemical reaction. This section describes the rate expressions and the forms of the rate constants

that are used in those expressions, with special emphasis placed on the conventions used in the

CMAQ system. The reader may also wish to refer to Chapter 15 and EPA (1998) for details on

how mechanism data are entered in the CMAQ system. 

8.3.1 Reaction Rates

The rate of a chemical reaction l (rl) can be expressed as the product of a rate constant (kl) and a

term that is dependent on the concentrations of the reactants:

rl 
 kl f (concentration) . (8-2)

For elementary reactions, the concentration dependent term is simply the product of reactant

concentrations, and the rate of reaction takes one of the following forms:

rl 


klC1 for first	order reactions

kl

C1C2 for second	order reactions

kl

C1C2C3 for third	order reactions

(8-3)

where C1, C2,and C3 refer to the concentration of reactants 1, 2 and 3, respectively. Note that

when a species reacts with itself, the concentration dependent term includes the species

concentration squared. Thus, the rate for the reaction NO + NO + O2  2NO2 is equal to

k[NO][NO][O2] and not k[NO][O2]. 

Several important ter-molecular reactions involve O2 and/or N2 which mediate those reactions by

absorbing energy from exothermic bi-molecular reactions. When either N2 or O2 serves this role,

the third body is usually referred to as “M”, where M = N2 + O2. Since their concentrations are

relatively stable in the atmosphere, some mechanism developers convert second- or third-order
EPA/600/R-99/030

8-12

reactions that include these species to a reaction one order lower by multiplying the higher-order

rate coefficient by the concentration of M, O2, or N2. The CMAQ convention is to include thirdbody reactants in the reaction rate calculations if they are explicitly shown in the reaction, and to

omit them if they are not shown or included only as comments. For example, consider the

bimolecular reaction: O1

D + O2  O3P + O2. If the reaction is written in this form, the reaction is

assumed to be second-order and the CCTM will use the appropriate concentration for O2 in the

rate computation. If the reaction is written as O1

D  O3P (or as O1D {+ O2}  O3P, where here

the braces denote a comment), the reaction rate will be assumed to be first-order and the CCTM

will not include the O2 concentration in the reaction rate calculation. In the latter case, the

mechanism developer must specify a pseudo first-order rate constant for the reaction. The same

convention also applies to H2O. 

8.3.2 Rate Constant Expressions

As shown in Equation 8-3, the rate of reaction is related to the concentration term by a constant

of proportionality kl. The rate constant kl can take many forms depending upon the

characteristics of the reaction. One important class of uni-molecular reactions involves the

absorption of radiant energy and subsequent dissociation of the reactant into product species. 

The rate constants for these types of reactions are functions of the incident radiant energy and

properties of the absorbing molecule, such as the absorption cross section and the quantum yield. 

In the CMAQ system, these rate constants are calculated by the photolytic rate processor, and

the details of these calculations are described in Chapter 14. The remainder of the reactions are

classified as thermal, and their rate constants are typically functions of temperature and

sometimes pressure. The calculation of these rate constants is discussed below.

To facilitate incorporating rate constant information for thermal reactions, the CMAQ

generalized mechanism processor (discussed in Chapter 15) has been designed to accept the

standard rate constant expressions used in NASA (1997). Rate constant information is most

often supplied in cms units (i.e., gas concentrations in molecules/cc and time in seconds), but

some mechanisms use mixing ratio units (i.e, gas concentrations converted to mixing ratios in

parts per million and time in minutes). The CMAQ generalized mechanism reader is designed to

accept either, but they must be consistent throughout the mechanism (i.e., the same units must be

used for all rate constant forms that can be expressed in either set of units). Some rate constant

expressions (e.g., falloff expressions and other special forms discussed below) can be expressed

only in cms units, however, and must always be in these units even when mixing ratio units are

being used for all other types of rate constants. The CCTM will automatically perform the

necessary units conversions during the model simulation. Nevertheless, since the CMAQ domain

typically extends through the entire troposphere, cms units are usually preferred because

differences in number density differences with height are explicitly accounted for with those

units.

Descriptions of the forms of rate constant expressions currently used in the CMAQ system are

presented next. 
EPA/600/R-99/030

8-13

& Arrhenius Equation. Many rate constants exhibit a temperature dependence that

corresponds to the Arrhenius equation: 

k 
 A e(	E/T ) (8-4)

where A is the pre-exponential factor, E is the activation energy divided by the gas 

constant R, and T is the temperature in degrees Kelvin. For this form of reaction, either 

cms or mixing ratio units may be used, and only A and E need to be specified. 

& Temperature Dependent A-factors. For some reactions, the temperature dependence of

the pre-exponential factor can become significant, and the Arrhenius equation does not

hold. These rate constant expressions can often be put in the following form that is

available in the CMAQ system:

k 
 A (T/ 300)B e(	E/T ) (8-5)

where A, E, and T are defined as above, and B is an empirically derived constant that

provides a best fit to the data (Pitts-Finlayson and Pitts, 1986). For this form, either set

of units can be used, and only A, E and B need to be specified.

& Falloff Expressions. Several ter-molecular reactions exhibit pressure dependencies that

can be significant when modeling atmospheric chemistry. These can be especially

important when modeling from the troposphere through the stratosphere. In these cases,

the rate constant increases with increasing pressure. In effect, the behavior of these

reactions approaches second-order at high pressure and third-order at low pressure. 

Equation 8-6 gives an effective second-order rate constant for the falloff region between

these two limits.

k 
 k0 [M]

1  k0[M]/k

F{1  [N	1 log(k0[M] /k)]2

}	1

C (8-6)

In Equation 8-6, k0 and k are the low- and high-pressure limiting rate constants,

respectively, and are calculated using the temperature dependent A-factor form described

above. The parameters FC and N are also reaction specific, but for atmospheric

conditions are very often 0.6 and 1.0 respectively (Finlayson-Pitts and Pitts, 1986). For

this type of rate constant expression, A, E, and B must be specified for both k0 and k ,

and only cms units are allowed. If the parameters N and Fc are not specified, the values

listed above will be used. 

& Special Forms. The following special rate constant forms are also in general use and

have been included in the CMAQ system:
EPA/600/R-99/030

8-14

k 
 k1  k2[M] (8-7)

k 
 k0  (

k3 [M]

1  k3[M] /k2

) (8-8)

k 
 A ( 1.0  0.6P ) (8-9)

Equation 8-7 is used for the rate constants of the reactions forming hydrogen peroxide

from hydroperoxy radicals (HO2 + HO2  H2O2 and HO2 + HO2 + H2O  H2O2). Equation

8-8 is used for the reaction of the hydroxyl radical with nitric acid (HO + HNO3  NO3 +

H2O), and Equation 8-9 is used for the reaction of the hydroxyl radical with carbon

monoxide (HO + CO  HO2 + CO2). In these equations, k0, k1, k2, and k3 are calculated

using the Arrhenius equation, and A and E must be specified for each, with A given in

cms units. In Equation 8-9, P is the atmospheric pressure in atmospheres and A can be

specified in either set of units.

& Reverse Equilibria Forms. The CMAQ system also includes a special reverse

equilibrium form for first-order decomposition reactions. With these types of reactions,

the equilibrium constant is input in a form similar to the Arrhenius equation. Thus, the

rate constant can be expressed as follows:

k 
 kf / Ae(	E / T ) (8-10)

In Equation 8-10, kf is the rate constant for the forward reaction forming a species, and

the denominator is an Arrhenius-like form for the equilibrium constant. These reaction

rate coefficient types are used, for example, for the decomposition of pernitric acid and

nitrogen pentoxide (i.e., HNO4  HO2 + NO2 and N2O5  NO2 + NO3). In the CMAQ

system, A, E, and the corresponding forward reaction must be specified. Either set of

units may be used with this form.

8.4 Mathematical Modeling

This section describes the mathematical modeling concepts used in the CCTM to simulate gasphase chemical reactions. The first sub-section describes the fundamental equations that must be

solved and some of the difficulties encountered in obtaining solutions to them. The next two subsections describe the two gas-phase chemistry solvers that are currently available in the CCTM.

The last sub-section summarizes some of the important solver characteristics.

8.4.1 Governing Equations

As described in Chapter 5, operator splitting allows gas-phase chemistry to be de-coupled from

physical processes such as advection, diffusion and deposition, and, as noted in the introduction

to this chapter, gas-phase chemistry is modeled separately from aerosol formation and aqueous

chemistry. As a consequence, continuity equations for each gas-phase mechanism species can
EPA/600/R-99/030

8-15

dCi

dt 
 Pi

(c,t) 	 Li(c,t) Ci 
 fi(c,t) i 
 1,2,á,N (8-14a)

be formulated and solved independently on a cell-by-cell basis. By using the kinetics laws for

elementary reactions and applying a mass balance to each species, the following equation for the

rate of change of each species concentration can be derived for a single cell:

dCi

dt 
 Pi 	 Li Ci (8-11)

where

Pi 
 M

mi

l
1

i,lrl (8-12)

and

Li Ci


 M

ni

l
1

rl (8-13)

In Equations 8-11 through 8-13, Ci

 is the concentration of species i, i,l is the stoichiometric

coefficient for species i in reaction l, and rl

 is the rate of reaction l. The sum l = 1...mi is over all

reactions in which species i appears as a product, and the sum l = 1...ni

 is over all reactions in

which species i appears as a reactant. 

Equation 8-11 states that the change in species concentration is equal to the chemical production

of that species minus its chemical loss, and it is the fundamental species continuity equation for

gas-phase chemistry that is solved in the CCTM. If the concentration of species i is known at

some particular time, its concentration can be computed at a later time by solving Equation 8-11. 

Since the production and loss terms contain references to other species concentrations, however,

Equation 8-11 must be solved as part of a coupled set of ordinary differential equations. 

It should also be noted that the CCTM contains an option for including emissions in either the

vertical diffusion process or in gas-phase chemistry. When emissions are included in gas-phase

chemistry, the fundamental form of the Equation 8-11 is not altered since an emission source

term is simply a zeroth-order production rate. Thus, for the discussions that follow, the

production term Pi

 is assumed to include an emission source term if species i is emitted and

emissions are included in gas-phase chemistry.

The system of non-linear, ordinary differential equations (ODEs) arising from Equation 8-11 for

N species can be expressed as follows:
EPA/600/R-99/030

8-16

c(t

0

) 
 c0 (8-14b)

with the initial conditions:

where c is the vector of species concentrations and N is the total number of species in the

chemical mechanism. Numerical “marching” methods are typically employed to obtain

approximate solutions for this class of problem. In these methods, the concentrations of all

species are given at the starting point and a solution is computed at selected time intervals (i.e.,

time steps) using the right hand side of Equation 8-14a. Two sources of difficulty arise in

obtaining numerical solutions to these equations as they apply to atmospheric chemistry

problems. First, the system is nonlinear because the production and loss terms include secondand third-order reactions. Second, the system of equations is “stiff” because of the widely

varying time scales of the chemical reactions and complex interactions among species. A stiff

system can be described mathematically as one in which all the eigenvalues of the Jacobian

matrix of Equation 8-14a are negative, and the ratio of the absolute values of the largest-tosmallest real parts of the eigenvalues is much greater than one. Systems are typically termed stiff

if the latter ratio is greater than 104

. For atmospheric chemistry problems, the ratio is often

greater than 1010, making the system very stiff (Gong and Cho, 1993). 

The stiffness problem coupled with the fact that these equations must be solved for tens of

thousands of cells in a typical modeling application require that special numerical methods be

employed. The use of standard explicit methods is often precluded because relatively small time

steps are required to maintain numerical stability and obtain accurate solutions. On the other

hand, classical implicit methods that are both accurate and stable have not often been used

because of high computational demands. As a result, several special techniques have been

developed to obtain reasonably accurate solutions in a computationally efficient manner. At

present, two solution techniques are available in the CCTM: the implicit Sparse-Matrix

Vectorized Gear algorithm (SMVGEAR) and a variant of the explicit Quasi-Steady State

Approximation (QSSA) method. Each of these is described in detail below. Although each of

these techniques, as well as others that have been used in atmospheric chemistry models, have

been designed to be computationally efficient, they still consume 50 to 90% of the total CPU

time used in a model simulation. Thus, obtaining a numerical solution to Equation 8-14a,b is

normally the most computationally intensive portion of the CCTM.

8.4.2 SMVGEAR

Numerical solvers based on the algorithm developed by Gear (1971b) have traditionally been

used to obtain accurate solutions to stiff ODE problems. The technique is implicit in method,

does not amplify errors from one step to another and incorporates automatic step size and error

control. In fact, solvers based on this method have often been used to evaluate other faster

solution methods for accuracy (e.g., Odman et al., 1992; Gong and Cho, 1993; Dabdub and

Seinfeld, 1995; and Saylor and Ford, 1995). Past versions of this code have rarely been installed
EPA/600/R-99/030

8-17

in Eulerian models, however, because of the high computational cost. Jacobson and Turco

(1994) have modified the Gear algorithm to obtain considerable speedups on vector computers. 

The SMVGEAR algorithm is highly vectorized to improve computational performance on vector

computers and it incorporates special sparse matrix techniques to increase computational

efficiency. Further enhancements have been obtained by ordering the cells for processing. Each

of these are described further below. Since the technique is based on Gear's original algorithm, it

is briefly described first. For more details on the Gear method, the reader is referred to Gear

(1971a) and Gear (1971b).

8.4.2.1 Standard Gear Algorithm

The Gear algorithm is one of a class of methods referred to as backward differentiation formulae

(BDF). The generalized BDF that forms the basis for Gear's method can be expressed as follows:

c n 
 h0 f(c n ,t

n )  M

p

j 
1

j cn 	j (8-15)

where n refers to the time step, h is the size of the time step, p is the assumed order, 0 and j are

scalar quantities that are functions of the order, and f(cn,tn) is the vector of production and loss

terms defined by the right hand side of Equation 8-14a. The method is implicit since

concentrations at the desired time step n depend on values of the first derivatives contained in

f(cn,tn) that are functions of the concentrations at the same time. The order of the method

corresponds to the number of concentrations at previous time steps that are incorporated in the

summation on the right hand side of Equation 8-15.

To facilitate changing step size and estimating errors, the multi-step method in Equation 8-15 is

transformed to a multi-value form in which information from only the previous step is retained,

but information on higher order derivatives is now used (Gear, 1971b). In this formulation, the

solution to Equation 8-14a,b is first approximated by predicting concentrations and higher order

derivatives at the end of a time step for each species using the following matrix equation:

zi,n,(0) 
 B zi,n	1 (8-16)

where zi

 = [ci, hc'i,..., hpci

(p)/p!]T

, the subscript n,(0) refers to the prediction at the end of time

step n, and the subscript n-1 refers to values obtained at the end of previous time step (or the

initial conditions when n = 1). B is the Pascal triangle matrix, the columns of which contain the

binomial coefficients:
EPA/600/R-99/030

8-18

B 


1111 à 1 1

123 à p	1 p

1 3 à

1 à



0 1 p

1

(8-17)

The prediction obtained from Equation 8-16 is then corrected by solving for zi,n such that the

following relations hold for all species:

zi,n 
 zi,n,(0)  r [ hfi

(c n ,t

n ) 	 h c

i,n,(0)] (8-18)

In Equation 8-18, r is a vector of coefficients that is dependent on the order, but r2, the element

corresponding to the first derivative location in z, is always equal to one. Thus, the correct value

of ci,n is obtained when the calculated value of c1i,n equals fi

(cn,tn) in Equation 8-18. An

approximate solution for ci,n is obtained by applying Newton's method to the system of equations

that correspond to the first equation in 8-18 for all species. This leads to the following corrector

iteration equation:

cn,(m1) 
 cn,(m)  [I 	 h0J ]	1 r1 [ hf(cn,(m)

,t

n ) 	 h
cn,(m)

] (8-19)

where m refers to the Newton iteration number, the vector f(cn,tn) is calculated using

concentrations computed for the m-th iteration, 
c is a vector containing the most recent

estimates of first derivatives, I is the identity matrix, and J is the Jacobian matrix whose entries

are defined as:

Jij 
 0 fi

( c,t

n )

0 cj

i,j 
 1,2,áN (8-20)

At the end of each iteration, the vector containing the first derivatives ( 
c) is updated, but higher

order derivatives in z need not be computed until convergence is achieved.

After convergence is achieved, the local truncation error for each species, ei

, is given by:

ei 
 1

p  2

h p 1 c

( p  1)

i,n  O(h p2 ) (8-21)

The error is estimated in the algorithm by neglecting the O(hp+2) term and approximating hp+1

ci

(p+1)

from the backward difference of hp

ci

(p)

/p! which can be calculated using the last components of
EPA/600/R-99/030

8-19

the vectors zi,n(m) and zi,n-1 defined above. These error estimates are used to control accuracy and

to change both the time step size and the order of the method when warranted. 

Although several variants of the basic Gear algorithm have been developed, the fundamental

computational scheme can be described generically as follows. At the beginning of any

integration interval, the order is set to one and the starting time step is either calculated or

selected by the user. Each time step is initiated by predicting concentrations at the end of the

time step using Equation 8-16. Corrector iterations are then carried out using Equation 8-19 until

prescribed convergence criteria are achieved or non-convergence is deemed to have occurred. 

When convergence is achieved, the error is computed using the approximation for Equation 8-

21. If the error is within prescribed limits, the solution for the step is accepted and the step size

and order to be used in the next step are estimated. The size of the time step is estimated for the

current order, the next lowest order, and the next highest order using error estimates derived

from Equation 8-21 for the next step. From these, the largest time-step size and its

corresponding order are then selected for use in the next step. If either the convergence or error

test fails, the integration is restarted from the beginning of the failed time step after re-evaluating

the Jacobian matrix, reducing the size of the time step, and/or lowering the order. 

The individual operations described above are normally handled automatically in Gear

algorithms. To reduce computational demands, the algorithms also utilize several empirically

based rules. For example, the Jacobian matrix is only updated after a prescribed number of

successful steps have been completed, if the order changes, or if a convergence or error test

failure occurs. In the Newton iterations, progress towards convergence is monitored and the

iterations halted if the progress is judged insufficient or if three complete iterations have been

performed without convergence being achieved. To maintain numerical stability, changes to the

size of the time step and the order are allowed no more than once every p+1 steps for a p-th

order method. 

8.4.2.2 Vectorized Gear Algorithm

Jacobson and Turco (1994) have modified the Gear algorithm to incorporate additional

computational efficiencies that can achieve speedups on the order of 100 on vector computers. 

About half of the improvement is attributed to enhanced vectorization, and half to improved

matrix operations. Because of the improved matrix operations, SMVGEAR also runs faster than

traditional Gear solvers on non-vector machines, but the greatest benefit will be obtained with

vector machines. The major enhancements incorporated in SMVGEAR are now described in

more detail.

In the conventional application of the Gear-type algorithm, the method is applied to each grid

cell individually. With this implementation, the length of the innermost loops in most

computations corresponds to the number of species, which is typically on the order of 30 to 100. 

In SMVGEAR, the modeling domain is divided into blocks of cells, and the Gear algorithm is

applied to each cell within a block simultaneously. With this structure, the length of the

innermost loops for most calculations is equal to the number of cells in a block. Substantial
EPA/600/R-99/030

8-20

improvements in vectorization can therefore be obtained if the block size is larger than the

number of species. Jacobson and Turco (1994) found that a block size on the order of 500 cells

achieves about 90% of the maximum vectorization speed on a Cray C-90 computer. The use of

larger block sizes may not substantially increase computational speed and may incur some

additional penalties. For example, memory requirements increase with increasing block size. 

Furthermore, the size of a time step in SMVGEAR is the same for each cell within a block and is

based on the time-step estimate for the stiffest cell in the block. Limiting the block size can

therefore reduce excess calculations that need to be performed for the less stiff cells. Jacobson

(1995) also achieved computational savings by ordering the cells by stiffness before dividing

them into blocks. Each block then tends to contain cells of similar stiffness, thereby reducing

excess computations for some cells. Jacobson found excess computations were reduced by about

a factor of two, and that these reductions more than offset the additional work incurred with

calculating and sorting the cells by stiffness. 

Much of the computational intensity associated with the Gear method arises from the matrix

operations that are needed to perform the Newton iterations in the corrector step. Jacobson and

Turco have introduced two techniques to improve the efficiency of these operations. First, all

known cases of multiplication by zero in matrix multiplication and decomposition are eliminated.

This is particularly beneficial for atmospheric chemistry problems since the Jacobian matrices are

almost always sparse (i.e., they contain a large number of zero entries). However, decomposition

techniques that are applied to these matrices often result in substantial fill-in, thereby reducing

the benefits of employing sparse-matrix techniques. To maintain maximum sparsity after the

decomposition operation, SMVGEAR orders the species in the Jacobian such that those with the

fewest partial derivative terms are located in the top rows, and those with the most are in the

bottom rows. At the very beginning of the program, the ordering is done and a symbolic

decomposition is performed to identify multiplies by zero. Since the computations associated

with the matrix operations are determined entirely by the structure of the chemical mechanism, it

is necessary to do this only once and the results can then be applied to every cell uniformly. 

The SMVGEAR algorithm has been implemented in the CCTM with minor changes to the

original algorithm but extensive changes to the original computer code. The code changes arose

from linking the algorithm to the generalized chemistry processor used in the CMAQ system, and

developing a driver routine specific to the CCTM structure. The only significant change to the

algorithm involved modifying the code to eliminate the possibility of obtaining negative

concentrations. With the standard Gear algorithm, negative concentrations can occur when a

species is rapidly depleted, although the magnitudes of these concentrations are extremely small. 

In the CCTM implementation, a lower bound on allowable concentrations is applied, and the

rates of change and the Jacobian matrix are modified to reflect that no changes in concentration

are occurring when the lower bound is reached. Comparisons with the standard Gear algorithm

show virtually no differences in species concentrations above the lower bound, but a small

penalty in computational performance is incurred. Nevertheless, the approach insures a positivedefinite solution.
EPA/600/R-99/030

8-21

The computational performance of SMVGEAR is also affected by the error tolerances used for

the Newton iteration convergence tests and the local truncation error tests. Error control in

SMVGEAR is similar to that used in LSODE (Hindmarsh, 1980). Both a relative and an absolute

tolerance must be specified. In their discussion of ODE solvers, Byrne and Hindmarsh (1987)

relate the relative error tolerance to the number of accurate digits and the absolute error

tolerance to the noise level (i.e., the size of the largest concentration that can be neglected). If r

is the number of accurate digits required, then Byrne and Hindmarsh suggest setting the relative

tolerance to 10-(r+1). The absolute error tolerances cannot be specified as generically because

particular model applications may require different accuracies for the mechanismn species. In

the CCTM implementation of SMVGEAR, the relative tolerance and absolute tolerances have

been preset to 10-3 and 10-9 ppm, respectively. However, these values can be changed by the

user relatively easily in the CCTM as described in EPA (1998). 

8.4.3 QSSA Solver

The QSSA solver is a low order, explicit solver that exhibits good stability for stiff systems. 

Although less accurate than the Gear solver, it is still a reasonably accurate, fast solver that is

especially suitable for large scale grid models. There are actually many versions of solvers that

go by the name “QSSA” (e.g., Mathur et al., 1998). The solver developed for the CCTM is a

predictor/corrector version based on the one developed by Lamb and used in the Regional

Oxidant Model (Lamb, 1983, and Young et al., 1993).

The QSSA method originates from assuming integration time steps sufficiently small such that in

Equation 8-11, the production and loss rate terms Pi and Li can be considered constant. If the

Jacobian is diagonally dominant, this assumption may be valid as t  0, and the time step

solution at tn+1 = tn + t can be written formally as:

Ci 
 Ci



 ( Ci

n 	 Ci



) e 	Li t (8-22)

where and is the solution at tn C . i




 Pi / Li Ci



The CCTM QSSA makes no a priori assumptions about reaction time scales. For example, there

are no assumed steady states. However, the algorithm separates the numerical computation into

either an Euler step, a fully explicit integration, or an asymptotic evaluation based on

photochemical lifetimes estimated from an initial, predictor calculation of Pi and Li. The cut-offs

and equations for each predictor step are:

Eulerstep: Li t z 0.01 Ci 
 Ci

n  ( Pi  Li Cin

) t

Explicit: 0.01 y Li t y 10.0 Ci 
 Ci



 ( Ci

n 	 Ci



) e 	L

Asymptotic: Li t | 10.0 Ci 
 Ci



(8-23)

The CMAQ QSSA algorithm proceeds in three stages: an optimal time step determination, a
EPA/600/R-99/030

8-22


 Ci 	 Ci

n 
 z  Cin

. (8-24)

Ctest 
 [ NO]  [ NO2]  [ O3] (8-26)


t

 
 	 1

L

ln 1 	 

Cn


 C

	 Cn 
 (8-27)

 
 0.001, if d[NO]

dt

/ [NO] | 0.5% per minute

0.005, otherwise

(8-29)

predictor evaluation, and a corrector evaluation. In the first stage, an optimal chemistry time

step interval t is determined at time tn based on a tolerance parameter, , such that

Substituting Equation 8-22 into 8-24 gives:

t z 	 1

Li

ln 1 	 

Ci

n


 Ci



	 Ci

n


 . (8-25)

The algorithm attempts to weight the time step determination against species whose

concentrations are very small compared to the primary oxidants. These usually include some of

the fastest reacting radicals. The following quantity is defined as

Then the following quantity is computed for only those species that satisfy C > J Ctest ( J = 0.01):

If L = 0, 


t

 
  Cn

P

(8-28)

The tolerance parameter  is controlled by the rate at which the key NO species concentrations

are changing; if they are changing too rapidly, the tolerance is tightened, otherwise it is relaxed:
EPA/600/R-99/030

8-23

After determining a time scale for each species , t is set to min{
t}. For computational

efficiency, t is further constrained to be no less than one second and of course is also

constrained to be no greater than the total integration time.

In the predictor step, the species concentrations are updated (Ci  Ci

* ) with the optimal time step

using the Euler-step, explicit or asymptotic calculations described above. Once Ci

* is calculated,

QSSA computes new production and loss rate coefficients Pi

*

 and Li

*

, respectively. 

In the corrector step, the final production rate is set as the average of the initial and predictor

values, , and the new concentration Ci for time tn+1 = tn P ̃ + t is computed using i 
 ( P 

i  Pi ) / 2

the same cut-offs based on Li that were determined in the predictor step: 

Eulerstep: Ci 
 Ci

n  ( P ̃

i  L 

i Ci

n

) t

Explicit: Ci 
 P ̃

i / L 

i  ( Ci

n 	 P ̃

i / L 

i ) e

	L

i t

Asymptotic: Ci 
 P ̃

i / L 

i

(8-30)

The algorithm has been optimized for vector computers by moving the grid cell loops into the

innermost position (Young et al., 1993) as is done in SMVGEAR described above. To minimize

storage requirements, grid cell blocking has been implemented wherein blocks of cells are

handed off to the solver in sequence. The CMAQ QSSA has also been optimized for the Cray

T3D by utilizing various coding techniques aimed specifically at that architecture. Some of these

optimizations are described in Chapter 19. 

8.4.4 Summary

Gear type solvers have generally been considered the most accurate for gas chemistry,

representing “exact solutions” (provided the controlling numerical tolerances are sufficiently

tight). Until the advent of SMVGEAR, however, it has not been feasible to use these solvers in

Eulerian models. SMVGEAR is designed to run optimally on high end vector computers such as

the Cray C90, but its use on scalar machines may be impractical. Although less accurate, the

QSSA solver may be more suitable for those types of computers.

The issue of accuracy versus computational speed is a continuing concern (Mathur et al., 1998),

particularly since the availability of high-end machines like the Cray C90 is limited. The CMAQ

QSSA solver presents a reasonable, numerically efficient alternative and, although not

considered as accurate as a Gear-type solver, may be sufficiently accurate for modeling, taking

into consideration the uncertainties of the other numerical modeling components. Accuracy can

be somewhat improved by using shorter integration steps in the solver, but then computational

work mounts, defeating the purpose. For the CMAQ QSSA, accuracy will be compromised when

the ODE system is very stiff and the system Jacobian strays from diagonal dominance. 
EPA/600/R-99/030

8-24

Nevertheless, the trade-off between solution efficiency and accuracy may still warrant its use in

these cases. 

Finally, both the SMVGEAR and the QSSA solvers have been incorporated in the CMAQ system

with the predefined accuracy controls that were described in the previous two sections. Of

course, these error controls can be changed by the user if desired, but that will of course affect

both the prediction accuracy and the efficiency of obtaining a solution. Note also, that either

solver can be used with any of the CMAQ chemical mechanisms that were described in section

8.2.

8.5 References

Atkinson R., Lloyd A. C. and Winges L. (1982) An updated chemical mechanism for

hydrocarbon/NOx/SO2 photooxidations suitable for inclusion in atmospheric simulation models.

Atmos. Environ., 16, 1,341-1,355.

Bowman F. M., Pilinis C., and Seinfeld J. (1995) Ozone and aerosol productivity of reactive.

Atmos. Environ., 29, 579-589.

Byrne G. D. and Hindmarsh A. C. (1987) Stiff ODE solvers: a review of current and coming

attractions. J. Comput. Phys. 70, 1-62.

Carter W. P. L. (1988) Appendix C Documentation of the SAPRC Atmospheric Photochemical

Mechanism Preparation and Emissions Processing Programs for Implementation in Airshed

Models. Final Report for California Air Resources Board Contract No. A5-122-32.

Carter W. P. L. (1990) A detailed mechanism for the gas-phase atmospheric reactions of organic

compounds. Atmos. Environ. 24A, 481-515.

Carter W. P. L. (1996) Condensed atmospheric photooxidation mechanisms for isoprene. Atmos.

Environ. 24, 4,275-4,290.

Carter W. P. L. and Atkinson R. (1996) Development and evaluation of a detailed mechanism

for the atmospheric reactions of isoprene and NOx. Int. J. Chem. Kinet. 28, 497-530.

Carter W. P. L., Luo D. and Malkina I. L. (1997) Environmental Chamber Studies for

Development of an Updated Photochemical Mechanism for Reactivity Assessment. Final Report

for California Air Resources Board Contract No. 92-345, Coordinating Research Council, Inc.,

Project M-9 and National Renewable Energy Laboratory, Contract ZF-2-12252-07. 

Chang J. S., Brost R. A. , Isaksen I. S. A., Madronich S., Middleton P., Stockwell W.R. and

Waleck C.J. (1987) A three-dimensional Eulerian acid deposition model: physical concepts and

formulation, J. geophys. Res., 92, 14,681 - 14,700.
EPA/600/R-99/030

8-25

Dabdub D. and Seinfeld J. H. (1995) Extrapolation techniques used in the solution of stiff ODEs

associated with chemical kinetics of air quality models. Atmos. Environ. 29, 403-410.

Dodge M.C. (1989) A comparison of three photochemical oxidant mechanisms, J. geophys. Res.,

94, 5,121-5,136.

EPA (1989) Procedures for Applying City-specific EKMA. EPA-450/4-89-012.

EPA (1991) User's Guide for the Urban Airshed Model, Volume I: User's Manual for UAM

(CB4). EPA-450/4-90-007a.

EPA (1998) EPA Third-Generation Air Quality Modeling System, Models-3 Volume 9b User

Manual. EPA-600/R-98/069b.

Gear C. W. (1971a) Numerical Initial Value Problems in Ordinary Differential Equations.

Prentice-Hall, Englewood Cliffs, NJ.

Gear C. W. (1971b) The automatic integration of ordinary differential equations. Comm. ACM

14, 176-179.

Gery M. W., Morris R. E., Greenfield S. M., Liu M. K., Whitten G. Z., and Fieber J. L. (1987)

Development of a Comprehensive Chemistry Acid Deposition Model (CCADM). Final Report

for Interagency Agreement DW 14931498, U. S. Environmental Protection Agency and U. S.

Department of Interior. 

Gery M. W., Whitten G. Z., Killus J. P. and Dodge M. C. (1989) A photochemical kinetics

mechanism for urban and regional scale computer modeling. J. geophys. Res. 94, 12,925-12,956.

Gong W. and Cho H. R. (1993) A numerical scheme for the integration of the gas-phase

chemical rate equations in three-dimensional atmospheric models. Atmos. Environ. 27A, 2,147-

2,160.

Hindmarsh A. C. (1980) LSODE and LSODI, two new initial value ordinary differential

equation solvers. ACM Newsl. 15, 10-11.

Hough A. (1988) An intercomparison of mechanisms for the production of photochemical

oxidants. J. geophys. Res., 93, 3,789-3,812.

Jacobson M. and Turco R. P. (1994) SMVGEAR: A sparse-matrix, vectorized Gear code for

atmospheric models. Atmos. Environ. 28, 273-284.

Jacobson M. (1995) Computation of global photochemistry with SMVGEAR II. Atmos. Environ.

29, 2,541-2,546.
EPA/600/R-99/030

8-26

Jeffries H. E. (1995) Photochemical Air Pollution. Chapter 5 in Composition, Chemistry, and

Climate of the Atmosphere. Ed. H. B. Singh, Von Nostand-Reinhold, New York.

Jeffries H. E., Gery M. and Murphy K. (1993) Advanced Chemical Reaction Mechanisms and

Solvers for Models-3. Progress Report for EPA Cooperative Agreement CR-820425.

Lamb, R.G. (1983) A Regional Scale (1000 km) Model of Photochemical Air Pollution. Part I -

Theoretical Formulation. EPA-600/3-83-035, U. S. Environmental Protection Agency, Research

Triangle Park, NC.

Leone J.A. and Seinfeld J.H. (1985) Comparative analysis of chemical reaction mechanisms for

photochemical smog. Atmos. Environ., 19, 437-464.

Lurmann F. W., Carter W. P. L. and Coyner L. A. (1987) A Surrogate Species Chemical

Reaction Mechanism for Urban Scale Air Quality Simulation Models Volume 1. EPA-600/3-87-

014a.

Mathur R., Young J. O., Schere K. L., and Gipson G. L. (1998) A Comparison of Numerical

Techniques for Solution of Atmospheric Kinetic Equations. Atmos. Environ., 32, 1,535-1,553.

NASA (1997). Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling

Evaluation No. 12. JPL Publication 97-4, Jet Propulsion Laboratory, Pasedena, CA.

Odman, M. T., Kumar N. and Russell A. G. (1992) A comparison of fast chemical kinetic solvers

for air quality modeling. Atmos. Environ. 26A, 1,783-1,789.

Pandis S. N., Harley R. A., Cass G. R. and Seinfeld J. H.(1992) secondary aerosol formation and

transport. Atmos. Environ. 26A, 2,269-2,282.

Pitts-Finlayson B.J. and Pitts J.N. (1986) Atmospheric Chemistry: Fundamentals and

Experimental Techniques, J. Wiley and Sons, New York.

SAI (1993) Systems Guide to the Urban Airshed Model (UAM-V). Systems Applications

International, San Rafael, CA.

Saylor, R. D. and Ford G. D. (1995) On the comparison of numerical methods for the integration

of kinetic equations in atmospheric chemistry and transport models. Atmos. Environ.29, 2,585-

2,593.

Stockwell W. R., Middleton P. and Chang J. S. (1990) The second generation regional acid

deposition model chemical mechanism for regional air quality modeling. J. geophys. Res. 95

(d10), 16,343-16,367.
EPA/600/R-99/030

8-27

Stockwell W.R. (1986) A homogeneous gas phase mechanism for use in a regional acid

deposition model, Atmos. Environ., 20, 1,615-1,632.

Stockwell W. R., Kirchner F., Kuhn M., and S. Seefeld (1997) A new mechanism for regional

atmospheric chemistry modeling. J. geophys. Res. 102 (D22), 25,847-25,879.

Whitten G. Z., Hogo H. and Killus J. P. (1980) The carbon bond mechanism: a condensed kinetic

mechanism for photochemical smog. Envir. Sci. Technol. 14, 690-701. 

Young J. O., Sills E., Jorge D. (1993) Optimization of the Regional Oxidant Model for the Cray

Y-MP. EPA/600/R-94-065, U. S. Environmental protection Agency, Research Triangle Park,

NC.

Appendix 8A Chemical Mechanisms Included in the CMAQ System

Table 8A-1. CB4 Mechanism Species List

Table 8A-2. RADM2 Mechanism Species List

Table 8A-3. CB4 Mechanism

Table 8A-4. CB4_AE Mechanism 

Table 8A-5. CB4_AQ Mechanism 

Table 8A-6. CB4_AE_AQ Mechanism

Table 8A-7. RADM2 and RADM2_AQ Mechanisms

Table 8A-8. RADM2_AE and RADM2_AE_AQ Mechanisms

Table 8A-9. RADM2_CIS1 and RADM2_CIS1_AQ Mechanisms

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms 

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms 

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

8-28

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms 

Notes to Tables 8A-3 through 8A-12:

a) The mechanism listings are divided into two parts. The first lists the reactions and the

second lists the rate constant expressions.

b) The parameters for the rate constants are given in cms units. Rate constants

calculated in cms units for T=298 °K and P= 1 atm are shown in the rightmost

column of these listings.

c) For photolytic reactions, photo table refers to the photolysis rates described in

Chapter 14. The rate constant for all photolytic contains a zero entry in these tables,

but is calculated in the CCTM as the product of the scale factor and the photolysis

rate that is calculated by the CMAQ photolysis rate processor.

d) The falloff rate expression referred to in these tables is Equation 8-6 in Section 8.3.2.

Table 8A-1

CB4 Mechanism Species List

Nitrogen Species

NO Nitric oxide

NO2 Nitrogen dioxide

HONO Nitrous acid

NO3 Nitrogen trioxide

N2O5 Nitrogen pentoxide

HNO3 Nitric acid

PNA Peroxynitric acid

Oxidants

O3 Ozone

H2O2 Hydrogen peroxide

Sulfur Species

SO2 Sulfur dioxide

SULF Sulfuric acid

Atomic Species

O Oxygen atom (triplet)

O1D Oxygen atom (singlet)

Odd Hydrogen Species

OH Hydroxyl radical

HO2 Hydroperoxy radical

Carbon oxides

CO Carbon monoxide

Hydrocarbons

PAR Paraffin carbon bond (C-C)

ETH Ethene (CH2=CH2)

OLE Olefinic carbon bond (C=C)

TOL Toluene (C6H4-CH3)

XYL Xylene (C6H5-(CH3)2)

ISOP Isoprene

Carbonyls and phenols

FORM Formaldehyde

ALD2 Acetaldehyde and higher aldehydes

MGLY Methyl glyoxal (CH3C(O)C(O)H)

CRES Cresol and higher molecular weight phenols

Organic nitrogen

PAN Peroxyacyl nitrate (CH3C(O)OONO2)

NTR Organic nitrate

Organic Radicals

C2O3 Peroxyacyl radical (CH3C(O)OO·)

ROR Secondary organic oxy radical

CRO Methylphenoxy radical

Operators

XO2 NO-to-NO2 Operation

XO2N NO-to-nitrate operation
EPA/600/R-99/030

8-29

Products of organics

TO2 Toluene-hydroxyl radical adduct

OPEN High molecular weight aromatic

oxidation ring fragment

ISPD Products of isoprene reactions

Species added for aerosols

SULAER Counter species for H2SO4 production

TOLAER Counter species for toluene reaction

XYLAER Counter species for xylene reaction

CSLAER Counter species for cresol reaction

TERPAER Counter species for terpene reaction

TERP Monoterpenes

Species added for aqueous chemistry

FACD Formic acid 

AACD Acetic and higer acids 

PACD Peroxy acetic acid 

UMHP Upper limit of methylhydroperoxide 
EPA/600/R-99/030

8-30

Table 8A-2

RADM2 Mechanism Species List

Nitrogen Species

NO Nitric oxide

NO2 Nitrogen dioxide

HONO Nitrous acid

NO3 Nitrogen trioxide

N2O5 Nitrogen pentoxide

HNO3 Nitric acid

HNO4 Peroxynitric acid

Oxidants

O3 Ozone

H2O2 Hydrogen peroxide

Sulfur Species

SO2 Sulfur dioxide

SULF Sulfuric acid

Atomic Species

O3P Oxygen atom (triplet)

O1D Oxygen atom (singlet)

Odd Hydrogen Species

HO Hydroxyl radical

HO2 Hydroperoxy radical

Carbon oxides

CO Carbon monoxide

Alkanes

ETH Ethane

HC3 Alkanes w/ 2.7x10-13 > k OH < 3.4x10-12

HC5 Alkanes w/ 3.4x10-12 > k OH < 6.8x10-12

HC8 Alkanes w/ k OH > 6.8x10-12

Alkenes

OL2 Ethene

OLT Terminal olefins

OLI Internal olefins

ISO Isoprene

Aromatics

TOL Toluene and less reactive aromatics

XYL Xylene and more reactive aromatics

CSL Cresol and other hydroxy substituted aromatics 

Carbonyls

HCHO Formaldehyde

ALD Acetaldehyde and higher aldehydes

KET Ketones

GLY Glyoxal

MGLY Methyl glyoxal 

DCB Unsaturated dicarbonyl

Organic nitrogen

PAN Peroxyacetyl nitrate and higher PANs

TPAN H(CO)CH=CHCO3NO2

ONIT Organic nitrate

Organic peroxides

OP1 Methyl hydrogen peroxide

OP2 Higher organic peroxides

PAA Peroxyacetic acid

Organic acids

ORA1 Formic acid

ORA2 Acetic and higher acids

Peroxy radicals from alkanes

MO2 Methyl peroxy radical

ETHP Peroxy radical formed from ETH

HC3P Peroxy radical formed from HC3

HC5P Peroxy radical formed from HC5

HC8P Peroxy radical formed from HC8

Peroxy radicals from alkenes

OL2P Peroxy radical formed from OL2P

OLTP Peroxy radical formed from OLTP

OLIP Peroxy radical formed from OLIP

Peroxy radicals from aromatics

TOLP Peroxy radical formed from TOL

XYLP Peroxy radical formed from XYL

Peroxy radicals with carbonyl groups

ACO3 Acetylperoxy radical

KETP Peroxy radical formed from KET

TCO3 H(CO)CH=CHCO3

Peroxy radicals involving nitrogen

XO2 NO-to-NO2 Operator

XNO2 NO-to-nitrate operator

OLN NO3-alken adduct

Species added for aerosols

SULAER Counter species for H2SO4 production

HC8AER Counter species for HC8 reaction

OLIAER Counter species for OLI reaction 

TOLAER Counter species for toluene reaction

XYLAER Counter species for xylene reaction

CSLAER Counter species for cresol reaction

TERPAER Counter species for terpene reaction

TERP Monoterpenes
EPA/600/R-99/030

8-31

Table 8A-3. CB4 Mechanism

 Reaction List

 >----------------------------------------------------------------------<

 { 1} NO2 + hv --> NO + O

 { 2} O + [O2] --> O3

 { 3} O3 + NO --> NO2

 { 4} O + NO2 --> NO

 { 5} O + NO2 --> NO3

 { 6} O + NO --> NO2

 { 7} O3 + NO2 --> NO3

 { 8} O3 + hv --> O

 { 9} O3 + hv --> O1D

 { 10} O1D + [N2] --> O

 { 11} O1D + [O2] --> O

 { 12} O1D + [H2O] --> 2.000*OH

 { 13} O3 + OH --> HO2

 { 14} O3 + HO2 --> OH

 { 15} NO3 + hv --> 0.890*NO2 + 0.890*O + 0.110*NO

 { 16} NO3 + NO --> 2.000*NO2

 { 17} NO3 + NO2 --> NO + NO2

 { 18} NO3 + NO2 --> N2O5

 { 19} N2O5 + [H2O] --> 2.000*HNO3

 { 20} N2O5 --> NO3 + NO2

 { 21} NO + NO + [O2] --> 2.000*NO2

 { 22} NO + NO2 + [H2O] --> 2.000*HONO

 { 23} OH + NO --> HONO

 { 24} HONO + hv --> OH + NO

 { 25} HONO + OH --> NO2

 { 26} HONO + HONO --> NO + NO2

 { 27} OH + NO2 --> HNO3

 { 28} OH + HNO3 --> NO3

 { 29} HO2 + NO --> OH + NO2

 { 30} HO2 + NO2 --> PNA

 { 31} PNA --> HO2 + NO2

 { 32} PNA + OH --> NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + hv --> 2.000*OH

 { 36} H2O2 + OH --> HO2

 { 37} CO + OH --> HO2

 { 38} FORM + OH --> HO2 + CO

 { 39} FORM + hv --> 2.000*HO2 + CO

 { 40} FORM + hv --> CO

 { 41} FORM + O --> OH + HO2 + CO

 { 42} FORM + NO3 --> HNO3 + HO2 + CO

 { 43} ALD2 + O --> C2O3 + OH

 { 44} ALD2 + OH --> C2O3

 { 45} ALD2 + NO3 --> C2O3 + HNO3

 { 46} ALD2 + hv --> XO2 + 2.000*HO2 + CO

 + FORM

 { 47} C2O3 + NO --> NO2 + XO2 + FORM

 + HO2

 { 48} C2O3 + NO2 --> PAN

 { 49} PAN --> C2O3 + NO2

 { 50} C2O3 + C2O3 --> 2.000*XO2 + 2.000*FORM + 2.000*HO2

 { 51} C2O3 + HO2 --> 0.790*FORM + 0.790*XO2 + 0.790*HO2

 + 0.790*OH

 { 52} OH --> XO2 + FORM + HO2

 { 53} PAR + OH --> 0.870*XO2 + 0.130*XO2N + 0.110*HO2

 + 0.110*ALD2 + 0.760*ROR - 0.110*PAR

 { 54} ROR --> 1.100*ALD2 + 0.960*XO2 + 0.940*HO2

 - 2.100*PAR + 0.040*XO2N + 0.020*ROR

 { 55} ROR --> HO2

 { 56} ROR + NO2 --> NTR

 { 57} OLE + O --> 0.630*ALD2 + 0.380*HO2 + 0.280*XO2

 + 0.300*CO + 0.200*FORM + 0.020*XO2N

 + 0.220*PAR + 0.200*OH

 { 58} OLE + OH --> FORM + ALD2 + XO2

 + HO2 - PAR

 { 59} OLE + O3 --> 0.500*ALD2 + 0.740*FORM + 0.330*CO

 + 0.440*HO2 + 0.220*XO2 + 0.100*OH

 - PAR

 { 60} OLE + NO3 --> 0.910*XO2 + 0.090*XO2N + FORM
EPA/600/R-99/030

Table 8A-3. CB4 Mechanism

8-32

 + ALD2 - PAR + NO2

 { 61} ETH + O --> FORM + 0.700*XO2 + CO

 + 1.700*HO2 + 0.300*OH

 { 62} ETH + OH --> XO2 + 1.560*FORM + HO2

 + 0.220*ALD2

 { 63} ETH + O3 --> FORM + 0.420*CO + 0.120*HO2

 { 64} TOL + OH --> 0.080*XO2 + 0.360*CRES + 0.440*HO2

 + 0.560*TO2

 { 65} TO2 + NO --> 0.900*NO2 + 0.900*HO2 + 0.900*OPEN

 + 0.100*NTR

 { 66} TO2 --> CRES + HO2

 { 67} CRES + OH --> 0.400*CRO + 0.600*XO2 + 0.600*HO2

 + 0.300*OPEN

 { 68} CRES + NO3 --> CRO + HNO3

 { 69} CRO + NO2 --> NTR

 { 70} XYL + OH --> 0.700*HO2 + 0.500*XO2 + 0.200*CRES

 + 0.800*MGLY + 1.100*PAR + 0.300*TO2

 { 71} OPEN + OH --> XO2 + 2.000*CO + 2.000*HO2

 + C2O3 + FORM

 { 72} OPEN + hv --> C2O3 + HO2 + CO

 { 73} OPEN + O3 --> 0.030*ALD2 + 0.620*C2O3 + 0.700*FORM

 + 0.030*XO2 + 0.690*CO + 0.080*OH

 + 0.760*HO2 + 0.200*MGLY

 { 74} MGLY + OH --> XO2 + C2O3

 { 75} MGLY + hv --> C2O3 + HO2 + CO

 { 76} ISOP + O --> 0.750*ISPD + 0.500*FORM + 0.250*XO2

 + 0.250*HO2 + 0.250*C2O3 + 0.250*PAR

 { 77} ISOP + OH --> 0.912*ISPD + 0.629*FORM + 0.991*XO2

 + 0.912*HO2 + 0.088*XO2N

 { 78} ISOP + O3 --> 0.650*ISPD + 0.600*FORM + 0.200*XO2

 + 0.066*HO2 + 0.266*OH + 0.200*C2O3

 + 0.150*ALD2 + 0.350*PAR + 0.066*CO

 { 79} ISOP + NO3 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO2 + 0.800*ALD2

 + 2.400*PAR

 { 80} XO2 + NO --> NO2

 { 81} XO2 + XO2 -->

 { 82} XO2N + NO --> NTR

 { 83} SO2 + OH --> SULF + HO2

 { 84} SO2 --> SULF

 { 85} XO2 + HO2 -->

 { 86} XO2N + HO2 -->

 { 87} XO2N + XO2N -->

 { 88} XO2N + XO2 -->

 { 89} ISPD + OH --> 1.565*PAR + 0.167*FORM + 0.713*XO2

 + 0.503*HO2 + 0.334*CO + 0.168*MGLY

 + 0.273*ALD2 + 0.498*C2O3

 { 90} ISPD + O3 --> 0.114*C2O3 + 0.150*FORM + 0.850*MGLY

 + 0.154*HO2 + 0.268*OH + 0.064*XO2

 + 0.020*ALD2 + 0.360*PAR + 0.225*CO

 { 91} ISPD + NO3 --> 0.357*ALD2 + 0.282*FORM + 1.282*PAR

 + 0.925*HO2 + 0.643*CO + 0.850*NTR

 + 0.075*C2O3 + 0.075*XO2 + 0.075*HNO3

 { 92} ISPD + hv --> 0.333*CO + 0.067*ALD2 + 0.900*FORM

 + 0.832*PAR + 1.033*HO2 + 0.700*XO2

 + 0.967*C2O3

 { 93} ISOP + NO2 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO + 0.800*ALD2

 + 2.400*PAR

 >----------------------------------------------------------------------<

 Rate Expression Rate Constant 

 ===============================================================================

 k( 1) uses photo table NO2_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) is a falloff expression using: {1.37387E-14}

 k0 = 6.0000E-34 * (T/300)**(-2.30)

 kinf = 2.8000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 3) = 1.8000E-12 * exp( -1370.0/T) {1.81419E-14}

 k( 4) = 9.3000E-12 {9.30000E-12}

 k( 5) is a falloff expression using: {1.57527E-12}

 k0 = 9.0000E-32 * (T/300)**(-2.00)

 kinf = 2.2000E-11 * (T/300)**( 0.00)
EPA/600/R-99/030

Table 8A-3. CB4 Mechanism

8-33

 F = 0.60, n = 1.00

 k( 6) is a falloff expression using: {1.66375E-12}

 k0 = 9.0000E-32 * (T/300)**(-1.50)

 kinf = 3.0000E-11 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 7) = 1.2000E-13 * exp( -2450.0/T) {3.22581E-17}

 k( 8) uses photo table NO2_CBIV88 , scaled by 5.30000E-02 {0.00000E+00}

 k( 9) uses photo table O3O1D_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) = 1.8000E-11 * exp( 107.0/T) {2.57757E-11}

 k( 11) = 3.2000E-11 * exp( 67.0/T) {4.00676E-11}

 k( 12) = 2.2000E-10 {2.20000E-10}

 k( 13) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 14) = 1.4000E-14 * exp( -580.0/T) {1.99920E-15}

 k( 15) uses photo table NO2_CBIV88 , scaled by 3.39000E+01 {0.00000E+00}

 k( 16) = 1.3000E-11 * exp( 250.0/T) {3.00805E-11}

 k( 17) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 18) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 19) = 1.3000E-21 {1.30000E-21}

 k( 20) = k( 18) / Keq, where Keq = 2.700E-27 * exp( 11000.0/T) {4.36029E-02}

 k( 21) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 22) = 4.4000E-40 {4.39999E-40}

 k( 23) is a falloff expression using: {6.69701E-12}

 k0 = 6.7000E-31 * (T/300)**(-3.30)

 kinf = 3.0000E-11 * (T/300)**(-1.00)

 F = 0.60, n = 1.00

 k( 24) uses photo table NO2_CBIV88 , scaled by 1.97500E-01 {0.00000E+00}

 k( 25) = 6.6000E-12 {6.60000E-12}

 k( 26) = 1.0000E-20 {1.00000E-20}

 k( 27) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 28) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 29) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 30) is a falloff expression using: {1.48014E-12}

 k0 = 2.3000E-31 * (T/300)**(-4.60)

 kinf = 4.2000E-12 * (T/300)**( 0.20)

 F = 0.60, n = 1.00

 k( 31) = k( 30) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {9.17943E-02}

 k( 32) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 33) = 5.9000E-14 * exp( 1150.0/T) {2.79783E-12}

 k( 34) = 2.2000E-38 * exp( 5800.0/T) {6.23927E-30}

 k( 35) uses photo table HCHOmol_CBIV88 , scaled by 2.55000E-01 {0.00000E+00}

 k( 36) = 3.1000E-12 * exp( -187.0/T) {1.65514E-12}

 k( 37) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 38) = 1.0000E-11 {1.00000E-11}

 k( 39) uses photo table HCHOrad_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 40) uses photo table HCHOmol_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 41) = 3.0000E-11 * exp( -1550.0/T) {1.65275E-13}

 k( 42) = 6.3000E-16 {6.30000E-16}

 k( 43) = 1.2000E-11 * exp( -986.0/T) {4.38753E-13}

 k( 44) = 7.0000E-12 * exp( 250.0/T) {1.61972E-11}

 k( 45) = 2.5000E-15 {2.50000E-15}

 k( 46) uses photo table ALD_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 47) = 3.4900E-11 * exp( -180.0/T) {1.90766E-11}

 k( 48) = 2.6300E-12 * exp( 380.0/T) {9.41356E-12}

 k( 49) = 2.0000E+16 * exp(-13500.0/T) {4.23268E-04}

 k( 50) = 2.5000E-12 {2.50000E-12}

 k( 51) = 6.5000E-12 {6.50000E-12}

 k( 52) = 1.1000E+02 * exp( -1710.0/T) {3.54242E-01}

 k( 53) = 8.1000E-13 {8.10000E-13}

 k( 54) = 1.0000E+15 * exp( -8000.0/T) {2.19325E+03}

 k( 55) = 1.6000E+03 {1.60000E+03}

 k( 56) = 1.5000E-11 {1.50000E-11}

 k( 57) = 1.2000E-11 * exp( -324.0/T) {4.04572E-12}

 k( 58) = 5.2000E-12 * exp( 504.0/T) {2.82173E-11}

 k( 59) = 1.4000E-14 * exp( -2105.0/T) {1.19778E-17}
EPA/600/R-99/030

Table 8A-3. CB4 Mechanism

8-34

 k( 60) = 7.7000E-15 {7.70000E-15}

 k( 61) = 1.0000E-11 * exp( -792.0/T) {7.01080E-13}

 k( 62) = 2.0000E-12 * exp( 411.0/T) {7.94340E-12}

 k( 63) = 1.3000E-14 * exp( -2633.0/T) {1.89105E-18}

 k( 64) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 65) = 8.1000E-12 {8.10000E-12}

 k( 66) = 4.2000E+00 {4.20000E+00}

 k( 67) = 4.1000E-11 {4.10000E-11}

 k( 68) = 2.2000E-11 {2.20000E-11}

 k( 69) = 1.4000E-11 {1.40000E-11}

 k( 70) = 1.7000E-11 * exp( 116.0/T) {2.50901E-11}

 k( 71) = 3.0000E-11 {3.00000E-11}

 k( 72) uses photo table HCHOrad_CBIV88 , scaled by 9.04000E+00 {0.00000E+00}

 k( 73) = 5.4000E-17 * exp( -500.0/T) {1.00858E-17}

 k( 74) = 1.7000E-11 {1.70000E-11}

 k( 75) uses photo table HCHOrad_CBIV88 , scaled by 9.64000E+00 {0.00000E+00}

 k( 76) = 3.6000E-11 {3.60000E-11}

 k( 77) = 2.5400E-11 * exp( 407.6/T) {9.97368E-11}

 k( 78) = 7.8600E-15 * exp( -1912.0/T) {1.28512E-17}

 k( 79) = 3.0300E-12 * exp( -448.0/T) {6.73819E-13}

 k( 80) = 8.1000E-12 {8.10000E-12}

 k( 81) = 1.7000E-14 * exp( 1300.0/T) {1.33359E-12}

 k( 82) = 8.1000E-12 {8.10000E-12}

 k( 83) = 4.3900E-13 * exp( 160.0/T) {7.51005E-13}

 k( 84) = 1.3600E-06 {1.36000E-06}

 k( 85) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 86) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 87) = 1.7300E-14 * exp( 1300.0/T) {1.35712E-12}

 k( 88) = 3.4500E-14 * exp( 1300.0/T) {2.70640E-12}

 k( 89) = 3.3600E-11 {3.36000E-11}

 k( 90) = 7.1100E-18 {7.11000E-18}

 k( 91) = 1.0000E-15 {1.00000E-15}

 k( 92) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k( 93) = 1.4900E-19 {1.49000E-19}

 ===============================================================================
EPA/600/R-99/030

8-35

Table 8A-4. CB4_AE Mechanism

 Reaction List

 >----------------------------------------------------------------------------------<

 { 1} NO2 + hv --> NO + O

 { 2} O + [O2] --> O3

 { 3} O3 + NO --> NO2

 { 4} O + NO2 --> NO

 { 5} O + NO2 --> NO3

 { 6} O + NO --> NO2

 { 7} O3 + NO2 --> NO3

 { 8} O3 + hv --> O

 { 9} O3 + hv --> O1D

 { 10} O1D + [N2] --> O

 { 11} O1D + [O2] --> O

 { 12} O1D + [H2O] --> 2.000*OH

 { 13} O3 + OH --> HO2

 { 14} O3 + HO2 --> OH

 { 15} NO3 + hv --> 0.890*NO2 + 0.890*O + 0.110*NO

 { 16} NO3 + NO --> 2.000*NO2

 { 17} NO3 + NO2 --> NO + NO2

 { 18} NO3 + NO2 --> N2O5

 { 19} N2O5 + [H2O] --> 2.000*HNO3

 { 20} N2O5 --> NO3 + NO2

 { 21} NO + NO + [O2] --> 2.000*NO2

 { 22} NO + NO2 + [H2O] --> 2.000*HONO

 { 23} OH + NO --> HONO

 { 24} HONO + hv --> OH + NO

 { 25} HONO + OH --> NO2

 { 26} HONO + HONO --> NO + NO2

 { 27} OH + NO2 --> HNO3

 { 28} OH + HNO3 --> NO3

 { 29} HO2 + NO --> OH + NO2

 { 30} HO2 + NO2 --> PNA

 { 31} PNA --> HO2 + NO2

 { 32} PNA + OH --> NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + hv --> 2.000*OH

 { 36} H2O2 + OH --> HO2

 { 37} CO + OH --> HO2

 { 38} FORM + OH --> HO2 + CO

 { 39} FORM + hv --> 2.000*HO2 + CO

 { 40} FORM + hv --> CO

 { 41} FORM + O --> OH + HO2 + CO

 { 42} FORM + NO3 --> HNO3 + HO2 + CO

 { 43} ALD2 + O --> C2O3 + OH

 { 44} ALD2 + OH --> C2O3

 { 45} ALD2 + NO3 --> C2O3 + HNO3

 { 46} ALD2 + hv --> XO2 + 2.000*HO2 + CO

 + FORM

 { 47} C2O3 + NO --> NO2 + XO2 + FORM

 + HO2

 { 48} C2O3 + NO2 --> PAN

 { 49} PAN --> C2O3 + NO2

 { 50} C2O3 + C2O3 --> 2.000*XO2 + 2.000*FORM + 2.000*HO2

 { 51} C2O3 + HO2 --> 0.790*FORM + 0.790*XO2 + 0.790*HO2

 + 0.790*OH

 { 52} OH --> XO2 + FORM + HO2

 { 53} PAR + OH --> 0.870*XO2 + 0.130*XO2N + 0.110*HO2

 + 0.110*ALD2 + 0.760*ROR - 0.110*PAR

 { 54} ROR --> 1.100*ALD2 + 0.960*XO2 + 0.940*HO2

 - 2.100*PAR + 0.040*XO2N + 0.020*ROR

 { 55} ROR --> HO2

 { 56} ROR + NO2 --> NTR

 { 57} OLE + O --> 0.630*ALD2 + 0.380*HO2 + 0.280*XO2

 + 0.300*CO + 0.200*FORM + 0.020*XO2N

 + 0.220*PAR + 0.200*OH

 { 58} OLE + OH --> FORM + ALD2 + XO2

 + HO2 - PAR

 { 59} OLE + O3 --> 0.500*ALD2 + 0.740*FORM + 0.330*CO

 + 0.440*HO2 + 0.220*XO2 + 0.100*OH

 - PAR

 { 60} OLE + NO3 --> 0.910*XO2 + 0.090*XO2N + FORM

 + ALD2 - PAR + NO2

 { 61} ETH + O --> FORM + 0.700*XO2 + CO
EPA/600/R-99/030

Table 8A-4. CB4_AE Mechanism

8-36

 + 1.700*HO2 + 0.300*OH

 { 62} ETH + OH --> XO2 + 1.560*FORM + HO2

 + 0.220*ALD2

 { 63} ETH + O3 --> FORM + 0.420*CO + 0.120*HO2

 { 64} TOL + OH --> 0.080*XO2 + 0.360*CRES + 0.440*HO2

 + 0.560*TO2 + TOLAER

 { 65} TO2 + NO --> 0.900*NO2 + 0.900*HO2 + 0.900*OPEN

 + 0.100*NTR

 { 66} TO2 --> CRES + HO2

 { 67} CRES + OH --> 0.400*CRO + 0.600*XO2 + 0.600*HO2

 + 0.300*OPEN + CSLAER

 { 68} CRES + NO3 --> CRO + HNO3 + CSLAER

 { 69} CRO + NO2 --> NTR

 { 70} XYL + OH --> 0.700*HO2 + 0.500*XO2 + 0.200*CRES

 + 0.800*MGLY + 1.100*PAR + 0.300*TO2

 + XYLAER

 { 71} OPEN + OH --> XO2 + 2.000*CO + 2.000*HO2

 + C2O3 + FORM

 { 72} OPEN + hv --> C2O3 + HO2 + CO

 { 73} OPEN + O3 --> 0.030*ALD2 + 0.620*C2O3 + 0.700*FORM

 + 0.030*XO2 + 0.690*CO + 0.080*OH

 + 0.760*HO2 + 0.200*MGLY

 { 74} MGLY + OH --> XO2 + C2O3

 { 75} MGLY + hv --> C2O3 + HO2 + CO

 { 76} ISOP + O --> 0.750*ISPD + 0.500*FORM + 0.250*XO2

 + 0.250*HO2 + 0.250*C2O3 + 0.250*PAR

 { 77} ISOP + OH --> 0.912*ISPD + 0.629*FORM + 0.991*XO2

 + 0.912*HO2 + 0.088*XO2N

 { 78} ISOP + O3 --> 0.650*ISPD + 0.600*FORM + 0.200*XO2

 + 0.066*HO2 + 0.266*OH + 0.200*C2O3

 + 0.150*ALD2 + 0.350*PAR + 0.066*CO

 { 79} ISOP + NO3 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO2 + 0.800*ALD2

 + 2.400*PAR

 { 80} XO2 + NO --> NO2

 { 81} XO2 + XO2 -->

 { 82} XO2N + NO --> NTR

 { 83} SO2 + OH --> SULF + HO2 + SULAER

 { 84} SO2 --> SULF + SULAER

 { 85} XO2 + HO2 -->

 { 86} XO2N + HO2 -->

 { 87} XO2N + XO2N -->

 { 88} XO2N + XO2 -->

 { 89} ISPD + OH --> 1.565*PAR + 0.167*FORM + 0.713*XO2

 + 0.503*HO2 + 0.334*CO + 0.168*MGLY

 + 0.273*ALD2 + 0.498*C2O3

 { 90} ISPD + O3 --> 0.114*C2O3 + 0.150*FORM + 0.850*MGLY

 + 0.154*HO2 + 0.268*OH + 0.064*XO2

 + 0.020*ALD2 + 0.360*PAR + 0.225*CO

 { 91} ISPD + NO3 --> 0.357*ALD2 + 0.282*FORM + 1.282*PAR

 + 0.925*HO2 + 0.643*CO + 0.850*NTR

 + 0.075*C2O3 + 0.075*XO2 + 0.075*HNO3

 { 92} ISPD + hv --> 0.333*CO + 0.067*ALD2 + 0.900*FORM

 + 0.832*PAR + 1.033*HO2 + 0.700*XO2

 + 0.967*C2O3

 { 93} ISOP + NO2 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO + 0.800*ALD2

 + 2.400*PAR

 { 94} TERP + OH --> TERPAER + OH

 { 95} TERP + NO3 --> TERPAER + NO3

 { 96} TERP + O3 --> TERPAER + O3

 >----------------------------------------------------------------------------------<

Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) is a falloff expression using: {1.37387E-14}

 k0 = 6.0000E-34 * (T/300)**(-2.30)

 kinf = 2.8000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 3) = 1.8000E-12 * exp( -1370.0/T) {1.81419E-14}

 k( 4) = 9.3000E-12 {9.30000E-12}

 k( 5) is a falloff expression using: {1.57527E-12}
EPA/600/R-99/030

Table 8A-4. CB4_AE Mechanism

8-37

 k0 = 9.0000E-32 * (T/300)**(-2.00)

 kinf = 2.2000E-11 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 6) is a falloff expression using: {1.66375E-12}

 k0 = 9.0000E-32 * (T/300)**(-1.50)

 kinf = 3.0000E-11 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 7) = 1.2000E-13 * exp( -2450.0/T) {3.22581E-17}

 k( 8) uses photo table NO2_CBIV88 , scaled by 5.30000E-02 {0.00000E+00}

 k( 9) uses photo table O3O1D_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) = 1.8000E-11 * exp( 107.0/T) {2.57757E-11}

 k( 11) = 3.2000E-11 * exp( 67.0/T) {4.00676E-11}

 k( 12) = 2.2000E-10 {2.20000E-10}

 k( 13) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 14) = 1.4000E-14 * exp( -580.0/T) {1.99920E-15}

 k( 15) uses photo table NO2_CBIV88 , scaled by 3.39000E+01 {0.00000E+00}

 k( 16) = 1.3000E-11 * exp( 250.0/T) {3.00805E-11}

 k( 17) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 18) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 19) = 1.3000E-21 {1.30000E-21}

 k( 20) = k( 18) / Keq, where Keq = 2.700E-21 * exp( 11000.0/T) {4.36029E-08}

 k( 21) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 22) = 4.4000E-40 {4.39999E-40}

 k( 23) is a falloff expression using: {6.69701E-12}

 k0 = 6.7000E-31 * (T/300)**(-3.30)

 kinf = 3.0000E-11 * (T/300)**(-1.00)

 F = 0.60, n = 1.00

 k( 24) uses photo table NO2_CBIV88 , scaled by 1.97500E-01 {0.00000E+00}

 k( 25) = 6.6000E-12 {6.60000E-12}

 k( 26) = 1.0000E-20 {1.00000E-20}

 k( 27) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 28) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 29) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 30) is a falloff expression using: {1.48014E-12}

 k0 = 2.3000E-31 * (T/300)**(-4.60)

 kinf = 4.2000E-12 * (T/300)**( 0.20)

 F = 0.60, n = 1.00

 k( 31) = k( 30) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {9.17943E-02}

 k( 32) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 33) = 5.9000E-14 * exp( 1150.0/T) {2.79783E-12}

 k( 34) = 2.2000E-38 * exp( 5800.0/T) {6.23927E-30}

 k( 35) uses photo table HCHOmol_CBIV88 , scaled by 2.55000E-01 {0.00000E+00}

 k( 36) = 3.1000E-12 * exp( -187.0/T) {1.65514E-12}

 k( 37) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 38) = 1.0000E-11 {1.00000E-11}

 k( 39) uses photo table HCHOrad_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 40) uses photo table HCHOmol_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 41) = 3.0000E-11 * exp( -1550.0/T) {1.65275E-13}

 k( 42) = 6.3000E-16 {6.30000E-16}

 k( 43) = 1.2000E-11 * exp( -986.0/T) {4.38753E-13}

 k( 44) = 7.0000E-12 * exp( 250.0/T) {1.61972E-11}

 k( 45) = 2.5000E-15 {2.50000E-15}

 k( 46) uses photo table ALD_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 47) = 3.4900E-11 * exp( -180.0/T) {1.90766E-11}

 k( 48) = 2.6300E-12 * exp( 380.0/T) {9.41356E-12}

 k( 49) = 2.0000E+16 * exp(-13500.0/T) {4.23268E-04}

 k( 50) = 2.5000E-12 {2.50000E-12}

 k( 51) = 6.5000E-12 {6.50000E-12}

 k( 52) = 1.1000E+02 * exp( -1710.0/T) {3.54242E-01}

 k( 53) = 8.1000E-13 {8.10000E-13}

 k( 54) = 1.0000E+15 * exp( -8000.0/T) {2.19325E+03}

 k( 55) = 1.6000E+03 {1.60000E+03}

 k( 56) = 1.5000E-11 {1.50000E-11}

 k( 57) = 1.2000E-11 * exp( -324.0/T) {4.04572E-12}
EPA/600/R-99/030

Table 8A-4. CB4_AE Mechanism

8-38

 k( 58) = 5.2000E-12 * exp( 504.0/T) {2.82173E-11}

 k( 59) = 1.4000E-14 * exp( -2105.0/T) {1.19778E-17}

 k( 60) = 7.7000E-15 {7.70000E-15}

 k( 61) = 1.0000E-11 * exp( -792.0/T) {7.01080E-13}

 k( 62) = 2.0000E-12 * exp( 411.0/T) {7.94340E-12}

 k( 63) = 1.3000E-14 * exp( -2633.0/T) {1.89105E-18}

 k( 64) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 65) = 8.1000E-12 {8.10000E-12}

 k( 66) = 4.2000E+00 {4.20000E+00}

 k( 67) = 4.1000E-11 {4.10000E-11}

 k( 68) = 2.2000E-11 {2.20000E-11}

 k( 69) = 1.4000E-11 {1.40000E-11}

 k( 70) = 1.7000E-11 * exp( 116.0/T) {2.50901E-11}

 k( 71) = 3.0000E-11 {3.00000E-11}

 k( 72) uses photo table HCHOrad_CBIV88 , scaled by 9.04000E+00 {0.00000E+00}

 k( 73) = 5.4000E-17 * exp( -500.0/T) {1.00858E-17}

 k( 74) = 1.7000E-11 {1.70000E-11}

 k( 75) uses photo table HCHOrad_CBIV88 , scaled by 9.64000E+00 {0.00000E+00}

 k( 76) = 3.6000E-11 {3.60000E-11}

 k( 77) = 2.5400E-11 * exp( 407.6/T) {9.97368E-11}

 k( 78) = 7.8600E-15 * exp( -1912.0/T) {1.28512E-17}

 k( 79) = 3.0300E-12 * exp( -448.0/T) {6.73819E-13}

 k( 80) = 8.1000E-12 {8.10000E-12}

 k( 81) = 1.7000E-14 * exp( 1300.0/T) {1.33359E-12}

 k( 82) = 8.1000E-12 {8.10000E-12}

 k( 83) = 4.3900E-13 * exp( 160.0/T) {7.51005E-13}

 k( 84) = 1.3600E-06 {1.36000E-06}

 k( 85) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 86) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 87) = 1.7300E-14 * exp( 1300.0/T) {1.35712E-12}

 k( 88) = 3.4500E-14 * exp( 1300.0/T) {2.70640E-12}

 k( 89) = 3.3600E-11 {3.36000E-11}

 k( 90) = 7.1100E-18 {7.11000E-18}

 k( 91) = 1.0000E-15 {1.00000E-15}

 k( 92) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k( 93) = 1.4900E-19 {1.49000E-19}

 k( 94) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 95) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k( 96) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 ===============================================================================
EPA/600/R-99/030

8-39

Table 8A-5. CB4_AQ Mechanism

 Reaction List 

 >----------------------------------------------------------------------<

 { 1} NO2 + hv --> NO + O

 { 2} O + [O2] --> O3

 { 3} O3 + NO --> NO2

 { 4} O + NO2 --> NO

 { 5} O + NO2 --> NO3

 { 6} O + NO --> NO2

 { 7} O3 + NO2 --> NO3

 { 8} O3 + hv --> O

 { 9} O3 + hv --> O1D

 { 10} O1D + [N2] --> O

 { 11} O1D + [O2] --> O

 { 12} O1D + [H2O] --> 2.000*OH

 { 13} O3 + OH --> HO2

 { 14} O3 + HO2 --> OH

 { 15} NO3 + hv --> 0.890*NO2 + 0.890*O + 0.110*NO

 { 16} NO3 + NO --> 2.000*NO2

 { 17} NO3 + NO2 --> NO + NO2

 { 18} NO3 + NO2 --> N2O5

 { 19} N2O5 + [H2O] --> 2.000*HNO3

 { 20} N2O5 --> NO3 + NO2

 { 21} NO + NO + [O2] --> 2.000*NO2

 { 22} NO + NO2 + [H2O] --> 2.000*HONO

 { 23} OH + NO --> HONO

 { 24} HONO + hv --> OH + NO

 { 25} HONO + OH --> NO2

 { 26} HONO + HONO --> NO + NO2

 { 27} OH + NO2 --> HNO3

 { 28} OH + HNO3 --> NO3

 { 29} HO2 + NO --> OH + NO2

 { 30} HO2 + NO2 --> PNA

 { 31} PNA --> HO2 + NO2

 { 32} PNA + OH --> NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + hv --> 2.000*OH

 { 36} H2O2 + OH --> HO2

 { 37} CO + OH --> HO2

 { 38} FORM + OH --> HO2 + CO

 { 39} FORM + hv --> 2.000*HO2 + CO

 { 40} FORM + hv --> CO

 { 41} FORM + O --> OH + HO2 + CO

 { 42} FORM + NO3 --> HNO3 + HO2 + CO

 { 43} ALD2 + O --> C2O3 + OH

 { 44} ALD2 + OH --> C2O3

 { 45} ALD2 + NO3 --> C2O3 + HNO3

 { 46} ALD2 + hv --> XO2 + 2.000*HO2 + CO

 + FORM

 { 47} C2O3 + NO --> NO2 + XO2 + FORM

 + HO2

 { 48} C2O3 + NO2 --> PAN

 { 49} PAN --> C2O3 + NO2

 { 50} C2O3 + C2O3 --> 2.000*XO2 + 2.000*FORM + 2.000*HO2

 { 51} C2O3 + HO2 --> 0.790*FORM + 0.790*XO2 + 0.790*HO2

 + 0.790*OH + 0.210*PACD

 { 52} OH --> XO2 + FORM + HO2

 { 53} PAR + OH --> 0.870*XO2 + 0.130*XO2N + 0.110*HO2

 + 0.110*ALD2 + 0.760*ROR - 0.110*PAR

 { 54} ROR --> 1.100*ALD2 + 0.960*XO2 + 0.940*HO2

 - 2.100*PAR + 0.040*XO2N + 0.020*ROR

 { 55} ROR --> HO2

 { 56} ROR + NO2 --> NTR

 { 57} OLE + O --> 0.630*ALD2 + 0.380*HO2 + 0.280*XO2

 + 0.300*CO + 0.200*FORM + 0.020*XO2N

 + 0.220*PAR + 0.200*OH

 { 58} OLE + OH --> FORM + ALD2 + XO2

 + HO2 - PAR

 { 59} OLE + O3 --> 0.500*ALD2 + 0.740*FORM + 0.330*CO

 + 0.440*HO2 + 0.220*XO2 + 0.100*OH

 + 0.200*FACD + 0.200*AACD - PAR

 { 60} OLE + NO3 --> 0.910*XO2 + 0.090*XO2N + FORM

 + ALD2 - PAR + NO2

 { 61} ETH + O --> FORM + 0.700*XO2 + CO
EPA/600/R-99/030

Table 8A-5. CB4_AQ Mechanism

8-40

 + 1.700*HO2 + 0.300*OH

 { 62} ETH + OH --> XO2 + 1.560*FORM + HO2

 + 0.220*ALD2

 { 63} ETH + O3 --> FORM + 0.420*CO + 0.120*HO2

 + 0.400*FACD

 { 64} TOL + OH --> 0.080*XO2 + 0.360*CRES + 0.440*HO2

 + 0.560*TO2

 { 65} TO2 + NO --> 0.900*NO2 + 0.900*HO2 + 0.900*OPEN

 + 0.100*NTR

 { 66} TO2 --> CRES + HO2

 { 67} CRES + OH --> 0.400*CRO + 0.600*XO2 + 0.600*HO2

 + 0.300*OPEN

 { 68} CRES + NO3 --> CRO + HNO3

 { 69} CRO + NO2 --> NTR

 { 70} XYL + OH --> 0.700*HO2 + 0.500*XO2 + 0.200*CRES

 + 0.800*MGLY + 1.100*PAR + 0.300*TO2

 { 71} OPEN + OH --> XO2 + 2.000*CO + 2.000*HO2

 + C2O3 + FORM

 { 72} OPEN + hv --> C2O3 + HO2 + CO

 { 73} OPEN + O3 --> 0.030*ALD2 + 0.620*C2O3 + 0.700*FORM

 + 0.030*XO2 + 0.690*CO + 0.080*OH

 + 0.760*HO2 + 0.200*MGLY

 { 74} MGLY + OH --> XO2 + C2O3

 { 75} MGLY + hv --> C2O3 + HO2 + CO

 { 76} ISOP + O --> 0.750*ISPD + 0.500*FORM + 0.250*XO2

 + 0.250*HO2 + 0.250*C2O3 + 0.250*PAR

 { 77} ISOP + OH --> 0.912*ISPD + 0.629*FORM + 0.991*XO2

 + 0.912*HO2 + 0.088*XO2N

 { 78} ISOP + O3 --> 0.650*ISPD + 0.600*FORM + 0.200*XO2

 + 0.066*HO2 + 0.266*OH + 0.200*C2O3

 + 0.150*ALD2 + 0.350*PAR + 0.066*CO

 { 79} ISOP + NO3 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO2 + 0.800*ALD2

 + 2.400*PAR

 { 80} XO2 + NO --> NO2

 { 81} XO2 + XO2 -->

 { 82} XO2N + NO --> NTR

 { 83} SO2 + OH --> SULF + HO2

 { 84} SO2 --> SULF

 { 85} XO2 + HO2 --> UMHP

 { 86} XO2N + HO2 -->

 { 87} XO2N + XO2N -->

 { 88} XO2N + XO2 -->

 { 89} ISPD + OH --> 1.565*PAR + 0.167*FORM + 0.713*XO2

 + 0.503*HO2 + 0.334*CO + 0.168*MGLY

 + 0.273*ALD2 + 0.498*C2O3

 { 90} ISPD + O3 --> 0.114*C2O3 + 0.150*FORM + 0.850*MGLY

 + 0.154*HO2 + 0.268*OH + 0.064*XO2

 + 0.020*ALD2 + 0.360*PAR + 0.225*CO

 { 91} ISPD + NO3 --> 0.357*ALD2 + 0.282*FORM + 1.282*PAR

 + 0.925*HO2 + 0.643*CO + 0.850*NTR

 + 0.075*C2O3 + 0.075*XO2 + 0.075*HNO3

 { 92} ISPD + hv --> 0.333*CO + 0.067*ALD2 + 0.900*FORM

 + 0.832*PAR + 1.033*HO2 + 0.700*XO2

 + 0.967*C2O3

 { 93} ISOP + NO2 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO + 0.800*ALD2

 + 2.400*PAR

 >----------------------------------------------------------------------<

 Rate Expression Rate Constant 

 ===============================================================================

 k( 1) uses photo table NO2_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) is a falloff expression using: {1.37387E-14}

 k0 = 6.0000E-34 * (T/300)**(-2.30)

 kinf = 2.8000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 3) = 1.8000E-12 * exp( -1370.0/T) {1.81419E-14}

 k( 4) = 9.3000E-12 {9.30000E-12}

 k( 5) is a falloff expression using: {1.57527E-12}

 k0 = 9.0000E-32 * (T/300)**(-2.00)

 kinf = 2.2000E-11 * (T/300)**( 0.00)

 F = 0.60, n = 1.00
EPA/600/R-99/030

Table 8A-5. CB4_AQ Mechanism

8-41

 k( 6) is a falloff expression using: {1.66375E-12}

 k0 = 9.0000E-32 * (T/300)**(-1.50)

 kinf = 3.0000E-11 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 7) = 1.2000E-13 * exp( -2450.0/T) {3.22581E-17}

 k( 8) uses photo table NO2_CBIV88 , scaled by 5.30000E-02 {0.00000E+00}

 k( 9) uses photo table O3O1D_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) = 1.8000E-11 * exp( 107.0/T) {2.57757E-11}

 k( 11) = 3.2000E-11 * exp( 67.0/T) {4.00676E-11}

 k( 12) = 2.2000E-10 {2.20000E-10}

 k( 13) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 14) = 1.4000E-14 * exp( -580.0/T) {1.99920E-15}

 k( 15) uses photo table NO2_CBIV88 , scaled by 3.39000E+01 {0.00000E+00}

 k( 16) = 1.3000E-11 * exp( 250.0/T) {3.00805E-11}

 k( 17) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 18) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 19) = 1.3000E-21 {1.30000E-21}

 k( 20) = k( 18) / Keq, where Keq = 2.700E-27 * exp( 11000.0/T) {4.36029E-02}

 k( 21) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 22) = 4.4000E-40 {4.39999E-40}

 k( 23) is a falloff expression using: {6.69701E-12}

 k0 = 6.7000E-31 * (T/300)**(-3.30)

 kinf = 3.0000E-11 * (T/300)**(-1.00)

 F = 0.60, n = 1.00

 k( 24) uses photo table NO2_CBIV88 , scaled by 1.97500E-01 {0.00000E+00}

 k( 25) = 6.6000E-12 {6.60000E-12}

 k( 26) = 1.0000E-20 {1.00000E-20}

 k( 27) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 28) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 29) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 30) is a falloff expression using: {1.48014E-12}

 k0 = 2.3000E-31 * (T/300)**(-4.60)

 kinf = 4.2000E-12 * (T/300)**( 0.20)

 F = 0.60, n = 1.00

 k( 31) = k( 30) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {9.17943E-02}

 k( 32) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 33) = 5.9000E-14 * exp( 1150.0/T) {2.79783E-12}

 k( 34) = 2.2000E-38 * exp( 5800.0/T) {6.23927E-30}

 k( 35) uses photo table HCHOmol_CBIV88 , scaled by 2.55000E-01 {0.00000E+00}

 k( 36) = 3.1000E-12 * exp( -187.0/T) {1.65514E-12}

 k( 37) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 38) = 1.0000E-11 {1.00000E-11}

 k( 39) uses photo table HCHOrad_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 40) uses photo table HCHOmol_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 41) = 3.0000E-11 * exp( -1550.0/T) {1.65275E-13}

 k( 42) = 6.3000E-16 {6.30000E-16}

 k( 43) = 1.2000E-11 * exp( -986.0/T) {4.38753E-13}

 k( 44) = 7.0000E-12 * exp( 250.0/T) {1.61972E-11}

 k( 45) = 2.5000E-15 {2.50000E-15}

 k( 46) uses photo table ALD_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 47) = 3.4900E-11 * exp( -180.0/T) {1.90766E-11}

 k( 48) = 2.6300E-12 * exp( 380.0/T) {9.41356E-12}

 k( 49) = 2.0000E+16 * exp(-13500.0/T) {4.23268E-04}

 k( 50) = 2.5000E-12 {2.50000E-12}

 k( 51) = 6.5000E-12 {6.50000E-12}

 k( 52) = 1.1000E+02 * exp( -1710.0/T) {3.54242E-01}

 k( 53) = 8.1000E-13 {8.10000E-13}

 k( 54) = 1.0000E+15 * exp( -8000.0/T) {2.19325E+03}

 k( 55) = 1.6000E+03 {1.60000E+03}

 k( 56) = 1.5000E-11 {1.50000E-11}

 k( 57) = 1.2000E-11 * exp( -324.0/T) {4.04572E-12}

 k( 58) = 5.2000E-12 * exp( 504.0/T) {2.82173E-11}

 k( 59) = 1.4000E-14 * exp( -2105.0/T) {1.19778E-17}

 k( 60) = 7.7000E-15 {7.70000E-15}
EPA/600/R-99/030

Table 8A-5. CB4_AQ Mechanism

8-42

 k( 61) = 1.0000E-11 * exp( -792.0/T) {7.01080E-13}

 k( 62) = 2.0000E-12 * exp( 411.0/T) {7.94340E-12}

 k( 63) = 1.3000E-14 * exp( -2633.0/T) {1.89105E-18}

 k( 64) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 65) = 8.1000E-12 {8.10000E-12}

 k( 66) = 4.2000E+00 {4.20000E+00}

 k( 67) = 4.1000E-11 {4.10000E-11}

 k( 68) = 2.2000E-11 {2.20000E-11}

 k( 69) = 1.4000E-11 {1.40000E-11}

 k( 70) = 1.7000E-11 * exp( 116.0/T) {2.50901E-11}

 k( 71) = 3.0000E-11 {3.00000E-11}

 k( 72) uses photo table HCHOrad_CBIV88 , scaled by 9.04000E+00 {0.00000E+00}

 k( 73) = 5.4000E-17 * exp( -500.0/T) {1.00858E-17}

 k( 74) = 1.7000E-11 {1.70000E-11}

 k( 75) uses photo table HCHOrad_CBIV88 , scaled by 9.64000E+00 {0.00000E+00}

 k( 76) = 3.6000E-11 {3.60000E-11}

 k( 77) = 2.5400E-11 * exp( 407.6/T) {9.97368E-11}

 k( 78) = 7.8600E-15 * exp( -1912.0/T) {1.28512E-17}

 k( 79) = 3.0300E-12 * exp( -448.0/T) {6.73819E-13}

 k( 80) = 8.1000E-12 {8.10000E-12}

 k( 81) = 1.7000E-14 * exp( 1300.0/T) {1.33359E-12}

 k( 82) = 8.1000E-12 {8.10000E-12}

 k( 83) = 4.3900E-13 * exp( 160.0/T) {7.51005E-13}

 k( 84) = 1.3600E-06 {1.36000E-06}

 k( 85) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 86) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 87) = 1.7300E-14 * exp( 1300.0/T) {1.35712E-12}

 k( 88) = 3.4500E-14 * exp( 1300.0/T) {2.70640E-12}

 k( 89) = 3.3600E-11 {3.36000E-11}

 k( 90) = 7.1100E-18 {7.11000E-18}

 k( 91) = 1.0000E-15 {1.00000E-15}

 k( 92) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k( 93) = 1.4900E-19 {1.49000E-19}

 ===============================================================================
EPA/600/R-99/030

8-43

Table 8A-6. CB4_AE_AQ Mechanism

 Reaction List

 >----------------------------------------------------------------------------------<

 { 1} NO2 + hv --> NO + O

 { 2} O + [O2] --> O3

 { 3} O3 + NO --> NO2

 { 4} O + NO2 --> NO

 { 5} O + NO2 --> NO3

 { 6} O + NO --> NO2

 { 7} O3 + NO2 --> NO3

 { 8} O3 + hv --> O

 { 9} O3 + hv --> O1D

 { 10} O1D + [N2] --> O

 { 11} O1D + [O2] --> O

 { 12} O1D + [H2O] --> 2.000*OH

 { 13} O3 + OH --> HO2

 { 14} O3 + HO2 --> OH

 { 15} NO3 + hv --> 0.890*NO2 + 0.890*O + 0.110*NO

 { 16} NO3 + NO --> 2.000*NO2

 { 17} NO3 + NO2 --> NO + NO2

 { 18} NO3 + NO2 --> N2O5

 { 19} N2O5 + [H2O] --> 2.000*HNO3

 { 20} N2O5 --> NO3 + NO2

 { 21} NO + NO + [O2] --> 2.000*NO2

 { 22} NO + NO2 + [H2O] --> 2.000*HONO

 { 23} OH + NO --> HONO

 { 24} HONO + hv --> OH + NO

 { 25} HONO + OH --> NO2

 { 26} HONO + HONO --> NO + NO2

 { 27} OH + NO2 --> HNO3

 { 28} OH + HNO3 --> NO3

 { 29} HO2 + NO --> OH + NO2

 { 30} HO2 + NO2 --> PNA

 { 31} PNA --> HO2 + NO2

 { 32} PNA + OH --> NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + hv --> 2.000*OH

 { 36} H2O2 + OH --> HO2

 { 37} CO + OH --> HO2

 { 38} FORM + OH --> HO2 + CO

 { 39} FORM + hv --> 2.000*HO2 + CO

 { 40} FORM + hv --> CO

 { 41} FORM + O --> OH + HO2 + CO

 { 42} FORM + NO3 --> HNO3 + HO2 + CO

 { 43} ALD2 + O --> C2O3 + OH

 { 44} ALD2 + OH --> C2O3

 { 45} ALD2 + NO3 --> C2O3 + HNO3

 { 46} ALD2 + hv --> XO2 + 2.000*HO2 + CO

 + FORM

 { 47} C2O3 + NO --> NO2 + XO2 + FORM

 + HO2

 { 48} C2O3 + NO2 --> PAN

 { 49} PAN --> C2O3 + NO2

 { 50} C2O3 + C2O3 --> 2.000*XO2 + 2.000*FORM + 2.000*HO2

 { 51} C2O3 + HO2 --> 0.790*FORM + 0.790*XO2 + 0.790*HO2

 + 0.790*OH + 0.210*PACD

 { 52} OH --> XO2 + FORM + HO2

 { 53} PAR + OH --> 0.870*XO2 + 0.130*XO2N + 0.110*HO2

 + 0.110*ALD2 + 0.760*ROR - 0.110*PAR

 { 54} ROR --> 1.100*ALD2 + 0.960*XO2 + 0.940*HO2

 - 2.100*PAR + 0.040*XO2N + 0.020*ROR

 { 55} ROR --> HO2

 { 56} ROR + NO2 --> NTR

 { 57} OLE + O --> 0.630*ALD2 + 0.380*HO2 + 0.280*XO2

 + 0.300*CO + 0.200*FORM + 0.020*XO2N

 + 0.220*PAR + 0.200*OH

 { 58} OLE + OH --> FORM + ALD2 + XO2

 + HO2 - PAR

 { 59} OLE + O3 --> 0.500*ALD2 + 0.740*FORM + 0.330*CO

 + 0.440*HO2 + 0.220*XO2 + 0.100*OH

 + 0.200*FACD + 0.200*AACD - PAR

 { 60} OLE + NO3 --> 0.910*XO2 + 0.090*XO2N + FORM

 + ALD2 - PAR + NO2

 { 61} ETH + O --> FORM + 0.700*XO2 + CO
EPA/600/R-99/030

Table 8A-6. CB4_AE_AQ Mechanism

8-44

 + 1.700*HO2 + 0.300*OH

 { 62} ETH + OH --> XO2 + 1.560*FORM + HO2

 + 0.220*ALD2

 { 63} ETH + O3 --> FORM + 0.420*CO + 0.120*HO2

 + 0.400*FACD

 { 64} TOL + OH --> 0.080*XO2 + 0.360*CRES + 0.440*HO2

 + 0.560*TO2 + TOLAER

 { 65} TO2 + NO --> 0.900*NO2 + 0.900*HO2 + 0.900*OPEN

 + 0.100*NTR

 { 66} TO2 --> CRES + HO2

 { 67} CRES + OH --> 0.400*CRO + 0.600*XO2 + 0.600*HO2

 + 0.300*OPEN + CSLAER

 { 68} CRES + NO3 --> CRO + HNO3 + CSLAER

 { 69} CRO + NO2 --> NTR

 { 70} XYL + OH --> 0.700*HO2 + 0.500*XO2 + 0.200*CRES

 + 0.800*MGLY + 1.100*PAR + 0.300*TO2

 + XYLAER

 { 71} OPEN + OH --> XO2 + 2.000*CO + 2.000*HO2

 + C2O3 + FORM

 { 72} OPEN + hv --> C2O3 + HO2 + CO

 { 73} OPEN + O3 --> 0.030*ALD2 + 0.620*C2O3 + 0.700*FORM

 + 0.030*XO2 + 0.690*CO + 0.080*OH

 + 0.760*HO2 + 0.200*MGLY

 { 74} MGLY + OH --> XO2 + C2O3

 { 75} MGLY + hv --> C2O3 + HO2 + CO

 { 76} ISOP + O --> 0.750*ISPD + 0.500*FORM + 0.250*XO2

 + 0.250*HO2 + 0.250*C2O3 + 0.250*PAR

 { 77} ISOP + OH --> 0.912*ISPD + 0.629*FORM + 0.991*XO2

 + 0.912*HO2 + 0.088*XO2N

 { 78} ISOP + O3 --> 0.650*ISPD + 0.600*FORM + 0.200*XO2

 + 0.066*HO2 + 0.266*OH + 0.200*C2O3

 + 0.150*ALD2 + 0.350*PAR + 0.066*CO

 { 79} ISOP + NO3 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO2 + 0.800*ALD2

 + 2.400*PAR

 { 80} XO2 + NO --> NO2

 { 81} XO2 + XO2 -->

 { 82} XO2N + NO --> NTR

 { 83} SO2 + OH --> SULF + HO2 + SULAER

 { 84} SO2 --> SULF + SULAER

 { 85} XO2 + HO2 --> UMHP

 { 86} XO2N + HO2 -->

 { 87} XO2N + XO2N -->

 { 88} XO2N + XO2 -->

 { 89} ISPD + OH --> 1.565*PAR + 0.167*FORM + 0.713*XO2

 + 0.503*HO2 + 0.334*CO + 0.168*MGLY

 + 0.273*ALD2 + 0.498*C2O3

 { 90} ISPD + O3 --> 0.114*C2O3 + 0.150*FORM + 0.850*MGLY

 + 0.154*HO2 + 0.268*OH + 0.064*XO2

 + 0.020*ALD2 + 0.360*PAR + 0.225*CO

 { 91} ISPD + NO3 --> 0.357*ALD2 + 0.282*FORM + 1.282*PAR

 + 0.925*HO2 + 0.643*CO + 0.850*NTR

 + 0.075*C2O3 + 0.075*XO2 + 0.075*HNO3

 { 92} ISPD + hv --> 0.333*CO + 0.067*ALD2 + 0.900*FORM

 + 0.832*PAR + 1.033*HO2 + 0.700*XO2

 + 0.967*C2O3

 { 93} ISOP + NO2 --> 0.200*ISPD + 0.800*NTR + XO2

 + 0.800*HO2 + 0.200*NO + 0.800*ALD2

 + 2.400*PAR

 { 94} TERP + OH --> TERPAER + OH

 { 95} TERP + NO3 --> TERPAER + NO3

 { 96} TERP + O3 --> TERPAER + O3

 >----------------------------------------------------------------------------------<

Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) is a falloff expression using: {1.37387E-14}

 k0 = 6.0000E-34 * (T/300)**(-2.30)

 kinf = 2.8000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 3) = 1.8000E-12 * exp( -1370.0/T) {1.81419E-14}

 k( 4) = 9.3000E-12 {9.30000E-12}
EPA/600/R-99/030

Table 8A-6. CB4_AE_AQ Mechanism

8-45

 k( 5) is a falloff expression using: {1.57527E-12}

 k0 = 9.0000E-32 * (T/300)**(-2.00)

 kinf = 2.2000E-11 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 6) is a falloff expression using: {1.66375E-12}

 k0 = 9.0000E-32 * (T/300)**(-1.50)

 kinf = 3.0000E-11 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 7) = 1.2000E-13 * exp( -2450.0/T) {3.22581E-17}

 k( 8) uses photo table NO2_CBIV88 , scaled by 5.30000E-02 {0.00000E+00}

 k( 9) uses photo table O3O1D_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) = 1.8000E-11 * exp( 107.0/T) {2.57757E-11}

 k( 11) = 3.2000E-11 * exp( 67.0/T) {4.00676E-11}

 k( 12) = 2.2000E-10 {2.20000E-10}

 k( 13) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 14) = 1.4000E-14 * exp( -580.0/T) {1.99920E-15}

 k( 15) uses photo table NO2_CBIV88 , scaled by 3.39000E+01 {0.00000E+00}

 k( 16) = 1.3000E-11 * exp( 250.0/T) {3.00805E-11}

 k( 17) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 18) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 19) = 1.3000E-21 {1.30000E-21}

 k( 20) = k( 18) / Keq, where Keq = 2.700E-27 * exp( 11000.0/T) {4.36029E-02}

 k( 21) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 22) = 4.4000E-40 {4.39999E-40}

 k( 23) is a falloff expression using: {6.69701E-12}

 k0 = 6.7000E-31 * (T/300)**(-3.30)

 kinf = 3.0000E-11 * (T/300)**(-1.00)

 F = 0.60, n = 1.00

 k( 24) uses photo table NO2_CBIV88 , scaled by 1.97500E-01 {0.00000E+00}

 k( 25) = 6.6000E-12 {6.60000E-12}

 k( 26) = 1.0000E-20 {1.00000E-20}

 k( 27) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 28) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 29) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 30) is a falloff expression using: {1.48014E-12}

 k0 = 2.3000E-31 * (T/300)**(-4.60)

 kinf = 4.2000E-12 * (T/300)**( 0.20)

 F = 0.60, n = 1.00

 k( 31) = k( 30) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {9.17943E-02}

 k( 32) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 33) = 5.9000E-14 * exp( 1150.0/T) {2.79783E-12}

 k( 34) = 2.2000E-38 * exp( 5800.0/T) {6.23927E-30}

 k( 35) uses photo table HCHOmol_CBIV88 , scaled by 2.55000E-01 {0.00000E+00}

 k( 36) = 3.1000E-12 * exp( -187.0/T) {1.65514E-12}

 k( 37) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 38) = 1.0000E-11 {1.00000E-11}

 k( 39) uses photo table HCHOrad_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 40) uses photo table HCHOmol_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 41) = 3.0000E-11 * exp( -1550.0/T) {1.65275E-13}

 k( 42) = 6.3000E-16 {6.30000E-16}

 k( 43) = 1.2000E-11 * exp( -986.0/T) {4.38753E-13}

 k( 44) = 7.0000E-12 * exp( 250.0/T) {1.61972E-11}

 k( 45) = 2.5000E-15 {2.50000E-15}

 k( 46) uses photo table ALD_CBIV88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 47) = 3.4900E-11 * exp( -180.0/T) {1.90766E-11}

 k( 48) = 2.6300E-12 * exp( 380.0/T) {9.41356E-12}

 k( 49) = 2.0000E+16 * exp(-13500.0/T) {4.23268E-04}

 k( 50) = 2.5000E-12 {2.50000E-12}

 k( 51) = 6.5000E-12 {6.50000E-12}

 k( 52) = 1.1000E+02 * exp( -1710.0/T) {3.54242E-01}

 k( 53) = 8.1000E-13 {8.10000E-13}

 k( 54) = 1.0000E+15 * exp( -8000.0/T) {2.19325E+03}

 k( 55) = 1.6000E+03 {1.60000E+03}

 k( 56) = 1.5000E-11 {1.50000E-11}
EPA/600/R-99/030

Table 8A-6. CB4_AE_AQ Mechanism

8-46

 k( 57) = 1.2000E-11 * exp( -324.0/T) {4.04572E-12}

 k( 58) = 5.2000E-12 * exp( 504.0/T) {2.82173E-11}

 k( 59) = 1.4000E-14 * exp( -2105.0/T) {1.19778E-17}

 k( 60) = 7.7000E-15 {7.70000E-15}

 k( 61) = 1.0000E-11 * exp( -792.0/T) {7.01080E-13}

 k( 62) = 2.0000E-12 * exp( 411.0/T) {7.94340E-12}

 k( 63) = 1.3000E-14 * exp( -2633.0/T) {1.89105E-18}

 k( 64) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 65) = 8.1000E-12 {8.10000E-12}

 k( 66) = 4.2000E+00 {4.20000E+00}

 k( 67) = 4.1000E-11 {4.10000E-11}

 k( 68) = 2.2000E-11 {2.20000E-11}

 k( 69) = 1.4000E-11 {1.40000E-11}

 k( 70) = 1.7000E-11 * exp( 116.0/T) {2.50901E-11}

 k( 71) = 3.0000E-11 {3.00000E-11}

 k( 72) uses photo table HCHOrad_CBIV88 , scaled by 9.04000E+00 {0.00000E+00}

 k( 73) = 5.4000E-17 * exp( -500.0/T) {1.00858E-17}

 k( 74) = 1.7000E-11 {1.70000E-11}

 k( 75) uses photo table HCHOrad_CBIV88 , scaled by 9.64000E+00 {0.00000E+00}

 k( 76) = 3.6000E-11 {3.60000E-11}

 k( 77) = 2.5400E-11 * exp( 407.6/T) {9.97368E-11}

 k( 78) = 7.8600E-15 * exp( -1912.0/T) {1.28512E-17}

 k( 79) = 3.0300E-12 * exp( -448.0/T) {6.73819E-13}

 k( 80) = 8.1000E-12 {8.10000E-12}

 k( 81) = 1.7000E-14 * exp( 1300.0/T) {1.33359E-12}

 k( 82) = 8.1000E-12 {8.10000E-12}

 k( 83) = 4.3900E-13 * exp( 160.0/T) {7.51005E-13}

 k( 84) = 1.3600E-06 {1.36000E-06}

 k( 85) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 86) = 7.6700E-14 * exp( 1300.0/T) {6.01684E-12}

 k( 87) = 1.7300E-14 * exp( 1300.0/T) {1.35712E-12}

 k( 88) = 3.4500E-14 * exp( 1300.0/T) {2.70640E-12}

 k( 89) = 3.3600E-11 {3.36000E-11}

 k( 90) = 7.1100E-18 {7.11000E-18}

 k( 91) = 1.0000E-15 {1.00000E-15}

 k( 92) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k( 93) = 1.4900E-19 {1.49000E-19}

 k( 94) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 95) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k( 96) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 ===============================================================================
EPA/600/R-99/030

8-47

Table 8A-7. RADM2 and RADM2_AQ Mechanisms

 Reaction List

 >----------------------------------------------------------------------<

 { 1} NO2 + hv --> O3P + NO

 { 2} O3 + hv --> O1D

 { 3} O3 + hv --> O3P

 { 4} HONO + hv --> HO + NO

 { 5} HNO3 + hv --> HO + NO2

 { 6} HNO4 + hv --> HO2 + NO2

 { 7} NO3 + hv --> NO

 { 8} NO3 + hv --> NO2 + O3P

 { 9} H2O2 + hv --> 2.000*HO

 { 10} HCHO + hv --> CO

 { 11} HCHO + hv --> HO2 + HO2 + CO

 { 12} ALD + hv --> MO2 + HO2 + CO

 { 13} OP1 + hv --> HCHO + HO2 + HO

 { 14} OP2 + hv --> ALD + HO2 + HO

 { 15} PAA + hv --> MO2 + HO

 { 16} KET + hv --> ACO3 + ETHP

 { 17} GLY + hv --> 0.130*HCHO + 1.870*CO

 { 18} GLY + hv --> 0.450*HCHO + 1.550*CO + 0.800*HO2

 { 19} MGLY + hv --> ACO3 + HO2 + CO

 { 20} DCB + hv --> 0.980*HO2 + 0.020*ACO3 + TCO3

 { 21} ONIT + hv --> 0.200*ALD + 0.800*KET + HO2

 + NO2

 { 22} O3P + [M] + [O2] --> O3

 { 23} O3P + NO2 --> NO

 { 24} O1D + [N2] --> O3P

 { 25} O1D + [O2] --> O3P

 { 26} O1D + [H2O] --> 2.000*HO

 { 27} O3 + NO --> NO2

 { 28} O3 + HO --> HO2

 { 29} O3 + HO2 --> HO

 { 30} HO2 + NO --> NO2 + HO

 { 31} HO2 + NO2 --> HNO4

 { 32} HNO4 --> HO2 + NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + HO --> HO2

 { 36} NO + HO --> HONO

 { 37} NO + NO + [O2] --> 2.000*NO2

 { 38} O3 + NO2 --> NO3

 { 39} NO3 + NO --> 2.000*NO2

 { 40} NO3 + NO2 --> NO + NO2

 { 41} NO3 + HO2 --> HNO3

 { 42} NO3 + NO2 --> N2O5

 { 43} N2O5 --> NO2 + NO3

 { 44} N2O5 + [H2O] --> 2.000*HNO3

 { 45} HO + NO2 --> HNO3

 { 46} HO + HNO3 --> NO3

 { 47} HO + HNO4 --> NO2

 { 48} HO + HO2 -->

 { 49} HO + SO2 --> SULF + HO2

 { 50} CO + HO --> HO2

 { 51} HO --> MO2

 { 52} ETH + HO --> ETHP

 { 53} HC3 + HO --> 0.830*HC3P + 0.170*HO2 + 0.009*HCHO

 + 0.075*ALD + 0.025*KET

 { 54} HC5 + HO --> HC5P + 0.250*XO2

 { 55} HC8 + HO --> HC8P + 0.750*XO2

 { 56} OL2 + HO --> OL2P

 { 57} OLT + HO --> OLTP

 { 58} OLI + HO --> OLIP

 { 59} TOL + HO --> 0.750*TOLP + 0.250*CSL + 0.250*HO2

 { 60} XYL + HO --> 0.830*XYLP + 0.170*CSL + 0.170*HO2

 { 61} CSL + HO --> 0.100*HO2 + 0.900*XO2 + 0.900*TCO3

 { 62} CSL + HO --> CSL

 { 63} HCHO + HO --> HO2 + CO

 { 64} ALD + HO --> ACO3

 { 65} KET + HO --> KETP

 { 66} GLY + HO --> HO2 + 2.000*CO

 { 67} MGLY + HO --> ACO3 + CO

 { 68} DCB + HO --> TCO3

 { 69} OP1 + HO --> 0.500*MO2 + 0.500*HCHO + 0.500*HO

 { 70} OP2 + HO --> 0.500*HC3P + 0.500*ALD + 0.500*HO
EPA/600/R-99/030

Table 8A-7. RADM2 and RADM2_AQ Mechanisms

8-48

 { 71} PAA + HO --> ACO3

 { 72} PAN + HO --> HCHO + NO3 + XO2

 { 73} ONIT + HO --> HC3P + NO2

 { 74} ISO + HO --> OLTP

 { 75} ACO3 + NO2 --> PAN

 { 76} PAN --> ACO3 + NO2

 { 77} TCO3 + NO2 --> TPAN

 { 78} TPAN --> TCO3 + NO2

 { 79} MO2 + NO --> HCHO + HO2 + NO2

 { 80} HC3P + NO --> 0.750*ALD + 0.250*KET + 0.090*HCHO

 + 0.036*ONIT + 0.964*NO2 + 0.964*HO2

 { 81} HC5P + NO --> 0.380*ALD + 0.690*KET + 0.080*ONIT

 + 0.920*NO2 + 0.920*HO2

 { 82} HC8P + NO --> 0.350*ALD + 1.060*KET + 0.040*HCHO

 + 0.240*ONIT + 0.760*NO2 + 0.760*HO2

 { 83} OL2P + NO --> 1.600*HCHO + HO2 + NO2

 + 0.200*ALD

 { 84} OLTP + NO --> ALD + HCHO + HO2

 + NO2

 { 85} OLIP + NO --> HO2 + 1.450*ALD + 0.280*HCHO

 + 0.100*KET + NO2

 { 86} ACO3 + NO --> MO2 + NO2

 { 87} TCO3 + NO --> NO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 { 88} TOLP + NO --> NO2 + HO2 + 0.170*MGLY

 + 0.160*GLY + 0.700*DCB

 { 89} XYLP + NO --> NO2 + HO2 + 0.450*MGLY

 + 0.806*DCB

 { 90} ETHP + NO --> ALD + HO2 + NO2

 { 91} KETP + NO --> MGLY + NO2 + HO2

 { 92} OLN + NO --> HCHO + ALD + 2.000*NO2

 { 93} HCHO + NO3 --> HO2 + HNO3 + CO

 { 94} ALD + NO3 --> ACO3 + HNO3

 { 95} GLY + NO3 --> HNO3 + HO2 + 2.000*CO

 { 96} MGLY + NO3 --> HNO3 + ACO3 + CO

 { 97} DCB + NO3 --> HNO3 + TCO3

 { 98} CSL + NO3 --> HNO3 + XNO2 + 0.500*CSL

 { 99} OL2 + NO3 --> OLN

 {100} OLT + NO3 --> OLN

 {101} OLI + NO3 --> OLN

 {102} ISO + NO3 --> OLN

 {103} OL2 + O3 --> HCHO + 0.400*ORA1 + 0.420*CO

 + 0.120*HO2

 {104} OLT + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {105} OLI + O3 --> 0.180*HCHO + 0.720*ALD + 0.100*KET

 + 0.230*CO + 0.060*ORA1 + 0.290*ORA2

 + 0.260*HO2 + 0.140*HO + 0.310*MO2

 {106} ISO + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {107} HO2 + MO2 --> OP1

 {108} HO2 + ETHP --> OP2

 {109} HO2 + HC3P --> OP2

 {110} HO2 + HC5P --> OP2

 {111} HO2 + HC8P --> OP2

 {112} HO2 + OL2P --> OP2

 {113} HO2 + OLTP --> OP2

 {114} HO2 + OLIP --> OP2

 {115} HO2 + KETP --> OP2

 {116} HO2 + ACO3 --> PAA

 {117} HO2 + TOLP --> OP2

 {118} HO2 + XYLP --> OP2

 {119} HO2 + TCO3 --> OP2

 {120} HO2 + OLN --> ONIT

 {121} MO2 + MO2 --> 1.500*HCHO + HO2

 {122} MO2 + ETHP --> 0.750*HCHO + HO2 + 0.750*ALD

 {123} MO2 + HC3P --> 0.840*HCHO + 0.770*ALD + 0.260*KET

 + HO2

 {124} MO2 + HC5P --> 0.770*HCHO + 0.410*ALD + 0.750*KET

 + HO2

 {125} MO2 + HC8P --> 0.800*HCHO + 0.460*ALD + 1.390*KET
EPA/600/R-99/030

Table 8A-7. RADM2 and RADM2_AQ Mechanisms

8-49

 + HO2

 {126} MO2 + OL2P --> 1.550*HCHO + 0.350*ALD + HO2

 {127} MO2 + OLTP --> 1.250*HCHO + 0.750*ALD + HO2

 {128} MO2 + OLIP --> 0.890*HCHO + 0.725*ALD + HO2

 + 0.550*KET

 {129} MO2 + KETP --> 0.750*HCHO + 0.750*MGLY + HO2

 {130} MO2 + ACO3 --> HCHO + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {131} MO2 + TOLP --> HCHO + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + 2.000*HO2

 {132} MO2 + XYLP --> HCHO + 0.450*MGLY + 0.806*DCB

 + 2.000*HO2

 {133} MO2 + TCO3 --> 0.500*HCHO + 0.445*GLY + 0.055*MGLY

 + 0.500*ORA2 + 0.025*ACO3 + 0.460*HO2

 + 0.475*CO + XO2

 {134} MO2 + OLN --> 1.750*HCHO + 0.500*HO2 + ALD

 + NO2

 {135} ETHP + ACO3 --> ALD + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {136} HC3P + ACO3 --> 0.770*ALD + 0.260*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {137} HC5P + ACO3 --> 0.410*ALD + 0.750*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {138} HC8P + ACO3 --> 0.460*ALD + 1.390*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {139} OL2P + ACO3 --> 0.800*HCHO + 0.600*ALD + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {140} OLTP + ACO3 --> ALD + 0.500*HCHO + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {141} OLIP + ACO3 --> 0.725*ALD + 0.550*KET + 0.140*HCHO

 + 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 {142} KETP + ACO3 --> MGLY + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {143} ACO3 + ACO3 --> 2.000*MO2

 {144} ACO3 + TOLP --> MO2 + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + HO2

 {145} ACO3 + XYLP --> MO2 + 0.450*MGLY + 0.806*DCB

 + HO2

 {146} ACO3 + TCO3 --> MO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 {147} ACO3 + OLN --> HCHO + ALD + 0.500*ORA2

 + NO2 + 0.500*MO2

 {148} OLN + OLN --> 2.000*HCHO + 2.000*ALD + 2.000*NO2

 {149} XO2 + HO2 --> OP2

 {150} XO2 + MO2 --> HCHO + HO2

 {151} XO2 + ACO3 --> MO2

 {152} XO2 + XO2 -->

 {153} XO2 + NO --> NO2

 {154} XNO2 + NO2 --> ONIT

 {155} XNO2 + HO2 --> OP2

 {156} XNO2 + MO2 --> HCHO + HO2

 {157} XNO2 + ACO3 --> MO2

 {158} XNO2 + XNO2 -->

 >----------------------------------------------------------------------<

 Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) uses photo table O3O1D_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 3) uses photo table O3O3P_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 4) uses photo table HONO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 5) uses photo table HNO3_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 6) uses photo table HNO4_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 7) uses photo table NO3NO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 8) uses photo table NO3NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 9) uses photo table H2O2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) uses photo table HCHOmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 11) uses photo table HCHOrad_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 12) uses photo table ALD_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 13) uses photo table MHP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 14) uses photo table HOP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 15) uses photo table PAA_RADM88 , scaled by 1.00000E+00 {0.00000E+00}
EPA/600/R-99/030

Table 8A-7. RADM2 and RADM2_AQ Mechanisms

8-50

 k( 16) uses photo table KETONE_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 17) uses photo table GLYform_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 18) uses photo table GLYmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 19) uses photo table MGLY_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 20) uses photo table UDC_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 21) uses photo table ORGNIT_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 22) = 6.0000E-34 * (T/300)**(-2.30) {6.09302E-34}

 k( 23) = 6.5000E-12 * exp( 120.0/T) {9.72293E-12}

 k( 24) = 1.8000E-11 * exp( 110.0/T) {2.60365E-11}

 k( 25) = 3.2000E-11 * exp( 70.0/T) {4.04730E-11}

 k( 26) = 2.2000E-10 {2.20000E-10}

 k( 27) = 2.0000E-12 * exp( -1400.0/T) {1.82272E-14}

 k( 28) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 29) = 1.1000E-14 * exp( -500.0/T) {2.05452E-15}

 k( 30) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 31) is a falloff expression using: {1.39058E-12}

 k0 = 1.8000E-31 * (T/300)**(-3.20)

 kinf = 4.7000E-12 * (T/300)**(-1.40)

 F = 0.60, n = 1.00

 k( 32) = k( 31) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {8.62399E-02}

 k( 33) is a special rate expression of the form: {3.01634E-12}

 k = k1 + k2[M], where

 k1 = 2.2000E-13 * exp( 620.0/T)

 k2 = 1.9000E-33 * exp( 980.0/T)

 k( 34) is a special rate expression of the form: {6.78905E-30}

 k = k1 + k2[M], where

 k1 = 3.0800E-34 * exp( 2820.0/T)

 k2 = 2.6600E-54 * exp( 3180.0/T)

 k( 35) = 3.3000E-12 * exp( -200.0/T) {1.68671E-12}

 k( 36) is a falloff expression using: {4.87144E-12}

 k0 = 7.0000E-31 * (T/300)**(-2.60)

 kinf = 1.5000E-11 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 37) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 38) = 1.4000E-13 * exp( -2500.0/T) {3.18213E-17}

 k( 39) = 1.7000E-11 * exp( 150.0/T) {2.81225E-11}

 k( 40) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 41) = 2.5000E-12 {2.50000E-12}

 k( 42) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 43) = k( 42) / Keq, where Keq = 1.100E-27 * exp( 11200.0/T) {5.47034E-02}

 k( 44) = 2.0000E-21 {2.00000E-21}

 k( 45) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 46) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 47) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 48) = 4.6000E-11 * exp( 230.0/T) {9.95294E-11}

 k( 49) is a falloff expression using: {8.88848E-13}

 k0 = 3.0000E-31 * (T/300)**(-3.30)

 kinf = 1.5000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 50) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 51) = 2.8300E+01 * (T/300)**( 2.00) * exp( -1280.0/T) {3.80672E-01}

 k( 52) = 1.2330E-12 * (T/300)**( 2.00) * exp( -444.0/T) {2.74210E-13}

 k( 53) = 1.5900E-11 * exp( -540.0/T) {2.59669E-12}

 k( 54) = 1.7300E-11 * exp( -380.0/T) {4.83334E-12}

 k( 55) = 3.6400E-11 * exp( -380.0/T) {1.01696E-11}

 k( 56) = 2.1500E-12 * exp( 411.0/T) {8.53916E-12}

 k( 57) = 5.3200E-12 * exp( 504.0/T) {2.88684E-11}

 k( 58) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 59) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 60) = 1.8900E-11 * exp( 116.0/T) {2.78943E-11}

 k( 61) = 4.0000E-11 {4.00000E-11}

 k( 62) = 9.0000E-01 * k( 61) {3.60000E-11}

 k( 63) = 9.0000E-12 {9.00000E-12}

 k( 64) = 6.8700E-12 * exp( 256.0/T) {1.62197E-11}
EPA/600/R-99/030

Table 8A-7. RADM2 and RADM2_AQ Mechanisms

8-51

 k( 65) = 1.2000E-11 * exp( -745.0/T) {9.85020E-13}

 k( 66) = 1.1500E-11 {1.15000E-11}

 k( 67) = 1.7000E-11 {1.70000E-11}

 k( 68) = 2.8000E-11 {2.80000E-11}

 k( 69) = 1.0000E-11 {1.00000E-11}

 k( 70) = 1.0000E-11 {1.00000E-11}

 k( 71) = 1.0000E-11 {1.00000E-11}

 k( 72) = 6.1650E-13 * (T/300)**( 2.00) * exp( -444.0/T) {1.37105E-13}

 k( 73) = 1.5500E-11 * exp( -540.0/T) {2.53137E-12}

 k( 74) = 2.5500E-11 * exp( 409.0/T) {1.00601E-10}

 k( 75) = 2.8000E-12 * exp( 181.0/T) {5.13974E-12}

 k( 76) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 77) = 4.7000E-12 {4.70000E-12}

 k( 78) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 79) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 80) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 81) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 82) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 83) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 84) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 85) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 86) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 87) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 88) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 89) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 90) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 91) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 92) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 93) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 94) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 95) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 96) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 97) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 98) = 2.2000E-11 {2.20000E-11}

 k( 99) = 2.0000E-12 * exp( -2923.0/T) {1.09940E-16}

 k(100) = 1.0000E-11 * exp( -1895.0/T) {1.73099E-14}

 k(101) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k(102) = 5.8100E-13 {5.81000E-13}

 k(103) = 1.2000E-14 * exp( -2633.0/T) {1.74559E-18}

 k(104) = 1.3200E-14 * exp( -2105.0/T) {1.12933E-17}

 k(105) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 k(106) = 1.2300E-14 * exp( -2013.0/T) {1.43295E-17}

 k(107) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(108) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(109) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(110) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(111) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(112) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(113) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(114) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(115) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(116) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(117) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(118) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(119) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(120) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(121) = 1.9000E-13 * exp( 220.0/T) {3.97533E-13}

 k(122) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(123) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(124) = 3.4000E-14 * exp( 220.0/T) {7.11376E-14}

 k(125) = 2.9000E-14 * exp( 220.0/T) {6.06762E-14}

 k(126) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(127) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(128) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(129) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(130) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(131) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(132) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(133) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(134) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(135) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(136) = 1.0000E-13 * exp( 220.0/T) {2.09228E-13}

 k(137) = 8.4000E-14 * exp( 220.0/T) {1.75752E-13}

 k(138) = 7.2000E-14 * exp( 220.0/T) {1.50644E-13}
EPA/600/R-99/030

Table 8A-7. RADM2 and RADM2_AQ Mechanisms

8-52

 k(139) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(140) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(141) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(142) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(143) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(144) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(145) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(146) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(147) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(148) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(149) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(150) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(151) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(152) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(153) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(154) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(155) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(156) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(157) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(158) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 ===============================================================================
EPA/600/R-99/030

8-53

Table 8A-8. RADM2_AE and RADM2_AE_AQ Mechanisms

 Reaction List

 >----------------------------------------------------------------------------------<

 { 1} NO2 + hv --> O3P + NO

 { 2} O3 + hv --> O1D

 { 3} O3 + hv --> O3P

 { 4} HONO + hv --> HO + NO

 { 5} HNO3 + hv --> HO + NO2

 { 6} HNO4 + hv --> HO2 + NO2

 { 7} NO3 + hv --> NO

 { 8} NO3 + hv --> NO2 + O3P

 { 9} H2O2 + hv --> 2.000*HO

 { 10} HCHO + hv --> CO

 { 11} HCHO + hv --> HO2 + HO2 + CO

 { 12} ALD + hv --> MO2 + HO2 + CO

 { 13} OP1 + hv --> HCHO + HO2 + HO

 { 14} OP2 + hv --> ALD + HO2 + HO

 { 15} PAA + hv --> MO2 + HO

 { 16} KET + hv --> ACO3 + ETHP

 { 17} GLY + hv --> 0.130*HCHO + 1.870*CO

 { 18} GLY + hv --> 0.450*HCHO + 1.550*CO + 0.800*HO2

 { 19} MGLY + hv --> ACO3 + HO2 + CO

 { 20} DCB + hv --> 0.980*HO2 + 0.020*ACO3 + TCO3

 { 21} ONIT + hv --> 0.200*ALD + 0.800*KET + HO2

 + NO2

 { 22} O3P + [M] + [O2] --> O3

 { 23} O3P + NO2 --> NO

 { 24} O1D + [N2] --> O3P

 { 25} O1D + [O2] --> O3P

 { 26} O1D + [H2O] --> 2.000*HO

 { 27} O3 + NO --> NO2

 { 28} O3 + HO --> HO2

 { 29} O3 + HO2 --> HO

 { 30} HO2 + NO --> NO2 + HO

 { 31} HO2 + NO2 --> HNO4

 { 32} HNO4 --> HO2 + NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + HO --> HO2

 { 36} NO + HO --> HONO

 { 37} NO + NO + [O2] --> 2.000*NO2

 { 38} O3 + NO2 --> NO3

 { 39} NO3 + NO --> 2.000*NO2

 { 40} NO3 + NO2 --> NO + NO2

 { 41} NO3 + HO2 --> HNO3

 { 42} NO3 + NO2 --> N2O5

 { 43} N2O5 --> NO2 + NO3

 { 44} N2O5 + [H2O] --> 2.000*HNO3

 { 45} HO + NO2 --> HNO3

 { 46} HO + HNO3 --> NO3

 { 47} HO + HNO4 --> NO2

 { 48} HO + HO2 -->

 { 49} HO + SO2 --> SULF + HO2 + SULAER

 { 50} CO + HO --> HO2

 { 51} HO --> MO2

 { 52} ETH + HO --> ETHP

 { 53} HC3 + HO --> 0.830*HC3P + 0.170*HO2 + 0.009*HCHO

 + 0.075*ALD + 0.025*KET

 { 54} HC5 + HO --> HC5P + 0.250*XO2

 { 55} HC8 + HO --> HC8P + 0.750*XO2 + HC8AER

 { 56} OL2 + HO --> OL2P

 { 57} OLT + HO --> OLTP

 { 58} OLI + HO --> OLIP + OLIAER

 { 59} TOL + HO --> 0.750*TOLP + 0.250*CSL + 0.250*HO2

 + TOLAER

 { 60} XYL + HO --> 0.830*XYLP + 0.170*CSL + 0.170*HO2

 + XYLAER

 { 61} CSL + HO --> 0.100*HO2 + 0.900*XO2 + 0.900*TCO3

 + CSLAER

 { 62} CSL + HO --> CSL

 { 63} HCHO + HO --> HO2 + CO

 { 64} ALD + HO --> ACO3

 { 65} KET + HO --> KETP

 { 66} GLY + HO --> HO2 + 2.000*CO

 { 67} MGLY + HO --> ACO3 + CO
EPA/600/R-99/030

Table 8A-8. RADM2_AE and RADM2_AE_AQ Mechanisms

8-54

 { 68} DCB + HO --> TCO3

 { 69} OP1 + HO --> 0.500*MO2 + 0.500*HCHO + 0.500*HO

 { 70} OP2 + HO --> 0.500*HC3P + 0.500*ALD + 0.500*HO

 { 71} PAA + HO --> ACO3

 { 72} PAN + HO --> HCHO + NO3 + XO2

 { 73} ONIT + HO --> HC3P + NO2

 { 74} ISO + HO --> OLTP

 { 75} ACO3 + NO2 --> PAN

 { 76} PAN --> ACO3 + NO2

 { 77} TCO3 + NO2 --> TPAN

 { 78} TPAN --> TCO3 + NO2

 { 79} MO2 + NO --> HCHO + HO2 + NO2

 { 80} HC3P + NO --> 0.750*ALD + 0.250*KET + 0.090*HCHO

 + 0.036*ONIT + 0.964*NO2 + 0.964*HO2

 { 81} HC5P + NO --> 0.380*ALD + 0.690*KET + 0.080*ONIT

 + 0.920*NO2 + 0.920*HO2

 { 82} HC8P + NO --> 0.350*ALD + 1.060*KET + 0.040*HCHO

 + 0.240*ONIT + 0.760*NO2 + 0.760*HO2

 { 83} OL2P + NO --> 1.600*HCHO + HO2 + NO2

 + 0.200*ALD

 { 84} OLTP + NO --> ALD + HCHO + HO2

 + NO2

 { 85} OLIP + NO --> HO2 + 1.450*ALD + 0.280*HCHO

 + 0.100*KET + NO2

 { 86} ACO3 + NO --> MO2 + NO2

 { 87} TCO3 + NO --> NO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 { 88} TOLP + NO --> NO2 + HO2 + 0.170*MGLY

 + 0.160*GLY + 0.700*DCB

 { 89} XYLP + NO --> NO2 + HO2 + 0.450*MGLY

 + 0.806*DCB

 { 90} ETHP + NO --> ALD + HO2 + NO2

 { 91} KETP + NO --> MGLY + NO2 + HO2

 { 92} OLN + NO --> HCHO + ALD + 2.000*NO2

 { 93} HCHO + NO3 --> HO2 + HNO3 + CO

 { 94} ALD + NO3 --> ACO3 + HNO3

 { 95} GLY + NO3 --> HNO3 + HO2 + 2.000*CO

 { 96} MGLY + NO3 --> HNO3 + ACO3 + CO

 { 97} DCB + NO3 --> HNO3 + TCO3

 { 98} CSL + NO3 --> HNO3 + XNO2 + 0.500*CSL

 + 0.500*CSLAER

 { 99} OL2 + NO3 --> OLN

 {100} OLT + NO3 --> OLN

 {101} OLI + NO3 --> OLN + OLIAER

 {102} ISO + NO3 --> OLN

 {103} OL2 + O3 --> HCHO + 0.400*ORA1 + 0.420*CO

 + 0.120*HO2

 {104} OLT + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {105} OLI + O3 --> 0.180*HCHO + 0.720*ALD + 0.100*KET

 + 0.230*CO + 0.060*ORA1 + 0.290*ORA2

 + 0.260*HO2 + 0.140*HO + 0.310*MO2

 + OLIAER

 {106} ISO + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {107} HO2 + MO2 --> OP1

 {108} HO2 + ETHP --> OP2

 {109} HO2 + HC3P --> OP2

 {110} HO2 + HC5P --> OP2

 {111} HO2 + HC8P --> OP2

 {112} HO2 + OL2P --> OP2

 {113} HO2 + OLTP --> OP2

 {114} HO2 + OLIP --> OP2

 {115} HO2 + KETP --> OP2

 {116} HO2 + ACO3 --> PAA

 {117} HO2 + TOLP --> OP2

 {118} HO2 + XYLP --> OP2

 {119} HO2 + TCO3 --> OP2

 {120} HO2 + OLN --> ONIT

 {121} MO2 + MO2 --> 1.500*HCHO + HO2

 {122} MO2 + ETHP --> 0.750*HCHO + HO2 + 0.750*ALD
EPA/600/R-99/030

Table 8A-8. RADM2_AE and RADM2_AE_AQ Mechanisms

8-55

 {123} MO2 + HC3P --> 0.840*HCHO + 0.770*ALD + 0.260*KET

 + HO2

 {124} MO2 + HC5P --> 0.770*HCHO + 0.410*ALD + 0.750*KET

 + HO2

 {125} MO2 + HC8P --> 0.800*HCHO + 0.460*ALD + 1.390*KET

 + HO2

 {126} MO2 + OL2P --> 1.550*HCHO + 0.350*ALD + HO2

 {127} MO2 + OLTP --> 1.250*HCHO + 0.750*ALD + HO2

 {128} MO2 + OLIP --> 0.890*HCHO + 0.725*ALD + HO2

 + 0.550*KET

 {129} MO2 + KETP --> 0.750*HCHO + 0.750*MGLY + HO2

 {130} MO2 + ACO3 --> HCHO + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {131} MO2 + TOLP --> HCHO + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + 2.000*HO2

 {132} MO2 + XYLP --> HCHO + 0.450*MGLY + 0.806*DCB

 + 2.000*HO2

 {133} MO2 + TCO3 --> 0.500*HCHO + 0.445*GLY + 0.055*MGLY

 + 0.500*ORA2 + 0.025*ACO3 + 0.460*HO2

 + 0.475*CO + XO2

 {134} MO2 + OLN --> 1.750*HCHO + 0.500*HO2 + ALD

 + NO2

 {135} ETHP + ACO3 --> ALD + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {136} HC3P + ACO3 --> 0.770*ALD + 0.260*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {137} HC5P + ACO3 --> 0.410*ALD + 0.750*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {138} HC8P + ACO3 --> 0.460*ALD + 1.390*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {139} OL2P + ACO3 --> 0.800*HCHO + 0.600*ALD + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {140} OLTP + ACO3 --> ALD + 0.500*HCHO + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {141} OLIP + ACO3 --> 0.725*ALD + 0.550*KET + 0.140*HCHO

 + 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 {142} KETP + ACO3 --> MGLY + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {143} ACO3 + ACO3 --> 2.000*MO2

 {144} ACO3 + TOLP --> MO2 + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + HO2

 {145} ACO3 + XYLP --> MO2 + 0.450*MGLY + 0.806*DCB

 + HO2

 {146} ACO3 + TCO3 --> MO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 {147} ACO3 + OLN --> HCHO + ALD + 0.500*ORA2

 + NO2 + 0.500*MO2

 {148} OLN + OLN --> 2.000*HCHO + 2.000*ALD + 2.000*NO2

 {149} XO2 + HO2 --> OP2

 {150} XO2 + MO2 --> HCHO + HO2

 {151} XO2 + ACO3 --> MO2

 {152} XO2 + XO2 -->

 {153} XO2 + NO --> NO2

 {154} XNO2 + NO2 --> ONIT

 {155} XNO2 + HO2 --> OP2

 {156} XNO2 + MO2 --> HCHO + HO2

 {157} XNO2 + ACO3 --> MO2

 {158} XNO2 + XNO2 -->

 {159} TERP + HO --> TERPAER + HO

 {160} TERP + NO3 --> TERPAER + NO3

 {161} TERP + O3 --> TERPAER + O3

 >----------------------------------------------------------------------------------<

 Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) uses photo table O3O1D_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 3) uses photo table O3O3P_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 4) uses photo table HONO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 5) uses photo table HNO3_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 6) uses photo table HNO4_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 7) uses photo table NO3NO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}
EPA/600/R-99/030

Table 8A-8. RADM2_AE and RADM2_AE_AQ Mechanisms

8-56

 k( 8) uses photo table NO3NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 9) uses photo table H2O2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) uses photo table HCHOmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 11) uses photo table HCHOrad_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 12) uses photo table ALD_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 13) uses photo table MHP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 14) uses photo table HOP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 15) uses photo table PAA_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 16) uses photo table KETONE_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 17) uses photo table GLYform_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 18) uses photo table GLYmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 19) uses photo table MGLY_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 20) uses photo table UDC_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 21) uses photo table ORGNIT_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 22) = 6.0000E-34 * (T/300)**(-2.30) {6.09302E-34}

 k( 23) = 6.5000E-12 * exp( 120.0/T) {9.72293E-12}

 k( 24) = 1.8000E-11 * exp( 110.0/T) {2.60365E-11}

 k( 25) = 3.2000E-11 * exp( 70.0/T) {4.04730E-11}

 k( 26) = 2.2000E-10 {2.20000E-10}

 k( 27) = 2.0000E-12 * exp( -1400.0/T) {1.82272E-14}

 k( 28) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 29) = 1.1000E-14 * exp( -500.0/T) {2.05452E-15}

 k( 30) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 31) is a falloff expression using: {1.39058E-12}

 k0 = 1.8000E-31 * (T/300)**(-3.20)

 kinf = 4.7000E-12 * (T/300)**(-1.40)

 F = 0.60, n = 1.00

 k( 32) = k( 31) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {8.62399E-02}

 k( 33) is a special rate expression of the form: {3.01634E-12}

 k = k1 + k2[M], where

 k1 = 2.2000E-13 * exp( 620.0/T)

 k2 = 1.9000E-33 * exp( 980.0/T)

 k( 34) is a special rate expression of the form: {6.78905E-30}

 k = k1 + k2[M], where

 k1 = 3.0800E-34 * exp( 2820.0/T)

 k2 = 2.6600E-54 * exp( 3180.0/T)

 k( 35) = 3.3000E-12 * exp( -200.0/T) {1.68671E-12}

 k( 36) is a falloff expression using: {4.87144E-12}

 k0 = 7.0000E-31 * (T/300)**(-2.60)

 kinf = 1.5000E-11 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 37) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 38) = 1.4000E-13 * exp( -2500.0/T) {3.18213E-17}

 k( 39) = 1.7000E-11 * exp( 150.0/T) {2.81225E-11}

 k( 40) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 41) = 2.5000E-12 {2.50000E-12}

 k( 42) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 43) = k( 42) / Keq, where Keq = 1.100E-27 * exp( 11200.0/T) {5.47034E-02}

 k( 44) = 2.0000E-21 {2.00000E-21}

 k( 45) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 46) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 47) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 48) = 4.6000E-11 * exp( 230.0/T) {9.95294E-11}

 k( 49) is a falloff expression using: {8.88848E-13}

 k0 = 3.0000E-31 * (T/300)**(-3.30)

 kinf = 1.5000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 50) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 51) = 2.8300E+01 * (T/300)**( 2.00) * exp( -1280.0/T) {3.80672E-01}

 k( 52) = 1.2330E-12 * (T/300)**( 2.00) * exp( -444.0/T) {2.74210E-13}

 k( 53) = 1.5900E-11 * exp( -540.0/T) {2.59669E-12}

 k( 54) = 1.7300E-11 * exp( -380.0/T) {4.83334E-12}

 k( 55) = 3.6400E-11 * exp( -380.0/T) {1.01696E-11}

 k( 56) = 2.1500E-12 * exp( 411.0/T) {8.53916E-12}
EPA/600/R-99/030

Table 8A-8. RADM2_AE and RADM2_AE_AQ Mechanisms

8-57

 k( 57) = 5.3200E-12 * exp( 504.0/T) {2.88684E-11}

 k( 58) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 59) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 60) = 1.8900E-11 * exp( 116.0/T) {2.78943E-11}

 k( 61) = 4.0000E-11 {4.00000E-11}

 k( 62) = 9.0000E-01 * k( 61) {3.60000E-11}

 k( 63) = 9.0000E-12 {9.00000E-12}

 k( 64) = 6.8700E-12 * exp( 256.0/T) {1.62197E-11}

 k( 65) = 1.2000E-11 * exp( -745.0/T) {9.85020E-13}

 k( 66) = 1.1500E-11 {1.15000E-11}

 k( 67) = 1.7000E-11 {1.70000E-11}

 k( 68) = 2.8000E-11 {2.80000E-11}

 k( 69) = 1.0000E-11 {1.00000E-11}

 k( 70) = 1.0000E-11 {1.00000E-11}

 k( 71) = 1.0000E-11 {1.00000E-11}

 k( 72) = 6.1650E-13 * (T/300)**( 2.00) * exp( -444.0/T) {1.37105E-13}

 k( 73) = 1.5500E-11 * exp( -540.0/T) {2.53137E-12}

 k( 74) = 2.5500E-11 * exp( 409.0/T) {1.00601E-10}

 k( 75) = 2.8000E-12 * exp( 181.0/T) {5.13974E-12}

 k( 76) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 77) = 4.7000E-12 {4.70000E-12}

 k( 78) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 79) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 80) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 81) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 82) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 83) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 84) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 85) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 86) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 87) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 88) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 89) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 90) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 91) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 92) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 93) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 94) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 95) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 96) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 97) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 98) = 2.2000E-11 {2.20000E-11}

 k( 99) = 2.0000E-12 * exp( -2923.0/T) {1.09940E-16}

 k(100) = 1.0000E-11 * exp( -1895.0/T) {1.73099E-14}

 k(101) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k(102) = 5.8100E-13 {5.81000E-13}

 k(103) = 1.2000E-14 * exp( -2633.0/T) {1.74559E-18}

 k(104) = 1.3200E-14 * exp( -2105.0/T) {1.12933E-17}

 k(105) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 k(106) = 1.2300E-14 * exp( -2013.0/T) {1.43295E-17}

 k(107) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(108) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(109) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(110) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(111) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(112) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(113) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(114) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(115) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(116) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(117) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(118) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(119) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(120) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(121) = 1.9000E-13 * exp( 220.0/T) {3.97533E-13}

 k(122) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(123) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(124) = 3.4000E-14 * exp( 220.0/T) {7.11376E-14}

 k(125) = 2.9000E-14 * exp( 220.0/T) {6.06762E-14}

 k(126) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(127) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(128) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(129) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(130) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}
EPA/600/R-99/030

Table 8A-8. RADM2_AE and RADM2_AE_AQ Mechanisms

8-58

 k(131) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(132) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(133) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(134) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(135) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(136) = 1.0000E-13 * exp( 220.0/T) {2.09228E-13}

 k(137) = 8.4000E-14 * exp( 220.0/T) {1.75752E-13}

 k(138) = 7.2000E-14 * exp( 220.0/T) {1.50644E-13}

 k(139) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(140) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(141) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(142) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(143) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(144) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(145) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(146) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(147) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(148) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(149) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(150) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(151) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(152) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(153) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(154) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(155) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(156) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(157) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(158) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(159) = 1.0000E+00 * k( 58) {6.75269E-11}

 k(160) = 1.0000E+00 * k(101) {1.22539E-12}

 k(161) = 1.0000E+00 * k(105) {1.61125E-16}

 ===============================================================================
EPA/600/R-99/030

8-59

Table 8A-9. RADM2_CIS1 and RADM2_CIS1_AQ Mechanisms

 Reaction List

 >----------------------------------------------------------------------------------------<

 { 1} NO2 + hv --> O3P + NO

 { 2} O3 + hv --> O1D

 { 3} O3 + hv --> O3P

 { 4} HONO + hv --> HO + NO

 { 5} HNO3 + hv --> HO + NO2

 { 6} HNO4 + hv --> HO2 + NO2

 { 7} NO3 + hv --> NO

 { 8} NO3 + hv --> NO2 + O3P

 { 9} H2O2 + hv --> 2.000*HO

 { 10} HCHO + hv --> CO

 { 11} HCHO + hv --> HO2 + HO2 + CO

 { 12} ALD + hv --> MO2 + HO2 + CO

 { 13} OP1 + hv --> HCHO + HO2 + HO

 { 14} OP2 + hv --> ALD + HO2 + HO

 { 15} PAA + hv --> MO2 + HO

 { 16} KET + hv --> ACO3 + ETHP

 { 17} GLY + hv --> 0.130*HCHO + 1.870*CO

 { 18} GLY + hv --> 0.450*HCHO + 1.550*CO + 0.800*HO2

 { 19} MGLY + hv --> ACO3 + HO2 + CO

 { 20} DCB + hv --> 0.980*HO2 + 0.020*ACO3 + TCO3

 { 21} ONIT + hv --> 0.200*ALD + 0.800*KET + HO2

 + NO2

 { 22} O3P + [M] + [O2] --> O3

 { 23} O3P + NO2 --> NO

 { 24} O1D + [N2] --> O3P

 { 25} O1D + [O2] --> O3P

 { 26} O1D + [H2O] --> 2.000*HO

 { 27} O3 + NO --> NO2

 { 28} O3 + HO --> HO2

 { 29} O3 + HO2 --> HO

 { 30} HO2 + NO --> NO2 + HO

 { 31} HO2 + NO2 --> HNO4

 { 32} HNO4 --> HO2 + NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + HO --> HO2

 { 36} NO + HO --> HONO

 { 37} NO + NO + [O2] --> 2.000*NO2

 { 38} O3 + NO2 --> NO3

 { 39} NO3 + NO --> 2.000*NO2

 { 40} NO3 + NO2 --> NO + NO2

 { 41} NO3 + HO2 --> HNO3

 { 42} NO3 + NO2 --> N2O5

 { 43} N2O5 --> NO2 + NO3

 { 44} N2O5 + [H2O] --> 2.000*HNO3

 { 45} HO + NO2 --> HNO3

 { 46} HO + HNO3 --> NO3

 { 47} HO + HNO4 --> NO2

 { 48} HO + HO2 -->

 { 49} HO + SO2 --> SULF + HO2

 { 50} CO + HO --> HO2

 { 51} HO --> MO2

 { 52} ETH + HO --> ETHP

 { 53} HC3 + HO --> 0.830*HC3P + 0.170*HO2 + 0.009*HCHO

 + 0.075*ALD + 0.025*KET

 { 54} HC5 + HO --> HC5P + 0.250*XO2

 { 55} HC8 + HO --> HC8P + 0.750*XO2

 { 56} OL2 + HO --> OL2P

 { 57} OLT + HO --> OLTP

 { 58} OLI + HO --> OLIP

 { 59} TOL + HO --> 0.750*TOLP + 0.250*CSL + 0.250*HO2

 { 60} XYL + HO --> 0.830*XYLP + 0.170*CSL + 0.170*HO2

 { 61} CSL + HO --> 0.100*HO2 + 0.900*XO2 + 0.900*TCO3

 { 62} CSL + HO --> CSL

 { 63} HCHO + HO --> HO2 + CO

 { 64} ALD + HO --> ACO3

 { 65} KET + HO --> KETP

 { 66} GLY + HO --> HO2 + 2.000*CO

 { 67} MGLY + HO --> ACO3 + CO

 { 68} DCB + HO --> TCO3

 { 69} OP1 + HO --> 0.500*MO2 + 0.500*HCHO + 0.500*HO

 { 70} OP2 + HO --> 0.500*HC3P + 0.500*ALD + 0.500*HO
EPA/600/R-99/030

Table 8A-9. RADM2_CIS1 and RADM2_CIS1_AQ Mechanisms

8-60

 { 71} PAA + HO --> ACO3

 { 72} PAN + HO --> HCHO + NO3 + XO2

 { 73} ONIT + HO --> HC3P + NO2

 { 74} ACO3 + NO2 --> PAN

 { 75} PAN --> ACO3 + NO2

 { 76} TCO3 + NO2 --> TPAN

 { 77} TPAN --> TCO3 + NO2

 { 78} MO2 + NO --> HCHO + HO2 + NO2

 { 79} HC3P + NO --> 0.750*ALD + 0.250*KET + 0.090*HCHO

 + 0.036*ONIT + 0.964*NO2 + 0.964*HO2

 { 80} HC5P + NO --> 0.380*ALD + 0.690*KET + 0.080*ONIT

 + 0.920*NO2 + 0.920*HO2

 { 81} HC8P + NO --> 0.350*ALD + 1.060*KET + 0.040*HCHO

 + 0.240*ONIT + 0.760*NO2 + 0.760*HO2

 { 82} OL2P + NO --> 1.600*HCHO + HO2 + NO2

 + 0.200*ALD

 { 83} OLTP + NO --> ALD + HCHO + HO2

 + NO2

 { 84} OLIP + NO --> HO2 + 1.450*ALD + 0.280*HCHO

 + 0.100*KET + NO2

 { 85} ACO3 + NO --> MO2 + NO2

 { 86} TCO3 + NO --> NO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 { 87} TOLP + NO --> NO2 + HO2 + 0.170*MGLY

 + 0.160*GLY + 0.700*DCB

 { 88} XYLP + NO --> NO2 + HO2 + 0.450*MGLY

 + 0.806*DCB

 { 89} ETHP + NO --> ALD + HO2 + NO2

 { 90} KETP + NO --> MGLY + NO2 + HO2

 { 91} OLN + NO --> HCHO + ALD + 2.000*NO2

 { 92} HCHO + NO3 --> HO2 + HNO3 + CO

 { 93} ALD + NO3 --> ACO3 + HNO3

 { 94} GLY + NO3 --> HNO3 + HO2 + 2.000*CO

 { 95} MGLY + NO3 --> HNO3 + ACO3 + CO

 { 96} DCB + NO3 --> HNO3 + TCO3

 { 97} CSL + NO3 --> HNO3 + XNO2 + 0.500*CSL

 { 98} OL2 + NO3 --> OLN

 { 99} OLT + NO3 --> OLN

 {100} OLI + NO3 --> OLN

 {101} OL2 + O3 --> HCHO + 0.400*ORA1 + 0.420*CO

 + 0.120*HO2

 {102} OLT + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {103} OLI + O3 --> 0.180*HCHO + 0.720*ALD + 0.100*KET

 + 0.230*CO + 0.060*ORA1 + 0.290*ORA2

 + 0.260*HO2 + 0.140*HO + 0.310*MO2

 {104} HO2 + MO2 --> OP1

 {105} HO2 + ETHP --> OP2

 {106} HO2 + HC3P --> OP2

 {107} HO2 + HC5P --> OP2

 {108} HO2 + HC8P --> OP2

 {109} HO2 + OL2P --> OP2

 {110} HO2 + OLTP --> OP2

 {111} HO2 + OLIP --> OP2

 {112} HO2 + KETP --> OP2

 {113} HO2 + ACO3 --> PAA

 {114} HO2 + TOLP --> OP2

 {115} HO2 + XYLP --> OP2

 {116} HO2 + TCO3 --> OP2

 {117} HO2 + OLN --> ONIT

 {118} MO2 + MO2 --> 1.500*HCHO + HO2

 {119} MO2 + ETHP --> 0.750*HCHO + HO2 + 0.750*ALD

 {120} MO2 + HC3P --> 0.840*HCHO + 0.770*ALD + 0.260*KET

 + HO2

 {121} MO2 + HC5P --> 0.770*HCHO + 0.410*ALD + 0.750*KET

 + HO2

 {122} MO2 + HC8P --> 0.800*HCHO + 0.460*ALD + 1.390*KET

 + HO2

 {123} MO2 + OL2P --> 1.550*HCHO + 0.350*ALD + HO2

 {124} MO2 + OLTP --> 1.250*HCHO + 0.750*ALD + HO2

 {125} MO2 + OLIP --> 0.890*HCHO + 0.725*ALD + HO2

 + 0.550*KET
EPA/600/R-99/030

Table 8A-9. RADM2_CIS1 and RADM2_CIS1_AQ Mechanisms

8-61

 {126} MO2 + KETP --> 0.750*HCHO + 0.750*MGLY + HO2

 {127} MO2 + ACO3 --> HCHO + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {128} MO2 + TOLP --> HCHO + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + 2.000*HO2

 {129} MO2 + XYLP --> HCHO + 0.450*MGLY + 0.806*DCB

 + 2.000*HO2

 {130} MO2 + TCO3 --> 0.500*HCHO + 0.445*GLY + 0.055*MGLY

 + 0.500*ORA2 + 0.025*ACO3 + 0.460*HO2

 + 0.475*CO + XO2

 {131} MO2 + OLN --> 1.750*HCHO + 0.500*HO2 + ALD

 + NO2

 {132} ETHP + ACO3 --> ALD + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {133} HC3P + ACO3 --> 0.770*ALD + 0.260*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {134} HC5P + ACO3 --> 0.410*ALD + 0.750*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {135} HC8P + ACO3 --> 0.460*ALD + 1.390*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {136} OL2P + ACO3 --> 0.800*HCHO + 0.600*ALD + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {137} OLTP + ACO3 --> ALD + 0.500*HCHO + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {138} OLIP + ACO3 --> 0.725*ALD + 0.550*KET + 0.140*HCHO

 + 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 {139} KETP + ACO3 --> MGLY + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {140} ACO3 + ACO3 --> 2.000*MO2

 {141} ACO3 + TOLP --> MO2 + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + HO2

 {142} ACO3 + XYLP --> MO2 + 0.450*MGLY + 0.806*DCB

 + HO2

 {143} ACO3 + TCO3 --> MO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 {144} ACO3 + OLN --> HCHO + ALD + 0.500*ORA2

 + NO2 + 0.500*MO2

 {145} OLN + OLN --> 2.000*HCHO + 2.000*ALD + 2.000*NO2

 {146} XO2 + HO2 --> OP2

 {147} XO2 + MO2 --> HCHO + HO2

 {148} XO2 + ACO3 --> MO2

 {149} XO2 + XO2 -->

 {150} XO2 + NO --> NO2

 {151} XNO2 + NO2 --> ONIT

 {152} XNO2 + HO2 --> OP2

 {153} XNO2 + MO2 --> HCHO + HO2

 {154} XNO2 + ACO3 --> MO2

 {155} XNO2 + XNO2 -->

 {156} ISO + HO --> ISO_RO2 + 0.079*XO2

 {157} ISO_RO2 + NO --> 0.088*ONIT + 0.912*NO2 + 0.912*HO2

 + 0.912*ISOPROD + 0.629*HCHO

 {158} ISO_RO2 + HO2 --> OP2

 {159} ISO_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + ISOPROD

 {160} ISO_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + ISOPROD

 {161} ISO + O3 --> 0.600*HCHO + 0.650*ISOPROD + 0.390*ORA1

 + 0.270*HO + 0.070*HO2 + 0.070*CO

 + 0.200*XO2 + 0.200*ACO3 + 0.150*ALD

 {162} ISO + O3P --> 0.750*ISOPROD + 0.250*ACO3 + 0.250*HCHO

 + 0.250*MO2

 {163} ISO + NO3 --> ISON_RO2

 {164} ISON_RO2 + NO --> NO2 + 0.800*ALD + 0.800*ONIT

 + 0.800*HO2 + 0.200*ISOPROD + 0.200*NO2

 {165} ISON_RO2 + HO2 --> ONIT

 {166} ISON_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + ALD + ONIT

 {167} ISON_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + ALD

 + ONIT

 {168} ISOPROD + HO --> 0.500*ACO3 + 0.500*IP_RO2 + 0.200*XO2

 {169} IP_RO2 + NO --> NO2 + HO2 + 0.590*CO

 + 0.550*ALD + 0.250*HCHO + 0.080*GLY

 + 0.340*MGLY + 0.630*KET

 {170} IP_RO2 + HO2 --> OP2
EPA/600/R-99/030

Table 8A-9. RADM2_CIS1 and RADM2_CIS1_AQ Mechanisms

8-62

 {171} IP_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.500*ALD + 0.500*KET

 {172} IP_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.500*ALD

 + 0.500*KET

 {173} ISOPROD + O3 --> 0.268*HO + 0.100*HO2 + 0.114*ACO3

 + 0.054*MO2 + 0.070*XO2 + 0.155*CO

 + 0.146*HCHO + 0.020*ALD + 0.010*GLY

 + 0.850*MGLY + 0.090*KET + 0.462*ORA1

 {174} ISOPROD + hv --> 0.970*ACO3 + 0.333*HO2 + 0.700*MO2

 + 0.200*HCHO + 0.333*CO + 0.067*ALD

 + 0.033*KET

 {175} ISOPROD + NO3 --> 0.075*ACO3 + 0.075*HNO3 + 0.643*CO

 + 0.282*HCHO + 0.925*ONIT + 0.282*ALD

 + 0.925*HO2 + 0.925*XO2

 >----------------------------------------------------------------------------------------<

 Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) uses photo table O3O1D_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 3) uses photo table O3O3P_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 4) uses photo table HONO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 5) uses photo table HNO3_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 6) uses photo table HNO4_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 7) uses photo table NO3NO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 8) uses photo table NO3NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 9) uses photo table H2O2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) uses photo table HCHOmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 11) uses photo table HCHOrad_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 12) uses photo table ALD_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 13) uses photo table MHP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 14) uses photo table HOP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 15) uses photo table PAA_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 16) uses photo table KETONE_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 17) uses photo table GLYform_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 18) uses photo table GLYmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 19) uses photo table MGLY_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 20) uses photo table UDC_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 21) uses photo table ORGNIT_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 22) = 6.0000E-34 * (T/300)**(-2.30) {6.09302E-34}

 k( 23) = 6.5000E-12 * exp( 120.0/T) {9.72293E-12}

 k( 24) = 1.8000E-11 * exp( 110.0/T) {2.60365E-11}

 k( 25) = 3.2000E-11 * exp( 70.0/T) {4.04730E-11}

 k( 26) = 2.2000E-10 {2.20000E-10}

 k( 27) = 2.0000E-12 * exp( -1400.0/T) {1.82272E-14}

 k( 28) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 29) = 1.1000E-14 * exp( -500.0/T) {2.05452E-15}

 k( 30) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 31) is a falloff expression using: {1.39058E-12}

 k0 = 1.8000E-31 * (T/300)**(-3.20)

 kinf = 4.7000E-12 * (T/300)**(-1.40)

 F = 0.60, n = 1.00

 k( 32) = k( 31) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {8.62399E-02}

 k( 33) is a special rate expression of the form: {3.01634E-12}

 k = k1 + k2[M], where

 k1 = 2.2000E-13 * exp( 620.0/T)

 k2 = 1.9000E-33 * exp( 980.0/T)

 k( 34) is a special rate expression of the form: {6.78905E-30}

 k = k1 + k2[M], where

 k1 = 3.0800E-34 * exp( 2820.0/T)

 k2 = 2.6600E-54 * exp( 3180.0/T)

 k( 35) = 3.3000E-12 * exp( -200.0/T) {1.68671E-12}

 k( 36) is a falloff expression using: {4.87144E-12}

 k0 = 7.0000E-31 * (T/300)**(-2.60)

 kinf = 1.5000E-11 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 37) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 38) = 1.4000E-13 * exp( -2500.0/T) {3.18213E-17}

 k( 39) = 1.7000E-11 * exp( 150.0/T) {2.81225E-11}

 k( 40) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 41) = 2.5000E-12 {2.50000E-12}

 k( 42) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)
EPA/600/R-99/030

Table 8A-9. RADM2_CIS1 and RADM2_CIS1_AQ Mechanisms

8-63

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 43) = k( 42) / Keq, where Keq = 1.100E-27 * exp( 11200.0/T) {5.47034E-02}

 k( 44) = 2.0000E-21 {2.00000E-21}

 k( 45) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 46) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 47) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 48) = 4.6000E-11 * exp( 230.0/T) {9.95294E-11}

 k( 49) is a falloff expression using: {8.88848E-13}

 k0 = 3.0000E-31 * (T/300)**(-3.30)

 kinf = 1.5000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 50) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 51) = 2.8300E+01 * (T/300)**( 2.00) * exp( -1280.0/T) {3.80672E-01}

 k( 52) = 1.2330E-12 * (T/300)**( 2.00) * exp( -444.0/T) {2.74210E-13}

 k( 53) = 1.5900E-11 * exp( -540.0/T) {2.59669E-12}

 k( 54) = 1.7300E-11 * exp( -380.0/T) {4.83334E-12}

 k( 55) = 3.6400E-11 * exp( -380.0/T) {1.01696E-11}

 k( 56) = 2.1500E-12 * exp( 411.0/T) {8.53916E-12}

 k( 57) = 5.3200E-12 * exp( 504.0/T) {2.88684E-11}

 k( 58) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 59) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 60) = 1.8900E-11 * exp( 116.0/T) {2.78943E-11}

 k( 61) = 4.0000E-11 {4.00000E-11}

 k( 62) = 9.0000E-01 * k( 61) {3.60000E-11}

 k( 63) = 9.0000E-12 {9.00000E-12}

 k( 64) = 6.8700E-12 * exp( 256.0/T) {1.62197E-11}

 k( 65) = 1.2000E-11 * exp( -745.0/T) {9.85020E-13}

 k( 66) = 1.1500E-11 {1.15000E-11}

 k( 67) = 1.7000E-11 {1.70000E-11}

 k( 68) = 2.8000E-11 {2.80000E-11}

 k( 69) = 1.0000E-11 {1.00000E-11}

 k( 70) = 1.0000E-11 {1.00000E-11}

 k( 71) = 1.0000E-11 {1.00000E-11}

 k( 72) = 6.1650E-13 * (T/300)**( 2.00) * exp( -444.0/T) {1.37105E-13}

 k( 73) = 1.5500E-11 * exp( -540.0/T) {2.53137E-12}

 k( 74) = 2.8000E-12 * exp( 181.0/T) {5.13974E-12}

 k( 75) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 76) = 4.7000E-12 {4.70000E-12}

 k( 77) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 78) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 79) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 80) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 81) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 82) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 83) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 84) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 85) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 86) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 87) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 88) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 89) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 90) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 91) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 92) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 93) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 94) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 95) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 96) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 97) = 2.2000E-11 {2.20000E-11}

 k( 98) = 2.0000E-12 * exp( -2923.0/T) {1.09940E-16}

 k( 99) = 1.0000E-11 * exp( -1895.0/T) {1.73099E-14}

 k(100) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k(101) = 1.2000E-14 * exp( -2633.0/T) {1.74559E-18}

 k(102) = 1.3200E-14 * exp( -2105.0/T) {1.12933E-17}

 k(103) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 k(104) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}
EPA/600/R-99/030

Table 8A-9. RADM2_CIS1 and RADM2_CIS1_AQ Mechanisms

8-64

 k(105) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(106) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(107) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(108) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(109) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(110) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(111) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(112) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(113) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(114) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(115) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(116) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(117) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(118) = 1.9000E-13 * exp( 220.0/T) {3.97533E-13}

 k(119) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(120) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(121) = 3.4000E-14 * exp( 220.0/T) {7.11376E-14}

 k(122) = 2.9000E-14 * exp( 220.0/T) {6.06762E-14}

 k(123) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(124) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(125) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(126) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(127) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(128) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(129) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(130) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(131) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(132) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(133) = 1.0000E-13 * exp( 220.0/T) {2.09228E-13}

 k(134) = 8.4000E-14 * exp( 220.0/T) {1.75752E-13}

 k(135) = 7.2000E-14 * exp( 220.0/T) {1.50644E-13}

 k(136) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(137) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(138) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(139) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(140) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(141) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(142) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(143) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(144) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(145) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(146) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(147) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(148) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(149) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(150) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(151) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(152) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(153) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(154) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(155) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(156) = 2.5400E-11 * (T/300)**( 1.00) * exp( 407.6/T) {9.90719E-11}

 k(157) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(158) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(159) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(160) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(161) = 7.8600E-15 * (T/300)**( 1.00) * exp( -1912.2/T) {1.27569E-17}

 k(162) = 3.6000E-11 {3.60000E-11}

 k(163) = 3.0300E-12 * (T/300)**( 1.00) * exp( -447.9/T) {6.69552E-13}

 k(164) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(165) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(166) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(167) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(168) = 3.3600E-11 {3.36000E-11}

 k(169) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(170) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(171) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(172) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(173) = 7.1100E-18 {7.11000E-18}

 k(174) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k(175) = 1.0000E-15 {1.00000E-15}

 ===============================================================================
EPA/600/R-99/030

8-65
EPA/600/R-99/030

8-66

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms

 Reaction List

 >----------------------------------------------------------------------------------------<

 { 1} NO2 + hv --> O3P + NO

 { 2} O3 + hv --> O1D

 { 3} O3 + hv --> O3P

 { 4} HONO + hv --> HO + NO

 { 5} HNO3 + hv --> HO + NO2

 { 6} HNO4 + hv --> HO2 + NO2

 { 7} NO3 + hv --> NO

 { 8} NO3 + hv --> NO2 + O3P

 { 9} H2O2 + hv --> 2.000*HO

 { 10} HCHO + hv --> CO

 { 11} HCHO + hv --> HO2 + HO2 + CO

 { 12} ALD + hv --> MO2 + HO2 + CO

 { 13} OP1 + hv --> HCHO + HO2 + HO

 { 14} OP2 + hv --> ALD + HO2 + HO

 { 15} PAA + hv --> MO2 + HO

 { 16} KET + hv --> ACO3 + ETHP

 { 17} GLY + hv --> 0.130*HCHO + 1.870*CO

 { 18} GLY + hv --> 0.450*HCHO + 1.550*CO + 0.800*HO2

 { 19} MGLY + hv --> ACO3 + HO2 + CO

 { 20} DCB + hv --> 0.980*HO2 + 0.020*ACO3 + TCO3

 { 21} ONIT + hv --> 0.200*ALD + 0.800*KET + HO2

 + NO2

 { 22} O3P + [M] + [O2] --> O3

 { 23} O3P + NO2 --> NO

 { 24} O1D + [N2] --> O3P

 { 25} O1D + [O2] --> O3P

 { 26} O1D + [H2O] --> 2.000*HO

 { 27} O3 + NO --> NO2

 { 28} O3 + HO --> HO2

 { 29} O3 + HO2 --> HO

 { 30} HO2 + NO --> NO2 + HO

 { 31} HO2 + NO2 --> HNO4

 { 32} HNO4 --> HO2 + NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + HO --> HO2

 { 36} NO + HO --> HONO

 { 37} NO + NO + [O2] --> 2.000*NO2

 { 38} O3 + NO2 --> NO3

 { 39} NO3 + NO --> 2.000*NO2

 { 40} NO3 + NO2 --> NO + NO2

 { 41} NO3 + HO2 --> HNO3

 { 42} NO3 + NO2 --> N2O5

 { 43} N2O5 --> NO2 + NO3

 { 44} N2O5 + [H2O] --> 2.000*HNO3

 { 45} HO + NO2 --> HNO3

 { 46} HO + HNO3 --> NO3

 { 47} HO + HNO4 --> NO2

 { 48} HO + HO2 -->

 { 49} HO + SO2 --> SULF + HO2 + SULAER

 { 50} CO + HO --> HO2

 { 51} HO --> MO2

 { 52} ETH + HO --> ETHP

 { 53} HC3 + HO --> 0.830*HC3P + 0.170*HO2 + 0.009*HCHO

 + 0.075*ALD + 0.025*KET

 { 54} HC5 + HO --> HC5P + 0.250*XO2

 { 55} HC8 + HO --> HC8P + 0.750*XO2 + HC8AER

 { 56} OL2 + HO --> OL2P

 { 57} OLT + HO --> OLTP

 { 58} OLI + HO --> OLIP + OLIAER

 { 59} TOL + HO --> 0.750*TOLP + 0.250*CSL + 0.250*HO2

 + TOLAER

 { 60} XYL + HO --> 0.830*XYLP + 0.170*CSL + 0.170*HO2

 + XYLAER

 { 61} CSL + HO --> 0.100*HO2 + 0.900*XO2 + 0.900*TCO3

 + CSLAER

 { 62} CSL + HO --> CSL

 { 63} HCHO + HO --> HO2 + CO

 { 64} ALD + HO --> ACO3

 { 65} KET + HO --> KETP

 { 66} GLY + HO --> HO2 + 2.000*CO

 { 67} MGLY + HO --> ACO3 + CO
EPA/600/R-99/030

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms

8-67

 { 68} DCB + HO --> TCO3

 { 69} OP1 + HO --> 0.500*MO2 + 0.500*HCHO + 0.500*HO

 { 70} OP2 + HO --> 0.500*HC3P + 0.500*ALD + 0.500*HO

 { 71} PAA + HO --> ACO3

 { 72} PAN + HO --> HCHO + NO3 + XO2

 { 73} ONIT + HO --> HC3P + NO2

 { 74} ACO3 + NO2 --> PAN

 { 75} PAN --> ACO3 + NO2

 { 76} TCO3 + NO2 --> TPAN

 { 77} TPAN --> TCO3 + NO2

 { 78} MO2 + NO --> HCHO + HO2 + NO2

 { 79} HC3P + NO --> 0.750*ALD + 0.250*KET + 0.090*HCHO

 + 0.036*ONIT + 0.964*NO2 + 0.964*HO2

 { 80} HC5P + NO --> 0.380*ALD + 0.690*KET + 0.080*ONIT

 + 0.920*NO2 + 0.920*HO2

 { 81} HC8P + NO --> 0.350*ALD + 1.060*KET + 0.040*HCHO

 + 0.240*ONIT + 0.760*NO2 + 0.760*HO2

 { 82} OL2P + NO --> 1.600*HCHO + HO2 + NO2

 + 0.200*ALD

 { 83} OLTP + NO --> ALD + HCHO + HO2

 + NO2

 { 84} OLIP + NO --> HO2 + 1.450*ALD + 0.280*HCHO

 + 0.100*KET + NO2

 { 85} ACO3 + NO --> MO2 + NO2

 { 86} TCO3 + NO --> NO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 { 87} TOLP + NO --> NO2 + HO2 + 0.170*MGLY

 + 0.160*GLY + 0.700*DCB

 { 88} XYLP + NO --> NO2 + HO2 + 0.450*MGLY

 + 0.806*DCB

 { 89} ETHP + NO --> ALD + HO2 + NO2

 { 90} KETP + NO --> MGLY + NO2 + HO2

 { 91} OLN + NO --> HCHO + ALD + 2.000*NO2

 { 92} HCHO + NO3 --> HO2 + HNO3 + CO

 { 93} ALD + NO3 --> ACO3 + HNO3

 { 94} GLY + NO3 --> HNO3 + HO2 + 2.000*CO

 { 95} MGLY + NO3 --> HNO3 + ACO3 + CO

 { 96} DCB + NO3 --> HNO3 + TCO3

 { 97} CSL + NO3 --> HNO3 + XNO2 + 0.500*CSL

 + 0.500*CSLAER

 { 98} OL2 + NO3 --> OLN

 { 99} OLT + NO3 --> OLN

 {100} OLI + NO3 --> OLN + OLIAER

 {101} OL2 + O3 --> HCHO + 0.400*ORA1 + 0.420*CO

 + 0.120*HO2

 {102} OLT + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {103} OLI + O3 --> 0.180*HCHO + 0.720*ALD + 0.100*KET

 + 0.230*CO + 0.060*ORA1 + 0.290*ORA2

 + 0.260*HO2 + 0.140*HO + 0.310*MO2

 + OLIAER

 {104} HO2 + MO2 --> OP1

 {105} HO2 + ETHP --> OP2

 {106} HO2 + HC3P --> OP2

 {107} HO2 + HC5P --> OP2

 {108} HO2 + HC8P --> OP2

 {109} HO2 + OL2P --> OP2

 {110} HO2 + OLTP --> OP2

 {111} HO2 + OLIP --> OP2

 {112} HO2 + KETP --> OP2

 {113} HO2 + ACO3 --> PAA

 {114} HO2 + TOLP --> OP2

 {115} HO2 + XYLP --> OP2

 {116} HO2 + TCO3 --> OP2

 {117} HO2 + OLN --> ONIT

 {118} MO2 + MO2 --> 1.500*HCHO + HO2

 {119} MO2 + ETHP --> 0.750*HCHO + HO2 + 0.750*ALD

 {120} MO2 + HC3P --> 0.840*HCHO + 0.770*ALD + 0.260*KET

 + HO2

 {121} MO2 + HC5P --> 0.770*HCHO + 0.410*ALD + 0.750*KET

 + HO2

 {122} MO2 + HC8P --> 0.800*HCHO + 0.460*ALD + 1.390*KET
EPA/600/R-99/030

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms

8-68

 + HO2

 {123} MO2 + OL2P --> 1.550*HCHO + 0.350*ALD + HO2

 {124} MO2 + OLTP --> 1.250*HCHO + 0.750*ALD + HO2

 {125} MO2 + OLIP --> 0.890*HCHO + 0.725*ALD + HO2

 + 0.550*KET

 {126} MO2 + KETP --> 0.750*HCHO + 0.750*MGLY + HO2

 {127} MO2 + ACO3 --> HCHO + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {128} MO2 + TOLP --> HCHO + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + 2.000*HO2

 {129} MO2 + XYLP --> HCHO + 0.450*MGLY + 0.806*DCB

 + 2.000*HO2

 {130} MO2 + TCO3 --> 0.500*HCHO + 0.445*GLY + 0.055*MGLY

 + 0.500*ORA2 + 0.025*ACO3 + 0.460*HO2

 + 0.475*CO + XO2

 {131} MO2 + OLN --> 1.750*HCHO + 0.500*HO2 + ALD

 + NO2

 {132} ETHP + ACO3 --> ALD + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {133} HC3P + ACO3 --> 0.770*ALD + 0.260*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {134} HC5P + ACO3 --> 0.410*ALD + 0.750*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {135} HC8P + ACO3 --> 0.460*ALD + 1.390*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {136} OL2P + ACO3 --> 0.800*HCHO + 0.600*ALD + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {137} OLTP + ACO3 --> ALD + 0.500*HCHO + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {138} OLIP + ACO3 --> 0.725*ALD + 0.550*KET + 0.140*HCHO

 + 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 {139} KETP + ACO3 --> MGLY + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {140} ACO3 + ACO3 --> 2.000*MO2

 {141} ACO3 + TOLP --> MO2 + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + HO2

 {142} ACO3 + XYLP --> MO2 + 0.450*MGLY + 0.806*DCB

 + HO2

 {143} ACO3 + TCO3 --> MO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 {144} ACO3 + OLN --> HCHO + ALD + 0.500*ORA2

 + NO2 + 0.500*MO2

 {145} OLN + OLN --> 2.000*HCHO + 2.000*ALD + 2.000*NO2

 {146} XO2 + HO2 --> OP2

 {147} XO2 + MO2 --> HCHO + HO2

 {148} XO2 + ACO3 --> MO2

 {149} XO2 + XO2 -->

 {150} XO2 + NO --> NO2

 {151} XNO2 + NO2 --> ONIT

 {152} XNO2 + HO2 --> OP2

 {153} XNO2 + MO2 --> HCHO + HO2

 {154} XNO2 + ACO3 --> MO2

 {155} XNO2 + XNO2 -->

 {156} TERP + HO --> TERPAER + HO

 {157} TERP + NO3 --> TERPAER + NO3

 {158} TERP + O3 --> TERPAER + O3

 {159} ISO + HO --> ISO_RO2 + 0.079*XO2

 {160} ISO_RO2 + NO --> 0.088*ONIT + 0.912*NO2 + 0.912*HO2

 + 0.912*ISOPROD + 0.629*HCHO

 {161} ISO_RO2 + HO2 --> OP2

 {162} ISO_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + ISOPROD

 {163} ISO_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + ISOPROD

 {164} ISO + O3 --> 0.600*HCHO + 0.650*ISOPROD + 0.390*ORA1

 + 0.270*HO + 0.070*HO2 + 0.070*CO

 + 0.200*XO2 + 0.200*ACO3 + 0.150*ALD

 {165} ISO + O3P --> 0.750*ISOPROD + 0.250*ACO3 + 0.250*HCHO

 + 0.250*MO2

 {166} ISO + NO3 --> ISON_RO2

 {167} ISON_RO2 + NO --> NO2 + 0.800*ALD + 0.800*ONIT

 + 0.800*HO2 + 0.200*ISOPROD + 0.200*NO2

 {168} ISON_RO2 + HO2 --> ONIT

 {169} ISON_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2
EPA/600/R-99/030

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms

8-69

 + ALD + ONIT

 {170} ISON_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + ALD

 + ONIT

 {171} ISOPROD + HO --> 0.500*ACO3 + 0.500*IP_RO2 + 0.200*XO2

 {172} IP_RO2 + NO --> NO2 + HO2 + 0.590*CO

 + 0.550*ALD + 0.250*HCHO + 0.080*GLY

 + 0.340*MGLY + 0.630*KET

 {173} IP_RO2 + HO2 --> OP2

 {174} IP_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.500*ALD + 0.500*KET

 {175} IP_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.500*ALD

 + 0.500*KET

 {176} ISOPROD + O3 --> 0.268*HO + 0.100*HO2 + 0.114*ACO3

 + 0.054*MO2 + 0.070*XO2 + 0.155*CO

 + 0.146*HCHO + 0.020*ALD + 0.010*GLY

 + 0.850*MGLY + 0.090*KET + 0.462*ORA1

 {177} ISOPROD + hv --> 0.970*ACO3 + 0.333*HO2 + 0.700*MO2

 + 0.200*HCHO + 0.333*CO + 0.067*ALD

 + 0.033*KET

 {178} ISOPROD + NO3 --> 0.075*ACO3 + 0.075*HNO3 + 0.643*CO

 + 0.282*HCHO + 0.925*ONIT + 0.282*ALD

 + 0.925*HO2 + 0.925*XO2

 >----------------------------------------------------------------------------------------<

 Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) uses photo table O3O1D_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 3) uses photo table O3O3P_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 4) uses photo table HONO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 5) uses photo table HNO3_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 6) uses photo table HNO4_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 7) uses photo table NO3NO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 8) uses photo table NO3NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 9) uses photo table H2O2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) uses photo table HCHOmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 11) uses photo table HCHOrad_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 12) uses photo table ALD_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 13) uses photo table MHP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 14) uses photo table HOP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 15) uses photo table PAA_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 16) uses photo table KETONE_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 17) uses photo table GLYform_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 18) uses photo table GLYmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 19) uses photo table MGLY_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 20) uses photo table UDC_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 21) uses photo table ORGNIT_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 22) = 6.0000E-34 * (T/300)**(-2.30) {6.09302E-34}

 k( 23) = 6.5000E-12 * exp( 120.0/T) {9.72293E-12}

 k( 24) = 1.8000E-11 * exp( 110.0/T) {2.60365E-11}

 k( 25) = 3.2000E-11 * exp( 70.0/T) {4.04730E-11}

 k( 26) = 2.2000E-10 {2.20000E-10}

 k( 27) = 2.0000E-12 * exp( -1400.0/T) {1.82272E-14}

 k( 28) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 29) = 1.1000E-14 * exp( -500.0/T) {2.05452E-15}

 k( 30) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 31) is a falloff expression using: {1.39058E-12}

 k0 = 1.8000E-31 * (T/300)**(-3.20)

 kinf = 4.7000E-12 * (T/300)**(-1.40)

 F = 0.60, n = 1.00

 k( 32) = k( 31) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {8.62399E-02}

 k( 33) is a special rate expression of the form: {3.01634E-12}

 k = k1 + k2[M], where

 k1 = 2.2000E-13 * exp( 620.0/T)

 k2 = 1.9000E-33 * exp( 980.0/T)

 k( 34) is a special rate expression of the form: {6.78905E-30}

 k = k1 + k2[M], where

 k1 = 3.0800E-34 * exp( 2820.0/T)

 k2 = 2.6600E-54 * exp( 3180.0/T)

 k( 35) = 3.3000E-12 * exp( -200.0/T) {1.68671E-12}

 k( 36) is a falloff expression using: {4.87144E-12}

 k0 = 7.0000E-31 * (T/300)**(-2.60)

 kinf = 1.5000E-11 * (T/300)**(-0.50)
EPA/600/R-99/030

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms

8-70

 F = 0.60, n = 1.00

 k( 37) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 38) = 1.4000E-13 * exp( -2500.0/T) {3.18213E-17}

 k( 39) = 1.7000E-11 * exp( 150.0/T) {2.81225E-11}

 k( 40) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 41) = 2.5000E-12 {2.50000E-12}

 k( 42) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 43) = k( 42) / Keq, where Keq = 1.100E-27 * exp( 11200.0/T) {5.47034E-02}

 k( 44) = 2.0000E-21 {2.00000E-21}

 k( 45) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 46) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 47) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 48) = 4.6000E-11 * exp( 230.0/T) {9.95294E-11}

 k( 49) is a falloff expression using: {8.88848E-13}

 k0 = 3.0000E-31 * (T/300)**(-3.30)

 kinf = 1.5000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 50) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 51) = 2.8300E+01 * (T/300)**( 2.00) * exp( -1280.0/T) {3.80672E-01}

 k( 52) = 1.2330E-12 * (T/300)**( 2.00) * exp( -444.0/T) {2.74210E-13}

 k( 53) = 1.5900E-11 * exp( -540.0/T) {2.59669E-12}

 k( 54) = 1.7300E-11 * exp( -380.0/T) {4.83334E-12}

 k( 55) = 3.6400E-11 * exp( -380.0/T) {1.01696E-11}

 k( 56) = 2.1500E-12 * exp( 411.0/T) {8.53916E-12}

 k( 57) = 5.3200E-12 * exp( 504.0/T) {2.88684E-11}

 k( 58) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 59) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 60) = 1.8900E-11 * exp( 116.0/T) {2.78943E-11}

 k( 61) = 4.0000E-11 {4.00000E-11}

 k( 62) = 9.0000E-01 * k( 61) {3.60000E-11}

 k( 63) = 9.0000E-12 {9.00000E-12}

 k( 64) = 6.8700E-12 * exp( 256.0/T) {1.62197E-11}

 k( 65) = 1.2000E-11 * exp( -745.0/T) {9.85020E-13}

 k( 66) = 1.1500E-11 {1.15000E-11}

 k( 67) = 1.7000E-11 {1.70000E-11}

 k( 68) = 2.8000E-11 {2.80000E-11}

 k( 69) = 1.0000E-11 {1.00000E-11}

 k( 70) = 1.0000E-11 {1.00000E-11}

 k( 71) = 1.0000E-11 {1.00000E-11}

 k( 72) = 6.1650E-13 * (T/300)**( 2.00) * exp( -444.0/T) {1.37105E-13}

 k( 73) = 1.5500E-11 * exp( -540.0/T) {2.53137E-12}

 k( 74) = 2.8000E-12 * exp( 181.0/T) {5.13974E-12}

 k( 75) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 76) = 4.7000E-12 {4.70000E-12}

 k( 77) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 78) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 79) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 80) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 81) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 82) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 83) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 84) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 85) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 86) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 87) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 88) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 89) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 90) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 91) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 92) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 93) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 94) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 95) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 96) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}
EPA/600/R-99/030

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms

8-71

 k( 97) = 2.2000E-11 {2.20000E-11}

 k( 98) = 2.0000E-12 * exp( -2923.0/T) {1.09940E-16}

 k( 99) = 1.0000E-11 * exp( -1895.0/T) {1.73099E-14}

 k(100) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k(101) = 1.2000E-14 * exp( -2633.0/T) {1.74559E-18}

 k(102) = 1.3200E-14 * exp( -2105.0/T) {1.12933E-17}

 k(103) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 k(104) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(105) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(106) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(107) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(108) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(109) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(110) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(111) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(112) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(113) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(114) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(115) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(116) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(117) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(118) = 1.9000E-13 * exp( 220.0/T) {3.97533E-13}

 k(119) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(120) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(121) = 3.4000E-14 * exp( 220.0/T) {7.11376E-14}

 k(122) = 2.9000E-14 * exp( 220.0/T) {6.06762E-14}

 k(123) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(124) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(125) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(126) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(127) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(128) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(129) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(130) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(131) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(132) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(133) = 1.0000E-13 * exp( 220.0/T) {2.09228E-13}

 k(134) = 8.4000E-14 * exp( 220.0/T) {1.75752E-13}

 k(135) = 7.2000E-14 * exp( 220.0/T) {1.50644E-13}

 k(136) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(137) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(138) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(139) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(140) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(141) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(142) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(143) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(144) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(145) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(146) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(147) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(148) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(149) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(150) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(151) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(152) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(153) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(154) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(155) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(156) = 1.0000E+00 * k( 58) {6.75269E-11}

 k(157) = 1.0000E+00 * k(100) {1.22539E-12}

 k(158) = 1.0000E+00 * k(103) {1.61125E-16}

 k(159) = 2.5400E-11 * (T/300)**( 1.00) * exp( 407.6/T) {9.90719E-11}

 k(160) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(161) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(162) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(163) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(164) = 7.8600E-15 * (T/300)**( 1.00) * exp( -1912.2/T) {1.27569E-17}

 k(165) = 3.6000E-11 {3.60000E-11}

 k(166) = 3.0300E-12 * (T/300)**( 1.00) * exp( -447.9/T) {6.69552E-13}

 k(167) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(168) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(169) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(170) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}
EPA/600/R-99/030

Table 8A-10. RADM2_CIS1_AE and RADM2_CIS1_AE_AQ Mechanisms

8-72

 k(171) = 3.3600E-11 {3.36000E-11}

 k(172) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(173) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(174) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(175) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(176) = 7.1100E-18 {7.11000E-18}

 k(177) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k(178) = 1.0000E-15 {1.00000E-15}

 ===============================================================================
EPA/600/R-99/030

8-73

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms

 Reaction List

 >----------------------------------------------------------------------------------------<

 { 1} NO2 + hv --> O3P + NO

 { 2} O3 + hv --> O1D

 { 3} O3 + hv --> O3P

 { 4} HONO + hv --> HO + NO

 { 5} HNO3 + hv --> HO + NO2

 { 6} HNO4 + hv --> HO2 + NO2

 { 7} NO3 + hv --> NO

 { 8} NO3 + hv --> NO2 + O3P

 { 9} H2O2 + hv --> 2.000*HO

 { 10} HCHO + hv --> CO

 { 11} HCHO + hv --> HO2 + HO2 + CO

 { 12} ALD + hv --> MO2 + HO2 + CO

 { 13} OP1 + hv --> HCHO + HO2 + HO

 { 14} OP2 + hv --> ALD + HO2 + HO

 { 15} PAA + hv --> MO2 + HO

 { 16} KET + hv --> ACO3 + ETHP

 { 17} GLY + hv --> 0.130*HCHO + 1.870*CO

 { 18} GLY + hv --> 0.450*HCHO + 1.550*CO + 0.800*HO2

 { 19} MGLY + hv --> ACO3 + HO2 + CO

 { 20} DCB + hv --> 0.980*HO2 + 0.020*ACO3 + TCO3

 { 21} ONIT + hv --> 0.200*ALD + 0.800*KET + HO2

 + NO2

 { 22} O3P + [M] + [O2] --> O3

 { 23} O3P + NO2 --> NO

 { 24} O1D + [N2] --> O3P

 { 25} O1D + [O2] --> O3P

 { 26} O1D + [H2O] --> 2.000*HO

 { 27} O3 + NO --> NO2

 { 28} O3 + HO --> HO2

 { 29} O3 + HO2 --> HO

 { 30} HO2 + NO --> NO2 + HO

 { 31} HO2 + NO2 --> HNO4

 { 32} HNO4 --> HO2 + NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + HO --> HO2

 { 36} NO + HO --> HONO

 { 37} NO + NO + [O2] --> 2.000*NO2

 { 38} O3 + NO2 --> NO3

 { 39} NO3 + NO --> 2.000*NO2

 { 40} NO3 + NO2 --> NO + NO2

 { 41} NO3 + HO2 --> HNO3

 { 42} NO3 + NO2 --> N2O5

 { 43} N2O5 --> NO2 + NO3

 { 44} N2O5 + [H2O] --> 2.000*HNO3

 { 45} HO + NO2 --> HNO3

 { 46} HO + HNO3 --> NO3

 { 47} HO + HNO4 --> NO2

 { 48} HO + HO2 -->

 { 49} HO + SO2 --> SULF + HO2

 { 50} CO + HO --> HO2

 { 51} HO --> MO2

 { 52} ETH + HO --> ETHP

 { 53} HC3 + HO --> 0.830*HC3P + 0.170*HO2 + 0.009*HCHO

 + 0.075*ALD + 0.025*KET

 { 54} HC5 + HO --> HC5P + 0.250*XO2

 { 55} HC8 + HO --> HC8P + 0.750*XO2

 { 56} OL2 + HO --> OL2P

 { 57} OLT + HO --> OLTP

 { 58} OLI + HO --> OLIP

 { 59} TOL + HO --> 0.750*TOLP + 0.250*CSL + 0.250*HO2

 { 60} XYL + HO --> 0.830*XYLP + 0.170*CSL + 0.170*HO2

 { 61} CSL + HO --> 0.100*HO2 + 0.900*XO2 + 0.900*TCO3

 { 62} CSL + HO --> CSL

 { 63} HCHO + HO --> HO2 + CO

 { 64} ALD + HO --> ACO3

 { 65} KET + HO --> KETP

 { 66} GLY + HO --> HO2 + 2.000*CO

 { 67} MGLY + HO --> ACO3 + CO

 { 68} DCB + HO --> TCO3

 { 69} OP1 + HO --> 0.500*MO2 + 0.500*HCHO + 0.500*HO

 { 70} OP2 + HO --> 0.500*HC3P + 0.500*ALD + 0.500*HO
EPA/600/R-99/030

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms

8-74

 { 71} PAA + HO --> ACO3

 { 72} PAN + HO --> HCHO + NO3 + XO2

 { 73} ONIT + HO --> HC3P + NO2

 { 74} ACO3 + NO2 --> PAN

 { 75} PAN --> ACO3 + NO2

 { 76} TCO3 + NO2 --> TPAN

 { 77} TPAN --> TCO3 + NO2

 { 78} MO2 + NO --> HCHO + HO2 + NO2

 { 79} HC3P + NO --> 0.750*ALD + 0.250*KET + 0.090*HCHO

 + 0.036*ONIT + 0.964*NO2 + 0.964*HO2

 { 80} HC5P + NO --> 0.380*ALD + 0.690*KET + 0.080*ONIT

 + 0.920*NO2 + 0.920*HO2

 { 81} HC8P + NO --> 0.350*ALD + 1.060*KET + 0.040*HCHO

 + 0.240*ONIT + 0.760*NO2 + 0.760*HO2

 { 82} OL2P + NO --> 1.600*HCHO + HO2 + NO2

 + 0.200*ALD

 { 83} OLTP + NO --> ALD + HCHO + HO2

 + NO2

 { 84} OLIP + NO --> HO2 + 1.450*ALD + 0.280*HCHO

 + 0.100*KET + NO2

 { 85} ACO3 + NO --> MO2 + NO2

 { 86} TCO3 + NO --> NO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 { 87} TOLP + NO --> NO2 + HO2 + 0.170*MGLY

 + 0.160*GLY + 0.700*DCB

 { 88} XYLP + NO --> NO2 + HO2 + 0.450*MGLY

 + 0.806*DCB

 { 89} ETHP + NO --> ALD + HO2 + NO2

 { 90} KETP + NO --> MGLY + NO2 + HO2

 { 91} OLN + NO --> HCHO + ALD + 2.000*NO2

 { 92} HCHO + NO3 --> HO2 + HNO3 + CO

 { 93} ALD + NO3 --> ACO3 + HNO3

 { 94} GLY + NO3 --> HNO3 + HO2 + 2.000*CO

 { 95} MGLY + NO3 --> HNO3 + ACO3 + CO

 { 96} DCB + NO3 --> HNO3 + TCO3

 { 97} CSL + NO3 --> HNO3 + XNO2 + 0.500*CSL

 { 98} OL2 + NO3 --> OLN

 { 99} OLT + NO3 --> OLN

 {100} OLI + NO3 --> OLN

 {101} OL2 + O3 --> HCHO + 0.400*ORA1 + 0.420*CO

 + 0.120*HO2

 {102} OLT + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {103} OLI + O3 --> 0.180*HCHO + 0.720*ALD + 0.100*KET

 + 0.230*CO + 0.060*ORA1 + 0.290*ORA2

 + 0.260*HO2 + 0.140*HO + 0.310*MO2

 {104} HO2 + MO2 --> OP1

 {105} HO2 + ETHP --> OP2

 {106} HO2 + HC3P --> OP2

 {107} HO2 + HC5P --> OP2

 {108} HO2 + HC8P --> OP2

 {109} HO2 + OL2P --> OP2

 {110} HO2 + OLTP --> OP2

 {111} HO2 + OLIP --> OP2

 {112} HO2 + KETP --> OP2

 {113} HO2 + ACO3 --> PAA

 {114} HO2 + TOLP --> OP2

 {115} HO2 + XYLP --> OP2

 {116} HO2 + TCO3 --> OP2

 {117} HO2 + OLN --> ONIT

 {118} MO2 + MO2 --> 1.500*HCHO + HO2

 {119} MO2 + ETHP --> 0.750*HCHO + HO2 + 0.750*ALD

 {120} MO2 + HC3P --> 0.840*HCHO + 0.770*ALD + 0.260*KET

 + HO2

 {121} MO2 + HC5P --> 0.770*HCHO + 0.410*ALD + 0.750*KET

 + HO2

 {122} MO2 + HC8P --> 0.800*HCHO + 0.460*ALD + 1.390*KET

 + HO2

 {123} MO2 + OL2P --> 1.550*HCHO + 0.350*ALD + HO2

 {124} MO2 + OLTP --> 1.250*HCHO + 0.750*ALD + HO2

 {125} MO2 + OLIP --> 0.890*HCHO + 0.725*ALD + HO2

 + 0.550*KET
EPA/600/R-99/030

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms

8-75

 {126} MO2 + KETP --> 0.750*HCHO + 0.750*MGLY + HO2

 {127} MO2 + ACO3 --> HCHO + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {128} MO2 + TOLP --> HCHO + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + 2.000*HO2

 {129} MO2 + XYLP --> HCHO + 0.450*MGLY + 0.806*DCB

 + 2.000*HO2

 {130} MO2 + TCO3 --> 0.500*HCHO + 0.445*GLY + 0.055*MGLY

 + 0.500*ORA2 + 0.025*ACO3 + 0.460*HO2

 + 0.475*CO + XO2

 {131} MO2 + OLN --> 1.750*HCHO + 0.500*HO2 + ALD

 + NO2

 {132} ETHP + ACO3 --> ALD + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {133} HC3P + ACO3 --> 0.770*ALD + 0.260*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {134} HC5P + ACO3 --> 0.410*ALD + 0.750*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {135} HC8P + ACO3 --> 0.460*ALD + 1.390*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {136} OL2P + ACO3 --> 0.800*HCHO + 0.600*ALD + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {137} OLTP + ACO3 --> ALD + 0.500*HCHO + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {138} OLIP + ACO3 --> 0.725*ALD + 0.550*KET + 0.140*HCHO

 + 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 {139} KETP + ACO3 --> MGLY + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {140} ACO3 + ACO3 --> 2.000*MO2

 {141} ACO3 + TOLP --> MO2 + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + HO2

 {142} ACO3 + XYLP --> MO2 + 0.450*MGLY + 0.806*DCB

 + HO2

 {143} ACO3 + TCO3 --> MO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 {144} ACO3 + OLN --> HCHO + ALD + 0.500*ORA2

 + NO2 + 0.500*MO2

 {145} OLN + OLN --> 2.000*HCHO + 2.000*ALD + 2.000*NO2

 {146} XO2 + HO2 --> OP2

 {147} XO2 + MO2 --> HCHO + HO2

 {148} XO2 + ACO3 --> MO2

 {149} XO2 + XO2 -->

 {150} XO2 + NO --> NO2

 {151} XNO2 + NO2 --> ONIT

 {152} XNO2 + HO2 --> OP2

 {153} XNO2 + MO2 --> HCHO + HO2

 {154} XNO2 + ACO3 --> MO2

 {155} XNO2 + XNO2 -->

 {156} ISO + HO --> ISO_RO2 + 0.079*XO2

 {157} ISO_RO2 + NO --> 0.088*ONIT + 0.912*NO2 + 0.912*HO2

 + 0.362*ISOPROD + 0.230*MACR + 0.320*MVK

 + 0.629*HCHO + 0.079*XO2

 {158} ISO_RO2 + HO2 --> OP2

 {159} ISO_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.362*ISOPROD + 0.230*MACR + 0.320*MVK

 + 0.629*HCHO

 {160} ISO_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.362*ISOPROD

 + 0.230*MACR + 0.320*MVK + 0.629*HCHO

 {161} ISO + O3 --> 0.600*HCHO + 0.390*MACR + 0.160*MVK

 + 0.390*ORA1 + 0.270*HO + 0.070*HO2

 + 0.070*CO + 0.200*XO2 + 0.200*MCO3

 + 0.150*ALD + 0.100*ISOPROD

 {162} ISO + O3P --> 0.750*ISOPROD + 0.250*MCO3 + 0.250*HCHO

 + 0.250*MO2

 {163} ISO + NO3 --> ISON_RO2

 {164} ISON_RO2 + NO --> NO2 + 0.800*ALD + 0.800*ONIT

 + 0.800*HO2 + 0.200*ISOPROD + 0.200*NO2

 {165} ISON_RO2 + HO2 --> ONIT

 {166} ISON_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + ALD + ONIT

 {167} ISON_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.500*ALD

 + 0.500*ONIT

 {168} MACR + HO --> 0.500*MCO3 + 0.500*MACR_RO2
EPA/600/R-99/030

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms

8-76

 {169} MACR_RO2 + NO --> NO2 + HO2 + 0.840*KET

 + 0.840*CO + 0.150*HCHO + 0.150*MGLY

 {170} MACR_RO2 + HO2 --> OP2

 {171} MACR_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.840*KET + 0.840*CO + 0.150*HCHO

 + 0.150*MGLY

 {172} MACR_RO2 + MO2 --> 0.650*HCHO + 0.500*HO2 + 0.840*KET

 + 0.840*CO + 0.150*MGLY

 {173} MACR + O3 --> 0.630*ORA1 + 0.210*HO + 0.110*HO2

 + 0.110*CO + 0.200*HCHO + 0.100*XO2

 + 0.100*ACO3

 {174} MACR + hv --> 0.660*HO2 + 0.330*MCO3 + 0.670*CO

 + 0.670*HCHO + 0.670*ACO3 + 0.340*HO

 + 0.340*XO2

 {175} MACR + NO3 --> 0.500*MCO3 + 0.500*HNO3 + 0.500*CO

 + 0.500*HO2 + 0.500*ONIT + 0.500*XO2

 {176} MVK + HO --> MVK_RO2

 {177} MVK_RO2 + NO --> NO2 + 0.700*ALD + 0.700*XO2

 + 0.700*ACO3 + 0.300*HCHO + 0.300*MGLY

 + 0.300*HO2

 {178} MVK_RO2 + HO2 --> OP2

 {179} MVK_RO2 + ACO3 --> 0.500*HO2 + 1.200*MO2 + 0.500*ORA2

 + 0.700*ALD + 0.300*HCHO + 0.300*MGLY

 {180} MVK_RO2 + MO2 --> 0.800*HCHO + 0.500*HO2 + 0.700*ALD

 + 0.700*MO2 + 0.300*MGLY

 {181} MVK + O3 --> 0.670*ORA1 + 0.160*HO + 0.110*HO2

 + 0.110*CO + 0.950*MGLY + 0.100*HCHO

 + 0.050*XO2 + 0.050*ACO3

 {182} MVK + hv --> 0.700*ISOPROD + 0.700*CO + 0.300*MO2

 + 0.300*MCO3

 {183} MPAN --> MCO3 + NO2

 {184} MCO3 + NO --> NO2 + HCHO + ACO3

 {185} MCO3 + NO2 --> MPAN

 {186} MCO3 + HO2 --> PAA

 {187} MCO3 + MO2 --> 2.250*HCHO + 0.500*HO2 + 0.500*MO2

 {188} MCO3 + ACO3 --> 2.000*MO2 + HCHO

 {189} MCO3 + MCO3 --> 2.000*MO2 + 2.000*HCHO

 {190} ISOPROD + HO --> 0.313*ACO3 + 0.687*IP_RO2

 {191} IP_RO2 + NO --> NO2 + HO2 + 0.610*CO

 + 0.270*ALD + 0.030*HCHO + 0.180*GLY

 + 0.210*MGLY + 0.700*KET

 {192} IP_RO2 + HO2 --> OP2

 {193} IP_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.500*ALD + 0.500*KET

 {194} IP_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.500*ALD

 + 0.500*KET

 {195} ISOPROD + O3 --> 0.476*HO + 0.072*HO2 + 0.168*MO2

 + 0.237*ACO3 + 0.100*XO2 + 0.243*CO

 + 0.218*HCHO + 0.062*ALD + 0.278*KET

 + 0.031*GLY + 0.653*MGLY + 0.044*ORA1

 {196} ISOPROD + hv --> 1.216*CO + 0.434*ALD + 0.350*HCHO

 + 0.216*KET + 1.216*HO2 + 0.784*ACO3

 {197} ISOPROD + NO3 --> 0.668*CO + 0.332*HCHO + 0.332*ALD

 + ONIT + HO2 + XO2

 >----------------------------------------------------------------------------------------<

 Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) uses photo table O3O1D_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 3) uses photo table O3O3P_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 4) uses photo table HONO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 5) uses photo table HNO3_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 6) uses photo table HNO4_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 7) uses photo table NO3NO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 8) uses photo table NO3NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 9) uses photo table H2O2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) uses photo table HCHOmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 11) uses photo table HCHOrad_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 12) uses photo table ALD_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 13) uses photo table MHP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 14) uses photo table HOP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 15) uses photo table PAA_RADM88 , scaled by 1.00000E+00 {0.00000E+00}
EPA/600/R-99/030

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms

8-77

 k( 16) uses photo table KETONE_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 17) uses photo table GLYform_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 18) uses photo table GLYmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 19) uses photo table MGLY_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 20) uses photo table UDC_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 21) uses photo table ORGNIT_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 22) = 6.0000E-34 * (T/300)**(-2.30) {6.09302E-34}

 k( 23) = 6.5000E-12 * exp( 120.0/T) {9.72293E-12}

 k( 24) = 1.8000E-11 * exp( 110.0/T) {2.60365E-11}

 k( 25) = 3.2000E-11 * exp( 70.0/T) {4.04730E-11}

 k( 26) = 2.2000E-10 {2.20000E-10}

 k( 27) = 2.0000E-12 * exp( -1400.0/T) {1.82272E-14}

 k( 28) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 29) = 1.1000E-14 * exp( -500.0/T) {2.05452E-15}

 k( 30) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 31) is a falloff expression using: {1.39058E-12}

 k0 = 1.8000E-31 * (T/300)**(-3.20)

 kinf = 4.7000E-12 * (T/300)**(-1.40)

 F = 0.60, n = 1.00

 k( 32) = k( 31) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {8.62399E-02}

 k( 33) is a special rate expression of the form: {3.01634E-12}

 k = k1 + k2[M], where

 k1 = 2.2000E-13 * exp( 620.0/T)

 k2 = 1.9000E-33 * exp( 980.0/T)

 k( 34) is a special rate expression of the form: {6.78905E-30}

 k = k1 + k2[M], where

 k1 = 3.0800E-34 * exp( 2820.0/T)

 k2 = 2.6600E-54 * exp( 3180.0/T)

 k( 35) = 3.3000E-12 * exp( -200.0/T) {1.68671E-12}

 k( 36) is a falloff expression using: {4.87144E-12}

 k0 = 7.0000E-31 * (T/300)**(-2.60)

 kinf = 1.5000E-11 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 37) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 38) = 1.4000E-13 * exp( -2500.0/T) {3.18213E-17}

 k( 39) = 1.7000E-11 * exp( 150.0/T) {2.81225E-11}

 k( 40) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 41) = 2.5000E-12 {2.50000E-12}

 k( 42) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 43) = k( 42) / Keq, where Keq = 1.100E-27 * exp( 11200.0/T) {5.47034E-02}

 k( 44) = 2.0000E-21 {2.00000E-21}

 k( 45) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 46) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 47) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 48) = 4.6000E-11 * exp( 230.0/T) {9.95294E-11}

 k( 49) is a falloff expression using: {8.88848E-13}

 k0 = 3.0000E-31 * (T/300)**(-3.30)

 kinf = 1.5000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 50) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 51) = 2.8300E+01 * (T/300)**( 2.00) * exp( -1280.0/T) {3.80672E-01}

 k( 52) = 1.2330E-12 * (T/300)**( 2.00) * exp( -444.0/T) {2.74210E-13}

 k( 53) = 1.5900E-11 * exp( -540.0/T) {2.59669E-12}

 k( 54) = 1.7300E-11 * exp( -380.0/T) {4.83334E-12}

 k( 55) = 3.6400E-11 * exp( -380.0/T) {1.01696E-11}

 k( 56) = 2.1500E-12 * exp( 411.0/T) {8.53916E-12}

 k( 57) = 5.3200E-12 * exp( 504.0/T) {2.88684E-11}

 k( 58) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 59) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 60) = 1.8900E-11 * exp( 116.0/T) {2.78943E-11}

 k( 61) = 4.0000E-11 {4.00000E-11}

 k( 62) = 9.0000E-01 * k( 61) {3.60000E-11}

 k( 63) = 9.0000E-12 {9.00000E-12}

 k( 64) = 6.8700E-12 * exp( 256.0/T) {1.62197E-11}
EPA/600/R-99/030

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms

8-78

 k( 65) = 1.2000E-11 * exp( -745.0/T) {9.85020E-13}

 k( 66) = 1.1500E-11 {1.15000E-11}

 k( 67) = 1.7000E-11 {1.70000E-11}

 k( 68) = 2.8000E-11 {2.80000E-11}

 k( 69) = 1.0000E-11 {1.00000E-11}

 k( 70) = 1.0000E-11 {1.00000E-11}

 k( 71) = 1.0000E-11 {1.00000E-11}

 k( 72) = 6.1650E-13 * (T/300)**( 2.00) * exp( -444.0/T) {1.37105E-13}

 k( 73) = 1.5500E-11 * exp( -540.0/T) {2.53137E-12}

 k( 74) = 2.8000E-12 * exp( 181.0/T) {5.13974E-12}

 k( 75) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 76) = 4.7000E-12 {4.70000E-12}

 k( 77) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 78) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 79) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 80) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 81) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 82) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 83) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 84) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 85) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 86) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 87) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 88) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 89) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 90) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 91) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 92) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 93) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 94) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 95) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 96) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 97) = 2.2000E-11 {2.20000E-11}

 k( 98) = 2.0000E-12 * exp( -2923.0/T) {1.09940E-16}

 k( 99) = 1.0000E-11 * exp( -1895.0/T) {1.73099E-14}

 k(100) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k(101) = 1.2000E-14 * exp( -2633.0/T) {1.74559E-18}

 k(102) = 1.3200E-14 * exp( -2105.0/T) {1.12933E-17}

 k(103) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 k(104) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(105) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(106) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(107) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(108) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(109) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(110) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(111) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(112) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(113) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(114) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(115) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(116) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(117) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(118) = 1.9000E-13 * exp( 220.0/T) {3.97533E-13}

 k(119) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(120) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(121) = 3.4000E-14 * exp( 220.0/T) {7.11376E-14}

 k(122) = 2.9000E-14 * exp( 220.0/T) {6.06762E-14}

 k(123) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(124) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(125) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(126) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(127) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(128) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(129) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(130) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(131) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(132) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(133) = 1.0000E-13 * exp( 220.0/T) {2.09228E-13}

 k(134) = 8.4000E-14 * exp( 220.0/T) {1.75752E-13}

 k(135) = 7.2000E-14 * exp( 220.0/T) {1.50644E-13}

 k(136) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(137) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(138) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}
EPA/600/R-99/030

Table 8A-11. RADM2_CIS4 and RADM2_CIS4_AQ Mechanisms

8-79

 k(139) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(140) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(141) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(142) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(143) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(144) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(145) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(146) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(147) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(148) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(149) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(150) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(151) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(152) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(153) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(154) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(155) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(156) = 2.5400E-11 * (T/300)**( 1.00) * exp( 407.6/T) {9.90719E-11}

 k(157) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(158) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(159) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(160) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(161) = 7.8600E-15 * (T/300)**( 1.00) * exp( -1912.2/T) {1.27569E-17}

 k(162) = 3.6000E-11 {3.60000E-11}

 k(163) = 3.0300E-12 * (T/300)**( 1.00) * exp( -447.9/T) {6.69552E-13}

 k(164) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(165) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(166) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(167) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(168) = 1.8600E-11 * (T/300)**( 1.00) * exp( 176.1/T) {3.33618E-11}

 k(169) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(170) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(171) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(172) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(173) = 1.3600E-15 * (T/300)**( 1.00) * exp( -2113.5/T) {1.12330E-18}

 k(174) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k(175) = 1.5000E-12 * (T/300)**( 1.00) * exp( -1726.0/T) {4.54753E-15}

 k(176) = 4.1400E-12 * (T/300)**( 1.00) * exp( 452.9/T) {1.87990E-11}

 k(177) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(178) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(179) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(180) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(181) = 7.5100E-16 * (T/300)**( 1.00) * exp( -1519.7/T) {4.54966E-18}

 k(182) uses photo table ACROLEIN , scaled by 1.11000E-02 {0.00000E+00}

 k(183) = 1.6000E+16 * (T/300)**( 1.00) * exp(-13486.0/T) {3.52536E-04}

 k(184) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(185) = 2.8000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {5.10890E-12}

 k(186) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(187) = 9.6000E-13 * (T/300)**( 1.00) * exp( 221.4/T) {2.00460E-12}

 k(188) = 1.1900E-12 * (T/300)**( 1.00) * exp( 221.4/T) {2.48486E-12}

 k(189) = 1.1900E-12 * (T/300)**( 1.00) * exp( 221.4/T) {2.48486E-12}

 k(190) = 3.3600E-11 {3.36000E-11}

 k(191) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(192) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(193) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(194) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(195) = 7.1100E-18 {7.11000E-18}

 k(196) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k(197) = 1.0000E-13 {1.00000E-13}

 ===============================================================================
EPA/600/R-99/030

8-80

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms

 Reaction List

 >----------------------------------------------------------------------------------------<

 { 1} NO2 + hv --> O3P + NO

 { 2} O3 + hv --> O1D

 { 3} O3 + hv --> O3P

 { 4} HONO + hv --> HO + NO

 { 5} HNO3 + hv --> HO + NO2

 { 6} HNO4 + hv --> HO2 + NO2

 { 7} NO3 + hv --> NO

 { 8} NO3 + hv --> NO2 + O3P

 { 9} H2O2 + hv --> 2.000*HO

 { 10} HCHO + hv --> CO

 { 11} HCHO + hv --> HO2 + HO2 + CO

 { 12} ALD + hv --> MO2 + HO2 + CO

 { 13} OP1 + hv --> HCHO + HO2 + HO

 { 14} OP2 + hv --> ALD + HO2 + HO

 { 15} PAA + hv --> MO2 + HO

 { 16} KET + hv --> ACO3 + ETHP

 { 17} GLY + hv --> 0.130*HCHO + 1.870*CO

 { 18} GLY + hv --> 0.450*HCHO + 1.550*CO + 0.800*HO2

 { 19} MGLY + hv --> ACO3 + HO2 + CO

 { 20} DCB + hv --> 0.980*HO2 + 0.020*ACO3 + TCO3

 { 21} ONIT + hv --> 0.200*ALD + 0.800*KET + HO2

 + NO2

 { 22} O3P + [M] + [O2] --> O3

 { 23} O3P + NO2 --> NO

 { 24} O1D + [N2] --> O3P

 { 25} O1D + [O2] --> O3P

 { 26} O1D + [H2O] --> 2.000*HO

 { 27} O3 + NO --> NO2

 { 28} O3 + HO --> HO2

 { 29} O3 + HO2 --> HO

 { 30} HO2 + NO --> NO2 + HO

 { 31} HO2 + NO2 --> HNO4

 { 32} HNO4 --> HO2 + NO2

 { 33} HO2 + HO2 --> H2O2

 { 34} HO2 + HO2 + [H2O] --> H2O2

 { 35} H2O2 + HO --> HO2

 { 36} NO + HO --> HONO

 { 37} NO + NO + [O2] --> 2.000*NO2

 { 38} O3 + NO2 --> NO3

 { 39} NO3 + NO --> 2.000*NO2

 { 40} NO3 + NO2 --> NO + NO2

 { 41} NO3 + HO2 --> HNO3

 { 42} NO3 + NO2 --> N2O5

 { 43} N2O5 --> NO2 + NO3

 { 44} N2O5 + [H2O] --> 2.000*HNO3

 { 45} HO + NO2 --> HNO3

 { 46} HO + HNO3 --> NO3

 { 47} HO + HNO4 --> NO2

 { 48} HO + HO2 -->

 { 49} HO + SO2 --> SULF + HO2 + SULAER

 { 50} CO + HO --> HO2

 { 51} HO --> MO2

 { 52} ETH + HO --> ETHP

 { 53} HC3 + HO --> 0.830*HC3P + 0.170*HO2 + 0.009*HCHO

 + 0.075*ALD + 0.025*KET

 { 54} HC5 + HO --> HC5P + 0.250*XO2

 { 55} HC8 + HO --> HC8P + 0.750*XO2 + HC8AER

 { 56} OL2 + HO --> OL2P

 { 57} OLT + HO --> OLTP

 { 58} OLI + HO --> OLIP + OLIAER

 { 59} TOL + HO --> 0.750*TOLP + 0.250*CSL + 0.250*HO2

 + TOLAER

 { 60} XYL + HO --> 0.830*XYLP + 0.170*CSL + 0.170*HO2

 + XYLAER

 { 61} CSL + HO --> 0.100*HO2 + 0.900*XO2 + 0.900*TCO3

 + CSLAER

 { 62} CSL + HO --> CSL

 { 63} HCHO + HO --> HO2 + CO

 { 64} ALD + HO --> ACO3

 { 65} KET + HO --> KETP

 { 66} GLY + HO --> HO2 + 2.000*CO

 { 67} MGLY + HO --> ACO3 + CO
EPA/600/R-99/030

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms

8-81

 { 68} DCB + HO --> TCO3

 { 69} OP1 + HO --> 0.500*MO2 + 0.500*HCHO + 0.500*HO

 { 70} OP2 + HO --> 0.500*HC3P + 0.500*ALD + 0.500*HO

 { 71} PAA + HO --> ACO3

 { 72} PAN + HO --> HCHO + NO3 + XO2

 { 73} ONIT + HO --> HC3P + NO2

 { 74} ACO3 + NO2 --> PAN

 { 75} PAN --> ACO3 + NO2

 { 76} TCO3 + NO2 --> TPAN

 { 77} TPAN --> TCO3 + NO2

 { 78} MO2 + NO --> HCHO + HO2 + NO2

 { 79} HC3P + NO --> 0.750*ALD + 0.250*KET + 0.090*HCHO

 + 0.036*ONIT + 0.964*NO2 + 0.964*HO2

 { 80} HC5P + NO --> 0.380*ALD + 0.690*KET + 0.080*ONIT

 + 0.920*NO2 + 0.920*HO2

 { 81} HC8P + NO --> 0.350*ALD + 1.060*KET + 0.040*HCHO

 + 0.240*ONIT + 0.760*NO2 + 0.760*HO2

 { 82} OL2P + NO --> 1.600*HCHO + HO2 + NO2

 + 0.200*ALD

 { 83} OLTP + NO --> ALD + HCHO + HO2

 + NO2

 { 84} OLIP + NO --> HO2 + 1.450*ALD + 0.280*HCHO

 + 0.100*KET + NO2

 { 85} ACO3 + NO --> MO2 + NO2

 { 86} TCO3 + NO --> NO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 { 87} TOLP + NO --> NO2 + HO2 + 0.170*MGLY

 + 0.160*GLY + 0.700*DCB

 { 88} XYLP + NO --> NO2 + HO2 + 0.450*MGLY

 + 0.806*DCB

 { 89} ETHP + NO --> ALD + HO2 + NO2

 { 90} KETP + NO --> MGLY + NO2 + HO2

 { 91} OLN + NO --> HCHO + ALD + 2.000*NO2

 { 92} HCHO + NO3 --> HO2 + HNO3 + CO

 { 93} ALD + NO3 --> ACO3 + HNO3

 { 94} GLY + NO3 --> HNO3 + HO2 + 2.000*CO

 { 95} MGLY + NO3 --> HNO3 + ACO3 + CO

 { 96} DCB + NO3 --> HNO3 + TCO3

 { 97} CSL + NO3 --> HNO3 + XNO2 + 0.500*CSL

 + 0.500*CSLAER

 { 98} OL2 + NO3 --> OLN

 { 99} OLT + NO3 --> OLN

 {100} OLI + NO3 --> OLN + OLIAER

 {101} OL2 + O3 --> HCHO + 0.400*ORA1 + 0.420*CO

 + 0.120*HO2

 {102} OLT + O3 --> 0.530*HCHO + 0.500*ALD + 0.330*CO

 + 0.200*ORA1 + 0.200*ORA2 + 0.230*HO2

 + 0.220*MO2 + 0.100*HO

 {103} OLI + O3 --> 0.180*HCHO + 0.720*ALD + 0.100*KET

 + 0.230*CO + 0.060*ORA1 + 0.290*ORA2

 + 0.260*HO2 + 0.140*HO + 0.310*MO2

 + OLIAER

 {104} HO2 + MO2 --> OP1

 {105} HO2 + ETHP --> OP2

 {106} HO2 + HC3P --> OP2

 {107} HO2 + HC5P --> OP2

 {108} HO2 + HC8P --> OP2

 {109} HO2 + OL2P --> OP2

 {110} HO2 + OLTP --> OP2

 {111} HO2 + OLIP --> OP2

 {112} HO2 + KETP --> OP2

 {113} HO2 + ACO3 --> PAA

 {114} HO2 + TOLP --> OP2

 {115} HO2 + XYLP --> OP2

 {116} HO2 + TCO3 --> OP2

 {117} HO2 + OLN --> ONIT

 {118} MO2 + MO2 --> 1.500*HCHO + HO2

 {119} MO2 + ETHP --> 0.750*HCHO + HO2 + 0.750*ALD

 {120} MO2 + HC3P --> 0.840*HCHO + 0.770*ALD + 0.260*KET

 + HO2

 {121} MO2 + HC5P --> 0.770*HCHO + 0.410*ALD + 0.750*KET

 + HO2

 {122} MO2 + HC8P --> 0.800*HCHO + 0.460*ALD + 1.390*KET
EPA/600/R-99/030

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms

8-82

 + HO2

 {123} MO2 + OL2P --> 1.550*HCHO + 0.350*ALD + HO2

 {124} MO2 + OLTP --> 1.250*HCHO + 0.750*ALD + HO2

 {125} MO2 + OLIP --> 0.890*HCHO + 0.725*ALD + HO2

 + 0.550*KET

 {126} MO2 + KETP --> 0.750*HCHO + 0.750*MGLY + HO2

 {127} MO2 + ACO3 --> HCHO + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {128} MO2 + TOLP --> HCHO + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + 2.000*HO2

 {129} MO2 + XYLP --> HCHO + 0.450*MGLY + 0.806*DCB

 + 2.000*HO2

 {130} MO2 + TCO3 --> 0.500*HCHO + 0.445*GLY + 0.055*MGLY

 + 0.500*ORA2 + 0.025*ACO3 + 0.460*HO2

 + 0.475*CO + XO2

 {131} MO2 + OLN --> 1.750*HCHO + 0.500*HO2 + ALD

 + NO2

 {132} ETHP + ACO3 --> ALD + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {133} HC3P + ACO3 --> 0.770*ALD + 0.260*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {134} HC5P + ACO3 --> 0.410*ALD + 0.750*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {135} HC8P + ACO3 --> 0.460*ALD + 1.390*KET + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {136} OL2P + ACO3 --> 0.800*HCHO + 0.600*ALD + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {137} OLTP + ACO3 --> ALD + 0.500*HCHO + 0.500*HO2

 + 0.500*MO2 + 0.500*ORA2

 {138} OLIP + ACO3 --> 0.725*ALD + 0.550*KET + 0.140*HCHO

 + 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 {139} KETP + ACO3 --> MGLY + 0.500*HO2 + 0.500*MO2

 + 0.500*ORA2

 {140} ACO3 + ACO3 --> 2.000*MO2

 {141} ACO3 + TOLP --> MO2 + 0.170*MGLY + 0.160*GLY

 + 0.700*DCB + HO2

 {142} ACO3 + XYLP --> MO2 + 0.450*MGLY + 0.806*DCB

 + HO2

 {143} ACO3 + TCO3 --> MO2 + 0.920*HO2 + 0.890*GLY

 + 0.110*MGLY + 0.050*ACO3 + 0.950*CO

 + 2.000*XO2

 {144} ACO3 + OLN --> HCHO + ALD + 0.500*ORA2

 + NO2 + 0.500*MO2

 {145} OLN + OLN --> 2.000*HCHO + 2.000*ALD + 2.000*NO2

 {146} XO2 + HO2 --> OP2

 {147} XO2 + MO2 --> HCHO + HO2

 {148} XO2 + ACO3 --> MO2

 {149} XO2 + XO2 -->

 {150} XO2 + NO --> NO2

 {151} XNO2 + NO2 --> ONIT

 {152} XNO2 + HO2 --> OP2

 {153} XNO2 + MO2 --> HCHO + HO2

 {154} XNO2 + ACO3 --> MO2

 {155} XNO2 + XNO2 -->

 {156} TERP + HO --> TERPAER + HO

 {157} TERP + NO3 --> TERPAER + NO3

 {158} TERP + O3 --> TERPAER + O3

 {159} ISO + HO --> ISO_RO2 + 0.079*XO2

 {160} ISO_RO2 + NO --> 0.088*ONIT + 0.912*NO2 + 0.912*HO2

 + 0.362*ISOPROD + 0.230*MACR + 0.320*MVK

 + 0.629*HCHO + 0.079*XO2

 {161} ISO_RO2 + HO2 --> OP2

 {162} ISO_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.362*ISOPROD + 0.230*MACR + 0.320*MVK

 + 0.629*HCHO

 {163} ISO_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.362*ISOPROD

 + 0.230*MACR + 0.320*MVK + 0.629*HCHO

 {164} ISO + O3 --> 0.600*HCHO + 0.390*MACR + 0.160*MVK

 + 0.390*ORA1 + 0.270*HO + 0.070*HO2

 + 0.070*CO + 0.200*XO2 + 0.200*MCO3

 + 0.150*ALD + 0.100*ISOPROD

 {165} ISO + O3P --> 0.750*ISOPROD + 0.250*MCO3 + 0.250*HCHO

 + 0.250*MO2

 {166} ISO + NO3 --> ISON_RO2
EPA/600/R-99/030

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms

8-83

 {167} ISON_RO2 + NO --> NO2 + 0.800*ALD + 0.800*ONIT

 + 0.800*HO2 + 0.200*ISOPROD + 0.200*NO2

 {168} ISON_RO2 + HO2 --> ONIT

 {169} ISON_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + ALD + ONIT

 {170} ISON_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.500*ALD

 + 0.500*ONIT

 {171} MACR + HO --> 0.500*MCO3 + 0.500*MACR_RO2

 {172} MACR_RO2 + NO --> NO2 + HO2 + 0.840*KET

 + 0.840*CO + 0.150*HCHO + 0.150*MGLY

 {173} MACR_RO2 + HO2 --> OP2

 {174} MACR_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.840*KET + 0.840*CO + 0.150*HCHO

 + 0.150*MGLY

 {175} MACR_RO2 + MO2 --> 0.650*HCHO + 0.500*HO2 + 0.840*KET

 + 0.840*CO + 0.150*MGLY

 {176} MACR + O3 --> 0.630*ORA1 + 0.210*HO + 0.110*HO2

 + 0.110*CO + 0.200*HCHO + 0.100*XO2

 + 0.100*ACO3

 {177} MACR + hv --> 0.660*HO2 + 0.330*MCO3 + 0.670*CO

 + 0.670*HCHO + 0.670*ACO3 + 0.340*HO

 + 0.340*XO2

 {178} MACR + NO3 --> 0.500*MCO3 + 0.500*HNO3 + 0.500*CO

 + 0.500*HO2 + 0.500*ONIT + 0.500*XO2

 {179} MVK + HO --> MVK_RO2

 {180} MVK_RO2 + NO --> NO2 + 0.700*ALD + 0.700*XO2

 + 0.700*ACO3 + 0.300*HCHO + 0.300*MGLY

 + 0.300*HO2

 {181} MVK_RO2 + HO2 --> OP2

 {182} MVK_RO2 + ACO3 --> 0.500*HO2 + 1.200*MO2 + 0.500*ORA2

 + 0.700*ALD + 0.300*HCHO + 0.300*MGLY

 {183} MVK_RO2 + MO2 --> 0.800*HCHO + 0.500*HO2 + 0.700*ALD

 + 0.700*MO2 + 0.300*MGLY

 {184} MVK + O3 --> 0.670*ORA1 + 0.160*HO + 0.110*HO2

 + 0.110*CO + 0.950*MGLY + 0.100*HCHO

 + 0.050*XO2 + 0.050*ACO3

 {185} MVK + hv --> 0.700*ISOPROD + 0.700*CO + 0.300*MO2

 + 0.300*MCO3

 {186} MPAN --> MCO3 + NO2

 {187} MCO3 + NO --> NO2 + HCHO + ACO3

 {188} MCO3 + NO2 --> MPAN

 {189} MCO3 + HO2 --> PAA

 {190} MCO3 + MO2 --> 2.250*HCHO + 0.500*HO2 + 0.500*MO2

 {191} MCO3 + ACO3 --> 2.000*MO2 + HCHO

 {192} MCO3 + MCO3 --> 2.000*MO2 + 2.000*HCHO

 {193} ISOPROD + HO --> 0.313*ACO3 + 0.687*IP_RO2

 {194} IP_RO2 + NO --> NO2 + HO2 + 0.610*CO

 + 0.270*ALD + 0.030*HCHO + 0.180*GLY

 + 0.210*MGLY + 0.700*KET

 {195} IP_RO2 + HO2 --> OP2

 {196} IP_RO2 + ACO3 --> 0.500*HO2 + 0.500*MO2 + 0.500*ORA2

 + 0.500*ALD + 0.500*KET

 {197} IP_RO2 + MO2 --> 0.500*HCHO + 0.500*HO2 + 0.500*ALD

 + 0.500*KET

 {198} ISOPROD + O3 --> 0.476*HO + 0.072*HO2 + 0.168*MO2

 + 0.237*ACO3 + 0.100*XO2 + 0.243*CO

 + 0.218*HCHO + 0.062*ALD + 0.278*KET

 + 0.031*GLY + 0.653*MGLY + 0.044*ORA1

 {199} ISOPROD + hv --> 1.216*CO + 0.434*ALD + 0.350*HCHO

 + 0.216*KET + 1.216*HO2 + 0.784*ACO3

 {200} ISOPROD + NO3 --> 0.668*CO + 0.332*HCHO + 0.332*ALD

 + ONIT + HO2 + XO2

 >----------------------------------------------------------------------------------------<

 Rate Expression Rate Constant

 ===============================================================================

 k( 1) uses photo table NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 2) uses photo table O3O1D_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 3) uses photo table O3O3P_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 4) uses photo table HONO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 5) uses photo table HNO3_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 6) uses photo table HNO4_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 7) uses photo table NO3NO_RADM88 , scaled by 1.00000E+00 {0.00000E+00}
EPA/600/R-99/030

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms

8-84

 k( 8) uses photo table NO3NO2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 9) uses photo table H2O2_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 10) uses photo table HCHOmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 11) uses photo table HCHOrad_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 12) uses photo table ALD_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 13) uses photo table MHP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 14) uses photo table HOP_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 15) uses photo table PAA_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 16) uses photo table KETONE_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 17) uses photo table GLYform_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 18) uses photo table GLYmol_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 19) uses photo table MGLY_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 20) uses photo table UDC_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 21) uses photo table ORGNIT_RADM88 , scaled by 1.00000E+00 {0.00000E+00}

 k( 22) = 6.0000E-34 * (T/300)**(-2.30) {6.09302E-34}

 k( 23) = 6.5000E-12 * exp( 120.0/T) {9.72293E-12}

 k( 24) = 1.8000E-11 * exp( 110.0/T) {2.60365E-11}

 k( 25) = 3.2000E-11 * exp( 70.0/T) {4.04730E-11}

 k( 26) = 2.2000E-10 {2.20000E-10}

 k( 27) = 2.0000E-12 * exp( -1400.0/T) {1.82272E-14}

 k( 28) = 1.6000E-12 * exp( -940.0/T) {6.82650E-14}

 k( 29) = 1.1000E-14 * exp( -500.0/T) {2.05452E-15}

 k( 30) = 3.7000E-12 * exp( 240.0/T) {8.27883E-12}

 k( 31) is a falloff expression using: {1.39058E-12}

 k0 = 1.8000E-31 * (T/300)**(-3.20)

 kinf = 4.7000E-12 * (T/300)**(-1.40)

 F = 0.60, n = 1.00

 k( 32) = k( 31) / Keq, where Keq = 2.100E-27 * exp( 10900.0/T) {8.62399E-02}

 k( 33) is a special rate expression of the form: {3.01634E-12}

 k = k1 + k2[M], where

 k1 = 2.2000E-13 * exp( 620.0/T)

 k2 = 1.9000E-33 * exp( 980.0/T)

 k( 34) is a special rate expression of the form: {6.78905E-30}

 k = k1 + k2[M], where

 k1 = 3.0800E-34 * exp( 2820.0/T)

 k2 = 2.6600E-54 * exp( 3180.0/T)

 k( 35) = 3.3000E-12 * exp( -200.0/T) {1.68671E-12}

 k( 36) is a falloff expression using: {4.87144E-12}

 k0 = 7.0000E-31 * (T/300)**(-2.60)

 kinf = 1.5000E-11 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 37) = 3.3000E-39 * exp( 530.0/T) {1.95397E-38}

 k( 38) = 1.4000E-13 * exp( -2500.0/T) {3.18213E-17}

 k( 39) = 1.7000E-11 * exp( 150.0/T) {2.81225E-11}

 k( 40) = 2.5000E-14 * exp( -1230.0/T) {4.03072E-16}

 k( 41) = 2.5000E-12 {2.50000E-12}

 k( 42) is a falloff expression using: {1.26440E-12}

 k0 = 2.2000E-30 * (T/300)**(-4.30)

 kinf = 1.5000E-12 * (T/300)**(-0.50)

 F = 0.60, n = 1.00

 k( 43) = k( 42) / Keq, where Keq = 1.100E-27 * exp( 11200.0/T) {5.47034E-02}

 k( 44) = 2.0000E-21 {2.00000E-21}

 k( 45) is a falloff expression using: {1.14885E-11}

 k0 = 2.6000E-30 * (T/300)**(-3.20)

 kinf = 2.4000E-11 * (T/300)**(-1.30)

 F = 0.60, n = 1.00

 k( 46) is a special rate expression of the form: {1.47236E-13}

 k = k0 + {k3[M] / (1 + k3[M]/k2)}, where

 k0 = 7.2000E-15 * exp( 785.0/T)

 k2 = 4.1000E-16 * exp( 1440.0/T)

 k3 = 1.9000E-33 * exp( 725.0/T)

 k( 47) = 1.3000E-12 * exp( 380.0/T) {4.65309E-12}

 k( 48) = 4.6000E-11 * exp( 230.0/T) {9.95294E-11}

 k( 49) is a falloff expression using: {8.88848E-13}

 k0 = 3.0000E-31 * (T/300)**(-3.30)

 kinf = 1.5000E-12 * (T/300)**( 0.00)

 F = 0.60, n = 1.00

 k( 50) = 1.5000E-13 * (1.0 + 0.6*Pressure) {2.40000E-13}

 k( 51) = 2.8300E+01 * (T/300)**( 2.00) * exp( -1280.0/T) {3.80672E-01}

 k( 52) = 1.2330E-12 * (T/300)**( 2.00) * exp( -444.0/T) {2.74210E-13}

 k( 53) = 1.5900E-11 * exp( -540.0/T) {2.59669E-12}

 k( 54) = 1.7300E-11 * exp( -380.0/T) {4.83334E-12}

 k( 55) = 3.6400E-11 * exp( -380.0/T) {1.01696E-11}

 k( 56) = 2.1500E-12 * exp( 411.0/T) {8.53916E-12}
EPA/600/R-99/030

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms

8-85

 k( 57) = 5.3200E-12 * exp( 504.0/T) {2.88684E-11}

 k( 58) = 1.0700E-11 * exp( 549.0/T) {6.75269E-11}

 k( 59) = 2.1000E-12 * exp( 322.0/T) {6.18715E-12}

 k( 60) = 1.8900E-11 * exp( 116.0/T) {2.78943E-11}

 k( 61) = 4.0000E-11 {4.00000E-11}

 k( 62) = 9.0000E-01 * k( 61) {3.60000E-11}

 k( 63) = 9.0000E-12 {9.00000E-12}

 k( 64) = 6.8700E-12 * exp( 256.0/T) {1.62197E-11}

 k( 65) = 1.2000E-11 * exp( -745.0/T) {9.85020E-13}

 k( 66) = 1.1500E-11 {1.15000E-11}

 k( 67) = 1.7000E-11 {1.70000E-11}

 k( 68) = 2.8000E-11 {2.80000E-11}

 k( 69) = 1.0000E-11 {1.00000E-11}

 k( 70) = 1.0000E-11 {1.00000E-11}

 k( 71) = 1.0000E-11 {1.00000E-11}

 k( 72) = 6.1650E-13 * (T/300)**( 2.00) * exp( -444.0/T) {1.37105E-13}

 k( 73) = 1.5500E-11 * exp( -540.0/T) {2.53137E-12}

 k( 74) = 2.8000E-12 * exp( 181.0/T) {5.13974E-12}

 k( 75) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 76) = 4.7000E-12 {4.70000E-12}

 k( 77) = 1.9500E+16 * exp(-13543.0/T) {3.57235E-04}

 k( 78) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 79) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 80) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 81) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 82) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 83) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 84) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 85) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 86) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 87) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 88) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 89) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 90) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 91) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k( 92) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 93) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 94) = 6.0000E-13 * exp( -2058.0/T) {6.01030E-16}

 k( 95) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 96) = 1.4000E-12 * exp( -1900.0/T) {2.38307E-15}

 k( 97) = 2.2000E-11 {2.20000E-11}

 k( 98) = 2.0000E-12 * exp( -2923.0/T) {1.09940E-16}

 k( 99) = 1.0000E-11 * exp( -1895.0/T) {1.73099E-14}

 k(100) = 3.2300E-11 * exp( -975.0/T) {1.22539E-12}

 k(101) = 1.2000E-14 * exp( -2633.0/T) {1.74559E-18}

 k(102) = 1.3200E-14 * exp( -2105.0/T) {1.12933E-17}

 k(103) = 7.2900E-15 * exp( -1136.0/T) {1.61125E-16}

 k(104) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(105) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(106) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(107) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(108) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(109) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(110) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(111) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(112) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(113) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(114) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(115) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(116) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(117) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(118) = 1.9000E-13 * exp( 220.0/T) {3.97533E-13}

 k(119) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(120) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(121) = 3.4000E-14 * exp( 220.0/T) {7.11376E-14}

 k(122) = 2.9000E-14 * exp( 220.0/T) {6.06762E-14}

 k(123) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(124) = 1.4000E-13 * exp( 220.0/T) {2.92919E-13}

 k(125) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(126) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(127) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}

 k(128) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(129) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(130) = 9.6000E-13 * exp( 220.0/T) {2.00859E-12}
EPA/600/R-99/030

Table 8A-12. RADM2_CIS4_AE and RADM2_CIS4_AE_AQ Mechanisms

8-86

 k(131) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(132) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(133) = 1.0000E-13 * exp( 220.0/T) {2.09228E-13}

 k(134) = 8.4000E-14 * exp( 220.0/T) {1.75752E-13}

 k(135) = 7.2000E-14 * exp( 220.0/T) {1.50644E-13}

 k(136) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(137) = 3.4000E-13 * exp( 220.0/T) {7.11376E-13}

 k(138) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(139) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(140) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(141) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(142) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(143) = 1.1900E-12 * exp( 220.0/T) {2.48981E-12}

 k(144) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(145) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(146) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(147) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(148) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(149) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(150) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(151) = 4.2000E-12 * exp( 180.0/T) {7.68378E-12}

 k(152) = 7.7000E-14 * exp( 1300.0/T) {6.04038E-12}

 k(153) = 1.7000E-14 * exp( 220.0/T) {3.55688E-14}

 k(154) = 4.2000E-14 * exp( 220.0/T) {8.78758E-14}

 k(155) = 3.6000E-16 * exp( 220.0/T) {7.53221E-16}

 k(156) = 1.0000E+00 * k( 58) {6.75269E-11}

 k(157) = 1.0000E+00 * k(100) {1.22539E-12}

 k(158) = 1.0000E+00 * k(103) {1.61125E-16}

 k(159) = 2.5400E-11 * (T/300)**( 1.00) * exp( 407.6/T) {9.90719E-11}

 k(160) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(161) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(162) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(163) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(164) = 7.8600E-15 * (T/300)**( 1.00) * exp( -1912.2/T) {1.27569E-17}

 k(165) = 3.6000E-11 {3.60000E-11}

 k(166) = 3.0300E-12 * (T/300)**( 1.00) * exp( -447.9/T) {6.69552E-13}

 k(167) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(168) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(169) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(170) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(171) = 1.8600E-11 * (T/300)**( 1.00) * exp( 176.1/T) {3.33618E-11}

 k(172) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(173) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(174) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(175) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(176) = 1.3600E-15 * (T/300)**( 1.00) * exp( -2113.5/T) {1.12330E-18}

 k(177) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k(178) = 1.5000E-12 * (T/300)**( 1.00) * exp( -1726.0/T) {4.54753E-15}

 k(179) = 4.1400E-12 * (T/300)**( 1.00) * exp( 452.9/T) {1.87990E-11}

 k(180) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(181) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(182) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(183) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(184) = 7.5100E-16 * (T/300)**( 1.00) * exp( -1519.7/T) {4.54966E-18}

 k(185) uses photo table ACROLEIN , scaled by 1.11000E-02 {0.00000E+00}

 k(186) = 1.6000E+16 * (T/300)**( 1.00) * exp(-13486.0/T) {3.52536E-04}

 k(187) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(188) = 2.8000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {5.10890E-12}

 k(189) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(190) = 9.6000E-13 * (T/300)**( 1.00) * exp( 221.4/T) {2.00460E-12}

 k(191) = 1.1900E-12 * (T/300)**( 1.00) * exp( 221.4/T) {2.48486E-12}

 k(192) = 1.1900E-12 * (T/300)**( 1.00) * exp( 221.4/T) {2.48486E-12}

 k(193) = 3.3600E-11 {3.36000E-11}

 k(194) = 4.2000E-12 * (T/300)**( 1.00) * exp( 181.2/T) {7.66335E-12}

 k(195) = 7.7000E-14 * (T/300)**( 1.00) * exp( 1298.3/T) {5.96598E-12}

 k(196) = 8.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {1.75402E-13}

 k(197) = 3.4000E-14 * (T/300)**( 1.00) * exp( 221.4/T) {7.09961E-14}

 k(198) = 7.1100E-18 {7.11000E-18}

 k(199) uses photo table ACROLEIN , scaled by 3.60000E-03 {0.00000E+00}

 k(200) = 1.0000E-13 {1.00000E-13}

 ===============================================================================
EPA/600/R-99/030

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: James M. Godowitch, MD-80, Research Triangle Park, NC 27711. E-mail:

jug@hpcc.epa.gov

Chapter 9

PLUME-IN-GRID TREATMENT OF MAJOR POINT SOURCE EMISSIONS

N. V. Gillani 

Earth System Science Laboratory

University of Alabama in Huntsville

Huntsville, Alabama 35899

James M. Godowitch*

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency 

Research Triangle Park, North Carolina 27711 

ABSTRACT

A plume-in-grid (PinG) technique has been developed to more realistically treat the dynamic and

chemical processes impacting selected, major point source pollutant plumes in the Community

Multiscale Air Quality (CMAQ) modeling system. The principal science algorithms include a

Plume Dynamics Model (PDM) and a Lagrangian reactive plume code. The PDM processor

simulates plume rise, horizontal and vertical plume growth, and transport of each plume section

during the subgrid scale phase. It generates a data file of this information for use by the PinG

module. In contrast to the traditional Eulerian grid modeling method of instantly mixing the

emissions from each point source into an entire grid cell volume, the PinG module simulates the

relevant physical and chemical processes during a subgrid scale phase which allows each plume

section to expand in a realistic manner and to evolve chemically. The PinG module is fully

integrated into the CMAQ Chemical Transport Model (CCTM) in order to utilize the grid

concentrations as boundary conditions and it provides a feedback of the plume pollutants to the

grid model concentration field at the proper time and grid location. The technical approaches

and the model formulation of the relevant processes treated by this plume-in-grid approach are

described. The capabilities and limitations of the initial version of PinG are also discussed and

selected results from a test application for a single point source are briefly described.
EPA/600/R-99/030

9-1

9.0 PLUME-IN-GRID TREATMENT OF MAJOR POINT SOURCE EMISSIONS

9.1 Introduction

Significant emissions of anthropogenic nitrogen oxides (NOx) and sulfur oxides (SOx) are released

from individual elevated point sources into the atmosphere at various levels. These major point

source emissions are distributed throughout the U.S. The physical dimensions of their plumes are

relatively small initially and expand at finite growth rates. This diffusion-limited nature of

plumes is in sharp contrast to the traditional method applied in Eulerian photochemical grid

modeling, which has been to uniformly and instantly mix point source emissions into the entire

volume of a model grid cell. Depending on the meteorological conditions, however, pollutant

plumes may require up to several hours to grow to the typical size of a regional model grid cell. 

Since the horizontal grid resolution of regional scale domains for Eulerian models has generally

been 20-30 km or greater, a real-world pollutant plume may remain a subgrid scale feature at

current regional model grid resolutions for a substantial time period and considerable distance

after release. Thus, the widely-used grid modeling approach inadequately treats subgrid scale

plume transport and diffusion.

 

There are also important implications on the chemical processes in models due to the inability of

large grid cells to adequately resolve a major point source plume. As a real-world plume

gradually grows, it concurrently evolves chemically as it entrains surrounding ambient air often

richer in volatile organic compounds (VOCs). However, these dynamic and chemical processes

of plumes are neglected when large point source emissions are instantly diluted into large grid

cells with other anthropogenic area emissions, which may actually be separated spatially from a

plume. The effect is that the simultaneous availability of NOx and VOC's in a large grid cell

prematurely initiates rapid photochemistry leading to distortion in the spatial and temporal

features of secondary species concentrations. This overdilution of point source emissions and the

subsequent distortion of chemical processes contribute to model uncertainty. Consequently, it

has been recognized that a realistic, subgrid scale modeling approach is needed which simulates

the relevant physical and chemical processes impacting this notable class of large point source

emissions, and in particular, that has the capability of properly resolving the spatial scale of

plumes and their growth.

There are approaches which have been applied in attempts to resolve fine scale emissions in

regional grid models. These have included uniform, nested grid modeling (Odman and Russell,

1991; Chang et al., 1993), non-uniform grid modeling (Mathur et al., 1992), and the plume-ingrid modeling (PinG) technique. The nested grid (telescoping) modeling approach employs the

same Eulerian model and simulations are performed with progressively finer-mesh grid sizes

within a domain to better resolve small scale emission features. While an advantage of this

approach is the use of a single model algorithm, a disadvantage is the successively higher

computational burden as the grid cell size is reduced in order to resolve major emission sources. 

Efforts to implement and apply the plume-in-grid technique, in particular, have been performed

by Seigneur et al. (1983) in a version of the Urban Airshed Model (UAM-PARIS), by Morris et

al. (1992) in the UAM-V model, by Kumar and Russell (1996) in the Urban-Regional Model
EPA/600/R-99/030

9-2

(URM), and by Myer et al. (1996) in the SAQM (SARMAP Air Quality Model) model. Briefly,

each of these PinG efforts simulate multiple plumes or puffs in a domain with no interaction

between individual plumes. Seigneur et al. (1983) employed a rectangular plume cross-section

divided into vertically well-mixed plume cells exhibiting varying widths to maintain equal

pollutant mass among the cells. It was applied to an urban domain with a 4 km grid cell size. 

The other efforts employ an elliptical plume section divided into concentric rings, except for the

Kumar and Russell (1996) PinG. Plume material in an outermost elliptic ring or shell is

sequentially transferred to the grid model as it attains the grid size. In the treatment by Kumar

and Russell, the plume was returned to the grid model after one hour. The general result of

applications from these PinG implementations was that noticeable differences were found

primarily within or near the grid cells containing the major point sources and negligible impact

was found far downwind. This finding is to be expected since these formulations seemed to

focus on the plume-core chemistry only in an early phase of plume chemical evolution with the

feedback of plume pollutants occurring rather quickly to the grid model.

A cooperative research and development effort was undertaken to design and implement a

plume-in-grid (PinG) capability in the Models-3 CMAQ Chemical Transport Model (CCTM) in

order to address the need for an improved approach to treat major point source emissions. The

current PinG approach has been designed to be suitable for the largest, isolated point source

emissions with grid resolutions of regional modeling domains, where the subgrid scale error in the

representation of these sources is expected to be greatest without a PinG treatment. An

important consideration is to be able to spatially resolve a pollutant plume and to adequately

simulate physical expansion so that the chemical evolution can occur gradually.

Therefore, the objectives with this PinG technique are to provide an improved characterization of

the near-source pollutant field from the subgrid scale plume concentrations and to also generate

better regional pollutant concentrations downwind due to the feedback of the PinG

concentrations to the gridded domain. Consequently, when the PinG approach is applied to the

largest point source emissions in a regional, coarse-grid domain, improved initial and boundary

conditions are anticipated for use with subsequent simulations for a subdomain of the same grid

resolution or for fine-mesh nested domains that also need the regional gridded concentration

fields.

In this chapter, the conceptual design of the PinG approach is discussed. The key modeling

components are a Plume Dynamics Model (PDM) and a Lagrangian reactive plume model 

designated as the PinG module since it is fully integrated and coupled with the CCTM Eulerian

grid model. The PDM has been developed to serve as a processor program to generate plume

dimensions, plume position information and related parameters needed by the PinG module. The

descriptions of the mathematical formulations and numerical techniques contained in these

modeling components are also presented. Their solutions form the basis of the physical-chemical

simulations of subgrid scale plumes as implemented in the principal algorithms of the PinG

modeling components.
EPA/600/R-99/030

9-3

9.2 Overview of the Conceptual Framework of the Plume-in-Grid Treatment

The PinG technique is intended for the largest point sources, designated as major elevated point

source emissions (MEPSEs), which are isolated from notable area emission sources. A complete

description of the various criteria available to classify a point source as a MEPSE is provided in

the emission processing system in chapter 4. In the context of photochemical modeling, the NOx

emission rate is a useful criterion to classify a major point source as a MEPSE from the

thousands of individual major point sources in an inventory. Based on a NOx emission rate

criterion of 50 tons/day as a lower limit, Figure 9-1 depicts the group of fewer than 100 MEPSEs

in a 36 km gridded domain covering the eastern US with emission rates greater than this criterion. 

The MEPSE sources are situated away from major metropolitan emission source areas. It reveals

that numerous MEPSEs are distributed throughout the Ohio River and Tennessee River valley

regions. Since the current PinG technique also relies on linear superposition of MEPSE plumes

for determining the impact on grid concentration, the relatively isolated MEPSEs located in these

remote rural environments also provide for the lowest likelihood of plume-plume interactions. 

 

An important feature of a PinG treatment is that it must be able to reproduce the various stages

in the chemical evolution found in a large, rural point source plume. Based on daytime

experimental field study plume data, Gillani and Wilson (1980) documented three distinct stages,

as displayed in Figure 9-2, in the chemical evolution of ozone (O3) in a pollutant plume from a

high NOx source. The O3 data measured across a plume at different downwind distances in

Figure 9-2 illustrate ozone evolution in a large NOx point source plume. Although NOx was not

obtained, it would display a similar variation to SO2 shown in Figure 9-2. During the first stage,

the relatively fresh plume is dominated by primary NOx emissions and an O3 deficit exists in the

plume due to titration by very high NO concentrations. The chemistry in stage 1 is mostly

inorganic and VOC-limited since MEPSE plumes generally exhibit low VOC emissions. The

second stage represents a transition in the chemistry with rapid production of O3 along the plume

edges and some O3 recovery in the plume core. Plume growth from dispersion processes allows

for entrainment of background air which generally contains a richer supply of ambient VOC

concentrations. Consequently, this promotes rapid photochemical O3 production which leads to

the characteristically higher O3 concentrations observed at the edges of a plume during this stage. 

Figure 9-2 reveals that stage 2 certainly exhibits considerable subgrid scale plume structure in

species concentrations. Therefore, the proper simulation of plume chemistry throughout stage 2

is a key phase for a realistic, overall characterization of plume chemical evolution. In fact, full

completion of stage 2 is an important requirement for a chemical criterion during the PinG

simulation before the plume pollutants are transferred to the grid system. In stage 3, the plume is

chemically mature and substantially diluted. In this mature stage, the broad plume would also

exhibit a high VOC/NOx ratio, low NOx concentrations, and O3 concentrations in excess of

background levels. In the modeling system, background (boundary) concentrations are provided

from a CCTM grid cell containing the subgrid scale plume section.

The chemical evolution, as described above, for a large MEPSE plume in the eastern US

generally may take up to several hours to reach full maturity even during the daytime period. 

The photochemical cycle is strongly influenced by the plume growth rate, particularly the rate of
EPA/600/R-99/030

9-4

horizontal spread, with stage 3 achieved when a typical MEPSE plume attains a width of about

30 km during the daytime period. In addition, the time period to reach chemical maturity is also

a function of the emission rate. There is a range of emission rates even within a MEPSE group. 

For example, particular MEPSE plume with lower NOx emissions is expected to exhibit a faster

chemical evolution than a MEPSE with a higher emission rate, assuming other factors being the

same. Nevertheless, during the subgrid scale simulation period, the plume may travel a

considerable distance downwind (i.e. several model grid cells) of its source location in the

daytime planetary boundary layer (PBL) during the summer before reaching a width comparable

to the grid cell size.

The conceptual design of the Models-3 PinG is illustrated in Figure 9-3. PinG components

simulate the relevant processes impacting the hourly emission rate of all pollutant species during

the subgrid scale phase and it provides a feedback, or "handover", of the modeled plume species

concentrations at an appropriate handover time (tH/O) to the CCTM grid framework. The PinG

module operates in a Lagrangian modeling framework to simulate the dynamics and kinetics in a

moving plume section during the subgrid scale phase whose duration depends primarily upon

source strength, plume growth rate, chemical composition of the background CCTM grid

concentrations, and sunlight. The PinG module simulates the plume processes concurrently

during the simulation of the CCTM grid model.

The PinG module contains a series of rectangular plume cross-sections, each of which are

composed of a contiguous, crosswind array of plume cells with the depth of each cell extending

vertically from plume bottom to a top height. As displayed in Figure 9-3a, the vertical depth of

the single-layer plume model may be elevated initially, however, it eventually extends from the

surface to the PBL height (zi

 ). This one-layer plume structure in the initial PinG module also

presents a limitation under high wind speed shear conditions since this situation cannot be

modeled adequately. While strong speed shears are more frequent during the nocturnal period,

the vertical extent of a plume is also generally confined, which lessens the possible impact of

speed shear. Nevertheless, this condition is identified and appropriately handled by the PinG

components.

9.3 Formulation of the Plume-in-Grid Modeling Components 

9.3.1 Description of the Plume Dynamics Model 

The PDM was developed to serve as a processor program in order to provide data needed for the

CCTM/PinG simulation. Therefore, the PDM and the PinG module are closely linked through

the PDM data file. The key processes simulated by the PDM include plume rise, plume

transport, and plume dispersion of each MEPSE plume cross-section. The PDM also specifies

when a particular plume section is to be transferred to the grid model based on an indicator flag

which communicates to the PinG module when this process is to be performed. The PDM is

capable of simultaneously treating up to 100 MEPSEs in a single simulation with the impact on

computational time a function of the number of MEPSEs simulated. In addition, the maximum
EPA/600/R-99/030

9-5

Wp 
 a)y (9-1a)

simulation period is currently limited to 24 hours. Therefore, a single simulation of the CCTM

with PinG is also limited to a 24-hour time period.

9.3.1.1 Aspects of Plume Rise of MEPSE Sources

The plume rise treatment implemented in PDM contains the same algorithms applied in the

Emissions-Chemistry Interface Processor (ECIP). A detailed discussion of the plume rise

equations and treatment has been provided in section 4.4.2 of chapter 4 on the MEPPS system

and therefore is not repeated herein.

The plume rise algorithms handle the entire diurnal cycle since plume sections are released

hourly throughout the 24 hour cycle. The temporal variation of the final effective plume height

for hourly MEPSE plume releases is illustrated in Figure 9-4. In this case, a diurnal variation in

the final plume height is evident with lower plume rise occurring at night believed to be due in

part to stronger wind speeds. The plume height increases during the morning period as the PBL

height grows and the relatively high values found in the afternoon display little variation until the

end of the daytime period.

A notable feature of MEPSE plumes also revealed in Figure 9-4 is the rather significant height

often attained by this class of point sources. Statistics of the stack parameters from MEPSE and

non-MEPSE groups of major point sources were determined. A comparison indicates notable

differences in certain stack parameters between these source groups. The average values from a

MEPSE group containing 84 stacks compared to the other major point source class containing

6539 stacks show a stack height of 207 m versus 45 m , a stack velocity of 20 m/s versus 12.5

m/s , a stack diameter of 7.5 m versus 2.3 m, a stack exit temperature of 410o

 K versus 424o K,

and a stack exit flow rate of 908 m3

/s versus 105 m3/s, respectively. Clearly, these results

indicate why MEPSE plume heights attain higher levels than most point sources. In general,

MEPSE stacks are considerably higher and their plumes exhibit greater buoyancy flux due

primarily to greater physical dimensions which contribute to higher plume rise heights.

9.3.1.2 Plume Dispersion Methods

A key aspect of modeling a subgrid scale reactive plume, as noted earlier, is the importance of

realistically specifying plume dimensions during travel time downwind. Practical methods have

been applied in the initial version of PDM to determine the horizontal and vertical dimensions of

each Lagrangian plume section throughout its life cycle.

Each rectangular plume cross-section has a width (Wp) and an overall height from plume bottom

to top denoted by Hp . The traditional dispersion parameters in the horizontal ()y) and vertical

()z) have been employed in order to derive these plume dimensions. In the current version, the

plume width and plume height values are determined according to
EPA/600/R-99/030

9-6

Hp 
 hT 	 hb (9-1b)

)yo 
 h/3.5 (9-2)

)zo 
 Ae (	BdT/dz) (9-3)

where a has been set to 3.545 which is obtained from 2(%)

1⁄2, an adjustment parameter from an

elliptical shape to the rectangular plume. The top and bottom heights of each plume crosssection are denoted by hT and hb , respectively. The methods used to determine values for the

parameters in Equations 9-1a and 9-1b are discussed next.

During the plume rise phase, a plume experiences initial growth due to buoyancy-induced

turbulence. To account for this process, practical methods have been used to determine initial

values for the dispersion parameters. The initial value of )y is computed according an expression

suggested in Irwin (1979), as advanced by Pasquill (1976), given by

In Equation 9-2, the initial value is a function of the plume rise (h) above the stack top.

Two methods have been installed to prescribe an initial vertical plume thickness. The widely

used approach advanced by Briggs (1975) is to define Hp to be equivalent to the amount of

plume rise (h). This method can result in a rather thick plume when there is considerable plume

rise, particularly, at night when experimental evidence suggests nocturnal plumes may be

relatively thin. Consequently, an optional approach provided as an experimental alternative has

been included. It consists of an empirical form developed by Gillani (1996) which is based on

analyses of observed plume data taken during a field study (Gillani et al., 1981). His regression

analyses produced an expression given by

 

where dT/dz is the vertical ambient temperature gradient at the plume centerline height and the

best-fit values for A and B are 15 and 117, respectively. A minimum )zo value is set to 3 m. 

Then, the initial Hp is determined from SZ0FA times )zo. SZ0FA is a user-specified input

parameter for a PDM simulation and it is currently set to 3.545.

Atmospheric turbulence and wind direction shear contribute to lateral plume growth during travel

downwind. During the daytime convective period, the turbulence component is often dominant,

although directional shear across the PBL also has an important role in contributing to plume

spread with travel distance. In contrast, turbulence is generally weak at night, and horizontal
EPA/600/R-99/030

9-7

)

2

y 
 )

2

yt  )

2

ys  )

2

yo (9-4)

)yt 
 )vTf(T/-L) (9-5)

f 
 1

(1  T/2-L)

1⁄2 (9-6)

)

2

yt 
 2)

2

v-LT (9-7)

plume expansion may be dominated by wind direction shear over a plume's depth. Thus, the

composite horizontal (lateral) dispersion parameter ()y ) can be defined by 

where the turbulence ()yt) and direction shear ()s) terms may both contribute to horizontal plume

growth after the initial plume spread.

A general form for )yt can be expressed by

where )v is the standard deviation of the lateral wind (v) component, T is travel time, and -L is

the Lagrangian time scale. Although various expressions for the function, f(t/-L), have emerged

(e.g., Draxler, 1976; Irwin, 1983), the following form from Weil (1985;1988) and applied by

others (eg.,Venkatram, 1988) has been adopted.

This form is advantageous since it fits dispersion at both the short (t < -L) and also long travel

times (t>>-L). Since the Lagrangian time scale is small relative to the plume section travel times

which are often several hours, the expressions above reveal the familiar relation that )yt increases

with the square root of travel time. Therefore, the following form according to Weil (1988) at

long travel times, which has been examined by Clarke et al. (1983), is given by 

The above equation also displays the square root of time increase for the lateral dispersion

parameter. Using modeled meteorological parameters from data files generated by MCIP, 

methods have been incorporated to determine the key parameters needed to solve the above

expressions for )yt. Values for )v and -L are computed with a set of formulas presented in Hanna

et al. (1982) and Hanna (1984), respectively, for various stability conditions based on MoninObhukov length (L) limits. For unstable conditions with L < 0 
EPA/600/R-99/030

9-8

)v 
 u(12 	 0.5zi

/L)

1/3 (9-8)

-L 
 0.15zi

/)v (9-9)

)v 
 1.3u(1 	 z/zi

) (9-10)

-L 
 0.07zi

/)v(z/zi)

0.5 (9-11)

-L 
 0.5z/)v

(1  15fz/u) (9-13)

)v 
 1.3e

(	2fz/u) (9-12)

)

2

ys 
 2

X 2 (9-14)

where zi is the PBL height and u* is the surface friction velocity. Under stable conditions

defined by L > 0,

and z is the height of the plume centerline. For neutral conditions (L = 0), values are determined

by 

where f is the Coriolis parameter. Using )v and -L values, the contribution from the turbulence

component is computed incrementally from the derivative of Equation 9-7 and solved at each

time step. The turbulence term is accumulated with time. Other semi-empirical methods

available in PDM provide an alternative set of parameterizations for )v as provided by Weil

(1988), Nieuwstadt(1984), and Arya(1984) for the different stability regimes, which may be

selected from an input option when exercising PDM.

Wind direction shear due to turning of the wind over the vertical extent of a plume can also

provide an important contribution to horizontal plume growth. While turbulence often dominates

in the daytime PBL, direction shear during the nocturnal period is the principal mechanism for

lateral plume expansion since turbulence is generally weak. An expression by Pasquill (1979)

has been applied for all conditions to derive the direction shear term and is given by 
EPA/600/R-99/030

9-9

)

2

z 
 )

2

zo

(1  bT 0.5)

(1  bT 0.5

o ) (9-15)

)z 
 )w T f(T/-Lz) (9-16)

)w 
 0.6w (convective case) (9-17)

)w 
 1.3u(1 	 z/zi

)

3/4 neutral/stable (9-18)

-Lz 
 0.15 zi

)w

[1 	 e

	5z/zi

] (unstable) (9-19)

where  is 0.03, X is distance traveled by a plume section over a particular time interval, and 

is the wind direction difference (radians) over the vertical extent of the plume. The shear and

turbulence terms are combined to solve for the total )y

2

 in Equation 9-4.

After the initial plume thickness has been determined, the treatment for )z differs based on

whether the plume height is above or below the PBL height. When the plume centerline height is

above zi

 , then the following expression from Gillani (1996) is applied to determine )z .

where b is 2.3 and T is travel time. Equation 9-15 is applied for T < 4 hours. At longer travel

times, )z is set to zero for plumes existing above the PBL in the free atmosphere.

When a plume section is inside the PBL, the parameterization for the vertical plume dispersion

parameter can be expressed by the same general form as )yt .

As before, T is the travel time, and f has the same functional form as used for )yt although it now

contains the Lagrangian time scale in the vertical (-Lz). The standard deviation of the vertical

wind component ()w) is computed from the following expressions as given by Weil (1988) for

unstable conditions and from Venkatram et al (1984) for neutral/stable conditions, respectively.

The MCIP data files provide values for the fraction velocity (u*), the convective velocity scale

(w*) and zi

. The plume centerline height is represented by z. The value of -Lz is computed from

the following expressions by Hanna et al. (1982) for unstable and by Venkatram et al. (1984) for

neutral/stable conditions.
EPA/600/R-99/030

9-10

-Lz 
 l

)w

(neutral/stable) (9-20)

In the latter expression, the length scale (l) is derived according to Venkatram et al. (1984).

An example application of these methods from a PDM simulation for a plume released at night

from a MEPSE tall stack is shown in Figure 9-5. It shows the plume remains rather narrow and it

stays elevated during the night. However, once the PBL grows beyond the plume height during

the morning period, the plume thickness expands to fill the entire PBL with the plume top height

matching zi

 until it reaches a maximum height. The temporal variation of the plume width for the

same example case is displayed in Figure 9-6. It shows that since the plume has a limited vertical

extent at night, the plume width increases at a relatively slow rate as sufficient direction shear

existed over the plume depth to cause lateral spreading. During the daytime, however, horizontal

plume expansion occurs at a faster rate due to both greater turbulence and shear contributions. 

For a regional grid cell size of 36 km, the plume width for this release reached the physical grid

size during the mid-morning hour. These results and other simulation results obtained from a

daytime release versus observed values (Godowitch et al., 1995) provide preliminary evidence

that these methods give a realistic depiction of the temporal behavior of the magnitudes of plume

width and depth. Additional cases have also been exercised, although results are not shown

herein, in order to assess the robustness and capability of the algorithms for different days. An

extensive evaluation of these dispersion methods in PDM is planned against field study data

obtained in the vicinity of major point sources in the Nashville, Tennessee area during the

Southern Oxidant Study experimental period in the summer of 1995.

9.3.1.3 Plume Transport

With the updated plume top and bottom heights, the mean wind components are determined by

averaging the winds over the layers spanned by the plume from hb to hT. This approach is

currently applicable because of the single vertical layer structure of the current PinG module. 

The mean plume transport speed is used to determine an updated plume centerline position over

the time interval. In addition, the positions of the plume edges at the bottom and top are also

found in order to derive grid indices for later use in applying the proper grid cell concentrations

for boundary conditions of each plume section.

9.3.2 Formulation of the Plume-in-Grid Module

9.3.2.1 Overview of the Plume Conceptual Framework

The Lagrangian plume model described originally by Gillani (1986) provided the conceptual

basis for the Models-3 PinG module. However, the computer algorithms in the CCTM/ PinG
EPA/600/R-99/030

9-11

Wp 
 M

NL

i
1 wLi  M

NR

i
1 wRi

N 
 NL  NR

(9-21)

(wi

)L/R 
 (yi1 	 yi)L/R (9-22)

i 
 yi

Wp

(9-23)

have been rewritten to contain updated methods for the key processes to be described in a later

section.

In a modeling framework, a PinG plume cross-section can be described as a semi-infinite vertical

slab moving along a Lagrangian trajectory with a mean wind flow. A plume cross-section is

considered rectangular with a vertical height (Hp ) and a width (Wp ). Temporally, plume spread

in the vertical and horizontal is specified by growth rates dHp/dt and dWp/dt, respectively. A

plume cross-section is discretized laterally into an array of attached plume cells or pillars with the

same Hp at time t, as depicted in Figure 9-7. Each plume section consists of N plume cells 

(currently, N = 10) with the width of each cell being equal. With respect to the plume

centerline, there are NL cells on the left side and NR cells to the right side, such that

Currently, NL = NR as L and R refer to the cells on the left and right sides, respectively. With

respect to the plume centerline, the right side of the plume section expands to the right and the

left side expands to the left. The width (wi ) of each plume cell is given by 

where y values represent distances from the plume centerline position. Normalization of the

plume cell widths is performed such that as the plume expands laterally, each cell width increases

in the same proportion as the overall plume width. Thus, since the individual cell width is

normalized with respect to the total plume width, the result is a transformed moving crosswind

gridded array which is invariant with respect to time. The transformed crosswind 

coordinate () of the model is given by

and di /dt is zero. Therefore, although Wp and yi

 are time dependent, i remains constant during

a simulation. Additionally, although the fractional width of the cells across the plume section in

the PinG has been prescribed to be equal in the current setup of the module, the algorithms have

been generalized to allow for unequal plume cell widths and a different number of cells on the

left and right sides of the plume centerline as described in Gillani (1986).

9.3.2.2 Formulation of the Plume Mass Balance Equation
EPA/600/R-99/030

9-12

0mi 
 (0mi

)Disp  (0mi)Emis  (0mi)Chem  (0mi)Dep (9-24)

0mi 
 m tdt

i 	 m ti 
 Ctdti lH tdtp W tdtp 	 Cti lH tpW tp (9-25)

The relevant processes, as noted in Figure 9-7, have been incorporated into the plume equation

for the mass balance of individual species. They include dilution and entrainment due to vertical

plume expansion, dilution and entrainment/detrainment due to horizontal plume expansion,

lateral diffusion, gas-phase chemistry, surface removal, and surface emission.

The subscript i denotes plume cell i (left or right of the plume centerline), subscript j denotes

species j, and superscript t denotes a particular time. Thus, Ct

ji is the concentration of species j in

cell i at time t, and mt

ji is mass of species j in cell i at time t. In the following derivation of the

terms of the mass balance equation for any species j in cell i, the subscript j is omitted for

convenience; also, the equations and terms do not show “L” or “R” representing a left or right

plume cell, since the equation and terms apply similarly to both sides. Consequently, consider

the mass balance of (left or right) cell i (for species j) corresponding to the its expansion during a

small time interval dt.

Now, the following expression is also applicable for the plume cell mass.

Herein the alongwind dimension in the downwind direction (l = Udt) is prescribed, which is

determined from the initial mean transport speed (U) over the time interval dt.

Mathematical expressions are presented in subsequent sections for the updated concentration of

species j in cell i due to the action of the individual processes during time interval dt. In the

current version of PinG, only surface emissions after plume touchdown are included in the

emission term since (non-MEPSE) point-source emissions into grid cells (above the lowest cell

layer) neighboring the MEPSE plume are released uniformly into the entire emission grid cell and

impact the MEPSE plume only through the boundary conditions. Surface removal is due to dry

deposition at the ground. Gas-phase chemistry is included with the full chemical mechanisms of

the CCTM in the chemistry term. In the future, the PinG will be adapted to employ the same

aerosol module used by the CCTM. No wet processes are treated in the initial PinG version. 

The current approach to address limitations in the initial version of PinG is to transfer the plume

over to the grid solution whenever conditions exist (e.g., precipitation) which the PinG treatment

cannot adequately accommodate. This issue will be addressed in more detail in the section on

plume handover.

9.3.2.3 Treatment of Plume Expansion and Diffusion Processes
EPA/600/R-99/030

9-13

(0mi

)Disp 
 (0mi)Dil/E/D  (0mi)Dif (9-26)

(0mi

)Dil/E/D 
 (m tdt

i 	 m ti)Dil/E/D (9-27)

m tdt

i 
 m ti  (0mi

)Latdil/E/D (0mi)Vertdil/E/D (9-28)

(0mi

)Latdil/E/D
 lHt

p(Cti10yi1	 Cti 0yi

) (9-29)

0yi 
 i

0Wp (9-30)

Dispersion affects the mass balance of a plume cell as a result of dilution and

entrainment/detrainment processes related to the lateral and vertical expansion of a plume crosssection during a time interval dt, as well as mass diffusion which impacts cell concentrations as a

result of concentration gradients between adjacent cells. The dispersion processes can be

expressed by

where the first term on the right side of Equation 9-26 represents the dilution / entrainment /

detrainment processes and the last term is the eddy diffusion process.

The relationships developed herein apply to cells on either side of the plume centerline, since the

only difference occurs in their application when different boundary conditions occur at each

edge.

refers to the change of mass in plume cell i (for any transported species j) during dt as a result of

dilution and entrainment/detrainment. The changes due to just the horizontal and vertical

exchange processes can be expressed by

where Latdil refers to horizontal (lateral) dilution. In practice, the lateral dilution/

entrainment/detrainment term in Equation 9-28 is determined and then the last term is solved.

The lateral dilution term in Equation 9-28 is given by

However, the following relationship also exists.
EPA/600/R-99/030

9-14

(0mi

)Latdil/E/D
 lH t

p(i1Cti1 	 i

Ct

i)0Wp (9-31)

(0mi)Vertdil/E/D
 lwtdt

i (Ctdta 0Ha  Ctdtb 0Hb) (9-32)

0Ha 
 0Hb 
 0.50Hp (9-33)

0Ha 
 0Hp

0Hb 
 0 (9-34)

(0mi

)Vertdil/E/D
 lwtdt

i Ctdt

 0Hp (9-35)

Ctdt

 
 (Ca  Cb) (elevated plume)

Ctdt

 
 Ctdt

a (surface	based plume)

(9-36)

since  is invariant. Therefore, Equation 9-29 can be revised to the following form.

At this time, (i.e., after lateral dilution/entrainment/detrainment) the width of a plume cell is wi

t+dt. 

With the cell widths remaining unchanged, plume vertical expansion occurs (i.e., in the up and

down direction for an elevated plume, and up only after plume touchdown). Let Ca

t+dt and Cbt+dt

denote the concentrations of species j above and below plume cell i, respectively, for the

elevated plume case. Ca and Cb represent the CCTM grid concentrations at t+dt. Once the

plume becomes surface-based, only Ca is relevant. The equation for the vertical dilution term is

given by

where the changes in Ha and Hb denote plume vertical expansion of the upper and lower plume

boundaries, respectively. An assumption is made that 

for an elevated plume cross-section, and after a plume reaches the surface

are applicable. Equation 9-32 can be rewritten accordingly as

where
EPA/600/R-99/030

9-15

(0m i

)Dil/E/D 
 lH t

p 0Wp(i1C ti1 	 i

C t

i )  l0Hpwtdti Ctdt

 (9-37)

(0mi

)Dil/E/D
 Ctdt

i lH tdtp wtdti 	 Cti lH tpw ti (9-38) 

Ctdt

i 
 Ci

H t

p

wt

i

H tdt

p

wtdt

i  H t

p

H tdt

p

0Wp

wtdt

i

(i1C t

i1 	 i

Ct

i)  0Hp

H tdt

p

Ctdt

 (9-39) 

w t

i 
 y ti1 	 y ti 
 Wp(i1 	 i

)

wtdt

i 
 W tdtp (i1 	 i

) 
 (i1 	 i)(Wp  0Wp)

H tdt

p 
 H tp  0Hp

(9-40)

Ctdt

i 
 C ti

(HpWp)

t

(HpWp)

tdt  0Hp

H tddt

p

Ctdt

  H t

p

H tdt

p

0Wp

Wp

(i1C t

i1 	 i

C t

i )

(i1 	 i

) (9-41)

for an elevated plume and a plume bottom at the surface, respectively. The combination of

Equations 9-31 and 9-35 produces the following form.

However, by substituting the next expression,

and rearranging, the concentration after the total dilution/entrainment/detrainment step is

The first term on the right-side is related to the dilution effect and the next two terms are the

lateral and vertical entrainment/detrainment effects, respectively. The subsequent expressions

are also applicable.

By substituting the above expressions into Equation 9-39, and rearranging gives 

However, Equation 9-41 can be simplified and re-written as
EPA/600/R-99/030

9-16

Ctdt

i 
 1

1H

(HCtdt

  1

1W

[(C t

i  w

i1 	 i

(i1C t

i1 	 i

Ct

i )] (9-42)

H 
 0Hp

Hp

, W 
 0Wp

Wp

. (9-43) 

i 
 1 ; i 
 1 
 0

i 
 NL , i 
 NR ; Ci1 
 Ctdt

bg

(9-44) 

y tdt

i  y ti1 , 2  i  NL , R (9-45)

where

When applying Equation 9-42, certain boundary conditions must be specified. In particular, if

where Cbg

t+dt and C*t+dt are the particular grid cell concentrations from the CCTM solution for the

current time step.

In the execution of the CCTM/PinG, both the grid-cell and plume-cell concentrations are

updated by numerical integration of the corresponding mass balance equations from time t to

t+dt, where dt is the CCTM advection time step (MSTEP). The sequence is that CCTM

performs this integration and updates the concentration field first, generating Ct+dt in each grid

cell, before PinG is called to do the same. PinG performs the integration in a fractional step

approach; first for plume dispersion (step 1) then for the surface emission and removal processes

(step 2), and finally for plume chemistry (step 3). The chemistry integration is actually

performed in smaller chemistry time steps, internally determined for the plume cells by the

chemical solver, in sequence, until the integration is completed for the time interval dt. The

emission/removal step is implemented in a single integration time step. The dispersion step is

performed sequentially in subtime steps until dt is reached. The PinG dispersion time step is

constrained by a restriction when applying Equation 9-42 arising from the fact that, in a given

time step, the location after expansion of the inner interface of a given plume cell (i.e. yi

t+dt)

cannot pass beyond the location of the outer interface of that cell at the start of the ex expansion. 

Therefore, the following constraint applies.
EPA/600/R-99/030

9-17

0t

disp 

(i1 	 i)

i

1



W

(9-46)



W 
 1

Wp

dWp

dt (9-47)

w 
 


tdt

t wdt (9-48)

0Ci

0t 
 00y

(Ky

0Ci

0y

) (9-49)

Ky 
 1

2

d

dt()

2

y) (9-50)

Ky 
 W 2

p

a 2



w (9-51) 

This criterion requires that the following limit for the PinG time step must be satisfied.

It should also be noted that W

* is related to w according to

During the model simulation, Wp (t) and dWp /dt are provided to the PinG module from the PDM

data file. Thus, W

*

 is determined directly, and W can also be computed using the plume widths

from time t and t+dt.

The dispersion step is not complete without inclusion of the diffusion term. The diffusion

equation of a species concentration for any plume cell i may be expressed by

where Ky is the horizontal eddy diffusion coefficient. It can be expressed by

By applying the relationship between )y and Wp in Equation 9-1, the following form for Ky can

be derived.
EPA/600/R-99/030

9-18

Ck1

i	1 [	 Ky0t

(yi1	 yi

)(yi1	 yi	1)

]  Ck1

i [1 Ky0t

(yi1	 yi

)(yi2	 yi)]  Ky0t

(yi1	 yi

)(yi1	 yi	1)

]

 Ck1

i1 [	 Ky0t

(yi1	 yi

)(yi2	 yi)

] 
 C k

i	1

Ky0t

(yi1	 yi

)(yi1	 yi	1)

]

 C k

i [1 	 Ky0t

(yi1	 yi

)(yi2	 yi) 	 Ky0t

yi1	 yi

)(yi1	 yi	1)

]  C k

i1[

Ky0t

(yi1	 yi

)(yi2	 yi)

]

i 
 Ky0t

W 2

p

1

(i1	 i)(i1	 i	1) (9-53)

i 
 K0t

W 2

p

1

(i1	 i)(i2	 i) (9-54)

Numerical integration of a form like Equation 9-49 is solved with the Crank-Nicholson method in

which centered differencing is used for both time and space derivatives to solve the diffusion

equation. This technique provided stable numerical solutions compared to an explicit method. 

The resulting finite-difference equation is then solved by matrix decomposition of the

coefficient-matrix into upper and lower (LU) triangular matrices. For convenience in setting up

the matrix form of the finite difference diffusion equation for all plume cross-section cells, a set

of simultaneous equations is developed which are written in a vector-matrix form for solving by

LU decomposition.

The derivation of the set of equations is provided. By averaging Equation 9-49 in time to obtain

0C/0t at t+0t, and using center-differencing to solve for 02

C/0y2, simplification leads to

(9-52)

where small k is used as a time index for time t, and k+1 represents t+0t, i is the index to the left

edge of plume cell i, and y is the distance from the new reference position at the left 

background location of the plume cross-section. By using the relationship that yi = i

Wp, the

following relations can be defined.
EPA/600/R-99/030

9-19

i 
 i  i (9-55)

	i

Ck1

i	1  (1i

)Ck1

i 	 i

Ck1

i1 
 i

C k

i	1  (i	i

)C k

i  i

C k

i1 (9-56)

Ax 
 b (9-57)

0C j

i 
 kj

qj

xy

0t

Hp

(9-58) 

By substituting the above expressions into Equation 9-52, the following formula is obtained.

Equation 9-56 represents a system of simultaneous equations in the form,

where, x = (Ci

k+1 + ....CN+2k+1 )

t and N is the total number of plume cells. Additionally, the

expression, A = I - G, is defined where A is a square matrix of size (N+1)x(N+2), and b =

(I+G)Ck . In these expressions, I is the identity matrix, and G is a tridiagonal matrix of the form,

G = tridiag (, ,  ) , and is of size (N+2)x(N+2). Subsequently, the simultaneous system of

equations given by Equation 9-57 is solved using LU decomposition.

 

The boundary conditions are also included in the above system of equations since N+2 is used. 

Appropriate boundary conditions are provided by the CCTM grid concentrations for the right and

left edges of each plume cross-section. At left edge boundary, 1 = 1 = 1 and b1 = C1 = Cbg

L

. 

At the right edge boundary, N+2 , N+2, and N+2 are zero which leads to bn+2 = CN+2 = Cbg

R

. 

9.3.2.4 Surface Area Emissions and Dry Deposition

During the PinG simulation, surface emissions are injected into individual surface-based plume

cells. The surface emissions, contained in layer 1 values of the 3-D emissions file which is also

employed by the CCTM, are used in all plume cells of a plume cross-section. For each grid cell,

there is an emission rate for certain species (qj

). In particular, a MEPSE plume cross-section

passes over such gridded surface emissions. Consequently, the change in concentration of plume

cell i during a time step from surface emissions is

where kj

 herein is an appropriate species-specific factor for the conversion of concentration from

a mass unit to the appropriate volume unit.
EPA/600/R-99/030

9-20

0C j

i

0t 
 	 V j

d

Hp

C j

i (9-59)

Since the PinG formulation is composed of a single vertical layer, it was not designed to have the

capability to properly ingest other elevated point-source emissions into the MEPSE plume crosssection. As long as such an along-path, point-source emission remain at a relatively low value,

the impact on the MEPSE concentration field is assumed to be felt through background

entrainment of the expanding MEPSE plume. If the other point source emission was ingested, of

course, such entrained mass is currently dispersed instantaneously throughout the vertical extent

of the plume. For this reason, when point-source emissions larger than a critical value are

encountered by the MEPSE plume, the current logic is to handover the MEPSE plume to the grid

solution.

Dry deposition is a sink term and occurs at the bottom of each plume cell based on the deposition

velocity concept.

where Ci

j

 denotes the concentration of species j and the species-specific deposition velocity (Vd

j

)

values are available from a gridded data file. The same deposition velocity is applied to all cells

of a plume section using the Vd values from the grid cell in which the plume centerline is located.

9.3.2.5 Gas-phase Chemistry of Plumes

A gas-phase chemistry mechanism implemented in the CCTM is also invoked by the PinG

module. The current mechanisms include the RADM2 and carbon bond (CB-4) chemical

mechanisms. Details about these chemical mechanisms are provided in section 8. In addition,

there is a separate PinG module version for each chemical solver (i.e., SMVGEAR and QSSA). 

Minor revisions were needed in the PinG versions of the solver codes to customize them to deal

with the plume concentration array whose dimensionality differs from the CCTM gridded

concentration array. Nevertheless, the PinG gas photochemistry treatment is identical to that of

the CCTM. Since only gas-phase plume chemistry has currently been implemented, when

conditions conducive to extensive aqueous chemistry are encountered, a plume section is

transferred to the CCTM grid system, as discussed in the handover section below. Future plans

include implementation of the existing CCTM aerosol module into PinG so that it also has the

capability to treat aerosol and particulate species.

9.3.2.6 Plume Initialization

The initialization of each plume cross-section is the first key procedure performed at the start of

its simulation. The PinG initialization of a new MEPSE release occurs when a plume crosssection width reaches a minimum width. The width criterion is a user-specified variable and it is

specified for the PDM simulation. A flag indicator variable in the PDM file communicates to

PinG when a plume cross-section is ready to be initialized. The current minimum width for

initialization of a MEPSE plume section has tentatively been set at 2 km. At initialization, it is 
EPA/600/R-99/030

9-21

Cij(0) 
 kj

qj

UHp

1

2%)y

exp[	0.5(y 

i /)y

)

2

] (9-60)

mP 
 Vp(Cp 	 Cbg) (9-61)

assumed that the lateral concentration distribution across the plume section of the primary

emission species exhibits a Gaussian shape. For all other species, initial concentrations have

been set to a machine minimum-value (ie. 10-30).

The lateral concentration distribution of the primary species in the plume cells (i.e., “initial

condition” of the plume concentration field) is given by

where, y* is (yi - yo), the distance of the outer edge of cell i from the plume centerline, 

and U is the mean transport speed, qj is the MEPSE emission rate of species j, and

kj

 is the appropriate species specific mass-to-volume conversion factor.

In PinG, it is assumed that the MEPSE emissions are at an hourly resolution, and that we are

performing plume simulations of hourly releases. The assumption is made that the emission rate

(qj

) remains constant over the hour. Consequently, at the handover time, the transformed mass

impacted by the various plume dynamic and chemical processes corresponding to one hour of

emission is released to the grid solution.

9.3.2.7 Methodology for Plume Feedback to the Eulerian Grid

When the subgrid scale phase of a plume section simulation has been completed, the plume

material is ready for transfer to the CCTM grid. The total concentration of each species in any

plume cell is composed of a component equal to the background concentration, and an additional

component consisting of the plume concentration, which differs from the background grid level. 

In performing the handover, the conceptual basis is that only the plume component is related to

the corresponding MEPSE emissions. Thus, the feedback is restricted to the plume contribution. 

Additionally, since hourly plume releases are simulated from each MEPSE source in PinG, and

since the assumption has been made that each such hourly emission remains constant for the full

hour, the current practice is to handover the contents of a plume section corresponding to a full

hour release. Thus, for each plume species,

where average values for the plume and background grid concentrations are employed. The

average plume concentration (Cp ) of each species is determined from all plume cells. The

background grid value (Cbg ) represents the average of the CCTM grid-cell concentrations on

each side of the plume for all appropriate layers over the vertical extent of the plume. The

handover plume mass is distributed into the column of cells up to Hp in which the plume
EPA/600/R-99/030

9-22

CadjVG 
 (Cp 	 Cbg)Vp (9-62) 

Vp 
 WpHp(Ut) (9-63)

VG 
 xGyG(Z t

G 	 Z bG) (9-64)

Cadj 
 (Cp 	 Cbg)

HpWpxp

VG

(9-65)

centerline is located at the handover time. The feedback of plume mass represents an adjustment

to the CCTM grid cell concentrations from an average concentration (Cadj). From a mass balance

perspective, 

where VG is the CCTM grid cell volume. The plume volume (Vp ) is determined from

where U is the mean horizontal wind speed, t is a 1-hour interval and Ut corresponds to the

alongwind dimension (xp) spanned by the plume section. In a similar fashion, the grid volume

impacted by the plume is given by

where xG and yG are the horizontal grid cell sizes, and ZG

t

 and Z G

b

 are the heights of the top

and bottom of the model layers spanned by the plume.

Substituting the above expression into Equation 9-62 yields:

In the initial release version of PinG when plume handover is triggered, an entire hour’s worth of

plume release in its transformed state is transferred to the appropriate column of grid cells during

a CCTM advection time step. In the future, the intention is to incrementally transfer the same

plume excess to the impacted grid cells over a one hour period of model time steps. In this

manner, the continuous emissions after being treated in PinG would be transferred during a one

hour period following the handover time.

PinG simulations are primarily intended for the coarse-grid, regional modeling grid sizes with the

horizontal resolution () of nominally 20-40 km. Daytime MEPSE plumes reach or are close to

chemical maturity when the plume width attains these grid sizes. However, PinG simulations at

finer grid sizes are possible, however, test runs have not been performed but are needed in order

to assess the benefits of this approach at urban grid cell sizes. As the primary purpose of PinG is
EPA/600/R-99/030

9-23

Wp



 cr (9-66)

O3

Ox

 rchem (9-67)

to improve the subgrid-scale treatment of large point-source plumes, the key handover size

criterion based on plume width relative to grid cell size has been prescribed according to

The default value for cr is 1.0. Therefore, when a plume section width attains the grid cell size,

a flag indicator variable generated by PDM triggers PinG to perform the handover process. 

Currently, the CCTM system is operated in a 1-way nesting mode, as multiple nested grids are

not performed in a single simulation. Consequently, PinG is not equipped to handle the

movement of a plume from a larger to a finer gridded domain within the same simulation.

Ideally, plume handover also occurs when the plume has also reached chemical maturation when

concentration differences within the plume become rather small. A chemical criterion also

incorporated into PinG involves a default condition recognizing chemical maturation. It is based

on an average plume concentration ratio of O3 /Ox ,where Ox = O3+NO2 denotes the principal

oxidant species using concentrations from all cells in a plume section. This ratio is employed as a

surrogate indicator of plume chemical age. The specific chemical maturation criterion is:

where rchem represents the critical value. The default value has been set at 0.99. Tests have

indicated this value to be a good indicator corresponding to a chemically-mature stage 3 plume.

The use of O3 / Ox as a surrogate for plume age is not common compared to NOx / NOy where

NOy includes all the reactive oxides of nitrogen. However, NOx/NOy has not been applied as a

chemical criterion because injection of fresh emissions from large point sources has been

observed to suddenly decrease the chemical age of the background which leads to “premature”

activation of the chemical criterion. Experience from testing with the first chemical criterion has

proved it to be more satisfactory.

In the initial version of the Models-3 PinG , additional criteria are needed which can also trigger

plume handover to the Eulerian grid cells. As the PinG module is upgraded in the future, the

these criteria may be avoided.

 

The next two criteria are related to non-MEPSE emissions in the immediate vicinity of a MEPSE

plume cross-section.

Urban Criterion
EPA/600/R-99/030

9-24

fq (NOx) {1012 molecules/cm 2

/s (9-68)

qNOx | 0.3 kg/s (9-69)

PinG currently does not have the facility to injest different surface emissions into individual

plume cells. Such a condition is likely to be encountered by a MEPSE plume after touch-down

when it passes over an urban-industrial area with a very inhomogeneous spatial distribution of

emissions. Gillani and Pleim (1996) have identified such “urban” areas based on the following

criterion pertaining to the emissions of NOx .

This condition denotes a fairly high NOx surface emission flux (fq ). The critical value of 1012

chosen by Gillani and Pleim (1996) was based on an emission inventory with a horizontal spatial

resolution of about 20 km. For such a grid size, this condition corresponds to an emission rate of

about 0.3 kg/s. Thus, the selected “urban” emissions handover criterion is:

The above condition must be satisfied to trigger plume section handover, and the plume bottom

must also be at the ground for this criterion to activate. 

Point-source Emissions Criterion

The initial PinG version does not possess multiple vertical layer resolution of the plume. Thus, if

a plume section entrains the elevated concentration of a primary species in a background grid

cell from a fresh NOx emission from a non-MEPSE major point source, such entrained mass is

instantaneously mixed vertically throughout the MEPSE plume. If the non-MEPSE point source

emission is large enough, the related error of its treatment in the MEPSE plume relative to its

treatment in the gridded solution becomes large. Thus, it is advantageous to handover the

MEPSE plume under this circumstance. A handover criterion of 3.33 x 10-6 ppm/s has been set

which corresponds to about 2 ppb/10 minutes. If the new non-MEPSE point-source emissions in

the immediate vicinity of the MEPSE plume are large enough to raise the average background

concentration (left/right and vertically-averaged over MEPSE plume height) by more than 2 ppb

in 10 minutes, then handover is also triggered.

Precipitation Criterion

PinG has no facility to handle wet removal of the plume. Consequently, if the total (convective

and non-convective) precipitation rate in the cell containing the MEPSE centroid exceeds a
EPA/600/R-99/030

9-25

critical value, a plume handover is also triggered. Currently, the default value of this critical

precipitation rate is 0.00008 cm/s or about 0.3 cm/hr.

Excessive Wind-Shear Criterion

Since the plume treatment is PinG is based on a Lagrangian simulation for a single vertical layer,

there is no facility to properly treat the effect of wind shear. When excessive speed wind shear

over the vertical extent of the plume exceeds a critical value, plume section handover will occur

on the basis that the treatment of such wind shear will be better treated in the multi-layer grid

model.

Domain Boundary Criterion

Finally, a MEPSE plume section is transferred to grid cell in which the centroid of the MEPSE is

located if it is about to exit the gridded domain. Otherwise the plume concentration contribution

cannot be accounted for if the plume travels beyond the model domain boundary.

In all handover cases considered above, the entire MEPSE plume section is transferred. There is

a particular condition in which only a top portion of the plume may be handed over, while the

remaining part of the plume continues to be simulated. This type of premature partial handover

is forced because PinG does not possess adequate vertical resolution, and also because the plume

simulation in PinG is based on a Lagrangian approach. This condition arises when the plume is

well-mixed throughout the daytime PBL, and the PBL height decreases significantly along the

path of the plume, for whatever reason. In reality, in such a case, the plume would be split

between an upper portion above the PBL and a lower portion remaining within the PBL. The

two portions could then experience very diverse stability and flow conditions which cannot be

accommodated in the current version of PinG.

The approach is that once the PBL height begins to decrease, and it decreases by more than 15%

of the previous zi

 , the plume section is handed over. However, the lower portion continues to be

simulated. If the decrease in zi

 is temporary and it later begins to increase again, the remaining

simulated plume would expand vertically just as if it was the full plume. When zi

 continues to

decrease, as during the evening transition period, then the partial handover would continue

incrementally as the PBL decreases by each 15% segment until the nocturnal mixing height is

reached, at which time the remaining plume is also handed over. In this manner, PinG does not

continue to simulate the well-mixed daytime plume into the night. This approach avoids the

Lagrangian simulation of the deep night-time plume which frequently experiences substantial

wind shear conditions related to nocturnal jets and inertial oscillations.

The situation is different for a fresh MEPSE release into the nocturnal stable layer above the

shallow mixing layer. Such a plume is likely to be thin in the vertical and, therefore, not very

likely experience excessive shearing conditions. In our Lagrangian approach, therefore, PinG

will generally simulate fresh nighttime plume sections which do not experience excessive shear

because of their limited vertical extent.
EPA/600/R-99/030

9-26

9.3.2.8 Test Application of the Plume-in-Grid Modeling Approach

The schematic diagram in Figure 9-8 shows how the PDM and PinG fit into the overall

Models-3 CMAQ system of science programs. Since PDM serves as a processor program, it is

exercised in advance of the CCTM/PinG simulation. PDM requires the MEPSE stack parameter

file generated by the MEPPS emissions system, and a set of meteorological data files prepared by

MCIP from an MM5 simulation. The details of these input files which are needed to perform a

PDM simulation are described in the Models-3 user guide (EPA, 1998). Input and output

parameters for the PDM processor are also defined in the user guide.

 

The PinG module is an integral part of the CCTM, as depicted in Figure 9-8, and it is invoked by

the CCTM driver program along with the other science processes. In the sequence of processes,

PinG is called just before the grid model performs the gas-chemistry step. Consequently, when

PinG completes a time step, the CCTM driver calls the chemistry to undertake gasphotochemistry on the 3-D gridded array. When PinG is being exercised, it needs data files

generated by ECIP, MCIP, PDM and also the MEPSE emission file from MEPPS processing. 

The PinG module also generates a plume concentration file containing the species concentrations

in each plume cell for each plume cross-section. Since the PinG concentration file is a Models-3

specific format, it can be viewed in a visualization software package designed for such data files. 

In addition, an effort is planned to visualize both the plume and grid concentrations on the same

display.

The plume-in-grid algorithms were exercised for a single MEPSE within a 36 km gridded domain. 

The plume cell O3 concentrations in Figure 9-9 are for various times from a selected plume

section released during the early afternoon. The PinG module simulated 10 plume cells in this

plume section, with the concentrations on each edge of the cross-section at various times being

the CCTM gridded values used as background conditions. It is evident that the modeled O3

concentrations displays the same chemical stages described earlier. A significant ozone deficit

exists in the narrow plume for 1-2 hours after release. As the plume expanded, the O3 

concentration gradually recovers and exhibits higher O3 in some cells outside the plume core of

the cross-section at 15:30 than the grid value at each edge or in the plume core. This represents

stage 2 of plume chemical evolution. Eventually, stage 3 was attained as all plume cell O3

concentrations exceeded the CCTM concentrations on each side of the plume with the maximum

excess of about 10 ppb in this case. Shortly after 1730 LST, the last time displayed in Figure 9-9

for this plume section, it was transferred to the CCTM grid system. Therefore, this plume section

was active in the subgrid phase about 5 hours in this case. Once the feedbeack of a plume

section occurs, PinG no longer simulates it which reduces computational time.

The results of this test case and others not described herein are encouraging since they compare

rather favorably in a qualitative sense with observed concentrations (not shown) across the same

MEPSE plume at about the same time. Nevertheless, an extensive evaluation of the PinG is

planned for several case study days with plume data for various species obtained during the

Southern Oxidant Study 1995 experimental intensive program conducted in the Nashville,
EPA/600/R-99/030

9-27

Tennessee area. The evaluation will assess the capability of the PinG components to treat

pollutant plumes and determine the impacts on the regional grid concentrations.

9.4 Summary

A plume-in-grid technique has been developed for use in the Models-3 Community Multiscale

Air Quality modeling system. The key algorithms include a plume dynamics Model (PDM)

processor designed to generate a data file for use in the PinG module simulation. The PinG

module has been fully integrated into the CCTM Eulerian grid model to provide a more refined,

realistic treatment of the physical and chemical processes impacting selected major point source

emissions during a subgrid scale plume phase in a regional model application. The initial release

version is limited to performing gas-phase photochemistry within the plumes. A future PinG

version is expected to include an aerosol and particulate modeling capability. Test simulation

results have been conducted and qualitative results are encouraging regarding the treatment of

plume growth and plume concentrations. However, a rigorous diagnostic evaluation of the

various processes is planned using the 1995 Southern Oxidant Study-Nashville experimental

plume data. Future advancements and refinements of the initial plume-in-grid algorithms are

anticipated and upgraded algorithms will be reflected in upcoming releases.

9.5 References

Arya, P., 1984: Parametric relations for the atmospheric boundary layer. Boundary-Layer 

Meteorol.,30, 57-73.

Briggs, G.A., 1975: Plume rise predictions. In: Lectures on Air Pollution and Environmental 

Impact Analyses, Workshop Proceeding, Boston, MA, 1975, pp 59-111.

Chang, J.S., K.H. Chang, and S. Jin, 1993: Two-way and one-way nested SARMAP air 

quality model. International Conf. on Regional Photochemical Measurement & Modeling 

Studies, November 8-12, San Diego, CA, A&WMA, Pittsburgh, PA.

Clarke, J.F., J. Ching, J.M. Godowitch, 1983: Lagrangian and eulerian time scales 

relationships and plume dipsersion from the Tennessee Plume Study. Sixth Symp. on

Turbulence and Diffusion, March 22-25, 1983, Amer. Meteorol. Soc., Boston, MA.

Draxler, R.R, 1976: Determination of atmospheric diffusion parameters. Atmos. Environ., 10, 

99-105.

EPA, 1998: Models-3 Volume 9b: User Manual, EPA-600/R-98/069b, U.S. Environmental 

Protection Agency, Research Triangle Park, NC 27711.

Gillani, N.V. and W.E. Wilson, 1980: Formation and transport of ozone and aerosols in 

power plant plumes. Ann. N.Y. Acad. Sci., 338, 276-296.
EPA/600/R-99/030

9-28

Gillani, N.V., S. Kohli, and W.E. Wilson, 1981: Gas-to-particle conversion of sulfur in 

power plant plumes: I: Parameterization of the conversion rate for moderately polluted 

ambient conditions. Atmos. Environ., 15, 2293-2313.

Gillani, N.V. and J. E. Pleim, 1996: Subgrid scale features of anthropogenic emissions of 

NOx and VOC in the context of regional eulerian models. Atmos. Environ., 30, 2043- 

2059.

Gillani, N.V., 1986: Ozone Formation in pollutant plumes: A reactive plume model with 

arbitrary crosswind resolution. U.S. Environmental Protection Agency, EPA-600/3-86-051, 

Research Triangle Park, NC, 85 pp.

Gillani, N.V., 1996: Personal communication.

Godowitch, J.M., J. Ching, and N.V. Gillani, 1995: A treatment for Lagrangian transport and 

diffusion of subgrid scale plumes in an eulerian grid framework. Eleventh Symp. on 

Boundary Layers & Turb., March 27-31, Charlotte, NC, Amer. Meteorol. Soc., Boston, 

MA, 86-89.

Hanna, S.R., G.A. Briggs, and R.P. Hosker, 1982: Handbook on atmospheric diffusion, U.S. 

DOE, DOE/TIC-11223, DE82002045, National Technical Info. Center, Springfield, VA.

Hanna, S.R., 1984: Applications in air pollution modeling, Chap. 7, Atmos. Turb. & Air Poll. 

Modeling, Ed. F.T.M. Nieuwstadt and H. van Dop, D. Reidel Publishing Co., Kluwer 

Academic Publishers, Hingham, MA.

Hicks, B.B., 1985: Behavior of turbulence statistics in the convective boundary layer. J. of 

Clim. and Applied Meteorology. 24, 607-614. 

Irwin, J.S., 1979: Scheme for estimating dispersion parameters as a function of release height, 

EPA-600/4-79-062, Research Triangle Park, NC., 56 pp.

Irwin, J.S., 1983: Estimating plume dispersion - a comparison of several sigma schemes. J. 

Clim. And Appl. Meteorol., 22, 92-114.

Kumar, N. and A.G. Russell, 1996: Development of a computationally efficient, reactive subgrid scale plume model and the impact in the northeastern United State using increasing 

levels of chemical detail. J. of Geophys. Res., 101, 16737-16744.

Mathur, R., L.K. Peters, and R.D. Saylor, 1992: Sub-grid presentation of emission source 

clusters in regional air quality modeling. Atmos. Environ., 26A, 3219-3238.
EPA/600/R-99/030

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Morris, R.E. M.A. Yocke, T.C. Myers, and V. Mirabella, 1992: Overview of the variable-grid 

Urban Airshed Model (UAM-V) 85th Annual Meeting of the A&WMA, June 21-26, 

1992, Kansas City, MO., AWMA, Pittsburgh, PA.

Myer, T.C., P.D. Guthrie and S.Y. Wu, 1996: The implementation of a plume-in-grid module 

in the SARMAP air quality model (SAQM). SYSAPP-96-06, Systems Applications 

International, Inc., Available from Technical Support Div., California Air Resources 

Board, Sacramento CA.

Niewstadt, F.T.M., 1984: Some aspects of the turbulent stable boundary layer. BoundaryLayer Meteorol., 30, 31-55. 

Odman, M. T. and A.G. Russell, 1991: Multiscale modeling of pollutant transport and 

chemistry. J. of Geophys. Res., 96, D4, 7363-7370.

Pasquill, F., 1976: Atmospheric dispersion parameters in Gaussian plum modeling: Part II. 

Possible requirements for change in the Turner workbook values. EPA-600/4-76-030b, US

EPA, Research Triangle Park, NC , 53 pp.

Pasquill, F., 1979: Atmospheric dispersion modeling. J. of the Air Poll. Contrl. Assoc., 29, 

117-119.

Seigneur, C., T.W. Tesche, P.M. Roth, and M.K. Liu, 1983: On the treatment of point source 

emissions in urban air quality. Atmos. Environ., 17(9), 1655-1676.

Turner, D.B., T. Chico and J.A. Catalano, 1986: TUPOS - a multiple source gaussian 

dispersion algorithm using on-site turbulence data. U.S. Environmental Protection 

Agency, EPA/600/8-86-010, National Technical Information Center, Springfield, VA.

Venkatram, A., D. Strimaitis, D. Cicristofaro, 1984: A semiempirical model to estimate 

dispersion of evelated releases in the stable boundary layer. Atmos. Environ., 18, 923- 

928.

Venkatram, A. 1988: Dispersion in the stable boundary layer. Chapter 5, In Lectures on Air 

Pollution Modeling, A. Venkatram abd J. Wyngaard, Eds., Amer. Meteorol. Soc., Boston, 

MA., 1988.

Weil, J.C., 1988: Dispersion in the convective boundary layer. Chapter 4, In Lectures on Air 

Pollution Modeling, A. Venkatram and J. Wyngaard, Eds., Amer. Meteorol. Soc., Boston, 

MA., 1988.
EPA/600/R-99/030

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This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

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Figure 9-1 Location of MEPSEs depicted in individual grid cells.
EPA/600/R-99/030

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Figure 9-2. Chemical stages of a plume are depicted by aircraft plume data of SO2, ozone,

sulfate, and aerosol scattering coefficient (Bscat) from crosswind traverses through a large

MEPSE plume. Measurements are from the daytime period of the 23 August 1978 Tennessee

Plume Study experiment. (Adapted from Gillani et al, 1981)
EPA/600/R-99/030

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Figure 9-3. Schematics of the a) time-height view and b) top view of the modeling concept of

the subgrid scale plume in the Models-3 PinG approach.
EPA/600/R-99/030

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Figure 9-4. Example of the final plume height after plume rise for hourly releases from a

MEPSE 300 m stack height.
EPA/600/R-99/030

9-35

Figure 9-5. Time variation of the plume bottom (hb) and top (hT) heights and the PBL height

(Zi) for a nocturnal release.
EPA/600/R-99/030

9-36

Figure 9-6. Time variation of plume width (Wp) from a nocturnal plume release. A plume width

of about 30 km is achieved during the morning period about 10 hours after release.
EPA/600/R-99/030

9-37

Figure 9-7. An illustration of the PinG module formulation depicting the relevant processes; 

a) time-height view and b) cross-sectional view. 
EPA/600/R-99/030

9-38

Figure 9-8. Flow diagram of the PDM processor and PinG module with associated programs in

the Models-3 CMAQ system.
9-39

Figure 9-9 Plume ozone concentrations in an expanding cross-section in the subgrid scale pphase at various times (o - 14:00, * - 14:30,  - 15:30, ° - 15:30, & - 17:30 ). Plume section 

released at 13:00. Symbol at each edge is the grid boundary concentration.
EPA/600/R-99/030

Chapter 10

AEROSOLS IN MODELS-3 CMAQ

Francis S. Binkowski*

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, North Carolina 27711

ABSTRACT

The aerosol module of the CMAQ is designed to be an efficient and economical depiction of

aerosol dynamics in the atmosphere. The approach taken represents the particle size distribution

as the superposition of three lognormal subdistributions, called modes. The processes of

coagulation, particle growth by the addition of new mass, particle formation, etc. are included. 

Time stepping is done with analytical solution to the differential equations for the conservation of

number and species mass conservation. The module considers both PM2.5 and PM10 and includes

estimates of the primary emissions of elemental and organic carbon, dust and other species not

further specified. Secondary species considered are sulfate, nitrate, ammonium, water and organic

from precursors of anthropogenic and biogenic origin. Extinction of visible light by aerosols

represented by two methods, a parametric approximation to Mie extinction and an empirical

approach based upon field data. The algorithms describing cloud interactions are also included in

this chapter.

 

*On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Francis S. Binkowski, MD-80, Research Triangle Park, NC 27711. E-mail:

fzb@hpcc.epa.gov
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10.0 THE AEROSOL PORTION OF MODELS-3 CMAQ

Inclusion of aerosol particles in an air quality model presents several challenges. Among these are

the differences between the physical characteristics of gases and particles. In treating gases in an

air quality model, the size of the gas molecules is not usually of primary importance. In contrast,

particle size is of primary importance. The interaction between condensing vapors and the target

particle depends in an important way on the particle size in relation to the mean free path in the

atmosphere. For gases, once the concentration is known, the corresponding number of molecules

is known. This is not the case for particles. Thus, including aerosol particles in an air quality

model means choosing how the total number, total mass, and size distribution of the particles is

represented. Once this choice is made, then important physical and chemical processes involving

particles must be represented. Particles may be emitted into the air by natural processes such as

wind blowing dust from a desert. Human activities may disturb the soil to allow wind to blow soil

particles off the ground. Sea salt particles come into the atmosphere by wind driven waves on the

sea surface. Volcanic activity is another source of particles for both the troposphere and the

stratosphere. Particles can be made in the atmosphere directly from chemical reaction. The most

important example of this is the transformation of sulfur dioxide, a by-product of fossil fuel

combustion, into sulfate particles. Hydroxyl radicals attack the sulfur dioxide and make sulfuric

acid that then may nucleate in the presence of water vapor and ammonia to produce new particles.

 If there are particles already present in the atmosphere, the new sulfate may condense on the

existing particles or nucleate to form new particles depending upon conditions which are only

recently beginning to be understood. Reactions of organic precursors such as natural

monoterpenes and anthropogenic organic species with ozone and other oxidants or radicals make

new species that condense on existing particles or make new particles depending upon conditions.

 Combustion sources emit particles composed of mixtures of organic carbon and elemental

carbon. The exact mixture of organic and elemental carbon is a strong function of the conditions

of combustion. Once these particles are in the air, they may grow by condensing of species upon

them as has already been mentioned. For a large group of particles made in the air, i.e., secondary

particles, growth may be related to relative humidity because of water condensing on the particles.

 Another gas-particle interaction is the chemical equilibration of species within or on the surface

of a particle with gases and vapors within the air. Unlike gases, particles coagulate, e.g., collide

and form a particle whose mass and volume are the sums of the masses and volumes of the

colliding particles. Thus, adding particles to an air quality model means adding a new set of

physical processes.

In designing the aerosol component of CMAQ the following assumptions were made. Any

representation of particles had to be consistent with observations of particles. The representation

had to be mathematically and numerically efficient to minimize computer time. And finally the

representation had to be usable for regional to urban simulations. These assumptions led to a

choice of two methods. The first method would be to model particle behavior in set of bins of

increasing size. This approach is quite popular and is described originally by Gelbard et. al.

(1980) and more recently by Jacobson (1997). The second approach, the one chosen for

implementation in CMAQ, is to follow Whitby (1978) and model the particles as a superposition

of lognormal subdistributions called modes. The sectional method using the discrete size bins

requires a large number of bins to capture the size distribution. If one wishes to model several

chemical components then the number of components is multiplied by the number of bins. This
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leads to a very large number of variables that must be added to an air quality model to capture

particle behavior. In the modal approach, using the three modes suggested by Whitby(1978), only

three integral properties of the distribution, the total particle number concentration, the total

surface area concentration, and the total mass concentration of the individual chemical

components in each of the three mode. The current approach differs from that taken by

Binkowski and Shankar (1995) where the sixth moment was chosen as a third in integral property

in place of the second moment. That moment as chosen because of a mathematical simplification

(see Whitby and McMurry, 1997). The mathematical simplifications of the modal method allow

analytical solutions to be used for the aerosol dynamics. The current approach uses numerical

quadratures to calculate all of the coagulation terms. The numerical quadratures were compared

with the analytical expressions exhibited in Whitby et al. (1991) and are accurate to six decimal

places. The choice of using numerical quadratures was made to reduce the memory requirements

associated with a variable geometric standard deviation and because the second moment unlike

the sixth moment does not have an analytical form.

The aerosol component of the CMAQ is derived from the Regional Particulate Model (RPM)

(Binkowski and Shankar, 1995) which in, turn, is based upon the paradigm of the Regional Acid

Deposition Model (RADM), an Eulerian framework model (Chang et al., 1990). The particles are

divided into two groups, which are fine particles and coarse particles. These groups generally

have separate source mechanisms and chemical characteristics. The fine particles result from

combustion processes and chemical production of material that then condenses upon existing

particles or forms new particles by nucleation. The coarse group is composed of material such as

wind-blown dust and marine particles (sea salt). The anthropogenic component of the coarse

particles is most often identified with industrial processes. The common EPA nomenclature used

in air quality refers to PM2.5 (particles with diameters less than 2.5 μm) and PM10 (particles with

diameters less than 10μm). Note that PM10 includes PM2.5. Thus, in the present context, coarse

particles are those with diameters between 2.5 and 10 μm. Then, the mass of the coarse particles

is the difference between the masses in PM10 and PM2.5. 

As already noted, the aerosol particle size distribution is modeled using the concepts developed by

Whitby (1978). That is, PM2.5 is treated by two interacting subdistributions or modes. The

coarse particles form a third mode. Conceptually within the fine group, the smaller (nuclei or

Aitken), i-mode represents fresh particles either from nucleation or from direct emission, while

the larger (accumulation), j-mode represents aged particles. Primary emissions may also be

distributed between these two modes. The two modes interact with each other through

coagulation. Each mode may grow through condensation of gaseous precursors; each mode is

subject to wet and dry deposition. Finally, the smaller mode may grow into the larger mode and

partially merge with it. These processes are described in the following subsections. The chemical

species treated in the aerosol component are fine species sulfates, nitrates, ammonium, water,

anthropogenic and biogenic organic carbon, elemental carbon, and other unspecified material of

anthropogenic origin. The coarse-mode species include sea salt, wind-blown dust, and other

unspecified material of anthropogenic origin. Because atmospheric transparency or visual range is

an important air quality related value, the aerosol component also calculates estimates of visual

range and aerosol extinction coefficient. 
EPA/600/R-99/030

10-3

10.1 Aerosol Dynamics

The particle dynamics of this aerosol distribution are described fully in Whitby et al. (1991) and

Whitby and McMurry 1997); therefore, only a brief summary of the method is given here. 

(Note: In the following equations repeated subscripts are not summed.) 

10.1.1 Modal Definitions

Given a lognormal distribution defined as

n(lnD) =

N

2π ln σg

exp -0.5

ln D

Dg

ln σg

2

,

(10-1)

where N is the particle number concentration, D the particle diameter, and Dg and σg the

geometric mean diameter and standard deviation of the distribution, respectively. The kth

moment of the distribution is defined as

Mk = D

k

−∞

∞

n ln D d ln D

(10-2)

with the result

Mk = N Dg

k

exp

k

2

2

ln

2

σg

.

(10-3)

M0 is the total number, N, of aerosol particles within the mode suspended in a unit volume of air.

For k = 2, the moment is proportional to the total particulate surface area within the mode per

unit volume of air. For k = 3, the moment is proportional to the total particulate volume within the

mode per unit volume of air. The constant of proportionality between M2and surface area is π;

the constant of proportionality between M3 and volume is π/6. Note that the geometric standard

deviation is the same no matter which moment is selected. M3 is determined from the nine distinct

fine aerosol species (including water) listed in Table 10-1 as follows:

M3i

=

φi

n

π

6

ρn

Σn = 1

nmax

(10-4a)

M3j =

φ j

n

π

6

ρn

Σn = 1

nmax

(10-4b)

where φi

n

 and φ j

n

 are the species mass concentrations of the nth species in each mode in 

[μg m-3], ρn is the average density of the nth species. The third moment for the coarse mode is
EPA/600/R-99/030

10-4

obtained in a similar manner. Given a value of third moment concentration and number

concentration, the geometric mean standard deviation and the geometric mean diameter for each

mode is diagnosed from

ln2

σ

g

=

1

3

2 ln M3 – 3 ln N – ln M2

(10-5a)

Dg

3

=

M3

Nexp

9

2

ln2

σg

.

(10-5b)

The prediction equations for number, second moment and species mass are given in Section

10.1.4.

10.1.2 New Particle Production by Nucleation

The CMAQ aerosol component has a choice of two particle production mechanisms, those of

Harrington and Kreidenweis (1998a,b) and Kulmala et al. (1998). Both of these methods predict

the rate of increase of the number of particles, J, (in number per unit volume per unit time) by the

nucleation from sulfuric acid vapor. In order to predict the rate of increase on new mass and new

second moment an assumption about particle size is necessary. Following work by Weber et al.

(1997), it is assumed that the new particles are 3.5 nm in diameter. Weber et al. reported

measurements of the concentration of particles that are in the size range 2.7 to 4.nm. For

simplicity we have chosen 3.5 nm as a representative diameter. 

Using either of these methods, the production rate of new particle mass [ μg m-3 s

-1 ] is then

d Mass

dt =

π

6

ρd3.5

3

J

(10-6a)

and that for number [ m-3 s

-1 ] is

d Num

dt = J

(10-6b)

and that for second moment [ m2 m-3 s-1 ] is

d M2

dt = d3.5

2

J

(10-6c)

where d3.5 is the diameter of the 3.5 nm particle and ρ is the density of the particle (taken as

sulfuric acid) at ambient relative humidity (Nair and Vohra, 1975).

10.1.3 Primary Emissions

The EPA emission inventory for PM2.5 and PM10 does not currently contain information about

neither size distribution nor chemical speciation. In the CMAQ work, the assumption is that the
EPA/600/R-99/030

10-5

major part of PM2.5 particulate mass emissions are in the accumulation mode with a small fraction

in the Aitken mode; i.e. a fraction of 0.999 of PM2.5 is assumed to be in the accumulation mode

and the remaining fraction, 0.001, is assigned to the Aitken mode. Sensitivity studies will be

conducted to evaluate this assumption. In order to estimate the emissions rate for number and

second moment from the mass emissions rate an assumed mass size distribution is required. It is

convenient to express the emission rate for number, E0, and that for second moment E2 in terms

of a total emissions rate for third moment. This is shown schematically as follows where En is the

mass emissions rate for species n and ρn is the density for that species

E3n

=

6

p

En

ρ

n (10-7a)

E0 =

Σn

E3n

Dgv

3

exp –

9

2

ln2

σg

(10-7b)

E2 =

Σn

E3n

Dgvexp –

1

2

ln2

σg

(10-7c)

where the sum is taken over all emitted species.

In Equation 10-7b,c, E0 and E2 schematically represent the emissions rates for the various modes.

In Section 10.1.4, the nomenclature used to represent the emissions rate for number for each of

the three modes will be respectively E0i, E0j, and E0cor.

We have chosen values of 0.3 μm for the geometric mean diameter for mass, D

gv

, and 2.0 for the

geometric standard deviation, σg  for the accumulation mode. The corresponding values for the

Aitken mode are 0.03 μm and 1.7, and those for the coarse mode are 6 μm and 2.2.

The current emissions inventory estimates that 90% of PM10 is fugitive dust, and that 70% of this

dust consists of PM2.5 particles. The paradigm adopted for the CMAQ is that fugitive dust is a

coarse mode phenomenon with a tail that overlaps the PM2.5 range. Therefore, 90% of PM10

emissions are assigned entirely to the coarse mode species ASOIL. Sulfate emissions are treated

differently in CMAQ than in RPM. In RPM sulfate emissions were treated as particles and

distributed between the Aitken and accumulation modes. In CMAQ, the photochemical module

has sulfate emissions incorporated into the chemical solver. Thus, the production rate for sulfuric

acid will include direct emissions of sulfate. This rate is passed from the photochemical module to

the aerosol module. Assigning fractional amounts of emitted PM2.5 and PM10 to the specific

species in Table 10-1 is a matter of ongoing discussions with those responsible for preparing the

national emissions inventory.
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10.1.4 Numerical Solvers

The numerical solvers for the two fine particle modes in the Models-3 aerosol component have

been modified from those in RPM, which followed from Whitby et al. (1991). The major

difference is that the RPM solvers linearized the quadratic term for intramodal coagulation in the

equation for modal number concentration. The new solvers in CMAQ retain this quadratic term.

The number concentrations for the Aitken and accumulation modes are denoted as Ni and Nj

respectively. Intramodal coagulation coefficients are functions only of the geometric mean

diameters and geometric standard deviations for each mode and are denoted as F0ii and F0jj. 

Similarly, the intermodal coagulation coefficient for coagulation between the Aitken and

accumulation modes is F0ij. For simplicity the following coefficients are defined.

For the Aitken mode:

ai = F0ii , bi = Nj F0ij , and

ci

=

d Num

dt

+ E0i

, with

d Num

dt

from (10-6b);

and for the accumulation mode:

aj = F0jj, and cj = E0j

The emissions rates for number concentration are E0i and E0j and are set to values determined for

each mode from Equation 10-7b.

We may now write for the particle number concentrations

∂Ni

∂t

= ci– ai Ni

2

– b iNi; and

(10-8a)

∂Nj

∂t

= c j– a jNj

2

.

(10-8b)

Equation 10-8a, a Riccati type equation and Equation 10-8b, a logistics type equation, have

different analytical solutions depending upon whether ci and cj are zero or nonzero. These

analytic solutions are used in the CMAQ solver with the coefficients being held constant over one

model time step. In discussing the analytical solutions to Equations 10-8a and b, subscripts will

be omitted for simplicity

The solution to Equation 10-8a for ci ≠ 0 is of the form

N t =

r1 + r2P exp Dt

a 1 + P exp Dt
EPA/600/R-99/030

10-7

where

D = b

2 + 4ac

1

2

, r

1

=

2ac

b + D

, r

2

= –

b + D

2

, P = –

r1 – a N t0

r2– a N t

0

.

 For ci = 0, the solution to Equation 10-8a is of the form

N t =

bN t

0

exp –bt

b + aN t

0

1 – exp –bt

.

The solution to Equation 10-8b when cj ≠ 0 is of the same form as that to Equation 10-8a except

b = 0. The solution when cj = 0, known as Smoluchowski’s solution, is:

N t =

N t0

1 + aN t0t

.

The equations for the prediction of second moment, M2, in the Aitken and accumulation modes

are both of the form

∂M2

∂t

= P2– L2M2;

with solutions of the form

M2t =

P2

L2

+ M2t

0

–

P2

L2

exp – L2t .

In these equations, production of second moment is denoted by P2 and loss by L2 .For the Aitken

mode, the production term includes the rate of second moment increase by new particle formation

from Equation 10-6c, condensational growth (Equation 7a of Binkowski and Shankar, 1995) and

by primary emissions from Equation 10-7c. The loss term accounts for the loss of second

moment by intramodal coagulation, as well as including the transfer of second moment to the

accumulation mode by intermodal coagulation. For the accumulation mode, the production term

includes the transfer of second moment by intermodal coagulation, condensational growth

(Equation 7b of Binkowski and Shankar, 1995) and the contribution of primary emissions from

Equation 10-7c. The loss term accounts for intramodal coagulation. 

It is important to note that the history variable in CMAQ is the modal surface area, which, as

already noted, is π time the second moment. For convenience, however, within the internal

aerosol subroutines, the second moment is the treated. Before returning to the main CMAQ

routines, the second moment is multiplied by π. That is why species number 23 and 24 in Table

10-1 are identified as modal surface areas. It is also important to note that the surface area

predicted by CMAQ is the surface area for spherical particles and may not represent the true

surface area available in nonspherical particles or in porous particles such as carbon soot.
EPA/600/R-99/030

10-8

Empirical correction factors may be needed for use of CMAQ surface area predictions in certain

applications.

The equations for mass concentration of species n may be written as:

∂φi

n

∂t

= Pi

n – Liφi

n

; and (10-9a)

∂φ j

n

∂t

= P j

n

,

(10-9b)

where Pi

n

= φi

n

+ Ei

n

+ R

nΩi

 and Li = NiN jF3ij / M3i

with φi

n

=

d Mass

dt

 from Equation 10-6a, when n denotes sulfate, and where n Ei

and n Ej

are the

emission rates and R

n

is the gas-phase production rate for species n. The factors Ωi and Ωj,

defined by Equations A17 and A18 of Binkowski and Shankar (1995) represent the fractional

apportionment of condensing species. F3ij is the coagulation coefficient for the third moment.

Note that the loss of mass in Equation 10-9a is a gain of mass in Equation 10-9b. This represents

the transfer of mass by intermodal coagulation. There is no such transfer of number in Equations

10-8a,b because of the convention that when a smaller particle coagulates with a larger particle

there is a loss of number from the population of smaller particles, but no gain of number in the

population of larger particles. There is, however, a transfer of mass. Equations 10-9a and b have

an analytic solution holding the coefficients constant for the time step of the form:

φ t =

P

L

+ φ t

0

–

P

L

exp – Lt .

The solution to Equation 10-9b are by an Euler forward step once again holding the production

terms constant over that time step.

The equation for the prediction of coarse mode mass is

∂φcor

n

∂t

= Ecor

n

,

The solution is by an Euler forward step. The equation for coarse mode number is similar because

coagulation is ignored for the coarse mode, and is also solved by an Euler forward step.

10.1.5 Mode Merging by Renaming

In Binkowski and Shankar (1995), the Aitken mode diameters grew over the simulation period to

become as large as those in the accumulation mode. While this is probably true in nature, it

violates the modeling paradigm that two modes of distinct size ranges always exist. This

phenomenon can be modeled by mode merging as follows. The Aitken mode approaches the

accumulation mode by small increments over any model time step when particle growth and

nucleation are occurring. Thus, an algorithm is needed that transfers number and mass
EPA/600/R-99/030

10-9

concentration from the Aitken mode to the accumulation mode when the Aitken mode forcing

exceeds the accumulation mode forcing and the number of particles in the accumulation mode is

no larger than that in the Aitken mode.

This algorithm is formulated as follows (Binkowski et al., 1996). When Equation 10-10 is

satisfied, the diameter of overlap, d , for the modal number distributions can be calculated exactly.

 Given this diameter, the fraction of the total number of Aitken mode particles greater than this

diameter is easily calculated from the complementary error function

Fnum= 0.5 1 + erfc (xnum) , where

xnum =

ln d

dgni

2 ln σgi

(10-10a)

and dgni is the geometric mean diameter for the Aitken mode number distribution.

The number concentration corresponding to these particles is transferred to the accumulation

mode, a processes denoted here as renaming the particles. A similar process is used to transfer

mass (third moment) concentration and surface area (second moment) concentration from the

Aitken to the accumulation mode using the complementary error function corresponding to the

third moment. 

Fk = 0.5 1 + erfc (xk) ,

where xk = xnum –

k ln σgi

2

.

(10-10b)

For numerical stability, the transfer of number and mass is limited so that no more than one half of

the Aitken mode mass may be transferred at any given time step. 

This is accomplished by requiring that 

3 ln σgi

2

≤ xnum .

The fraction of the total number and surface area (k= 2) and mass (k=3) remaining in the Aitken

mode is calculated from the error function of the overlap diameters as:

Φnum= 0.5 1 + erf (xnum)

(10-10c)

Φk = 0.5 1 + erf(xk

)

(10-10d)

Using these fractions, Aitken and accumulation mode number and mass concentrations are

updated as

Nj = Nj + FnumNi

(10-11a)
EPA/600/R-99/030

10-10

φj

n

= φj

n

+ F3φi

n (10-11b)

M2 j= M2 j + F2M2i (10-11c)

Ni= ΦnumNi

(10-11d)

φi

n

= Φ3φ i

n (10-11e)

M2i = Φ2M2i

(10-11f)

This method of particle renaming is analogous to the procedure discussed by Jacobson (1997)

where particles are reassigned in the moving center concept of a bin model. When the particles

grow beyond the boundaries of their size bin, they are reassigned to a larger bin and averaged

with the new bin.

10.2 Aerosol Dry Deposition

The rate of dry deposition of particle zeroth and third moment to the earth's surface provides the

lower boundary condition for the vertical diffusion of aerosol number and species mass,

respectively. The method of doing this follows the RPM approach with the following exceptions.

 In RPM total fine mass was deposited. In CMAQ the species mass in each mode is deposited

separately using the dry deposition velocity for the third moment. The impaction term is omitted

for the coarse mode particles in both the zeroth and third moment dry deposition velocities. See

Binkowski and Shankar (1995) Equations A25 through A34 for details.

10.3 Cloud Processing of Aerosols

Clouds are formed when the relative humidity reaches a value at which existing aerosol particles

are activated. That is, they pass through a potential barrier and grow rapidly from a few

micrometers to several micrometers to become cloud droplets (cloud nucleation). Soluble gases

are then dissolved into the cloud droplets where aqueous-phase chemical equilibria and reactions

occur. The attack on dissolved sulfur dioxide by hydrogen peroxide produces a dissolved sulfate

species (oxidation of Sulfur (IV) to Sulfur (VI)). Because these processes are very complex in

detail and occur at subgrid scale, most cloud modeling in mesoscale meteorological models and in

air quality models uses simplified parametric approaches to model the effect of clouds rather than

modeling the clouds directly. This approach was used in RADM and RPM and is applied in the

first version of CMAQ.

The assumptions for aerosol behavior in clouds are:

• The Aitken ( i ) mode forms interstitial aerosol which is scavenged by the cloud droplets. 

All three integral properties of the Aitken mode respond to in-cloud scavenging.
EPA/600/R-99/030

10-11

• The accumulation ( j ) mode forms cloud condensation nuclei and thus is distributed as

aerosol within the cloud water. Mass and number in this mode may be lost through

precipitation. Mass but not number is increased by in-cloud scavenging of the Aitken

mode.

• All new sulfate mass produced by aqueous production is added to the accumulation mode,

but the number of accumulation mode particles is unchanged as is the geometric standard

deviation, σg, of the accumulation mode processes (cf Leaitch, 1996 for cumulus clouds).

• The assumption about the accumulation mode geometric standard deviation means that

the surface area of the accumulation mode is reconstucted from the new mass and new

number in the accumulation mode at the end of the cloud lifetime.

• The aerosol is mixed vertically by the same mechanisms mixing other species. The wet

removal of aerosol is proportional to wet removal of sulfate (See Chapter 11).

The limitations are:

• The cloud process modules are similar to those of RPM and RADM with cloud droplet

number concentrations being modeled by an empirical fit to data from Bower and

Choularton (1992).

• Cloud droplet size distributions are lognormal with σg set to 1.2. Using the cloud liquid

water content and the cloud droplet number concentration, the geometric mean cloud

droplet diameter, d

g,

 can be calculated.

The mathematical approach begins with an extension (Binkowski and Shankar, 1994; Shankar and

Binkowski, 1994) of Slinn's (1974) two-step model as used by Chaumerliac (1984).

The in-cloud scavenging of interstitial Aitken mode number, surface area and mass concentration,

yak, may be represented by:

dyak

dt = -αk

yak

(10-12)

with solution

yak t + τ

cld

= yak 0 exp –α

k

τ

cld

(10-13)

where αk (k = 0,2,3) is the attachment rate for interstitial aerosol concentration. The attachment

rate is assumed to be held constant over the cloud lifetime τcld. The initial values yak(0) are

determined after cloud mixing (see Equations 11-4 and 11-5).

The cloud water aerosol concentration is represented by
EPA/600/R-99/030

10-12

dyck

dt = δ

k3

αk

yak+ P – βδ

k0

yck, k ≠ 2

(10-14)

where β is the precipitation removal rate, and P is the production of new sulfate mass by aqueous

chemistry. The first Kronecker delta indicates that only mass (k=3) is increased for the

accumulation mode by chemical production and in-cloud scavenging. The second Kronecker delta

indicates that only number (k=0) is removed by the precipitation removal term in this form. Mass

is removed explicitly in the cloud processor.

The attachment rates, αk, using the form recommended by Pruppacher and Keltt (1978) and

including an enhancement factor for the settling velocity of the cloud droplets, vdc are given by:

αk = 2πm1cDpk

1 + 0.5 Pek

1/3

, k = 0,2,3;

(10-15)

Where

m1c

= Ncddgexp 1

2

ln2 σdg.

Nc

 and dd are the cloud droplet number concentration and geometric mean

diameter respectively.

Pek =

vdcdd

Dpk

is a Peclet number.

The polydisperse diffusivity is given by

Dpk =

kbT

3πυρair Dg

×

exp

–2k + 1

2

ln2σg+ 1.246Kn gexp

–4k + 4

2

ln2σg

and is the same form as that for dry deposition algorithm

(see Binkowski and Shankar, 1995, Equation A29).

(10-16)

(10-17)

(10-18)

The precipitation removal rate for number is given by

β =

1

τcld

δSO4 wetdep

SO4 init

+ SO4 scav+ δSO4 prod

(10-19)

where τcld is the cloud lifetime, [ δSO4]wetdep is the change in sulfate concentration due to

precipitation loss, and [ SO4]init is the sulfate concentration at the beginning of the cloud lifetime,

[SO4]scav is the amount of sulfate added from in-cloud scavenging of Aitken mode sulfate; [

δSO4]prod is the amount of new sulfate produced by aqueous chemistry.
EPA/600/R-99/030

10-13

10.4 Aerosol Chemistry

The aerosol chemical species are listed in Table 10-1. The secondary species sulfate is produced

by chemical reaction of hydroxyl radical on sulfur dioxide to produce sulfuric acid that may

condense on existing particles or nucleate to form new particles. Emissions of fresh primary

sulfate are treated in the gas-phase chemistry component, and this contributes to the total change

in sulfate from the chemistry component. This is a change from RPM where primary sulfate

emissions were treated as a source of new mass and new particle number. Other inorganic species

such as (ammonia and nitric acid) are equilibrated with the aerosols.

An assumption of the model is that organics influence neither the water content nor the ionic

strength of the system; however, this assumption may not be valid for many atmospheric aerosols.

 Although much progress has been made (e.g. Saxena et al., 1995; Saxena and Hildemann, 1996),

sufficient basic data are not yet available to treat the system in a more complete and correct way. 

Over continental North America for PM2.5, sea salt and soil particles are not considered in the

equilibria. Thus, for the initial release of CMAQ, only the equilibrium of the sulfate, nitrate,

ammonium and water system is considered. The equilibria and the associated constants are based

upon Kim et al. (1993a) and shown in Table 10-3.

The aerosol water content is computed using the ZSR method (see Kim et al., 1993a) from:

W =

Mn

mn0 aw

Σn

(10-20)

where W is the aerosol liquid water content [kg m-3], Mn is the atmospheric concentration of the

nth species [moles m-3], and mn0 is the molality [moles kg-3], of the nth species at a value of water

activity (fractional relative humidity) of aw. The values for the molality as a function of water

activity are calculated from laboratory data from Giauque et al. (1960), Tang and Munkelwitz

(1994), and Nair and Vohra (1975). The ZSR method is used in a somewhat different way than

usual. The water content of sulfate aerosols depends strongly upon the ionic ratio of ammonium

to sulfate. This ratio varies from zero for sulfuric acid to 2.0 for ammonium sulfate with

intermediate values of 1.0 for ammonium bisulfate, and 1.5 for letovicite. The usual method

would span this range with a single expression; however, Spann and Richardson (1985) have

shown that this is not correct. They proposed a modification which resulted in a correction term.

 A very similar result is obtained by using the ZSR method between the ranges of the ionic ratio of

sulfuric acid to ammonium bisulfate, ammonium bisulfate to letovicite, and letovicite to

ammonium sulfate. The binary activity coefficients are computed using Pitzer’s method and the

Bromley method is used for the multicomponent activity coefficients in the aqueous solution (see

Kim et al., 1993a) for details.

Two regimes of ammonium to sulfate ionic ratio are considered. The ammonia deficient regime

(in which the ionic ratio of ammonium to total sulfate ion is less than two) leads to an acidic

aerosol system with very low concentrations of dissolved nitrate ion which depend very strongly

on ambient relative humidity. The second regime is one in which the ammonium to sulfate ratio

exceeds two, the sulfate is completely neutralized, and there is excess ammonia. If there is nitric
EPA/600/R-99/030

10-14

acid vapor in the system, it will dissolve in the aqueous particles along with the excess ammonia

and produce abundant nitrate.

For cases when the relative humidity is so low that the aerosol liquid water content comprises less

than 20 percent of the total aerosol mass, and the ionic ratio of ammonium to sulfate is greater

than two, “dry ammonium nitrate” aerosol is calculated with the following equilibrium

relationship:

NH4NO 3(s) ⇔ NH 3(g) + HNO3(g) (10-21)

The value of the equilibrium constant is taken from Mozurkewich (1993) as noted in Table 10-2.

Precursors of anthropogenic organic aerosol (such as alkanes, alkenes, and aromatics) react with

hydroxyl radicals, ozone, and nitrate radicals to produce condensable material. Monoterpenes

react in a similar manner to produce biogenic organic aerosol species. The rates of production of

sulfuric acid and the organic species are passed from the photochemical component to the aerosol

component. The formation rates of aerosol mass (in terms of the reaction rates of the precursors)

are taken from Pandis et al. (1992). These factors are given in Table 10-3.

10.5 Visibility

Visibility is usually defined to mean the furthest distance one can see and identify an object in the

atmosphere. For a detailed presentation on the concepts of visibility, see Malm (1979). In a

perfectly clean atmosphere composed only of nonabsorbent gases, the only process restricting

visibility during daylight is the scattering of solar radiation from the molecules of the gases. This

is known as Rayleigh scattering. Scattering is usually represented by a scattering coefficient. If

absorption is also occurring in addition to scattering, an absorption coefficient may also be

defined. The sum of the scattering and absorption coefficients is called the extinction coefficient. 

If absorption is not occurring, the extinction coefficient is defined to be equal to the scattering

coefficient. The visibility in an atmosphere in which Rayleigh scattering is the only optical process

active may be taken as a reference. A useful index for quantifying the impairment of visibility by

the presence of atmospheric aerosol particles is the deciview (Pitchford and Malm, 1994). The

deciview index, deciV, is given as

deciV = 10 ln βext

0.01

(10-22)

where the value of 0.01 [km-1] is taken as a standard value for Rayleigh extinction. The aerosol

extinction coefficient, βext [km-1], must be calculated from ambient aerosol characteristics such as

index of refraction, volume concentration and size distribution. 

The extinction coefficient at a wavelength of λ for aerosol may be expressed as

βext =

3 π

2λ

Qext

α

dV

dlnα

dln α

–∞

∞

,

(10-23)
EPA/600/R-99/030

10-15

where the particle distribution is given in a lognormal form as

dV

dln α

= VT

A

π

1/2

exp – A ln2 α

αV

,

where α =

πD

λ

, αV =

πDgv

λ

, A =

1

2 ln

2

σg

.

(10-24)

VT is the total particle volume concentration, Qext, the Mie extinction efficiency factor, is a

function of α and the index of refraction of the particles. Willeke and Brockmann (1977) showed

that the behavior of the extinction coefficient is a smooth function of the geometric mean diameter

for the volume distribution Dgv, and the index of refraction. This smooth characteristic implies

that an accurate approximation to the Mie efficiency can be used in its place to reduce a very

computationally intensive task. The method of Evans and Fournier (1990), a highly accurate

approximation, is used to calculate Qext. 

Because routine measurements of aerosol species mass concentrations are often available, but

particle size distribution information is not, an additional method of calculating extinction has also

been included. This is an empirical approach known as reconstructed extinction. The method is

explained by Malm et al. (1994). The formula used here is a slight modification of their Equation

12 (Sisler, 1998).

βext [ 1/km] = 0.003* f(rh)*{ [ammonium sulfate] + [ammonium nitrate] }

+ 0.004 *[organic mass}

+ 0.01*[Light Absorbing Carbon] + 0.001*[fine soil]

+ 0.0006*[coarse mass]

(10-25)

In implementing this method, ammonium sulfate and ammonium nitrate were taken as the sum of

ammonium, plus sulfate, plus nitrate. Organic mass was taken as the sum of all organic species. 

Light absorbing carbon was taken as elemental carbon. Fine soil was taken as the unspeciated

portion of PM2.5 emitted species, and the coarse mass term was not implemented in CMAQ at this

time. The reason for not implementing coarse mass was that the uncertainty in the emissions was

deemed to be too large at the present time. The relative humidity correction, f(rh), is obtained

from a table of corrections with entries at one- percent intervals. The methodology for the

corrections is given in Malm et al. (1994).

10.6 Summary

The CMAQ aerosol component is a major extension of the RPM. Addition of the coarse mode

and primary emissions now allow both PM2.5 and PM10 to be treated. Ongoing work will improve

the representation of the production of secondary organic aerosol (SOA) material by including a

version of the method of Pankow (1994a,b) as discussed by Odum et al. (1996). This method,

based upon laboratory experiments, calculates the yield of SOA as a function of the amount of

organic material already in the particle phase. 
EPA/600/R-99/030

10-16

Kleeman et al. (1997) have shown that various source types have size and species information that

may be looked upon as a source signature. This assumes the availability of such source

characteristics for the entire modeling domain. As noted in Section 10.1.3, there are ongoing

discussions with those responsible for the national emissions inventory. As more information

becomes available, identification of source signatures may be possible for a larger domain than the

Los Angeles area, and an effort similar to Kleeman et al. (1997), albeit using a modal approach,

might be undertaken. Other planned improvements for primary particles are the inclusion of

marine aerosol as well as a better treatment of fugitive dust.

Future plans also include an intensive effort to evaluate the CMAQ aerosol component using

atmospheric observations from selected field studies in which aerosol particles were observed. 

Comparison with routine visual range observations during the field study periods will provide an

additional method of evaluation. 

10.7 References

Binkowski F. S., and U. Shankar, The regional particulate model 1. Model description and

preliminary results. J. Geophys. Res., 100, D12, 26191-26209, 1995.

Binkowski F. S., and U. Shankar, Development of an algorithm for the interaction of a

distribution of aerosol particles with cloud water for use in a three-dimensional eulaeian air quality

model, Presentation at the Fourth International Aerosol Conference, Los Angeles, CA, Aug. 29 -

Sept. 2, 1994.

Binkowski, F. S., S. M. Kreidenweis, D. Y. Harrington, and U. Shankar, Comparison of new

particle formation mechanisms in the regional particulate model, Presentataion at the Fifteenth

Annual Conference of the American Association for Aerosol Research, Orlando Florida, October

14-18, 1996.

Bower, K. N. and T. W. Choularton, A parameterisation of the effective radius of ice free clouds

for use in global climate models. Atmos. Res., 27, 305-339, 1992.

Bowman, F. M., C. Pilinis, and J. H. Seinfeld, Ozone and aerosol productivity of reactive

organics, Atmos. Environ., 29, 579-589, 1995.

Chang, J. S., F. S. Binkowski, N. L. Seaman, D. W. Byun, J. N. McHenry, P. J. Samson, W. R.

Stockwell, C. J. Walcek, S. Madronich, P. B. Middleton, J. E. Pleim, and H. L. Landsford, The

regional acid deposition model and engineering model, NAPAP SOS/T Report 4, in National

Acid Precipitation Assessment Program, Acidic Deposition: State of Science and Technology,

Volume I, Washington, D.C., 1990.

Chaumerliac, N., Evaluation des Termes de Captation Dynamique dans un Modele

Tridimensionel à Mesoechelle de Lessivage de L'Atmosphere, Thèse Présentée à L'Université de

Clermont II, U.E.R. de Recherche Scientifique et Technique, 1984.

Evans, T. N. and G. R. Fournier, Simple approximation to extinction efficiency valid over all size

ranges. Appl. Optics, 29, 4666-4670, 1990.
EPA/600/R-99/030

10-17

Gelbard, F., Y. Tambour, and J. H. Seinfeld, Sectional representations for simulating aerosol

dynamics. Jour.of Colloid and Interface. Sci., 76, 541-556, 1980.

Giauque, W. F., E. W. Hornung, J.E. Kunzler, and T. R. Rubin, The thermodynamics of aqueous

sulfuric acid solutions and hydrates from 15 to 300 K, J. Amer. Chem. Soc., 82, 62-67, 1960.

Harrington, D. Y. and S. M. Kreidenweis, Simulations of sulfate aerosol dynamics: Part I model

description, Atmos. Environ., 32, 1691-1700, 1998a.

Harrington, D. Y. and S. M. Kreidenweis, Simulations of sulfate aerosol dynamics: Part II model

intercomparison, Atmos. Environ., 1701-1709, 1998b.

Jacobson, M.Z. Development and application of a new air pollution modeling system-II. Aerosol

module structure and design, Atmos. Environ., 31, 131-144, 1997.

Kim,Y. P., J. H. Seinfeld, and P. Saxena, Atmospheric gas-aerosol equilibrium I. Thermodynamic

model, Aerosol Sci. and Technol., 19, 157-181, 1993a.

Kim,Y. P., J. H. Seinfeld, and P. Saxena, Atmospheric gas-aerosol equilibrium II. Analysis of

common approximations and activity coefficient calculation methods, Aerosol Sci. and Technol.,

19, 182-198, 1993b.

Kleeman, M.J., G.R. Cass and A. Eldering, Modeling the airborne particle complex as a sourceoriented external mixture. J. Geophys. Res., 102, 21355-21372, 1997.

Kulmala, M. , A. Laaksonen, and Liisa Pirjola, Parameterization for sulfuric acid/water nucleation

rates. J. Geophys. Res.,103, 8301-8307, 1998.

Leaitch, W. R., Observations pertaining to the effect of chemical transformation in cloud

on the anthropogenic aerosol size distribution, Aerosol Sci. and Technol., Vol. 25, pp 157-173,

1996.

Malm, W. C., Considerations in the measurements of visibility, J. Air Pollution Control Assoc.,

29, 1042-1052, 1979.

Malm, W. C., J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, Spatial and seasonal trends

in particle concentration and optical extinction in the United States, J. Geophys. Res., 99, 1347-

1370, 1994.

McElroy, M. W., R. C. Carr, D. S. Ensor, and G. R. Markowski, Size distribution of fine particles

from coal combustion, Science, 215, 13-19, 1982.

Middleton, P. B. and C. S. Kiang, A kinetic model for the formation and growth of secondary

sulfuric acid particles, J. Aerosol Sci., 9, 359-385, 1978.
EPA/600/R-99/030

10-18

Mozurkewich, M. The dissociation constant of ammonium nitrate and its dependence on

temperature, relative humidity, and particle size. Atmos. Environ., 27A, 261-270, 1993.

Nair, P. V. N. and K. G. Vohra, Growth of aqueous sulphuric acid droplets as a function of

relative humidity, J. Aerosol Sci., 6, 265-271, 1975.

Odum, J. R., T. Hoffman, F. Bowman, D. Collins, R.C. Flagan, and J.H Seinfeld, Gas/particle

partitioning and secondary organic aerosol yields. Environ. Sci. Technol., 30, 2580-2585, 1996.

Pandis, S. N., R. A. Harley, G. R. Cass, and J. H. Seinfeld, Secondary organic aerosol formation

and transport, Atmos. Environ., 26A, 2269-2282, 1992.

Pankow, J. F., An absorption model of gas/particle partitioning of organic compounds in the

atmosphere. Atmos. Environ., 28, 185-188, 1994a.

Pankow, J.F., An absorption model of gas/particle partitioning involved in the formation of

secondary organic aerosol, Atmos. Environ., 28, 189-193, 1994b. 

Pitchford, M. L. and W. C. Malm, Development and applications of a standard visual index,

Atmos. Environ., 28, 1049 - 1054, 1994.

Pratsinis, S. E., Simultaneous aerosol nucleation, condensation, and coagulation in aerosol

reactors, J. Colloid Interface Science, 124, 417-427, 1988.

Pruppacher, H. R. and J. D. Klett, Microphysics of Clouds and Precipitation, Reidel, Dordrecht,

Holland, 1978.

Saxena, P. and L. Hildemann, Water-soluble organics in atmospheric particles: a critical review of

the literature and application of thermodynamics to identify candidate compounds, J. Atmos.

Chem., 24, 57-109, 1996.

Saxena, P., L. M. Hildemann, P. H. McMurry, and J. H. Seinfeld, Organics alter hygroscopic

behavior of atmospheric particles, J. Geophys. Res., 100, 18755 - 18770, 1995.

Seinfeld, J. H., Atmospheric Chemistry and Physics of Air Pollution, Wiley, New York, 1986.

Shankar, U. and F. S. Binkowski, Sulfate aerosol wet deposition in a three-dimensional Eulerian

air quality modeling framework, Presentation at the Fourth International Aerosol Conference, Los

Angeles, CA, Aug. 29 - Sept. 2, 1994.

Sisler, J. Personal Communication

Slinn, W. G. N., Rate-limiting aspects of in-cloud scavenging, J. Atmos. Sci., 31, 1172-

1173, 1974.
EPA/600/R-99/030

10-19

Spann, J. F. and C. B. Richardson, Measurement of the water cycle in mixed ammonium acid

sulfate particles, Atmos. Environ., 19, 919-825, 1985.

Tang, I.N. and H.R. Munkelwitz, Water activities, densities, and refractive indices of aqueous

sulfates and sodium nitrate droplets of atmospheric importance, J. Geophys. Res., 99, 18801-

18808, 1994.

Van Dingenen, R. and F. Raes, Determination of the condensation accommodation coefficient of

sulfuric acid on water-sulfuric acid aerosol, Aerosol Sci. Technol., 15, 93-106, 1991.

Weber, R.J., J.J. Marti, P.H. McMurry, F.L. Eisele, D.J. Tanner, and A. Jefferson, Measurements

of new particle formation and ultrafine partilce growth rates at a clean continental site. J.

Geophys. Res.,102, 4375-4385, 1997.

Wesely, M. L., D. R. Cook, R. L. Hart, and R. E. Speer, Measurement and parameterization of

particulate sulfur dry deposition over grass. J. Geophys. Res., 90, 2131-2143, 1985.

Wexler, A. S., F. W. Lurmann, and J. H. Seinfeld, Modeling urban and regional aerosols: I.

Model development, Atmos. Envion., 28, 531-546, 1994.

Whitby, K. T., The physical characteristics of sulfur aerosols, Atmos. Environ., 12, 135-159,

1978.

Whitby, E. R.and P. H. McMurry, Modal aerosol dynamics modeling, Aerosol Sci. and Technol.,

27, 673-688, 1997.

Whitby, E. R., P. H. McMurry, U. Shankar, and F. S. Binkowski, Modal Aerosol Dynamics

Modeling, Rep. 600/3-91/020, Atmospheric Research and Exposure Assessment Laboratory, U.S.

Environmental Protection Agency, Research Triangle Park, N.C., (NTIS PB91- 161729/AS),

1991.

Willeke, K. and J. E. Brockmann, Extinction coefficients for multimodal atmospheric particle size

distributions, Atmos. Environ., 11, 995 - 999, 1977.

Youngblood, D.A. and S.M. Kreidenweis, Further development and testing of a bimodal aerosol

dynamics model. Colorado State University, Department of Atmospheric Sciences Report No.

550, 1994.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

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Table 10-1 Aerosol Species Concentrations

Units: mass [ μg m-3 ], number [ # m-3 ]

{ a1} ASO4 J Accumulation mode sulfate mass

{ a2} ASO4I Aitken mode sulfate mass

{ a3} ANH4J Accumulation mode ammonium mass

{ a4} ANH4I Aitken mode ammonium mass

{ a5} ANO3J Accumulation mode nitrate mass

{ a6} ANO3I Aitken mode aerosol nitrate mass

{ a7} AORGAJ Accumulation mode anthropogenic secondary organic mass

{ a8} AORGAI Aitken mode anthropogenic secondary organic mass

{ a9} AORGPAJ Accumulation mode primary organic mass

{a10} AORGPAI Aitken mode mode primary organic mass

{a11} AORGBJ Accumulation mode secondary biogenic organic mass

{a12} AORGBI Aitken mode biogenic secondary biogenic organic mass

{a13} AECJ Accumulation mode elemental carbon mass

{a14} AECI Aitken mode elemental carbon mass

{a15} A25J Accumulation mode unspecified anthropogenic mass

{a16} A25I Aitken mode unspecified anthropogenic mass

{a17} ACORS Coarse mode unspecified anthropogenic mass

{a18} ASEAS Coarse mode marine mass

{a19} ASOIL Coarse mode soil-derived mass

{a20} NUMATKN Aitken mode number

{a21} NUMACC Accumulation mode number

{a22} NUMCOR Coarse mode number

{a23} SRFATKN Aitken mode surface area

{a24} SRFACC Accumulation mode surface area

{a25} AH2OJ Accumulation mode water mass

{a26} AH2OI Aitken mode water mass
EPA/600/R-99/030

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Table 10-2. Equilibrium Relations and Constants

(Kim et al., 1993a)

Equilibrium Relation Constant K(298.15) a b Units

HSO4

–

(aq) ⇔ H

+

(aq) + SO4

2 –

(aq) H

+ SO4

2 –

γH

+γSO42 –

HSO4

–

γ HSO4

2 –

1.015E-02 8.85 25.14 mol / kg

NH3(g) ⇔ NH3(aq) NH3

(aq) γ NH3

PNH3

57.639 13.79 -5.39 mol / kg atm

NH3(aq) + H2O(aq) ⇔ NH4

+

(aq) + OH –(aq) NH4

+ OH–

γ NH+γ OH–

NH3(aq) γ NH3

a w

1.805E-05 -1.50 26.92 mol / kg

HNO3(g) ⇔ H

+

(aq) + NO3

–

(aq) H

+ NO3

–

γ H+γ NO3

–

PHNO3

2.511E06 29.17 16.83 mol2 / kg2atm

NH4NO3(s) ⇔ NH3(g) + HNO3(g) PNH3PHNO3

5.746E-17#-74.38#6.12#atm2

H2O(aq) ⇔ H

+

(aq) + OH–(aq) H

+ OH–

γH+γOH–

aw

1.010E-14 -22.52 26.92 mol2 / kg2

The constants a and b are used in the following to adjust for ambient temperature

K = K T0

exp a

T0

T

– 1 + b 1 + ln T0

T

–

T0

T

, T0= 298.15 [K]

#

 These values are only used by Kim et al. (1993a,b). The values used in the CMAQ are from Mozurkewich (1993):

K = exp 118.87 –

24084

T

– 6.025 ln T

where Mozurkevich reports in nanobars squared. This yields a value for the equilibrium constant of 43.11 [nb2] at 298.15 K.

EPA/600/R-99/030

10-23

Table 10-3. Organic Aerosol Yields in Terms of Amount of Precursor Reacted

(From Pandis et al. (1992) and Bowman et al. (1995))

Gas-Phase Organic Species Aerosol Yield

[μg m-3 / ppm(reacted)]

C8 and higher alkanes 380

Anthropogenic internal alkenes 247

monoterpenes 740

toluene 424

xylene 342

cresol 221
EPA/600/R-99/030

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Shawn J. Roselle, MD-80, Research Triangle Park, NC 27711. E-mail:

sjr@hpcc.epa.gov

**On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Chapter 11

CLOUD DYNAMICS AND CHEMISTRY

Shawn J. Roselle*

 and Francis S. Binkowski**

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, North Carolina 27711

ABSTRACT

Chapter 11 describes the cloud module that is currently incorporated into CMAQ. This module

simulates the physical and chemical processes of clouds that are important in air quality

simulations. Clouds affect pollutant concentrations by vertical-convective mixing, scavenging,

aqueous chemistry, and removal by wet deposition. The CMAQ cloud module includes

parameterizations for sub-grid convective precipitating and non-precipitating clouds and gridscale resolved clouds. Cloud effects on both gas-phase species and aerosols are simulated by the

cloud module.
EPA/600/R-99/030

11-1

( ) i

subcld

m

t

f mixing scav aqchem wetdep ∂

∂ ~ ,, , (11-2)

∂

∂

∂

∂

∂

∂

m

t

m

t

m

t

i

cld

i

subcld

i

rescld

= + (11-1)

11.0 CLOUD DYNAMICS AND CHEMISTRY

11.1 Background

Clouds play an important role in boundary layer meteorology and air quality. Convective clouds

transport pollutants vertically, allowing an exchange of air between the boundary layer and the

free troposphere. Cloud droplets formed by heterogeneous nucleation on aerosols grow into rain

droplets through condensation, collision, and coalescence. Clouds and precipitation scavenge

pollutants from the air. Once inside the cloud or rain water, some compounds dissociate into ions

and/or react with one another through aqueous chemistry (i.e., cloud chemistry is an important

process in the oxidation of sulfur dioxide to sulfate). Another important role for clouds is the

removal of pollutants trapped in rain water and its deposition onto the ground. Clouds can also

affect gas-phase chemistry by attenuating solar radiation below the cloud base which has a

significant impact on the photolysis reactions.

The Models-3/CMAQ cloud model incorporates many of these cloud processes. The model

includes parameterizations for several types of clouds, including sub-grid convective clouds

(precipitating and non-precipitating) and grid-scale resolved clouds. It includes an aqueous

chemistry model for sulfur, and includes a simple mechanism for scavenging.

11.2 Model Description

The cloud model can be divided into two main components, including the sub-grid cloud model

(subcld) and the resolved cloud model (rescld). For large horizontal grid resolutions, the grid

size will be larger than the size of a typical convective cloud, requiring a parameterization for

these sub-grid clouds. The sub-grid cloud scheme simulates convective precipitating and nonprecipitating clouds. The second component of the cloud model considers clouds which occupy

the entire grid cell and have been “resolved” by the meteorological model. The rate of change in

pollutant concentrations ( ) due to cloud processes is given by: mi

The terms on the right-hand side of Equation 11-1 are solved separately at different times. The

influence of sub-grid clouds are instituted once an hour while the resolved clouds impact

concentrations every synchronization timestep. Each subcomponent of the cloud model is

described in detail below.

11.2.1 Subgrid Convective Cloud Scheme
EPA/600/R-99/030

11-2

The current sub-grid cloud scheme in CMAQ was derived from the diagnostic cloud model in

RADM version 2.6 (Dennis et al., 1993; Walcek and Taylor, 1986; Chang, et al., 1987; Chang, et

al., 1990). Seaman (1998) noted that most convective parameterizations are based on the

assumption that “the area of an updraft is small compared to the area of the grid cell” and most

parameterizations can be used at grid resolutions a small as 12 km (Wang and Seaman, 1997). In

CMAQ, subgrid clouds are considered only for horizontal grid resolutions on the order of 12 km

or more. Seaman (1998) also pointed to a study by Weisman et al. (1997) that showed that

explicit cloud models can resolve convection for resolution finer than 5 km. Within CMAQ, for

resolutions of 4 km or less, vertical convection is assumed to be resolved at the grid level;

therefore, the resolved cloud model will be the only cloud scheme used at small grid scales.

The effects of sub-grid clouds on grid-averaged concentrations are parameterized by modeling

the mixing, scavenging, aqueous chemistry, and wet deposition of a “representative cloud”

within the grid cell. For all sub-grid clouds, a 1-hour lifetime (-cld) has been assumed. Sub-grid

clouds can be either precipitating or non-precipitating, and the non-precipitating subgrid clouds

are further categorized as pure fair weather (PFW) clouds and non-precipitating clouds

coexisting (CNP) with precipitating clouds.

The subgrid cloud model determines if precipitating or nonprecipitating clouds exist over each

grid cell. Precipitating clouds are simulated when the meteorological preprocessor (currently the

Mesoscale Model version 5 or MM5, Grell et al., 1994) indicates precipitation from its

convective cloud model. The CMAQ implementation differs from the RADM in that only the

convective precipitation amounts from MM5 are used to drive the subgrid precipitating cloud. 

RADM used the total precipitation (convective and nonconvective precipitation) to drive the

subgrid cloud model. In CMAQ, the nonconvective precipitation is used in the resolved cloud

model. Nonprecipitating clouds are modeled if the moisture and temperature profiles support the

development of a cloud (Dennis et al., 1993). Nonprecipitating clouds are modeled only when

the relative humidity of the source level is above 70% and the calculated cloud base is below

1500 m for PFW clouds or 3000 m for CNP clouds. For both precipitating and nonprecipitating

cloud types, the geometry of the cloud (base, top, and spatial extent) are determined next. The

cloud base is calculated by lifting a parcel of air from the cloud source level (the level between

the surface and 650 mb with the highest equivalent potential temperature) to the lifting

condensation level (LCL). The cloud top calculation depends upon the cloud type and

atmospheric stability. For precipitating clouds in unstable conditions, the cloud top is found by

following the moist adiabatic lapse rate from the cloud base up to the level where it becomes

cooler than the surrounding environment. For precipitating clouds under stable conditions, the

cloud top is set as the first layer above the cloud base in which the relative humidity falls below

65%, but limited to less than the 600 mb height. For nonprecipitating clouds, further restrictions

are placed on the cloud top. The cloud top calculation for nonprecipitating clouds uses the same

relative humidity criterion as the precipitating clouds, but the cloud top is allowed to extend up to

500 mb for CNP clouds and only to 1500 m for PFW clouds. If the atmosphere is unstable, the

nonprecipitating cloud top may be reduced in height if the parcel method calculated a lower

cloud top. The fractional cloud coverage calculations depend on cloud type and have been
EPA/600/R-99/030

11-3

m z f f m f mz f m i ( ) ( ) cld

ent side i

down

side i ent i

u p () () =− + 



 



 1 1 + − (11-3)

m

m z W z dz

W z dz

i

cld

i

cld

c

z

z

c

z

z

cbase

ctop

cbase

ctop

=

∫

∫

() ()

( )

(11-4)

m zt m zt [ ] m t

m t

i cfrac m z t cfrac cld i

cld i

cld

cld

i

cld

(, ) (, ) i

( )

( )

(, ) 0 0

0

0

+ = 0 1 + 















τ + −

τ (11-5)

described thoroughly by Dennis et al. (1993). For precipitating clouds, the model uses a

parameterization similar to approach of Kuo (1974). The fractional coverage parameterization

for the nonprecipitating clouds is based on relative humidity.

The convective cloud simulated by the sub-grid cloud model is considered to be composed of air

transported vertically-from below the cloud, entrained from above the cloud (for precipitating

clouds), and entrained from the sides of the cloud. Concentrations of pollutants for each layer of

the cloud are calculated by:

where fside is the fraction of entraining air originating from the side of the cloud. For

nonprecipitating clouds, no entrainment of air from above the cloud is allowed and therefore

fside=1. The entrainment, fent, is calculated by iteratively solving conservation and

thermodynamic equations (Dennis et al., 1993; Chang et al, 1990,1987; and Walcek and Taylor,

1986). The terms and represent the above and below cloud concentrations, mi

up

mi

down

respectively. Once the cloud volume has been determined, vertically-averaged cloud

temperature, pressure, liquid water content, total water content, and pollutant concentrations, are

computed with liquid water content (Wc) as the weighting function (gives the most weight to the

layers with the highest liquid water content). Thus, the average pollutant concentrations within

the cloud are calculated by:

With the averages over the cloud volume, the processes of scavenging, aqueous chemistry, and

wet deposition are considered. The final step in cloud mixing is the reapportioning of mass back

into individual layers. This is accomplished using cloud fractional coverage, initial in-cloud

concentrations, final in-cloud concentration, and the initial vertical concentration profile. For

precipitating clouds, the average pollutant concentration for the grid cell within the cloud layers

is computed by:
EPA/600/R-99/030

11-4

∂

∂ τ

α τ m

t

m

i e

cld

scav

i

cld

cld

i cld

=  −



 





− 1

(11-6)

α

τ

i

washout

i

TWF

H

=

+ 



 





1

1 (11-7)

TWF

W RT

H O

T

= ρ 2 (11-8)

τ

ρ

washout

T cld

HO r

W z

P = ∆

2

(11-9)

where cfrac is the fractional cloud coverage. There are variations on this equation for below

cloud, above cloud, and for nonprecipitating clouds.

11.2.1.1 Scavenging and Wet Deposition

Pollutant scavenging is calculated by two methods, depending upon whether the pollutant

participates in the cloud water chemistry and on the liquid water content. (1) For those

pollutants that are absorbed into the cloud water and participate in the cloud chemistry (and

provided that the liquid water content is > 0.01 g/m3

), the amount of scavenging depends on

Henry's law constants, dissociation constants, and cloud water pH. (2) For pollutants which do

not participate in aqueous chemistry (or for all water-soluble pollutants when the liquid water

content is below 0.01 g/m3

), the model uses the Henry's Law equilibrium equation to calculate

ending concentration and deposition amounts. The rate of change for in-cloud concentrations

(mi

cld) for each pollutant (i) following the cloud timescale (-cld) is given by:

where i is the scavenging coefficient for the pollutant. For subgrid convective clouds, -cld is 1

hour and for grid resolved clouds it is equal to the CMAQ’s synchronization timestep. For gases,

the scavenging coefficient is given by:

where Hi is the Henry’s Law coefficient for the pollutant, TWF is the total water fraction given

by:

where 'H2O is the density of water, is the mean total water content (kg/m3 W T ), R is the

Universal gas constant, and T is the in-cloud air temperature (K). The washout time, -washout

represents the amount of time required to remove all of the water from the cloud volume at the

specified precipitation rate (Pr), 

and is given by:

Here, °zcld is the cloud thickness.
EPA/600/R-99/030

11-5

α

τ

i

washout

= 1

(11-10)

i i

cld

wdep m P dt r

cld

= ∫

0

τ

(11-11)

The accumulation mode and coarse mode aerosols are assumed to be completely absorbed by the

cloud and rain water. Therefore, the scavenging coefficients for these two aerosol modes are

simply a function of the washout time:

The Aitken mode aerosols are treated as interstitial aerosol and are slowly absorbed into the

cloud/rain water. This process is discussed in detail in the aerosol chapter (Chapter 10).

The wet deposition algorithms in CMAQ were taken from the RADM (Chang et al., 1987). In

the current implementation, deposition is accumulated over 1-hour increments before being

written to the output file. The wet deposition amount of chemical species i (wdepi) depends upon

the precipitation rate (Pr) and the cloud water concentration (mi

cld):

Deposition amounts are accumulated for each of the modeled species, but the user specified

which species are written to the output file. This is handled in the Program Control Processor

(see Chapter 15).

11.2.1.2 Aqueous Chemistry

The aqueous chemistry model evolved from the original RADM model (Chang et al., 1987; and

Walcek and Taylor, 1986). The model considers the absorption of chemical compounds into the

cloud water; the amount that gas-phase species absorb into the cloud water depends on

thermodynamic equilibrium, while accumulation-mode aerosols are considered to have been the

nucleation particles for cloud droplet formation and are 100% absorbed into the cloud water. 

Then the model calculates the dissociation of compounds into ions, oxidation of S(IV) to S(VI),

and wet deposition. The species that participate in the aqueous chemistry are given in Table 11-

1. This version of the aqueous chemistry model differs from Walcek’s scheme in that it tracks

contributions from gases and aerosols separately. It also considers the scavenging of interstitial

aerosols, and it allows for variable-length cloud time scales.
EPA/600/R-99/030

11-6

Wz Qz Qz z C CR () () () = + [ ]ρ( ) (11-12)

Table 11-1. List of Species Considered in the Aqueous Chemistry Model

Gases Aerosols

SO2 SO4

=

 (Aitken & accumulation)

HNO3 NH4

+

 (Aitken & accumulation)

N2O5 NO3

-

 (Aitken, accumulation, & coarse)

CO2 Organics (Aitken & accumulation)

NH3 Primary (Aitken, accumulation, & coarse)

H2O2 CaCO3

O3 MgCO3

formic acid NaCl

methyl hydrogen peroxide Fe3+

peroxy acetic acid Mn2+

H2SO4 KCl

Number (Aitken, accumulation, & coarse)

11.2.2 Resolved Cloud Scheme

At any grid resolution, clouds may be resolved by the MM5, which could include stratus,

cumulus, or cirrus type clouds. The resolved clouds have been simulated by the MM5 to cover

the entire grid cell. No additional cloud dynamics are considered in CMAQ for this cloud type

since any convection and/or mixing would have been resolved and considered in the vertical

wind fields provided by MM5. A resolved cloud horizontally covers the entire grid cell and

vertically extends over the whole depth of the layer, thus and are equivalent in mi

cld

mi

resolved clouds. These clouds are activated in MM5 when the humidity is high enough for water

vapor to condense, and then MM5 computes cloud and rain water amounts according to any of

several microphysical submodels. Using the total of the condensed cloud water and rain water

reported by MM5, the CMAQ resolved cloud model then considers scavenging, aqueous

chemistry, and wet deposition. The average liquid water content in a model layer (z) W c for the

resolved cloud is given by:

where QC(z) is the cloud water mixing ratio (kg/kg), QR(z) is the rain water mixing ratio (kg/kg),

'(z) is the air density (kg/m3

). Precipitation amounts for resolved cloud layers, Pr(z), are derived
EPA/600/R-99/030

11-7

( ) ( )

( ) Pz R W z

W z dz r n

c

c

=

∫

















(11-13)

∂

∂

∂

∂

∂

∂

m

t

m

t

m

t

i

rescld

i

scav

i

aq chem

= + (11-14)

using the MM5 non-convective precipitation amounts (Rn), apportioned into individual model

layers with the vertical profile of condensed liquid water as follows:

Once quantities for precipitation rate, liquid water content, etc. have been calculated, then the

scavenging, aqueous chemistry, and wet deposition are solved using the same procedures as in

the subgrid clouds.

Several assumptions have been made in the current implementation of the resolved cloud model. 

(1) The lifetime of the resolved cloud computations varies based on the synchronization timestep

of CMAQ. (2) Following the method of operator splitting, the effect of the resolved clouds on

pollutant concentrations occurs at the end of the cloud lifetime, thus no exchange between layers

is permitted during the cloud life-cycle. (3) The pollutants, cloud water, and rain water are

uniformly distributed within the grid cell. Because of the separation of MM5 from CMAQ, we

do not have the information to do precipitation fluxes. Even if a complete cloud precipitation

model was developed within CMAQ, there is no guarantee that it would be consistent with what

was done in MM5.

11.3 Conclusions

One of the concepts for Models-3 was that multiple modules may exist for each physical process

of the air quality model. The implementation described here is the first module available for

modeling cloud physics and chemistry. Other subgrid cloud models (i.e., the Kain-Fritsch (1990,

1993) and Betts-Miller (1986)) are under consideration and may be included as optional modules

for CMAQ. In addition, a more detailed resolved cloud model is under development which will

include a microphysical submodel for following the evolution of the cloud (i.e., cloud droplet

formation, growth of rain droplets, and descent through model layers to the ground). It will also

consider resolved cloud lifetimes which extend beyond the CMAQ synchronization timestep,

thus maintaining the partition between gas and aqueous-phase pollutants during the gas-phase

chemistry calculations. The current implementation of the cloud model in CMAQ will be

evaluated using available datasets and will be used as a reference for evaluating future cloud

modules for CMAQ.
EPA/600/R-99/030

11-8

11.4 References

Betts, A.K. and M.J. Miller, 1986. A new convective adjustment scheme. Part II: Single column

tests using GATE wave, BOMEX, ATEX, and arctic air- mass data sets. Quarterly J. Roy.

Meteor. Soc., 112, 693-709.

Chang, J.S., R.A. Brost, I.S.A. Isaksen, S. Madronich, P. Middleton, W.R. Stockwell, and C.J.

Walcek, 1987. A three-dimensional Eulerian acid deposition model: Physical concepts and

formation. J. Geophys. Res., 92, 14681-14700.

Chang, J.S., P.B. Middleton, W.R. Stockwell, C.J. Walcek, J.E. Pleim, H.H. Lansford, F.S.

Binkowski, S. Madronich, N.L. Seaman, D.R. Stauffer, D. Byun, J.N. McHenry, P.J. Samson, H.

Hass., 1990. The regional acid deposition model and engineering model, Acidic Deposition:

State of Science and Technology, Report 4, National Acid Precipitation Assessment Program.

Dennis, R.L., J.N. McHenry, W.R. Barchet, F.S. Binkowski, and D.W. Byun, 1993. Correcting

RADM’s sulfate underprediction: Discovery and correction of model errors and testing the

corrections through comparisons against field data, Atmos. Environ., 26A(6), 975-997.

Grell, G.A., J. Dudhia, and D.R. Stauffer, 1994. A description of the fifth generation Penn

State/NCAR mesoscale model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 138 pp.

Kain, J.S. and J.M. Fritsch, 1990. A one-dimensional entraining/detraining plume model and its

application in convective parameterization. J. Atmos. Sci, 47, 2784-2802.

Kain, J.S. and J.M. Fritsch, 1993. Convective parameterization for mesoscale models: The KainFritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor.

Monogr., 46, Amer. Meteor. Soc., 165-170.

Kuo, H.L., 1974. Further studies of the parameterization of the influence of cumulus convection

on large-scale flow, J. Atmos. Sci., 31, 1232-1240.

Seaman, N.L., 1988. Meteorological Modeling for Air-Quality Assessments: A NARSTO Review

Paper, Submitted to Atmos. Environ.

Walcek, C.J. and G.R. Taylor, 1986. A theoretical method for computing vertical distributions of

acidity and sulfate production within cumulus clouds, J. Atmos. Sci 43, 339-355.

Wang, W. and N.L. Seaman, 1997. A comparison study of convective parameterization schemes

in a mesoscale model. Mon. Wea. Rev., 125, 252-278.

Weisman, L.M., W.C. Skamarock and J.B. Klemp, 1997. The resolution dependence of

explicitly modeled convective systems, Mon. Wea. Rev., 125, 527-548.
EPA/600/R-99/030

11-9

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

Chapter 12

METEOROLOGY-CHEMISTRY INTERFACE PROCESSOR (MCIP) FOR

MODELS-3 COMMUNITY MULTISCALE AIR QUALITY (CMAQ) MODELING

SYSTEM

Daewon W. Byun*

 and Jonathan E. Pleim**

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

Ruen Tai Tang

Dyntel Corporation

Research Triangle Park, NC 27711

Al Bourgeois

Lockheed Martin/U.S. EPA Scientific Visualization Center

Research Triangle Park, NC 27711

ABSTRACT

The Meteorology-Chemistry Interface Processor (MCIP) links meteorological models such as

MM5 with the Chemical Transport Model (CTM) of the Models-3 Community Multiscale Air

Quality (CMAQ) modeling system to provide a complete set of meteorological data needed for air

quality simulations. Because most meteorological models are not built for air quality modeling

purpose, MCIP deals with issues related to data format translation, conversion of units of

parameters, diagnostic estimations of parameters not provided, extraction of data for appropriate

window domains, and reconstruction of meteorological data on different grid and layer structures.

To support the multiscale generalized coordinate implementation of the CMAQ CTM, MCIP

provides appropriate dynamic meteorological parameters to allow mass-consistent air quality

computations. The current implementation of MCIP links MM5 meteorological data to CMAQ

CTM. Because its code has a streamlined modular computational structure, adapting the system to

other inputs only require inclusion of a reader module and coordinate related routines specific for

the meteorological model.

 

* On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Daewon W. Byun, MD-80, Research Triangle Park, NC 27711. E-mail:

bdx@hpcc.epa.gov

** On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.
EPA/600/R-99/030

12-1

12.0 METEOROLOGY-CHEMISTRY INTERFACE PROCESSOR (MCIP) FOR

MODELS-3 COMMUNITY MULTISCALE AIR QUALITY (CMAQ) MODELING

SYSTEM

12.1 Introduction

Models-3 Community Multiscale Air Quality (CMAQ) modeling system is a next generation

modeling system designed to handle research and application issues for multiscale (urban and

regional) and multi-pollutant (oxidants, acid deposition, and particulates) air quality problems. Its

Chemical Transport Model (CTM) uses a generalized coordinate system. To accommodate

meteorological inputs from a variety of meteorological models using different coordinate systems,

CMAQ CTM (CCTM) requires information about the coordinates and grid as well as the

meteorological data. The Meteorology-Chemistry Interface Processor (MCIP) links a

meteorological model with CCTM to provide a complete set of meteorological data needed for air

quality simulation. Because most meteorological models are not built for air quality modeling

purposes, MCIP takes care of many issues related to data format translation, conversion of units of

parameters, diagnostic estimations of parameters not provided, extraction of data for appropriate

window domains, and reconstruction of meteorological data on different horizontal and vertical

grid resolutions through interpolations as needed. Considering these functions, it is not difficult to

see that MCIP is a key processor in the Models-3 CMAQ system.

In the Models-3 CMAQ system, the role of MCIP is further expanded to enforce consistency

among the meteorological variables. The consistency among meteorological parameters and the

way they are utilized in a CTM greatly influence the success of air quality simulations. This issue

becomes a dominant concern for the CCTM, which uses a generalized coordinate system, because

it should be able to deal with data from different meteorological models that may or may not use

fully compressible formulations (or assumptions on the atmospheric dynamics such as hydrostatic

or nonhydrostatic approximation). Chapters 5 and 6 of this science document provide detailed

descriptions on the generalized coordinate system.

CMAQ’s MCIP provides similar functions as the meteorological preprocessor for Regional Acid

Deposition Model (RADM) (Chang et al., 1987, 1990). MCIP’s code has a streamlined

computational structure, incorporating many of the physical and dynamical algorithms necessary to

prepare meteorological inputs used by CMAQ. Some of the planetary boundary layer (PBL)

parameterizations are extensively updated subroutines of the RADM’s meteorological preprocessor

which was described in Byun and Dennis (1995). MCIP is highly modularized to accommodate

data from different meteorological models. This versatility is accomplished by allowing

incorporation of a different set of input modules for a specific meteorological model. At present,

two sets of input modules are available. One links to the output of Pensylvania State

University/National Center for Atmospheric Research (PSU/NCAR) Mesoscale Modeling System

Generation 5 (MM5) with CCTM and the other links to meteorological data already in the Models-3

input/output applications programming interface (I/O API) format. MM5 can be run either in

hydrostatic mode using a time dependent terrain-following hydrostatic pressure coordinate, or in

nonhydrostatic mode using a time independent terrain-following reference pressure coordinate.

For the details on how MM5 simulations are conducted and how the reference state is determined,

refer to Seaman et al. (1995), Seaman and Stauffer (1993), Dudhia (1993), Grell et al. (1994),

Stauffer and Seaman (1993), Tesche and McNally (1993), and Haagenson et al. (1994). To
EPA/600/R-99/030

12-2

characterize past atmospheric conditions properly, MM5 is usually run with Four Dimensional Data

Assimilation (FDDA) for air quality simulations. It incorporates the results of intensive

meteorological observations into the model simulations so that the uncertainties associated with

meteorological input for a CTM are minimized (Stauffer and Seaman, 1993; Seaman et al., 1995).

Different output data generated by the different options, such as dynamics cloud parameterization

and surface-PBL algorithms used for the operation of MM5 operation, can be handled by MCIP

accordingly.

This chapter provides a detailed description of the functions and data flow of MCIP and

formulations used for estimating parameters diagnostically. Although this chapter mainly describes

the current implementation of MCIP written for MM5, it also provides key information necessary

to build different MCIP versions for other meteorological models. It is hoped that developers of

different MCIP versions can concentrate their efforts to read in data files from different

meteorological models with minimal modifications for diagnostic routines and output processes.

Section 12-1 describes basic functions and data dependency of MCIP. Section 12-2 deals with

meteorological data types, coordinates, and grids. Section 12-3 contains descriptions of diagnostic

algorithms used for estimating parameters necessary for air quality simulation and Section 12-4

describes additional parameters needed for the generalized coordinate system. Section 12-5

provides key operational operational details, such as building and executing MCIP including how

to set up grids/domains and environmental variables for different runtime options. Refer to Figure

12-1 for the structure of the contents of the present chapter.
EPA/600/R-99/030

12-3

MCIP

Overview (Section 12.1)

OPERATION

MCIP Modules

Building MCIP

Landuse Data Meteorological

Model Outputs

Environmental

Variable Inputs

DATA

DEPENDENCIES

(Section 12.1.2)

FUNCTIONS

Data Types

Coordinates & Grids

(Section 12.2)

Providing Consistent

Meteorological Data

for CMAQ

Overview (Section 12.1)

(Section 12.5)

(Section 12.3)

(Section 12.5.1)

(Section 12.5.2)

(Section 12.5.3)

(Section 12.5.4)

Executing MCIP

Defining Grid &

D omain

Ability to

incorporate

meteorological

model output

having different

coordinates and

dynamics

Estimation

of Physical

Parameters

Meteorological Data

with Generalized

Coordinate System

(Section 12.4)

Providing boundary

layer parameters

missing from or

inconsistent with

meteorological

model output (e.g.,

PBL height,

deposition velocities,

cloud parameters )

Figure 12-1. Contents and Structure of Chapter 12

12.1.1 MCIP Functions

One of MCIP’s functions is to translate meteorological parameters from the output of a mesoscale

model (e.g., MM5) to the Models-3 I/O API format (Coats, 1996), which is required for

operations of Models-3 CMAQ processors. Some other necessary parameters not available from

the meteorological model are estimated with appropriate diagnostic algorithms in the program. The

key functions of MCIP are summarized below.

 Reading in meteorological model output files: 

The EPA-enhanced MM5 version (Pleim et al., 1997) generates not only the standard MM5 output

but also several additional files that contain detailed PBL, cloud, and surface parameters. MCIP

reads these files and stores the information in the memory for further processing. Essential header

information is passed to the Models-3 I/O API file header.

 Extraction of meteorological data for CTM window domain: 

In general, the CCTM uses a smaller computational domain than MM5. Also, MM5 predictions in

the cells near the boundary may not be adequate for use in air quality simulation. Therefore, MCIP

extracts only the portion of the MM5 output data which falls within the CCTM’s main domain and

boundary cells.
EPA/600/R-99/030

12-4

Interpolation of coarse meteorological model output for finer grid: 

When user requests meteorological data on a finer resolution grid than that simulated in the

meteorological model, MCIP interpolates profile data using simple bilinear interpolation.

 Collapsing of meteorological profile data if coarse vertical resolution data is 

requested: 

MCIP performs a mass-weighted averaging of data in the vertical direction. For example, 30-layer

meteorological data may be lumped into 15 layers, or 6 layers for the CCTM.

 Computation or passing through surface and PBL parameters: 

Depending on the user options, MCIP either passes through surface and PBL parameters simulated

by the meteorology model directly or diagnoses them using the mean wind, temperature, and

humidity profiles, surface data, and detailed landuse information available.

 Diagnosing of cloud parameters: 

When important parameters needed for processing cloud effects in the CCTM are not provided by

the meteorological model, MCIP diagnoses cloud information (i.e., cloud top, base, liquid water

content, and coverage) using a simple convective parameterization. The information can be used in

the CCTM to process aqueous-phase chemistry and cloud mixing as well as to modulate photolysis

rates that reflect the effects of cloud.

 Computation of species-specific dry deposition velocities: 

MCIP computes dry deposition velocities for important gaseous species using either diagnosed

PBL parameters or the surface/PBL information passed through from the meteorological model.

 Generation of coordinate dependent meteorological data for the generalized 

coordinate CCTM simulation: 

Many of the coordinate-related functions traditionally treated in a CTM have been incorporated as a

part of the MCIP functions. This change was necessary to maintain modularity of the CCTM

regardless of the coordinates used and to eliminate many coordinate-dependent processor modules

in the CCTM. By incorporating dynamically consistent interpolation methods and associated

subroutines in the CCTM, the dynamic and thermodynamic consistencies among the

meteorological data can be maintained even after the temporal interpolations.

 Output meteorological data in Models-3 I/O API format: 

MCIP writes the bulk of its two- and three-dimensional meteorological and geophysical output data

in a transportable binary format using the Models-3 input/output applications program interface

(I/O API) library.
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12-5

12.1.2 MCIP’s Data Dependency

MCIP processes meteorological model output files in order to provide environmental data needed

for the other computational subsystems in Models-3 CMAQ. Landuse data is also required to

generate additional meteorological information needed for air quality simulations. MCIP utilizes

this and profiles of temperature, moisture, and wind components to estimate parameters for the

turbulence and surface exchange characteristics. When the meteorological model computes all the

necessary information, it can be passed through the MCIP as well. The inputs for MCIP consist of

operational inputs and meteorological model output files. These inputs are described below.

12.1.2.1 Environmental Variable Inputs

The user can select a computational path among the internal process options and define parameters

in MCIP output files by specifying several UNIX environmental variables. These settings allow

MCIP to be configured to fit a particular meteorological model simulation and to follow process

steps requested by the user. First, it defines the mode of meteorological model run to check if the

meteorology data linked have been generated using options compatible with the MCIP. Then it

assigns filenames of meteorology model output files, defines CTM model window domain offset

coordinates in terms of the meteorological model grid definition, determines simulation time and

duration of the MCIP, and assigns appropriate landuse data file type. Refer to Section 12-5 and

Table 12-10 for the details of the UNIX environmental variables used in MCIP for these settings.

12.1.2.2 Meteorology Model Outputs

It is anticipated that MCIP will include a unique set of reader modules for a variety of

meteorological models. Most of the idiosyncrasies of meteorological data from a specific

meteorological model should be resolved in this module. They include the number of files,

information on the data such as where they are stored and in what format, etc. In the following,

we provide a description of the output files from MM5 as an example.

 Standard MM5 output 

The standard MM5 time-stepped grid-domain output contains most of the key meteorological data

written by the MM5 subroutine OUTTAP. Each time-step includes a header record. This header is

read by MCIP at each time-step, but only the header from the first time-step is used and the

subsequent headers are ignored. Data following each header consist of two- and three-dimensional

arrays. The time-step interval for the meteorological data is taken from the header record on the

first time-step.

 EPA-added MM5 output 

EPA and MCNC added two more output files for additional information to facilitate air quality

modeling. One includes additional two-dimensional boundary layer parameters and flux values

and the other contains the detailed Kain-Fritsch (Kain and Fritsch, 1993) cloud data file, which

describes locations and cloud lifetimes of convective clouds. Currently, only the first file is used

to process CMAQ dry deposition module options and the second file is not actively used because
EPA/600/R-99/030

12-6

the CCTM does not yet support a corresponding aqueous-phase Kain-Fritsch cloud mixing

module.

12.1.2.3 Landuse Data

MCIP requires landuse data that define surface characteristics in order to compute dry deposition

velocities and other PBL parameters. Depending on the PBL and dry deposition modules desired,

the needs for landuse data vary. The RADM dry deposition algorithm (Wesely, 1989) needs 11-

category fractional landuse data. On the other hand, the new CMAQ deposition algorithm requires

cell-averaged parameters defining surface exchange characteristics (i.e., landuse dependent

parameters). The latter algorithm assumes that the landuse dependent subgrid effects are processed

in the meteorology modeling system. To avoid incorrect averaging of the land-surface parameters,

it distinguishes a dominant water cell from other landuse types.

Table 12-1. Relations Among MM5, CMAQ/RADM, and USGS Landuse Categories

MM5 MM5 Category MCIP CMAQ/RADM

Category

USGS USGS Category

1 Urban Land 1 Urban Land 1 Urban/built up

2 Agriculture Land 2 Agriculture 2 Dry cropland & pasture

3 Irrigated cropland & pasture

4 Mixed dryland/irrigated pasture

3 Range-Grassland 3 Range 7 Grassland

8 Shrubland

9 Mixed shrubland/grassland

10 Chaparral

4 Deciduous Forest 4 Deciduous Forest 12 Broadleaf deciduous forest

16 Deciduous coniferous forest

5 Coniferous Forest 5 Coniferous Forest 13 Evergreen coniferous forest

14 Sub alpine forest

17 Evergreen broadleaf

6 Mixed Forest/Wet

Land

6 Mixed Forest and

Wet Land

6 Woodland/cropland mosaic

15 Mixed forest

7 Water 7 Water 18 Water

8 Marsh or Wet Land 9 Nonforest Wet

Land

19 Herbaceous

20 Forested wetlands

9 Desert 11 Rock, Open Shrub 21 Barren or sparsely vegetated

10 Tundra 8 Barren Land 22 Shrub & brush tundra

23 Herbaceous tundra

24 Bare ground tundra

25 Wet tundra

26 mixed tundra

11 Permanent Ice 7 Water 27 Perennial snowfields or glaciers

12 Tropical Forest 3* Range*

13 Savannah 3 Range 11 Savannah

None 10 Mixed

Agriculture/Range

Land

5 Grassland/cropland mosaic

* Mapping “Tropical Forest” to “Range” is not appropriate in most locations.
EPA/600/R-99/030

12-7

Currently, MCIP accepts four different types of landuse data. Two types of landuse input (one

from MM5 directly, or the other from TERRAIN, a preprocessor for MM5 system) contain 13-

category data. The third one is a preprocessed landuse data set in an ASCII file. Recently, we

added a landuse processor (LUPROC) for the USGS vegetation information (described below) to

improve landuse data quality. For the case of MM5, the percentages of MM5’s 13 landuse

category are transformed into the CMAQ/RADM’s 11-category fractions in the landuse reader

module. The USGS vegetation category is also transformed into the 11-category fractions. Table

12-1 provides the conversion rules for landuse types from MM5 13-category, and USGS 27

(http://edcwww.cr.usgs.gov/landdaac/glcc/ nadoc1_1.html) category to CMAQ/RADM’s 11-

category. The USGS North America land cover characteristics data base has 1-km nominal spatial

resolution and is based on 1-km AVHRR data spanning April 1992 through March 1993. This

data base has been adapted to the CMAQ’s base map projection which uses Lambert conformal

projection with origins at latitude 40° N and longitude 90° W.

 Landuse Processor (LUPROC) 

CMAQ’s Landuse Processor (LUPROC) is a special processor that provides a high-resolution

landuse data base for the system. MCIP requires landuse data that define surface characteristics to

compute dry deposition and other PBL parameters. Depending on the PBL and dry deposition

modules desired, the needs for the landuse data are somewhat different.

LUPROC windows out the landuse data for the user-defined domain and converts percentages of

27 vegetation categories in the database into the fractional landuse data in RADM’s 11-category.

The output of the LUPROC should have the same resolution as the CCTM domain and the

LUPROC domain should include the boundary cells in addition to the CCTM’s computational

domain. In the near future, MM5 will be upgraded to allow use of the USGS land cover

characteristic data as an option. When the CMAQ dry deposition algorithm is used and necessary

PBL parameters are provided by the MM5 directly, LUPROC will not be needed.

12.1.3 Computational Structure

The MCIP data flow diagram, Figure 12-2, shows the key processing sequences. First, MCIP

executes the one-time processes such as: reading the header, processing other operational

information for the meteorological output, reading appropriate landuse data, and generating time

independent MCIP output files. Then, MCIP loops through the time stepped (hourly or subhourly depending on the meteorology data) input data from a meteorology model performing the

functions described above. The processing sequence of MCIP is summarized below:

• GETMET: reads and extracts meteorology data from standard MM5 output for the CCTM

window domain, converts variables into SI units and process special files (e.g., twodimensional surface/PBL data and Kain-Fritsch cloud files);

• PBLPKG/PBLSUB: computes PBL parameters using diagnostic method if desired;

• BCLDPRC_AK: computes diagnostic convective cloud parameters if needed;

• SOLAR: computes solar radiation parameters;

• RADMDRY/M3DDEP: computes dry deposition velocities; and
EPA/600/R-99/030

12-8

• METCRO_OUT & METDOT_OUT: computes additional meteorology data required for the

generalized CTM, interpolates mean profile data into finer grid resolution if needed, and

output Models-3 I/O API meteorology files.

START

• read met. data

• reconcile coordinate

• unit adjustment

• horizontal interpolation

• process special files

 (e.g., 2D met. & cloud files)

• compute Jacobian, entropy, density

GRID_OUT

BCLDPRC_AK

CLOUD

NO

YES

METCRO_OUT

METDOT_OUT

END

CONTINUE

GETMET

FIRST

TIME YES

NO

CALPBL

YES NO

PBLPKG PBLSUP

DEPV_OP

RADMDRY M3DRY

GETLUSE

compute all PBL parameters supplement PBL parameters

MET3DSUP

get env. variables

• complete met. data

SOLAR

Figure 12-2. Flow Chart of MCIP Showing Key Data Processing Sequence.
EPA/600/R-99/030

12-9

12.2 Data Types, Coordinates, and Grids

MCIP’s essential role is to provide consistent meteorological data for the CMAQ modeling system.

Therefore, it is very important to understand the vertical coordinate used in the meteorological

modeling system. For example, MM5 can be used either in hydrostatic mode, in which the

hydrostatic pressure (time dependent) is used to define the terrain-influenced vertical coordinate, or

in nonhydrostatic mode, where a reference hydrostatic pressure (time independent) in a normalized

height form is used as the vertical coordinate. Many parts of current MCIP code deal with these

differences in the vertical coordinate specifically. In the following we provide technical

information related with coordinates and grids used in MCIP.

12.2.1 Meteorological Data Types

Many different combinations of approximations are used for describing the atmosphere in

meteorological models. Therefore, classification of MCIP output parameters based on detailed

classification of vertical coordinate types (such as geometric height, pressure, terrain-following

coordinates, etc.), and their application approximations (such as hydrostatic and nonhydrostatic),

can be exceedingly complex for the CTM with generalized coordinate implementation. Unlike

previous use of detailed classification of meteorological coordinates for determining meteorological

data type, we classify the coordinate types mainly based on the temporal dependency of the

Jacobians (explained later). The benefit of this distinction is obvious. For example, a height

coordinate which is time independent may require only a time constant file for describing the

vertical coordinate while a dynamic pressure coordinate requires several parameters related with the

coordinate description that needs to be stored in a time dependent file.

A similar distinction is made based on the need for describing data in different horizontal positions,

such as flux-point data for horizontal wind components and cross-point for most other scalar

parameters. For MM5, two horizontal wind components are defined at so-called ‘dot’ points while

all other scalar values are at ‘cross’ points, following Arakawa-E grid definition. Refer to Figure

12-3 for the definitions of Arakawa C-grid and E-grid (Mesinger and Arakawa, 1976). For the

CCTM, certain flux data are defined on the Arakawa C-grid in which the flux points are not

collocated in xˆ

1

- and xˆ 2 -directions. Therefore, MCIP interpolates MM5’s dot-point wind

components linearly and multiplies the result with the two-point averaged density to provide the

flux-point momentum component data. Both the flux-point and dot point data require array sizes

larger than the cross-point data by one cell in each horizontal direction.

CMAQ utilizes contravariant wind components, instead of the regular wind components, to advect

tracer species. Figure 12-4 shows that the east-west component of the contravariant wind field, uˆ ,

is placed at the xˆ

1

-direction flux points (marked with the square symbol) and the north-south ( xˆ 2 -

direction) component of the contravariant wind field, vˆ, is placed at the xˆ 2 -direction flux points

(marked with the triangle symbol). The vertical wind component is defined at the full-layer height.

The Models-3 I/O API requires individual data components to have exactly the same temporal and

spatial dimensions in a file. Because the flux-point data and dot-point data both need additional

column or row positions, we can combine them together in a so-called DOT file, which is larger

than the CRO file by one cell for each horizontal direction. It is important to note that because the
EPA/600/R-99/030

12-10

flux points are different from the dot-points, they must be shifted by a half cell east or north

(depending on whether they are square-point or triangle-point flux values) for graphical

visualization of the flux-point parameters.

s

ρv

ρu

ρv ρv ρv

ρv ρv

ρv ρv ρv

ρv ρv ρv

s

s s s

s

s s s

ρu ρu ρu

ρu ρu ρu ρu

ρu ρu ρu ρu

s

u,v

s

s s s

s

s s s

u,v u,v u,v

u,v u,v u,v u,v

u,v u,v u,v u,v

u,v u,v u,v u,v

( C) ( B)

Figure 12-3. Two Different Grid Point Definitions, Arakawa C- and B-grids, Used in MCIP.

u and v are horizontal wind components, s represents a scalar quantity, and ρ is density of air. For

MM5, p*

 is used instead of ρ.

k+1/2

k-1/2

k

l l+1/2

m

m+1/2

m-1/2

xˆ

1

xˆ 2

xˆ 3

l-1/2

Figure 12-4. Computational Grid Points and Corresponding Indices Used in MCIP.

Markers are for dot points ( ), cross points ( ), x-direction flux points ( ), y-direction flux

points ( ), and vertical cross point at layer interface ( ).
EPA/600/R-99/030

12-11

Furthermore, when these two flux components are assigned to form vectors in a visualization

program like PAVE (Thorpe, 1996), the starting points of the vectors in the visualization are

relocated at the dot-points although the two components are actually not collocated there.

Data for the boundary cells are defined with a special I/O API boundary data type. Depending on

the need to describe boundary mass flux accurately, one may want to have a boundary domain with

NTHIK cells (see Figure 12-5). The boundary grid is represented as the external perimeter to the

main grid. This perimeter is NTHIK cells wide (where you may use a negative NTHIK to indicate

an internal perimeter as used by such air quality modeling systems ROM and RADM). The

boundary array is dimensioned in terms of the sizes of the arrays surrounding the main domain.

Current Models-3 CMAQ system uses NTHIK=1 throughout the system components.

Finally, the dimensionality of the parameters (i.e., whether they contain three-dimensional or twodimensional information) is used to distinguish the data type of meteorological parameters. In

vertical direction, we define half and full layer positions based on the values of the generalized

vertical coordinate, ( xˆ 3 ). Vertical wind component and flux values are examples of the full-layer

parameters. Although full-layer data require one more data point vertically, often the flux values at

the bottom boundary (i.e., at the lowest full-layer) are zero. Therefore, we do not need to use

additional data types for these, as long as we save the non-zero lowest full-layer data in a

corresponding two-dimensional data type file separately. (Refer to Table 12-2 for dimensions used

for each grid points.) Because a file represents a set of data with the same data type (with only a

few exceptions) in the Models-3 system, locating meteorological parameters from an appropriate

I/O API file is relatively easy. Table 12-3 summarizes the possible data types for the

meteorological parameters. Depending on the choice of coordinates and grids, some of data types

may not be relevant. For example, the current version of MCIP does not use GRID_DOT_3D and

MET_DOT_2D data types. Appendix 12A provides the list of MCIP output parameters in each

data file.
EPA/600/R-99/030

12-12

49 50 51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 71 72

1 2 3 4 5 6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24

c(-1)

26

28

30

32

34

36

38

40

42

44

46

48

25

27

29

31

33

35

37

39

41

43

45

47

74

76

78

80

82

84

86

88

90

92

94

96

73

75

77

79

81

83

85

87

89

91

93

95

r(-1)

c(0) c(1) c(2) c(3) c(4) c(5) c(6) c(7) c(8) c(9) c(10) c(11) c(12) =NCOLS+NTHIK

r(0)

r(1)

r(2)

r(3)

r(4)

r(6)

r(7)

r(8)

r(9)

r(10)

r(11)

r(12)

r(5)

x(1) x(2) x(3) x(4) x(5) x(6) x(7) x(8) x(9) x(10) x(11) x(12) x(13) x(14)

=NCOLS+2*NTHIK

y(1)

y(2)

y(3)

y(4)

y(5)

y(6)

y(8)

y(9)

y(10)

y(11)

y(12)

y(13)

y(14)

y(7)

=NROWS+NTHIK

=NROWS+2*NTHIK

NTHIK

Boundary Component-S

Boundary Component-E

Boundary Component-N

Boundary Component-W

NCOLS_EXT

NROWS_EXT=NROWS+2*NTHIK

=NCOLS+2*NTHIK

NCOLS

NROWS

(XORIG, YORIG)

Note: Individual boundary component grids are treated as a I/O API 2-D file

S(1:NCOLS+NTHIK, 1-NTHIK:0)

E(NCOLS+1:NCOLS+NTHIK, 1:NROWS+NTHIK)

N(1-NTHIK:NCOLS, NROWS+1:NROWS+NTHIK)

W(1-NTHIK:0, 1-NTHIK:NROWS)

MAIN GRID (NCOLS, NROWS) = (10,10)

Figure 12-5. Grid Data Structure for Models-3/CMAQ Showing Main Grid and Boundary

Components. Here NTHIK=2, NCOLS=10, NROWS=10 are used for the illustration.
EPA/600/R-99/030

12-13

Table 12-2. Dimensions and Indices for Grid Points used in MCIP and CCTM

Dot-Point

(start: end)

dimension

index

Cross-Point

(start: end)

dimension

index

xˆ

1

-

direction

Flux Point

xˆ 2 -direction

Flux Point

Full-Layer

(start: end)

dimension

index

Half-Layer

(start: end)

dimension

index

xˆ

1 (1:NCOLS+1)

NCOLS+1

l±1/2

(1:NCOLS)

NCOLS

l

(1:NCOLS+1)

NCOLS+1

l±1/2

(1:NCOLS)

NCOLS

l

N/A N/A

xˆ 2 (1:NROWS+1)

NROWS+1

m±1/2

(1:NROWS)

NROWS

m

(1: NROWS )

NROWS

m

(1: NROWS +1)

NROWS+1

m±1/2

N/A N/A

xˆ 3 N/A N/A N/A N/A (0:NLAYS)

NLAYS+1

k±1/2

(1:NLAYS)

NLAYS

k

Table 12-3. Classification of Meteorological Data Types in the CMAQ System.

Data types GRID_DOT_3D and MET_DOT_2D (in gray color) are not used in CMAQ currently.

Time Independent Time Dependent

GRID_CRO_2D GRID_CRO_3D MET_CRO_2D MET_CRO_3D

GRID_DOT_2D GRID_DOT_3D MET_DOT_2D MET_DOT_3D

GRID_BDY_2D GRID_BDY_3D MET_BDY_2D MET_BDY_3D

12.2.2 Coordinates

12.2.2.1 Horizontal Coordinates and Grid

MCIP can be configured with horizontal coordinates based on conformal map projections, such as

Lambert Conformal, Polar Sterographic, and Mercator. Table 12-4 summarizes the necessary

information for the description of the conformal map projections as defined in Models-3 I/O API.

To generate I/O API files, which require exact definitions of the grid and coordinate system, users

need to provide all the necessary map projection information in addition to vertical coordinate and

layering definitions. The Models-3 CMAQ system uses square cells for the horizontal grid

representation. A modeling domain is defined with the integer multiples of the square cells in E-W

(column-wise) and N-S (row-wise) directions. Although a rectangular cell shape can be handled

by the I/O API, the fractional time splitting approach used for the modularization of CTM

processes requires use of square grid to maintain the accuracy of the finite differencing algorithms

consistently. The effect of different horizontal coordinate is reflected in the values of the map scale
EPA/600/R-99/030

12-14

factor. Because of the need to couple the map scale factor (m) with other state variables and wind

components, MCIP provides map scale factor for both the dot- and cross-points.

Table 12-4. Map Scale Factors and Parameters Defining Horizontal Coordinates in Models-3 I/O

API (Coats, 1996)

Coordinate ID in

Models-3

I/O API

Map Parameters Map Scale (m) Note

lat.-long. LATGRD3=1 N/A N/A

m = 1

(x x ˆ , ˆ ) 1 2 =(long,lat) are in

degrees

Lambert LAMGRD3=2 Pα = φ1 ≤ Pβ = φ2

two latitudes that

determine the

projection cone.

Pγ = λo

, central

meridian

m

n

= −

−

−

−





 



 sin( / )

sin( / )

tan( / / )

tan( / / )

π φ

π φ

π φ

π φ

2

2

4 2

4 2

1

1

n = −

−





 



 ln sin( / )

sin( / )

π φ

π φ

2

2

2

1

• −

−





 









 





−

ln tan( / / )

tan( / / )

π φ

π φ

4 2

4 2

2

1

1

(x x ˆ cent cent , ˆ )(,) o o

1 2 = λ φ

for the center of

coordinate system.

(x x ˆ , ˆ ) 1 2 are in meters

Mercator MERGRD3=3 Pα = φo , Pβ = λo :

latitude longitude of

coordinate origin

within the tangent

circle.

Pγ : angle between

cylinder axis and the

North polar axis

m o = cos

cos

φ

φ (x x ˆ cent cent , ˆ )(,) o o

1 2 = λ φ

for the center of

coordinate system.

(x x ˆ , ˆ ) 1 2 are in meters

StereographicSTEGRD3=4 Pα = φo , Pβ = λo :

latitude and longitude

of the point of

tangency.

Pγ : angle from true

north to xˆ 2

-axis

m o = +

+

1

1

sin

sin

φ

φ (x x ˆ cent cent , ˆ )(,) o o

1 2 = λ φ

for the center of

coordinate system.

(x x ˆ , ˆ ) 1 2 are in meters

UTM UTMGRD3=5 Pα is the UTM zone

P P β γ , not used

m = 1 (x x ˆ cent cent , ˆ ) 1 2 are offset

from the UTM coordinate

origin.

(x x ˆ , ˆ ) 1 2 are in meters

12.2.2.2 Vertical Coordinates and Grid

The Models-3 CMAQ system allows many popular vertical coordinates used in meteorological

models. We expect that the Models-3 I/O API will be extended to include several other vertical

coordinates. The I/O API follows the definitions of vertical coordinates as used in meteorological

models. However, in CMAQ the vertical coordinates are redefined to increase monotonically with

height. This precaution is needed because the CMAQ code is expected to handle generalized

coordinate system. We found that this constraint in the vertical coordinate is extremely useful for
EPA/600/R-99/030

12-15

the implementation of CTM in the generalized coordinate system by removing possible sign errors

wherever vertical differentiations are involved. For example, the Jacobian information for a

coordinate can be directly used to replace some of the derivatives involved with the generalized

vertical coordinate. This internal change does not require redefinition of the vertical coordinates in

the MCIP output files. The impact of this constraint is limited to an include file that defines the

coordinates and vertical layers. In a typical Models-3 operation, this include file is automatically

generated by the system framework through the use of the coordinate/grid manager. In the

following two typical application examples are presented; one for the time dependent coordinate

and the other for time independent coordinate.

 Time dependent hydrostatic sigma-pressure coordinate 

For the MM5 system, this coordinate is used when the hydrostatic option is chosen. In general,

this coordinate can be used not only for the hydrostatic atmosphere simulations but also for

nonhydrostatic cases. For example, when a regional scale hydrostatic meteorological model

provides hydrostatic values, the same coordinate can be used in a nonhydrostatic nested model as

described by Jaung (1992). In MCIP implementation, we should view this coordinate as an

example of processing meteorological data with a dynamic vertical coordinate definition rather than

an example of a hydrostatic coordinate.

The CCTM utilizes a generalized coordinate system that allows construction of the vertical layering

consistent with the meteorological coordinate used. However, to maintain the vertical coordinate

definition monotonically increasing with height, the coordinate definition for the CCTM has been

modified as:

ˆ  ̃ x

p

3 = ≡− ξ σ 1 ; σ  ̃ *

 ̃

 ̃

 ̃

 ̃ p

T

s T

T p p

p p

p p

p = −− = − (12-1)

where px x x t  ̃( ˆ , ˆ , ˆ , ) 123 is the hydrostatic pressure, pT is the pressure at the model top which is held

constant, pxxt  ̃ ( ˆ , ˆ , ) s

1 2 is the surface pressure, and  ̃  ̃ * p pp = −s T . Because the pressure used in the

definition of the vertical coordinate is in hydrostatic balance, we have:

∂

∂ ρ  ̃  ̃ p

z = − g (12-2)

The Jacobian is then defined as:

J x

z p

p

z

p

g xˆ *

* ˆ

 ̃

 ̃  ̃

 ̃ 3

3 1 1

1 ≡ =− =

− −

∂

∂

∂

∂ ρ , (12-3)

and it is time dependent because the surface pressure and air density are time dependent.

 Time independent reference hydrostatic sigma-pressure coordinate 

In MM5 this coordinate is specifically used for the simulation of the nonhydrostatic atmosphere.

The layer structure is entirely different from the case when hydrostatic option is used. The
EPA/600/R-99/030

12-16

coordinates defined with this option are time independent and have very similar characteristic to

those of the normalized geometric height coordinates. The only difference is that the vertical layer

thickness is defined with a nonlinear function of the geometric height. Here, we should view this

coordinate as an example of processing meteorological data with time independent vertical

coordinate.

The terrain-following reference hydrostatic pressure (σ po ) coordinate, again in a monotonically

increasing form, is given as:

xˆ po

3 = ≡− ξ σ 1 ; σ p

o T

os T

o T

os

o

p p

p p

p p

p = −− = −

* (12-4)

where pxxx o ( ˆ , ˆ , ˆ ) 123 is the hydrostatic pressure of the reference atmosphere, pT is the pressure at

the model top, p xx os( ˆ , ˆ ) 1 2 is the reference surface pressure which is determined by the topographic

height zs , and pp p o os T

* = − .

Because the reference atmosphere is in hydrostatic balance, we have:

∂

∂ ρ pz

g o = − o (12-5)

The Jacobian is then defined as:

J x

z p

p

z

p

g x

o

o o

o

ˆ *

* ˆ 3

3 1 1

1 ≡ =− =

− −

∂

∂

∂

∂ ρ (12-6)

and it is time independent because it is a function of the time-independent surface pressure and the

density of the reference atmosphere. Here, the vertical coordinate z represents a height above the

lowest point in a modeling domain, or the mean sea level (MSL) height if there is no place lower

than the MSL. Usually, this type of vertical coordinate accompanies with a simple description of

reference temperature profile of the base state. For example, in MM5 the base temperature profile

is defined with a simple expression:

Tz T A p z

p o os

o

oo

( ) ln ( ) = + 



 



 (12-7)

where the reference values are chosen such thatTos is a sea level reference temperature in K, poo =

1000 mb = 105

 Pascal, and A, which is set to be 50 K, is a measure of atmospheric lapse rate

represented in temperature difference for the e-folding depth. With Equations 12-5 and 12-7 and

the Equation of State, we could relate the reference pressure in terms of height z in a differential

equation:
EPA/600/R-99/030

12-17

d pz

dz

g

R T A p A pz

o

os oo o

ln ( )

[ ln( )] ln( ( )) = − − +

1 (12-8)

which can be readily solved for p z o ( ) by the separation-of-variables technique. The solution is a

quadratic equation in terms of ln po . For typical tropospheric conditions, the base pressure can be

related with the geometric height by taking the positive square root term:

p z

b b Ac

A o ( ) exp = −+ −















2 2 (12-9)

where bT A p = − os oo (ln ) , and c g

R z Ap bp =− + oo oo [ (ln ) (ln )] 12

2 .

Equation 12-9 shows that p z o ( ) is a monotonic, but nonlinear, function of z.

12.2.3 Modification of Grid Structure

In CMAQ, the horizontal and vertical coordinate information (such as the map projection

parameters) for CTM simulation domains are required to be exactly the same as (or a derivative of)

the master coordinates used in the meteorological model simulation. However, the horizontal grid

structures of the CTM domains can be redefined depending on the need for air quality simulations.

Here, the concept of grid family is introduced. It is as a set of grid domain specifications with the

following properties:

1. the same coordinate origin and map projection;

2. a window domain for the parent domain; or

3. a nest (multi-stage) domain from a window or the parent domain.

The Models-3 I/O API file header helps to describe the horizontal grid and coordinates

unambiguously to position the background map correctly and to provide relations among the

members (multi-stage nesting domains) of the grid family. Only with a limited manner, the user is

allowed to modify the grids in the vertical directions because of the concern that ad hoc

interpolation may destroy the integrity of the meteorological data.

12.2.3.1 Windowing

The windowing functions in MCIP extract MM5 output for a CCTM window domain. As a rule of

thumb, a CCTM uses a smaller computational domain than the domain used by meteorological

models, because predictions in the cells near the boundaries may not be suitable for use in air

quality simulation. Therefore, MCIP extracts only the portion of the MM5 output data which falls

within the CTM’s main domain and boundary cells. The CTM domain should be located at least

four or five cells inside the MM5 domain to minimize the boundary effects. MCIP can, however,

generate output for the CMAQ domain as large as 2 cells smaller than the meteorology domain,

because it generates files for the boundary cells with NTHIK=1. (Note in MM5 terminology, it
EPA/600/R-99/030

12-18

may seem like the CMAQ domain is smaller by three because a DOT point concept is used in MM5

system for the grid definition.)

Limitation on the number of horizontal cells (to 120 cells) of the meteorology grid is coming from

the MCIP’s parameters defined in MCIPPARM.EXT:

 PARAMETER ( MAXI = 120, ! MET domain size in N-S dir.

 & MAXJ = 120 ) ! MET domain size in E-W dir.

When the meteorology data has larger dimensions, MAXI and MAXJ should be modified

accordingly. Also, there could be some limitations with reader routines specific for meteorology

models. Because these reader modules are essentially foreign codes, there is no easy way to

generalize the input process of the meteorological data. Refer to Figure 12-6, which shows the

relation among the meteorology domain, the window domain for meteorological data extraction,

and the CTM main and boundary domains.
EPA/600/R-99/030

12-19

YORIG_MM

NTHIK

(XORIG_MM, YORIG_MM)

J0

I0

(XORIG_X,YORIG_X)

XORIG_MM

(XORIG,YORIG)

Relations among MM grid, extented-CTM grid, and CTM grid for NDX=3

MM DOMAIN

WINDOW DOMAIN

EXTENDED CTM DOMAIN

CTM DOMAIN

(XCENT,YCENT)=(0,0)

NTHIK=2 DX

DX_MM

J=1

I=1

I = MAXI_MM

J=MAXJ_MM

Figure 6. Relations among the meteorology domain, window domain for data extraction,

and CTM's main and boundary domains.
EPA/600/R-99/030

12-20

12.2.3.2 Horizontal Interpolation

A horizontal interpolation function is provided to help users generate higher resolution data than the

input meteorological data. This function is used when higher resolution emissions data is available

but the detailed variations in meteorological fields can be neglected. This option is useful only

when the surface and PBL parameters are diagnosed in MCIP. If interpolation is desired, NDX

(defined in MCIPPARM.EXT) must be modified before the MCIP is compiled so that data arrays

are dimensioned properly. When interpolation is desired, MCIP copies contiguous grid cell values

from the coarse grid to the fine grid and then performs a two-dimensional bilinear interpolation on

the three-dimensional data. The interpolated temperature profile is updated using fine resolution

landuse data to reflect land-sea boundaries in the profile appropriately. The interpolated

temperature, moisture, and wind components profiles, together with the detailed landuse data, are

used to estimate surface and PBL parameters for the finer resolution. The user should be reminded

that this procedure generates higher resolution meteorological data without enhanced physics, thus

the newly generated data may have consistency problems. Therefore, such interpolation should be

used sparingly for cases such as testing higher resolution emissions data with a finer resolution

CTM. The procedure is never meant to replace or minimize the need for higher resolution

meteorological model runs. It should be noted that the interpolated temperature and moisture

profiles result in different estimations of cloud parameters (such as cloud bottom and top heights,

fractions, liquid water contents) as determined by the diagnostic Anthes-Kuo cloud routine.

12.2.3.3 Vertical Layer Collapsing

A vertical collapsing function is supplied to generate a smaller data set for testing CTM in a smaller

computer system. If desired, MCIP collapses MM5 profile data for the coarse vertical resolution

data as defined by the user. MCIP performs a mass-weighted averaging of data in the vertical

direction. For example, 30-layer MM5 data may be averaged into 15 or 6 CTM layers. During the

collapsing procedure, the layer description is modified accordingly. The resulting profile may have

consistency problems. This option is usually used to generate meteorology data for a system testrun for code debugging and development purposes. It is also appropriate to study the effects of the

vertical resolution in air quality simulation such as presented in Byun and Dennis (1995). Refer to

Table 12-5 as an example for the layer collapsing.

Defining the vertical layering structure for the CMAQ system requires consideration of several

factors. Depending on the layer definitions used, the model results will be affected considerably.

The implications of the layer definition are pervading across the entire system. For example, to

determine mass exchange between the boundary layer and free troposphere, a good resolution near

the boundary layer top is preferable. Also, different cloud parameterizations may perform

differently, depending on the layering structure. Aerodynamic resistance, which influences dry

deposition velocities, is a function of layer thickness and the boundary layer stability. For

emissions processing, the layer thickness affects the plume rises from major stacks. Also, the

vertical extent of the area emission effects is limited by the thickness of the lowest model layer for

the CCTM. Although 6-layer vertical grid definition is provided with the tutorial simulation

examples, we do not recommend it to be used for regulatory applications because of the difficulties

in simulating certain processes, such as dry deposition under stable atmospheric conditions.
EPA/600/R-99/030

12-21

Current limitation on the number of vertical layers to 30 comes from one of the MCIP’s parameters

defined in MCIPPARM.EXT:

 PARAMETER ( MAXK = 30 ) ! MET number of layers

When a meteorological data has more number of layers, the parameter MAXK should be increased

accordingly. Collapsing is done automatically when the COORD.EXT file (see Models-3 CMAQ

User’s Guide for the details) for the output grid has smaller number of layers than the input grid.

Table 12-5. An example of layer collapsing from 15 to 6 σ-layers. Full and half σ-levels and standard

heights are provided to show relations between the two vertical grid systems. (adapted from Byun and

Dennis, 1995)

Level

Index(15)

Level

Index(6)

σ-Level

Full(15) Half(15)

Standard Height (m)

Full(15) Half(15)

15 0.0 16069

0.05 13712

14 6 0.1 11998

0.15 10649

13 0.2 9512

0.25 8513

12 0.3 7621

0.35 6813

11 5 0.4 6073

0.45 5390

10 0.5 4754

0.55 4159

9 0.6 3600

0.65 3071

8 4 0.7 2570

0.74 2187

7 0.78 1818

0.81 1550

6 0.84 1289

3 0.865 1077

5 0.89 868

0.91 705

4 0.93 544

2 0.945 425

3 0.96 307

0.97 230

2 0.98 152

1 0.985 114

1 0.99 76

0.995 38

0 0 1.0 0
EPA/600/R-99/030

12-22

12.3 Estimation of Physical Parameters

MCIP’s essential role is to provide consistent meteorological data for the CMAQ modeling system.

However, the meteorological models used for air quality study may not provide important

boundary layer parameters at all, or may predict those at very coarse temporal resolution, or may

only compute a subset of the needed parameters. In such a case, it becomes necessary to estimate

remaining meteorological parameters using certain diagnostic methods. MCIP allows either the

direct pass through of the PBL parameters provided by MM5, or they can be computed from the

mean profiles of temperature, humidity and momentum together with the surface landuse data. In

the following, we explain the diagnostic methods used in MCIP. Note that the approaches

introduced here may not be consistent with MM5 directly and therefore may produce somewhat

different spatial distribution patterns for certain parameters. Basically, the diagnostic routines treat

meteorological model outputs as the pseudo radiosonde observations.

When desired, MCIP estimates key parameters for cloud distributions based on Anthes-Kuo

parameterization. They include precipitation rate, cloud fraction, and cloud base and top heights.

MCIP also provides estimated dry deposition velocities for various chemical species in the RADM

and carbon bond 4 (CB-4) mechanisms.

12.3.1 PBL Parameters

Depending on the user option, MCIP either passes through MM5 predicted surface and PBL

parameters or estimates them us the MM5 profile data and detailed landuse information. The

algorithms used for the diagnostic computation of PBL parameters are provided below.

12.3.1.1 Surface Flux Related Parameters

We utilize a diagnostic method based on similarity theory to estimate the turbulence flux related

parameters. When the meteorological model uses very high vertical resolution and the thickness of

lowest model layer is less than 20 m, we can utilize the surface similarity theory to determine

turbulence parameters for both stable and unstable atmosphere.

For the computation of the surface layer parameters, MCIP utilizes analytical solutions suggested

by Byun (1990) to minimize the needs for numerical iterations in solving the flux-profile relations.

The method has been reviewed and successfully applied in several surface layer studies (e.g.,

Hess, 1992; Lo, 1993 and 1995). Also, a weather research model, the Advanced Regional

Prediction System (ARPS) (Xue et al., 1995) utilizes it in the description of the surface layer. The

algorithm is summarized below.

The nondimensional surface layer profile functions for momentum (φ m ) and potential temperature

(φh) are defined as:

kz

u

U

z

z

L m

*

( ) ∂

∂ = φ (12-10a)
EPA/600/R-99/030

12-23

kz

z

z

L h θ

∂

∂ φ

*

( ) Θ = (12-10b)

where U and Θ are the horizontal wind speed and potential temperature in the boundary layer,

respectively,u* is the friction velocity, and θ* is the temperature scale representing the surface heat

flux (covariance of potential temperature and wind fluctuations) divided by the friction velocity. L

is the Monin-Obukhov length defined as:

L u

kg

o = Θ *

*

2

θ (12-11)

The similarity functional forms proposed by Businger et al. (1971) are used in MCIP as follows:

For moderately stable conditions ( 1≥ z/L ≥ 0 ) we have:

φ β m m

z

L

= +1 (12-12a)

φ β h o h

z

L

= + Pr ( ) 1 , (12-12b)

where Pro is the Prandtl number for neutral stability and β m and βh are the coefficients determined

through field experiments. Refer to Table 12-6 for the values of these coefficients used in MCIP.

For unstable conditions (z/L < 0 ), we have:

φ γ m m

z

L = − −

( ) /1 1 4 (12-13a)

φ γ h h

z

L = − −

( ) /1 1 2 (12-13b)

where γ m and γ h are coefficients of the profile functions. In addition, we added a function for the

very stable condition ( z/L ≥1 ) to extend the applicability of the surface layer similarity following

Holtslag et al. (1990):

φ β m m

z

L

= + (12-14a)

φ β h o h

z

L

= + Pr ( ) (12-14b)

To estimate surface turbulence fluxes with the layered data from a meteorological model, we utilize

the integrated flux-profile relationships: For ( z/L <1 ) we have profile functions represented as a

modified logarithmic functions, when integrated from the height of the roughness length (zo),
EPA/600/R-99/030

12-24

U z u

k

z

z

z

L

z

o L m

o ( ) ln ( , ) * = − 



 



ψ  (12-15a)

∆Θ( ) Pr ln ( , ) * z

k

z

z

z

L

z

L

o

o

h

o = − 



 



 θ

ψ (12-15b)

and for strongly stable conditions, ( z/L ≥1 ), we use direct integration of the profile functions:

U z u

k

z

z

z z

L m

o

o ( ) ln * = +

 −



 



β  (12-16a)

∆Θ( ) Pr ln * z

k

z

z

z z

L

o

h

o

o = +

 −



 



 θ β (12-16b)

The ψ functions are given by (e.g., Paulson 1970), for moderately stable conditions (1≥ z/L ≥ 0):

ψ β m m

o z

L

z z

L ( ) = − − (12-17a)

ψ β h h

o z

L

z z

L ( ) = − − (12-17b)

and for unstable conditions:

ψ m

o o

o

z

L

x

x

x

x

( ) ln ln tan ( ) tan ( ) = x x

+

+





 



 +

+

+





 



 − + − − 2 1

1

1

1

2 2

2

2

1 1 (12-18a)

ψ h

o

z

L

y

y

( ) ln = +

+





 

 2  1

1 , (12-18b)

where x

z

L = − m ( ) /

1 1 4 γ , x

z

L o m

o = − ( ) /

1 1 4 γ , and

y

z

L = − h ( ) /

1 1 2 γ , y

z

L o h

o = − ( ) /

1 1 2 γ .

One important fact to note here is that although the similarity functions for stable conditions,

Equations 12-12a-b and 12-14a-b, are continuous at z/L =1, their integrated profiles are not

continuous.

The flux profile relations described above are used to relate the Monin-Obukhov stability

parameters with the readily computable bulk Richardson number Rib:
EPA/600/R-99/030

12-25

Ri gz z

U b

o

o

= ( ) −

Θ

∆Θ

2 (12-19)

For moderately stable conditions (1> z/L ≥ 0 ), we have:

ζ β β β β β = −





 





− − −− +  −



 





















z

z z

z

z

Ri

Ri Ri o o

h m b

h b

h m b

o

ln

( ) ( ) ( )Pr

/

2 1

2 11 4

1 2

(12-20)

and for strongly stable conditions, (z/L ≥1 ), we can derive a similar solution following the same

procedure as described in Byun (1990) to give:

ζ

β

= −





 





− −− + − + − 











 





m

o o

o b

b b o bb

z

z z

z

z

Ri

Ri Ri Ri Ri

ln

Pr ( ) ( ) (Pr )

/ 1

2

1

2

2

1 2

(12-21)

Given a positive bulk Richardson number, one should use both Equations 12-20 and 12-21 to

compute ζ and choose the value in the correct range between the moderately stable and strongly

stable conditions.

For unstable conditions, we use an efficient analytical approximation by Byun (1990), for

( ) Q P b b

3 2 − ≥ 0,

ζ θ

γ ≈ −





 



 



 



 − +





 



 z

z z

z

z

Q

o o

b

b

m

ln cos( ) 2

3

1

3 (12-22)

and for ( ) Q P b b

3 2 − < 0,

ζ

γ ≈ −





 



 



 



 −+ +





 



 z

z z

z

z

T Q

o o T b

b

b m

ln ( ) 1

3 (12-23)

where s

Ri

b

b

o

= Pr ;

Q s b

m

h

m

= + b





 



 1

9

1 3 2

2

γ

γ

γ

;

P s b

m m

h

m

= −+ −+ b





 



 1

54

2 9 3 3

2

γ γ

γ

γ

( ) ;
EPA/600/R-99/030

12-26

θb

b

b

P

Q = 









 arccos

3 ; and

T PQP b b bb = −+ [ ] 2 3

1 3/

.

The above equations are used to estimate friction velocity, u*, by estimating the bulk Richardson

number using the layered meteorological data:

u

kU

zz zL z L o m mo

*

( )

ln( / ) ( / ) ( / ) = − +

1

Ψ Ψ (12-24)

Heat flux can be found by using the temperature scale estimated with:

H Cu = −ρ θ p * * (12-25)

where

θ*

[ ]

Pr [ln( / ) ( / ) ( / )] = −− +

k

zz zL zL

s

o o h h o

Θ Θ

Ψ Ψ

1

1 1

(12-26)

There have been several suggestions for the coefficients of the surface layer profile functions. For

example, Businger et al. (1971) suggested:

β m = 4 7. , βh = 6 35 . , γ m = 15 0. , γ h = 9 0. , Pr . o = 0 74

with the von Karman constant value of 0.35. On the other hand, Högström (1988) reanalyzed the

experimental data used for the determination of the similarity functions and suggested use of:

β m = 6 0. , βh = 8 21 . , γ m = 19 3. , γ h = 11 6. , Pr . o = 0 95

with the von Karman constant value of 0.40. In the current version of MCIP, the latter set of

coefficient values are used (refer to Table 12-6).

Moisture flux is found by using similar method as the potential temperature:

E uq = −ρ * * , (12-27)

where mixing ratio scale, q* , is determined with an equation similar to Equation 12-26 for given

∆qq q = −1 s (q1 and qs are the mixing ratios at the lowest model layer and at the surface,

respectively).
EPA/600/R-99/030

12-27

12.3.1.2 Estimation of Surface Fluxes Using PBL Profile Functions

Occasionally meteorological models use the lowest model layer thicker than 40 m or so. Under

this condition, it becomes difficult to believe that the lowest layer always belongs to the surface

layer all the time, especially for very stable conditions. To avoid this limitation, MCIP estimates

surface heat, momentum and moisture flux transfer parameters from MM5 surface wind and

temperature by using the boundary layer similarity profiles proposed by Byun (1991). In this

section, we describe the methods used in MCIP for estimating surface fluxes when the thickness of

the lowest model layer is too thick to rely on the surface layer similarity. The intention is to

provide a diagnostic method that can estimate the surface fluxes even when the lowest model layer

extends above the surface layer. It is difficult to expect that a layer with 40 m thick, for example,

continuously belongs to the surface layer though out a day.

Table 12-6. Parametric Constants Used to Describe the PBL in MCIP

Parameter Symbol Value

von Karman constant K 0.4

Coefficient in stable profile function for momentum β m 6.0

Coefficient in stable profile function for heat (scalar) βh 8.21

Coefficient in unstable profile function for momentum γ m 19.30

Coefficient in unstable profile function for heat (scalar) γ h 11.60

Prandtl number for neutral stability Pro 0.95

Critical Richardson Number Ricr 0.25

Maximum bulk Richardson number max( RiB) 0.70

Minimum bulk Richardson number min( RiB) -4.75

Minimum magnitude of Monin-Obukhov length abs(L) 4.0

Scale height ratio for neutral stability λo 0.07

Zilitinkevich ch ch 0.80

Neutral value of similarity function for wind component parallel to surface stress A(0) 1.70

Neutral value of similarity function for wind component normal to surface stress B(0) 4.50

Reference height zr 10 m

The wind and temperature predicted by a meteorological grid model represent layer averaged

values. In order to simplify computation of the surface fluxes, we apply the assumption that the

predicted wind for the lowest model layer has the same direction as the surface stress (i.e.,

uvU mm m

22 2 + ≈ , where um and vm are latitudinal and longitudinal components of the first layer mean

wind on the map and Um is the layer mean wind speed in the direction of surface stress). Applying

the PBL momentum profile functions of Byun (1991) and integrating them vertically from zo

(roughness length) to the top of the lowest CTM layer (z h F1 ≤ ), one can obtain wind and potential

temperature profiles in the form:
EPA/600/R-99/030

12-28

U u

k m u oF = P* (, , ) μη η , (12-28)

Θ Θ m o

o

o F k − = P Pr (, , ) θ*

θ μη η (12-29)

where ηo

o z

h = , ηF

Fz

h = 1 , and μ = h

L . For a detailed description of the notation used, refer to

Byun (1991) and Byun and Dennis (1995). Initially, the atmospheric stability (μ ) is approximated

by the analytical solutions of flux-profile relationships described earlier. Then, we compute μ, u*,

and θ* using Equations 12-28 and 12-29, with the Newton-Raphson iteration. Equation 12-29 is

then used to estimate temperatures at heights 1.5 m and 10 m in MCIP.

12.3.1.3 Utilization of Sub-grid Scale Landuse Information

Accurate description of atmospheric turbulence is one of the important elements in modeling the

deposition of pollutants. For Eulerian air quality models, grid-average surface roughness based on

sub-grid scale landuse information has played an important role in the characterization of the

surface condition, which in turn determines intensity of turbulence in the atmosphere. To represent

the atmospheric deposition process utilizing the available sub-grid landuse information, Walcek et

al. (1986) introduced a method to estimate friction velocity for each landuse patch, which is used in

the calculation of the subgrid-scale aerodynamic resistance. Also, several estimation methods have

been proposed for the effective roughness length for use in meteorological grid models. Compared

with the latter methods that estimate the representative grid values for the given sub-grid

information, Walcek et al. (1986) emphasized the description of the sub-grid flux estimation by

introducing a somewhat ad hoc, but useful assumption. They assumed that the quantity Uu* is

constant both for the cell averaged parameters and for the individual landuse patches, i.e.:

Uu U uj * * j = = constant, (12-30)

where the non-subscripted variables refer to grid-averaged values while the j-subscripted values

refer to the corresponding quantities over individual landuse types. Equation 12-30 is an intuitive

expression of the often observed condition that where wind speed is high, the turbulence is low,

and vice versa, under similar pressure gradient forcing. Strict validity of Equation 12-30 could be

controversial, however, this approach is more realistic than those that assume constant wind or

constant friction velocity. In the dimensional analysis point of view, the condition is a statement

about the conservation of kinematic energy in the presence of surface friction. A derivation leading

to Equation 12-30 is provided below using a combination of the surface layer similarity and the

mixing length theories.

The momentum flux is related with mean wind gradient as:

− == ( " ") uw u K *

U

z s m

2 ∂

∂ (12-31)
EPA/600/R-99/030

12-29

and the eddy diffusivity for momentum is given by:

K ku z

z L m

m

= *

φ (/ ) (12-32)

When we apply assumptions such as steady state flow and horizontal homogeneity of the each

landuse patch, the momentum conservation equation can be simplified to give:

U U

z

u w

z z p

∂

∂

∂

∂ ρ + =− ∇ "" 1 (12-33)

Coriolis forcing is neglected in deriving Equation 12-33 because we are dealing with only the subgrid scale variation of momentum field.

The right hand side of Equation 12-33 represents the pressure gradient forcing imposed over the

grid and is therefore not dependent on sub-grid representation. Within the surface layer, which is

treated as a constant flux layer, Equation 12-33 is further simplified to give:

U U

z

p const z

∂

∂ ρ =− ∇ = 1 . (12-34)

Combining Equations 12-31, 12-32 and 12-34, one obtains

Uu z L

kz

const m

*

φ (/ ) = . (12-35)

For the atmosphere at neutral stability, φ m = 1, and the same expression should be applicable for

each landuse patch. Then, Equation 12-35 becomes identical to Equation 12-30 at a given

reference height z z = r .

In addition to Equation 12-30, Walcek et al. (1986) assumed that the surface roughness length can

be averaged as

z fz o j oj = exp ln [ ] ∑ , (12-36)

where fj’s are fractions of different landuse types in a grid cell. Walcek et al. (1986) stated that

Equation 12-36 conforms to a logarithmic wind profile. In reality, however, Equation 12-36 can

be derived from a simple geometric averaging and it does not produce a logarithmic wind profile.

On the other hand, Mason (1987) suggest an averaging method based on the logarithmic wind

profile by introducing a blending height (lb ) concept:

ln

ln( / )

l

z

f

l z

b

o

j

b oj





 



 = 













 ∑

2 −

2

1

. (12-37)
EPA/600/R-99/030

12-30

Although this approach is a practical averaging method of the roughness length, this by itself

cannot be used to estimate landuse-dependent friction velocities. Therefore, here we compare

several other roughness length averaging schemes that satisfy both Equation 12-30 and the

logarithmic wind profile function for the neutral condition:

U z u

k

z

z r

r

o

( ) ln * = (12-38a)

and

U z

u

k

z

z j r

j r

oj

( ) ln * = (12-38b)

where zr is the reference height. The objective is to compute landuse specific friction velocities

from the cell average wind and friction velocity values while providing a consistent averaging

scheme for the roughness length. The simplest method for estimating the grid average values from

the sub-grid scale information is using the linear summation with the fractional weight:

< >= x fx ∑ j

j

j , (12-39)

where xj is a physical quantity and f ∑ j = 1. Because U uj * j

= constant, one can rewrite Equation

12-30 with Equation 12-39 as follows:

Uu U u f U u Uu j jj

j

** * * j j = = =< > ∑ (12-40)

If the surface wind is a quantity that follows Equation 12-39, a relation between the grid average

and sub-grid landuse dependent roughness lengths can be found as:

z z

fu z z

fu z z o r

j j r oj

j j r oj

= − ( ) 















∑

∑ exp

ln( / )

ln( / )

*

*

2

2 (12-41)

In order for the expression to be useful, u* j in Equation 12-41 should be eliminated. From

Equations 12-38a-b and 12-40, a simple relation for u* j is found in terms of known quantities:

u u

z z

z z j

r o

r oj

* *

/

ln( / )

ln( / ) = 















1 2

(12-42)

Substituting Equation 12-42 into Equation 12-41, we obtain a simple relation for the effective

roughness length that satisfies both the logarithmic wind profile and the linearly-additive wind

speed assumptions under the approximation, Equation 12-30:
EPA/600/R-99/030

12-31

z z f zz o r j r oj = −( ) 

  ∑  exp ln( / )

2

(12-43)

The reference height zr needs to be within the regime where the log-linear wind profile can be

satisfied. This means that it should be far away from zo, but still within the surface layer. In the

current MCIP, we are using zr=10m. The new method conserves wind speed and U uj * j

 under the

linear summation (Equation 12-39). With this assumption the turbulence momentum flux ( u*

2

 )

can be summed linearly when it is scaled with the factor ln( / ) / ln( / ) zz zz [ ] r o r oj . Depending on the

degree of inhomogeneity, this factor can be substantially different from unity, making less

consistent with the expectation that fluxes from different patches can be summed up. One may

expect that Equation 12-43 is sensitive to the choice of reference height zr ; however, the average

roughness length is not strongly sensitive to the reasonable value of zr between 1 to 10 m.

An alternative approach to the linearly-additive wind speed assumption is to assume that the subgrid scale momentum flux can be summed linearly:

u fu u j j

j

* **

2 22 = =< > ∑ (12-44)

Using Equation 12-39 and the logarithmic wind profiles, one can find:

1

2

2

2

ln( / )

( /)

z z ln( / )

f

U U

r o z z

j

j

r oj [ ] j

=

[ ] ∑ (12-45)

In order that Equation 12-45 to be useful, ( /) U Uj should be expressed in terms of zo, zoj , and zr .

This is accomplished by dividing Equation 12-38a with Equation 12-38b and substituting (/ ) u u * * j

with Equation 12-30 to get:

U

U

z z

z z

j r oj

r o

= 



 





ln( / )

ln( / )

1 2/

(12-46)

This leads to an averaging method for the sub-grid scale roughness length:

z z

f

z z o r

j

j r oj

= −

























 ∑

−

exp ln( / )

1

(12-47)

Another popular assumption is that at the reference height (or blending height) the drag coefficients

representing the individual landuse patches in a cell can be summed linearly, i.e.:

C u

U D j Dj fC C

j

≡ = =< > ∑ D

*

2

2 (12-48)
EPA/600/R-99/030

12-32

Unlike the two other assumptions introduced, this assumption does not depend on Equation 12-30.

The resulting equation for average roughness length is then identical to Equation 12-37.

z z

f

z z o r

j

r oj j

= − [ ]





























 ∑ 

−

exp

ln( / )

/

2

1 2

(12-37’)

Although the assumption in Equation 12-48 has been used often in the literature, it is not intuitive

that the sub-grid drag coefficients can be added linearly. The drag coefficient simply quantifies the

turbulence exchange characteristic of a landuse patch. By using this assumption together with the

Equation 12-30, one can readily show that:

C fC f

u

U uU f u uu U D j Dj

j

j

j

j j

j j

j

== = = < > ∑∑ ∑ *

*

*

*

*

2

2 22

4

4

2 2

1 (12-49)

It is difficult to expect that u*

4

 is a physical quantity that can be added linearly. In MCIP, we have

implemented both Equations 12-43 and 12-47 as a user option. Results of the comparison of the

two recommended methods should be available as the model evaluation project progresses.

12.3.1.4 Boundary Layer Heights

Boundary layer height is a key parameter that determines the domain of atmospheric turbulence in

which pollutants disperse. It is used as a fundamental scaling parameter for the similarity theory in

the description of atmospheric diffusion characteristics. Estimating PBL height has been one of the

key functions of meteorological pre-processors for air quality models. Below, we summarize PBL

height estimation algorithms used in MCIP.

 Unstable conditions 

MCIP estimates the PBL height using the vertical profiles of potential temperature and the bulk

Richardson number with an algorithm similar to the one reported in Holtslag et al. (1995). The

bulk Richardson number of each model layer with respect to the surface is given as:

( ) ( )

( ) Ri g zU B

k H

k

H

k

o

o H

k = Θ Θ−

Θ 2 (12-50)

where subscript H represents values at the layer middle (i.e., half sigma level).

First, the index of the PBL top (kPBL) is determined at the layer when RiB first becomes larger than

max( RiB). Then the proration factor of the bulk Richardson number relative to max( RiB) is

computed with:

f Ri Ri

Ri Ri Ri

B B

k

B

k

B

B k

PBL

PBL PBL

= −

−













−

min , −

max( ) ( )

() ()

1

1

1 (12-51)
EPA/600/R-99/030

12-33

where max( ) RiB =0.7 (refer to Table 12-6). Depending on the value of fRiB , the index kPBL and

fRiB are modified as follows:

for fRiB > 0.5, f f Ri Ri B B

' = − 0 5. ; k k PBL PBL

' = , and

for fRiB < 0.5, f f Ri Ri B B

' = + 0 5. ; k k PBL PBL

' = −1.

Once the fraction and index for the PBL top are determined, we estimate the initial PBL height

with:

h fz f z PBL Ri F

k

Ri F

k

B

PBL

B

PBL = +− ' ' − − ' / ' /

( ) 12 32 1 (12-52)

The above proration procedure ensures gradual increase of PBL height. Without the procedure,

the resolution of PBL height is limited by the layer thickness of the model. In the RADM

preprocessor, the PBL height is determined simply at the layer where the potential temperature first

becomes warmer than the surface temperature for convective conditions. Compared with the

RADM method, the present method takes into account effects of the wind shear as well.

 Stable conditions 

For stable conditions, the PBL height is determined by the maximum of the PBL height computed

with above method and the stable boundary layer height given by the Zilitinkevich’s (1989)

formula:

h kc L kc L ku c L

f PBL

h

o

h

o

=− + h





 



 +

















1

2

4

2 2 2

2

λ λ * (12-53)

 Limiting PBL heights 

Unlike the PBL height estimation algorithms based on temporal integration of surface heat flux

(e.g., Carson, 1973; Betts, 1973; Driedonks, 1981), the above diagnostic algorithm could predict

temporally disconnected PBL heights when the hourly meteorological data change abruptly. To

minimize this effect, following limits on the PBL height are imposed.

1. Compare with PBL height for neutral conditions, and take maximum except for the tropical

areas:

h h u

f PBL PBL o ' max{ , }* = λ (12-54)

2. Compare with the urban boundary layer height, which is approximated with:

h f h fh UBL urban urban =− + ( ) 1 PBLmin UBLmin (12-55)
EPA/600/R-99/030

12-34

 where furban is the fraction of urban landuse in a cell. In MCIP, the minimum PBL height

for urban area and other landuse types are set to be hUBLmin=300 m and hPBLmin=50 m.

Then, take a maximum of the two to reflect the effect of urban landuse:

h hh PBL PBL UBL ' max{ , } = (12-56)

 This step is introduced to apply the urban landuse classification, which is consistent with

the one used for the emission processing, for the determination of the PBL height.

3. Limit the PBL height with a maximum value ( hPBLmax=3000 m) in case the temperature

profile does not have a capping inversion:

h hh PBL PBL ' min{ , } = PBLmax . (12-57)

12.3.1.5 Aerodynamic Resistances

Aerodynamic resistance describes the ability of the atmospheric turbulence to transport pollutant to

the surface for the deposition. In this regard, it may well be described with the probability

concept. If 100 particles, say, are at height 20m, how many of them can reach the surface to be

available for deposition during a given time interval? Or, what is the transport rate of particles in

the air to the surface? The ratio represents the maximum potential deposition rate of particles

subjected to atmospheric turbulence. However, even those particles which arrive at the surface

may not all be deposited because of other resistances, which usually are parameterized using

characteristics of surface and gaseous elements.

There have been many efforts to compare different formulations for dry deposition velocities.

While there are a lot of uncertainties in describing atmospheric processes, the different

aerodynamic resistance formulas in the literature are mainly originated from the differences in the

applications and approximations of the same PBL theories and formulas. Among the components

involved in atmospheric resistance computation, formulations for aerodynamic resistance have the

least controversy. To compute the aerodynamic resistance, the parameterization of the eddy

diffusivity for the PBL should be known. The eddy-diffusivity formulations used in the derivation

of aerodynamic resistance are discussed below.

 Eddy diffusivity formulations 

The similarity theory suggests that eddy diffusivity in the surface layer for heat flux is given by:

K ku z

z L h

h

= *

φ (/ ) (12-58)

The profile function φh is defined in Equations 12-12b and 12-13b. Eddy diffusivity in the PBL

(above the surface layer) (Brost and Wyngaard 1978) is given as:
EPA/600/R-99/030

12-35

K ku z z h

z L h

PBL

h

= * − / ( /)

(/ )

1 3 2

φ (12-59a)

for stable atmosphere (z L/ > 0), and as:

K kw z z

h h

PBL

= − * ( ) 1 (12-59b)

for unstable atmosphere (z L/ ≤ 0), where the convective velocity scale w* is defined as

w g h u

o

* ** PBL

/

= −



 



 Θ

θ

1 3

(12-60)

 Aerodynamic resistance formulations 

We often characterize the ability of turbulent atmosphere to carry pollutants to the vegetation or

other surface elements using the aerodynamic resistance concept. Certain meteorological models

may use the resistance representation of surface exchange processes in lieu of the conventional

bulk aerodynamic methods and the aerodynamic resistance is available as a part of meteorological

data with other PBL parameters. Conversely, there are models that do not predict resistances and

related parameters needed. In such cases, we need to estimate it using PBL parameters and

profiles of state variables.

The aerodynamic resistance ( Ra ) and sub-layer resistance ( Rb ) are parameterized in terms of

friction velocity and surface roughness (Walcek, 1987; Chang et al., 1987 and 1990; Wesely,

1989; Wesely and Hicks, 1977). Although some consider the estimation of aerodynamic

resistance as an integral part of the dry deposition velocity computation, we treat the aerodynamic

resistance as an independent element that characterizes the effects of atmospheric turbulence. Here,

we provide a set of integrated equations, which allow robust estimation of aerodynamic resistance

compared with the method based on the nonintegrated form, which sometimes provides negative

fluxes for unstable conditions. Refer to Byun and Dennis (1995) for details.

General formulation for the aerodynamic resistance at the deposition height zdep (where

concentration is represented) is divided into two components; the resistance in the surface layer

(whose top is at zSL , height of the surface layer) and the resistance in the PBL above the surface

layer:

R dz

K z

dz

K z

dz

K z a R R

z z

z

z z

z

z z

z

aSL aPBL

o o

SL

SL

dep

= = + =+ ∫∫∫ () () () (12-61)
EPA/600/R-99/030

12-36

(a) For stable conditions:

R

ku

z

z

z z

L aSL

o SL

o

h

SL o = +

 −



 



 Pr ln( )

*

β (12-62a)

R

ku aPBL

o

dep SL

dep SL

dep SL

= +

− − +− +

−+ − + −

+ − −+ −

















Pr ( ) ( ) ln ( )( )

( )( ) *

2 1

1

2 1

1

11 11

11 11

β

η

β

η

η η

η η , (12-62b)

where β β = h

hPBL

L , ηdep

dep

PBL

z

h = and ηSL

SL

PBL

z

h = .

(b) For unstable conditions:

R

ku

z L zL

z L zL aSL

o h SL h o

h SL h o

= −+ + + +

+ + −+ +

















Pr ln ( / )( / )

( / )( / ) *

11 11

11 11

γ γ

γ γ

(12-63a)

R

kw aPBL

dep SL

SL dep

= −

−

















1 1

1 *

ln ( )

( )

η η

η η . (12-63b)

12.3.2 Dry Deposition Velocities

The term dry deposition represents a complex sequence of atmospheric phenomena resulting in the

removal of pollutants from the atmosphere to the surface of the earth. The rate of transfer of

pollutants between the air and exposed surfaces is controlled by a wide range of chemical,

physical, and biological factors, which vary in their relative importance according to the nature and

state of the surface, characteristics of the pollutant, and the strength of turbulence in the

atmosphere. The complexity of the individual processes involved and the variety of possible

interactions among them prohibits simple generalization of the process. Nevertheless, a

"deposition velocity," analogous to a gravitational falling speed is of considerable use. In practice,

the knowledge of dry deposition velocities enables fluxes to be estimated from airborne

concentrations. Two dry deposition estimation methods, that from Wesely (1989) currently as

implemented in CMAQ, and the new Models-3/CMAQ approach are presented.

12.3.2.1 RADM Method

The RADM dry deposition module in MCIP calculates deposition velocities of sixteen chemical

species (Table 12-7). It requires various ancillary 2-D meteorology fields such as the PBL height,

mixing scale velocities, Monin-Obukov length, etc. They are usually estimated from horizontal

wind components, temperature and humidity profiles. The dry deposition flux of each chemical

species from the atmosphere to surface is calculated in the CCTM by multiplying the concentration

in the lowest model layer with the dry deposition velocity. The dry deposition velocity (Vd ) is

computed from the resistance-in-series method;
EPA/600/R-99/030

12-37

V RRR d = ++ abc

− ( ) 1 (12-64)

where Ra is the aerodynamic resistance, Rb is the quasi-laminar boundary layer resistance, and Rc

is the canopy (surface) resistance. Refer to Figure 12-7. Vd is usually estimated from a series of

resistances to vertical transfer and surface uptake. Aerodynamic resistance (Ra ) is a function of

turbulent transfer in the atmospheric surface layer and can be estimated in several ways depending

on the instrumentation used or parameterizations provided.

The canopy resistances (Rc) for SO2 and O3 are estimated from available measurements as a

function of season, insolation, surface wetness, and land type (Walcek et al., 1986; Shieh et al.,

1979; Fowler, 1978). The surface resistances for all other gaseous species, due to the lack of

extensive measurements, are qualitatively scaled to the SO2 and O3 surface resistances according to

their reactivity and solubility. The surface resistance for particulate sulfate is parameterized in

terms of stability and friction velocity in the surface layer (Wesely, 1989), based on limited studies

that do not include water surfaces. In CMAQ this method only applies to the treatment of surrogate

gas-phase representation of sulfate species. Size dependent deposition velocities for particle

depositions are estimated inside the CCTM’s aerosol module. See Chapter 10 of this document

and Binkwoski and Shankar (1995) for details.

The laminar sub-layer resistance (Rb) depends on the landuse specific friction velocity and

molecular characteristics of gases. Using the landuse dependent friction velocity or the cell average

friction velocity, Rb’s for heat (Rbh) and trace gases (Rbx) are estimated with the Schmidt number

(Sc):

R

ku

Sc bh = 2 2 3

*

/ (for heat) (12-65a)

R

ku

Sc bx x = 2 2 3

*

/ (for trace gas species) (12-65b)

where Schmidt number is defined as the kinematic viscosity of air (ν = 0.146 cm s

2 1− ) divided by

molecular diffusivity ( i.e., Sc D = ν g / for heat and Sc D x gx = ν / for trace gases). Here, ν is

kinematic viscosity of air; Dg is molecular diffusivity of air (heat); and Dgx is molecular diffusivity

of trace species. For heat, the molecular thermal diffusivity ( Dg ) is 0.206 cm s

2 1− ; for water

vapor, molecular diffusivity ( Dgw ) is 0.244 cm s

2 1− ; and, for ozone molecular diffusivity ( DgO3 ) is

0.159 cm s

2 1− (molecular diffusivities of other chemical species are included in the model).
EPA/600/R-99/030

12-38

Figure 12-7. Schematic Diagram of Pathway Resistances Used in RADM Dry Deposition Model

Resistances with subscript x are for different chemical species.

Rc represents the canopy resistance defined as:

R

rr r rr rr c

sx mx lux dc clx ac gsx

= ++ +

+

+

+













−

111 1

1

(12-66)

where rsx = stomatal resistance;

rmx = mesophyl resistance;

rlux= resistance of the outer surface of leaves in the upper canopy;

rdc = resistance for the gas transfer affected by buoyant convection in canopy;

rclx = lower canopy resistance (uptake pathways at the leaves, twig, etc.);

rac = resistance that depends on the canopy height; and

rgsx= resistance of soil, leaf litter, and other ground materials.

Stomatal resistance for water is obtained using following equation:

r r

GTT sw s

sw c c

= +

+





 















 −





 

 min  . ()

1 200

0 1

400

40

2

(12-67)

where rsw = stomatal resistance for water;

rs min= minimum stomatal resistance for water, specified in Table 12-7;

Ambient Concentration

Rb

Ra

Rc

ground, water,

snow

cuticle,

stem

leaf

tissue

rsx

rmx

rlux

Vegetation

rac

rgsx

Rc

rdc

rclx

lower canopy
EPA/600/R-99/030

12-39

Tc = surface air temperature in the canopy in Celsius temperature; and

Gsw =- solar radiation reaching at the canopy in W/m2

 unit.

Then stomatal resistance for trace gas species is obtained with:

r r

D

D sx sw

gw

gx

= (12-68)

where Dgw is the molecular diffusivity of water. Ratio of molecular diffusivity of water to that of

each trace species is provided in Table 12-7.

The mesophyl resistance is parameterized as:

r

H f mx

x = + ox









−

*

3000

100

1

(12-69)

where H*x is Henry’s gas constant (in mole atm-1)for the species, and fox is the reaction intensity

factor.

Both the Henry’s gas constants and reaction intensity factors are provided in Table 12-7 as well.

rlux is related with the upper canopy resistance for water (rlu ) which is provided in Table 2 of

Wesely (1989) as:

rr Hf lux luw = +x ox

− − ( ) 10 *5 1 (12-70)

rdc is parameterized in terms of the available solar radiation and the slope of local terrain:

r G dc =+ + + sw

− − 100 1 1000 10 1 1000 1 1 [ ( ) ]( ) θ (12-71)

where θ is the slope of local terrain in radians. rclx and rgsx are estimated based on the respective

resistance values for SO2 and O3 as follows:

r

H

r

f

r

clx

x

clS

ox

clO

= + 



 





−

*

105

1

(12-72a)

r

H

r

f

r gsx

x

gsS

ox

gsO

= +













−

*

105

1

(12-72b)

where subscript S and O are for SO2 and O3, respectively. All of these values, and rac (the

resistance that depends on the canopy height) are landuse dependent and listed in Table 2 of

Wesely (1989).
EPA/600/R-99/030

12-40

Table 12-7. Gaseous Species Treated in RADM Dry Deposition Module and Their Properties

Relevant to Estimating Resistance Components as Implemented in MCIP

(Modified from Wesely, 1989.)

Gaseous species Symbol D D gw gx / H*x (mole atm-1) fox

Sulfur dioxide SO2 1.9 1.0X105 0.0

Sulfate SO4 ---

Nitrogen dioxide NO2 1.6 0.01 0.1

Nitric oxide NO 1.3 0.002 0.0

Ozone O3 1.6 0.01 1.0

Nitric acid vapor HNO3 1.9 1.0X1014 0.0

Hydrogen peroxide H2O2 1.4 1.0X105 1.0

Acetaldehyde ALD 1.6 15.0 0.0

Formaldehyde HCHO 1.3 6.0X103 0.0

Methyl hydroperoxide OP 1.6 240.0 0.1

Peroxyacetic acid PAA 2.0 540.0 0.1

Formic acid ORA 1.6 4.0X106 0.0

Ammonia NH3 1.0 2.0X104 0.0

Peroxyacetyl nitrate PAN 2.6 3.6 0.1

Nitrous acid HONO 1.6 1.0X105 0.1

Carbon monoxide CO 1.2 0.001 0.0

12.3.2.2 Models-3/CMAQ Dry Deposition Model

The Models-3/CMAQ dry deposition (M3DDEP) module estimates dry deposition velocities

according to the same electrical resistance analog represented by Equation 12-64. M3DDEP uses

common components with the new land-surface model that has recently been added to MM5.

Specifically, the aerodynamic resistance and the canopy or bulk stomatal resistance are the same as

those used in the modified MM5 (MM5PX) for computing evapotranspiration. Since the land

surface scheme includes soil moisture and has an indirect nudging scheme for improving soil

moisture estimates, the resulting stomatal resistance estimates should be better than those achieved

with a stand alone dry deposition model. Pleim and Xiu (1995) give a description of an early

prototype of the land surface model which is now coupled to MM5. Pleim et al (1996) and Pleim

et al. (1997) briefly describe the dry deposition model and some studies comparing model results

to field measurements of surface fluxes and PBL heights. The description which follows here is

partially drawn from these sources.

When using the M3DDEP option in the CMAQ system the aerodynamic resistance, as well as the

bulk stomatal resistance (rstbw; discussed below) is provided to MCIP from the MM5PX. Note that

these parameters are computed as part of the land surface model in the MM5PX and are not

available from the standard MM5. In MM5PX the aerodynamic resistance Ra is computed

assuming similarity with heat flux such that:
EPA/600/R-99/030

12-41

R C HR a pg = − ρΘΘ ( )1 − bh / (12-73)

where Rbh is the quasi-laminar resistance for heat (defined in Equation 12-65a), Θg and Θ1 are

potential temperature of the ground surface and the air, respectively, in the lowest model layer, and

H is the sensible heat flux defined in Equation 12-25. If the sensible heat flux is very small (as

during transition periods) the surface layer theory for neutral conditions is used as follows:

R

ku

z

z a

o

o

= 



 



 ∗

Pr ln 1 for |H/(ρ Cp)| < 10-15 [K m s-1] (12-74)

where z1 is the height of model layer 1 and zo is the roughness length. The heat and momentum

fluxes are derived from flux-profile relationships as in the MM5 (see Grell et al., 1995). The quasilaminar boundary layer resistance accounts for diffusive transfer across a thin laminar layer

adjacent to surfaces. Because of the no-slip condition, turbulent eddies cannot penetrate to a

surface. Therefore, there exists a thin layer of non-turbulent air where molecular diffusion is the

primary mechanism for transfer. While this concept is not relevant for momentum, it is relevant

for any quantity that directly interacts with the surface such as heat, moisture, and chemical

deposition. Therefore, for these quantities, the addition of a resistance based on molecular

diffusion is necessary. Deposition layer resistance varies by the transported quantity because of

differences in molecular diffusivity, which is defined earlier in Equations 12-65a and b.

The total surface resistance to dry deposition (Rs) has several components including bulk stomatal

resistance (rstb), dry cuticle resistance (rcut), wet cuticle resistance (rcw), ground resistance (rg), and

in-canopy aerodynamic resistance (rlc):

R f

r

LAI f f

r

f f

r

f

r

f

r r s

v

stb

v w

cut

v w

cw

v

g

v

lc g

= + − + 



 



 + − +

+

















−

( ) 1 1

1

(12-75)

Bulk stomatal resistance (rstb), vegetation fractional coverage (fv), leaf area index (LAI) and

fractional leaf area wetness (fw) are all provided by MM5PX since the same parameters are used in

the land surface scheme. Figure 12-8 shows a schematic representation of Equation 12-75. Note

that rstb, as output from MM5PX, is already a combination of stomatal resistance on a leaf area

basis rst, mesophyl resistance rm, and LAI as described below. A key component of the land

surface model in the MM5PX is the parameterization of the bulk stomatal resistance that is used to

compute evapotranspiration. The bulk stomatal resistance for water vapor is read in to MCIP from

MM5PX and adjusted for chemical dry deposition in the M3DDEP model by weighting with the

ratio of molecular diffusivities for water vapor and the chemical species:

r

D

D

r stbc

gw

gx

= stbw . (12-76)
EPA/600/R-99/030

12-42

Ambient Concentration

ground, water,

snow

cuticle,

stem

leaf

tissue

ground, water,

snow

Leaf

Ra

Rb

r

lc

r

g

r

g

r

m

r

st

r

cut











Rs





Figure 12-8. Schematic Diagram of Pathway Resistances Used in Models-3/CMAQ Dry

Deposition Model.

In general, the bulk stomatal resistance is related to leaf based stomatal resistance as:

r

P

LAI

r r stb

s = + st m ( ) (12-77)

where Ps is a shelter factor to account for shading in denser canopies. For water vapor and many

chemical species, such as O3 and SO2, rm is assumed to be zero, however, for many less soluble
EPA/600/R-99/030

12-43

species a non-zero value should be used. The shelter factor is given by: Ps = 0.3 LAI + 0.7 with a

minimum of Ps = 1.0. Leaf scale stomatal resistance, computed as:

r

r

F PAR F w F RH F T st

st

s a

= min

( )( )( )() 1 2 23 4

(12-78)

depends on four functions of environmental factors which influence stomatal function, and the

minimum stomatal resistance (rst min) which depends on vegetative species. The minimum stomatal

resistance is a bulk parameter which reflects the maximum conductance of a leaf per unit area under

unstressed conditions (well watered, full sunlight, and optimal temperature and humidity). This

parameter is specified in the model according to vegetation type. The key to the model’s ability to

simulate stomatal conductance in real world conditions is the four environmental stress functions,

F1-4 in Equation 12-78. This kind of stomatal model, with independent empirical stress functions,

is often called a Jarvis-type model after Jarvis (1976). Specifically, the land surface model in

MM5PX is based on Noilhan and Planton (1989) (hereafter referred to as NP89) with many

subsequent modifications. The radiation stress function is:

F f

fr r st st

1

1 = +

+ min max / (12-79)

with f R

R

G

GL

= 0 55 2 . where rst max is maximum stomatal resistance which is an arbitrarily large

number (5000 s/m), RG is solar radiation at the surface and the 0.55 factor is an approximation for

the photosynthetically active portion, and RGL is a limit value of 30 W/m2 for forest and 100 W/m2

for crops according to NP89. The only difference from the F1 in NP89 is that the dependence on

LAI has been removed since the effects of leaf shading within the canopy are now accounted for by

the shelter factor in Equation 12-77. Therefore, the F1 as defined here represents the effects of

sunlight on an individual leaf rather than the integrated effect on a canopy. The functions of root

zone soil moisture and air temperature (F2 and F4) were modified to follow the form of logistic

curves as suggested by Avissar et al. (1985). Logistic curves are “S”-shaped and therefore good

for representing a smooth transition from one state to another. Also, logistic curves can be defined

with varying degrees of abruptness, from an almost linear transition to an almost threshold

behavior, and can be altered while maintaining differentiability. The function of root zone soil

moisture (w2) is:

F wb 2 af w =+− + 1 1 50 / exp . ( ) [ ] ( ) (12-80)

where the available soil moisture fraction is:

w

w w

w w af

wlt

fc wlt

= −

−

2

and the half point of the function (where F2 = 0.5) is:
EPA/600/R-99/030

12-44

b ww w w = − ( ) fc wlt wlt / 3 +

where wwlt is the wilting point and wfc is the field capacity. All soil moisture values (w) are in

volumetric fraction. In many previous models, including NP89, Jacquemin and Noilhan (1990),

Wetzel and Chang (1988), Mihailocic et al. (1993), Sellers et al. (1986), and Avissar et al (1985),

the function of air humidity (F3) is expressed in terms of vapor pressure deficit between the inside

of the leaf, assumed to be saturated at leaf temperature, and ambient air humidity (vpd = es(Ts)-ea).

However, recent advances in plant physiology research have led to a new generation of stomatal

models based on leaf photosynthesis (Sellers et al., 1997) in which stomatal conductance (gst =

1/rst) is a linear function of relative humidity at the leaf surface (Collatz et al., 1991):

g g RH b st st s = ′ + (12-81)

where g′

st is the stomatal conductance at RHs = 1 and b is the minimum stomatal conductance at

RHs = 0. Clearly, it makes more sense that stomata react to the humidity at the surface of the leaf

rather than the ambient air humidity at some height above the canopy. Although, a physical

mechanism for this linear relationship to leaf surface RH has not been determined, experimental

data shows it to be a very good fit (Ball et al., 1987). Since leaf surface relative humidity is neither

an easily measured nor a modeled quantity, it must be computed from other parameters. According

to the electrical analog, the humidity at the leaf surface (ql) is an intermediate potential between the

ambient air humidity (qa) and the leaf interior humidity, qs(Ts,), where Ts is surface temperature and

qs is saturation humidity (see Figure 12-9 for the schematics of the derivation). Assuming

constant flux from the ambient air to the leaf interior, the relative humidity at the leaf surface (RHs

= ql/qs(Ts)) can be represented as:

RH qg qg

g gq s

a a s st

st a s

= +

( ) +

(12-82)

where ga is the air conductance (1/(Ra+Rbw)) and qs is short hand for qs(Ts). If we assume that b in

Equation 12-81 is small compared to gst, which will be true in all but the driest conditions, and g’st

is the result of Equation 12-78 without the effects of humidity (g’st = F3/rst), then RHs is the

solution of a quadratic equation which can be computed, once all the other components of Equation

12-78 have been determined. F3 is equal to RHs but with a minimum imposed at 0.25.
EPA/600/R-99/030

12-45

Ambient Humidity

Leaf Surface

• qa

•

•

•

qleaf

qsat

Leaf Surface

Humidity

= 1/gst

= 1/ga

Ra

Rb

Rst

Figure 12-9. Derivation of Leaf Surface Relative Humidity

The fourth environmental stress function (F4 ) is related to ambient temperature. Again, we deviate

from the NP89 formulation which used a quadratic function peaking at the optimal temperature of

298 K. Instead, we followed the method of Avissar et al. (1985) which results in a function with a

plateau over a range of optimal temperatures, the idea being that temperature (Ta ) inhibits stomatal

function only at extremes of heat or cold. F4 is defined as:

F aT b 4 Ta T =+ − 1 1/ exp ( ) [ ] ( ) (12-83)

where aT = -0.41 and bT = 282.05 K for Ta ≤ 302.15 K and aT =1.18 and bT = 314 K for Ta >

302.15 K. Note that the high side of the function extends into higher temperatures than suggested

by Avissar et al. (1985) who used a bT = 307.95. The current function is very similar to the

function used by Rochette et al. (1991) and is close to the high side of the NP89 F4 function.

Resistances for all of the non-stomatal dry deposition pathways in the M3DDEP module of MCIP

are similar to the dry deposition model developed for the Acid Deposition and Oxidant Model
EPA/600/R-99/030

12-46

(ADOM ) by Pleim et al. (1984) and later evaluated and modified by Padro et al. (1991). As in

ADOM, surface resistances to ground and leaf cuticles are scaled relative to the most well measured

chemical species such as SO2 and O3. The term used for the scaling factor: relative reactivity has

caused considerable confusion since many users try to find a chemical definition for this parameter.

This factor has no chemical definition but is simply meant to be a relative scaling factor for the

removal rate of different species at the ground or cuticle surfaces. It is assumed that the relative

propensity to deposit to different surfaces is similar, so that the same scaling factor can be used for

ground and cuticles:

rg = rgo Ao/A (12-84a)

rcut = rcuto Ao/A (12-84b)

where rgo and rcuto are the ground and cuticle resistances, respectively, for the reference chemical

species (usually SO2 or O3) and Ao and A are the relative reactivities for the reference species and

the modeled species, respectively.

One improvement from the original ADOM model is the inclusion of an in-canopy aerodynamic

resistance which is added in series to the ground resistance for the vegetated portion of the modeled

area (fv) according to Erissman et al. (1994):

rlc = 14 LAI hc / u* (12-85)

where hc is the height of the canopy. For wet or partially wet canopies (fw), the surface resistance

to wet cuticle is estimated as:

rcw = rcwoKH / α* (12-86)

where KH is the nondimensional Henry’s law constant and α* is an aqueous dissociation factor.

The empirical factor (rcwo ) is set to 2.4x108

 s m-1, which is similar to Wesely (1989). For O3, rcw

is set to 1250 s m-1 based on field measurements. The pH of the canopy water can be specified to

compute α* for species such as SO2 and NH3 which readily dissociate. The canopy wetness

fraction (fw) is provided by the surface model in MM5PX. For deposition to open water, the

ground resistance is replaced by a water surface resistance according to Slinn et al. (1978):

rgw = KH /(4.8e-4 α* u*) (12-87)

The parameters needed for the non-stomatal part of this model are quite uncertain for many

chemical species. Our latest estimation of these parameters for the species in the RADM2 chemical

mechanism for which dry deposition is considered to be an important process are presented in

Table 12-8. The Henry's law coefficients in Table 12-8 are in non-dimensional form as the ratio of

gas- to aqueous-phase.

Molecular diffusivity and Henry’s law have the least amount of uncertainty since these have

definite chemical definitions and can be experimentally determined. Relative reactivity, however,
EPA/600/R-99/030

12-47

is less well defined and is estimated according to experimental and modeling studies in the

published literature . The only organic species for which dry deposition is considered significant

are the aldehydes, peroxides, and acids, all of which are soluble in water. For these organic

lumped species the numbers for reactivity are merely educated guesses.

Table 12-8. Chemical Dependent Parameters for M3DDEP

Species Diff

(cm2/s) α*

(dimensionless)

Reactivity

(dimensionless) Henry's law& ( KH )

(dimensionless)

SO2 0.1509 1000.0 8.00 0.04

NO2 0.1656 1.0 2.00@ 3.5

O3 0.1594 10.0 16@ 2.0

H2O2 0.2402 1.0 30@ 4.e-7

HNO3 0.1628 1.0e9 800@ 2.7e-7

NH3 0.2626 1.0e5 10.0 6.6e-4

PAN 0.0938# 1.0 4.0 0.01

NO 0.1877# 1.0 2.0+ 23.

HCHO 0.1877# 1.0 10.0+ 4.E-6

ALD 0.1525# 1.0 10.0+ 2.7e-3#

OP 0.1525# 1.0 10.0+ 1.7e-4#

PAA 0.1220# 1.0 20.0+ 7.6e-5#

ORA 0.1525# 1.0 20.0+ 1.0e-8#

HONO 0.1525# 1.0 20.0+ 4.1e-7#

CO 0.2033# 1.0 5.0 40.

@ Updates based on literature review

#

 Diff and H based on Wesely (1989) same as RADM

+

 Estimated

& gaseous phase value/aqueous phase value

The dissociation factor (α*) is simply defined as the ratio of the effective Henry’s law coefficient

to the actual Henry’s law coefficient. In this case, the effective coefficient is meant to include both

aqueous dissociation and aqueous reactions. The α*s for SO2 and NH3 are particularly important

since their solubilities are greatly effected by dissociation, which is a strong function of pH for

both species. Therefore, the model enables the user to specify the pH of the rainwater wetting the

canopy and let the model compute α* rather than use the default values in Table 12-7. The α* for

O3 is also important since O3 is only slightly soluble so any enhancement can have a large effect.

The value of 10 for O3 is meant to account for, very approximately, aqueous reactions such as the

oxidation of S(IV) to S(VI). Clearly, all of these parameters are quite uncertain and subject to

revision.

The main advantage of the M3DDEP model over the many similar models previously used in air

quality modeling is the coupling to the land surface model for description of the stomatal pathway.

This is a very important feature for certain chemical species, particularly O3 and SO2, which have
EPA/600/R-99/030

12-48

been shown experimentally to have a strong stomatal pathway components. Several studies with

this model have demonstrated its ability to realistically simulate both latent heat flux, with a large

fraction from evapotranspiration, and ozone dry deposition, over corn and soybeans (Pleim et al.,

1996; Pleim et al., 1997). These studies are continuing and are being extended to other chemical

species (SO2), and land-use types (deciduous and coniferous forests).

12.3.3 Cloud Parameters and Solar Radiation

Cloud information is developed and used in many different ways throughout the Models-3 CMAQ

system. For example, MM5 includes parameterizations related with subgrid convective clouds,

grid resolved cloud water and microphysics, and cloud effects on radiation. The CCTM needs

cloud information for photolysis, convective transport, and aqueous chemistry. Therefore, MCIP

has an important role in providing cloud information to CTMs by either propagating information

from upstream processors (MM5) or by parameterization.

MCIP has multiple cloud parameterizations and functions depending on the options selected.

There are currently two main options related to MM5 runs, either the standard MM5 version 2.6

which does not include cloud cover and radiation parameters in its output, and MM5PX which

does. Later versions of MM5 (2.7, 2.8, and 2.9) also output these additional parameters.

However, when MM5v2.6 or earlier versions are used, it is necessary to compute these parameters

in MCIP. Incident solar radiation at the surface is an important output from MCIP since it is used

to estimate biogenic emissions in the emissions processor.

Another cloud function in MCIP is to diagnose cloud information (such as cloud top, cloud base,

liquid water content, and cloud coverage) which is passed to the CCTM to adjust actinic fluxes for

computation of photolysis rates. This function is executed regardless of the choice of the MM5

version used. In addition, grid resolved cloud water and rain water are propagated through MCIP

from the MM5 output to CMAQ for use in aqueous chemistry and for photolysis calculations at the

4 km grid resolution.

12.3.3.1 Cloud Coverage

The fractional cloud coverage scheme currently used in MCIP is the same as used in MM5PX and

similar to the scheme used in the standard MM5. Cloud cover fraction ( fc

k

) above the boundary

layer is computed at each vertical model level k , according to Geleyn et al. (1982), as:

f RH RH

RH c

k

k

c

c

= −

−





 



 1

2

(12-88)

where RHc is the critical relative humidity defined as a function of σ as:

RHc cc c =− − + − 1 2 1 1 1 732 0 5 σσ σ ( )[ . ( . )]

where σ c

k k

p p PBL = / .
EPA/600/R-99/030

12-49

We have modified the Geleyn scheme to avoid the overprediction of clouds in well-mixed

boundary layers. Within the convective boundary layer (CBL) when RH RH > c the cloud cover is

estimate by:

f RH RH

RH c

k

k

c

c

= −

− 0 341 . (12-89)

where the critical relative humidity (RHc) within the CBL is set to be 0.98. The factor 0.34 is from

the suggestion that convective mixing induced clouds within the CBL should not exceed the

fractional area of the updrafts at top of CBL, which large eddy simulations estimate to be about

34% (Schumann, 1989; Wyngaard and Brost, 1984) when inactive clouds are disregarded. The

resulting layered cloud fractions, from Equations 12-88 and 12-89, are used for both functions;

namely, to be used in the surface radiation calculation when these parameters are not read from

MM5, and to derive the cloud parameters needed for the photolysis calculations.

For the surface radiation calculation, the layered cloud cover fractions are aggregated into the same

three broad vertical cloud layers (low, middle, and high) as in MM5, assuming maximum overlap.

Each layer is defined by pressure such that the low layer is between 97 and 80 kPa, the middle

layer is between 80 and 45 kPa and the high layer is above 45 kPa. These three cloud layer

fractions are then used in the radiation calculation described in this section (12.3.3.2).

The photolysis model requires cloud information in a different form. For the sake of consistency,

these parameters are estimated from the same layer resolved fractional coverage described above

(Equations 12-88 and 12-89). The photolysis model assumes a single uniform, vertically mixed

cloud layer. Therefore, the required parameters are; cloud top, cloud base, cloud fractional

coverage, and average liquid water content. Cloud top and base layers ( ktop and kbase ) are

determined by looking up and down from level of maximum coverage to where the fractional

coverage first becomes 50% of the maximum. The layer average cloud cover is then computed

from the volume averaging of layer cloud fractions between ktop and kbase :

f fz z c

Tot

c

k

F

k

k

k

F

k

k

k

base

top

base

top

= ∑ ∑ ∆ ∆ / (12-90)

Once the base, top, and fraction of the cloud layer are determined, the average liquid water content

of the cloud is computed assuming convective characteristics as described by Walcek and Taylor

(1986), Chang et al. (1987), and Chang et al. (1990). The lifted condensation level is assumed to

be at the cloud base, defined as the bottom boundary of cloud layer kbase , where the air is saturated

at the model’s ambient temperature. The in-cloud liquid water profile (qc) is then computed as a

fraction of the adiabatic liquid water profile (qad):

q q c = α ad (12-91)
EPA/600/R-99/030

12-50

whereα = − 07 8 02 . exp / . [ ] ( ) p plcl + and plcl is the pressure (in KPa) at the lifting condensation

level according to Warner (1970). The layer liquid cloud water values are then vertically averaged

in the same way as fractional coverage (Equation 12-90).

12.3.3.2 Computation of Solar Radiation Components

To meet air quality modeling needs, MCIP outputs several parameters related with radiation at the

surface including: incident surface shortwave radiation (Rgrnd), absorbed surface shortwave

radiation (Gsw), net long wave radiation at the ground (Glw), total net radiation at the ground (Rnet),

and surface albedo (A). These radiation components are used in several CMAQ processors. For

example, photosynthetically active radiation (PAR), which is needed for the biogenic emissions

processing, is estimated with PAR R = grnd 0 55 . . Depending on which version of MM5 is used,

surface radiation parameters are either passed through from MM5 or computed in MCIP. The

computation of surface radiation parameters in MCIP is identical to the surface radiation option in

MM5, as described in Grell et al. (1995), except that the dependence on zenith angle is added to the

land use specified albedo (Alu) such that:

AA Z = + lu 0 1 0 00386 1 0 [ ] ( ) − 3 2 . exp . . / (12-92)

where Z is zenith angle in degrees.

Note that MCIP computations of surface radiation parameters, which essentially replicate MM5,

are a stop gap measure for use with MM5v2.6 which does not output these values. All later

versions of MM5 do output these parameters which will be read and passed through by MCIP as is

now done for the MM5PX option. It will be preferable in future applications of Models-3 to

directly propagate the radiation parameters from MM5 to CMAQ so that the more sophisticated

radiation models now available in MM5 can be used. The currently used surface radiation option

includes effects of clouds, aerosols, and water vapor on radiation but neglects radiation effects on

the atmosphere. Therefore, many future applications may utilize either the Dudhia radiation

scheme (Dudhia, 1989) or the CCM2 scheme (Hack et al., 1993) which include atmospheric

radiation effects. See Chapter 3, section 3.3.4.1, for description of MM5 radiation options.
EPA/600/R-99/030

12-51

12.4 Meteorological Data for CCTM with Generalized Coordinate System

One feature of the CMAQ system that is distinct from other Eulerian air quality modeling systems

is its ability to incorporate meteorological models with various different coordinates and dynamics.

This functionality is achieved by recasting meteorological parameters in terms of the variables used

in the governing set of equations for the fully compressible atmosphere in generalized coordinate

system (Byun, 1999a). Key dynamic and thermodynamic parameters are estimated for the given

coordinates in such a way to ensure consistencies among the meteorological data. The consistency

can be maintained throughout CCTM simulations when appropriate temporal interpolation methods

are used.

12.4.1 Thermodynamic Variables: Pressure, Density and Entropy

To facilitate mass-consistent interpolation among the thermodynamic variables, the governing set

of equations for the fully compressible atmosphere is used in the CMAQ system. The system

includes prognostic equations for entropy and air density as suggested by Ooyama (1990). The

algorithms used for estimating the thermodynamic parameters are presented below. For a detailed

discussion on the governing set of equations and mass-consistent interpolation algorithm, refer to

Byun (1999a and b).

12.4.1.1 Pressure, Density of Air and Density of Water Vapor

Like most of the other meteorological models, MM5 does not use a predictive equation for air

density. Instead, air density is estimated with the equation of state using predicted pressure and

temperature. For a terrain-influenced pressure coordinate, when it is applied for hydrostatic

atmosphere, the hydrostatic pressure ( p ̃ ) can be computed with  ̃ * p available from MM5.

ppp p T p== +  ̃  ̃ ̃

* σ (12-93)

The total pressure (p) in the terrain-influenced reference pressure coordinate (applied for a

nonhydrostatic atmosphere in MM5) is the sum of the reference pressure and perturbation pressure:

pp p p p p =+= ++ op oT p σ * (12-94)

Once p is known, virtual temperature (Tv ) and density of the (moist) air are computed with:

T T

m

m

p

p

v w

d

w

=

1 1 + − ( )

, (12-95)

where mw and md are the molecular weights of water vapor and dry air, respectively , and

ρ = p

R Td v

. (12-96)
EPA/600/R-99/030

12-52

The water vapor partial pressure ( pv ) can be found from the vapor mixing ratio (r) supplied by

MM5 using the following equation:

p r

R

R v p v

d

= d . (12-97)

Then, the density of water vapor is simply given as:

ρ ρ v

r

r = 1+

. (12-98)

12.4.1.2 Entropy

In the CMAQ system, entropy is treated as one of the key thermodynamic parameters. Because its

conservation equation follows similar continuity equation for air density, entropy can be

interpolated using the same interpolation scheme as air density. Then, we can reconstruct

temperature and pressure for the intermediate time steps from the interpolated densities (for air and

water) and entropy. This type of interpolation will maintain mass consistency among the

thermodynamic variables for air quality applications. Using the density of moist air and density of

water vapor obtained above, the entropy for moist air can be computed with:

ζρ ρ ρ ρ ρ

ρ

ρ ρ

ρ

= + +− − ( )ln( ) ln( ) ln( )

*

d vd v vv

oo

v oo d d

d

doo

v v

v

v o

C C T

T

Λ R R , (12-99)

where ρ ρρ d = − v , poo =105

 Pascal,Λoo is the specific entropy of saturated vapor, ρdoo is the

density of reference dry air, and ρv o* is the density of reference state water vapor saturated over

water at reference temperatureToo , 273.15 K. The integral constants are computed following

Ooyama (1990):

ρd

oo

d oo

oo

p

R T = (12-100)

Λ Λ oo oo v oo

c

c T

T RT d ET

dT oo

= = ( ) ln ( ) (12-101)

ρ ρ v o v oo

c

v T

T E T

R T oo

* * ( ) ( ) = = , (12-102)

where T T c = − 273 15 . .

For the basic formulation of the saturation vapor pressure approximation, we use the AERK

formula recommended by Alduchov and Eskridge (1996):
EPA/600/R-99/030

12-53

E T ae c

bT c T c c ( ) /( ) = + (12-103a)

d ET

dT

bc

c T

c

c c

ln ( )

( ) = + 2 , (12-103b)

where a=610.94, b=17.625, c=243.04 and E Tc ( ) is in Pascal. With this information we can

evaluate the integration constants, and thus the entropy using Equation 12-99.

12.4.2 Vertical Jacobian and Layer Height

In the CCTM, Jacobian is used for the definition of vertical and horizontal coordinates/grid system

at every model synchronization time step. The Jacobian characterizes the coordinate transformation

and is treated as one of the fundamental parameters defining grid structure of the CTM. Depending

on the horizontal map projections and vertical coordinates, the physical characteristics of the

Jacobian change.

12.4.2.1 Jacobian for Coordinate Transformation

The vertical Jacobian defines the coordinate transformation rules. For a vertical coordinate xˆ 3 = ξ ,

where ξ is a monotonically increasing function of height, the Jacobian is related with the

geopotential height, Φ = gz, as:

J

g g ξ

∂

∂ξ

∂

∂ξ = = 1 1 Φ Φ (12-104)

 Sigma- p ̃ , time dependent coordinate 

For hydrostatic application of MM5, the vertical coordinate is the same as the terrain-influenced

sigma- p ̃ coordinate, whose vertical Jacobian is defined as

J p xyt

g σ p ρ  ̃

 ̃ (, ,)

 ̃

*

= (12-105)

Note that Equations 12-3 and 12-105 are identical although CMAQ uses monotonically increasing

coordinate ξ and MM5 uses monotonically decreasing sigma- p ̃ coordinate.

Using the Equation of State and the definition of the sigma- p ̃ coordinate, the vertical Jacobian can

be obtained using the temperature and surface pressure from MM5.

Jacobian at half sigma-level is estimated for 1≤ ≤ k K with:

J Rp T

g pp p H

k

air vH

k

H

k

T

σ σ  ̃

 ̃

(  ̃ )

*

( ) * = •

+

, (12-106)
EPA/600/R-99/030

12-54

where K is the number of model layer (i.e., NLAYS in Models-3 I/O API), and Jacobian at full

sigma-level is computed for 1≤ ≤ k K-1 with:

J Rp T T

g pp p F

k

air vH

k

vH

k

F

k

T

σ σ  ̃

/

/

 ̃ ( )

(  ̃ )

*

( ) * = • +

+

+

+

+ 1 2 1

1 2 2 (12-107)

and, at the surface (k=1/2) with:

J Rp T

g pp p F

k

air vs

F

k

T

σ σ  ̃

/

/

 ̃

(  ̃ )

*

( ) * = •

+

=

=

1 2

1 2 , (12-108)

where we have used Tvs to represent the virtual air temperature at the surface.

For the thirty layer MM5 sigma- p ̃ coordinate, whose sigma value for the top of first layer is set

0.995 (i.e., about 38 m in the standard atmosphere), the reference temperature is estimated from

the average between the skin temperature (Tg ) and air temperature at the lowest model layer. The

virtual air temperature at the surface is computed with the assumption that the relative humidity at

the surface is the same as the relative humidity at the middle of first layer.

 Time independent coordinate 

For the nonhydrostatic application of MM5, we use the terrain-following sigma- po coordinate

whose vertical Jacobian is defined as:

J p xy

g po

o

o

σ ρ =

*

(,) (12-109)

Again, Equations 12-6 and 12-109 are identical although CMAQ uses monotonically increasing

coordinate ξ and MM5 uses monotonically decreasing coordinate. Using the Equation of State for

the reference hydrostatic atmosphere and the definition of the sigma- po coordinate, the vertical

Jacobian can be obtained using the temperature and surface pressure from MM5. Jacobian at half

σ-height is estimated for 1≤ ≤ k K with:

J

Rp T A p p

p

g pp po H

k air o os

H

k

o T

oo

H

k

o T

σ

σ

σ ( ) =

• +

 +



 





+

*

*

*

ln( )

( ) (12-110)

and Jacobian at full σ-height is computed for 0 ≤ ≤ k K with:

J

Rp T A p p

p

g pp po F

k air o os

F

k

o T

oo

F

k

o oT

σ

σ

σ ( ) =

• +

 +



 





+

+

+

+

1 2

1 2

1 2

/

/

/

*

*

*

ln( )

( ) (12-111)
EPA/600/R-99/030

12-55

The Jacobian does not depend on MM5 data except for the topographic height and sigma-layer

definition.

 Total Jacobian 

The total Jacobian ( γˆ / ξ ≡ J m2) is used in the governing equations for the CCTM. The trace

species concentrations are coupled with the total Jacobian. Because of the need to couple with both

the trace species concentrations (defined at the layer middle) and vertical flux variables (defined at

the layer interface), total Jacobians at the half and full level values are stored in the MET_CRO_3D

file. The total Jacobian at the surface, J p F

k

σ  ̃

/

( ) =1 2

 divided by the map scale factor squared, is stored

in the MET_CRO_2D file. For hydrostatic applications of MM5 the Jacobian varies with time and

for nonhydrostatic applications it is constant with time. Although we could have saved some file

space by distinguishing this feature, the Jacobians are stored in MET_CRO_3D and

MET_CRO_2D files to maintain the compatibility of data structure for both time-dependent and

time-independent coordinate systems.

For use in the mass-conserving temporal interpolation, Jacobian weighted densities at the halflevels defined for 1≤ ≤ k K as:

( / ) ( / ) () J m Jm H

k

H

k

H

k

ξ ξ ρ ρ 2 2 = • (12-112a)

( / ) (/ ) () J m Jm v H

k

H

k

v H

k

ξ ξ ρ ρ 2 2 = • (12-112b)

are stored in the MET_CRO_3D file. Like density, the Jacobian weighted entropy at the layer

middle is obtained for 1≤ ≤ k K with:

( / ) ( / ) () J m Jm H

k

H

k

H

k

ξ ξ

ζ ζ 2 2 = • (12-113)

They are stored in the MET_CRO_3D file as the Jacobian-weighted total air density and water

vapor density, and entropy, respectively.

12.4.2.2 Layer Heights

In CMAQ, layer heights are computed using the basic definition of the geopotential height in terms

of Jacobian instead of relying on the coordinate-specific analytic equations, such as a hypsometric

equation for a hydrostatic coordinate. The height above mean sea level (MSL) is defined in terms

of the vertical Jacobian as:

z g z Jd ˆ / ˆ ' s s

= =+ Φ ∫ ξ ξ

ξ

ξ (12-114)

The layer heights at the interface and middle of the layers above the ground level (AGL) are

computed with:
EPA/600/R-99/030

12-56

z z z Jd J F

k

F

k

s H

j

F

j

j

k

F

j

s

F

k

++ +

=

= −= ≅ −

+

−

∫ ∑ 12 12

1 2

12 12

1

/ /

/

/ / ˆ ˆ '( ) ξ ξ

ξ

ξ ξ ξξ (12-115a)

for 1 ≤ ≤ k K+1, where

zF

k

k

+

= = 1 20

0 / (12-115b)

and for 2≤ ≤ k K with:

z z z Jd H

k k

s s

H

k

= −= ∫ ˆ ˆ ' ξ ξ

ξ

ξ

 ≅+ + − − −

=

z JJ H ∑ H

j

H

j

H

j

j

k

H

1 11 1 j

2 2

( )( ) ξ ξ ξ ξ (12-116a)

where

z JJ H H F H F

1 12 12 1

2

1 1 =+ − ( )( ) / /

ξ ξ ξ ξ (12-116b)

Note that both zF

k +1 2/

 and zH

k are stored either in the GRID_CRO_3D file for the time independent

vertical coordinate, or in the file MET_CRO_3D for time dependent one. Because zF

k

k

+

=

1 2

0

/

 is

always zero for the terrain-influenced coordinates, it is not stored in any of MCIP files.

12.4.3 Contravariant Velocity Components

The generalized CCTM requires a set of contravariant velocity components to simulate numerical

advection. Contravariant velocity components are scaled components of the wind vectors for the

transformed coordinates. When the true velocity components (i.e., wind components for earthtangential coordinates) are predicted in a meteorological model, they need to be transformed

accordingly.

12.4.3.1 Horizontal Wind Components

MM5 predicts horizontal wind velocity components defined on the spherical earth in the coupled

form with the surface pressure scale p* . First, we need to de-couple the surface pressure scale as

follows:

U pU p lm lm lm ++ ++ ++ = 12 12 12 12 12 12 // // // , * , *, ( ) /( ) (12-117a)

V pV p lm lm lm ++ ++ ++ = 12 12 12 12 12 12 // // // , * , *, ( ) /( ) (12-117b)
EPA/600/R-99/030

12-57

for 0 ≤ ≤l L and 0 ≤ ≤ m M, where L is the number of columns and M is the number of rows for the

rectangular modeling domain. In the expression, p* represents either  ̃ * p or po

* depending on the

hydrostatic/nonhydrostatic option in MM5. The value p* at the dot-point is approximated with:

( ) [( ) ( ) ( ) ( ) ] * , *, * , * , *, / /p pp p p

l m lm l m l m lm + + + ++ + = ++ + 12 12 1

4

1 11 1 (12-118)

The next step is to compute the contravariant components u mU ξ = and v mV ξ = at the dot-point:

( ) // // // , ,, u mU lm lm lm

ξ

++ ++ ++ = 12 12 12 12 12 12 (12-119a)

( ) // // // , ,, v mV lm lm lm

ξ

++ ++ ++ = 12 12 12 12 12 12 (12-119b)

Because the Jacobian-mass weighted contravariant wind components are needed for the mass

consistent interpolation, we estimate these quantities at the square-point (flux point) for xˆ

1

-

direction and at the triangle-point (flux point) for xˆ 2 -direction, respectively:

( ) [( ) ( ) ][( ) ( ) ] / , , ,, / / /, / ρ ρρ ξ

ξ

ξ ξ

ξ ξ

J

m

u

J

m

J

m

u u

l m lm l m l m l m

2 22

12 1 1 1 1 12 12 12 32 1

4

+ + + ++ + + + + ≅+ + (12-120a)

( ) [( ) ( ) ][( ) ( ) ] , ,,, / / / /, / ρ ρρ ξ

ξ

ξ ξ

ξ ξ

J

m

v

J

m

J

m

v v

l m lm lm l m l m

2 22

1 12 1 1 1 12 12 32 12 1

4

+ + + ++ + + + + ≅+ + (12-120b)

Both of these parameters, together with the contravariant wind components uξ and vξ at the DOT

points, are stored in the MET_DOT_3D file.

12.4.3.2 Vertical Wind Component

In most meteorological models with terrain-influenced coordinates, the contravariant vertical

velocity components are not computed directly because of the complex representation of the

divergence term in the generalized coordinate system. In the generalized coordinate system, the

prognostic equation for the vertical component contains Christoffel-symbols-of-the-second-type

terms that make the equation not only complicated but also make conservation of momentum or

kinetic energy difficult (Byun, 1999a). To circumvent this difficulty, some meteorological models

use the prognostic equations of motion for the true vertical wind component.

For the MM5 hydrostatic application, the terrain-influenced hydrostatic pressure coordinate allows

diagnostic computation of the contravariant vertical velocity. The continuity equation for air

density becomes a diagnostic equation for this application. Here, the expressions are written with

the normalized vertical coordinate, which increases with geometric height, ξ σ ≡ −1

p ̃ . By

selecting the integration limits as ξ = 0 to 1, (i.e., σ

ps ̃ = 1 to σ pT ̃ = 0 ) and using the boundary

conditions at the top and bottom  ̇

ξ = = vˆ

3 0 , the tendency term can be computed with:
EPA/600/R-99/030

12-58

∂ ρ

∂

∂

∂ ρ ξ ξ ρ

ξ

ξ ( )  ̃ [  ̃  ̃ ˆ

] 

*

*

* J

t

p

t

p

Q

m

p

m

= = − ∇• d ∫ 2

2

0

1 V

(12-121)

This equation predicts time rate change of the hydrostatic pressure component whose vertical

gradient is in balance with gravitational acceleration. In the geometric height coordinate, this

equation does not exist. However, the height coordinate does not require surface pressure

tendency to close the system because the coordinate is time independent. Because the hydrostatic

pressure coordinate ξ σ ≡ −1

p ̃ is a material coordinate, the mass continuity equation can also be

used to estimate contravariant vertical velocity component by integrating the wind divergence term

either from the bottom to a level ξ or from the top to ξ.

 ̇ [

ˆ

] ' ( ) ξ

ρ

ρ ξ ξ

ρ

∂ ρ

∂ ξ

ξ ρ ξ

ξ ξ

ξ

ξ

ξ = − ∇• − ∫ 1 2

2

0 J JQ m

J

m

d

J

J

t

V

(12-122a)

 ̇ [

ˆ

] ' ( ) ( ) ξ

ρ

ρ ξ ξ ξ

ρ

∂ ρ

∂ ξ

ξ ρ ξ

ξ ξ

ξ

ξ

ξ

ξ = − ∇• − − ∫ 1 2

2 J JQ m

J

m

d

J

J

t T

T

V

(12-122b)

where ξT = 1.

For other coordinates that do not have diagnostic relations, the contravariant vertical velocity

component should be estimated using standard coordinate transformation

 ̇

ξ ˆ ( ) ∂ξ

∂

∂ξ

∂ ξ ξ = = + − •∇ + 



 

 v 

t

m hw

z

T

3 V (12-123)

where hT is the height of the coordinate surface and w is the regular vertical component of wind.

For nonhydrostatic MM5 applications, ξ σ ≡ −1 po is the corresponding vertical coordinate in

CMAQ. Equation 12-122a can be rewritten as:

 ̇  ̇ [ ˆ ]( ) [ ˆ ]( ) *

*

*

*

* ξ σ σ ∂

∂

σ ∂

∂

ρ =− = + + po

po

o

o po

o

o o

p o

p

x

mU

p

p

x

mV g

p

1 2 w (12-124)

Like the horizontal momentum components, we need the Jacobian-mass weighted contravariant

vertical wind for the mass consistent interpolation. The quantity is computed with the thicknessweighted density as:

(  ̇) ( ) ( )( ) // / /  ̇ ρ ξ ρ ρ ξ ξ ξξ J

m

f

J

m

f

J

m

k

z

k k

z

k kk

2 22

12 12 12 1 12 1 + + + ++ ≅ +−





 



 • (12-125)

where f z zz z z

k

F

k

H

k

H

k

H

+ + k =− − 12 12 1 / / +

( ) /( ). Note that (  ̇) ρ ξ ξ J

m

2 is defined at the layer interfaces. It is

zero at the earth’s surface (no-penetration boundary condition) and therefore not included in the
EPA/600/R-99/030

12-59

output. It also vanishes at the top of the modeled atmosphere. The quantity (  ̇

) ρ ξ ξ J

m

2 is stored in

the MET_CRO_3D file from k=1 to K ( i.e., NLAYS) with the variable name (WHAT_JD).

12.4.4 Mass Consistent Temporal Interpolation of Meteorological

Parameters

In the CCTM, the temporal interpolations of meteorological data are needed because the output

frequency of the meteorological data is usually much coarser than the synchronization time step of

the chemistry-transport model. Consistency in meteorological parameters such as, Jacobian,

density of air (total), density of water vapor, entropy (or temperature), and pressure are important

for the science modules in the CCTM.

Here, we recommend interpolation schemes for density and velocity fields that maintain mass

consistency. First, the Jacobian and density at a time t tt α =− + α α n n+ ( ) 1 1 between the two

consecutive output time steps, tn and tn+1 , are expected to be interpolated with:

( ) ( )( ) ( ) J JJ ξ α =− + α α ξ ξ n n+ 1 1 (12-126)

( ) ( )( ) ( ) ρ α ρ αρ ξ α ξ ξ J JJ =− +n n+ 1 1 (12-127)

where 0 1 ≤ ≤ α . The Models-3 I/O API provides a convenient function call (INTERP3) for the

linear interpolation of grid variables. The premise used here is that the Jacobian is a fundamental

quantity that determines the coordinate system. Density of water vapor ( ρv ) and entropy should

follow the same interpolation rule (Equation 12-127). Then densities and entropy at tn are

computed with

( ) ( )

( ) ρ

ρ

α

ξ α

ξ α

= J

J ; ( ) ( )( ) ρ

ρ ξ α

ξ α

v a

v J

J = ; ( ) ( )

( ) ζ ζ

α

ξ α

ξ α

= J

J (12-128)

It is obvious that the functional form of the Jacobian (which depends on a vertical coordinate)

changes the characteristic of density interpolation. For nonhydrostatic MM5 runs, where the

Jacobian is constant with time, the density is simply interpolated linearly with time.

When the density tendency term is available from the meteorological model, or can be computed

from diagnostic relations for certain choice of vertical coordinate system, one can use a piecewise

cubic spline interpolation method for ( ) ρJs :

( ) ρ ααα α J a b cd s = + ++ 3 2 (12-129)

where a t

J

t

t

J

t

J J s

n

s

n

= sn sn





 



 + 



 



 − − [ ] +

∆ ∆ +

∂ ρ

∂

∂ ρ

∂ ρ ρ () () () ()

1

2 1
EPA/600/R-99/030

12-60

bJ J t J

t

t

J

t sn sn

s

n

s

n

= − [ ] − 



 



 − 



 

 + 

+

3 2 1

1

() () () () ρ ρ ∂ ρ

∂

∂ ρ

∂

∆ ∆

c t

J

t

s

n

= 



 

 ∆  ∂ ρ

∂

( )

d J = s n ( ) ρ

The density of water vapor ( ρv ) and entropy should be interpolated with the same method. The

density of dry air from the total air density can be obtained by subtracting ρv from ρ. The

interpolated temperature is computed with:

T T R R

C C oo

d d d do v v v vo

d vd v vv

= + +

+

expζρ ρρ ρ ρρ ln( / ) ln( / )

ρ ρ

(12-130)

and entropy can be computed with Equation 12-99. The interpolated pressure is computed with the

ideal gas law,

p R RT = + d d v v ( ) ρ ρ (12-131)

Next, wind components multiplied with the Jacobian-weighted density are interpolated linearly and

the interpolated wind components are obtained by dividing the results with ( ) ρ α Js :

( ˆ ) ( )( ˆ ) ( ˆ ρ α ρ αρ ) α J JJ s s s sn s sn V VV =− + 1 +1 (12-132a)

(ρ α ρ αρ ˆ ) ( )( ˆ ) ( ˆ ) α Jv Jv Jv s sn sn

3 33 =− + 1 +1 (12-132b)

( ˆ ) ( ˆ )

( )

V V s

s s

s

J

J α

α

α

ρ

ρ = (12-133a)

(ˆ ) ( ˆ )

( )

v

J v

J

s

s

3

3

α

α

α

ρ

ρ = (12-133b)

When density and wind data are not collocated, the above procedure may incur spatial interpolation

errors.

12.4.5 Optional Conversion of Nonhydrostatic Data to Hydrostatic

Meteorological Data for MM5

There may be a special situation when a hydrostatic CTM run is desired while the MM5 run is

made with the nonhydrostatic option. In such a case one may want to redefine the nonhydrostatic

coordinate into hydrostatic one while keeping the profile data as provided. In spite of many

theoretical problems with this kind of data conversion, MCIP provides an option to convert the
EPA/600/R-99/030

12-61

nonhydrostatic coordinate into the hydrostatic pressure coordinate. Use of this option is not

recommended for scientifically rigorous computations. However, this is a useful option for certain

purposes such as code development and testing of a hydrostatic CTM.

Nonhydrostatic and hydrostatic coordinates can be compared in terms of the atmospheric pressure.

Pressure in a hydrostatic MM5 run is defined in Equation 12-93 while the same in a hydrostatic

MM5 is defined in Equation 12-94. Then, the difference in the nonhydrostatic and hydrostatic

pressures is:

p p pp p o p

* * =− −+ (  ̃) − − σ σ 1 1 (12-134)

If we force the hydrostatic pressure to be that of nonhydrostatic coordinate, i.e., p p ≈  ̃ at the

surface, the time dependent surface pressure, ps

* , can be estimated with:

ppp o pH

* * ≈ + ( ) σ1 (12-134’)

where σ σ F s

1 2 1 /

= = is used. Here, the perturbation pressure at the surface is assumed to be that of

layer 1 because the real surface perturbation pressure is not provided by the nonhydrostatic MM5.

One can redefine the vertical coordinate to be hydrostatic with the time dependent surface pressure.

The difficulty of converting nonhydrostatic meteorology data into hydrostatic data is not in the

estimation of pressure surfaces, but rather in the representativeness of profile data because of the

change in the layer definitions.
EPA/600/R-99/030

12-62

12.5 Operation of MCIP

Because MCIP is a Models-3 conformant processor, it needs to be compiled and executed using a

Models-3 build command (m3bld) with a configuration file. It requires the grid-domain object

include files to define output domain and resolution. In most cases, the user does not need to

define input data domains and resolutions because reader modules can extract the information from

file headers. MCIP code structure, compilation and execution procedures are discussed below.

Additional operational information for preparing MCIP through Models-3 system framework can

be found in Chapter 7 of the EPA Third-Generation Air Quality Modeling System User Manual.

Also, the User Manual Tutorial for the initial public release of Models-3 provides step-by-step

instructions for running MCIP with a set of sample examples.

12.5.1 MCIP Modules

MCIP code is archived with CVS (Concurrent Version System) (Cederqvist, 1993) in the Models3/CMAQ system. Currently, eleven module classes are defined for MCIP. The classification

makes it convenient to customize MCIP code for special situations. For example, when different

meteorological inputs and process options are needed to link with the CCTM, appropriate modules

from different classes can be used. Refer to Table 12-9 for the details of module descriptions and

associated source code.

12.5.2 Building MCIP

The MCIP code conforms to the Models-3 coding standard. It is designed to be compiled using

m3bld with a configuration file. Refer to Appendix 12C for a sample MCIP configuration file.

The user needs to retrieve the source code (main program, associated subroutines for selected

modules, and include files) appropriate to the user’s choice of optional modules through the CVS

system. There are four kinds of include files for this processor. Three include file types, Models3 I/O API include files, MCIP’s global include files, and MCIP module specific include files, are

fixed. The fourth include file type describes dimensional information of the input meteorology data

and, as an exception, must be edited to match the number of vertical layers in the input.

Therefore the parameter KMAX in MCIPPARM.EXT may need to be changed to match the

dimensions of working arrays. Horizontal domain information is obtained from the header of

MM5 files automatically. MCIP expects that include files for the CTM grid/domain domain

(HGRD.EXT, VGRD.EXT, COORD.EXT), for which the data will be extracted, are provide by

the user. Vertical collapsing is done automatically when the number of layers in VGRD.EXT is

less than the number of layers in input data and the coordinate interface values match as shown in

Table 12-5. When a few lowest input model layers are collapsed into one for the output, only

diagnostic option can be used because the surface flux values and aerodynamic resistance passed

through are no longer valid due to the change in the thickness of the lowest layer. The M3DDEP

option must not be used when collapsing the lowest model layers and doing so will be violating the

parameteric values passed through from the meteorological model.
EPA/600/R-99/030

12-63

Table 12-9. MCIP Module Definitions and Associated Source Code

Class Module Description Source Code

driver mcip controls main computational flow mcip.F, initx.F

input mm5 reads in MM5 output files getmet_mm5.F,

readmm1.F,

readmm2.F, getgist.F,

MM5INPUT.EXT,

MM5HEADER.EXT

m3 reads in MCIP output files getmet_m3.F

fakemet generates meteorology fields for idealized flow field

study

getmet_m3fake.F

rams reads in RAMS I/O API output files not available

landuse m3radm reads in landuse data in RADM dry deposition category getluse.F

pbl pblpkg computes PBL parameters pblpkg.F, pblpwr.F,

sfcflux.F, slflux.F

drydep radmdd computes dry deposition velocities using Wesely’s

RADM method

radmdry.F,

DDEPSPC.EXT

cmaqdd computes dry deposition velocities using Pleim’s

CMAQ method

not available

cloud radmkuo computes cloud parameters using convective column

assumption

bcldprc_ak.F

solar solar_px computes solar radiation using the algorithm

implemented in MM5-PX version

solar.F, transm.F

met3d m3sup computes supplemental three-dimensional variables

needed for CMAQ

layht.F, verthat.F,

vertnhy.F, verthyd.F,

jacobi.F, met3dsup.F

output stnd generates MCIP output for standard variable lists comheader.F, gridout.F,

metcro.F, metdot.F

util util collection of utility subroutines bilin2d.F, bilin3d.F,

cvbdx.F, collapx.F,

cvmgp.F, cvmgz.F,

ratint.F, errmsg.F,

sanity.F

icl icl MCIP specific include files CONST_mete.EXT,

CONST_pbl.EXT,

FILES3_MCIP.EXT,

GROUTCOM.EXT,

INFILES_MCIP.EXT,

LRADMDAT.EXT,

MCIPCOM.EXT,

MCIPPARM.EXT,

MCOUTCOM.EXT,

MDOUTCOM.EXT
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12.5.3 Executing MCIP

12.5.3.1 Run Script Command File

As with other interfaces, an execution run script is used to define key environmental variables

prescribing run-time characteristics and linkage between logical file names specified in the codes

and actual files for input and output. A sample script for MCIP execution can be retrieved from the

CVS archive and edited for the user’s particular application. The user may modify environmental

variables for choosing different processing options and for defining input and output files. Refer

to the APPENDIX D for a sample MCIP run script. For processing MM5 output, MCIP may not

need to be co-resident with MM5 if its output files are in IEEE binary format. MCIP can be run on

any UNIX computer for processing meteorological data in Models-3 I/O API format.

Input parameters METROW, METCOL, and METLAY are defined through the UNIX

environmental variable list. These are used to check if the input meteorology data have correct

dimensions as expected. Within MCIP, the actual values will be picked up from header

information of MM5 data file. When offset values (I0, J0) are inconsistent with the information in

MM5 header and in COORD.EXT, MCIP suggests a new set of (I0, J0) or (XORIG, YORIG)

values. Make sure to set NDEP to correspond to the number of lowest input layers being collapsed

into the lowest output model layer, so aerodynamic resistances are computed accordingly.

12.5.3.2 Input Files for MM5 Data Processing

Logical names of input files are described below:

• MMOUT_DOMAIN#: This standard MM5 file contains gridded hourly (or sub-hourly)

two- and three-dimensional meteorological data covering the entire MM5 domain.

• MDL3_DOMAIN#: This is optional EPA added MM5 output that contains file contains

PBL parameters needed when the pass-through option is chosen.

• LAND_CRO_2D_##KM: This is LUPROC output that contains 11-category fractional

land-use data covering the entire MM5 domain. If USGS North American land/vegetation

characteristic data base used as input to LUPROC is not enough to cover the desired

domain, dominant landuse file LANDUSE_DOMAIN# from TERRAIN, a preprocessor

for MM5 system, can be used.

12.5.3.3 Input Files for I/O API Meteorological Data Processing

MCIP can be used to extract meteorology data for a smaller window domain, to collapse number of

layers, or to process meteorological data already in I/O API format further. It treats gridded input

meteorological data as pseudo profiles for temperature, moisture and wind components. Required

I/O API meteorological inputs for this option are; GRID_CRO_2D, GRID_DOT_2D,

MET_CRO_2D, MET_CRO_3D, and MET_DOT_3D files. Because it does not use boundary

files as its input, the output domain can be as large as (NCOLS-2)x(NROWS-2) for windowing or

layer collapsing process. This option can be used to generate interpolated meteorology data for

higher resolution grid than the original input as well.
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Table 12-10. MCIP Environmental Variables

Environmental

Variables

Description Note

METLAY number of layers in input meteorology

data

should be larger than or equal to

CTM NLAYS

METCOL column (east-west) direction cell

dimension in input meteorology data

should be larger than CTM

NCOLS

METROW row (south-north) direction cell dimension

in input meteorology data

should be larger than CTM

NROWS

I0 location of CTM domain origin offset in

row direction = ROW_OFFSET

offset should be counted based on

the input grid definition

J0 location of CTM domain origin offset in

column direction = COL_OFFSET

offset should be counted based on

the input grid definition

LUTYPE file type for landuse data 1: TERRAIN binary 13 category

2: preprocessed ASCII 11

category

3: MM5 dominant landuse

category

4: use landuse in GRIDCRO2D

5: use USGS I/O API landuse

file

I0LUSE location of CTM domain origin offset in

row direction w.r.t. landuse data origin

offset should be counted based on

the input grid definition. For

LUTYPE 4 & 5, I0LUSE is not

used

J0LUSE location of CTM domain origin offset in

column direction w.r.t. landuse data origin

offset should be counted based on

the input grid definition. For

LUTYPE 4 & 5, J0LUSE is not

used

LCALCPBL flag for estimating PBL parameters of not TRUE: re-compute PBL

parameters

FALSE: pass through from

MM5

LSLFLUX flag for similarity algorithms TRUE: use surface layer

similarity

FALSE: use PBL similarity

LM3DDEP flag for dry deposition algorithm TRUE: use CMAQ dry

deposition

FALSE: use RADM dry

deposition
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Table 12-10. MCIP Environmental Variables (continued)

Environmental

Variables

Description Note

LWIND flag for wind field correction 0 (default): no correction

+/- 1,2,3 wind field correction

options (TBD)

LCALCCLD flag for cloud algorithm TRUE: compute cloud

parameters

FALSE: pass through from

MM5

LHYDOUT flag for hydrostatic output TRUE: forces hydrostatic data

output with approximations

FALSE: pass through from

MM5

CRO_FTYPE

DOT_FTYPE

flag for I/O API file type 1 (default): time dependent

0 (special): time independent

LSANITY flag for checking ranges of output

parameters

TRUE: check

FALSE: do not check

BMAX Maximum boost rate for urban area 2 (default): 100% increase when

urban and water areas are

coexisting

JUDATE Julian date for the start time (yyyyddd)

HSTRT start hour (hh)

HTOSKIP number of hours to skip MCIP process (hh)

HTORUN number of hours to run (hhh)

NDEP number of deposition layers 1 (default)

GRDNAM grid/domain name for MCIP output files

EXECUTION_ID user defined execution ID

SCENFILE user defined file path

IOAPI_CHECK_HEAD

ERS

flag for checking I/O API file headers FALSE (default)
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Table 12-11. MCIP File Linkage

Environmental

Variables

Description Note

MM51 Input filename for MM51 data file for mm5 input module

MM52 Input filename for MM52 data file for mm5 input module

LU13 Input filename for TERRAIN binary

landuse

applicable for LUTYPE = 1

LUSE input filename for I/O API landuse file applicable for LUTYPE = 4 or 5

GRID_CRO_2D input filename for GRID_CRO_2D for m3 input module

GRID_DOT_2D input filename for GRID_DOT_2D for m3 input module

MET_CRO_2D input filename for MET_CRO_2D for m3 input module

MET_CRO_3D input filename for MET_CRO_3D for m3 input module

MET_DOT_3D input filename for MET_DOT_3D for m3 input module

GRID_BDY_2D_G1 output filename for GRID_BDY_2D

GRID_BDY_3D_G1 output filename for GRID_BDY_3D

GRID_CRO_2D_G1 output filename for GRID_CRO_2D

GRID_CRO_3D_G1 output filename for GRID_CRO_3D

GRID_DOT_2D_G1 output filename for GRID_DOT_2D

MET_CRO_2D_G1 output filename for MET_CRO_2D

MET_CRO_3D_G1 output filename for MET_CRO_3D

MET_DOT_3D_G1 output filename for MET_DOT_3D

12.5.4 Defining Grid and Domain for MCIP

12.5.4.1 MM5 Grid and Domain Definitions

MM5 may output as many as nine grid domains (one coarse grid and up to eight nested grid

domains) per MM5 execution. The MM5 developers took the approach of compiling MM5 with

the appropriate dimensions for each study being performed. On the other hand, MCIP processes

output meteorological data one grid domain at a time. It needs to be compiled explicitly for each

grid domain. For multiple scale MM5 model runs, usually MM5 users have to define all the multilevel nest domains together with the coarse “mother” grid. The complication in defining MM5

domains as the Models-3 domain objects is caused by somewhat inauthentic use of the left-hand

coordinate system and dot-point grid/domain definitions in MM5. For the details on how to define

MM5 domains, users are recommended to read MM5 User’s Guide. In the following, we uses a

set of multi-level MM5 domains listed in Table 12-12 as the examples of the discussion.

Table 12-12. An Example Set of Multi-level Nesting MM5 Domains

(Note that (I, J) in MM5 corresponds to (ROW, COL) in CMAQ system.)

MM5

Domain

No. (N)

Resolution

(∆x=∆y)

Dimensions

(IX,JX) =

(ROWS+1,COLS+1)

Origin Relative to Base

Grid

(I_11,J_11)

Origin Relative to

Immediate Parent grid

( ROWoffset +1,COLoffset +1)

1 108km (41,61) (1,1) (1,1)

2 36km (67,82) (9,24) (9,24)

3 12km (82,100) (19.333333,35.333333) (32,35)

4 04km (100,82) (21.444444,41.555555) (20,57)
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a) Definitions for MM5 108 km mother grid (N=1)

In MM5, the grid is defined with the number of dot points. Therefore, to use MM5’s grid

definitions, for Models-3/CMAQ’s cross-point grid definitions, we need to use following

NCOLS = JX - 1 = 61-1 = 60 (12-138a)

NROWS = IX - 1 = 41-1 = 40. (12-138b)

For this grid, no “parent grid” is defined. Origins should be defined with the formula that is

specific to MM5’s method of grid/domain definition. Note that we require the MM5 mother

domain’s number of cells in horizontal directions (i.e., NCOLS and NROWS) to be even

numbers, so that the dimensions of the four quadrants relative to the center of the coordinates are

identical (Refer to Figure 12-9). The origin of the coarse MM5 grid is defined with

( , )( * , * ) x y

N

x

N

y orig orig

cols rows =− − 2 2

∆ ∆ (12-139)

Because it is the mother grid of the grid family, offsets should be set to zero:

( , ) (,) COL ROW offset offset = 0 0 (12-140)

Currently this domain is defined with resolution of 108km (see Table 12-12).

b) Definitions for MM5 36 km first-level nest grid/domain (N=2)

For this grid, the MM5 108km domain defined above is used as the “parent grid.” For the nested

domains, NCOLS and NROWS can be either even or odd numbers:

NCOLS = JX - 1 = 67-1 = 66 (12-141a)

NROWS = IX - 1 = 82-1 = 81. (12-141b)

Because the left-most and bottom corner of the nest 36km domain is defined with (, ) , , I J 11 11 in

MM5, we need to convert this information into (, ) COL ROW offset offset using following equation:

( , )( , ) COL ROW J I offset offset =− − 11 11 , , 1 1 (12-142)

Note that MM5 uses left-hand coordinate system, so that the index positions for (, ) , , I J 11 11 are

reversed with those for the Models-3/CMAQ’s (, ) COL ROW offset offset . In the following case, the

general equation for computing the offset numbers from (, ) , , I J 11 11 of the MM5 domains will be

presented. The coordinates of the origin is computed with:

( , )( , ) x y x COL x y ROW y orig orig orig

parent

offset

parent

orig

parent

offset

parent =+ + ∆ ∆ (12-143)
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c) Definitions for MM5 12 km and 4 km nest grid/domains (N=3, 4)

For the third, 12km domain (N=3),we have:

NCOLS = JX - 1 = 100-1 = 99 (12-144a)

NROWS = IX - 1 = 82-1 = 81 (12-144b)

and MM5 36km domain is used as the parent grid. Also, for the fourth 4 km domain (N=4), we

have:

NCOLS = JX - 1 = 82-1 = 81 (12-145a)

NROWS = IX - 1 = 100-1 = 99 (12-145b)

and MM5 12km domain is used as the parent grid. Usually, the offset values will be known to the

Models-3/CMAQ users.

II I

III IV

( xc , yc )

NCOLS

NROWS

MM5 Mother Grid/Domain and Coordinate Center

(xorig, yorig )

Figure 12-10. A Schematic of the MM5 Mother Grid Definitions.

Because MM5’s mother grid is defined from the coordinate center and grows outward, the

numbers of columns and rows for each quadrants relative to the coordinate center should be the

same, i.e., NCOLS and NROWS for the MM5 mother grid should be even numbers. In case the

offset information is not known a priori, one needs to compute the offset values using the header
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12-70

information in the MM5 output files. To use the information correctly, we need to know how the

MM5 nest domain’s left-most and bottom corner (, ) , , I J 11 11 is defined. In MM5, all the nest

domains are defined relative to the mother grid, and (, ) , , I J 11 11 provides the offset information of

the nest domains in terms of the mother grid’s resolution. The formula linking a nest MM5’s

domain (, ) , , I J 11 11 and Models-3/CMAQ’s offset values (, ) COL ROW offset offset are given for N ≥ 2 as:

(,) ( )

( /) , ( )( /) , , J I

COL

x x

ROW

y y

N

offset k

parent k

k

N

offset k

parent k

k

N

11 11 2

2

2

2

= +1 1 



 



 +





 













 −  =

−

=

∑ ∑ ∆∆ ∆∆ (12-146)

where ( /) ∆ ∆ x x parent = 3 for the current MM5 application example. Because our objective is to

help users to find out (, ) COL ROW offset offset for the nest grid, we need to rewrite Equation 12-146

for (, ) COL ROW offset offset . Assuming we know all the coarser grid/domains offset values,

(, ) COL ROW offset offset for the current nesting level N ≥ 2 can be found as:

( ) ( /) () ( )

( /)

COL x x J ,

COL

x x offset N

parent N

N

offset k

parent k

k

N

= −− 



 



 −

−

=

−

∆ ∆ ∑ ∆ ∆

2

1 1 2

2

1

1 (12-147a)

( ) ( / ) () ( )

( /) ROW y y I ,

ROW

y y offset N

parent N

N

offset k

parent k

k

N

= −− 



 



 −

−

=

−

∆ ∆ ∑ ∆ ∆

2

1 1 2

2

1

1 (12-147b)

Although Equations 12-147 a and b look somewhat complicated, one can readily compute offset

numbers for Models-3 CMAQ’s grid/domain definitions for the example set of domains defined in

Table 12-11 as follows:

( ),( ) ( ),( ) [ , ] COL ROW offset offset N [ ] =− − [ ] = =2

24 1 9 1 23 8 (12-148a)

( ),( ) [( ) * ], [( ) * ] COL ROW offset offset N [ ] = −− −− 



 

 =3 

0 0 3 35 1

3

1 3 23 3 19 1

3

138

 = [,] 34 31 (12-148b)

( ),( ) [( ) ], [( ) ] COL ROW offset offset N [ ] = −− − −− − 



 

 =4 

2

0

2

0 3 415

9

1 23

3

34

3

3 21 4

9

1 8

3

31

3

 = [,] 56 19 (12-148c)

Most of the time, the above MM5 domain definitions are provided by the MM5 modelers and

Models-3/CMAQ users do not have to re-compute them.

12.5.4.2 CMAQ Grid Definitions

The horizontal grid structure used for the MM5 serves as the parent grid for the CCTM domains.

To define a CCTM grid, number of cells to be excluded from the parent domain must be
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determined. It is recommended that the CCTM grid be smaller than its parent MM5 grid by at least

4 grid cells (preferably by 6 grids) to avoid the possible numerical reflection problems at

boundaries of MM5 domain. Once the offset values are known, (,) x y orig orig of the nest domain can

be computed using Equation 12-143. Refer to Appendix 12B for other examples of other CCTM

nest domain definitions.

12.5.5 Extension of MCIP for Other Meteorological Models

The current release version of MCIP can only process MM5 output in binary format or previous

MCIP output in I/O API format. To realize the one-atmosphere concept for meteorological and air

quality modeling, CMAQ utilizes generalized coordinates. One advantage of the generalized

coordinate system is that a single CTM can adapt to any of the coordinate systems and dynamics

commonly used in meteorological modeling. Because most meteorological models are not

originally designed for air quality studies, they lack characteristics that are required for air quality

modeling. Consistencies in dynamic descriptions of atmosphere, physical parameterizations, and

numerical algorithms, where applicable, in meteorological and chemistry-transport models are

critical in determining the quality of air pollutant simulations. This issue becomes more critical

with high resolution air quality study where nonhydrostatic meteorological models must be used.

MCIP is the key processor allowing the consistent linkage between meteorological models and

CMAQ. Currently, different meteorological models are used by different atmospheric modeling

groups forming their own respective user communities. It is because these meteorological models

are applicable for a limited range of spatial and temporal scales. To expand the user base of the

Models-3 CMAQ system and to promote the one-atmosphere community modeling paradigm, it is

essential to continuously develop MCIP modules for several popular mesoscale meteorological

models such as RAMS, ARPS, HOTMAC, and others.

To build a version of MCIP for processing a set of meteorological model output, several issues

involved with different dynamics and coordinates must be considered. They are; (1) compatibility

of governing set of equations and state variables used, (2) scale limitations in subgrid scale

parameterizations such as cloud, turbulence, and surface exchange processes, and (3) consistency

in numerical algorithms and discretization methods. Before designing MCIP modules for other

meteorological model, developers should identify the structure, format, and frequency of data as

well as their impact on the processing structure of MCIP. MCIP expects time dependent

meteorological data in a structured grid system as the input. As this moment, there is no provision

for handling irregularly spaced data structure either from observations or from a meteorological

modeling system with unstructured adaptive (fixed or dynamic) grid structure, such as the one

used in OMEGA system (Bacon et al., 1996). If there is need for including these data, object

analysis tools must be used to prepare data in a structured grid system.

The essential information related to the coordinates and dynamic assumptions used in

meteorological models is captured in MCIP. Dynamic and thermodynamic state variables are recast

into the fully compressible system as described in Chapter 5 of this volume.

It is important to know the processing sequence and associated data structures used in the current

MCIP code. Major processing steps in MCIP can be summarized as follows: (1) Grid, coordinate,

and information on atmospheric dynamics are used to compute Jacobian and layer heights; (2) State
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variables in meteorological models are recast into density and entropy; (3) Contravariant wind

components are computed; (4) necessary two-dimensional parameters are diagnosed; and (5) Some

of two- and three-dimensional parameters are passed through. Figure 12-11 shows corresponding

data structures used at different phases. Input phase uses arrays with dimensions covering the full

meteorology domain (‘F-arrays’), processing phase uses arrays for extended domain covering both

the CMAQ and boundary domains (‘X-arrays’). During the output phase, the information in Xarrays are separated into the CMAQ and boundary domains for respective data types described in

Table 12-3.

NCOLS

NROWS

Met. Domain

‘F’-arrays

Extended CMAQ Domain

‘X’-arrays

CMAQ Domain

Dot & Cross

Boundary

Domain

Input phase Processing Output phase

Figure 12-11. Data Structures Corresponding to Input, Processing, and Output Phases of MCIP

Processing

12.6 Concluding Remarks

MCIP is a key processor linking meteorological models to the CMAQ modeling system. Its major

roles are:

1. To read meteorological data from a meteorological model and converts them in Models-3

I/O API format.

2. To provide all the necessary meteorological parameters for air quality simulations. When

necessary, PBL parameters and other derived quantities are computed using gridded

meteorology data and high-resolution fractional land use information.

3. To support multiscale generalized coordinate implementation of the CCTM.

Current implementation of MCIP is mainly for linking MM5 output to CCTM. Reader modules to

Regional Atmospheric Modeling System (RAMS) (Pielke et al., 1992), will be added. Users who

wish to link other meteorological models may need to modify and introduce appropriate input

modules.
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This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
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Appendix 12A MCIP Output Data

MCIP writes the bulk of its two- and three-dimensional meteorology and geophysical output data

in a transportable binary format using a tailored Models-3 input/output applications program

interface (I/O API) library. Depending on whether the meteorological vertical coordinate is time

dependent or not, the temporal characteristics of certain variables that belong to GRID data types

and MET data types may differ. For example, when the meteorological coordinate is σp, which is

time dependent, Jacobian is also time dependent. On the other hand for σ po coordinate, Jacobian

is time independent. However we are using a consistent list of meteorological variables for both

hydrostatic and nonhydrostatic coordinates for as the standard output. Tables 12A-1 through 12A6 provide lists of variables in each data type.

Table 12A1. Variables in GRIDCRO2D

Table 12A2. Variables in GRIDDOT2D

Variable Name Unit Description

LAT DEGREES latitude (south negative)

LON DEGREES longitude (west negative)

MSFX2 (M/M)**2 squared map-scale factor (CROSS)

HT M terrain elevation

ZZERO M roughness length

PSTAR0 Pascal pressure difference between top and

surface

JACOBS0 M total Jacobian at surface

LUSE_URBA fraction (0-1) landuse for URBAN_LAND

LUSE_AGRI fraction (0-1) landuse for AGRICILTURE

LUSE_RANG fraction (0-1) landuse for RANGE

LUSE_DECI fraction (0-1) landuse for DECIDUOUS_FOREST

LUSE_CONI fraction (0-1) landuse for CONIFEROUS_FOREST

LUSE_MIXF fraction (0-1) landuse for MIXFOREST_WETLND

LUSE_WATE fraction (0-1) landuse for WATER

LUSE_BARR fraction (0-1) landuse for BARREN_LAND

LUSE_NONE fraction (0-1) landuse for NONFOREST_WETLND

LUSE_MIXA fraction (0-1) landuse for MIXAGRI_RANGE

LUSE_DECI fraction (0-1) landuse for URBAN_LAND

LUSE_ROCK fraction (0-1) landuse for ROCKY_OPENSHRUB

Variable Name Unit Description

LAT DEGREES latitude (south negative)

LON DEGREES longitude (west negative)

MSFD2 (M/M)**2 squared map-scale factor (DOT)
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Table 12A3. Variables in GRIDCRO3D

Table 12A4. Variables in METCRO3D

Table 12A5. Variables in METDOT3D

Variable Name Unit Description

DENS0 KG/M**3 density of reference atmosphere

ENTRP0 J/K/M**3 entropy density of reference atmosphere

JACOB0F M total Jacobian at layer face

JACOB0M M total Jacobian at layer middle

TEMP0 K temperature of reference atmosphere

PRES0 Pascal pressure of reference atmosphere

X3HT0F M height of layer face (top) of reference

atmosphere

X3HT0M M height of layer middle of reference

atmosphere

Variable Name Unit Description

JACOBF M total Jacobian at layer face

JACOBM M total Jacobian at layer middle

DENSA_J KG/M**2 Jacobian weighted total air density

DENSW_J KG/M**2 Jacobian weighted density of vapor

ENTRP_J J/K/M**2 Jacobian weighted entropy of moist air

WHAT_JD KG/(M*S) J & Density weighted vertical contra-W

QC KG/KG cloud water mixing ratio

QR KG/KG rain water mixing ratio

QV KG/KG water vapor mixing ratio

TA K air temperature

PRES Pascal pressure

DENS KG/M**3 total density of air

WWIND M/S true W component of wind

ZH M mid-layer height above ground

ZF M full-layer height above ground

JDRATE KG/M**2/S time rate change of Jacob*Density

Variable Name Unit Description

UWIND M/S U-comp. of true wind at dot point

VWIND M/S V-comp. of true wind at dot point

UHAT_JD KG/(M*S) (contra_U*Jacobian*Density) at square pt

VHAT_JD KG/(M*S) (contra_V*Jacobian*Density) at triangle

pt
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Table 12A6. Variables in METCRO2D

Note: List of deposition velocities

VD_SO2 :"M/S" ; deposition velocity for species SO2

VD_SULF :"M/S" ; deposition velocity for species SULF

VD_NO2 :"M/S" ; deposition velocity for species NO2

VD_NO :"M/S" ; deposition velocity for species NO

VD_O3 :"M/S" ; deposition velocity for species O3

VD_HNO3 :"M/S" ; deposition velocity for species HNO3

VD_H2O2 :"M/S" ; deposition velocity for species H2O2

VD_ALD :"M/S" ; deposition velocity for species ALD

VD_HCHO :"M/S" ; deposition velocity for species HCHO

VD_OP :"M/S" ; deposition velocity for species OP

VD_ORA :"M/S" ; deposition velocity for species ORA

VD_NH3 :"M/S" ; deposition velocity for species NH3

VD_PAN :"M/S" ; deposition velocity for species PAN

VD_HONO :"M/S" ; deposition velocity for species HONO

VD_CO :"M/S" ; deposition velocity for species CO

Variable Name Unit Description

PSTAR Pascal pressure difference (PSURF - PTOP)

JACOBS M total Jacobian at surface

DENSAS KG/M**3 air density at surface

WSTAR M/S convective velocity scale

RIB NODIM bulk Richardson number

PBL M PBL height

ZRUF M surface roughness length

MOLI 1/M inverse of Monin-Obukhov length

HFX WATTS/M**2 sensible heat flux

QFX WATTS/M**2 latent heat flux

MOLI 1/M inverse of Monin-Obukhov length

RADYNI M/S inverse of aerodynamic resistance

RBNDYI M/S inverse of laminar bnd layer resistance

RSTOMI M/S bulk stomatal resistance for water

TEMPG K skin temperature at ground

TEMP10 K air temperature at 10 m

TEMP1P5 K air temperature at 1.5 m

SURF2 EMPTY surface parameter 1

ALBEDO NODIM surface albedo

FSOIL WATTS/M**2 heat flux in soil layers

GLW WATTS/M**2 longwave radiation at ground

GSW WATTS/M**2 solar radiation absorbed at ground

RGRND WATTS/M**2 solar radiation reaching surface

RNET WATTS/M**2 net radiation .

RN CM accumulated nonconvective hourly precip.

RC CM accumulated convective hourly precip.

CFRACH Fraction fraction of high cloud

CFRACM Fraction fraction of middle cloud

CFRACL Fraction fraction of low cloud

CFRAC Fraction total cloud fraction

CLDT M cloud top layer height

CLDB M cloud bottom layer height

WBAR G/M**3 liquid water content of cloud

VD_XXXX M/S dry deposition velocity for species XXXX
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Appendix 12B Examples of Nest Domain Definitions for CMAQ system

12B.1 Grid Domain Definitions for the Models-3 CMAQ Tutorial Study

Table 12B-1. Origins for the TUTORIAL MM5 domain, MCIP landuse domain, and CTM

domains. Note that (x,y) corresponds to (COL,ROW) in CMAQ. MCIP landuse domain is

smaller by one cell around than the original MM5 domain. Also, the CTM domain removes three

cells around from the original MM5 domain. Origin is measured from the center of Base 108 km

domain located at 90W and 40N.

Resolution

(∆x=∆y)

Origin for original MM5

Domain

(,) x y orig orig

Origin for MCIP Landuse

Domain

(,) x y orig orig

Origin for CTM Domain

(,) x y orig orig

108km (-3996x103, -2808x103) N/A N/A

36km (432x103, -432x103) (468x103, -396x103) (540x103, -324x103)

12km (972x103, -36x103) (984x103, -24x103) (1008x103, 0x103)

04km (1200x103, 120x103) (1204x103, 124x103) (1212x103, 132x103)

Table 12B-2. Offset Definitions for the Tutorial MM5 Nest Domains

MM5

Domain

Resolution

(km)

NCOLS NROWS Col. Offset

from Parent

Domain, D1

 Row Offset

from Parent

Domain, D1

Col. Offset

for nest

Row Offset

for nest

D1 108 7 4 5 2 0 0 0 0

D2 3 6 3 6 3 6 4 1 2 2 4 1 2 2

D3 1 2 3 9 3 6 4 7 26.666666 1 5 1 1

D4 4 3 6 3 6 48.666666 28.111111 1 9 1 3

Table 12B-3. Dimensions of Set of MM5, MCIP, and CTM Domains for Each Grid Resolution

for the Tutorial Study

Resolution MM5 NCOLS MM5 NROWS MCIP NCOLS MCIP NROWS CTM NCOLS CTM NROWS

108 74 52 N/A N/A N/A N/A

36 36 36 34 34 30 30

12 39 36 37 34 33 30

4 36 36 34 34 30 30
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12B.2Grid Domain Definitions for the Models-3 CMAQ Demonstration Study

Table 12B-4. Origins for the CMAQ demonstration MM5 domain, MCIP landuse domain, and

CTM domains. Note that (x,y) corresponds to (COL,ROW) in CMAQ. MCIP landuse domain is

smaller by one cell around than the original MM5 domain. Also, the CTM domain removes three

cells around from the original MM5 domain. Origin is measured from the center of Base 108 km

domain located at 90W and 40N.

Resolution

(∆x=∆y)

Origin for original MM5

Domain

(,) x y orig orig

Origin for MCIP Landuse

Domain

(,) x y orig orig

Origin for CTM Domain

(,) x y orig orig

108km (-3996x103, -2808x103) N/A N/A

36km (-1080x103, -1728x103) (-1044x103, -1692x103) (-864x103, -1512x103)

12km (486x103, -216x103) (480x103, -204x103) (540x103, -144x103)

04km (1140x103, 24x103) (1144x103, 28x103) (1164x103, 48x103)

Table 12B-5. Offset Definitions for the CMAQ Demonstration MM5 Nest Domains

MM5

Domain

Resolution

(km)

NCOLS NROWS Col. Offset

from Parent

Domain, D1

 Row Offset

from Parent

Domain, D1

Col. Offset

for nest

Row Offset

for nest

D1 108 7 4 5 2 0 0 0 0

D2 3 6 8 7 8 1 2 7 2 2 2 7 1 0

D3 1 2 102 8 4 42.333333 2 5 4 3 4 2

D4 4 8 7 105 48.555556 27.222222 5 6 2 0

Table B6. Dimensions of Set of MM5, MCIP, and CTM Domains for Each Grid Resolution for

the CMAQ Demonstration Study

Resolution MM5 NCOLS MM5 NROWS MCIP NCOLS MCIP NROWS CTM NCOLS CTM NROWS

108 74 52 N/A N/A N/A N/A

36 87 81 85 79 75 69

12 102 84 100 82 90 72

4 87 105 85 103 75 93
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Appendix 12C Sample MCIP Configuration File

// RCS file, release, date & time of last delta, author, state, [and locker]

// $Header: /project/work/rep/MCIP/src/sunOS5/sun_m3_12.cfg,v 1.1.1.1 1997/10/13 17:38:23 yoj

Exp $

// what(1) key, module and SID; SCCS file; date and time of last delta:

// @(#)sun_m3_12.cfg 1.1 /project/mod3/MCIP/doc/bldrun/sunOS5/SCCS/s.sun_m3_12.cfg 14 Jun

1997 15:41:54

// This is a configuration file for

 model mcip_m3_12;

// f77_flags "-e -Nl200 -fast -O4";

 f77_flags "-e -g -C";

// link_flags "-fast -O4";

 link_flags "-e -g -C";

 libraries "-L${M3TOOLS}/IOAPI/src_lib/SunOS5 -lm3io \

 -L${M3TOOLS}/netCDF/SunOS5 -lnetcdf";

// global { verbose | parse_only | compile_all | one_step | clean_up } ...

 global verbose;

// shared include files ////////////////////////////////////////////////

// Models-3 I/O API permanent includes

 include SUBST_IOPARMS $M3TOOLS/IOAPI/includes/PARMS3.EXT;

 include SUBST_IOFDESC $M3TOOLS/IOAPI/includes/FDESC3.EXT;

 include SUBST_IODECL $M3TOOLS/IOAPI/includes/IODECL3.EXT;

// Models-3 global constants for this processor

 include SUBST_CONST $M3MODEL/ICL/src/fixed/const/CONST.EXT;

// Models-3 grid definitions

 include SUBST_HGRD_ID $M3MODEL/ICL/src/grid/D_12_15/HGRD_21X21.EXT;

 include SUBST_VGRD_ID $M3MODEL/ICL/src/grid/D_12_15/VGRD.EXT;

 include SUBST_COORD_ID $M3MODEL/ICL/src/grid/D_12_15/COORD_21X21.EXT;

// Models-3 I/O API files for this processor

 include SUBST_INFILES $M3MODEL/MCIP/src/icl/icl/INFILES_MCIP.EXT;

 include SUBST_FILES $M3MODEL/MCIP/src/icl/icl/FILES3_MCIP.EXT;

 include SUBST_MET_CONST $M3MODEL/MCIP/src/icl/icl/CONST_mete.EXT;

 include SUBST_PBL_CONST $M3MODEL/MCIP/src/icl/icl/CONST_pbl.EXT;
EPA/600/R-99/030

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// MCIP parameters

 include SUBST_MPARM $M3MODEL/MCIP/src/icl/icl/MCIPPARM.EXT;

 include SUBST_MCMMN $M3MODEL/MCIP/src/icl/icl/MCIPCOM.EXT;

 include SUBST_MGOUT $M3MODEL/MCIP/src/icl/icl/GROUTCOM.EXT;

 include SUBST_MCOUT $M3MODEL/MCIP/src/icl/icl/MCOUTCOM.EXT;

 include SUBST_MDOUT $M3MODEL/MCIP/src/icl/icl/MDOUTCOM.EXT;

 include SUBST_LRADM $M3MODEL/MCIP/src/icl/icl/LRADMDAT.EXT;

////////////////////////////////////////////////////////////////////////

// the mcip driver class

 module mcip development;

// the landuse class

 module m3radm development;

// the input class

 module m3 development;

// the met3d class

 module m3sup development;

// the pbl class

 module pblpkg development;

// the drydep class

 module radmdd development;

// the cloud class

 module radmkuo development;

// the util class

 module util development;

// the output class

 module stnd development;
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Appendix 12D Sample MCIP Run Script

#! /bin/csh -f

# RCS file, release, date & time of last delta, author, state, [and locker]

# $Header: /project/work/rep/MCIP/src/sunOS5/sun_m3_12.q,v 1.1.1.1 1997/10/13 17:38:23 yoj

Exp $

# what(1) key, module and SID; SCCS file; date and time of last delta:

# @(#)sun_m3_12.q 1.2 /project/mod3/MCIP/doc/bldrun/sunOS5/SCCS/s.sun_m3_12.q 19 Jun 1997

08:26:34

# for Sun Sparc 20, UltraSparc 2

# method: sun_m3_12.q >&! sun_m3_12.log &

# QSUB -r sun_m3_12

# QSUB -eo -o /work/you/your_directory/sun_m3.log

# QSUB -lM 8Mw

# QSUB -lT 1800

 date; set timestamp; cat sun_m3_12.cfg; echo " "; set echo

 setenv M3HOME /home/models3

 setenv M3DATA $M3HOME/datasets

#------------------------------------------------------------

# set executable

#------------------------------------------------------------

 set EXEC = mcip_m3_12

#------------------------------------------------------------

# set base directory

#------------------------------------------------------------

#set BASE = /work/you/your_directory

 set BASE = $cwd

#------------------------------------------------------------

# set working directories

#------------------------------------------------------------

 set MCIPDIR = $BASE

 set OUTDIR = $cwd

#------------------------------------------------------------

# set input data directories

#------------------------------------------------------------

 set DATADIR = $M3HOME/datasets/nostudies

#-------------------------------------------------------------
EPA/600/R-99/030

12-87

# (METROW,METCOL,METLAY) is (ROWS, COLS, LAYS) for MM5 data

#-------------------------------------------------------------

 setenv METROW 25

 setenv METCOL 25

 setenv METLAY 15

#-------------------------------------------------------------

# (I0, J0): The left bottom loc. of CTM domain in MET terms

# In CTM terms, I0 = ROW_OFFSET, J0 = COL_OFFSET

#-------------------------------------------------------------

 setenv I0 1

 setenv J0 1

#-------------------------------------------------------------

# LUTYPE: Filetype for Landuse data:

# 1: BINARY 13 category directly from TERRAIN

# 2: Preprocessed ASCII 11 category

# 3: Use MM5 internal dominant landuse category

# 4: Use M3 landuse fractions available in GRIDCRO2D

#-------------------------------------------------------------

 setenv LUTYPE 4

#-------------------------------------------------------------

# (I0LUSE, J0LUSE): The left bottom loc. of CTM domain in

# LAND USE DATA GRID terms

#-------------------------------------------------------------

 setenv I0LUSE 1

 setenv J0LUSE 1

#-------------------------------------------------------------

# If LCALCPBL is: TRUE, Recompute PBL values

# FALSE, Read PBL values from MM52

#-------------------------------------------------------------

 setenv LCALCPBL T

#-------------------------------------------------------------

# If LSLFLUX is: TRUE, Use only surface layer similarity

# FALSE, Use PBL similarity

#-------------------------------------------------------------

 setenv LSLFLUX F

#-------------------------------------------------------------

# If LM3DDEP is: TRUE, Use Models-3 D. Dep routtine

# FALSE, Use RADM D. Dep. routine

#-------------------------------------------------------------

 setenv LM3DDEP F

#-------------------------------------------------------------

# If LCALCCLD is: TRUE: Recompute CLOUD values
EPA/600/R-99/030

12-88

# FALSE: Read CLOUD values from MM52

#-------------------------------------------------------------

 setenv LCALCCLD T

#-------------------------------------------------------------

# If LSANITY is: TRUE: check range of output parameters

# FALSE: do not check range of paramters

#-------------------------------------------------------------

 setenv LSANITY T

#-------------------------------------------------------------

# JUDATE : INITIAL JULIAN STUDY DATE (YYDDD)

# HSTRT : STARTING HOUR OF JUDATE FOR STUDY

# HTORUN : NUMBER OF HOURS TO USE FROM MM5

# HTOSKIP: NUMBER OF HOURS TO SKIP FIRST

#-------------------------------------------------------------

# 88218 00 0 2 ! John's data

# 88216 12 0 49 ! Dave's data

# 88214 12 10 108 ! Daewon's data

 setenv JUDATE 88209

 setenv HSTRT 00

 setenv HTOSKIP 00

 setenv HTORUN 25

#setenv HTORUN 108

#-------------------------------------------------------------

# input file linkage

# MM51: Filename for MM51 datafile

# MM52: Filename for MM52 datafile (NA if none)

# LU13: Filename for LU13 datafile (binary from TERRAIN)

#-------------------------------------------------------------

#setenv MM51 $INDIR/MM51_es80

#setenv MM52 $INDIR/MM52_es80

#setenv LU13 $INDIR/LU80

#setenv LUSE $DATADIR/LU11_80

#setenv LUSE /work/bdx/metpp/newmcip/input/LU11_80

#-------------------------------------------------------------

# number of iterations for vertical wind correction

# (Use 0, +/- 1,2,3,..)

#-------------------------------------------------------------

 setenv IWIND 0

#-------------------------------------------------------------

# number of deposition layers (default = 1)

# (for layer collapsing, it could be 2, or 3)

#-------------------------------------------------------------

 setenv NDEP 1
EPA/600/R-99/030

12-89

#-------------------------------------------------------------

# GRDNAM: Grid Name (User Defined)

#-------------------------------------------------------------

 setenv GRDNAM TUTOR12

#-------------------------------------------------------------

# EXECUTION_ID (User Defined)

#-------------------------------------------------------------

 setenv EXECUTION_ID MCIP_BETA

#-------------------------------------------------------------

# SCENFILE: file path(User Defined)

#-------------------------------------------------------------

#setenv SCENFILE $BASE/

#-------------------------------------------------------------

# If IOAPI_CHECK_HEADERS is: TRUE, Check the headers

# FALSE, Do NOT check headers

#-------------------------------------------------------------

 setenv IOAPI_CHECK_HEADERS F

#setenv LOGFILE mcip.log

#-------------------------------------------------------------

# Remove any previously generated output files

#-------------------------------------------------------------

#/bin/rm GRID_* MET_*

#/bin/rm ../output/GRID_* ../output/MET_*

#-------------------------------------------------------------

# Set up input files

#-------------------------------------------------------------

 setenv GRID_CRO_2D $DATADIR'/GRIDCRO2D_TUT12'

 setenv GRID_DOT_2D $DATADIR'/GRIDDOT2D_TUT12'

 setenv MET_CRO_2D $DATADIR'/METCRO2D_TUT12'

 setenv MET_CRO_3D $DATADIR'/METCRO3D_TUT12'

 setenv MET_DOT_3D $DATADIR'/METDOT3D_TUT12'

#-------------------------------------------------------------

# Set up output files

#-------------------------------------------------------------

 setenv GRID_BDY_2D_G1 $OUTDIR'/GRIDBDY2D_tut12'

 setenv GRID_BDY_3D_G1 $OUTDIR'/GRIDBDY3D_tut12'

 setenv GRID_CRO_2D_G1 $OUTDIR'/GRIDCRO2D_tut12'

 setenv GRID_CRO_3D_G1 $OUTDIR'/GRIDCRO3D_tut12'

 setenv GRID_DOT_2D_G1 $OUTDIR'/GRIDDOT2D_tut12'

 setenv MET_BDY_2D_G1 $OUTDIR'/METBDY2D_tut12'

 setenv MET_BDY_3D_G1 $OUTDIR'/METBDY3D_tut12'
EPA/600/R-99/030

12-90

 setenv MET_CRO_2D_G1 $OUTDIR'/METCRO2D_tut12'

 setenv MET_CRO_3D_G1 $OUTDIR'/METCRO3D_tut12'

 setenv MET_DOT_3D_G1 $OUTDIR'/METDOT3D_tut12'

#-------------------------------------------------------------

# Execute MCIP

#-------------------------------------------------------------

#cdbx "$EXEC -g -x"; exit

# ja

#/opt/SUNWspro/bin/debugger "$MCIPDIR/$EXEC"; exit

 $MCIPDIR/$EXEC

# ja -cshlt

 exit()

#-------------------------------------------------------------

# Move output to proper directory

#-------------------------------------------------------------

#/bin/mv GRID* ../output1/

#/bin/mv MET* ../output1/
EPA/600/R-99/030

*

Corresponding author address: Gerald L. Gipson, MD-80, Research Triangle Park, NC 27711. E-mail:

ggb@hpcc.epa.gov

Chapter 13

THE INITIAL CONCENTRATION AND BOUNDARY CONDITION PROCESSORS

Gerald L. Gipson*

Human Exposure and Atmospheric Sciences Division

National Exposure Research Laboratory

U. S. Environmental Protection Agency 

Research Triangle Park, NC 27711, USA

ABSTRACT

This chapter describes the two processors in the Community Multiscale Air Quality (CMAQ)

modeling system that generate the initial concentrations and boundary conditions that are

required by the CMAQ Chemical Transport Model (CCTM). The major emphasis is on the

functionality incorporated in those processors – the initial condition (ICON) and boundary

condition (BCON) processors. The chapter describes how each processor can be used to

generate initial concentrations and boundary conditions from one of two sources – from

predefined default vertical profiles or from other CMAQ simulation results when model nesting is

being performed. A description of generating initial and boundary concentrations for special

tracer species is also included. The procedures that are used in both processors for interpolating

in both the horizontal and vertical directions are described. A description of methods for

converting initial and boundary concentrations from one chemical mechanism form to another is

also presented. Finally, the manner in which each processor is applied within the Models3/CMAQ framework is addressed.
EPA/600/R-99/030

13-1

13.0 THE INITIAL CONCENTRATION AND BOUNDARY CONDITION

PROCESSORS

13.1 Introduction

The solution of partial and ordinary differential equations that arise in air quality models requires

both initial concentrations (ICs) and boundary conditions (BCs). This chapter describes the

Community Multiscale Air Quality (CMAQ) modeling system processors that generate these

quantities. In the discussions that follow, they will be referred to as the ICON and BCON

processors, respectively. The ICs and BCs generated by these two processors are used by the

CMAQ Chemical Transport Model (hereafter referred to as the CCTM). For ICs, the CCTM

requires that the concentrations of all model species within each grid cell in the modeling domain

be specified for the start of the simulation. Concentrations of all model species at the boundaries

of the modeling domain throughout the simulation are required as BCs to the CCTM. The

emphasis in this chapter is on how the ICs and BCs are generated rather than on how they are

used in the CCTM. The reader is referred to Chapter 5 for a discussion of the latter. 

The ICON and BCON processors have been designed to process data as automatically as

possible. Users should be aware of certain operational assumptions that are employed by the two

processors and the CCTM to insure that their applications are performed in the intended manner,

however. The discussion below begins with a brief overview of the processors and their

relationship to the CCTM. Several topics that address the various aspects of the IC/BC

processing are then presented, including the input sources, spatial interpolation, species

processing, and mechanism conversions. The last section provides a brief overview of how the

ICON and BCON processors are applied.

13.2 Overview of the ICON and BCON Processors

The ICON and BCON processors generate ICs and BCs for individual model species, which

include gas-phase mechanism species, aerosols, nonreactive species and tracer species. The

techniques for selecting and processing species data will be discussed in more detail below. It is

important to emphasize at the outset, however, that it is not necessary for the ICON and BCON

processors to generate ICs and BCs for every species that is being modeled. The CCTM will

attempt to extract ICs and BCs for each species being modeled from the input files. If a species

is not found on the file, the CCTM will automatically set its ICs and BCs to a minimum threshold

limit (i.e., a nominal zero). Any data on an IC or BC file for a species that is not being modeled

will simply be ignored by the CCTM. Therefore, the user is encouraged to check the ICON,

BCON, and CCTM output logs to insure that the ICs and BCs are being set in the intended

manner.

The ICON processor generates species concentrations for every cell in the modeling domain,

whereas the BCON processor generates species concentrations for the cells immediately

surrounding the modeling domain. At present, the thickness of the boundary cells is limited to

one, which is the thickness required for all the transport algorithms currently included as part of
EPA/600/R-99/030

13-2

the CCTM (e.g., see Chapter 7). The reader is referred to Chapters 6 and 7 for a description of

the CMAQ conventions used in establishing modeling domains and their boundary cells. 

Both the ICON and BCON processors write the output ICs and BCs to standard Models-3

Input/Output Application Programmer Interface (I/O API) files: 3-dimensional gridded files for

the ICs and 3-dimensional boundary files for the BCs. The opening, formatting, and writing of

these files are handled automatically by the ICON and BCON processors. It should be noted,

however, that the IO/API has a limit of 120 output variables (i.e., number of species) for any one

IO/API file. If the number of output variables exceeds the IO/API maximum, the ICON and

BCON processors will generate up to two additional files to hold the outputs. If more than 360

output variables are needed, however, code modifications will need to be made to the ICON and

BCON processors and the CCTM to accommodate the additional variables.

13.3 Input Sources

The ICON and BCON processors generate IC and BC files from one of three input sources. The

first is a time invariant set of vertical concentration profiles. The second source of input data

consists of existing Models-3 IO/API 3-dimensional concentration files, normally generated by

the CCTM. The final source of IC and BC data involves the generation of special tracer species

concentrations used to test numerical transport algorithms. Each of these will be discussed

below. It should be added, however, that the ICON/BCON processors can be bypassed if the

user desires to use a different method. The only requirement is that the IC and BC files that are

eventually fed to the CCTM must be standard Models-3 IO/API gridded concentration and

boundary concentration files. The reader is referred to IO/API documentation for a description

of the structure and format of those files (EPA, 1998). 

13.3.1 Time Invariant Concentration Profiles

This section describes the manner in which the ICON and BCON processors generate ICs and

BCs from predefined, vertical concentration profiles. The CMAQ system contains a set of

predefined profiles that can be used to generate the requisite ICs and BCs. These profiles give

species concentrations as a function of height, and are spatially independent for the ICON

processor and only minimally spatially dependent for the BCON processor. Both the ICON and

BCON profile data are time independent. Since these data are not highly resolved, they are

typically used when no other information about ICs and BCs is available. It should also be noted

that the predefined profile files can be replaced by user developed profile data provided that the

replacement files are in the same format as the predefined files. The discussion below begins with

a description of the predefined profile data, and is followed by a description of how the user can

prepare replacement data. 

The default IC and BC profiles have been developed for the RADM2 chemical mechanism and

the terrain following sigma-p coordinate system (see Chapter 6 for a discussion of CMAQ

coordinate types). Both the IC and BC profiles are intended to represent relatively clean air

conditions in the eastern-half of the United States, and have been formulated from available
EPA/600/R-99/030

13-3

measurements and results obtained from modeling studies. Thus, they do not represent any

specific time period. Although profiles for other chemical mechanisms and vertical coordinate

systems are not currently available in the CMAQ system, it may still be possible to use the

predefined profiles for these cases. Special procedures are included with the ICON and BCON

processors to allow conversion from one vertical resolution and/or chemical mechanism to

another. These procedures will be described in sections 13.4.2 and 13.6, respectively.

The predefined profile data are stored in ASCII files in the CMAQ system. Table 13-1 contains a

listing of the CMAQ predefined IC profile file. Note that line numbers have been added to the

listing for reference. The first three lines contain informational text that is not used by the ICON

processor. Line 4 contains the number of vertical layers and the number of species for which

profiles have been developed, followed by the vertical coordinate values of the sigma-p levels. 

The fifth line is blank and is ignored by the ICON processor. Lines 6 through 46 contain vertical

profiles for 43 different RADM2 gas-phase species. The species name is given in the first

column, followed by mixing ratios (in ppm) for each layer. The first entry for a species

corresponds to the lowest layer, whereas the last entry corresponds to the uppermost layer. 

Lines 47 through 52 contain analogous information for key aerosol species. The units for ASO4I,

ASO4J, and ASOIL are μg/m3

, and the units for NUMATKN, NUMACC, and NUMCOR are

number/m3

. 

Table 13-2 contains a listing of the corresponding predefined BC profile file. The format for this

file is similar to that for the IC file, except that one set of profiles is input for each of the four

different boundaries of the modeling domain (i.e., north, east, south and west). The BCON

processor uses the appropriate set of profiles to generate the BCs at each edge of the modeling

domain. Again, line five is blank and is ignored by the BCON processor.

As indicated above, the user can replace a CMAQ predefined profile file with one of their own

provided the same file format is used. As noted in the discussion above, none of the first three

text lines nor the fifth line in either file is used. Thus, those lines can contain any information or

be blank, but they must be present in the file. The remaining data lines are read in FORTRAN

list-directed format, so it is not necessary to align the data by columns. The only formatting

requirement is that all inputs be separated by commas or by one or more blanks. The species

names must not exceed 16 characters and must not contain any blanks. Also, it is not necessary

that a six-layer vertical resolution be used, but at least one layer must be present and no more

than 30 are allowed. Note that the number of layer heights on line 4 must be one greater than the

actual number of layers used. These layer heights must correspond to the heights of the layer

interfaces (i.e., not the mid-layer heights), and the first entry for any profile must be for the

lowest level (i.e., ground-level). The input mixing ratios, however, are interpreted as layer

average values as opposed to values at the layer interfaces. Finally, note that the BC vertical

profile data for each edge begins with a line that contains the edge name. Although the

processors do not require that these names be specified explicitly, a line corresponding to the

edge name line must be included and the processors expect the data for each edge to be input in

the order shown in Table 13-2 (i.e., north, east, south, and west).
EPA/600/R-99/030

13-4

13.3.2 CCTM Concentration files

Both the ICON and BCON processors can be configured to generate ICs and BCs from existing

Models-3 IO/API 3-dimensional, gridded, concentration files. This situation typically arises

when performing a nested model simulation and modeling results are available for a coarser grid. 

Unlike the predefined profile files described above, the CCTM concentration files are both

temporally and spatially resolved, necessitating some additional processing procedures. (The

subject of spatial interpolation is described in section 13.4.) It should be added, however, that it

is not necessary to use the ICON processor for a model continuation run (i.e., a run in which a

model simulation is started at the exact same time that a previous one ended and the same

modeling domain is being used). In such cases the CMAQ IO/API concentration file from the

previous run may be used directly as the input IC file to the CCTM. However, it will still be

necessary to generate a BC input file.

Since ICs are required only for the start of a model simulation, the ICON processor will generate

ICs for only one time step. BCs are required throughout a simulation, however, so the user must

prescribe the period of record for which to produce outputs. One set of BCs will be generated at

each time step for that period of record. To illustrate, consider the case in which a model

simulation has been performed for a coarse grid for a 24-hour period of record using 1-hour time

steps (i.e., the model concentrations were predicted at hourly intervals). The IO/API gridded

concentration file for the coarse grid will then contain species concentrations for 25 time steps,

one for the start of the simulation (i.e., the ICs for that simulation) and 24 time steps

corresponding to the model predictions at each hour. Now assume that it is desired to generate

ICs and BCs for a nested model simulation for the same time period. The user would select the

first time step for the ICON output, and the ICON processor would generate ICs for that time

step only. For the BCON processor, the period of record for the output BCs would be obtained

by selecting the same starting time and setting the duration for outputs at 24 hours. This

selection would produce 25 time steps on the output file, one for the start and 24 for each of the

subsequent simulation hours. The manner in which the time controls are set is described in the

Models-3 User Manual (EPA, 1998).

13.3.3 Tracer Species

The ICON and BCON processors also contain the capability to generate ICs and BCs for special

tracer species that can be used to investigate the accuracy of the various transport and diffusion

algorithms available in the CCTM system. This capability has been included primarily to

facilitate the evaluation of alternative algorithms, and thus would not likely be used in most air

quality modeling applications. 

ICs and BCs can be generated for eight different tracers. Each one can be used to examine

different properties of transport algorithms, and thus can be selected individually for output. 

They are chosen by including specially defined tracer names in the list of model species. The

defined names and a brief description of each tracer species follow. (Note that the ICs for these

tracers can be viewed with one of the visualization tools to examine the patterns more closely.)
EPA/600/R-99/030

13-5

hs 
 a 2

a

2  (x	xr

)

2  (y	yr

)

2 (13-1)

hB 
 2 qmax ( 1  hs ) 	 qmin , (13-2b)

hC 
 	 qmax ( 1  hs )  2 qmin , (13-2c)

hA 
 qmax ( 1  hs )  qmin , (13-2a)

& IC1_BC0: All ICs in the modeling domain are set to 1.0 and all BCs are set to 0.0.

& IC1_BC1: All ICs in the modeling domain are set to 1.0 and all BCs are set to 1.0.

& IC0_BC1: All ICs in the modeling domain are set to 0.0 and all BCs are set to 1.0.

& STREET: Within any horizontal cross-section of cells, IC cell concentrations are set to 

either 1.0 or 0.0 such that the overall domain pattern resembles a street grid. All BCs are 

set to zero.

& CHKBRD: Within any horizontal cross-section of cells, IC cell concentrations are set to 

either 1.0 or 0.0 such that the overall domain pattern resembles a checkerboard. All BCs 

are set to zero.

& SPOS_A: ICs and BCs are set such that a concentration mound is centered at cell (10,10)

in the modeling domain, and the concentration profile is defined below.

& SPOS_B: ICs and BCs are set such that a concentration mound is centered at cell (10,10)

in the modeling domain, and the concentration profile is defined below.

& SPOS_C: ICs and BCs are set such that a concentration mound is centered at cell (10,10)

in the modeling domain, and the concentration profile is defined below.

The last three tracer species are designed for superposition tests of transport algorithms. The

base shape of the concentration mounds is described by the Witch of Agnesi surface:where a is

the radius of the mound, xr and yr define the position of the peak of the mound, and hs is the

height of the mound. In the ICON and BCON processors, a is set to 3 and (xr, yr) to (10,10). The

three tracer signals hA, hB, and hC for SPOS_A, SPOS_B, and SPOS_C are then defined as

follows:

where qmax and qmin determine the amplitude and background values of the signals, and both are

set to 50 in the ICON and BCON processor. With these signals, the addition of mounds B and C
EPA/600/R-99/030

13-6

will yield mound A. Thus, the degree to which hA - (hB+ hC ) differs from zero in an advection test

provides a measure of the nonlinearity of the advection algorithm.

13.4 Spatial Interpolation

Both the ICON and BCON processors are designed to account for differences in spatial

resolution between the input files and the IC/BC output files on an automatic basis. As

described in Chapter 6, the CMAQ system is designed to handle different types of horizontal and

vertical coordinate systems. All of the data required to completely specify the horizontal and

vertical grid structure are contained in three INCLUDE files that are generated by the Models-3

framework: COORD.EXT, HGRD.EXT, and VGRD.EXT. When the CCTM is compiled (or

built), these three files are included with the source code, thereby providing the CCTM with all

of the necessary information on the grid structure that is being used. Both the ICON and BCON

processors operate in a similar fashion, and thus both processors must be built with the same

three INCLUDE files that are used to build the CCTM that will eventually use the ICs and BCs. 

Grid information on the IC/BC inputs is extracted from the input files themselves, so no

additional information is required for them. Note that either the horizontal and vertical

coordinates for the input file may be of a different type than that for the output file, or they may

be of the same type but have different extents or resolutions.

13.4.1 Horizontal Interpolation

Horizontal interpolation is required when a CCTM concentration file is being used as input to

either ICON or BCON and the horizontal coordinate system of the input file differs from that

needed for the output file. Such cases typically arise when ICs and BCs are being generated for

a nested modeling domain that has a finer resolution than a coarser, outer domain. Note that no

horizontal interpolation is necessary if both the input and output domains have the same structure

or if the time invariant profiles are being used to generate the ICs and BCs.

Disparities in horizontal grid structure are handled by mapping each vertical column of output

cells to a corresponding column of input cells. The vertical concentration profiles corresponding

to the input column of cells are then used as the vertical profiles for the output column of cells. 

Note that some vertical interpolation may also be required as described in the next section. The

horizontal mapping is done on the basis of cell proximity. The ground-level latitudes and

longitudes at the center of each vertical column of cells are first calculated for both the input and

output domains. These computed values are then used to find which input column is closest to

each output column. Since the ICON and BCON can compute latitude and longitude for any of

the available CMAQ map projections, the horizontal grid coordinate of the input and output files

do not have to be the same type. 

13.4.2 Vertical Interpolation

In some applications, the ICON and BCON may be required to generate ICs and BCs for a

vertical grid system that is different from the one used for the input file. The CCTM is capable of
EPA/600/R-99/030

13-7

handling several different vertical grid structures (e.g., sigma-p, sigma-z, pressure, etc.), and each

of those grid types can have different vertical resolutions (i.e., different numbers of vertical

layers or different spacings with the same number of layers). If the vertical structure of the input

and output grids is identical (i.e., both are of the same type and have the same vertical

resolution), then the processing of input data to output data is routine because of the one-to-one

correspondence of the vertical layers. If the vertical grid types or resolutions are different,

however, the ICON and BCON will convert from the input to the output vertical structure in

most cases. Conversions from one resolution to another can be performed using either profile

data or CCTM concentration files, but conversions from one grid type to another can only be

performed when using CCTM concentration files. Both the ICON and BCON processors assume

that the vertical grid-type of the profile data is the same as the required output structure, and thus

no conversions can be performed in that case. The two different vertical interpolation cases that

can be performed by the ICON and BCON processors are described next.

Identical Vertical Grid Types, Different Resolutions. When the input and output vertical grid

types are the same but vertical resolutions are different, both ICON and BCON will derive ICs or

BCs by linear interpolation using the layer heights contained in the input files and those

contained in the COORD.EXT INCLUDE file. These heights are in the units of the vertical

coordinate system (e.g., sigma-p, sigma-z, pressure, etc.) rather than height above ground level as

measured in distance units such as feet or meters. The vertical resolution of the input IC/BC data

can be either greater than or less than the output resolution. Linear interpolation is performed

using layer heights that correspond to the middle of the layers. Output concentrations are not

always interpolated for the bottommost and topmost layers, however. Output concentrations for

all layers with mid-layer heights less than the bottommost mid-layer height in the input file will

be set equal to the concentration of that bottommost layer. Similarly, output concentrations for

all layers above the input topmost mid-layer height will be set equal to the concentration of the

topmost layer.

Different Vertical Grid Types. A complete switch of vertical coordinate types can be carried out

when the following two conditions are met: 1) the input IC/BC data are in standard Models-3

IO/API files and 2) the gridded 3-dimensional meteorological files that contain the mid-layer

heights for both vertical coordinate systems are also available (see Chapter 12 for a description

of these meteorological files). When these conditions are met, the ICON and BCON processors

will use linear interpolation to convert from one coordinate system to another. The interpolation

is performed in exactly the same manner as described in the previous paragraph, except that the

mid-layer heights are taken from the 3-dimensional meteorological files which give the mid-layer

heights in meters above ground level for both the input IC/BC data and the output IO/API files.

Thus, the meteorological data files containing the layer heights in meters above ground level must

be available for both the input and output grids before the ICON and BCON processors can be

used. 
EPA/600/R-99/030

13-8

13.5 ICON/BCON Species Processing 

The selection of species that are to be modeled and thus require ICs and BCs is controlled by the

Program Control Processor (PCP). A detailed description of that processor is contained in

Chapter 15, and will not be repeated here. A brief overview of some of the relationships

between the PCP and the ICON/BCON processors is presented here to facilitate the description

of species processing, however. 

The species that are to be modeled in a CCTM simulation are determined when the user invokes

the PCP in the Models-3 framework to select a gas phase chemical mechanism, whether or not

aerosols are to be included, and whether to include other nonreactive and/or tracer species. The

Models-3 framework generates four INCLUDE files that contain the names of all species that are

to be modeled -- GC_SPC.EXT, AE_SPC.EXT, NR_SPC.EXT, and TR_SPC.EXT (collectively

referred to below as the SPC INCLUDE files). The Models-3 framework also allows the user to

invoke special treatment of the ICs and BCs for individual species by defining special surrogate

names and providing corresponding scale factors for the calculation of ICs (EPA, 1998). The

Models-3 framework generates four INCLUDE files that contain this information --

GC_ICBC.EXT, AE_ICBC.EXT, NR_ICBC.EXT, and TR_ICBC.EXT (collectively referred to

below as the ICBC INCLUDE files). Note that some of these files may not contain any entries

depending on the user's selection, but all files will be generated by the framework. Just as both

the SPC and ICBC INCLUDE files must be included when the CCTM is built, they must also be

included when the ICON and BCON processors are built.

The SPC INCLUDE files contain the names of all species to be modeled and will therefore

require ICs and BCs in the CCTM. The ICON/BCON processors use the information in both the

SPC and the ICBC INCLUDE files to determine which species data should be extracted from the

input file and be subsequently written to the output file. The ICON and BCON processors also

include an option to convert from one chemical mechanism to another. Since it represents a

special option with its own unique rules, it is described separately in section 13.6. The

subsequent discussion focuses on the treatment of individual species for two cases - one with and

one without associated surrogate names.

Consider first the case in which a surrogate name is not specified. This situation occurs when a

model species (i.e., one whose name is included in one of the SPC INCLUDE files) does not

have a surrogate name assigned to it. In this case, the ICON and BCON processors simply check

to see if the input file contains data for a species with the exact same name as the model species

name. If none is found, ICs and BCs are not generated for that species. If a match is found, the

data for that species are extracted from the input file, processed, and written to the IC and BC

output files.

The assignment of a surrogate name to a particular species complicates the processing slightly. 

Surrogate names in the CMAQ system arise at least in part from the generalized treatment of the

chemical mechanisms and the fact that species names are not "hardwired" in the CMAQ system.
EPA/600/R-99/030

13-9

Their primary function is to link a model species with data that are associated with a species of a

different name. Two examples are presented to illustrate potential uses.

The first example illustrates how surrogates can be used to provide simple links from one species

to another. First, suppose a series of CMAQ model simulations had been performed using the

CMAQ system standard RADM2 mechanism in which formaldehyde is named HCHO. Thus, all

of the data for that species will be associated with the name HCHO in the CMAQ system data

files. Now consider that a researcher wants to make use of that data but will be using their own

version of the RADM2 mechanism in which formaldehyde is named FORM. To use the older

modeling data, the researcher could either change the formaldehyde name in the chemical

mechanism to conform to the original RADM2 name or assign the surrogate HCHO for FORM. 

In the latter case, both the ICON/BCON processors and the CCTM are designed to extract

IC/BC data using the surrogate name in place the model species name. This will be explained in

more detail further below. 

The second example of using a surrogate name illustrates how scale factors can be used with

surrogates. Suppose a researcher is experimenting with a new chemical mechanism which

divides a particular species PAR into two new species, PAR1 and PAR2. Further, suppose the

researcher wants to use existing CMAQ model simulations with the PAR species to generate ICs

and BCs for both PAR1 and PAR2. The researcher will assume that 25% of the PAR IC/BC

concentrations will be assigned to PAR1 and 75% to PAR2. To effect this in the CMAQ

modeling system, the researcher can assign the species surrogate name PAR to both PAR1 and

PAR2, and assign 0.25 to the ICBC scale factor for PAR1 species and 0.75 to the ICBC scale

factor for PAR2. The ICON/BCON processors and CCTM will use this information to compute

the proper ICs and BCs for the two species PAR1 and PAR2 from the input PAR values. The

procedures followed by both the ICON/BCON and the CCTM are described next.

The introduction of surrogate names for IC and BC species affects the manner in which both the

ICON/BCON processors and the CCTM operate. Consider first the processing that takes place in

the ICON/BCON processors. Each species in the SPC INCLUDE files is selected for processing

individually. If a surrogate name is assigned to that species, the IC/BC input files are examined

to see if the surrogate name is included with the inputs. If the surrogate name is on the input file,

the data corresponding to that name are extracted from the input file, processed and output

under the surrogate name. Further, the ICBC scale factors are not applied in the ICON and

BCON. If the surrogate name is not found on the input data file, the ICON/BCON processors

will then check the input file using the model species name as if no surrogate name had existed. 

Again, if a match is found using the model species name, the corresponding data are extracted

and output under the model species name. If the input file does not contain any data under the

surrogate name or the model species name, then no IC/BC data are generated for that particular

model species. 

Now consider processing in the CCTM when surrogate names are used for ICs/BCs. The CCTM

processes each species in the SPC INCLUDE files individually. If a surrogate name is specified

for the model species and it is found on the IC/BC input files, the CCTM extracts the data for
EPA/600/R-99/030

13-10

that name, applies the scale factor to those data, and then assigns the scaled concentrations to the

ICs and BC concentrations for the model species. If the surrogate species name is not found on

the input IC/BC files, the input file is checked using the model species name contained in the

SPC INCLUDE files. If data for that model species are found, then the data are extracted and

used directly as ICs and BCs (i.e., no scale factors are applied). If data for the species are not

found on the input file, the ICs and BCs are set to the lower threshold limits. 

For most routine applications, users need not concern themselves with surrogate mapping issues. 

The ICON and BCON processors are designed to generate the appropriate ICs and BCs with

minimal user interaction, provided the correct input files and include files are used with the

processors. Both the ICON and the BCON processors generate a species map on the output log

that reports the relationship between the input and output IC and BC species. The user can check

these logs to insure that the desired species mapping has been performed. Further, the CCTM's

output log lists those species for which the lower threshold limits are used, and these should be

checked to insure that the ICs/BCs for an important species have not been omitted.

13.6 Mechanism Conversions

The vertical profile data and the CCTM concentration file data that were described above

normally correspond to one gas-phase, chemical mechanism. For example, the predefined,

vertical profile data presently in the CMAQ system were developed for the RADM2 chemical

mechanism. The capability to convert from one gas phase chemical mechanism to another has

been included in the ICON and BCON processors, however. It should be emphasized that there is

not always a definite correspondence between chemical mechanism species, and it is usually

necessary to make several assumptions to make such conversions. This is particularly true for

organic species that may be defined differently in two mechanisms. Nevertheless, some simple

mechanism conversion capabilities have been included for those cases in which approximations

are acceptable for converting from one mechanism to another. 

A special routine to generate ICs and BCs for the CB4 chemical mechanism from RADM2 gasphase mechanism inputs is included as part of the ICON and BCON processor options. At

present, no other "hardwired" conversion routines are available in the system, but it is

conceivable that some could be added in the future as more chemical mechanisms are added to

the CMAQ system. No conversion from CB4 to RADM2 format has been included because the

carbon bond lumping technique makes it difficult to disaggregate mechanism species into their

original chemical compounds. For a description of these two mechanisms, the reader is referred

to Chapter 8. The hardwired RADM2 to CB4 conversion procedures that are used are the same

as for the generalized conversion processor that is described next.

As a convenience for the user, a generalized mechanism conversion processor has also been

included in both the ICON and BCON processors. This conversion procedure requires the user

to generate an ASCII input file that contains mechanism conversion rules. Thus, the user is

responsible for defining how the mechanism conversion is to be performed. An example file

showing the conversion from RADM2 to CB4 is included in Table 13-3. The file contains the
EPA/600/R-99/030

13-11

expressions that are used to convert the ICs and BCs from one mechanism form to another. The

ICs and BCs for the CB4 species (i.e., those on the left hand side of the equal sign) are computed

from the RADM2 species concentrations (i.e., those on the right hand side of the equal sign)

according to the equations shown. As is evident, there is a simple one-to-one correspondence for

most species and lumping only occurs for relatively few species. It should also be noted that no

conversions will be performed for those species that are not included in the input file, and thus no

ICs or BCs will be generated for them. As mentioned previously, the user is advised to review

the species map on the ICON/BCON output log to insure that the conversions are being done as

intended. Finally, it should be added that the mechanism conversion option applies only to the

gas phase chemistry species. Aerosol, nonreactive and tracer species will be processed in the

standard way, regardless of whether a mechanism conversion is being performed.

The format for the mechanism conversion rules is relatively simple. Species names must be 16

characters or less and not contain any blanks. Only one species is permitted on the left-hand side

of the equation, and the species name should correspond to a name in the output mechanism. 

The equal sign must be present, and at least one species name must appear to the right of it. 

Coefficients for species are allowed on the right-hand side only, and they can be in either integer,

real, or exponential format. They must always be followed by an asterisk to indicate

multiplication. For expressions involving lumping of species, only addition is allowed and it is

indicated by a plus sign. Line-wrap is allowed so that a single lumping rule can span more than

one line. Each conversion rule must conclude with a semicolon, and the last command must be

“END;”. Finally, the input files are read in a free form input that generally ignores white spaces

between species names, coefficients, operators and line terminators.

13.7 ICON/BCON Applications

This section provides an overview of how the ICON and BCON processors are applied in

practice. Applications are normally carried out in two steps: compilation (or building) and

execution. As mentioned earlier, when the ICON and BCON executables are built, the grid

INCLUDE files for the modeling domain must be included. In addition, the user must select four

modules that determine the ICON/BCON processing routines to incorporate when the executable

is built. Two modules must always be present: icon (or bcon in the case of the BCON processor)

and icl. These two modules contain processing routines that are common to all applications. 

One of the following three modules must be chosen to include the routines to process the specific

input source: 1) profile for using a time invariant vertical concentration profile contained in an

ASCII file, 2) m3conc for processing a CMAQ IO/API concentration file, or 3) tracer for

generating special tracer species ICs and BCs. Finally, one of three modules must also be

selected to control the mechanism conversion procedure: 1) noop for no mechanism conversion,

2) radm2_to_cb4 for a CMAQ predefined RADM2 to CB4 conversion, or 3) user_defined to

process a user generated ASCII file (e.g., Table 13-3) containing mechanism conversion rules

that are used to generate ICs and BCs for one mechanism using input concentrations for a

different mechanism.
EPA/600/R-99/030

13-12

The second step involves running the processors with all necessary input files assigned and the

time control parameters set. Both are provided to the processors by means of environment

variables. The input and output files are assigned by means of predefined logical file names. The

ICON processor requires a starting date and time in the Models-3 conventional time stamp

format. The BCON processor requires both a starting date and time and a run duration

parameter.

For detailed information on compiling and running these processors, the reader is referred to the

Models-3 User Manual (EPA, 1998).

13.8 References

EPA, 1998. Models-3 Volume 9b: User Manual, Draft EPA report, U. S. Environmental

Protection Agency, Research Triangle Park, N.C.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

13-13

Table 13-1. CMAQ Predefined Vertical Profiles for Initial Concentrations

1 Optional boundary condition: The vertical coordinate of the model to

2 generate these b.c. is the terrain-following sigma coordinate. The number of

3 sigma layers and defined sigma levels are listed below. 

4 6 47 1.00 0.98 0.93 0.84 0.60 0.30 0.00 

5

6 SO2 0.300E-03 0.200E-03 0.100E-03 0.100E-03 0.200E-04 0.100E-04

7 SULF 0.150E-03 0.150E-03 0.100E-03 0.100E-03 0.200E-04 0.100E-04

8 NO2 0.200E-04 0.200E-04 0.100E-04 0.000E+00 0.000E+00 0.000E+00

9 NO 0.200E-04 0.200E-04 0.100E-04 0.000E+00 0.000E+00 0.000E+00

10 O3 0.350E-01 0.350E-01 0.400E-01 0.500E-01 0.600E-01 0.700E-01

11 HNO3 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.700E-04 0.100E-03

12 H2O2 0.100E-02 0.100E-02 0.150E-02 0.100E-02 0.800E-03 0.200E-03

13 ALD 0.300E-04 0.350E-04 0.300E-04 0.200E-04 0.200E-04 0.100E-04

14 HCHO 0.250E-03 0.250E-03 0.250E-03 0.200E-03 0.100E-03 0.500E-04

15 OP1 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

16 OP2 0.300E-07 0.350E-07 0.300E-07 0.200E-07 0.200E-07 0.100E-07

17 PAA 0.300E-04 0.300E-04 0.300E-04 0.250E-04 0.200E-04 0.150E-04

18 ORA1 0.100E-05 0.100E-05 0.500E-06 0.500E-06 0.500E-06 0.000E+00

19 ORA2 0.100E-05 0.100E-05 0.500E-06 0.500E-06 0.500E-06 0.000E+00

20 NH3 0.100E-03 0.100E-03 0.300E-04 0.200E-04 0.200E-04 0.100E-04

21 N2O5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

22 NO3 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

23 PAN 0.200E-04 0.200E-04 0.100E-04 0.100E-04 0.100E-04 0.000E+00

24 HC3 0.400E-04 0.400E-04 0.320E-04 0.120E-04 0.400E-05 0.000E+00

25 HC5 0.400E-04 0.400E-04 0.320E-04 0.120E-04 0.400E-05 0.000E+00

26 HC8 0.200E-04 0.200E-04 0.160E-04 0.600E-05 0.200E-05 0.000E+00

27 ETH 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

28 CO 0.800E-01 0.800E-01 0.800E-01 0.700E-01 0.650E-01 0.500E-01

29 OL2 0.500E-05 0.300E-05 0.200E-05 0.100E-05 0.100E-05 0.000E+00

30 OLT 0.200E-06 0.200E-06 0.100E-06 0.000E+00 0.000E+00 0.000E+00

31 OLI 0.100E-06 0.100E-06 0.000E+00 0.000E+00 0.000E+00 0.000E+00

32 TOL 0.100E-05 0.100E-05 0.100E-05 0.100E-05 0.000E+00 0.000E+00

33 XYL 0.200E-06 0.200E-06 0.100E-06 0.000E+00 0.000E+00 0.000E+00

34 ACO3 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

35 TPAN 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07

36 HONO 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

37 HNO4 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08

38 KET 0.300E-04 0.350E-04 0.300E-04 0.200E-04 0.200E-04 0.100E-04

39 GLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

40 MGLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

41 DCB 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

42 ONIT 0.200E-04 0.200E-04 0.160E-04 0.600E-05 0.200E-05 0.000E+00

43 CSL 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

44 ISO 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05

45 HO 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

46 HO2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

47 ASO4I 4.810E-02 3.207E-02 1.603E-02 1.603E-02 3.207E-03 1.603E-03

48 ASO4J 1.154E+00 7.696E-01 3.848E-01 3.848E-01 7.696E-02 3.848E-02

49 NUMATKN 1.437E+10 9.583E+09 4.791E+09 4.791E+09 9.583E+08 4.791E+08

50 NUMACC 4.110E+08 2.740E+08 1.370E+08 1.370E+08 2.740E+07 1.370E+07

51 ASOIL 1.000E+00 8.000E-01 4.000E-01 4.000E-01 8.000E-02 4.000E-02

52 NUMCOR 1.740E+04 1.392E+04 6.960E+03 6.960E+03 1.392E+03 6.960E+02
EPA/600/R-99/030

13-14

Table 13-2. CMAQ Predefined Vertical Profiles for Boundary Conditions

1 Optional boundary condition: The vertical coordinate of the model to

2 generate these b.c. is the terrain-following sigma coordinate. The number of

3 sigma layers and defined sigma levels are listed below. 

4 6 47 1.00 0.98 0.93 0.84 0.60 0.30 0.00 

5 

6 North 

7 

8 SO2 0.300E-03 0.200E-03 0.100E-03 0.100E-03 0.200E-04 0.100E-04

9 SULF 0.150E-03 0.150E-03 0.100E-03 0.100E-03 0.200E-04 0.100E-04

10 NO2 0.200E-04 0.200E-04 0.100E-04 0.000E+00 0.000E+00 0.000E+00

11 NO 0.200E-04 0.200E-04 0.100E-04 0.000E+00 0.000E+00 0.000E+00

12 O3 0.350E-01 0.350E-01 0.400E-01 0.500E-01 0.600E-01 0.700E-01

13 HNO3 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.700E-04 0.100E-03

14 H2O2 0.100E-02 0.100E-02 0.150E-02 0.100E-02 0.800E-03 0.200E-03

15 ALD 0.300E-04 0.350E-04 0.300E-04 0.200E-04 0.200E-04 0.100E-04

16 HCHO 0.250E-03 0.250E-03 0.250E-03 0.200E-03 0.100E-03 0.500E-04

17 OP1 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

18 OP2 0.300E-07 0.350E-07 0.300E-07 0.200E-07 0.200E-07 0.100E-07

19 PAA 0.300E-04 0.300E-04 0.300E-04 0.250E-04 0.200E-04 0.150E-04

20 ORA1 0.100E-05 0.100E-05 0.500E-06 0.500E-06 0.500E-06 0.000E+00

21 ORA2 0.100E-05 0.100E-05 0.500E-06 0.500E-06 0.500E-06 0.000E+00

22 NH3 0.100E-03 0.100E-03 0.300E-04 0.200E-04 0.200E-04 0.100E-04

23 N2O5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

24 NO3 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

25 PAN 0.200E-04 0.200E-04 0.100E-04 0.100E-04 0.100E-04 0.000E+00

26 HC3 0.400E-04 0.400E-04 0.320E-04 0.120E-04 0.400E-05 0.000E+00

27 HC5 0.400E-04 0.400E-04 0.320E-04 0.120E-04 0.400E-05 0.000E+00

28 HC8 0.200E-04 0.200E-04 0.160E-04 0.600E-05 0.200E-05 0.000E+00

29 ETH 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

30 CO 0.800E-01 0.800E-01 0.800E-01 0.700E-01 0.650E-01 0.500E-01

31 OL2 0.500E-05 0.300E-05 0.200E-05 0.100E-05 0.100E-05 0.000E+00

32 OLT 0.200E-06 0.200E-06 0.100E-06 0.000E+00 0.000E+00 0.000E+00

33 OLI 0.100E-06 0.100E-06 0.000E+00 0.000E+00 0.000E+00 0.000E+00

34 TOL 0.100E-05 0.100E-05 0.100E-05 0.100E-05 0.000E+00 0.000E+00

35 XYL 0.200E-06 0.200E-06 0.100E-06 0.000E+00 0.000E+00 0.000E+00

36 ACO3 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

37 TPAN 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07

38 HONO 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

39 HNO4 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08

40 KET 0.300E-04 0.350E-04 0.300E-04 0.200E-04 0.200E-04 0.100E-04

41 GLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

42 MGLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

43 DCB 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.100E-06 0.500E-07

44 ONIT 0.200E-04 0.200E-04 0.160E-04 0.600E-05 0.200E-05 0.000E+00

45 CSL 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

46 ISO 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05

47 HO 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

48 HO2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

49 ASO4I 2.405E-02 2.405E-02 1.603E-02 1.603E-02 3.207E-03 1.603E-03

50 ASO4J 5.772E-01 5.772E-01 3.848E-01 3.848E-01 7.696E-02 3.848E-02

51 NUMATKN 7.187E+09 7.187E+09 4.791E+09 4.791E+09 9.583E+08 4.791E+08

52 NUMACC 2.055E+08 2.055E+08 1.370E+08 1.370E+08 2.740E+07 1.370E+07

53 ASOIL 5.000E-01 5.000E-01 4.000E-01 4.000E-01 8.000E-01 3.000E-01

54 NUMCOR 8.750E+03 8.750E+03 7.000E+03 7.000E+03 1.400E+03 5.250E+02

55 East 

56 

57 SO2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

58 SULF 0.200E-03 0.200E-03 0.200E-03 0.200E-03 0.200E-04 0.100E-04
EPA/600/R-99/030

Table 13-2. CMAQ Predefined Vertical Profiles for Boundary Conditions

13-15

59 NO2 0.100E-04 0.100E-04 0.000E+00 0.000E+00 0.000E+00 0.000E+00

60 NO 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

61 O3 0.300E-01 0.350E-01 0.400E-01 0.500E-01 0.600E-01 0.700E-01

62 HNO3 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.150E-03

63 H2O2 0.200E-02 0.200E-02 0.200E-02 0.200E-02 0.150E-02 0.150E-02

64 ALD 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04

65 HCHO 0.250E-03 0.250E-03 0.250E-03 0.200E-03 0.150E-03 0.100E-03

66 OP1 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

67 OP2 0.400E-07 0.400E-07 0.400E-07 0.400E-07 0.400E-07 0.400E-07

68 PAA 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.500E-04

69 ORA1 0.150E-05 0.500E-06 0.500E-06 0.500E-06 0.500E-06 0.500E-06

70 ORA2 0.150E-05 0.500E-06 0.500E-06 0.500E-06 0.500E-06 0.500E-06

71 NH3 0.500E-04 0.500E-04 0.500E-04 0.200E-04 0.200E-04 0.200E-04

72 N2O5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

73 NO3 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

74 PAN 0.100E-04 0.100E-04 0.100E-04 0.100E-04 0.100E-04 0.100E-04

75 HC3 0.120E-04 0.120E-04 0.120E-04 0.800E-05 0.400E-05 0.400E-05

76 HC5 0.120E-04 0.120E-04 0.120E-04 0.800E-05 0.400E-05 0.400E-05

77 HC8 0.600E-05 0.600E-05 0.600E-05 0.400E-05 0.200E-05 0.200E-05

78 ETH 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

79 CO 0.800E-01 0.800E-01 0.800E-01 0.750E-01 0.700E-01 0.650E-01

80 OL2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

81 OLT 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

82 OLI 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

83 TOL 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

84 XYL 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

85 ACO3 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

86 TPAN 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07

87 HONO 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

88 HNO4 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08

89 KET 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04

90 GLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

91 MGLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

92 DCB 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

93 ONIT 0.600E-05 0.600E-05 0.600E-05 0.400E-05 0.200E-05 0.200E-05

94 CSL 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

95 ISO 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05

96 HO 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

97 HO2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

98 ASO4I 3.207E-02 3.207E-02 3.207E-02 3.207E-02 3.207E-03 1.603E-03

99 ASO4J 7.696E-01 7.696E-01 7.696E-01 7.696E-01 7.696E-02 3.848E-02

100 NUMATKN 9.583E+09 9.583E+09 9.583E+09 9.583E+09 9.583E+08 4.791E+08

101 NUMACC 2.740E+08 2.740E+08 2.740E+08 2.740E+08 2.740E+07 1.370E+07

102 ASOIL 8.000E-01 8.000E-01 8.000E-01 8.000E-01 8.000E-02 4.000E-02

103 NUMCOR 1.392E+04 1.392E+04 1.392E+04 1.392E+04 1.392E+03 6.960E+02

104 South 

105 

106 SO2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

107 SULF 0.200E-03 0.200E-03 0.200E-03 0.100E-03 0.500E-04 0.200E-04

108 NO2 0.100E-04 0.100E-04 0.000E+00 0.000E+00 0.000E+00 0.000E+00

109 NO 0.100E-04 0.100E-04 0.000E+00 0.000E+00 0.000E+00 0.000E+00

110 O3 0.300E-01 0.350E-01 0.400E-01 0.500E-01 0.600E-01 0.700E-01

111 HNO3 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.500E-04 0.150E-03

112 H2O2 0.200E-02 0.200E-02 0.200E-02 0.200E-02 0.150E-02 0.100E-02

113 ALD 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.500E-05

114 HCHO 0.250E-03 0.250E-03 0.250E-03 0.200E-03 0.150E-03 0.100E-03

115 OP1 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

116 OP2 0.400E-07 0.400E-07 0.400E-07 0.400E-07 0.400E-07 0.500E-08

117 PAA 0.100E-03 0.100E-03 0.100E-03 0.100E-03 0.500E-04 0.500E-04
EPA/600/R-99/030

Table 13-2. CMAQ Predefined Vertical Profiles for Boundary Conditions

13-16

118 ORA1 0.150E-05 0.500E-06 0.500E-06 0.500E-06 0.500E-06 0.500E-06

119 ORA2 0.150E-05 0.500E-06 0.500E-06 0.500E-06 0.500E-06 0.500E-06

120 NH3 0.500E-04 0.500E-04 0.500E-04 0.300E-04 0.200E-04 0.200E-04

121 N2O5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

122 NO3 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

123 PAN 0.100E-04 0.100E-04 0.100E-04 0.100E-04 0.100E-04 0.100E-04

124 HC3 0.120E-04 0.120E-04 0.120E-04 0.400E-05 0.400E-05 0.400E-05

125 HC5 0.120E-04 0.120E-04 0.120E-04 0.400E-05 0.400E-05 0.400E-05

126 HC8 0.600E-05 0.600E-05 0.600E-05 0.200E-05 0.200E-05 0.200E-05

127 ETH 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

128 CO 0.700E-01 0.700E-01 0.700E-01 0.700E-01 0.650E-01 0.550E-01

129 OL2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

130 OLT 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

131 OLI 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

132 TOL 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

133 XYL 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

134 ACO3 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

135 TPAN 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07

136 HONO 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

137 HNO4 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08

138 KET 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.500E-05

139 GLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

140 MGLY 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

141 DCB 0.250E-06 0.250E-06 0.250E-06 0.200E-06 0.150E-06 0.100E-06

142 ONIT 0.600E-05 0.600E-05 0.600E-05 0.200E-05 0.200E-05 0.200E-05

143 CSL 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

144 ISO 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05

145 HO 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

146 HO2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

147 ASO4I 3.207E-02 3.207E-02 3.207E-02 1.603E-02 3.207E-03 1.603E-03

148 ASO4J 7.696E-01 7.696E-01 7.696E-01 3.848E-01 7.696E-02 3.848E-02

149 NUMATKN 9.583E+09 9.583E+09 9.583E+09 4.791E+09 9.583E+08 4.791E+08

150 NUMACC 2.740E+08 2.740E+08 2.740E+08 1.370E+08 2.740E+07 1.370E+07

151 ASOIL 8.000E-01 8.000E-01 8.000E-01 4.000E-01 8.000E-02 4.000E-02

152 NUMCOR 1.400E+04 1.400E+04 1.400E+04 7.000E+03 1.400E+03 7.000E+02

153 West 

154 

155 SO2 0.300E-03 0.200E-03 0.200E-03 0.100E-03 0.000E+00 0.000E+00

156 SULF 0.300E-03 0.200E-03 0.200E-03 0.100E-03 0.000E+00 0.000E+00

157 NO2 0.100E-03 0.100E-03 0.100E-03 0.500E-04 0.000E+00 0.000E+00

158 NO 0.500E-04 0.500E-04 0.500E-04 0.200E-04 0.000E+00 0.000E+00

159 O3 0.350E-01 0.400E-01 0.450E-01 0.500E-01 0.600E-01 0.700E-01

160 HNO3 0.500E-03 0.500E-03 0.500E-03 0.500E-03 0.200E-03 0.100E-03

161 H2O2 0.200E-02 0.200E-02 0.200E-02 0.200E-02 0.800E-03 0.200E-03

162 ALD 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.500E-05

163 HCHO 0.400E-03 0.400E-03 0.400E-03 0.400E-03 0.100E-03 0.500E-04

164 OP1 0.400E-06 0.400E-06 0.400E-06 0.400E-06 0.100E-06 0.500E-07

165 OP2 0.400E-07 0.400E-07 0.400E-07 0.400E-07 0.400E-07 0.500E-08

166 PAA 0.250E-04 0.250E-04 0.250E-04 0.250E-04 0.200E-04 0.100E-04

167 ORA1 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.500E-06 0.500E-06

168 ORA2 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.500E-06 0.500E-06

169 NH3 0.300E-03 0.300E-03 0.300E-03 0.200E-03 0.100E-03 0.500E-04

170 N2O5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

171 NO3 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

172 PAN 0.100E-03 0.100E-03 0.100E-03 0.500E-04 0.100E-04 0.100E-04

173 HC3 0.800E-04 0.800E-04 0.800E-04 0.600E-04 0.800E-05 0.400E-05

174 HC5 0.800E-04 0.800E-04 0.800E-04 0.600E-04 0.800E-05 0.400E-05

175 HC8 0.400E-04 0.400E-04 0.400E-04 0.300E-04 0.400E-05 0.200E-05

176 ETH 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
EPA/600/R-99/030

Table 13-2. CMAQ Predefined Vertical Profiles for Boundary Conditions

13-17

177 CO 0.800E-01 0.800E-01 0.800E-01 0.800E-01 0.650E-01 0.500E-01

178 OL2 0.100E-04 0.100E-04 0.500E-05 0.500E-05 0.100E-05 0.000E+00

179 OLT 0.200E-05 0.100E-05 0.500E-06 0.300E-06 0.000E+00 0.000E+00

180 OLI 0.100E-05 0.200E-06 0.100E-06 0.000E+00 0.000E+00 0.000E+00

181 TOL 0.100E-04 0.500E-05 0.500E-05 0.300E-05 0.000E+00 0.000E+00

182 XYL 0.300E-05 0.200E-05 0.400E-06 0.400E-06 0.000E+00 0.000E+00

183 ACO3 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

184 TPAN 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07 0.100E-07

185 HONO 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

186 HNO4 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08 0.200E-08

187 KET 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.400E-04 0.500E-05

188 GLY 0.400E-06 0.400E-06 0.400E-06 0.400E-06 0.100E-06 0.500E-07

189 MGLY 0.400E-06 0.400E-06 0.400E-06 0.400E-06 0.100E-06 0.500E-07

190 DCB 0.400E-06 0.400E-06 0.400E-06 0.400E-06 0.100E-06 0.500E-07

191 ONIT 0.400E-04 0.400E-04 0.400E-04 0.300E-04 0.400E-05 0.200E-05

192 CSL 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08 0.100E-08

193 ISO 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05 0.250E-05

194 HO 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

195 HO2 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

196 ASO4I 4.810E-02 3.207E-02 3.207E-02 1.603E-02 3.207E-03 1.603E-03

197 ASO4J 1.154E+00 7.696E-01 7.696E-01 3.848E-01 7.696E-02 3.848E-02

198 NUMATKN 1.437E+10 9.583E+09 9.583E+09 4.791E+09 9.583E+08 4.791E+08

199 NUMACC 4.110E+08 2.740E+08 2.740E+08 1.370E+08 2.740E+07 1.370E+07

200 ASOIL 1.000E+00 8.000E-01 8.000E-01 4.000E-01 8.000E-02 4.000E-02

201 NUMCOR 1.750E+04 1.400E+04 1.400E+04 7.000E+03 1.400E+03 7.000E+02
EPA/600/R-99/030

13-18

Table 13-3. Example RADM2 to CB4 Conversion Rules

 NO2 = NO2 ;

 NO = NO ; 

 O = O3P; 

 O3 = O3 ; 

 NO3 = NO3; 

 O1D = O1D; 

 OH = HO ; 

 HO2 = HO2 ;

 N2O5 = N2O5;

 HNO3 = HNO3;

 HONO = HONO;

 PNA = HNO4;

 H2O2 = H2O2;

 CO = CO; 

 SO2 = SO2; 

 SULF = SULF;

 PAN = PAN;

 FACD = ORA1;

 AACD = ORA2;

 PACD = PAA;

 UMHP = OP1;

 MGLY = MGLY;

 OPEN = DCB;

 CRES = CSL; 

 FORM = HCHO + 1.0 * GLY; 

 ALD2 = 1.0 * ALD + 2.0 * OLI; 

 PAR = 0.4 * ETH + 2.9 * HC3 + 4.8 * HC5 + 

 7.9 * HC8 + 0.8 * OLT + 0.8 * OLI +

 3.9 * KET; 

 OLE = OLT; 

 TOL = TOL; 

 ISOP = ISO; 

 ETH = OL2; 

 XYL = XYL;

 TERP = TERP; 

 END;
EPA/600/R-99/030

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Shawn Roselle, MD-80, Research Triangle Park, NC 27711. E-mail:

sjr@hpcc.epa.gov

**On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Chapter 14

PHOTOLYSIS RATES FOR CMAQ

Shawn J. Roselle,* Kenneth L. Schere,** and Jonathan E. Pleim**

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, North Carolina 27711

Adel F. Hanna

MCNC-North Carolina Supercomputing Center

Research Triangle Park, North Carolina 27709

ABSTRACT

The method for calculating photodissociation reaction rates (photolysis rates) for CMAQ is

described in this chapter. The description includes the photolysis rate preprocessor (JPROC) and

CMAQ subroutine PHOT. JPROC produces a clear-sky photolysis rate look-up table. The

look-up table consists of photolysis rates at various altitudes, latitudes, and hour angles. The

look-up table is recalculated for each simulation day and is dependent upon the chemical

mechanism. Within CMAQ, photolysis rates for individual grid cells are interpolated from the

look-up table in subroutine PHOT. PHOT also uses a parameterization to correct the clear-sky

photolysis rates for cloud cover.
EPA/600/R-99/030

14-1

Ji 
 P

2

1

F())i

()1i()d (14-1)

14.0 PHOTOLYSIS RATES FOR CMAQ

14.1 Background

Many chemical reactions in the atmosphere are initiated by the photodissociation of numerous

trace gases. These photodissociative reactions are responsible for most of the smog buildup

detrimental to humans, animals, plant life and materials. In order to accurately model and predict

the effects of air pollution, good photodissociation reaction rate (or photolysis rate) estimates

must be made.

Photodissociation is the conversion of solar radiation into chemical energy to activate and

dissociate chemical species. Examples of species that photodissociate include many important

trace constituents of the troposphere such as NO2, O3, HCHO, CH3CHO, HONO, the NO3

radical, and H2O2 (also see Table 14.1). The simulation accuracy of the entire chemical system is

highly dependent upon the accuracy of photolysis rates, which are the primary sources of

radicals in the troposphere. Photolysis rates (min-1), sometimes called J-values, are computed for

photodissociation reaction (i) by

where, F() is the actinic flux (photons cm-2 min-1 nm-1), )i

() the absorption cross section for the

molecule undergoing photodissociation (cm2

 molecule-1), 1i() the quantum yield of the

photolysis reaction (molecules photon-1), and  the wavelength (nm). Absorption cross sections

and quantum yields are functions of wavelength, and may also be functions of temperature and

pressure; they are unique to species and reactions. Laboratory experiments measuring the

absorption cross sections and quantum yields. have been conducted for many species that

photodissociate in the troposphere. Actinic flux is a radiometric quantity that measures the

spectral radiance integrated over all solid angles per unit area. The spherical receiving surface

distinguishes the actinic flux from the more commonly measured irradiance, which is the

radiance falling on a horizontal surface. Thus, the actinic flux can be called spherical spectral

irradiance. The actinic flux changes with time of day, longitude, latitude, altitude, and season,

and is governed by the astronomical and geometrical relationships between the sun and the earth. 

It is greatly affected by the earth's surface albedo as well as by various atmospheric scatterers

and absorbers. Hence, correct model calculation of the temporal and spatial variation of the

actinic flux is critical to obtaining accurate photolysis rates for regional and mesoscale episodic

photochemical modeling.

The current approach taken for setting photolysis rates in the Models-3/CMAQ framework

follows that of the Regional Acid Deposition Model (RADM) (Chang et al., 1987). It includes

two stages of processing: (1) a table of clear-sky photolysis rates is calculated for specified

heights, latitudes, and hours from local noon; and (2) photolysis rates are interpolated from the
EPA/600/R-99/030

14-2

table within the CMAQ Chemistry Transport Model (CCTM) based on grid cell location and the

model time, and are corrected for cloud cover. This approach is computationally efficient and

has been shown by Madronich (1987) to give clear-sky photolysis rates within the uncertainty of

the surface-based measurements.

14.2 Preprocessor JPROC: Calculate Clear-sky Photolysis Rate Table

Preprocessor JPROC calculates a table of clear-sky photolysis rates (or J-values) for a specific

date. The table is dimensioned by latitude, altitude, and time. Currently, J-values are calculated

for 6 latitudinal bands (10(N, 20(N, 30(N, 40(N, 50(N, and 60(N), 7 altitudes (0 km, 1 km, 2

km, 3 km, 4 km, 5 km, and 10 km), and ±9 hours from local noon (0 h, 1 h, 2 h, 3 h, 4 h, 5 h, 6 h,

7 h, and 8 h). There is a separate table for each photolysis reaction. In order to compute the

photolysis rates using Equation 14.1, the actinic flux, absorption cross section, and quantum yield

must be determined as a function of wavelength.

The delta-Eddington two-stream radiative transfer model (Joseph et al., 1976; Toon et al., 1989)

is used for computing the actinic flux. The two-stream approximations are limited in application

to cases where the scatter is not highly anisotropic. In computing the actinic flux, a description

of the extraterrestrial radiation, aerosol, ozone absorption, oxygen absorption in the

Schumann-Runge Bands, Rayleigh scattering (WMO, 1985) and surface albedo are provided to

the radiation model.

Extraterrestrial radiation is specified by a user input file. JPROC is flexible enough to use any

extraterrestrial radiation data distribution specified by the user. However, the wavelength

distribution of the extraterrestrial radiation data is important because this is also the distribution

that will be used in the integration of Equation 14.1. Therefore, the user should choose a

wavelength distribution that resolves the features that are important to the photolysis reactions of

interest. A modified WMO extraterrestrial radiation data distribution (Chang, et al., 1990) is

used as input to JPROC, which has a variable wavelength resolution ranging from 1 nm to 10 nm.

The O2 and O3 absorption cross section data are specified by user input files, but it is

recommended that the most recent NASA data (DeMore et al., 1994) be used in the calculations. 

Vertical ozone profiles are set by interpolating seasonal profiles from a user input file, and if total

ozone column data are available (such as data measured by the Total Ozone Mapping

Spectrometer (TOMS) instrument aboard the sun-synchronous polar orbiting Nimbus satellite),

then the interpolated vertical profiles are uniformly rescaled so that the profiles integrated total

ozone column value matches the measured total ozone column data. TOMS data are archived

and available at the National Satellite Service Data Center (NSSDC) in the form of digital daily

maps with a resolution of 1 degree latitude by 1.25 degrees longitude. The TOMS data are

averaged over each latitudinal band in JPROC. Nimbus-7 TOMS data are available for years

1978 through 1993; Meteor-3 TOMS data are available for 1991-1994; ADEOS TOMS data are

available for 1996-1997; and Earth Probe TOMS data are available for 1996-1998. These data

can be downloaded from site http://jwocky.gsfc.nasa.gov.
EPA/600/R-99/030

14-3

Jbelow 
 Jclear [1cfrac (1.6tr

cos()	1)] (14-2)

tr 
 5	e 	-cld

43-cld(1	f) (14-3)

The albedo data given by Demerjian et al. (1980), which have been used extensively in radiative

transfer models, are given as a function of wavelength and are used in the current version of

JPROC. Currently, a single vertical profile of aerosol attenuation coefficients (Elterman, 1968)

is used in JPROC. An effort is underway to incorporate predicted aerosol parameters from

CMAQ into the photolysis rate calculations.

Several factors in JPROC depend on the vertical profiles of temperature and pressure, including

ozone absorption and the absorption cross sections and quantum yields for individual photolysis

reactions. JPROC interpolates seasonal profiles of temperature and pressure. We use the same

vertical profile data that are used in the RADM (Chang et al., 1987).

Absorption cross section and quantum yield data are specified by the user through input files.

Input files depend on the chemical mechanism selected by the user in the Program Control

Processor (see Chapter 15). The original sets of cross section/quantum yield data published with

the Carbon Bond Mechanism IV (Gery et al., 1989), the Regional Acid Deposition Model

mechanism version 2 (RADM2) (Stockwell et al., 1990), and the SAPRC mechanism (Carter,

1990) are available for use in JPROC. However, users can deviate from these standard sets to

test other data, including the revisions suggested by NASA (DeMore et al., 1994). Table 14.1

lists the photolysis reactions for the RADM2 mechanism.

14.3 Subroutine PHOT: Table Interpolation and Cloud Attenuation

Subroutine PHOT within the CCTM has two basic functions, including interpolation of the clearsky photolysis rate table and application of a cloud correction factor to the clear-sky values. The

interpolation step is fairly simple. For each grid cell, the latitude, height, and time from local

noon are determined and used to interpolate clear-sky values from the photolysis rate table. The

cloud correction step is a little more complicated. The method used to correct for cloud cover in

PHOT was taken from RADM (Chang et al., 1987; Madronich, 1987). The correction of clearsky values depends on whether the location is below, above, or within the cloud. The below

cloud photolysis rate ( Jbelow) is calculated as:

where cfrac is the cloud coverage fraction (cloud fraction is interpolated from hourly data for

each grid cell),  is the zenith angle, and tr is the cloud transmissivity. Below cloud photolysis

rates will be lower than the clear-sky values due to the reduced transmission of radiation through

the cloud. The cloud transmissivity is calculated by:
EPA/600/R-99/030

14-4

log(-cld) 
 0.26331.7095ln[log(W)] (14-4)

Jabove 
 Jclear[1cfrac(i

(1	tr)cos()] (14-5)

where f is the scattering phase function asymmetry factor (assumed to be 0.86) and -cld is the

cloud optical depth. We have replaced the cloud optical depth equation in RADM with one

taken from Stephens (1978). The original RADM equation for -cld required an estimate of the

cloud droplet radius, which is not readily available. In RADM, the cloud droplet radius was

assumed to be 10μm. The empirical formula for -cld from Stephens (1978):

is only a function of liquid water path (W), where W=Lz (g/m2

), L is the liquid water content

(g/m3

), and z is the cloud thickness. The above cloud top factor (Fa) is calculated as:

This equation allows for enhancement of photolysis rates above the cloud due to the reflected

radiation from the cloud. It also includes a reaction dependent coefficient (i

) which allows for

further above cloud enhancements (Chang et al., 1987). Within the cloud, the cloud correction

factor is a simple linear interpolation of the below cloud factor at cloud base to the above cloud

factor at cloud top. Once computed, the below, above, and within cloud factor are used to scale

the clear sky photolysis rates to account for the presence of clouds. In the current

implementation, all cloud types (including clouds composed of ice crystals) are treated the same

using the above outlined procedure.

14.4 Summary

The current method for calculating photolysis rates in CMAQ, which was derived from RADM,

uses a preprocessor to compute a look-up table and a subroutine within the chemistry transport

model to interpolate J-values and apply a cloud-cover correction. Other approaches and

enhancements are being developed and tested. One enhancement to be added in the future is the

dynamic link between aerosol predictions and photolysis rate calculations. Another is to replace

the two-stream model with a more comprehensive multi-stream radiative transfer model

(Stamnes et al., 1988). Other absorption cross section and quantum yield data will be added or

updated using the DeMore et al. (1997) revisions.

14.5 References

Carter, W.P.L., 1990: A detailed mechanism for the gas-phase atmospheric reactions of organic

compounds, Atmos. Environ., 24(A), 481-518.
EPA/600/R-99/030

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Chang, J.S., R.A. Brost, I.S.A. Isaksen, S. Madronich, P. Middleton, W.R. Stockwell, and C.J.

Walcek, 1987: A three-dimensional eulerian acid deposition model: physical concepts and

formulation, J. Geophys. Res. 92 (D12): 14681-14700.

Chang, J.S., P.B. Middleton, W.R. Stockwell, C.J. Walcek, J.E. Pleim, H.H. Lansford, F.S.

Binkowski, S. Madronich, N.L. Seaman, D.R. Stauffer, D. Byun, J.N. McHenry, P.J. Samson, H.

Hass, 1990: The regional acid deposition model and engineering model, Acidic Deposition: State

of Science and Technology, Report 4, National Acid Precipitation Assessment Program.

Demerjian, K.L., K.L. Schere, J.T. Peterson, 1980: Theoretical estimates of actinic (spherically

integrated) flux and photolytic rate constants of atmospheric species in the lower troposphere.

Advances in Environmental Science and Technology, Vol. 10, by John Wiley & Sons, Inc.,

369-459.

DeMore, W.B., S.P. Sander, D.M. Golden, R.F. Hampson, M.J. Kurylo, C.J. Howard, A.R.

Ravishankara, C.E. Kolb, and M.J. Molina, 1994: Chemical Kinetics and Photochemical Data for

Use in Stratospheric Modeling: Evaluation Number 11, JPL Pub. 94-26. Pasadena, CA: National

Aeronautics and Space Administration, Jet Propulsion Laboratory.

DeMore, W.B., S.P. Sander, D.M. Golden, R.F. Hampson, M.J. Kurylo, C.J. Howard, A.R.

Ravishankara, C.E. Kolb, and M.J. Molina, 1997: Chemical Kinetics and Photochemical Data for

Use in Stratospheric Modeling: Evaluation Number 12, JPL Pub. 97-4. Pasadena, CA: National

Aeronautics and Space Administration, Jet Propulsion Laboratory.

Elterman, L, 1968: UV, Visible, and IR Attenuation for Altitudes to 50 km; AFCRL-68-0153.

Bedford, MA: Air Force Cambridge Res. Lab.

Gery, M.W., G.Z. Whitten, J.P. Killus, M.C. Dodge, 1989: A photochemical mechanism for

urban and regional scale computer modeling, J. Geophys. Res., 94, 12925-12956.

Joseph, J.H., W.J. Wiscombe, and J.A. Weinman, 1976: The delta-Eddington approximation for

radiative flux transfer, J. Atmos. Sci., 33, 2452-2459.

Madronich, S, 1987: Photodissociation in the Atmosphere: 1. Actinic flux and the effects of

ground reflections and clouds, J. Geophys. Res. 92 (D8): 9740-9752.

Stamnes, K., S. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm for

discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,

Appl. Opt., 27, 2502-2509.

Stephens, G.L., 1978: Radiation profiles in extended water clouds. II.: Parameterization schemes,

J. Atmos. Sci. 35: 2123-2132.
EPA/600/R-99/030

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Stockwell, W.R., P. Middleton, and J.S. Chang, 1990: The second generation regional acid

deposition model chemical mechanism for regional air quality modeling, J. Geophys. Res. 95

(D10): 16343-16367.

Toon, O.B., C.P. Mckay, and T.P. Ackerman, 1989: Rapid calculation of radiative heating rates

and photodissociation rates in inhomogeneous multiple scattering atmospheres, J. Geophys. Res.,

94, 16287-16301.

World Meteorological Organization, 1986: "Atmospheric Ozone 1985: Assessment of Our

Understanding of the Processes Controlling its Present Distribution and Change"; WMO Rep.

No. 16; Global Ozone Research and Monitoring Project, Geneva, Switzerland.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
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Table 14-1. RADM2 Photolysis Reactions (Adapted from Stockwell et al., 1990.)

Reaction Description

O3 + h  O2 + O1

D Ozone Photolysis to O1D

O3 + h  O2 + O3

P Ozone Photolysis to O3P

NO2 + h  NO + O3

P Nitrogen Dioxide Photolysis

NO3 + h  NO + O2 Nitrate Photolysis to NO

NO3 + h  NO2 + O3

P Nitrate Photolysis to NO2

HONO + h  OH + NO Nitrous Acid Photolysis

HNO3 + h  OH + NO2 Nitric Acid Photolysis

HNO4 + h  HO2 + NO2 Pernitric Acid Photolysis

H2O2 + h  OH + OH Hydrogen Peroxide Photolysis

HCHO + h  H + HCO Formaldehyde Photolysis to Radicals

HCHO + h  H2 + CO Formaldehyde Photolysis to Molecular

Hydrogen

CH3CHO + h (+2O2)  CH3OO + HO2 + CO Acetaldehyde Photolysis

CH3COCH3 + h  CH3 + CH3CO Acetone Photolysis

CH3COC2H5 + h  ACO3 + ETH Methyl Ethyl Ketone Photolysis

HCOCHO + h  HCHO + CO Glyoxal Photolysis to Formaldehyde

HCOCHO + h  2CO + H2

Glyoxal Photolysis to Molecular

Hydrogen

CH3COCHO + h  ACO3 + HO2 + CO Methyl Glyoxal Photolysis

HCOCH=CHCHO + h  0.98HO2 + TCO3 +

0.02ACO3

Unsaturated Dicarbonyl Photolysis

CH3OOH + h  CH2O + OH + HO2 Methyl Hydrogen Peroxide Photolysis

CH3ONO2 + h  0.2ALD + 0.8KET + HO2 + NO2 Organic Nitrate Photolysis

C3H4O + h  products Acrolein Photolysis
EPA/600/R-99/030

Chapter 15

PROGRAM CONTROL PROCESSING IN MODELS-3

Jeffrey Young*

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

ABSTRACT

Based on user choices and input, the Models-3 framework creates objects and include files that

control the complete problem domain under which a CMAQ model is built and executed. The

general concepts underlying the definition of these objects and the creation of the include files are

discussed.

 

*On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Jeffrey Young, MD-80, Research Triangle Park, NC 27711. E-mail:

yoj@hpcc.epa.gov
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15.0 PROGRAM CONTROL PROCESSING IN MODELS-3

Program control processing (PCP) refers to setting up internal arrays and mappings, global

parameters, and data linkages to establish the complete problem domain in which the programs, or

“models,” in the Community Multiscale Air Quality (CMAQ) system are built and executed.

Controlled by user choices, the Models-3 framework carries out this processing automatically and

provides the key to modularity and ensures uniform, consistent internal dimensioning, looping

parameters and solver data in the compiled codes for all the CMAQ system models. Thus,

modularity and consistency in establishing the computational domain and chemical mechanism for

any particular application of the CMAQ system are assured by PCP. Modelers can easily and

relatively safely carry out many different applications at different scales, or with different

chemistry, or different solvers. Model developers can readily study the effects of different

schemes and determine optimal implementations of the science and codes. PCP helps to establish

a true “one-atmosphere” approach to modeling.

PCP involves both the Models-3 framework's graphical user interface and specialized processors

that are launched from the framework. In the Models-3 framework, a user selects the

computational grid and domain characteristics, the vertical layer structure, and the chemical

mechanism to be used in building (compiling and linking) a model (an executable). How these

choices get transformed automatically into compiled code is discussed in the following sections.

This chapter focuses on the CMAQ Chemical Transport Model (CCTM) since the CCTM

requires the most extensive use of PCP. However, some or all of the user choices made to set up

a particular CCTM determine the particular application characteristics for all of the supporting

processors (or “models”). In addition to the CCTM, CMAQ is comprised of eight additional

processors as follows:

• The Models-3 emissions processing and projection system (MEPPS), described in Chapter

4.

• The emissions-chemistry interface processor (ECIP), described in Chapter 4.

• The plume-in-grid dynamics processor (PDM), described in Chapter 9.

• The meteorology-chemistry input processor (MCIP), described in Chapter 12.

• The land-use processor (LUPROC), described in Chapter 12.

• The initial and boundary conditions processors (ICON and BCON), described in Chapter

13.

• The photolytic J-value processor (JPROC), described in Chapter 14.

• The process analysis processor (PROCAN), described in Chapter 16. PROCAN is

launched by the Models-3 framework and its execution is transparent to the user. The

outputs from PROCAN are used to control CCTM diagnostic outputs (see Section 15.3.1

below).
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Building a particular model in the Models-3/CMAQ system requires the creation of Fortran

include files that populate the model's codes to set the specific computational grid and domain

characteristics, the vertical layer structure, the chemical mechanism, and (for the CCTM) the

process analysis to be used for the particular model. Once these model configuration objects are

set by the user in the Models-3 Science Manager, the Models-3 framework automatically

generates the required global Fortran include files. The use of global Fortran include files, the

notion of “Global Name Table Data,” and the design concepts that govern this implementation are

discussed in Chapter 18, Sections 18.5 and 18.7.

15.1 Domain Configuration

The computational domain configuration data are contained in three include files:

• HGRD.EXT - The horizontal grid dimensions in terms of the number of grid cell columns

and rows and the number of grid cells for which the computational domain boundary is

extended for boundary data. The number of these perimeter boundary cells is also

specified.

• VGRD.EXT - The vertical layer dimensions as the number of vertical layers. This include

file also contains declarations for the layer surface and layer center arrays.

• COORD.EXT - The domain coordinate data:

! The map projection type (Lambert, Mercator, Stereographic, UTM, or latitudelongitude).

! The map projection parameters.

! The center of the grid's coordinate system with respect to the “mother grid” or

parent grid (usually the main grid from the meteorology pre-processing).

! The horizontal grid cell sizes in meters.

! The vertical layer type. There are 7 currently defined:

1. σp coordinates.

2. σp(0) coordinates.

3. σz coordinates.

4. ηp coordinates.

5. Pressure coordinates.

6. Z coordinates (meters above ground).

7. H coordinates (meters above mean sea level).

! The units of the top vertical layer value.

! The value of the top vertical layer variable.

! The units of the vertical layer surface values.

! The list of vertical layer surface values.

! The list of vertical layer surface values converted to values monotonically

increasing with altitude.

! The grid name used for header description data in I/O API files (discussed in

Section 15.2).
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15.2 Input/Output Applications Programming Interface

Input and output data access for the CMAQ system is accomplished mainly through the

Input/Output Applications Programmer's Interface (I/O API) sub-system [1]. The CMAQ system

implementation of the I/O API is described in Chapter 18, Section 18.3. In order to access I/O

API files and use other I/O API functions, it is necessary to specify the required declarations and

parameters. Some or all of the following include files are needed in each subroutine that uses the

I/O API:

• PARMS3.EXT - I/O API dimensioning parameters, file type and file characteristic

parameters, coordinate system and map projection parameters, and vertical layer

parameters.

• FDESC3.EXT - Fortran common blocks that contain a complete I/O API file description.

The data in these common blocks are loaded from an I/O API file when opened and read.

These data must be supplied from the user subroutine when an I/O API file is opened for

writing.

• IODECL3.EXT - Declarations and usage comments for I/O API functions and routines.

• XSTAT3.EXT - Exit codes for the I/O API M3EXIT function. Generally, M3EXIT is

called from any subroutine that produces a fatal error during I/O API access.

15.3 Other CCTM Configuration Control

15.3.1 CCTM Process Analysis

The Models-3/CMAQ system provides a diagnostic tool that allows a user to probe into the way

the science processing is actually being executed in the CCTM. The process analysis tool

optionally provides two types of information, which are termed Integrated Process Rates (IPR)

and Integrated Reaction Rates (IRR). Note that these diagnostic tools apply only for the CCTM

and not for the other models. The reader is referred to Chapter 16 for the details, but briefly the

IPR processing captures the changes to the concentration field for different species, or groupings

of species, for each individual science process modeled. The IRR processing focuses on the gasphase chemistry and allows a detailed examination of various characteristics of the chemical

mechanism implemented in the CCTM for the chosen scenario. The data produced by these tools

are collected in I/O API output files, which can be further processed or examined using the

visualization tools.

The CCTM requires three include files, even if neither IPR nor IRR processing is selected.1These

include files are automatically generated from PROCAN, and the Models-3 framework then

incorporates them in the CCTM build process. The three IPR/IRR include files are:

 

1

 If process analysis is not requested while building a CCTM model executable, the Models-3 framework

automatically supplies the include files.
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• PA_CTL.EXT - The declarations and values of the two flags that determine if IPR or IRR

(or both) processing is to be performed.

• PA_CTM.EXT - Declarations and parameters that define the domain, output file

descriptions, arrays and dimensions, IPR and IRR loop variables, and named common

blocks for computational data.

• PA_DAT.EXT - Data statements containing values for the variables needed to fill in the

common blocks in PA_CTM.EXT.

15.3.2 CCTM Fixed Data

The Models-3/CMAQ system can deal with other types of global include files and reference them

from a user-supplied full path to build a model. The following three categories of global include

files apply to the CCTM. The other processor models (MCIP, ECIP, etc.) also have include files

in this category, but not as extensively.

• FILES_CTM.EXT - The set of logical file names used in the current CCTM

implementation. The include file contains data statements for the file names as variables

used in the codes and values for the variables. The values are character strings that are

UNIX environment variable values set in the scripts launched by the Models-3 framework

to run the models.

• CONST.EXT, CONST3_RADM.EXT - These include files contain parameter statements

to define basic and frequently used air quality and meteorological modeling physical and

mathematical constants. Inclusion of these files in the model codes helps to assure

consistency in the science calculations across all the processes and modules.

• BLKPRM_500.EXT - Computational blocking: For computational efficiency and reduced

memory requirements, operations may be performed on groups of grid cells (a block of

cells) at a time. This include file provides convenient definitions to use 500-cell blocking.

• GRID_DECL.EXT - Declarations for the dimensions and species classes offsets in the

main concentration array. See Chapter 18, Section 18.2.2 for details.

• EMISPRM.chem.EXT, EMISPRM.vdif.EXT - These two include files contain the

declarations that control in which process the emissions sources are injected; either the

vertical diffusion process of the gas-phase chemistry solver process. By using a C preprocessor (cpp) #ifdef directive, one or the other include file is actually included when the

code is compiled. The cpp directive is set by the user during the model building phase.

The reader is referred to Chapter 18, Section 18.5 for more details.
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15.4 Generalized Chemistry

15.4.1 Design

In the past, a particular chemical mechanism was generally “hardwired” into a chemical transport

model with mechanism parameters and variables embedded in the solver codes. Implementing

even minor changes incurred a high potential for code and consistency errors. Additionally, some

mechanism changes necessitated extensive coding changes, requiring careful tracing through all

the mechanism dependencies. Worse, not finding these dependencies led to errors that were not

necessarily detected. The Models-3/CMAQ system employs a generalized chemical mechanism

processor (MP), also called the “mechanism reader,” which greatly simplifies the task of

implementing or altering gas-phase chemical mechanisms and provides the capability of easily and

safely using different mechanisms in the CMAQ system.

MP reads an ASCII file that contains a symbolic description of a gas-phase chemical mechanism,

and generates three ASCII Fortran source files. The input ASCII file is called a mechanism

description, or simply, “mechanism.”

The ASCII mechanism description file is formatted according to a simple set of rules in a freeform format similar to the approaches used by Jeffries et al. [2] and Gery and Crouse [3]. The

types of reactions that are supported are described below in Section 15.4.3, and the specific

formats are described in the Models-3 User Manual, Appendix M [4].

The Fortran files that are generated are incorporated as include files in the CMAQ Fortran codes.

They consist of:

• Fortran named common blocks that declare parameters and explicitly dimensioned arrays

associated with gas chemistry kinetic and photolytic reactions.

• Fortran data statements that fill in the common block arrays with actual values determined

from the input ASCII mechanism file.

The common blocks and the data statements files are global and are used in all the codes that

require gas chemistry information.

Another file that is generated from the mechanism description file by MP, which is transparent to

the user, is a species list found in the mechanism description. This file is used by the framework

to generate all the gas chemistry species global include files that are required in the model codes.

In order to implement the mechanism reader's capabilities, the CMAQ system requires generalized

gas-phase chemistry solvers. At present, there are two such solvers available, SMVGEAR and

QSSA, which are described in detail in Chapter 8. The use of generalized solvers precludes some

code optimizations that can increase performance, but significantly facilitates implementing new

or altered chemical mechanisms.
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15.4.2 Operation

The CMAQ system accounts for chemistry in three forms: gas phase, aerosols (liquid and solid

phase), and the aqueous phase. Therefore, the Models-3 framework controls certain aspects of

how the model species are treated in a model simulation and provides linkages between species in

different phases. Setting up the linkages is accomplished by means of a series of four species

tables in a spread sheet format that are filled out by the user. These tables also allow the user to

control some aspects of the simulation and generated outputs and provide links to data such as

emissions, initial and boundary concentrations, and dry deposition velocities that are generated by

the CMAQ input processors. The mechanism definition and species tables become objects that

the Models-3 framework stores in its database. Therefore if a required chemical mechanism

already exists in the database as a predefined mechanism, the user does not have to enter any

mechanism data into the framework.

Since different gas-phase chemical mechanisms can be used in the CMAQ system and these

mechanisms may employ different species names, it is necessary to supply the linkages among the

gas-phase species, the fixed aerosol species, and the species that participate in aqueous-phase

chemistry. Similarly, it is also necessary to link the gas-phase species to emissions, deposition

velocities, and to aqueous-phase scavenging. In addition, the species tables allow the user to

select which species concentrations are written to the output files and whether or not they are to

be advected or diffused. In the same manner, most of these linkages must be established for

aerosol, non-reactive, and possibly tracer species.

The methodology used to establish links between species names involves the concept of surrogate

names. Surrogate names are used to provide linkages between model species within the CCTM

and to link the model species to those that represent data provided by other CMAQ processors.

For example the emissions-chemistry interface processor, ECIP, that links the Models-3 emissions

processing and projection system (MEPPS) with the CCTM could write a species named XXX

that represents xxx emissions rates. However, the CCTM that uses xxx may have the

corresponding model species named YYY. Using the surrogate name concept, emissions species

XXX gets mapped to model species YYY. The reader is referred to the Models-3 User Manual

[4] for more details on the implementation of the set of predefined surrogate names used in the

current version.

An additional feature that can be applied to any of the surrogate species linkages is the application

of a multiplicative, or scale factor. The user can set the factor to be other than unity (the default)

to easily modify some model input data related to the selected species and process linkage. For

example, this could be used to test the effect of changing the deposition velocity for a certain

species, or to modify initial or boundary conditions data. Also, the factors can be set to modify

certain data between model species groups within the CCTM, such as in the gas-phase to aerosol

linkage.

These linkages are set by the user and are distributed among the four tables that establish the

linkages among gas-phase, aerosols, non-reactive, and (possibly) tracer species. Non-reactive

species are gas-phase, but do not participate in gas-phase reactions. Optional tracer species are

inert and may have special, user-defined initial and boundary concentrations as well as emissions
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sources. The reader is referred to the Models-3 User Manual [4] for more details and a complete

description of the species tables.

The following is a list of the linkages set up in the current implementation of the Models3/CMAQ system. The linkages take place with respect to the CCTM or model species name; the

surrogate names and flags point to this name.

1. Model species molecular weight.

2. Emissions species surrogate name.

3. Emissions species scale factor.

4. Initial and boundary concentrations species surrogate name.

5. Initial and boundary concentrations species scale factor.

6. Deposition velocity species surrogate name.

7. Deposition velocity species scale factor.

8. Gas-phase to aerosol linkage species surrogate name.

9. Gas-phase to aqueous-phase linkage species surrogate name.

10. Gas-phase aqueous scavenging linkage species surrogate name.

11. Gas-phase aqueous scavenging linkage species scale factor.

12. Aerosol to aqueous-phase linkage species surrogate name.

13. Aerosol aqueous scavenging linkage species surrogate name.

14. Aerosol aqueous scavenging linkage species scale factor.

15. Non-reactive to aerosol linkage species surrogate name.

16. Non-reactive to aqueous-phase linkage species surrogate name.

17. Non-reactive aqueous scavenging linkage species surrogate name.

18. Non-reactive aqueous scavenging linkage species scale factor.

19. Model species flag for participation in the advection processes.

20. Model species flag for participation in the diffusion processes.

21. Model species flag for inclusion in the concentration output file.

22. Model species flag for inclusion in the dry deposition output file.

23. Model species flag for inclusion in the wet deposition output file.

24. Tracer species - similar linkages to any of the above.

It should be noted that items 1 - 7 and 19 - 23 apply to all of the four groups of species (gas

phase, aqueous phase, solid and liquid aerosols).
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15.4.3 Supported Reaction Types

In this section we describe the types of gas-phase chemical reactions supported by the generalized

mechanism processor, MP, in the current version of the Models-3/CMAQ system. The reader is

referred to Chapter 8 for a description of the available mechanisms.

The gas-phase mechanism description file is a list of mechanism reactions. The mechanism

reactions list consists of lines of symbolic descriptions of elementary reactions among modeled

chemical species, followed by a rule-based symbolic description of the reaction rate expression for

that reaction. The reader is referred to Chapter 8 for mechanism description examples.

These mechanism reaction lists are generally “free-form,” in that spacing of the symbols on the

page is not important (except, perhaps for readability), and reaction descriptions may span many

lines if necessary. Liberal use of comments is facilitated by allowing for comment lines and

comments embedded within the reaction lines. In addition, each reaction may be labeled for

subsequent reference. The photolysis reactions are given labels for a specific photolytic table

reference. These tables are generated by the J-value processor and are used in the CCTM for the

gas-phase chemistry processing. Currently, there are 10 different rate constant expressions

available for thermal reactions, including Arrhenius-type expressions and the class of so-called

fall-off reactions (Type f, below). New expressions can be added, as necessary.

The type of reaction rate expressions that can be calculated are:

Type 1 : k = A

Type 2 : k = A(T/300)B, where T = temperature in deg K.

Type 3 : k = Ae(-C/T), where C = Ea / R,

Ea is the activation energy, and

R is the gas constant.

Type 4 : k = A(T/300)Be

(-C/T)

Type 5 : k = kr = kf /Ae(-C/T), where kf is any previously defined forward reaction.

Type 6 : k = Akn, where kn refers to the nth reaction.

Type 7 : k = A(1.0 + 0.6P), where P = pressure in atmospheres.

Type 8: [ ]

[ ]

2

3

3

0

k

k

1

k

k k

M

M

+

= + , where k0, k2, and k3 are Type 3.

Type 9: k = k1 + k2[M], where k1 and k2 are Type 3.

Type f: k = [ ]

[ ]

k =

k

k k

0

i

M

M

F

G

1 0 + /

where k0 and ki may be Type 1, 2, 3, or 4,

G = {1 + [ln( k0 [M] / ki) / n]2 }-1,

F = 0.6 (usually), and

n = 1.0 (usually).
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15.4.4 Mechanism Parsing Rules

The mechanism description file that MP reads must follow a set of format rules in order to

describe the reactions listed above. Generally, reserved ASCII characters and keywords on one

line (which may wrap around the page) represent parts of a reaction, including species reactants

and products, stoichiometric coefficients and rate expressions. In addition, labels are supported,

which function to allow one reaction to refer to another and to fix photolytic reaction table names

for photolytic reactions. As mentioned above, the reader is referred to Chapter 8 for mechanism

description examples. Also, Appendix M of the Models-3 User Manual contains a complete

description of these formats.

15.4.5 Chemical Species Include Files

As described above, MP reads and processes the mechanism description file, and one of the

outputs it generates is a file that contains the list of chemical species found in the mechanism. The

Models-3 framework reads this species file to initialize the gas-phase species table in a format

similar to a spreadsheet, which the user completes by inserting data such as molecular weights,

surrogate names and factors, and processing flags. The initial set-up presented to the user

consists of all blank entries in each spreadsheet cell, but with the first column filled in with the

species found in the MP-generated species file. Thus all the species in the mechanism are listed in

the order in which they were found in the mechanism description file. The top row is also filled in

with category headers that are related to the linkages described above and that determine the

framework-generated Fortran include files to be used in the codes.

There are three additional tables that are initialized for aerosols, non-reactive and tracer species.

They do not have the first column set up, but the first row is set as in the gas-phase table. It is up

to the user to fill in the first column, as with all the other spreadsheet cells. Appendix M of the

Models-3 User Manual describes the details of how to enter data into these tables.

The following sections describe all the standard include files that are generated from the species

tables and the behavior of the models when accessing the data declared in the include files.

15.4.5.1 Gas-Phase Reactions

The gas-phase reactions data are required in the CCTM by the gas-phase chemistry solvers and

the subroutine PHOT, which calculates the photolysis rate constants. These data are also

required in JPROC, the processor model that calculates the table-based photolysis rates (see

Chapter 14). There are two include files associated with this data:

• RXCM.EXT - contains all the declarations, parameter statements and array definitions

associated with the gas-phase chemistry reactions. This file also contains three named

common blocks for memory allocation of the data from RXDT.EXT.

• RXDT.EXT - contains data statements associated with the parameters and arrays declared

in RXCM.EXT. These data fill the arrays in the named common blocks in RXCM.EXT.
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The CCTM driver program must include both of these files in its declaration section. The

subroutines in the gas-phase chemistry solver process module must include only the common

block file, RXCM.EXT. That goes for the subroutine PHOT, as well. PHOT is called from the

gas-phase chemistry “class-driver,” the top-level subroutine (see Section 18.2.2 in Chapter 18).

The CCTM driver, by including both files, causes the common blocks to be loaded with the

necessary data used by all the modules that need the chemistry data, including the process analysis

module, PROCAN.

The remaining sections describe the global include files associated with the four species tables. As

mentioned above, these files are automatically generated by the Models-3 framework, according

to the user-specified linkages and flags, and are targeted for inclusion in all model routines that

require the specific chemistry data in them. For additional details the reader is referred to the

Models-3 User Manual [4]. Each of the include files contains declarations and parameter

statements for the loop index and array dimensioning for each particular species group. If a

particular species group is not used (e.g., aerosols or tracers), the include file contains

declarations and parameter statements that set the species loop counter to zero and its array

dimensioning parameter to one, thus maintaining complete generality and modularity within the

codes. In addition, by setting the dimensioning value to one (Fortran does not allow zero), the

compiled codes do not waste memory, a typical problem when coding in Fortran with some predetermined maximum dimension to hopefully account for all cases.

15.4.5.2 Model Species

The framework generates four model species include files that together contain the names and

molecular weights of all the chemical species available globally to the model.

The model species include files are:

• GC_SPC.EXT - gas-phase model species names and molecular weights.

• AE_SPC.EXT - aerosol species names and molecular weights.

• NR_SPC.EXT - non-reactive species names and molecular weights.

• TR_SPC.EXT - tracer species names and molecular weights.

The next three sections describe include files that are associated with data access by the CCTM

from external files. The data are referenced from I/O API files by means of file variable names

that are contained in headers in each of the files.

15.4.5.3 Emissions

The CCTM reads the emissions data from an I/O API file produced by ECIP using the surrogate

name concept discussed above. The data are read by file variable names (surrogates) and stored

in arrays that are linked to the corresponding model species names.
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The CCTM has the option of emissions sources injected as part of the vertical diffusion process or

as part of the chemistry solver process, where the injected sources are treated as part of the

chemical production terms. To read source emissions data into the CCTM for processing either

in the vertical diffusion or in the gas-phase chemistry modules, the following include files are

required:

• GC_EMIS.EXT - gas-phase emissions surrogate species names with scale factors and

indices that point to the positions of the species in the model species name table (in

GC_SPC.EXT).

• AE_EMIS.EXT - aerosol emissions surrogate species names with scale factors and indices

that point to the positions of the species in the model species name table (in

AE_SPC.EXT).

• NR_EMIS.EXT - non-reactive emissions surrogate species names with scale factors and

indices that point to the positions of the species in the model species name table (in

NR_SPC.EXT).

• TR_EMIS.EXT - tracer emissions surrogate species names with scale factors and indices

that point to the positions of the species in the model species name table (in

TR_SPC.EXT).

15.4.5.4 Initial and Boundary Conditions

For both the initial and boundary concentrations the CCTM reads I/O API input data by variable

name reference. The processing first checks to see if the model species name is on the file and

reads the data associated with that name. If the model species name is not on the file, it checks

for the surrogate name. If that, too is not available, the input value is set to a minimum value

(“model zero”). Additional information on initial and boundary conditions and how they are

implemented in the Models-3/CMAQ system can be found in Chapter 14.

• GC_ICBC.EXT - gas-phase initial and boundary conditions surrogate species names with

scale factors and indices that point to the positions of the species in the model species

name table (in GC_SPC.EXT).

• AE_ICBC.EXT - aerosol initial and boundary conditions surrogate species names with

scale factors and indices that point to the positions of the species in the model species

name table (in AE_SPC.EXT).

• NR_ICBC.EXT - non-reactive initial and boundary conditions surrogate species names

with scale factors and indices that point to the positions of the species in the model species

name table (in NR_SPC.EXT).

• TR_ICBC.EXT - tracer initial and boundary conditions surrogate species names with scale

factors and indices that point to the positions of the species in the model species name

table (in TR_SPC.EXT)
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15.4.5.5 Dry Deposition

The following include files are used to read in dry deposition velocities from an I/O API file

produced by the meteorology-chemistry input processor, MCIP. Using the surrogate name

concept discussed above, the data are read by file variable names (surrogates) and stored in arrays

that are linked to the corresponding model species names.

• GC_DEPV.EXT - gas-phase deposition velocity surrogate species names with scale

factors and indices that point to the positions of the species in the model species name

table (in GC_SPC.EXT).

• AE_DEPV.EXT - aerosol deposition velocity surrogate species names with scale factors

and indices that point to the positions of the species in the model species name table (in

AE_SPC.EXT).

• NR_DEPV.EXT - non-reactive deposition velocity surrogate species names with scale

factors and indices that point to the positions of the species in the model species name

table (in NR_SPC.EXT).

• TR_DEPV.EXT - tracer deposition velocity surrogate species names with scale factors

and indices that point to the positions of the species in the model species name table (in

TR_SPC.EXT).

15.4.5.6 Wet Scavenging

In both the scavenging and the cross-phase linkages it is necessary to set up a mapping from the

gas-phase species to the generic species names that are associated with aerosols and aqueousphase chemistry and to the names of species that are absorbed by cloud and rain water. Because

of the generality with respect to the gas-phase species names, these generic names are set in the

subroutines associated with aerosols, aqueous chemistry, and removal by in-cloud and

precipitation scavenging. They are linked to the model species names by employing the surrogate

name concept described above.

• GC_SCAV.EXT - gas-phase scavenging surrogate species names with scale factors and

indices that point to the positions of the species in the model species name table (in

GC_SPC.EXT).

• AE_SCAV.EXT - aerosol scavenging surrogate species names with scale factors and

indices that point to the positions of the species in the model species name table (in

AE_SPC.EXT).

• NR_SCAV.EXT - non-reactive scavenging surrogate species names with scale factors and

indices that point to the positions of the species in the model species name table (in

NR_SPC.EXT).
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• TR_SCAV.EXT - tracer scavenging surrogate species names with scale factors and

indices that point to the positions of the species in the model species name table (in

TR_SPC.EXT).

15.4.5.7 Cross-Phase Linkage

• GC_G2AE.EXT - surrogate names for gas-phase model species that participate in aerosol

chemistry with scale factors and indices that point to the positions of the species in the

model species name table (in GC_SPC.EXT).

• GC_G2AQ.EXT - surrogate names for gas-phase model species that participate in

aqueous-phase chemistry with scale factors and indices that point to the positions of the

species in the model species name table (in GC_SPC.EXT).

• AE_A2AQ.EXT - surrogate names for aerosol species that participate in aqueous-phase

chemistry with scale factors and indices that point to the positions of the species in the

model species name table (in AE_SPC.EXT).

• NR_N2AE.EXT - surrogate names for non-reactive species that participate in aerosol

chemistry with scale factors and indices that point to the positions of the species in the

model species name table (in NR_SPC.EXT).

• NR_N2AQ.EXT - surrogate names for non-reactive species that participate in aqueousphase chemistry with scale factors and indices that point to the positions of the species in

the model species name table (in NR_SPC.EXT).

• TR_T2AE.EXT - surrogate names for tracer species that participate in aerosol chemistry

with scale factors and indices that point to the positions of the species in the model species

name table (in TR_SPC.EXT).

• TR_T2AQ.EXT - surrogate names for tracer species that participate in aqueous-phase

chemistry with scale factors and indices that point to the positions of the species in the

model species name table (in TR_SPC.EXT).

15.4.5.8 Operational Choices

The Models-3 framework provides the capability of allowing the user to control how some of the

processing is carried out with respect to the chemical species in the CCTM. The following lists

describe the include files that the framework generates for the various processes:

1. Advected species: In order to save memory storage or to minimize computation, the user

may choose not to advect certain modeled species such as some radicals. In general, the

special “counter species” used in a mechanism should not be advected.

• GC_ADV.EXT - names of gas-phase model species that are advected and indices

that point to the positions of the species in the model species name table (in

GC_SPC.EXT).
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• AE_ADV.EXT - names of aerosol species that are advected and indices that point

to the positions of the species in the model species name table (in AE_SPC.EXT).

• NR_ADV.EXT - names of non-reactive species that are advected and indices that

point to the positions of the species in the model species name table (in

NR_SPC.EXT).

• TR_ADV.EXT - names of tracer species that are advected and indices that point

to the positions of the species in the model species name table (in TR_SPC.EXT).

2. Species that undergo diffusive processes: The comment above, for advected species,

applies also to diffused species.

• GC_DIFF.EXT - names of gas-phase model species that are diffused and indices

that point to the positions of the species in the model species name table (in

GC_SPC.EXT).

• AE_DIFF.EXT - names of aerosol species that are diffused and indices that point

to the positions of the species in the model species name table (in AE_SPC.EXT).

• NR_DIFF.EXT - names of non-reactive species that are diffused and indices that

point to the positions of the species in the model species name table (in

NR_SPC.EXT).

• TR_DIFF.EXT - names of tracer species that are diffused and indices that point to

the positions of the species in the model species name table (in TR_SPC.EXT).

3. Species that are saved to the dry deposition output file: Generally, all the dry

deposition species that are modeled would be saved to the output file, but a user might

elect to reduce the number and save only a subset.

• GC_DDEP.EXT - names of gas-phase model species that are written to the dry

deposition output file and indices that point to the positions of the species in the

model species name table (in GC_SPC.EXT).

• AE_DDEP.EXT - names of aerosol species that are written to the dry deposition

output file and indices that point to the positions of the species in the model

species name table (in AE_SPC.EXT).

• NR_DDEP.EXT - names of non-reactive species that are written to the dry

deposition output file and indices that point to the positions of the species in the

model species name table (in NR_SPC.EXT).

• TR_DDEP.EXT - names of tracer species that are written to the dry deposition

output file and indices that point to the positions of the species in the model

species name table (in TR_SPC.EXT).

4. Species that are saved to the wet deposition output file: See the comment in item 3.

• GC_WDEP.EXT - names of gas-phase model species that are written to the wet

deposition output file and indices that point to the positions of the species in the

model species name table (in GC_SPC.EXT).

• AE_WDEP.EXT - names of aerosol species that are written to the wet deposition

output file and indices that point to the positions of the species in the model

species name table (in AE_SPC.EXT).
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• NR_WDEP.EXT - names of non-reactive species that are written to the wet

deposition output file and indices that point to the positions of the species in the

model species name table (in NR_SPC.EXT).

• TR_WDEP.EXT - names of tracer species that are written to the wet deposition

output file and indices that point to the positions of the species in the model

species name table (in TR_SPC.EXT).

5. Species that are saved to the concentration output file: See the comment in item 3.

• GC_CONC.EXT - names of gas-phase model species that are written to the

concentration output file and indices that point to the positions of the species in the

model species name table (in GC_SPC.EXT).

• AE_CONC.EXT - names of aerosol species that are written to the concentration

output file and indices that point to the positions of the species in the model

species name table (in AE_SPC.EXT).

• NR_CONC.EXT - names of non-reactive species that are written to the

concentration output file and indices that point to the positions of the species in the

model species name table (in NR_SPC.EXT).

• TR_CONC.EXT - names of tracer species that are written to the concentration

output file and indices that point to the positions of the species in the model

species name table (in TR_SPC.EXT).

15.4.5.9 Tracer Species

The use of tracer species is purely user-determined. An application with tracers can provide the

modeler with insights into how the model is simulating various physical processes, like advection

or diffusion. If tracer species are to be modeled, the user must have created the special table

entries appropriate to the application. In addition special data, such as emissions or initial and

boundary tracer concentrations, must be created in the corresponding I/O API files. The

specialized data creation is outside the scope of the Models-3 framework and must be carried out

by the user in conjunction with the application that is being modeled.

15.6 Conclusion

In this chapter we have described how PCP helps to establish modularity and consistency for

particular applications of models in the CMAQ system. The Models-3 framework processing,

through PCP, enables model developers and model users to study the effects of different

implementations of the science and codes or to execute different applications at various scales

with different chemical mechanisms or with different numerical solvers. The design and

implementation of the concepts in the program control processing helps to establish a true “oneatmosphere” approach to modeling.

15.7 References

[1] “The EDSS/Models-3 I/O API” http://sage.mcnc.org/products/I/O API/
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[2] Jeffries H. E. (1990), “User's Guide to Photochemical Kinetics Simulation System PCPKSS Software Version 3,” Chapel Hill, N.C. 27514

[3] Gery M. W. and R. R. Crouse (1990), “User's Guide for Executing OZIPR,” EPA/600/8-

90/069, U. S. Environmental protection Agency, Research Triangle Park, NC 27711

[4] EPA Third-Generation Air Quality Modeling System Models-3 Volume 9b, User Manual,

Appendices, June 1998, EPA-600/R-98/069(b)

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

*

Corresponding author address: Gerald L. Gipson, MD-80, Research Triangle Park, NC 27711. E-mail:

ggb@hpcc.epa.gov

Chapter 16

PROCESS ANALYSIS

Gerald L. Gipson*

Human Exposure and Atmospheric Sciences Division

National Exposure Research Laboratory

U. S. Environmental Protection Agency 

Research Triangle Park, NC 27711

ABSTRACT

The implementation of process analysis techniques in the Models-3 Community Multiscale Air

Quality (CMAQ) modeling system is described in this chapter. These techniques can be used in

Eulerian photochemical models such as the CMAQ Chemical Transport Model (CCTM) to obtain

information that provides insights into how model predictions are obtained. This type of

information is particularly useful when modeling nonlinear systems such as atmospheric

photochemistry. The two techniques available in the CMAQ system – integrated process rate

(IPR) analysis and integrated reaction rate analysis (IRR) -- are each described. The manner in

which IPR analysis can be used to determine the relative contributions of individual physical and

chemical processes is presented. Descriptions of how to employ IRR analysis to elucidate

important chemical pathways and to identify key chemical characteristics are included. Finally,

the procedures used to apply each technique in the CMAQ system are also described. 
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16.0 PROCESS ANALYSIS

A major function of air pollution models is to predict the spatial and temporal distributions of

ambient air pollutants and other species. For complex Eulerian grid models, output concentration

fields of these species are determined by solving systems of partial differential equations. These

equations define the time-rate of change in species concentrations due to a series of physical and

chemical processes (e.g., emissions, chemical reaction, horizontal advection, etc.). Since most

grid models are configured to output only the concentration fields that reflect the cumulative

effect of all processes, information about the impact of individual processes is usually not

available. Grid models can be configured to provide quantitative information on the effects of 

the chemical reactions and other atmospheric processes that are being simulated, however

(Pleim, 1990; Jeffries and Tonnesen, 1994; Jang et al., 1995a,b). This type of information has

been used to develop various process analyses that provide descriptions of how a model obtained

its predictions. This chapter provides background information on these methods and describes

how process analysis is implemented in the Models-3 Community Multiscale Air Quality

(CMAQ) modeling system.

Although process analysis does not have to be included in a grid model application, it can provide

supplemental information that can be quite useful in assessing a model's performance. 

Quantifying the contributions of individual processes to model predictions provides a

fundamental explanation of the reasons for a model's predictions and shows the relative

importance of each process. This information can be useful in identifying potential sources of

error in the model formulation or its inputs. It can also be useful in interpreting model outputs,

particularly with respect to understanding differences in model predictions that occur from a

change to the model itself or to its input. Further, information provided from the chemical

process analysis can be used to determine important characteristics of different chemical

mechanisms. This is particularly useful for investigating mechanistic differences under different

chemical regimes (e.g., VOC versus NOx limiting conditions).

The inclusion of process analysis in a model application is generally carried out in two steps. 

First, the model itself is “instrumented” (i.e., additional code or modules are added to the model)

to produce supplemental outputs about the contributions of individual processes and different

chemical reaction pathways to the model predictions. These data are then used with the

concentration fields in postprocessing operations to provide quantitative explanations of the

factors affecting a model's predictions. Although several specific postprocessing techniques have

been developed to reveal particular model features (e.g., Jeffries and Tonnesen, 1994; Jang et al.,

1995a,b), process analysis data can be extracted and analyzed in many different ways. The

implementation of process analysis in the CMAQ system has been structured to facilitate data

extraction for subsequent model analysis. Although the main focus of this chapter is on data

extraction techniques, some example process analyses are also presented to illustrate particular

applications.

For purposes of discussion, it is convenient to separate process analysis into two parts: integrated

process rate (IPR) analysis and integrated reaction rate (IRR) analysis. The first deals with the
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effects of all the physical processes and the net effect of chemistry on model predictions. IRR

analysis deals with the details of the chemical transformations that are described in the model's

chemical mechanism. In general, IPR analyses are generally much easier to apply and understand

than IRR analyses since the latter typically requires a fairly thorough understanding of

atmospheric chemistry. Thus, the discussion below describes each analysis method separately,

starting with IPR analyses. Users not familiar with atmospheric chemistry details may wish to

omit the sections on IRR analysis. It should be added that either analysis method can be applied

independently of the other.

The CMAQ implementation of process analysis includes a flexible user interface that allows the

user to request only those particular outputs that are needed for model analysis. The information

generated for both IPR analysis and IRR analysis is controlled by the Process Analysis Control

Program (PACP). The PACP processes user-specified commands to instrument the CMAQ

Chemical Transport Model (hereafter referred to as the CCTM) to generate the specific outputs

that are selected by the user. As a consequence, the PACP must be invoked before configuring a

CCTM and running a simulation. The details of how the PACP works and the syntax for the

commands are covered in the Models-3 User Manual (EPA, 1998), and they will not be repeated

in their entirety here. Nevertheless, some of the command syntax and some simple examples are

presented in the discussions that follow to illustrate how the PACP is used to set up a particular

process analysis.

16.1 Integrated Process Rate Analysis 

The governing equation for Eulerian models is the species continuity equation. Application of

the continuity equation to a group of chemically reactive species results in a system of partial

differential equations (PDEs) that gives the time-rate of change in species concentration as a

function of the rates of change due to various chemical and physical processes that determine the

ambient species concentrations. As noted in the introduction, the concentration fields that are

the numerical solutions to these PDEs reveal only the net effects of all processes. This section is

concerned with how the contributions of individual processes are determined and used in process

analyses. The first two subsections deal with the calculation and use of IPRs in general. The last

two subsections describe the CMAQ implementation of IPR analysis and the use of the PACP to

set up an IPR analysis.

16.1.1 Computation of Integrated Process Rates

All Eulerian models utilize the technique of operator splitting. As a result, it is relatively easy to

obtain quantitative information about the contribution of individual processes to total

concentrations. In operator splitting, solutions to the system of PDEs are obtained by separating

the continuity equation for each species into several simpler PDEs or ordinary differential

equations (ODEs) that give the impact of only one or two processes. These simpler PDEs or

ODEs are then solved separately to arrive at the final concentration. To illustrate, consider the

simple case of two-dimensional horizontal advection of a single species in the absence of any

other processes, for which the governing equation can be expressed as follows:
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0c

0t  0(uc)0x  0(vc)0y 
 0 , (16-1)

where c is the species concentration, and u and v are the x- and y-components of the wind

velocity vector, respectively. With operator splitting, this 2-dimensional equation is split into two

1-dimensional operators, one for each direction: 

0c

0t  0(uc)0x 
 0 (16-2a)

and

0c

0t  0(vc)0y 
 0 . (16-2b)

These two equations are then solved sequentially, with the solution to the first being used as the

initial condition for the second. The solution to the second equation then represents the final

solution and gives the net effect of 2-dimensional advection. 

The final solution for the example presented above can also be represented as follows: 

c(t  t) 
 c(t)  (c)

x  (c)y , (16-3)

where c(t+t) is the final solution, c(t) is the initial condition for the 2-dimensional problem, and

(c)x and (c)y are the changes in concentration produced by each of the 1-dimensional

operators. (c)x and (c)y give the impact of each operator in moving from the initial to the final

concentration and are equivalent to the results obtained by integrating the process rates

individually. Hence the term integrated process rates is used to describe them. Note that they

can be computed with little additional work since they are simply equal to the difference between

the final and initial concentrations for each operator. 

From the above example, it should be evident that a general mathematical representation of IPRs

for individual processes can be expressed as follows: 

(c)

n 
 P

tt

t

Ln dt , (16-4)

where (c)n is the change in a species' concentration due to operator n, Ln is the differential

operator associated with a process, and t is the model synchronization time step (which is

equivalent to tsync in Chapter 6). Refer to Chapter 6 for a discussion of the various time steps

used in CMAQ. The integration in equation (16-4) is performed by the model regardless of

whether it has been instrumented for process analysis. Thus, it is only necessary to save the

(c)n to obtain process analysis capabilities. In a few cases, however, models may be structured

such that one operator deals with two or three processes simultaneously. In those cases, the
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(c)n obtained after the integration would represent the compound effect of all of those

processes and it would not be possible to discern the impacts of the individual processes. 

Normally, the only way that information could be obtained would be to integrate the process

rates separately. In some instances, however, it may still be possible to isolate the impacts of the

individual processes without performing additional integrations. For example, the CCTM treats

vertical diffusion, emissions, and dry deposition simultaneously in one operator, but the amount

of material deposited by dry deposition is tabulated and the amount of material that is emitted is

known. As a consequence, mass balance techniques can be used to compute the contribution of

each process subsequent to the simultaneous integration of the process rates without separately

integrating each process rate. Thus, the IPRs that are available for process analysis are to some

degree determined by the underlying structure of the photochemical model that is being used and

by the effort that is invested in separating individual components when processes are coupled in

a single operator. 

Analogous to equation (16-3), the concentration at the end of a time step can be expressed as

follows:

c(tt) 
 c(t) M

N

n
1

(c)

n , (16-5)

where the model is assumed to have N operators. It should be noted that most IPRs can be either

positive or negative since most processes can cause concentrations to either increase or decrease. 

Further, it should also be evident that the IPRs in the above expression are additive. Thus, for

example, the IPRs for horizontal advection and vertical advection could be summed to give one

IPR that represents the net impact of the two advection processes. The differential operators (Ln)

themselves are most often nonlinear, however. Because of these nonlinearities, the magnitude of

the IPRs for most processes would change if the order of the model’s operators was altered or

even if only one of the operators was changed. Thus, the additive property for IPRs holds only

for a particular application of the model. 

16.1.2 Example IPR Analyses

The tabulation and subsequent output of IPRs provide the user with quantitative information on

the effects of individual processes, and these can be examined and depicted in a number of

ways. Figures 16-1 and 16-2 contain two types of displays that were developed to depict process

contribution data graphically (Jeffries, 1996). Figure 16-1 is a time series plot showing both

predicted concentrations and integrated process rates. This type of plot shows the hourly

variations at a cell (or group of cells if the data are aggregated) of a predicted species

concentration and the change in concentration caused by each process (i.e., the IPRs). Plots of

this type illustrate the variations in process contributions during the simulation period. Figure 16-

2 shows process contributions and total concentrations for different model formulations, in this

case, different grid resolutions. Here the data have been aggregated over several cells and hours,

but could be developed for a single cell or time period just as well. This figure highlights how

cumulative process contributions are altered by the different model formulations. For a more
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thorough discussion of how this type of data can be used to assist in the evaluation of a model's

performance, the reader is referred to Jang et al. (1995a and 1995b) and to Pleim (1990).

16.1.3 Implementation of IPR Analysis in the CMAQ System

The previous section illustrated that instrumenting a model for process analysis involves

providing the capability to capture IPRs. Since an IPR can be calculated for every combination

of process and species, the amount of output data that can be generated is substantial. As a

consequence, the PACP has been designed to allow substantial flexibility in selecting the

particular IPRs for output. This is accomplished primarily by allowing the user to choose only

those particular species/process combinations that are of interest. Additional control and

flexibility are provided by including the ability to produce lumped IPRs, by allowing special

species families to be defined, and by providing controls to limit the size of the modeling domain

for which outputs are generated. These will be illustrated in the examples presented below.

The physical processes that are simulated in the CCTM and hence are available for IPR analysis

are shown in Table 16-1. As will be illustrated below, these processes are referenced in the

PACP by the codes shown in the first column. The procedure for selecting specific IPRs for

output is species oriented. Hence, a user selects a species and then indicates which processes

will be included in the IPR output. The species are referenced by their model names. In

addition, the user may also define a family of species that is a linear combination of the model

species (e.g., defining NOx as the sum of NO and NO2) and extract IPRs for the family. This can

be useful in saving disk space occupied by the output IPR files when information about

individual members of a family is not needed. 

It should be apparent from Table 16-1 that IPRs for some species will always be zero (e.g., those

species not emitted always have zero IPRs for that process). Thus, the size of the output file can

be minimized by not extracting those IPRs. The PACP also contains an option that allows the

user to limit the amount of output data by extracting IPR outputs for only part of the modeling

domain. Currently, the user is restricted to selecting a single, contiguous block of cells within the

domain for the IPR outputs. The block is defined relative to the modeling domain by selecting a

starting and ending column, row and level. A possible future enhancement would be to provide a

graphical interface to allow the user to select any particular cell or group of cells within the

domain.

The CCTM model has been instrumented to write the IPRs to an output file at the same time as

the output concentration files are written. Thus, the IPR outputs represent the cumulative impact

of the process integrations over the entire output time interval. Process contributions over

shorter time intervals can be obtained by increasing the frequency of writing outputs of both the

concentration fields and the IPRs. Finally, the IPR output files are standard Models-3 IO/API

gridded files, and can be viewed with the Models-3 visualization tools described in Models-3

User Manual (EPA, 1998).
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16.1.4 Use of the PACP to set up an IPR Analysis

This section illustrates how the PACP can be used to generate the IPR data for an analysis.

Details on formatting inputs and using the PACP are contained in the Models-3 User Manual

(EPA, 1998). This section borrows from that discussion to illustrate how the PACP is used. The

user selects and controls the form of the IPR output data by means of a PACP command file. A

few predefined command files are available to set up an analysis, or users can generate their own

files to customize their analyses. A command file consists of a series of commands and

definitions that contain instructions for generating IPR outputs. The commands are input in a

free form format to facilitate encoding, and they contain special keywords that have specific

meaning to the PACP. The commands related to IPR analysis have been divided into two

groups: Global commands and IPR output commands. A description of the commands within

each group will be presented first, followed by an example illustrating how these commands are

used. In the description that follows, the syntax for each command is given first, with bold type

used for PACP keywords and normal type used for user supplied input. Alternative inputs are

separated by vertical bars and completely optional inputs are enclosed in curly braces.

Global Commands:

OUTPUT_DOMAIN = {LOCOL[n1] + HICOL[n2] + LOROW[n3] + HIROW[n4]

 + LOLEV[n5] + HILEV[n6]};

The OUTPUT_DOMAIN command provides the capability to limit

the IPR output data to only one portion of the modeling domain. 

The ni

 in brackets are numbers that define the bounds of the output

domain relative to the number of columns, rows, and vertical levels

in the modeling domain. Thus, for example, the value for n1 must

be greater than or equal to one and less than or equal to the

number of columns in the domain. If this command is included, at

least one domain specifier must be present, and the end of the

domain is used for any that are missing. If the command is omitted

entirely, output is generated for the entire domain. 

DEFINE FAMILY familyname = {c1*}species1 {+ {c2*}species2 + ...};

The DEFINE FAMILY command is used to define a group of

species as members of a family. The user specified “familyname”

must be unique, and can be referenced in subsequent commands. 

The ci

 are numerical coefficients that default to one if not

specified; “speciesi

” are the names of individual model species. 
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ENDPA;

The ENDPA command signifies the end of the command input in

the PACP command file. 

IPR Output Command:

IPR_OUTPUT species|familyname|ALL {= pcode1 + pcode2 + ...};

The IPR_OUTPUT command defines specific IPR outputs to be

generated during a CMAQ simulation. A species name, family

name, or the keyword ALL must follow the IRR_OUTPUT

keyword. The keyword ALL refers to all model species. IPRs are 

generated for the selected species or family, and they are

controlled by the specified values of pcodei

, where pcodei

corresponds to one of the process codes listed in Table 16-1. If no

process codes are specified, IPRs will be generated for every

process. The output variables that are generated are named either

species_pcodei

 or familyname_pcodei

A listing of an example PACP command file is contained in Exhibit 16-1. To facilitate the

discussion that follows, the commands have been numbered, although this is not required by the

PACP. (Note that all information enclosed by curly braces in a command file is treated as

comments.) Each numbered line represents a command, and the input for each command is

terminated by a semicolon. This particular set of commands causes the CCTM to generate

several individual IPRs for a special user-defined sub-domain. Each of the commands is

described below.

Command 1 is used to restrict the process analysis output to a subset of the modeling domain. As

noted above, output would be generated for the entire computational domain if the

OUTPUT_DOMAIN were omitted. Since keywords for columns and rows are not present, the

PACP default is to include all rows and columns in the modeling domain. The keywords

“LOLEV” and “HILEV” restrict the output for the vertical level to layers 1 through 2. Thus, the

net effect of this command is to limit the IPR output to all cells within the first two vertical levels

of the modeling domain. 

Commands 2 and 3 are used to define families of species. The species names to the right of the

equal sign are model species. The effect of the numerical coefficients in the definition of the

VOC families is to convert the units of the IPRs for individual organics from ppm to ppmC. As

will be seen, these “defined” family names are referenced in subsequent commands. 

Commands 4 through 8 actually cause IPR outputs to be generated. As described above, IPRs

are generated for the species and the processes that are referenced by means of the codes listed

in Table 16-1. Since no process codes are specified in commands 4 and 5, IPRs will be generated
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for each of the twelve processes in Table 16-1 for the families NOX and VOC (i.e., a total of 24

IPRs). Command 6 causes three IPRs to be generated for species O3, one each for total

transport, chemistry, and clouds. Command 7 causes an IPR for vertical diffusion to be

generated for every model species. The last command signifies the end of the command inputs.

The CCTM will generate the IPR output data in a form comparable to the output concentration

files. Hence, the data are written to standard Models-3 IO/API gridded data files. The units of

the IPR data are normally the same as those for the species concentration data (i.e., ppm for gasphase species and either μg/m3

 or number/m3 for aerosols). As described in the example of

creating the family VOC with units of ppmC, however, different output units can be created

using special family definitions. 

The example just described was formulated primarily to illustrate how IPR commands are

structured to collect IPR information during a model simulation. In general, the particular data

that are collected for process analysis would be determined by the needs of the study, and thus it

is difficult to define a “default” process analysis. Nevertheless, a minimal process analysis for

studying ozone formation might involve collecting the process contributions for NOx, VOC, and

for ozone. The example in Exhibit 16-1 could be used as the starting point for such an analysis. 

Commands 4 and 5 capture all the IPRs for NOx and VOC. Command 6 could be modified to

capture all IPRs for ozone as well. Since it would not normally be necessary to capture vertical

diffusion IPRs for all species, command 7 could be dropped. Of course, the user would still be

required to define the domain for outputs (command 1) and to define the VOC family for the

mechanism that is being used (command 3). Thus, commands 1 through 5 with command 6

modified to collect all IPRs for ozone would provide some very basic process analysis

information on the formatio of ozone during a simulation.

16.2 Integrated Reaction Rate Analysis

The second major component of process analysis is IRR analysis. It is applied to investigate gasphase chemical transformations that are simulated in the model. Its primary use to date has been

to help explain how ambient ozone is formed in the chemical mechanisms that are used in

photochemical models (e.g., Jeffries and Tonnesen, 1994; Tonnesen and Jeffries, 1994). Thus,

the CMAQ implementation of IRR analysis currently addresses only gas-phase reactions. 

Nevertheless, the concepts should be adaptable to the modules simulating aerosol formation and

aqueous chemistry as well, and this is an area for future enhancement in the CCTM. The

remainder of this section describes how the IRRs are calculated and generated in the CMAQ

system.

16.2.1 Computation of Integrated Reaction Rates

As described in Chapter 8, the simulation of atmospheric chemistry is a key component of a

photochemical air quality model. The operator splitting techniques that are used in Eulerian

photochemical models typically result in a set of nonlinear, coupled, ordinary differential

equations (ODEs) that describe chemical interactions in the gas-phase. Solutions to these ODEs
EPA/600/R-99/030

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are obtained using numerical solvers to compute species concentrations as a function of time. 

Again, these computed concentrations show only the net effect of chemical transformations. As

has been done for physical processes, a technique has been developed to provide quantitative

information on individual chemical transformations (Jeffries and Tonnesen, 1994). Since the

technique involves integrating the rates of the individual chemical reaction, the method is termed

integrated reaction rate analysis.

As was noted in section 8.3.1, the mathematical expression for the rate of a chemical reaction

takes one of the forms of equation set 8-3. The reaction rate is used to compute the change in

species concentration that is caused by the reaction. Mathematically, this can be expressed as

follows:

Ml (tt) 
 Ml (t)  P

tt

t

rl dt , (16-6)

where Ml refers to the integrated reaction rate (IRR) for reaction l, t is the model

synchronization time step used by the chemical solver, and rl

 is the rate of reaction l

corresponding to one of the forms of equation set 8-3. The value of Ml

 represents the total

throughput of the reaction, and can be used with the appropriate stoichiometry to determine the

amount of an individual species that is produced or consumed by the reaction. For example,

assume the IRR for the reaction A + B  2C is 20 ppb for a given time period. Then, the amount

of A and B consumed in that time period by this reaction is 20 ppb, and correspondingly, the

amount of C produced is 40 ppb. Further, the net change in a species concentration due to all

chemical reactions is equivalent to the sum of all its production terms less the sum of all its loss

terms. As a consequence, the contribution of each reaction to the change in concentration of any

species is directly available from the IRRs. With this information, it is possible to identify the

important chemical pathways that affect species concentrations and thereby unravel the complex

chemical interactions that are being simulated. 

As described in Chapter 8-4, the chemistry solvers used in air quality models typically employ

marching methods that compute species concentrations at the end of a time step given the

concentrations at the beginning of the step. Since the solvers adjust the time steps to maintain

stability and accuracy, the reaction rates should not vary too greatly over a given time step. As a

consequence, it is possible to use a fairly simple numerical integration technique to compute the

IRRs. The technique used in the CCTM is the same the one used by Jeffries and Tonnesen

(1994) -- the trapezoid rule. With this method, the IRRs are computed as follows:

Ml (tt) 
 Ml (t)  1

2

[ rl

(t)  rl(tt)] . (16-7)

Thus, the IRRs are simply computed from the values of the reaction rates at the beginning and

the end of each chemistry integration time step. As the chemistry solver marches through time,

the variable Ml

 accumulates the IRRs over the simulation period. Although an IRR could be

accumulated for the entire simulation, more information can be gained on how the mechanistic

processes vary with time if the accumulated IRRs are periodically output and the value of Ml

 is

reset to zero. In the CCTM, the IRR output is synchronized with the outputs for the
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concentration fields and the integrated process rates. Thus, just like the IPRs, the IRRs that are

output represent the integral of the reaction rates over the output time interval.

16.2.2 Example IRR Analyses

Most IRR analysis performed to date has been devoted to studying mechanistic processes that

affect tropospheric ozone formation. One method that has been used involves analyzing two

important, interacting cycles: the OH radical cycle and the NOx oxidation cycle. This section

contains a brief discussion of these cycles and other important chemical parameters to illustrate

how integrated reaction rate analysis can be used to understand different chemical pathways. 

For more comprehensive discussions, the reader is referred to Jeffries (1995), Jeffries and

Tonnesen (1994), and Tonnesen and Jeffries (1994). 

Ozone is formed in the atmosphere via the photochemical cycle

NO2 + h  NO + O(3

P) (R1) 

O(3

P) + O2  O3 (R2)

NO + O3  NO2 . (R3)

If these were the only reactions taking place in the atmosphere, an equilibrium condition would

be established that would determine the ozone concentration. These levels are almost always

lower than what is observed in the atmosphere because of other interactions (Seinfeld, 1998). 

The presence of free radicals can alter the ozone production rate through the following reactions

that are competitive with R3:

 HO2 + NO  NO2 + OH (R4)

 RO2 + NO  NO2 + RO . (R5)

In these reactions, NO2 is produced in reactions that do not consume ozone, thereby introducing

a process by which ozone can accumulate. Furthermore, these reactions are radical propagation

reactions since a hydroxyl radical (OH) is produced from the hydroperoxy radical (HO2) and an

alkoxy radical (RO) is produced from an alkylperoxy radical (RO2). These product radicals are

then available to participate in other reactions, some of which lead to the regeneration of the

peroxy radicals. Thus, the production of ozone can be viewed as an autocatalytic process since

O3 can be produced without the loss of its precursor NO2. In the atmosphere, however, ozone

production is limited by termination reactions that remove either radicals or NO2 from the

system.

The ozone formation process has been represented by means of a schematic diagram, shown in

Figure 16-3a, that consists of two interacting cycles (Jeffries, 1995). The top portion of the

figure is the OH reaction cycle which consists of the three principal categories of reactions
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involving radicals: initiation, propagation, and termination. Radical initiation reactions are almost

always photolytic reactions that generate “new” radicals. Examples include the photolysis of

formaldehyde, hydrogen peroxide and ozone . Radical propagation reactions include reactions

such as R4 and R5 in which NO is converted to NO2 but no radicals are lost. Many reactions in

which organic compounds are oxidized also propagate radicals. The termination reactions

remove radicals through the formation of stable products. The bottom portion of Figure 16-3a

represents the NOx oxidation cycle. As with the radical cycle, processes in this cycle are

classified as either initiation, propagation, or termination. The initiation process for NOx

corresponds to emissions of NOx, and the termination process corresponds to reactions in which

NOx is converted to stable products. The NOx cycle is connected to the radical cycle by means

of the propagation steps that convert NO to NO2. 

One form of an IRR analysis that can be conducted involves using the IRRs to develop

quantitative information about the various initiation, propagation, and termination processes. 

Figure 16-3b shows a cycle diagram similar to Figure 16-3a in which the IRRs have been used to

compute the numerical values that are shown. These values include net throughput for several

parameters that serve to further characterize the state of the reacting system. For example, the

fraction of OH that is regenerated by the chemical reactions (0.776 in Figure 16-3b) can be

determined from the amount of OH that reacts (142.7 ppb) and the amount that is re-created

(110.8 ppb). This is directly related to the OH chain length parameter (4.46) which corresponds

to the average number of times each new OH is cycled until it is removed from the system. An

analogous chain length parameter (5.13) can be calculated for the NOx oxidation cycle in the

form of the NO chain length. The longer these chain lengths, the greater the potential for O3

formation per unit of NOx emissions. Other parameters such as the “NO oxidations per VOC

consumed” [(NONO2)/VOC = 1.71] and “O3 produced per O3

P generated by NO2 photolysis”

([O3]p/[O3

P] = 0.951) further quantify the relative efficiency of ozone production, the former

being particularly useful in providing a measure of the reactivity of the organic compounds. 

These types of analyses are particularly useful for comparing model results that are obtained

using different chemical mechanisms or that are obtained at different locations with the same

chemical mechanism. Other types of IRR analyses can provide other information as well. For

example, IRRs have been used to allocate the total production of O3 to the individual VOCs, to

examine individual characteristics of various chemical mechanisms such as yields of radicals

from different organics, and to quantify other entities such as the production and loss of oddoxygen (Ox), which can serve as surrogate for tracking the formation of ozone (Jeffries and

Tonnesen, 1994; Tonnesen and Jeffries, 1994). It can be expected that many other types of IRR

analyses will be developed, especially as newer and possibly more complex chemical

mechanisms are developed and used in models.

16.2.3 Implementation of IRR Analysis the CMAQ system 

As described in Chapter 8, the CMAQ system is designed to treat chemical mechanisms in a

generalized manner. Since a specific chemical mechanism is not embedded in the CCTM, a

comparable generalized method is needed to link IRR analysis with the chemical mechanism. 
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The technique that has been incorporated in the CMAQ system is one that provides the user with

the capability to formulate and then generate particular chemical parameters of interest. 

Presumably, these parameters would be chosen to reveal special properties of the mechanism

and/or to be used in generating photochemical cycle diagrams such as Figure 16-3b. To

illustrate, a special PACP command file has been prepared for the RADM2 mechanism. For

reference, a listing of the RADM2 mechanism is contained in Exhibit 16-2, and the reader is

referred to the Models-3 User Manual for a detailed explanation of the mechanism format. For

purposes of the discussion that follows, it is sufficient to note that reaction labels are enclosed in

“<” and “>” and precede each reaction, and that the reactants and products in each reaction are

model species. Both the reaction labels and the species names will be referenced in PACP

commands.

Table 16-2 lists the chemical parameters that are produced in this example IRR analysis for the

RADM2 mechanism. Most of these parameters could also be generated for other chemical

mechanisms, although the specific calculations that would have to be performed would

necessarily differ because of differences in the mechanisms. The parameters in Table 16-2 are

computed as simple, linear combinations of the IRRs that are calculated for each chemical

reaction. The domain controls that are specified for the integrated process rate outputs apply to

IRR outputs as well. Thus, both the IPR and IRR data will be generated for the same domain

and written to output files at the same time intervals. Similarly, the IRR output files are standard

Models-3 IO/API gridded files, and can be used with the standard Models-3 visualization tools. 

In addition, a special visualization tool that can generate “default” cycle diagrams similar to

Figure 16-3b is available and is described in Models-3 User Manual (EPA, 1998). Note,

however, that the IPR and IRR outputs are written to separate files.

One of the advantages of generating IRR data in the form of chemical parameters is that the

output file storage requirements can often be minimized. Note that there are fewer IRR

parameters in Table 16-2 than there are species in most mechanisms. The major disadvantage to

this approach is that new or different parameters cannot be computed without rerunning a model

simulation. As a consequence, the CMAQ implementation of IRR analysis also contains the

option to capture the complete set of IRRs rather than chemical parameters when a model is run. 

With this option, one IRR is generated for each chemical reaction, and these IRRs can then be

manipulated in postprocessing routines to form any particular chemical parameter of interest. 

Thus, it would be anticipated that the chemical parameters such as those in Table 16-2 would be

generated in fairly routine model applications, whereas IRRs for each reaction would be

generated for exploratory analyses. The form of the outputs is controlled by the PACP

commands that are described next.

16.2.4 Use of the PACP to set up an IRR Analysis

As with IPR analysis, the IRR outputs that are generated by the CCTM are controlled by

commands and special operators that are processed by the PACP. The global commands that

were described in the IPR section also apply to the IRR output. Thus, family names created with

the DEFINE FAMILY may also be used with several of the IRR commands and operators. 
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Before describing how the commands are used to construct an IRR analysis, a brief description

of each IRR command and operator is first presented. These are divided into three groups: IRR

global definitions, IRR operators and IRR output commands. Again, the same syntax

conventions are used, i.e., PACP keywords and symbols are in bold type, user supplied values

are in normal type, alternative inputs are separated by vertical bars, and completely optional

inputs are enclosed in braces.

IRR Global Definitions:

IRR_TYPE = FULL|PARTIAL|NONE;

The IRR_TYPE command defines the type of IRR analysis. With

the type set to FULL, IRRs for each reaction will be calculated and

written to the IRR output file, and all other IRR commands will be

ignored. IRR_TYPE set to PARTIAL indicates that the IRR

commands following this command are to be processed to

produced user defined IRR outputs. Type set to NONE causes all

other IRR commands to be ignored and no IRR output to be

generated. If the command is omitted, type PARTIAL is assumed. 

DEFINE CYCLE cyclename = species1;

The DEFINE CYCLE command is used to compute the net of all

chemical production and loss of a species involved in more than

one cyclical reaction set. Thus, this quantity is computed by

summing the IRRs for all reactions in which a species is consumed,

and then subtracting that sum from the sum of the IRRs for all

reactions in which the species is produced. The “cyclename” is a

user defined name that must be unique, and can be referenced in

subsequent IRR_OUTPUT commands.

DEFINE RXNSUM sumname = {±}{c1*}<rxlabl1> { ± {c2*} <rxlabl2> ± ...};

The RXSUM command is used to compute a linear combination of 

IRRs for individual reactions that can then be referenced in a

subsequent IRR_OUTPUT command; “sumname” is user defined

and must be unique. The linear combination of IRRs is defined

according to the expressions following the equal signs that specify

the reaction IRRs to sum. The “rxlabli

” is the reaction label that is

used by the generalized mechanism to identify each reaction and is

enclosed in “<” and “>”. The “ci

” are optional numerical

coefficients that default to one if not specified. 

IRR Output Operators:
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PROD[species1] {FROM[species2] {AND|OR [species3] }}

The production operator (PROD) is used to compute the total

production of a species by summing the IRRs of all reactions in

which species1 appears as a product. The optional qualifiers

FROM, AND, and OR restrict the sum to include only those

reactions in which species2 and/or species3 are reactants; “species1"

can be any gas-phase mechanism species or a family of gas-phase

species that was defined using the DEFINE FAMILY command as

described in the IPR section; “species2" or species3" may also be

the keyword HV to restrict the selection to photolytic reactions.

NETP[species1] {FROM[species2] {AND|OR [species3] }}

The net production operator (NETP) is very similar to the

production operator PROD since it is used to compute the

production of a species. Whereas the PROD operator includes

every reaction in which species occurs as a product, the NETP

operator includes only those reactions in which the net production

of species1 is greater than zero. Thus, if species1 appears as both a

reactant and a product with equal stoichiometry in a reaction, the

PROD operator will include it but the NETP operator will not. 

This operator is useful for getting the net production of a family,

for example, by eliminating those reactions in which the net effect

of the reaction on the family concentration is zero. The qualifiers

FROM, AND and OR restrict the inclusion of reactions to those in

which species2 and/or species3 are reactants.

LOSS[species1] {AND|OR [species2] }

The loss operator (LOSS) is used to compute the total loss of a

species by summing the IRRs of all reactions in which species1

appears as a reactant. The optional qualifier AND restricts the sum

to include only those reactions in which both species1 and species2

are reactants. Similarly, the OR qualifier includes all reactions in

which either “species1" or “species2" appears as a reactant. The

“species1" or “species2" can be any gas-phase species in the

mechanism, a family name that includes only gas-phase mechanism

species, or the keyword HV to restrict the selection of reactions to

those that are photolytic.

NETL[species1] {AND|OR [species2] }}
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The net loss operator (NETL) is very similar to the loss operator

since it is used to compute the loss of a species. However, it

includes only those reactions in which there is a net loss of

“species1" and/or “species2" . Thus, if species1 appears as both a

reactant and a product with equal stoichiometry in the reaction, the

NETL operator will not include it in summing the loss of that

species, whereas the LOSS operator will include the IRR for that

reaction. This operator is useful for getting the net loss of a family

of species.

NET[species1]

The net operator (NET) is very similar to the CYCLE definition

since it gives the net of the production and the loss of a species for

all reactions in which “species1" appears either as reactant or a

product; “species1" may be any gas-phase, mechanism species or

any family consisting wholly of gas-phase mechanism species.

IRR Output Commands:

IRR_OUTPUT irrname = {c1*}op1|cyclname{qual1}|sumname{qual1}|<rxlabl1>

 { ± {c2*}op2|cyclname{qual2}|sumname{qual2}|<rxlabl2> + ...}; 

The IRR_OUTPUT command defines a specific IRR output to be

generated during a CCTM simulation. It is constructed by

specifying a linear combination of IRR operators, IRR global

definitions, or IRRs for specified reactions. Each individual term

in the combination must include either one of the five IRR

operators just described (i.e., opi

), a cycle name, a reaction sum

name, or a reaction label enclosed in “greater than” and “less

than” signs. The optional qualifiers (quali

) for cyclename or

reaction sum name can be either POSONLY or NEGONLY. With

these qualifiers, the defined quantity is included as a term only

when it is positive or negative, respectively. If the name is not

qualified, the quantity is included regardless of sign. The

numerical coefficients for each term (ci

) are assumed to be one

unless they are explicitly included. The irrname that is supplied by

the user will be assigned as the variable name in the IO/API IRR

output file. 

DESCRIPTION = 'description';

The description command is provided to allow the user to specify a

long description of the output variable that will be included on the
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IO/API IRR output name. If a description is not specified for an

IRR_OUTPUT variable, the irrname (or short name) will be used in

the output file. If the description command is used, it should be

located immediately following the IRR_OUTPUT command to

which it applies.

Before describing how these commands are actually used, some additional comments are

warranted. First, the specification of any particular IRR output might be accomplished in several

different ways. For example, the net production of a species could be obtained using a CYCLE

definition, a RXNSUM definition, a NET operator, or simply specifying the appropriate sum of

IRRs directly in the IRR_OUTPUT command (i.e., via reaction labels). Although the user is free

to choose any particular approach, some computational efficiencies may be achieved by using

the CYCLE and RXNSUM definitions. The CCTM has been constructed to compute these

quantities just once, and then use them whenever they are referenced in an output command. 

Conversely, operator quantities are recomputed every time they are referenced. Thus, it is more

efficient to use the RXNSUM and CYCLE commands when they can be referenced several

different times in IRR_OUTPUT commands. Second, the NETP and NETL operators are

probably most useful for computing the production and loss of species families. When these

operators are used, a reaction is not included in the sum if there is no net loss or production of a

family member in the reaction. Thus, all reactions are eliminated from the computations when a

member of a family is formed from another member of the same family and there is no net

impact on the family concentration. Finally, the sign conventions employed in the CMAQ

process analysis need to be defined. IRRs for individual chemical reactions are always positive. 

Since IRRs can be subtracted when computing CYCLE, RXNSUM, and NET quantities, the

result can be either positive or negative. The production and loss operators always produce

positive values, however, since individual IRRs are always summed in their computation. 

To illustrate how these PACP commands are used to generate IRR output data, two examples are

presented. The first illustrates how to capture IRRs for each reaction. The second demonstrates

how PACP commands are used to compute the special chemical parameters in Table 16-2 for the

RADM2 chemical mechanism. 

Exhibit 16-3 contains the PACP commands for the first example that corresponds to a full IRR

analysis since IRRs will be calculated for each and every reaction. This option is invoked by the

first command that specifies that the IRR analysis type is FULL . Since no OUTPUT_DOMAIN

command is present, the IRR outputs will be generated for every cell in the modeling domain.

Exhibit 16-4 shows the PACP commands for the example IRR analysis that has been set up for

the RADM2 chemical mechanism. In a PACP command file, all lines that start with an

exclamation point (!) in the first column are comments. To facilitate the discussion below,

comment lines have been used to block the IRR commands into special groups. The first four

groups contain global commands or definitions. All blocks after the first four contain the IRR

commands that generate the particular parameters listed in Table 16-2. 
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The commands in the first group simply define the type of IRR analysis and the domain for

which the IRR outputs are to be generated. The second group includes family definitions. These

commands are of the same form as described for IPRs. The remaining two groups of commands

define chemical cycles and reaction sums that are subsequently referenced in IRR_OUTPUT

commands. As noted above, the cycle commands give the net production or loss of a species by

all chemical reactions. Several of the reaction sums that are defined here are also cycles in that

they generate the net effect of a few reactions on the production or loss of a few particular

species. Most of the others are used to define special quantities. For example, the defined

RXNSUM newMO2 in Exhibit 16-4 corresponds to the production of new MO2, where new

refers to an initiation reaction for the radical MO2. As is apparent from the IRR_OUTPUT

commands in the subsequent blocks, the cycle and reaction-sum names are referenced fairly

frequently. 

All of the remaining blocks of commands in Exhibit 16-4 contain the commands for IRR outputs. 

Again, one IRR output is generated for each IRR_OUTPUT command, and the outputs that are

produced correspond to the chemical parameters listed in Table 16-2. As indicated above, each

output is generated by the defined linear combination of predefined cycles, reaction sums, special

IRR operators, and/or specified reaction IRRs referenced by reaction label. It should be evident

that these commands are mechanism specific and require analysis of the mechanism itself to

formulate. Thus, this particular PACP command file would not be applicable to any mechanism

other than the RADM2. It should also be apparent that other important chemical parameters

could be formulated and generated in an analogous manner. In fact, this command file can be

used as the starting point for adding to or modifying some of the selected chemical parameters. 

As with IPR outputs, the CCTM will generate the IRR output data in a form comparable to the

output concentration files. That is, the data are contained in standard Models-3 IO/API gridded

data files. The IRR outputs are linear combinations of individual reaction throughput, and thus

have the same units as the gas-phase species concentrations (i.e., ppms). However, it should be

remembered that these are throughputs calculated by integrating reaction rates over the output

time interval, and not simply abundances at a particular time.

16.3 Conclusion

Process Analysis is a diagnostic method for evaluating the inner workings of a model. Although

specific types of techniques have been performed and used in the past, new ways of examining

and analyzing process data are likely to be developed and used in the future. As a consequence,

the emphasis in the CMAQ implementation of process analysis has been placed on providing

easy methods of extracting key process data from the CCTM simulations. The CMAQ

implementation also provides tools to allow users to customize their analyses. These tools are

designed to be easy to use and not require coding changes to the model.

As noted previously, a process analysis is set up by using the PACP before constructing and

running a CCTM simulation. Both IPR and IRR data can be gathered during a simulation, but

each are written to separate output files. To collect both sets of output during a single simulation
EPA/600/R-99/030

16-18

requires that the PACP command file contain both the IPR commands and the IRR commands. 

Although the IPR and IRR examples have been presented separately, both sets of outputs can be

produced with a single file containing both sets of commands. Recall, however, that the

OUTPUT_DOMAIN applies to both the IPR outputs and the IRR outputs. Thus, IPR and IRR

data cannot be generated for different parts of the domain in the same simulation. 

The PACP program performs a substantial amount of error checking. The program will check

for the proper syntax of the input commands and perform some logic checking. For example, it

checks to make sure that all species referenced in IRR commands are gas-phase mechanism

species and that the members of defined families are either all gas-phase species or all aerosol

species. As is apparent from Exhibit 16-4, however, the inputs for a comprehensive IRR analysis

can be fairly extensive. As a consequence, the PACP produces an output report that summarizes

what IRR and IPR outputs are being requested. One of its major functions is to report on the

effects of the special IRR operators that are used in the PACP command file. A user may wish

to review this report before proceeding to run the CCTM to insure that the desired outputs will

be generated. The reader is referred to the Models-3 User Manual (EPA, 1998) for an example

output report.

Finally, the default configuration for the CCTM is to omit process analysis outputs entirely. Thus,

no process analysis will be generated in this configuration. Any process analysis must be set up

in the Science Manager of the Models-3 framework. The reader is referred to the Models-3 User

Manual (EPA, 1998) for details on how this is done. 

16.4 References 

Jang, J. C., H. E. Jeffries, D. Byun, and J. E. Pleim, 1995a. “Sensitivity of Ozone to Model Grid

Resolution - I. Application of High-resolution Regional Acid Deposition Model”, Atmospheric

Environment, Volume 29, No. 21, 3085-3100.

Jang, J. C., H. E. Jeffries, and S. Tonnesen, 1995b. “Sensitivity of Ozone to Model Grid

Resolution - II. Detailed Process Analysis for Ozone Chemistry”, Atmospheric Environment,

Volume 29, No. 21, 3101-3114..

Jeffries, H. E., 1995. “Photochemical Air Pollution,” Chapter 9 in Composition, Chemistry, and

Climate of the Atmosphere, Ed. H. B. Singh, Van Nostand-Reinhold, New York, N.Y.

Jeffries, H.E., 1996. “Ozone Chemistry and Transport”, presentation to the FACA subcommittee

for Ozone, Particulate Matter and Regional Haze Implementation, March 21, Alexandria, Va. 

Jeffries, H. E. and S. Tonnesen, 1994. “A Comparison of Two Photochemical Reaction

Mechanisms Using Mass Balance and Process Analysis”, Atmospheric Environment, Volume 28,

No. 18, 2991-3003.
EPA/600/R-99/030

16-19

Pleim, J.E., 1990. Development and Application of New Modeling Techniques for Mesoscale

Atmospheric Chemistry, Ph.D. Thesis, State University of new York at Albany, Albany, New

York.

Seinfeld, J. H. and S. N. Pandis, 1998. Atmospheric Chemistry and Physics, From Air Pollution

to Climate Change, John Wiley and Sons, New York, New York.

Tonnesen, S. and H. E. Jeffries, 1994. “Inhibition of Odd Oxygen Production in the Carbon

Bond Four and Generic Reaction Set Mechanisms”, Atmospheric Environment, Volume 28, No.

7, 1339-1349.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
EPA/600/R-99/030

16-20

Table 16-1. 

 CCTM Processes and PACP Codes

PACP Code Process Description

XADV Advection in the E-W direction

YADV Advection in the N-S direction

ZADV Vertical advection

ADJC Mass adjustment for advection

HDIF Horizontal diffusion

VDIF Vertical diffusion

EMIS Emissions

DDEP Dry deposition

CHEMChemistry

AERO Aerosols

CLDS Cloud processes and aqueous chemistry

PING Plume-in-grid

 Note: The following process codes can also be used in the PACP. 

XYADV Sum of XADV and YADV

XYZADV Sum of XADV, YADV, and ZADV

TOTADV Sum of XADV, YADV, ZADV, and ADJC

TOTDIF Sum of HDIF and VDIF

TOTTRAN Sum of XADV, YADV, ZADV, ADJC, HDIF and VDIF
EPA/600/R-99/030

16-21

Table 16-2.

 Chemical Parameters Used in Default IRR Analysis

 {1} Production of Odd Oxygen (Ox)

 {2} Loss of Odd Oxygen (Ox)

 {3} Production of NOz from NOx

 {4} Production of NOx from NOz

 {5} Production of new OH from O1D

 {6} Production of new OH other than from O1D

 {7} Production of new HO2

 {8} Total production of HO2

 {9} Production of new RO2

 {10} Total Production of RO2

 {11} Loss of CO and CH4 by reaction with OH

 {12} Production of OH from HO2

 {13} Production of NO2 from HO2

 {14} Production of NO2 from RO2

 {15} Production of PAN and TPAN

 {16} Net Production of organic nitrates

 {17} Loss of VOCs by reaction with OH

 {18} Loss of OH by reaction with organics

 {19} Net Production or Loss of HNO3

 {20} Loss of HCHO by reaction with OH

 {21} Loss of isoprene by reaction with OH

 {22} Production of new HO2 from HCHO

 {23} Production of HO2 from PAN

 {24} Production of HO2 from RO2 and NO

 {25} Production of HO2 from RO2 reacting with RO2

 {26} Production of RO2 from OH

 {27} Production of HNO3 from NO2 reacting with OH

 {28} Production of new OH from H2O2

 {29} Production of new OH from organic peroxides

 {30} Production of OH from HONO

 {31} Termination of OH

 {31} Termination of HO2

 {31} Termination of HO2 by reaction with RO2

 {34} Termination of RO2

 {35} Termination of RO2 by reaction with HO2

 {36} Termination of RO2 by reaction with RO2

 {37} Loss of OH by reaction with daughter VOCs
EPA/600/R-99/030

16-22

Exhibit 16-1.

Example PACP Command File for IPR Analysis

{1} OUTPUT_DOMAIN = LOLEV[1] + HILEV[2];

{2} DEFINE FAMILY NOX = NO + NO2;

{3} DEFINE FAMILY VOC = 2.0*ETH + 2.9*HC3 + 4.8*HC5 + 7.9*HC8 

 + 2.0*OL2 + 3.8*OLT +

 4.8*OLI + 5.0*ISO + 7.1*TOL + 8.9*XYL

 + 1.0*HCHO + 2.4*ALD; 

{4} IPR_OUTPUT NOX;

{5} IPR_OUTPUT VOC;

{6} IPR_OUTPUT O3 = TOTTRAN + CHEM + CLDS;

{7} IPR_OUTPUT ALL = VDIF;

{8} ENDPA;
EPA/600/R-99/030

16-23

Exhibit 16-2. Listing of the RADM2 Chemical Mechanism

REACTIONS [cm] 

< P1> NO2 = O3P + NO # 1.0 /<NO2_RADM88>;

< P2> O3 = O1D # 1.0 /<O3O1D_RADM88>;

< P3> O3 = O3P # 1.0 /<O3O3P_RADM88>;

< P4> HONO = HO + NO # 1.0 /<HONO_RADM88>;

< P5> HNO3 = HO + NO2 # 1.0 /<HNO3_RADM88>;

< P6> HNO4 = HO2 + NO2 # 1.0 /<HNO4_RADM88>;

< P7> NO3 = NO # 1.0 /<NO3NO_RADM88>;

< P8> NO3 = NO2 + O3P # 1.0 /<NO3NO2_RADM88>;

< P9> H2O2 = 2.0* HO # 1.0 /<H2O2_RADM88>;

<P10> HCHO = CO # 1.0 /<HCHOmol_RADM88>;

<P11> HCHO = HO2 + HO2 + CO # 1.0 /<HCHOrad_RADM88>;

<P12> ALD = MO2 + HO2 + CO # 1.0 /<ALD_RADM88>;

<P13> OP1 = HCHO + HO2 + HO # 1.0 /<MHP_RADM88>;

<P14> OP2 = ALD + HO2 + HO # 1.0 /<HOP_RADM88>;

<P15> PAA = MO2 + HO # 1.0 /<PAA_RADM88>;

<P16> KET = ACO3 + ETHP # 1.0 /<KETONE_RADM88>;

<P17> GLY = 0.13*HCHO + 1.870*CO # 1.0 /<GLYform_RADM88>;

<P18> GLY = 0.45*HCHO + 1.550*CO + 0.800*HO2 # 1.0 /<GLYmol_RADM88>;

<P19> MGLY = ACO3 + HO2 + CO # 1.0 /<MGLY_RADM88>;

<P20> DCB = 0.98*HO2 + 0.020*ACO3 + TCO3 # 1.0 /<UDC_RADM88>;

<P21> ONIT = 0.20*ALD + 0.800*KET + HO2 + NO2 # 1.0 /<ORGNIT_RADM88>;

< 1> O3P + O2 + M = O3 # 6.0E-34^-2.3;

< 2> O3P + NO2 = NO # 6.5E-12 @ -120.0;

< 3> O1D + N2 = O3P # 1.8E-11 @ -110.0;

< 4> O1D + O2 = O3P # 3.2E-11 @ -70.0;

< 5> O1D + H2O = 2.0* HO # 2.20E-10;

< 6> O3 + NO = NO2 # 2.00E-12 @1400.0;

< 7> O3 + HO = HO2 # 1.60E-12 @ 940.0;

< 8> O3 + HO2 = HO # 1.10E-14 @ 500.0;

< 9> HO2 + NO = NO2 + HO # 3.70E-12 @ -240.0;

< 10> HO2 + NO2 = HNO4 # 1.8E-31^-3.2 &4.7E-12^-1.4;

< 11> HNO4 = HO2 + NO2 # 2.1E-27 @ -10900.0 *E< 10>;

< 12> HO2 + HO2 = H2O2 %3 # 2.20E-13@-620.0 & 1.90E-33@-980.0;

< 13> HO2 + HO2 + H2O = H2O2 %3 # 3.08E-34@-2820.0 & 2.66E-54@-3180.0;

< 14> H2O2 + HO = HO2 # 3.300E-12 @ 200.0;

< 15> NO + HO = HONO # 7.0E-31^-2.6 &1.5E-11^-0.5;

< 16> NO + NO + O2 = 2.0*NO2 # 3.300E-39 @ -530.0;

< 17> O3 + NO2 = NO3 # 1.4000E-13 @ 2500.0;

< 18> NO3 + NO = 2.0*NO2 # 1.7000E-11 @ -150.0;

< 19> NO3 + NO2 = NO + NO2 # 2.5000E-14 @ 1230.0;

< 20> NO3 + HO2 = HNO3 # 2.5000E-12;

< 21> NO3 + NO2 = N2O5 # 2.2E-30^-4.3 &1.5E-12^-0.5;

< 22> N2O5 = NO2 + NO3 # 1.10E-27 @ -11200.0 *E<21>;

< 23> N2O5 + H2O = 2.0*HNO3 # 2.00E-21;

< 24> HO + NO2 = HNO3 # 2.6E-30^-3.2 &2.4E-11^-1.3;

< 25> HO + HNO3 = NO3 %2 #7.2E-15@-785&4.1E-16@-1440&1.9E-33@-725;

< 26> HO + HNO4 = NO2 # 1.3000E-12 @ -380.0;

< 27> HO + HO2 = # 4.6000E-11 @ -230.0;

< 28> HO + SO2 = SULF + HO2 + SULAER # 3.0E-31^-3.3 &1.5E-12^0.0;

< 29> CO + HO = HO2 %1 #1.5000E-13;

< 30> HO = MO2 (X 300 SQUARED) # 28.3^2 @ 1280.0;

< 31> ETH + HO = ETHP (X 300 SQUARED) # 1.233E-12^2 @ 444.0;

< 32> HC3 + HO = 0.83*HC3P + 0.17*HO2 + 0.009*HCHO + 0.075*ALD

 + 0.025*KET # 1.59E-11 @ 540.0;

< 33> HC5 + HO = HC5P + 0.250*XO2 # 1.73E-11 @ 380.0;

< 34> HC8 + HO = HC8P + 0.750*XO2 + HC8AER # 3.64E-11 @ 380.0;

< 35> OL2 + HO = OL2P # 2.15E-12 @ -411.0;

< 36> OLT + HO = OLTP # 5.32E-12 @ -504.0;

< 37> OLI + HO = OLIP + OLIAER # 1.07E-11 @ -549.0;

< 38> TOL + HO = 0.75*TOLP + 0.250*CSL + 0.250*HO2

 + TOLAER # 2.10E-12 @ -322.0;

< 39> XYL + HO = 0.83*XYLP + 0.170*CSL + 0.170*HO2 

 + XYLAER # 1.89E-11 @ -116.0;

< 40> CSL + HO = 0.10*HO2 + 0.900*XO2 + 0.900*TCO3

 + CSLAER # 4.00E-11;

<40a> CSL + HO = CSL # 0.9*K<40>;

< 41> HCHO + HO = HO2 + CO # 9.0000E-12;

< 42> ALD + HO = ACO3 # 6.8700E-12 @ -256.0;

< 43> KET + HO = KETP # 1.2000E-11 @ 745.0;

< 44> GLY + HO = HO2 + 2.000*CO # 1.1500E-11;

< 45> MGLY + HO = ACO3 + CO # 1.7000E-11;

< 46> DCB + HO = TCO3 # 2.8E-11;
EPA/600/R-99/030

Exhibit 16-2. Listing of the RADM2 Chemical Mechanism

16-24

< 47> OP1 + HO = 0.5*MO2 + 0.500*HCHO +0.500*HO # 1.0000E-11;

< 48> OP2 + HO = 0.5*HC3P + 0.500*ALD + 0.500*HO # 1.0000E-11;

< 49> PAA + HO = ACO3 # 1.0000E-11;

< 50> PAN + HO = HCHO + NO3 + XO2 (x 300 sq) # 6.1650E-13^2 @ 444.0;

< 51> ONIT + HO = HC3P + NO2 # 1.5500E-11 @ 540.0;

< 52> ISO + HO = OLTP # 2.5500E-11 @ -409.0;

< 53> ACO3 + NO2 = PAN # 2.8000E-12 @ -181.0;

< 54> PAN = ACO3 + NO2 # 1.9500E+16 @ 13543.0;

< 55> TCO3 + NO2 = TPAN # 4.7000E-12;

< 56> TPAN = TCO3 + NO2 # 1.9500E+16 @ 13543.0;

< 57> MO2 + NO = HCHO + HO2 + NO2 # 4.2000E-12 @ -180.0;

< 58> HC3P + NO = 0.75*ALD + 0.25*KET + 0.09*HCHO + 0.036*ONIT

 + 0.964*NO2 + 0.964*HO2 # 4.2000E-12 @ -180.0;

< 60> HC5P + NO = 0.38*ALD + 0.69*KET + 0.08*ONIT

 + 0.92*NO2 + 0.92*HO2 # 4.2000E-12 @ -180.0;

< 62> HC8P + NO = 0.35*ALD + 1.06*KET + 0.04*HCHO

 + 0.24*ONIT + 0.76*NO2 + 0.76*HO2 # 4.2000E-12 @ -180.0;

< 64> OL2P + NO = 1.6*HCHO + HO2 + NO2 + 0.20*ALD # 4.2000E-12 @ -180.0;

< 65> OLTP + NO = ALD + HCHO + HO2 + NO2 # 4.2000E-12 @ -180.0;

< 66> OLIP + NO = HO2 + 1.45*ALD + 0.28*HCHO

 + 0.1*KET + NO2 # 4.2000E-12 @ -180.0;

< 67> ACO3 + NO = MO2 + NO2 # 4.2000E-12 @ -180.0;

< 68> TCO3 + NO = NO2 + 0.920*HO2 + 0.890*GLY + 0.110*MGLY

 + 0.050*ACO3 + 0.950*CO + 2.000*XO2

 # 4.2000E-12 @ -180.0;

< 69> TOLP + NO = NO2 + HO2 + 0.17*MGLY

 + 0.16*GLY + 0.70*DCB # 4.2000E-12 @ -180.0;

< 70> XYLP + NO = NO2 + HO2 + .45*MGLY + .806*DCB # 4.2000E-12 @ -180.0;

< 71> ETHP + NO = ALD + HO2 + NO2 # 4.2000E-12 @ -180.0;

< 72> KETP + NO = MGLY + NO2 + HO2 # 4.2000E-12 @ -180.0;

< 73> OLN + NO = HCHO + ALD + 2.0*NO2 # 4.2000E-12 @ -180.0;

< 74> HCHO + NO3 = HO2 + HNO3 + CO # 6.000E-13 @ 2058.0;

< 75> ALD + NO3 = ACO3 + HNO3 # 1.400E-12 @ 1900.0;

< 76> GLY + NO3 = HNO3 + HO2 + 2.000*CO # 6.000E-13 @ 2058.0;

< 77> MGLY + NO3 = HNO3 + ACO3 + CO # 1.400E-12 @ 1900.0;

< 78> DCB + NO3 = HNO3 + TCO3 # 1.400E-12 @ 1900.0;

< 79> CSL + NO3 = HNO3 + XNO2 + 0.500*CSL 

 + 0.500*CSLAER # 2.200E-11;

< 80> OL2 + NO3 = OLN # 2.000E-12 @ 2923.0;

< 81> OLT + NO3 = OLN # 1.000E-11 @ 1895.0;

< 82> OLI + NO3 = OLN + OLIAER # 3.230E-11 @ 975.0;

< 83> ISO + NO3 = OLN # 5.810E-13;

< 84> OL2 + O3 = HCHO + 0.400*ORA1 + 0.420*CO

 + 0.120*HO2 # 1.200E-14 @ 2633.0;

< 85> OLT + O3 = 0.53*HCHO + 0.500*ALD + 0.33*CO + 0.20*ORA1

 + 0.20*ORA2 + 0.23*HO2 + 0.22*MO2 + 0.10*HO

 # 1.3200E-14 @ 2105.0;

< 86> OLI + O3 = 0.18*HCHO + 0.72*ALD + 0.10*KET + 0.23*CO + 0.06*ORA1

 + 0.29*ORA2 + 0.26*HO2 + 0.14*HO + 0.31*MO2

 + OLIAER # 7.2900E-15 @ 1136.0;

< 87> ISO + O3 = 0.53*HCHO + 0.500*ALD + 0.33*CO + 0.20*ORA1

 + 0.20*ORA2 + 0.23*HO2 + 0.22*MO2 + 0.10*HO

 # 1.230E-14 @ 2013.0;

< 88> HO2 + MO2 = OP1 # 7.700E-14 @ -1300.0;

< 89> HO2 + ETHP = OP2 # 7.700E-14 @ -1300.0;

< 90> HO2 + HC3P = OP2 # 7.700E-14 @ -1300.0;

< 91> HO2 + HC5P = OP2 # 7.700E-14 @ -1300.0;

< 92> HO2 + HC8P = OP2 # 7.700E-14 @ -1300.0;

< 93> HO2 + OL2P = OP2 # 7.700E-14 @ -1300.0;

< 94> HO2 + OLTP = OP2 # 7.700E-14 @ -1300.0;

< 95> HO2 + OLIP = OP2 # 7.700E-14 @ -1300.0;

< 96> HO2 + KETP = OP2 # 7.700E-14 @ -1300.0;

< 97> HO2 + ACO3 = PAA # 7.700E-14 @ -1300.0;

< 98> HO2 + TOLP = OP2 # 7.700E-14 @ -1300.0;

< 99> HO2 + XYLP = OP2 # 7.700E-14 @ -1300.0;

<100> HO2 + TCO3 = OP2 # 7.700E-14 @ -1300.0;

<101> HO2 + OLN = ONIT # 7.700E-14 @ -1300.0;

<102> MO2 + MO2 = 1.5*HCHO + HO2 # 1.90E-13 @ -220.0;

<103> MO2 + ETHP = 0.75*HCHO + HO2 + 0.75*ALD # 1.40E-13 @ -220.0;

<104> MO2 + HC3P = 0.84*HCHO + 0.770*ALD + 0.260*KET

 + 1.000*HO2 # 4.20E-14 @ -220.0;

<105> MO2 + HC5P = 0.77*HCHO + 0.41*ALD + 0.75*KET

 + 1.000*HO2 # 3.40E-14 @ -220.0;

<106> MO2 + HC8P = 0.80*HCHO + 0.46*ALD + 1.39*KET
EPA/600/R-99/030

Exhibit 16-2. Listing of the RADM2 Chemical Mechanism

16-25

 + 1.000*HO2 # 2.90E-14 @ -220.0;

<107> MO2 + OL2P = 1.55*HCHO + 0.350*ALD + HO2 # 1.40E-13 @ -220.0;

<108> MO2 + OLTP = 1.25*HCHO + 0.750*ALD + HO2 # 1.40E-13 @ -220.0;

<109> MO2 + OLIP = 0.89*HCHO + 0.725*ALD + HO2

 + 0.55*KET # 1.70E-14 @ -220.0;

<110> MO2 + KETP = 0.75*HCHO + 0.750*MGLY + HO2 # 1.70E-14 @ -220.0;

<111> MO2 + ACO3 = HCHO + 0.5*HO2 + 0.5*MO2

 + 0.50*ORA2 # 9.60E-13 @ -220.0;

<112> MO2 + TOLP = HCHO + 0.17*MGLY + 0.16*GLY

 + 0.70*DCB + 2.0*HO2 # 1.70E-14 @ -220.0;

<113> MO2 + XYLP = HCHO + 0.45*MGLY + 0.806*DCB

 + 2.000*HO2 # 1.70E-14 @ -220.0;

<114> MO2 + TCO3 = .50*HCHO + 0.445*GLY + 0.055*MGLY

 + 0.50*ORA2 + 0.025*ACO3 + 0.460*HO2

 + 0.475*CO + XO2 # 9.60E-13 @ -220.0;

<138> MO2 + OLN = 1.75*HCHO + 0.50*HO2 + ALD + NO2 # 1.70E-14 @ -220.0;

<115> ETHP + ACO3 = ALD + 0.5*HO2 + 0.5*MO2

 + 0.5* ORA2 # 3.40E-13 @ -220.0;

<116> HC3P + ACO3 = .77*ALD + 0.26* KET + 0.5*HO2

 + 0.50*MO2 + 0.5*ORA2 # 1.00E-13 @ -220.0;

<117> HC5P + ACO3 = 0.41*ALD + 0.75*KET + 0.5*HO2

 + 0.50*MO2 + 0.5*ORA2 # 8.40E-14 @ -220.0;

<118> HC8P + ACO3 = 0.46*ALD + 1.39*KET + 0.5*HO2

 + 0.50*MO2 + 0.5*ORA2 # 7.20E-14 @ -220.0;

<119> OL2P + ACO3 = 0.80*HCHO + 0.6*ALD + 0.5*HO2

 + 0.5*MO2 + 0.5*ORA2 # 3.40E-13 @ -220.0;

<120> OLTP + ACO3 = ALD + 0.5*HCHO + 0.5*HO2

 + 0.5*MO2 + 0.5*ORA2 # 3.40E-13 @ -220.0;

<121> OLIP + ACO3 = 0.725*ALD + 0.55*KET + 0.14*HCHO

 + 0.5*HO2 + 0.50*MO2 + 0.5*ORA2 # 4.20E-14 @ -220.0;

<122> KETP + ACO3 = MGLY + 0.5*HO2 + 0.5*MO2

 + 0.5*ORA2 # 4.20E-14 @ -220.0;

<123> ACO3 + ACO3 = 2.0*MO2 # 1.19E-12 @ -220.0;

<124> ACO3 + TOLP = MO2 + 0.170*MGLY + 0.16*GLY

 + 0.70*DCB + HO2 # 4.20E-14 @ -220.0;

<125> ACO3 + XYLP = MO2 + 0.45*MGLY + 0.806*DCB

 + HO2 # 4.20E-14 @ -220.0;

<126> ACO3 + TCO3 = MO2 + 0.92*HO2 + 0.89*GLY

 + 0.11*MGLY + 0.05*ACO3 + 0.95*CO

 + 2.0*XO2 # 1.19E-12 @ -220.0;

<139> ACO3 + OLN = HCHO + ALD + 0.5*ORA2

 + NO2 + 0.5* MO2 # 4.20E-14 @ -220.0;

<140> OLN + OLN = 2.0*HCHO + 2.0*ALD + 2.0*NO2 # 3.60E-16 @ -220.0;

<127> XO2 + HO2 = OP2 # 7.70E-14 @ -1300.0;

<128> XO2 + MO2 = HCHO + HO2 # 1.70E-14 @ -220.0;

<129> XO2 + ACO3 = MO2 # 4.20E-14 @ -220.0;

<130> XO2 + XO2 = # 3.60E-16 @ -220.0;

<131> XO2 + NO = NO2 # 4.2000E-12 @ -180.0;

<132> XNO2 + NO2 = ONIT # 4.2000E-12 @ -180.0;

<133> XNO2 + HO2 = OP2 # 7.70E-14 @ -1300.0;

<134> XNO2 + MO2 = HCHO + HO2 # 1.70E-14 @ -220.0;

<135> XNO2 + ACO3 = MO2 # 4.20E-14 @ -220.0;

<136> XNO2 + XNO2 = # 3.60E-16 @ -220.0;

<AE1> TERP + HO = TERPAER + HO # 1.0*K<37>;

<AE1> TERP + NO3 = TERPAER + NO3 # 1.0*K<82>;

<AE1> TERP + O3 = TERPAER + O3 # 1.0*K<86>;

endmech
EPA/600/R-99/030

16-26

Exhibit 16-3. Example PACP Command File for a Full IRR Analysis

IRR_TYPE = FULL;

ENDPA;
EPA/600/R-99/030

16-27

Exhibit 16-4. Example PACP Commands for a Partial IRR Analysis

!***********************************************************************

! Example PACP Command File illustrating Partial IRR Analysis

!***********************************************************************

!=======================================================================

! IRR type and domain commands 

!=======================================================================

IRRTYPE = PARTIAL;

OUTPUT_DOMAIN = LOLEV[1] + HILEV[2];

!=======================================================================

! Family Definitions 

!=======================================================================

DEFINE FAMILY OX = O3 + NO2 + 2*NO3 + O3P +O1D + PAN + HNO4 + 3*N2O5 +

 TPAN + OLN + HNO3 + ONIT;

DEFINE FAMILY NOZ = PAN + TPAN + HONO + HNO4 + NO3 + N2O5 + ONIT + 

 OLN + HNO3;

DEFINE FAMILY NOX = NO + NO2;

DEFINE FAMILY VOCA = OL2 + OLI + OLT + ISO;

DEFINE FAMILY RO2 = MO2 + ETHP + HC3P + HC5P + HC8P + OL2P +

 OLTP + OLIP + TOLP + XYLP + ACO3 + KETP +

 TCO3 + XO2 + XNO2;

DEFINE FAMILY VOC = {CH4 +} CO + ETH + HC3 + HC5 + HC8 + OL2 + OLT + 

 OLI + ISO + TOL + CSL + XYL + HCHO + ALD + KET +

 GLY + MGLY + DCB;

DEFINE FAMILY dauHC = CSL + KET + GLY + MGLY + DCB + OP1 + OP2 +

 PAA + PAN + ONIT;

 

!=======================================================================

! Cycle Definitions 

!=======================================================================

DEFINE CYCLE PANcyc = PAN;

DEFINE CYCLE TPANcyc = TPAN;

DEFINE CYCLE HONOcyc = HONO;

DEFINE CYCLE HNO4cyc = HNO4;

!=======================================================================

! Reaction Sum Definitions 

!=======================================================================

DEFINE RXNSUM NO3cyc = < 17> - < P7> - < P8> - < 18> - < 19>;

DEFINE RXNSUM N2O5cyc = < 21> - < 22>;

DEFINE RXNSUM H2O2_OHcyc = < P9> - < 12> - < 13>;

DEFINE RXNSUM HNO3_OHcyc = < P5> - < 24>;

DEFINE RXNSUM OP1_OHcyc = <P13> - < 88>;

DEFINE RXNSUM OP2_OHcyc = <P14> - < 89> - < 90> - < 91> - < 92> -

 < 93> - < 94> - < 95> - < 96> - < 97> - 

 < 98> - < 99> - <100>{ - <101>}; 

DEFINE RXNSUM PAA_OHcyc = <P15> - < 97>;

DEFINE RXNSUM HNO4_HO2cyc = < P6> + < 11> - < 10>;

DEFINE RXNSUM OP2_HO2cyc = <P14> - < 89> - < 90> - < 91> - < 92> -

 < 93> - < 94> - < 95> - < 96> - < 97> - 

 < 98> - < 99> - <100> {- <101>} - <127> -

 <133>; 

DEFINE RXNSUM HOXcyc = < 7> - < 8>;

DEFINE RXNSUM newMO2 = <P12> + 0.22*< 85> + 0.31*< 86> + 0.22*< 87>;

DEFINE RXNSUM newACO3 = <P16> + <P19> + 0.02*<P20> + < 77>;

DEFINE RXNSUM newETHP = <P16>;

DEFINE RXNSUM newTCO3 = <P20> + < 78>;

DEFINE RXNSUM PAN_ACO3cyc = < 54> - < 53>;

DEFINE RXNSUM TPAN_TCO3cyc = < 56> - < 55>;

!DEFINE RXNSUM propRO2_NO = <67> + 4.05*<68> + 1.5*<126>;

!=======================================================================

! IRR_OUTPUT 1: OX Production 

!=======================================================================
EPA/600/R-99/030

Exhibit 16-4. Example PACP Commands for a Partial IRR Analysis

16-28

IRR_OUTPUT OXprod = NETP[OX];

DESCRIPTION = 'OX Production';

!=======================================================================

! IRR_OUTPUT 2: OX Loss 

!=======================================================================

IRR_OUTPUT OXloss = NETL[OX];

DESCRIPTION = 'OX Loss';

!=======================================================================

! IRR_OUTPUT 3: Production of NOZ from NOX 

!=======================================================================

IRR_OUTPUT NOZfromNOX = PANcyc[POSONLY] +

 TPANcyc[POSONLY] + 

 HONOcyc[POSONLY] +

 HNO4cyc[POSONLY] + 

 NO3cyc[POSONLY] +

 N2O5cyc[POSONLY] +

 < 24> + 0.036*< 58> + 0.08*< 60> +

 0.024*< 62> + <132>;

DESCRIPTION = 'NOZ produced from NOX';

!=======================================================================

! IRR_OUTPUT 4: Production of NOX from NOZ 

!=======================================================================

IRR_OUTPUT NOXfromNOZ = PANcyc[NEGONLY] +

 TPANcyc[NEGONLY] + 

 HONOcyc[NEGONLY] +

 HNO4cyc[NEGONLY] + 

 NO3cyc[NEGONLY] +

 N2O5cyc[NEGONLY] +

 < P5> + <P21> + < 51> +

 < 73> + <138> + <139> +

 2.0*<140>; 

DESCRIPTION = 'NOX produced from NOZ';

!=======================================================================

! IRR_OUTPUT 5: Production of new OH from O1D

!=======================================================================

IRR_OUTPUT OHfromO1D = PROD [HO] FROM [O1D];

DESCRIPTION = 'OH produced from O1D';

!=======================================================================

! IRR_OUTPUT 6: Production of new OH other than from O1D

!=======================================================================

IRR_OUTPUT newOH = 0.1*< 85> + 0.14*< 86> + 0.1*< 87> +

 2*H2O2_OHcyc[POSONLY] +

 HNO3_OHcyc[POSONLY] + 

 HONOcyc[NEGONLY] +

 OP1_OHcyc[POSONLY] + 

 OP2_OHcyc[POSONLY] + 

 PAA_OHcyc[POSONLY]; 

DESCRIPTION = 'new OH';

!=======================================================================

! IRR_OUTPUT 7: Production of new HO2

!=======================================================================

IRR_OUTPUT newHO2 = 2.0*<P11> + <P12> + 0.8*<P18> +

 <P19> + 0.98*<P20> + <P21> + 

 < 74> + < 76> + 0.12*< 84> +

 0.23*< 85> + 0.26*< 86> + 0.23*< 87> +
EPA/600/R-99/030

Exhibit 16-4. Example PACP Commands for a Partial IRR Analysis

16-29

 OP1_OHcyc[POSONLY] + 

 OP2_HO2cyc[POSONLY] + 

 HNO4_HO2cyc[POSONLY]; 

DESCRIPTION = 'new HO2';

!=======================================================================

! IRR_OUTPUT 8: Total Production of HO2

!=======================================================================

IRR_OUTPUT totalHO2 = 2.0*<P11> + <P12> + 0.8*<P18> +

 <P19> + 0.98*<P20> + <P21> + 

 < 74> + < 76> + 0.12*< 84> +

 {HO2new} 0.23*< 85> + 0.26*< 86> + 0.23*< 87> +

 OP1_OHcyc[POSONLY] + 

 OP2_HO2cyc[POSONLY] + 

 HNO4_HO2cyc[POSONLY] +

 

 {HO2propbyOH} PROD[HO2] FROM [HO] AND [VOC] +

 

 {HO2viaRO2_NO} PROD[HO2] FROM [NO] AND [RO2] +

 

 {HO2byRO2_RO2} PROD[HO2] FROM [RO2] AND [RO2] +

 

 {otherOH} HOXcyc[POSONLY];

 

DESCRIPTION = 'total HO2';

!=======================================================================

! IRR_OUTPUT 9: Production of new RO2

!=======================================================================

IRR_OUTPUT newRO2 = newMO2 + 

 newACO3 + 

 newETHP + 

 newTCO3 + 

 PAN_ACO3cyc[POSONLY] +

 TPAN_TCO3cyc[POSONLY]; 

DESCRIPTION = 'new RO2';

!=======================================================================

! IRR_OUTPUT 10: Total Production of RO2

!=======================================================================

IRR_OUTPUT TotalRO2 = newMO2 + 

 newACO3 + 

{newRO2} newETHP + 

 newTCO3 + 

 PAN_ACO3cyc[POSONLY] +

 TPAN_TCO3cyc[POSONLY] +

 

{propRO2_OH} PROD[RO2] FROM [HO] AND [VOC] + 

 < 30> + 0.5*< 47> + 0.5*<48> + 

 < 50> + < 51> + 

 

{propRO2_NO} PROD[RO2] FROM [NO];

DESCRIPTION = 'Total RO2';

!=======================================================================

! IRR_OUTPUT 11: Loss of CO & CH4 by reaction with OH

!=======================================================================

IRR_OUTPUT Loss_CO_CH4 = < 30> +

 LOSS [CO];

DESCRIPTION = 'Loss of CO & CH4';

!=======================================================================

! IRR_OUTPUT 12: Production of OH from HO2
EPA/600/R-99/030

Exhibit 16-4. Example PACP Commands for a Partial IRR Analysis

16-30

!=======================================================================

IRR_OUTPUT HO2toOH = HOXcyc[NEGONLY] + 

 <9> + 

 2.0*H2O2_OHcyc[POSONLY];

DESCRIPTION = 'HO2 to OH';

!=======================================================================

! IRR_OUTPUT 13: Production of NO2 from HO2

!=======================================================================

IRR_OUTPUT NO2fromHO2 = < 9>;

DESCRIPTION = 'NO2 FROM HO2';

!=======================================================================

! IRR_OUTPUT 14: Production of NO2 from RO2

!=======================================================================

IRR_OUTPUT NO2fromRO2 = < 57> + 0.964*< 58> + 0.92*< 60> +

 0.76*< 62> + < 64> + < 65> + 

 < 66> + < 67> + < 68> + 

 < 69> + < 70> + < 71> + 

 < 72> + < 73> + <131>;

DESCRIPTION = 'NO2 FROM HO2';

!=======================================================================

! IRR_OUTPUT 15: Production of PAN and TPAN

!=======================================================================

IRR_OUTPUT prodPAN_TPAN = PANcyc + TPANcyc;

DESCRIPTION = 'Production of PAN and TPAN';

!=======================================================================

! IRR_OUTPUT 16: Net Production of organic nitrates

!=======================================================================

IRR_OUTPUT netONIT = NET[ONIT];

DESCRIPTION = 'Net production of ONIT';

!=======================================================================

! IRR_OUTPUT 17: Loss of VOCs by reaction with OH

!=======================================================================

IRR_OUTPUT lossOH_HC = LOSS[VOC] AND [HO] +

 < 30> + < 47> + < 48> +

 < 49> + < 50> + < 51>;

DESCRIPTION = 'Loss of HC plus OH';

!=======================================================================

! IRR_OUTPUT 18: Loss of OH by reaction with inorganics

!=======================================================================

IRR_OUTPUT lossOH_INORG = < 7> + < 14> + < 15> + 

 < 24> + < 25> + < 26> + 

 < 27>;

DESCRIPTION = 'Loss of OH with iorganics';

!=======================================================================

! IRR_OUTPUT 19: Net production or loss of HNO3

!=======================================================================

IRR_OUTPUT netHNO3 = NET[HNO3];

DESCRIPTION = 'Net change in HNO3';
EPA/600/R-99/030

Exhibit 16-4. Example PACP Commands for a Partial IRR Analysis

16-31

!=======================================================================

! IRR_OUTPUT 20: Loss of HCHO by reaction with OH

!=======================================================================

IRR_OUTPUT lossHCHO_OH = LOSS[HCHO] AND [HO];

DESCRIPTION = 'Reaction OH HCHO with OH';

!=======================================================================

! IRR_OUTPUT 21: Loss of isoprene by reaction with OH

!=======================================================================

IRR_OUTPUT lossISO_OH = LOSS[ISO] AND [HO];

DESCRIPTION = 'Reaction of ISO with OH';

!=======================================================================

! IRR_OUTPUT 22: Production of new HO2 from HCHO

!=======================================================================

IRR_OUTPUT newHO2fromHCHO = PROD[HO2] FROM [HCHO] AND [hv];

DESCRIPTION = 'New HO2 from HCHO';

!=======================================================================

! IRR_OUTPUT 23: Production of HO2 from PAN

!=======================================================================

IRR_OUTPUT HO2fromPAN = PAN_ACO3cyc[POSONLY];

DESCRIPTION = 'HO2 from PAN';

!=======================================================================

! IRR_OUTPUT 24: Production of HO2 from RO2 and NO

!=======================================================================

IRR_OUTPUT HO2fromRO2_NO = PROD[HO2] FROM [NO] AND [RO2];

DESCRIPTION = 'HO2 from RO2 and NO';

!=======================================================================

! IRR_OUTPUT 25: Production of HO2 from RO2 and RO2

!=======================================================================

IRR_OUTPUT HO2fromRO2_RO2 = PROD[HO2] FROM [RO2] AND [RO2];

DESCRIPTION = 'HO2 from RO2 and RO2';

!=======================================================================

! IRR_OUTPUT 26: Production of RO2 from OH

!=======================================================================

IRR_OUTPUT RO2fromOH = PROD[RO2] FROM [HO];

DESCRIPTION = 'RO2 from OH';

!=======================================================================

! IRR_OUTPUT 27: Production of HNO3 from OH + NO2

!=======================================================================

IRR_OUTPUT HNO3fromOH_NO2 = < 24>;

DESCRIPTION = 'HNO3 from OH + NO2';

!=======================================================================

! IRR_OUTPUT 28: Production of new OH from H2O2

!=======================================================================

IRR_OUTPUT newOH_H2O2 = 2*H2O2_OHcyc[POSONLY];

DESCRIPTION = 'new OH from H2O2';
EPA/600/R-99/030

Exhibit 16-4. Example PACP Commands for a Partial IRR Analysis

16-32

!=======================================================================

! IRR_OUTPUT 29: Production of new OH from organic peroxides

!=======================================================================

IRR_OUTPUT newOH_OP1 = OP1_OHcyc[POSONLY] + 

 OP2_OHcyc[POSONLY] + 

 PAA_OHcyc[POSONLY];

DESCRIPTION = 'new OH from OP1 OP2 PAA';

!=======================================================================

! IRR_OUTPUT 30: Production of OH from HONO

!=======================================================================

IRR_OUTPUT newOHfromHONO = HONOcyc[NEGONLY];

DESCRIPTION = 'new OH from HONO';

!=======================================================================

! IRR_OUTPUT 31: OH Termination

!=======================================================================

IRR_OUTPUT OHterm = < 25> + <26> + <27> + < 50> + 

 HNO3_OHcyc[NEGONLY] +

 HONOcyc[POSONLY];

DESCRIPTION = 'OH Termination';

!=======================================================================

! IRR_OUTPUT 32: HO2 Termination

!=======================================================================

IRR_OUTPUT HO2term = < 20> + < 27> + <101> +

 2 * H2O2_OHcyc[NEGONLY] +

 HNO4_HO2cyc[NEGONLY];

DESCRIPTION = 'HO2 Termination';

!=======================================================================

! IRR_OUTPUT 33: Termination of HO2 by reaction with RO2

!=======================================================================

IRR_OUTPUT termHO2_RO2 = OP1_OHcyc[NEGONLY] + 

 OP2_HO2cyc[NEGONLY] + 

 PAA_OHcyc[NEGONLY];

DESCRIPTION = 'HO2 term with RO2';

!=======================================================================

! IRR_OUTPUT 34: RO2 Termination

!=======================================================================

IRR_OUTPUT termRO2 = .036*<58> + .08*<60> + .24*<62> + .03*<68> +

 PAN_ACO3cyc[NEGONLY] +

 TPANcyc[POSONLY];

DESCRIPTION = 'RO2 Termination';

!=======================================================================

! IRR_OUTPUT 35: Termination of RO2 by reaction with with HO2

!=======================================================================

IRR_OUTPUT termRO2_HO2 = OP1_OHcyc[NEGONLY] + 

 OP2_OHcyc[NEGONLY] + 

 PAA_OHcyc[NEGONLY];

DESCRIPTION = 'RO2 Termination with HO2';
EPA/600/R-99/030

Exhibit 16-4. Example PACP Commands for a Partial IRR Analysis

16-33

!=======================================================================

! IRR_OUTPUT 36: Termination of RO2 by reaction with RO2

!=======================================================================

IRR_OUTPUT termRO2_RO2 = <102> + <103> + <104> + <105> + <106> +

 <107> + <108> + <109> + <110> + <111> +

 1.515 * <114> + <115> + <116> + <117> +

 <118> + <119> + <120> + <121> + <122> +

 1.030 * <126> + 0.500 * <138> +

 0.500 * <139>;

DESCRIPTION = 'RO2 Termination with RO2';

!=======================================================================

! IRR_OUTPUTs 37: Loss of OH by reaction with daughter VOCs

!=======================================================================

IRR_OUTPUT dauHC_OH = LOSS [HO] AND [dauHC];

DESCRIPTION = 'OH + daughter HC';

ENDPA;
EPA/600/R-99/030

16-34

Figure 16-1. Example process analyses showing contributions of individual processes to model

predicted concentrations (Source: Jeffries, 1996).
EPA/600/R-99/030

16-35

Figure 16-2. Example Process Analyses showing model predicted concentrations and process

contributions for different model configurations (Source: Jeffries, 1996).
EPA/600/R-99/030

16-36

Figure 16-3a. Schematic of OH reaction with NO oxidation cycles (Source: Jeffries, 1996).

Figure 16-3b. Example photochemical cycle throughputs derived from integrated reaction rates

(Source: Jeffries, 1995).
EPA/600/R-99/030

*

On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Brian Eder, MD-80, Research Triangle Park, NC 27711. E-mail: eder@hpcc.epa.gov

**On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Chapter 17

AN AGGREGATION AND EPISODE SELECTION SCHEME 

DESIGNED TO SUPPORT MODELS-3 CMAQ

Richard D. Cohn

Analytical Sciences, Inc.

Durham, NC 27713

Brian K. Eder* and Sharon K. LeDuc**

Atmospheric Modeling Division

National Exposure Research Laboratory

Research Triangle Park, NC 27711

ABSTRACT

In support of studies mandated by the 1990 Clean Air Act Amendments, the Models-3 

Community Multiscale Air Quality (CMAQ) model can be used to estimate pollutant

concentrations and deposition associated with specified emission levels. Assessment studies

require CMAQ-based distributional estimates of ozone, acidic deposition, PM2.5, and visibility on

seasonal and annual time frames. Because it is not financially feasible to execute CMAQ over

such extended time periods, CMAQ must be executed for a finite number of episodes under a

variety of meteorological classes. A statistical procedure called aggregation, must then be

applied to the CMAQ outputs to derive seasonal and annual estimates. 

The objective of this research is to develop an aggregation approach and set of episodes that

would support model-based distributional estimates (over the continental domain) of air quality

parameters. The approach utilized cluster analysis and the 700 mb u and v wind field

components over the time period 1984-1992 to define homogeneous meteorological clusters. A

total of 20 clusters (five per season) were identified by the technique. A stratified sample of 40

events was selected from the clusters, using a systematic sampling technique. 

This stratified sample is then evaluated through a comparison of aggregated estimates of the

mean extinction coefficients (bext) to the actual mean bext observed at 201 stations nationwide for

a nine year period (1984-1992). The bext, a measure of visibility, was selected for use in the

evaluation for two reasons. First, of all of the air quality parameters simulated by CMAQ, this

visibility parameter provides one of the most spatially and temporally comprehensive data sets

available, and second, the bext can serve as a surrogate for PM2.5 for which little data exists. 

Results from the evaluation revealed a high level of agreement (r2

 = 0.988) indicating that the

aggregation and episode selection scheme was indeed representative.
EPA/600/R-99/030

17-1

17.0 AN AGGREGATION AND EPISODE SELECTION SCHEME DESIGNED TO

SUPPORT MODELS-3 CMAQ

17.1 Introduction

This chapter describes the development of an aggregation and episode selection scheme to

support the derivation of annual and seasonal estimates of air quality parameters in Models-3 

CMAQ. Relevant background information regarding this activity, as well as a precise statement

of the present objectives, is provided in this section. Section 17.2 summarizes the important

elements of the approach and the overall strategy, including the rationale behind the methods and

the limitations associated with them. Details of the development of an aggregation and episode

selection are provided in sections 17.3, 17.4, and 17.5. Section 17.6 contains an example

application and evaluation of the methodology using one particular air quality parameter (bext ),

and section 17.7 provides a summary and discussion.

17.1.1 Background

In support of studies mandated by the 1990 Clean Air Act Amendments, the Models-3 

Community Multiscale Air Quality (CMAQ) model is used by EPA Program Offices to estimate

deposition and air concentrations associated with specified levels of emissions. Assessment

studies and effects models require CMAQ-based distributional estimates (such as annual and

seasonal averages) of ozone, acidic deposition, and measures related to visibility. Such estimates

would ideally be obtained by using CMAQ to simulate atmospheric chemical processes

associated with meteorological conditions occurring on a daily basis over several years. 

However, for logistical and cost reasons it is not currently feasible to execute CMAQ over an

extended time period such as a full year. Therefore, in practice CMAQ must be executed for a

finite number of episodes or “events,” which are selected to represent a variety of

meteorological classes. A statistical procedure called aggregation, must then be applied to the

outputs from CMAQ to derive the required annual- and seasonal-average estimates from this

finite number of events. The objective of the research described in this chapter is to develop

such an aggregation approach and evaluate its effectiveness using the bext.

The basic problem of developing representative meteorological categories has been explored by

other researchers for a variety of purposes, including Fernau and Samson (1990a,b); Davis and

Kalkstein (1990); Eder et al. (1994). The approach used here is based on a variation of the

methods previously used by Brook et al. (1995a,b) in selecting a 30-event aggregation set for the

Regional Acid Deposition Model (RADM). The approach of Brook et al. involved four major

components. Cluster analysis of wind fields was used to determine meteorologically

representative categories. The determination of the number of clusters to retain was based upon

within-group variance patterns and prior work by Fernau and Samson (1990a,b). A procedure

for aggregating the episodic results into annual totals and averages involved frequency-weighted

sums and estimated deposition-precipitation relationships. Event selection procedures were

designed to emphasize categories that accounted for most of the annual wet sulfate deposition,
EPA/600/R-99/030

17-2

1. Determination of categories

• Used Ward’s (1963) method of cluster analysis, which minimizes within-cluster sums of squares, in an

agglomerative, hierarchical mode for wind flow parameters. Used eastern North American zonal u and

meridional v 85-kPa wind components for 0000 UTC with 5( spatial resolution (two variables at 48 grid

nodes over three days).

• Clustered “consecutive” 3-day periods from 1979, 1981, and 1983, with subsequent classification of

remaining “running” 3-day periods from 1979-1985 into one of these clusters.

2. Determination of number of clusters to retain

• Examined stepwise increases in within-group variance with decreasing number of clusters, expressed

through F-statistic.

• Retained 19 clusters based on results for wind flow, sulfate deposition, and prior work by Fernau and

Samson (1990a,b). Used quantitative information but somewhat subjective criteria.

3. Development of aggregation procedure

• Estimated total deposition for the group of sampled categories, from the sampled events (weighted sum,

accounting for the number of events sampled from each cluster and frequency of occurrence of the

clusters).

• Scaled up by ratio of total annual deposition to an estimate of annual deposition that is based on

aggregating the sampled categories. Estimates used either mean deposition from a sampled category or

deposition estimated from the deposition-precipitation relationship in the category.

4. Selection of “optimum” set of events

• Subdivided the 19 categories into wet and dry subsets, resulting in 38 new categories.

• Primarily represented categories that accounted for most of the annual wet sulfate deposition (at least

75% when combined). Selected 19 events from these categories. Also selected 11 events from winter

(5) and dry (6) events to represent seasonal deposition differences, dry periods, and possible nonlinear

effects.

• Number of events selected from each category was based on proportionality to the frequency of

occurrence of the category and the percent of total sulfate accounted for by the category.

• Examined 20 potential sets (each randomly generated) meeting all criteria, selected the one that

minimized RMSE for annual sulfate deposition (primarily) and precipitation (secondarily) at 13 sites. 

Selected sets in stages, first choosing a set of 19 events from the wet categories and then a set of 11

events from winter and dry periods.

while also representing some winter and dry events. A summary of some specific elements of

their approach is provided in Table 17-1.

Table 17-1 Summary of Methodology Used by Brook et al. (1995a; 1995b) for RADM

17.1.2 Objectives

The present objectives differ somewhat from those which motivated the earlier research. RADM 

was primarily designed to address issues involving acidic deposition. CMAQ addresses a more

diverse collection of air quality parameters with equal importance. In addition, CMAQ will be
EPA/600/R-99/030

17-3

applied to a continental domain that is significantly larger than geographic area for which

estimates are supplied by RADM. The extension from the RADM domain to a continental

domain is extremely ambitious as it relates to episode selection and aggregation. Therefore, the

development of an approach that accommodates this larger continental domain is particularly

challenging.

The objective of the activity described in this chapter is the development of an aggregation and

episode selection approach that supports model-based annual and seasonal air quality estimates

that are at least as accurate (with respect to sampling uncertainty) as those achieved by RADM,

in consideration of the more general applicability envisioned for CMAQ both with respect to air

quality parameters and geographic representation. This accuracy must be preserved while

minimizing any additional cost. In essence, “cost” refers to the number of events for which the

model provides estimates, each of which adds cost in the form of both computational processing

time and human labor.

17.2 Summary of the Approach

The analysis was carried out in phases, with information gathered in each phase contributing to

the design of the next. For this reason, this chapter is structured to present complete descriptions

of the methodology and results achieved in each phase, in sequence, in sections 17.3, 17.4, and

17.5. This section is intended as an overview of the process prior to those detailed descriptions. 

This overview consists of descriptions of some key elements of the methodology, the rationale,

scope, and limitations associated with the methodology, and the strategy used to move in phases

toward the final result.

17.2.1 Basic Elements of the Methodology

Simply stated, the methods that we have employed involve the determination of meteorologically

representative categories, the selection of events from those categories, and the use of evaluative

tools to ensure that the detailed aspects of those activities are defined in such a way as to achieve

optimal results, to the extent that we can measure optimality.

A specific goal is the definition of meteorological categories that account for a significant

proportion of the variability exhibited by the air quality characterizations of interest. The basic

approach used in the current analysis for the determination of categories and event selection

components is related to that of Brook et al. (1995a,b), but certain fundamental considerations

have been modified to reflect the differences inherent in the present objectives as described in

section 17.1. The common element is the cluster analysis of zonal u and meridional v wind

components to define meteorological categories.

The definition of meteorological categories is designed to support the selection of events from

those categories in a process known as stratified sampling (Cochran, 1977). Stratified sampling

exploits the internal homogeneity of the meteorological categories, or “strata,” to achieve more

precise estimates than would be possible using simple random sampling (i.e., randomly selecting
EPA/600/R-99/030

17-4

events without regard to meteorological category). Certain variations of stratified sampling are

relevant to this analysis. One relatively inefficient option for invoking stratified sampling would

involve selecting the same number of events from each category/stratum. This is known as

“equal allocation.” An alternative is “proportional allocation,” which involves selecting numbers

of events in direct proportion to the size of the stratum. Thus, more events are selected from

strata that contain large numbers of events than from smaller strata. This is potentially much

more efficient than equal allocation, in the sense that it leads to much more precise (i.e., lower

variance) estimates. Estimates exhibiting absolute maximum efficiency (i.e., minimum variance)

are obtained by modifying this method slightly so that the number of events selected from each

stratum is in direct proportion to the product of the size of the stratum times the internal

variability (as characterized by the standard deviation of the measurement of interest) within the

stratum. Thus, strata exhibiting significant variability among events are sampled more heavily

than strata in which events are more uniform. This is known as “optimum allocation,” which is

identical to proportional allocation when within-stratum variances are equal.

While wind flow parameters were used to define the meteorological categories, other

meteorological parameters were used in subsequent phases of the analysis to refine aspects of the

episode selection methodology, and as evaluative tools to assess the effectiveness of the

approach. These parameters include visibility (as represented by the bext), temperature, and

relative humidity. Their specific roles are discussed in more detail in the following sections.

17.2.2 Rationale, Scope, and Limitations

As stated previously, the approach to selecting an aggregation and episode scheme is based upon

the definition of meteorological categories that account for a significant proportion of the

variability exhibited by the air quality characterizations of interest. Strictly speaking these

characterizations include parameters such as acidic deposition, air concentrations, and measures

of visibility. Therefore, it might be argued that the definition of categories should be formulated

directly using these parameters that are ultimately of interest. However, it is equally important

that the model simulate the particular transport mechanisms involved in the associated

atmospheric processes, and in particular that source-attribution analyses be facilitated. This

requires that categories be defined with an emphasis on wind flow parameters. Indeed,

characterizations of basic wind field patterns in essence describe frontal passages, along with all

of the meteorological properties typically associated with them.

In view of the importance placed on the accurate simulation of transport mechanisms, a complete

evaluation of the episode selection and aggregation methodology would require an assessment of

the accuracy with which transport is represented. However, this accuracy cannot be measured,

as there is no technique available to support a direct, quantifiable assessment of the

representation of atmospheric transport. In addition, with the exception of bext, there are little air

quality data available with the required spatial and temporal resolution and range to support a

direct evaluation of the methods described in this chapter with regard to the outcome parameters

that will be of primary interest in CMAQ.
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For these reasons two meteorological parameters (in addition to bext), which are known to be

related to many of the air quality parameters of interest, and for which appropriately resolved

data are available, were used as evaluative measures in this analysis. Specifically, temperature

and relative humidity were used; however, primary emphasis will be placed upon the bext, which

provides a surrogate measure for fine particles. It must be recognized that this constitutes a

secondary evaluative tool, in the sense that the effectiveness of the approach cannot be directly

measured as it relates to atmospheric transport or to specific air quality parameters, both of

which are primary outcomes. For this reason, the methods were not developed and refined solely

toward the goal of optimizing performance associated with the estimation of visibility. Instead,

this performance was evaluated in combination with other considerations that were believed to

be important but for which performance may not be readily quantifiable.

17.2.3 Strategy

The basic strategy used for the selection of events to support aggregation-based estimation is

described in the steps outlined below. The term “cluster” describes a collection of events that

are defined to be meteorologically similar based upon cluster analysis results. The term

“stratum” describes a collection of meteorologically similar events to be used in stratified

sampling. In this chapter, “stratum” and “cluster” are essentially interchangeable since the

clusters defined in the analysis are ultimately used as the strata for sampling purposes.

1. We explored different approaches to the cluster analysis of wind components, each of

which resulted in the definition of a set of clusters (strata) of meteorologically similar

events, for possible use in alternative stratification schemes. Some alternatives that were

explored include annually defined clusters (i.e., strata defined using cluster analysis of

daily wind field data from several years, without regard to season), seasonally defined

clusters (i.e., strata defined using distinct cluster analyses of wind field data pertaining to

different seasons), and regionally defined clusters (i.e., strata defined using distinct cluster

analyses of wind field data for different geographic regions).

2. The alternative stratification schemes explored in step 1 were compared using relative

efficiencies and meteorological considerations. The concept of relative efficiency relates

to the variance associated with an estimate derived using different sampling schemes. 

We explored the variances associated with estimates of the annual means of the

evaluative meteorological parameters described above (visibility, temperature, relative

humidity). The relative efficiency of each stratification scheme is defined as the ratio of

the variance associated with simple random sampling to the variance associated with

stratified sampling using that scheme. A large relative efficiency is indicative of a high

degree of precision (lower variance) associated with the estimate of interest. As discussed

previously, since these evaluative meteorological parameters do not afford a complete,

direct assessment of the validity of process with regard to the parameters to which it is

ultimately to be applied, meteorological considerations were taken into account in

combination with the relative efficiencies in order to select a general stratification
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scheme. The selected scheme (seasonal stratification) was considered for more detailed

refinement in step 3.

3. We determined an appropriate number of clusters to retain in combination with an

acceptable number of events that would be necessary to achieve the objectives. The

determination was based on estimated standard deviations associated with several

alternative formulations, as well as other considerations. The standard deviations relate

specifically to estimates of the annual means and 90th percentiles of the evaluative

meteorological parameters. The “other considerations” included the objective of

matching or exceeding the performance of the current aggregation methodology used for

RADM, as well as a goal of avoiding unsampled clusters. Unsampled clusters (the

inclusion of clusters for which no events would be selected) were considered to be

undesirable because there would be no information available in the aggregation process to

account for events contained in such a cluster. In concept, our view was that any

unsampled cluster should be combined with another cluster to which it is most similar. In

practice, we achieved this by constraining ourselves to collections of clusters that were

adequate to support the sampling of at least one event from each cluster. Twenty clusters

were ultimately retained, consisting of five clusters defined in each of the four seasons,

and the number of events necessary to achieve the objectives was determined to be 40.

4. A stratified sample of 40 events was randomly selected from the 20 clusters defined in

step 3. Proportional allocation was used in determining the number of events to be

selected from each cluster (stratum). Optimum allocation was considered but was not

used for several reasons, including: (1) it requires the quantification of the variance of a

primary outcome parameter, whereas only secondary evaluative outcomes (visibility,

temperature, relative humidity) were available as discussed previously, and (2) the

variance of any outcome parameter varies geographically, so that optimum allocation

would likely result in differing numbers of events depending upon the geographic

location, whereas proportional allocation would not. It was verified that, at least based

upon the evaluative outcome parameters that are available, in most geographic locations

the distribution of events that arises from proportional allocation does not differ

substantially from that arising from optimum allocation.

Details concerning the implementation of this approach are discussed in the following sections. 

Sections 17.3 and 17.4 correspond to steps 1 and 2 in the strategy outlined above, and section

17.5 includes a discussion of steps 3 and 4.

17.3 Cluster Analysis of Wind Fields

The cluster analysis of wind components is described in this section. This includes a description

of the wind field data, the basic analysis technique, variations of the basic technique, and

methods of presentation. Some graphical results of exploratory analyses are also included.
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17.3.1 Description of Wind Data

To accommodate the continental domain and to achieve adequate spatial resolution, the cluster

analysis involves data at 336 grid nodes with 2.5( spatial resolution, as obtained from the

NCEP/NCAR 40-year reanalysis project (Kalnay et al., 1996). In this analysis, 700 mb wind

components for 1800 UTC have been used, in consideration of the mountainous western regions

in the domain. Corners of the grid were cut back to guard against excessive influence from

ocean-based meteorology. Graphical illustrations of this domain are referenced later in this

section.

17.3.2 Basic Cluster Analysis Technique

Cluster analysis, in the present formulation, involves the classification of a set of observations

into categories that are internally homogeneous with respect to defined multivariate relationships

in the data. In this case “multivariate” refers to the multiple variables used to characterize wind

fields, consisting of the u and v components applicable to each location within the previously

described domain and extending over an event that includes multiple days.

A 12-year period (1984-1995) was considered in the exploratory cluster analyses, later refined to

a 9-year period (1984-1992) for the final clustering upon which episode selection was based. 

Since CMAQ is actually run for a 5-day period for each event (the first two days establish initial

conditions, and model predictions from days 3-5 are saved as a “3-day event”), 5-day periods

were clustered rather than 3-day periods. To make the analysis computationally feasible, the

first, third, and fifth days of each 5-day event were considered. Based upon the performance

noted by Fernau and Samson (1990a,b), Ward’s method of cluster analysis was used (Ward,

1963), minimizing within-cluster sums of squares, in an agglomerative (i.e., moving from many

clusters toward fewer clusters), hierarchical (i.e., once clusters are joined they cannot be

separated) process. Thus, if a single observation (event) is considered to consist of 2,016

elements (the 2 u and v components × 336 grid nodes × 3 days considered per event), then the

objective of the cluster analysis is to divide these observations into clusters (categories) for which

the within-cluster sum of squares (sum of squared differences between the elements of individual

observations or means) is minimized.

In the exploratory analyses, clusters were initially defined based upon “consecutive” rather than

“running,” or overlapping 5-day periods from 1987-1992. Then, each remaining event

(“running” 5-day periods from 1984 through 1995) was classified into the cluster that minimizes

the sum (over the 336 grid nodes and three days) of the squared deviations of each u and v

component from the cluster mean u and v. In the final cluster analysis, using 1984-1992 data,

consecutive 5-day periods from 1984 through 1992 were clustered, and remaining events were

classified into those clusters according to the same criteria described above. Cluster analyses

were carried out using SAS (SAS Institute Inc., 1989); however, due to the extreme

computational burden of these analyses it was necessary to calculate the distance matrix

externally from the clustering procedure itself.
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17.3.3 Illustration of Cluster Analysis Results

Representative results from the selected exploratory analyses, as well as all results from the final

cluster formulation, are illustrated graphically. Specifically, cluster definitions are illustrated

using maps of cluster average wind fields. In some cases, these are supplemented with

specialized maps illustrating the intracluster variability in the wind fields. Star chart histograms

are also used to illustrate the frequency of occurrence of events from each cluster, for each

month of the year.

To provide proper perspective for a review of this analysis, it is useful to consider preliminary

results for a set of 30 clusters initially defined using annual data from 1984-1995. The most

prevalent cluster (labeled Cluster 1) accounted for 12.19% of all 5-day events during this time

period, with nearly all of those events occurring during the summer months. Map-based graphs

of mean wind vectors for this cluster are contained in Figure 17-1 (a-c). Three maps are

included, representing mean vectors for days 1, 3, and 5 of the 5-day event. These maps

illustrate largely stagnant conditions associated with an anticyclonic pattern centered over the

southeastern U.S.; a zonal flow over southern Canada and a trough over the west coast of the

U.S. 

As a second example, Figure 17-2(a-c) illustrates mean wind vectors for a somewhat less

prevalent cluster that accounted for 3.65% of all 5-day events during this time period (ranking

ninth in overall prevalence and labeled as Cluster 9). Most of these events occurred between the

months of October and April, characterized by northwesterly winds associated with a large-scale

trough moving through the central and eastern portion of the domain.

While these maps are effective in illustrating average behavior associated with each cluster, they

do not give any indication of the variability inherent in the clusters. Figures 17-4 (a-c) and 17-5

(a-c) contain additional maps that address this issue. The first map (Figure 17-3a) illustrates the

wind field for the third day of an individual event (January 23-27, 1989) that was assigned to

Cluster 9. Comparison of this map to the mean wind field for day 3 of Cluster 9 (Figure 17-2b)

reveals fairly close resemblance between the two. By contrast, the maps in Figures 17-3b and

17-4c depict the third day from two other events belonging to Cluster 9. These patterns do not

resemble the mean wind field as closely, and are indicative of the variability among individual

events that were assigned to this cluster.

Clearly it would be useful to simultaneously visualize the variability exhibited by all of the wind

fields assigned to each day of Cluster 9, and Figure 17-4 (a-c) represents an attempt to do this. 

These maps contain the mean wind vectors for each day of Cluster 9 on a thinned-out grid that

only includes alternating grid nodes. In addition, the maps contain groups of small dots, each of

which depicts the location of the wind vector arrowhead for an individual event assigned to this

cluster. The groups of dots collectively illustrate the distribution of arrowheads for all events

belonging to Cluster 9.
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The dots surrounding each mean wind vector arrowhead appear in a somewhat circular pattern,

and the extent of spread exhibited by the dots illustrates the degree of variability among wind

vectors assigned to the cluster. Similar patterns characterize the variability associated with other

clusters (not shown). Clearly there is substantial variability associated with the wind vectors

assigned to individual clusters. This variability emphasizes the ambitious nature of the endeavor. 

In essence, the goal is to categorize many years worth of meteorological patterns into a finite

number of classes. Furthermore, each meteorological pattern does not simply describe a single

location at a given point in time; it is required to simultaneously represent a broad spatial domain

over a significant temporal period. Indeed, it should not be surprising that a substantial amount

of variability is associated with the result.

Figure 17-5 (a-e) contains star chart histograms of the 30 clusters defined using annual data. 

Each chart illustrates the frequency of 5-day events belonging to a given cluster, and the clusters

themselves are ordered according to overall frequency of occurrence. As shown on the charts,

events from Cluster 1 accounted for 12.19% of all 5-day events between 1984 and 1995, those

from Cluster 2 accounted for 12.10% of all events, etc. The numbers arranged radially on each

chart depict the number of events belonging to the cluster from each month of the year. The

length of the line pointing to each month is proportional to this frequency of occurrence, and the

ends of the lines are connected to facilitate the visualization of patterns.

Several observations may be made based upon these charts:

• Although defined using annual data, the cluster frequencies reveal definite seasonal

tendencies. That is, clusters do not occur randomly throughout the year, but rather

exhibit a tendency to occur more frequently within specific seasons. Thus, the annual

clustering procedure successfully identifies and discriminates wind field patterns that are

associated with seasonally distinct meteorological classes.

• While clusters containing summer events tend to be quite distinct from those containing

winter events (and vice versa), many clusters contain events from a combined

“transitional” season that includes both spring and fall months.

• The two most prevalent clusters heavily emphasize the summer months; each of these

clusters includes more than twice as many events as any other cluster, with the vast

majority of summer events contained in them.

The disproportionate representation of summer events by two of the 30 clusters is not surprising,

since the wind fields are expected to be less variable in the summer. However, seasonal

differences in meteorology and atmospheric chemistry are important in explaining the variability

exhibited by the air quality parameters of interest. The addition of more warm season clusters

could provide improved resolution in this regard. This is the primary motivation for conducting

analyses using seasonally distinct clustering.
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17.4 Evaluation of Alternative Aggregation Approaches

The previous illustration clarifies the motivation for investigating seasonally distinct clustering. 

Similarly, regionally distinct clustering offers an alternative that might provide improved

resolution of wind field groupings on smaller spatial scales. An added dimension to the problem

is that the number of clusters to be retained clearly affects the degree of resolution. To gain an

understanding of the importance of these considerations as they relate to estimation of the

meteorological parameters used as evaluative tools in this analysis, these and other alternatives

were explored in several combinations. These explorations, designed to expose patterns and

trends from which to make an informed selection of a general approach, are described in this

section.

17.4.1 Description of Alternative Approaches

Several variations of the u and v wind vector clustering were investigated. As discussed

previously, these were selected to investigate patterns and properties, and not necessarily to be

considered as final candidates for cluster definitions. They are as follows:

• Annually defined strata with variations in the number of strata: 5, 10, 20, 30, 60, and 90

clusters;

• Seasonally defined strata using warm and cold seasons: totals of 10, 20, 30, and 60

clusters equally divided between the warm season April-September period and the cold

season October-March period;

• Seasonally defined strata approximately equally divided among summer (June, July,

August), winter (December, January, February), and transitional (spring and autumn

combined) seasons: totals of 20, 30, and 60 clusters;

• Seasonally defined strata equally divided between summer and winter seasons, and with

approximately twice as many strata defined for the transitional season: totals of 20 and 30

clusters;

• Seasonally defined strata approximately equally divided among summer, winter, spring

(March, April, May), and autumn (September, October, November) seasons: totals of 20

and 30 clusters; and

• Regionally defined strata: 30 clusters identified in each of four separate cluster analyses

for the northeast, southeast, northwest, and southwest subsets of the domain

We also investigated the alternatives of strata defined to simply mirror the four seasons

(disregarding all clusters), strata defined by clustering of 3-day events rather than 5-day events,

and strata defined by clustering the meteorological parameters used to evaluate the approach.
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17.4.2 Description of Meteorological Data

For the alternative stratification schemes, preliminary testing was performed by examining the

uncertainty associated with the use of cluster-based stratified sampling to estimate the annual

mean of daily noontime levels of visibility, temperature, and relative humidity, with primary

emphasis placed upon visibility as discussed previously. Visibility (units of km1

) was specifically

expressed as the light extinction (bext), less observations with precipitation, and less observations

with relative humidity greater than 90%. The light-extinction coefficient is often used to

characterize visibility, although in general, it has limited ability to predict human visibility. The

visual range vr (km) can be estimated from the bext by using the Koschmieder equation:

v (17-1) b r

ext

= 3 91 .

Temperature is in units of degrees Celsius, and relative humidity in percent. These parameters

were taken from 201 locations in the continental U.S. for which coverage was at least 99%, as

illustrated in Figure 17-6. This was specifically defined as sites exhibiting at least 99%

completeness for light extinction coefficient; allowances were made for missing observations that

were associated with precipitation so as not to bias the inclusion of sites toward drier climates.

17.4.3 Analysis Methods

The average relative efficiency associated with the estimation of mean annual visibility,

temperature, and relative humidity, using each alternative stratification scheme, was used for

comparison of the schemes. Specifically, at each location and for each scheme, the variance of

an aggregation-based estimate (Cochran, 1977) of the annual mean was determined in three

ways, assuming that the estimated mean was calculated using (1) a stratified sample with equal

allocation across strata, (2) a stratified sample with proportional allocation across strata, and (3)

simple random sampling, with a total sample size consisting of the same numbers of events in

each case. Also at each location, the ratio of the simple random sampling variance to the

variance associated with each of the two stratified sampling designs was calculated and

expressed as the relative efficiency of each of those designs. Finally, those relative efficiencies

were averaged across sites to provide an indication of the overall efficiency of each scheme.

This is best explained using a specific example. First, suppose that the mean annual temperature

at a given location is estimated as the average of the daily temperatures from 30 randomly

sampled 3-day events from the period 1984-1992, completely disregarding any information

related to clusters. Suppose that the standard deviation associated with that estimate is 1.5(C, so

that a 95% confidence interval would yield the estimated mean ±2.94(C (=1.96×1.5). Second,

suppose that the mean is instead estimated as a weighted average from 30 3-day events, using

two events per cluster (i.e., stratified sampling with equal allocation), and using the frequency of

occurrence of each cluster as the weight applied to the temperature from the corresponding

event. Suppose that the standard deviation associated with that estimate is 1.0(C, compared to
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1.5(C from simple random sampling. Last, suppose that 30 events are selected using

proportional allocation (i.e., the number of events selected from a cluster is proportional to the

number of events belonging to the cluster), and that the standard deviation of the resulting

estimated annual mean temperature is 0.8(C. These standard deviations (1.5, 1.0, and 0.8)

translate to variances of 2.25, 1.0, and 0.64 for simple random sampling, stratified sampling with

equal allocation, and stratified sampling with proportional allocation, respectively. Thus, for this

hypothetical location, the relative efficiency of stratified sampling with equal allocation is

2.25/1.0=2.25, and the relative efficiency of stratified sampling with proportional allocation is

2.25/0.64=3.52. Proportional allocation is more efficient than equal allocation in the sense that it

leads to lower variances and therefore tighter confidence intervals bounding the estimated mean.

17.4.4 Results

Tables 17-2 (a-b) and 17-3 present mean relative efficiencies associated with annual means of

the daily noontime temperature, relative humidity, and extinction coefficient, as estimated using

aggregation approaches based upon the various schemes described above. In each table, results

are presented to illustrate the relative efficiency of estimation methods using equal allocation

(equal numbers of events selected to represent each cluster) and proportional allocation

(numbers of events selected in direct proportion to the total number of events categorized into

the given cluster). Relative efficiencies reported in this section are valid for any number of

events that might be selected, as relative efficiency is invariant to sample size under equal or

proportional allocation

In the case of proportional allocation, the relative efficiency actually refers to the minimum

variance that might theoretically be achieved if proportional allocation were carried out

precisely. In practice this might only be possible if a very large number of events were to be

sampled, since the appropriate proportions might otherwise dictate sampling of fractional

numbers of events from some clusters. Therefore, the relative efficiency reported for

proportional allocation may be thought of as an upper limit to the relative efficiency that might

actually be achieved in practice. In all likelihood, this upper limit cannot be attained, but it

should be possible to achieve a relative efficiency occurring somewhere within the range defined

by this upper limit and the relative efficiency associated with equal allocation of events among

clusters.

The first six rows in Table 17-2a illustrate relative efficiencies associated with various numbers

of annually defined strata (i.e., clusters emerging from cluster analyses of daily wind field data

from 1984-1995 without regard to season). Several observations may be made by inspecting the

first six rows in Table 17-2a:

• The relative efficiency associated with the estimation of mean temperature is consistently

highest, followed by that of relative humidity. This implies that the meteorological

clusters are most useful in distinguishing between events with regard to temperature, and

least useful in distinguishing extinction coefficient.
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• In the case of temperature, the variability associated with stratified sampling using wind

field-based clusters is consistently less than the variability associated with simple random

sampling (i.e., relative efficiencies are uniformly greater than 1.0). Thus, in each scheme

the clusters contribute important information that explains variation in temperature.

• For the estimation of mean relative humidity and mean extinction coefficient, the use of

stratified sampling based upon wind field clusters is consistently more efficient than

simple random sampling if proportional allocation is approximately satisfied. In most

cases, the use of equal allocation actually results in less efficient estimation than simple

random sampling; this reflects a wide range of stratum sizes that would be inappropriately

represented using equal allocation.

• As would be expected, the efficiency associated with proportional allocation increases as

the number of strata increases, incorporating more refined representations of the

meteorological classes within the strata.

• The efficiency associated with equal allocation decreases as the number of strata

increases. The stratum sizes become more divergent when more strata are defined, so

that the inefficiency of equal allocation is magnified.

Based upon the well-known properties of stratified sampling discussed above, our objective was

to design and implement a scheme based upon approximate proportional allocation. The

numbers for equal allocation in these tables merely served to provide a lower bound on the

efficiency that could be realized, since it was known that the precise degree of efficiency

reported for proportional allocation might not be achievable in practice due to the requirement of

sampling integer-valued numbers of events.

As discussed in section 17.3.3 above in regard to the analysis illustrated in the “30 Strata” row of

the table, summer events are disproportionately represented by two of the 30 clusters. To

evaluate the effect of improving the resolution of summer meteorological patterns, as well as the

effects of imposing constraints that would alter the resolution of families of clusters under a

variety of scenarios, various implementations of seasonally distinct clustering were investigated. 

The last four rows of Table 17-2a illustrate results associated with stratum definitions based upon

a simple warm/cold seasonal dichotomy, in which separate cluster analyses were conducted to

force equal numbers of strata for each season. The following observations may be made based

upon this portion of the table:

• With the exception of extinction coefficient estimation under proportional allocation,

stratification using seasonally defined clusters consistently yields improved efficiency

over stratification using the same number of annually defined clusters. Thus, although the

annually defined clusters do adhere to a seasonal pattern, the improved resolution

afforded by the forced inclusion of more warm weather clusters (and reduction of cold

weather clusters) is particularly effective in explaining variation in temperature.
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• For seasonally defined clusters, the relative gains in efficiency associated with using equal

allocation are large as compared to the potential gains associated with using proportional

allocation. Thus, in departing from proportional allocation (which is not precisely

achievable in practice as discussed above), seasonally defined clusters are likely to afford

improved efficiency over annually defined clusters.

Results associated with further seasonal stratification schemes are illustrated in Table 17-2b. The

first two rows correspond to approximately equal numbers of clusters divided among summer,

winter, and transitional (spring and autumn combined) seasons, the next two rows correspond to

equal numbers of clusters divided between summer and winter with approximately twice as many

transitional season clusters, and the fifth and sixth rows correspond to approximately equal

numbers of clusters divided among four seasons. In each case, the exact distributions are

constrained to result in total numbers of strata that are directly comparable to the numbers of

strata investigated in other seasonal and annual analyses.

Under proportional allocation, stratification schemes based on three or four seasons offer

significantly improved efficiency in the estimation of mean temperature compared to two-season

and annual stratification schemes with comparable total numbers of strata. They also

demonstrate slight but uniform improvement in the estimation of extinction coefficient, and

mixed results in the estimation of relative humidity.
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Table 17-2a. Mean relative efficiency1 associated with estimation of the annual (1984-1995)

mean of the indicated parameter, using various stratified2

 sampling3 approaches relative to simple

random sampling. Continental analysis.

Method

Temperature Relative Humidity

RH-Adjusted Extinction

Coefficient

Equal

Allocation

Across

Strata

Proportional

Allocation

Equal

Allocation

Across

Strata

Proportional

Allocation

Equal

Allocation

Across

Strata

Proportional

Allocation

5 Strata 2.34 2.41 1.14 1.18 1.01 1.12

10 Strata 2.29 2.50 1.09 1.22 0.90 1.14

20 Strata 2.11 2.83 0.88 1.26 0.69 1.16

30 Strata 2.08 2.86 0.86 1.28 0.67 1.17

60 Strata 1.81 3.05 0.76 1.32 0.59 1.19

90 Strata 1.43 3.10 0.62 1.33 0.53 1.20

10 Strata Defined Seasonally (5 Warm, 5 Cold) 2.62 2.94 1.11 1.26 0.93 1.13

20 Strata Defined Seasonally (10 Warm, 10 Cold) 2.91 3.54 1.11 1.35 0.89 1.16

30 Strata Defined Seasonally (15 Warm, 15 Cold) 3.14 3.60 1.17 1.37 0.91 1.17

60 Strata Defined Seasonally (30 Warm, 30 Cold) 2.74 3.89 0.98 1.39 0.77 1.20

1 Relative efficiency is defined as the ratio of the variance associated with simple random sampling to the

variance associated with stratified sampling. The table entries are means of station-specific efficiency

ratios, averaged across stations within the continental domain. 2 Unless otherwise noted, stratum definitions are based on annual clustering of 5-day events from a

temporal subsample of the wind field data; the remainder of the sample is then classified into those

strata. 3

Reflects sampling of 3-day events from 1984-1995.
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Table 17-2b. Mean relative efficiency1 associated with estimation of the annual (1984-1995)

mean of the indicated parameter, using various stratified sampling2

 approaches relative to simple

random sampling. Continental analysis.

Method

Temperature Relative Humidity

RH-Adjusted Extinction

Coefficient

Equal

Allocation

Across

Strata

Proportional

Allocation

Equal

Allocation

Across

Strata

Proportional

Allocation

Equal

Allocation

Across

Strata

Proportional

Allocation

20 Strata Defined Seasonally (6 Summer, 6

Winter, 7 Transitional)

2.66 3.91 0.95 1.31 0.90 1.18

30 Strata Defined Seasonally (10 Summer, 10

Winter, 10 Transitional)

2.60 4.12 0.87 1.35 0.78 1.20

20 Strata Defined Seasonally (5 Summer, 5

Winter, 10 Transitional)

3.31 4.06 1.06 1.33 0.89 1.19

30 Strata Defined Seasonally (8 Summer, 8

Winter, 14 Transitional)

2.91 4.17 0.96 1.36 0.80 1.20

20 Strata Defined Seasonally (5 Summer, 5

Winter, 5 Spring, 5 Fall)

3.23 3.86 1.11 1.36 0.92 1.18

30 Strata Defined Seasonally (8 Summer, 8

Winter, 7 Spring, 7 Fall)

2.82 3.88 1.03 1.38 0.84 1.19

4 Strata Defined as

Seasons (Dec-Feb, etc.) 2.93 2.93 1.21 1.21 1.12 1.12

30 Strata Defined by

Clustering 3-Day Events

2.24 2.78 0.97 1.29 0.76 1.16

30 Strata; Seasonality

Removed from Met.

Parameters

0.92 1.28 0.74 1.15 0.63 1.09

30 Strata Defined by

Clustering Lt. Ext. Coeff. 0.51 1.89 0.30 1.11 0.57 1.45

1 Relative efficiency is defined as the ratio of the variance associated with simple random sampling to the

variance associated with stratified sampling. The table entries are means of station-specific efficiency

ratios, averaged across stations within the continental domain. 2 Reflects sampling of 3-day events from 1984-1995.
EPA/600/R-99/030

17-17

The final four rows of Table 17-2b address issues that are useful in that they provide additional

perspective for this analysis. They are discussed in sequence below:

• In view of the improvement associated with seasonal stratification schemes relative to

annual stratification, a natural question to ask is whether a seasonal scheme with one

stratum per season (i.e., no cluster analysis) is sufficient to support comparable

efficiency. Based upon the results in Table 17-2b, this method offers overall

improvement relative to an annual scheme with an approximately equal number of strata

(i.e., five strata as shown in the first row of Table 17-2a). As might be expected, it is

significantly less efficient than the use of 20 strata equally divided among four seasons,

but not dramatically so.

• Another natural question is whether the clustering of five-day events (using wind data

from the first, third, and fifth days) has a noticeable impact on this analysis relative to the

clustering of three-day events that previous investigators have pursued. Based upon

results in Table 17-2b, the definition of 30 strata using annual clustering of three-day

events produces similar results to those associated with 30 strata using five-day event

clustering (fourth row of 17-2a) with respect to the evaluative parameters. Note that this

does not necessarily address differences with respect to the characterization of transport.

• A consistent result in these analyses is that the relative efficiency associated with the

estimation of mean temperature is much greater than that associated with the estimation

of mean relative humidity, which in turn is slightly greater than the relative efficiency

associated with extinction coefficient. Since the preliminary results demonstrate

associations between the clusters and the seasons (even for annually defined clusters),

one might hypothesize that this characteristic is related to the more pronounced seasonal

trends associated with temperature and the less pronounced trends associated with

extinction coefficient. Table 17-2b illustrates relative efficiencies associated with the

three meteorological parameters following the removal of seasonal trends from each. 

(Trends were removed by analyzing deviations of each parameter from a sinusoidal curve

fitted to the raw data at each location.) Indeed, the relative efficiencies for the three

parameters are much more comparable in this context, and much more similar to the

results for extinction coefficient in other analyses. This analysis lends support to the use

of extinction coefficient as the primary evaluative outcome, because it reflects the ability

of each scheme to characterize short-term meteorological patterns apart from long-term

seasonal trends.

• A final investigation in Table 17-2b also relates to the utility of extinction coefficient as

the primary evaluative outcome. Under proportional allocation, the relative efficiencies

associated with it are not dramatically greater than 1.0, indicating that stratified sampling

based upon wind field clustering produces consistent but not dramatic gains in efficiency

(relative to simple random sampling) in the estimation of mean extinction coefficient. To

put this observation in its proper perspective, it is useful to consider the maximum relative

efficiency that might be achieved from any stratified analysis. In particular, a
EPA/600/R-99/030

17-18

stratification of events was performed based upon extinction coefficient itself (rather than

wind fields). Under these optimal conditions, the relative efficiency associated with a 30-

stratum scheme was still only 1.45, compared to a range of 1.17–1.20 for other 30-

stratum schemes based upon wind field clusters. Considered in this context, relative

efficiencies encountered in these tables are encouraging. (This clustering of extinction

coefficient provides some useful perspective regarding this evaluative outcome

parameter, but is not pursued as a recommended methodology for estimation based upon

the rationale outlined in section 2.2.)

To evaluate the utility of regionally distinct stratification schemes, the continental domain was

divided into four quadrants and cluster analyses were performed on wind fields within each

region, resulting in four sets of 30 annually defined strata. For each region, relative efficiencies

were summarized as in the previously described analyses. Since the mean relative efficiencies

are constrained to sites within each region, results in Table 17-2a are inappropriate for

comparison to these regional mean relative efficiencies. Therefore, Table 17-3 also includes

mean relative efficiencies only for the sites within each region, from comparable clustering of

continental data. These are displayed in combination with the results for strata defined using

regional data.

For example, using 30 strata under proportional allocation, clustering of wind fields in the

northeast quadrant of the domain results in a mean relative efficiency (averaged over sites in that

quadrant) of 1.65 associated with the estimation of mean temperature. For 30 strata, from

clusters defined over the entire continental domain, the mean relative efficiency, over those same

northeast sites is 3.14. The results in Table 17-3 collectively demonstrate that, under

proportional allocation, regional stratification produces either no gains or only slight gains in

efficiency in both the southeast and southwest regions for any of the evaluative parameters. In

the northeast and northwest regions, this technique is markedly less efficient than continental

clustering with regard to temperature, and somewhat less efficient with regard to relative

humidity. There is only a negligible effect on extinction coefficient.

This result has significant importance, because it demonstrates that in the northern half of the

domain, clustering of continental wind field data is actually more effective than clustering

regional data in explaining variation in some meteorological parameters on a regional scale. 

Thus, the wind field patterns associated with different levels of temperature (and, less markedly,

relative humidity) in a northern region are more distinctly identified on a continental scale than

on a regional scale. Furthermore, wind field patterns associated with different levels of

extinction coefficient (a primary evaluative parameter due to its close association with fine

particles) in a given region are no more distinctly identified on a regional scale than on a

continental scale.
EPA/600/R-99/030

17-19

Table 17-3. Mean relative efficiency1 associated with estimation of the annual (1984-1995)

mean of the indicated parameter, using various stratified sampling2

 approaches relative to simple

random sampling. Regional analysis.

Region/Method

Temperature Relative Humidity

RH-Adjusted Extinction

Coefficient

Equal

Allocation

Across

Strata

Proportional

Allocation

Equal

Allocation

Across

Strata

Proportional

Allocation

Equal

Allocation

Across

Strata

Proportional

Allocation

Northeast; 30 Strata Def.

Using Regional Data 1.41 1.65 0.98 1.15 0.95 1.27

Northeast; 30 Strata Def.

Using Continental Data 2.27 3.14 0.77 1.20 0.61 1.28

Southeast; 30 Strata Def.

Using Regional Data 2.35 2.72 1.04 1.32 0.77 1.22

Southeast; 30 Strata Def.

Using Continental Data 2.02 2.62 0.83 1.24 0.61 1.20

Southwest; 30 Strata Def.

Using Regional Data 1.95 2.42 0.94 1.26 0.81 1.01

Southwest; 30 Strata Def.

Using Continental Data 1.88 2.43 0.89 1.22 0.84 1.04

Northwest; 30 Strata Def.

Using Regional Data 1.17 1.66 0.92 1.27 0.82 1.08

Northwest; 30 Strata Def.

Using Continental Data 1.96 2.82 1.01 1.47 0.71 1.03

1 Relative efficiency is defined as the ratio of the variance associated with simple random sampling to the

variance associated with stratified sampling. The table entries are means of station-specific efficiency

ratios, averaged across stations within the continental domain. 2 Reflects sampling of 3-day events from 1984-1995.

In view of the current objective of matching or exceeding the performance of the current RADM

stratification scheme over the continental domain, it is appropriate to compare the relative

efficiency of the stratification scheme used in the aggregation of RADM output compared to the

relative efficiency of the schemes defined above. Table 17-4 addresses this specific issue. In

addition to the results associated with equal and proportional allocation, this table illustrates the

mean relative efficiencies associated with the actual allocation of the 30 RADM events, which

lies somewhere between those extremes. (Proportional allocation was not a specific goal of the

methods developed for RADM, although it is not inconsistent with the less formally stated goal

of selecting more events from the clusters that accounted for most of the acidic deposition.)
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17-20

Table 17-4. Mean relative efficiency1 associated with estimation of the annual (1982-1985)

mean of the indicated parameter, using various stratified sampling2

 approaches relative to simple

random sampling. RADM comparative analysis.

Method

Temperature Relative Humidity

RH-Adjusted Extinction

Coefficient

Equal

Alloc.

Proportional

Alloc.

Actual

Alloc. of

RADM

Events

Equal

Alloc.

Proportional

Alloc.

Actual

Alloc. of

RADM

Events

Equal

Alloc.

Proportional

Alloc.

Actual

Alloc. of

RADM

Events

19 Existing RADM Strata

Defined from Clustering

1979-83 3-Day Events

0.98 1.58 1.45 0.76 1.18 1.07 0.67 1.18 1.11

38 Existing RADM Strata

Defined After Separating

Wet & Dry Categories

0.83 1.76 1.12 0.59 1.19 0.88 0.49 1.17 0.92

4 Strata Defined as

Seasons (Dec-Feb, etc.) 3.06 3.05 2.77 1.13 1.13 1.02 1.17 1.18 1.11

1 The table entries are means of station-specific efficiency ratios, averaged across stations within the

RADM geographic domain. 2 Reflects sampling of 3-day events from 1982-1985.

In the RADM development, 19 strata were defined based upon clustering of 3-day events

occurring between 1979 and 1983. These were then subdivided into wet and dry categories,

ultimately resulting in twice as many (38) strata that are actually employed in aggregation-based

estimation. (Events from the 1982-1985 time period were classified into these strata, with 30

events selected for use in RADM.) The temporal and spatial domains applicable to the RADM

development differ from those of the current analysis; therefore, any comparisons should be

considered in this context.

The RADM domain approximately corresponds to the combined northeast and southeast regions

displayed in Table 17-3. A comparison of Table 17-4 to Table 17-3 results under proportional

allocation suggests superior performance associated with the strata identified using clustering of

continental wind field data, with respect to the outcome measures used here. When the actual

allocation of RADM events is considered, the superiority of proportional allocation associated

with the continental analysis is further elevated.

17.5 Refinement of the Sampling Approach

Based, in part, on the results discussed in section 17.4, a stratified sampling scheme involving

seasonal clustering based upon four distinct seasons was selected for further consideration and

refinement. The general superiority of three- and four-season stratification schemes was

discussed previously in relation to results depicted in Table 17-2 (a-b), and a four-season scheme

was selected following additional considerations regarding differences in emission patterns
EPA/600/R-99/030

17-21

between spring and autumn that would not be apparent using our evaluative parameters alone. 

Another benefit of using this type of scheme is that it naturally lends itself to the development of

seasonal estimates based upon four-season partitions. The derivation of such estimates from a

two- or three-season scheme would not be as well defined, and the estimates themselves would

likely be less precise.

Having selected this general approach, refinements were needed to determine an appropriate

number of strata, and to arrive at an adequate number of events for sampling. These

refinements, and a description of the sample of events that ultimately was selected, are discussed

in this section. This aspect of the analysis was limited to a refined time frame consisting of the

nine-year period from 1984-1992, which was targeted to ultimately represent baseline

meteorology for use in modeling.

17.5.1 Determination of Appropriate Numbers of Strata and Events

The analysis proceeded under the assumption that, in order to satisfy the goal of matching or

exceeding the performance of the RADM 30-event stratification scheme, a minimum of 30

events would be required in the framework of the continental domain. The precision associated

with the estimation of annual means of the evaluative parameters was investigated for a range of

30 to 60 events, and for 16, 20, 24, and 28 seasonally defined strata (4, 5, 6, and 7 strata per

season, respectively).

These numbers of strata were chosen as candidates because 19 wind field-based clusters were

defined in the RADM scheme, which offers a certain degree of resolution with regard to the

characterization of transport (which is not specifically addressed by the evaluative parameters

investigated here). The range of 16 to 28 strata was selected to provide comparable resolution of

wind fields and associated transport, noting that higher numbers of strata result in greater

variation in the sizes of those strata, and this would force a more pronounced deviation from the

goal of proportional allocation. As discussed previously, a primary goal was to ensure that every

stratum is sampled, i.e., that there are no clusters which go unrepresented in the final set of

events.

Note that we did not adhere to traditional rules of thumb regarding the determination of

appropriate numbers of clusters to retain. These rules are based upon an assumption that some

finite number of clusters is appropriate to represent the variability inherent in these patterns, and

that additional clusters beyond that point add relatively little information. In reality, clusters

defined during this process represent a continuum, and traditional F-test statistics illustrate this

continuum quite smoothly. There is no magic number of clusters after which the relative

importance of additional clusters drops noticeably. Indeed, as cluster analysis is used here

merely for the definition of strata and not as an end in itself, there is no compelling reason to be

restricted by existing conventions regarding determinations of an optimal number of clusters.

Standard deviations associated with estimation under all of the combinations described above are

illustrated in Table 17-5. Furthermore, the process was repeated after seasonal adjustment of
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17-22

each outcome parameter (seasonality was removed by analyzing deviations from a fitted

sinusoidal curve), to ensure that long-term seasonal trends do not unduly influence any pattern. 

The standard deviations in Table 17-5 provide an indication of the degree of precision associated

with estimation, and are influenced by the observed within-stratum variability of the parameter. 

One would expect the inclusion of more strata to facilitate greater precision, unless this increased

precision is offset by incurred deviations from proportional allocation.

Table 17-5. Standard deviation1

 associated with estimation of the annual mean of the indicated

parameter, using stratified sampling2

 with 16, 20, 24, or 28 strata and 30, 35, 40, 45, 50, 55, or 60

events. Continental analysis.

No. of

Events

Temperature, deg. C Relative Humidity, % RH-Adjusted Extinction

Coefficient, km-1 (×103)

16

Strata

20

Strata

24

Strata

28

Strata

16

Strata

20

Strata

24

Strata

28

Strata

16

Strata

20

Strata

24

Strata

28

Strata

NOT SEASONALLY ADJUSTED

30 0.97 0.98 0.95 0.95 2.38 2.40 2.38 2.40 6.69 6.73 6.73 6.77

35 0.89 0.89 0.87 0.87 2.19 2.20 2.20 2.21 6.03 6.08 6.10 6.23

40 0.83 0.83 0.81 0.81 2.04 2.05 2.06 2.05 5.71 5.63 5.70 5.71

45 0.79 0.77 0.76 0.75 1.93 1.92 1.93 1.93 5.38 5.34 5.33 5.36

50 0.74 0.74 0.72 0.72 1.82 1.83 1.82 1.82 5.09 5.06 5.07 5.08

55 0.71 0.70 0.69 0.68 1.74 1.74 1.73 1.73 4.78 4.79 4.83 4.83

60 0.67 0.67 0.66 0.65 1.66 1.66 1.65 1.65 4.62 4.62 4.60 4.60

SEASONALLY ADJUSTED

30 0.75 0.76 0.75 0.75 2.32 2.34 2.33 2.35 6.67 6.70 6.70 6.75

35 0.69 0.69 0.69 0.69 2.14 2.15 2.16 2.16 6.01 6.05 6.08 6.21

40 0.64 0.64 0.64 0.64 1.99 2.01 2.02 2.01 5.69 5.61 5.68 5.69

45 0.61 0.60 0.60 0.60 1.89 1.88 1.89 1.88 5.36 5.32 5.31 5.34

50 0.57 0.57 0.57 0.57 1.78 1.79 1.78 1.78 5.07 5.04 5.05 5.06

55 0.54 0.54 0.54 0.54 1.70 1.70 1.70 1.69 4.77 4.78 4.81 4.81

60 0.52 0.52 0.51 0.51 1.62 1.62 1.62 1.62 4.60 4.60 4.59 4.59

1 The table entries reflect the standard deviation associated with the average station-specific variances

(averaged across stations within the continental domain). 2 Results reflect sampling of 3-day events from 1984-1992.

For temperature and relative humidity, the table suggests that for any given number of events,

any effect associated with different numbers of strata is negligible. For extinction coefficient,
EPA/600/R-99/030

17-23

standard deviations for 30 and 35 event schemes increase slightly with increasing numbers of

strata. There is a minimum standard deviation associated with 20 strata for the 40-event scheme,

and only negligible effects across strata for greater numbers of events.

The objective of this determination was to develop a sufficiently large set of strata to provide

some resolution with regard to the characterization of transport, yet be sufficiently concise to

avoid any reduction in precision that would result from unsampled strata or from the inability to

approximately satisfy proportional allocation. In consideration of these criteria and the above

results, 20 strata were determined to constitute an appropriately sized set.

Figure 17-7 (a-c) provides perspective regarding the relative precision provided by sample sizes

of 25 or more events associated with estimation of annual means of the evaluative parameters,

based upon the use of 20 seasonally defined clusters as strata. The standard deviation displayed

in each graph is actually associated with the average of the variances across sites. These graphs

illustrate the advantage of stratified sampling with proportional allocation relative to simple

random sampling. They also illustrate the relative gains in precision (expressed as reduction in

standard deviation) that are realized as the number of events is increased. The star symbols

plotted on the graphs indicate the actual standard deviation that would be realized for selected

sample sizes under a 20-stratum scheme, with events distributed in accordance with proportional

allocation to the extent possible. The selected sample sizes were chosen based upon practical

limitations involving the number of events that might realistically be implemented. The stars do

not fall strictly on the proportional allocation curve because of limitations associated with the

sampling of integer-valued numbers of events.

These graphs indicate that, for temperature, it might be practical to achieve a standard deviation

in the range of 0.6–1.0oC, and that a much larger sample size would be needed to reduce the

standard deviation below 0.5oC. Similarly, standard deviations associated with estimates of mean

relative humidity can possibly be achieved in the range of 1.5–2.5%, and realistic standard

deviations associated with extinction coefficient might be in the range of 0.0045–0.0070 km1

. 

Geographic variability with respect to many of these results is described later in this section.

Although the estimation of mean levels of parameters is likely to be a primary point of emphasis

for many model-based results, the accurate estimation of extremes is also of significant

importance. This issue was specifically addressed by investigating the precision associated with

the estimation of the 90th percentiles of the evaluative parameters.

In contrast to the standard deviations associated with estimation of the mean, there is no closedform solution to determine the variability associated with the estimation of 90th percentiles. 

Therefore, a Monte Carlo-type resampling approach was utilized to estimate these standard

deviations. This specifically involved randomly selecting 200 artificial samples of actual data,

each consisting of the required number of events, from the 20 seasonally defined strata. From

each sample and at each site location, the 90th percentile of the parameter was estimated. The

variance of the resulting collection of 200 estimates was averaged across sites, and the associated
EPA/600/R-99/030

17-24

standard deviation served as an estimate of the precision associated with the particular sample

size. This exercise was repeated for sets of 30, 40, 50, and 60 events.

The graphs in Figure 17-8(a-c) illustrate the resulting standard deviations, along with the standard

deviations associated with estimation of the mean using the indicated number of events. As

would be expected, the standard deviations associated with estimation of the 90th percentile are

higher than those associated with estimation of the mean of each parameter. This difference is

most pronounced for extinction coefficient, with standard deviations for 90th percentile

estimation being approximately three times those for mean estimation. For relative humidity,

they are approximately twice as large. The difference is least pronounced for temperature,

where the increase is less then 20%. In each case, there is only slight, gradual improvement in

the precision of 90th percentile estimation for sample sizes of greater than 40 events.

The next step is to arrive at an appropriate number of events to be distributed among these 20

strata. Table 17-6 displays the standard deviation associated with the estimation of the annual

mean of each evaluative parameter (both raw and seasonally adjusted) that would result from

samples consisting of 30, 40, 50, and 60 events. For comparison purposes, these standard

deviations represent average variances restricted to the RADM geographic domain. The table

also displays the standard deviation associated with the aggregation of 30 3-day events in a

sample stratified using the original RADM clusters. From this, it is clear that any number of

events would be sufficient to provide improved resolution relative to the RADM scheme, in the

context of the evaluative parameters reviewed here.

Although these results suggest that a 30-event sample would be sufficient to meet the objective

of matching or exceeding the performance of the RADM approach with regard to estimation

precision for these outcome parameters, other results displayed in this section demonstrate clear

improvement in the precision associated with estimation of both means and extremes by moving

from a 30-event sample to a 40-event sample. In addition, a 40-event set is needed to ensure

equal precision to the RADM approach with regard to the estimation of wet deposition amounts. 

The RADM set of 30 events included 20 events from categories that were identified as “wet”,

i.e., for which average wet SO4

2

 deposition exceeded the median for each cluster. In other

words, 20 events were selected from the “wettest” 50% of all events.

This oversampling of wet events was originally pursued to ensure the adequate representation of

those events that contributed most significantly to wet deposition, because the accurate

characterization of wet deposition was the primary purpose of RADM at that time. However,

concerns have since arisen that the disproportionate representation of these events may have

introduced an overall bias with regard to the ambient concentrations of pollutants that are

influenced by cloud cover and precipitation. In view of these concerns, and since wet deposition

is not the primary focus for CMAQ, the oversampling of wet events was deemed inappropriate

for present purposes. In the absence of this oversampling, it is still necessary to include a

sufficient number of events to ensure that wet deposition is characterized as accurately here as in

the RADM approach. This would require approximately 20 wet events, and the same median-
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17-25

based definition of wet versus dry events implies that approximately 20 dry events should also be

included. Therefore, a total of 40 events was deemed necessary to satisfy all of the objectives.

Table 17-6. Standard deviation1 associated with estimation of the annual mean of the indicated

parameter, using stratified sampling2

 with 20 strata and 30, 40, 50, or 60 events. RADM

comparative analysis.

No.

of

Eve

nts

Temperature, deg. C Relative Humidity, % RH-Adjusted Extinction

Coefficient, km-1 (×103)

20 Strata

Existing

RADM

Sample

(30 Events)

20 Strata

Existing

RADM

Sample

(30 Events)

20 Strata

Existing

RADM

Sample

(30 Events)

NOT SEASONALLY ADJUSTED

30 0.96

1.78

2.34

2.58

6.65

8.28

40 0.82 2.01 5.60

50 0.73 1.79 5.01

60 0.66 1.63 4.59

SEASONALLY ADJUSTED

30 0.74

0.82

2.32

2.41

6.64

8.23

40 0.63 1.99 5.60

50 0.56 1.77 5.00

60 0.51 1.61 4.58

1 The table entries reflect the standard deviation associated with the average station-specific variances

(averaged across stations within the RADM geographic domain). 2 “Existing RADM Sample” results reflect sampling of 3-day events from 1982-1985. Other results reflect

sampling of 3-day events from 1984-1992.

Recalling that for 40 events the precision associated with the estimation of mean annual

extinction coefficient (the primary evaluative parameter) was optimized using 20 seasonally

defined strata (Table 17-5), a final plan was adopted for sampling 40 events from 20 strata (5

strata per season) using approximately proportional allocation.

Figure 17-9(a-d) displays star chart histograms of the 20 clusters defined as strata in this

arrangement. Each chart illustrates the frequency of occurrence of 5-day events belonging to a

given cluster, and the clusters themselves are ordered according to overall frequency of

occurrence. The numbers arranged radially on each chart depict the number of events belonging

to the cluster from each month of the year. Map-based graphs of mean wind vectors for day 3 of

each cluster are contained in Figures 17-10 through 17-29. 
EPA/600/R-99/030

17-26

In order to examine the impact of this scheme geographically (in the context of the precision

associated with the estimation of mean levels of the evaluative parameters), we examined

graphically (not shown), the standard deviation at each site location alongside the actual mean

with which that standard deviation is associated. Similarly, analogous information associated

with the estimation of 90th percentiles were examined. This examination confirmed the relative

geographic uniformity with respect to the standard deviations, which serves as support for the

use of “average” standard deviations in drawing conclusions throughout this section.

17.5.2 Selection of Stratified Sample of Events

A stratified sample of events was randomly selected from the 20 seasonally defined strata for the

period 1984-1992. The sample was selected without replacement to ensure that no single day

was selected into more than one five-day event, i.e., that there was no overlap between selected

events. Systematic sampling (Cochran, 1977) was used within each stratum for which more than

one event was to be selected. Specifically, all events assigned to the stratum were ordered

chronologically, an event was selected near the beginning of that ordering, and subsequent events

were selected to be evenly spaced throughout the remainder of the ordering. If k events were to

be sampled from a cluster containing n events, to illustrate the simple case in which n/k is integer

valued, the first event would be randomly selected from any of the chronologically first n/k

events, and every (n/k)th subsequent event would be selected. The purpose of this approach was

to ensure appropriate representation over the entire nine-year period.

Table 17-7 displays the total number of events belonging to each stratum, the number of events

sampled, and the dates of the sampled events. These dates are the middle dates of the three-day

events for which the model ultimately is to be run (i.e., the last three days of the sampled fiveday event). This sample of 40 events includes representation from every month of the year, and

from every year during the period 1984-1992. Table 17-8 illustrates this representation by

displaying the number of events selected from each month and from each year.
EPA/600/R-99/030

17-27

Table 17-7. Stratum sizes, number of sampled events per stratum, and dates of events in sample.

Dates shown are for middle day of 3-day event.

Stratum Season

Total # of

Days in

Stratum,

1984-1992

Number

of

Sampled

Events Event Dates

1 Spring 292 3 12 March 1985, 08 May 1987, 27 March 1990

2 Summer 267 3 17 July 1985, 20 August 1987, 10 August 1990

3 Autumn 238 3 08 September 1986, 12 October 1988, 08 October 1991

4 Winter 210 3 04 January 1986, 15 December 1988, 02 December 1992

5 Spring 200 2 07 May 1984, 06 March 1990

6 Winter 188 2 03 January 1987, 07 January 1992

7 Spring 185 2 01 April 1986, 26 March 1991

8 Summer 171 2 05 August 1986, 29 June 1992

9 Summer 171 2 07 August 1984, 12 July 1989

10 Winter 170 2 18 January 1984, 25 January 1989

11 Autumn 168 2 18 October 1985, 12 September 1991

12 Autumn 150 2 17 November 1987, 14 September 1992

13 Winter 139 2 19 February 1985, 27 January 1990

14 Autumn 135 2 17 October 1988, 24 November 1991

15 Summer 129 2 03 July 1987, 09 July 1992

16 Autumn 128 2 25 November 1985, 07 November 1990

17 Winter 102 1 18 December 1989

18 Summer 90 1 22 July 1989

19 Spring 89 1 09 May 1990

20 Spring 62 1 30 April 1991
EPA/600/R-99/030

17-28

Table 17-8. Number of sampled events representing each month of the year and each year from

the period 1984-1992.

Month Number of Events in

Sample Year Number of Events inSample

January 6 1984 3

February 1

1985 5

March 4

1986 4 April 2

May 3 1987 5

June 1

1988 3

July 5

1989 4 August 4

September 3 1990 6

October 4

1991 5

November 4

December 3 1992 5

17.6 Application and Evaluation

In this section, examples of the aggregation calculation for annual mean concentrations and total

wet depositions, applicable to this sample of events, are provided. Following this example is a

description of an evaluation exercise in which the aggregation calculation was carried out for

light extinction coefficient, and the aggregated estimates were compared to the actual values

based on data from all of the days in the period.

17.6.1 Application of the Aggregation Procedure

Aggregation calculations will be applied to model-based depositions and concentrations obtained

for each sampled event, to achieve unbiased estimates for annual and seasonal means and other

summary statistics within each grid cell. Since the goal of sampling from every defined stratum is

achieved in this approach, these calculations are simplified in comparison to earlier aggregation

methods (NAPAP, 1991). In essence, these aggregation calculations merely produce weighted

means, totals, or other summary measures, from the sample of events.

To illustrate the aggregation approach, consider the estimation of a mean annual air

concentration using model output for the 40 events selected above. These events represent 20

strata; denote these using the subscript i, i=1,2, . . . , 20. Let fi denote the frequency of
EPA/600/R-99/030

17-29

C ̄

MODELi

Mean Air Concentration 





20

i
1

fiC ̄

MODELi




20

i
 1

fi

. (17-2)

D ̄

MODELi

, P ̄

MODELi

, PMEASi

Total Wet Deposition 
 


20

i
1

D ̄

MODELi

P ̄

MODELi

× PMEASi×

1

3×9 . (17-3)

occurrence associated with stratum i, i.e., the total number of 3-day events belonging to the

stratum during the period 1984-1992. For an individual grid cell, also let

represent the mean model-based concentration associated with all sampled events from stratum i. 

Thus, for strata with a single sampled event, it is just the event mean concentration in the grid

cell. For strata with two or three sampled events, it is the mean concentration for all of those

events. Then the estimated annual mean air concentration is given by

Estimates for most other parameters (e.g., dry depositions) and other summary statistics are

calculated using similar methods. The calculation for wet deposition is different, primarily

because the weighting is partially dictated by precipitation. Let

represent the mean 3-day modeled deposition for sampled events in stratum i, the mean 3-day

modeled precipitation for sampled events in stratum i, and the total measured precipitation

accounted for by all events belonging to stratum i, respectively. Then the estimated total annual

wet deposition is given by 

This expression can be thought of as a weighted sum in which the model-estimated wet

concentration for a stratum is weighted by the total measured precipitation associated with the

stratum. The final component of this expression is included to reflect the fact that each day is

counted three times in the calculated sum (due to the use of 3-day events) and that the strata are

defined over a nine-year period.
EPA/600/R-99/030

17-30

17.6.2 Evaluation

In order to determine the effectiveness of the aggregation technique and subsequent episode

selection, comparisons were made between the observed mean bexts for the period 1984-1992 and

the aggregated estimates of that mean using the stratified sample of events described in 17.5.2

and listed in Table 17-7. This preliminary evaluation, which includes simple regression analysis,

is similar to that performed on RADM (Eder and LeDuc, 1996; Eder et al.,1996). 

Results comparing the observed and aggregated mean bexts (based on Equation 17-2) are

promising as seen in the scatterplot provide in Figure 17-30. The correlation between the 201

observed and aggregated mean bext was very high correlation (r2

 = 0.988). Estimates of the

regression coefficients between the observed and aggregated mean bexts reveal an intercept value

of -0.0012 that is not significantly different from zero ( = 0.05). The slope (1.018), however; is

significantly different from 1.0, ( = 0.05) indicating a slight tendency for these particular

episodes to provide an over-estimate of the expected mean bext. This slight, “apparent” bias is,

however, well within the expected variability associated with the particular set of episodes in this

stratified sample. To wit, selection of a different random set of episodes would just as likely

result in a slight under-estimate of the expected mean bext.

Perhaps a better way to illustrate the effectiveness of this technique can be shown through an

examination of the percent deviation in aggregate estimates of the mean bext (where the

deviations are relative to the observed mean (aggregated bext - observed bext / bext observed). 

These percent deviations, which were calculated over the period 1984 -1992, are presented in

Figure 17-31. For the most part, the deviations are within ± 10%, indicating excellent agreement

between the actual mean bext and the aggregated estimates of the mean bext.

The slight over prediction tendency mentioned above appears to be somewhat spatially biased as

also seen in Figure 17-31. As seen in the top of the figure, areas of generally positive deviations

(aggregation approach yields a higher bext, hence lower visibilities than observed) appear to

concentrate from east Texas into the southeastern states and again in the upper midwest between

Minnesota and the Dakotas. The states of California and Idaho also exhibit positive deviations. 

Negative deviations, presented in the bottom of the Figure 17-31, tend to predominate from the

northeast states into the Great Lake States and southwestward toward the states of Kansas, New

Mexico and Arizona. This spatial dependence of the estimates is, once again, well within the

expected variability. Selection of a different random set of episodes would likely result in a

different pattern of positive and negative deviations, as there is a natural tendency for sites at

close proximity to behave in a similar fashion.

The scatter plot in Figure 17-30 also reveals an increase in variance about the regression line

starting at an observed mean bext of 0.085. Unlike the positive bias, discussed above, this

increase in variance does not appear to be spatially biased, but rather exhibits a random

distribution across the domain. This is represented in Figure 17-31 by the scattering of the larger

biases (i.e. biases > 5.0%) evenly across the domain.
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17-31

17.7 Summary and Discussion

The objective of this research was to develop a new aggregation approach and set of events to

support model-based distributional estimates of air quality parameters (acidic deposition, air

concentrations, and measures related to visibility) over the continental domain. The basic

approach is to define meteorological categories that account for a significant proportion of the

variability exhibited by these air quality parameters, as well as the particular transport

mechanisms involved, so that source-attribution analyses are facilitated. This requires that

categories be defined with an emphasis on wind flow parameters. To this end, the cluster

analysis of zonal u and meridional v wind field components has been used to determine

meteorologically representative categories.

The research described in this chapter was carried out in three phases:

• Phase 1: Various stratification schemes were evaluated and compared on different

temporal and geographic scales to support the selection of a preferred general

methodology. The selected methodology involved clustering of wind field data over the

continental domain within each of the four seasons, and defining strata to be equivalent to

the resulting clusters. This methodology demonstrated superior relative efficiency

compared to methods defined on an annual time frame or on a regional scale for estimates

involving the evaluative meteorological parameters, and is designed to support seasonal

estimation with both simplicity and precision.

• Phase 2: Determinations were made regarding appropriate numbers of clusters and events

to support sampling using the general methodology selected in Phase 1. The resulting

scheme involved a total of 20 clusters (5 per season), and 40 events, defined over the

time period 1984-1992. This scheme affords superior precision to previous approaches

for estimates involving the evaluative meteorological parameters, supports approximately

equivalent representation of wet events to those approaches without oversampling, and

provides adequate resolution of wind field patterns that characterize transport.

• Phase 3: A stratified sample of events was selected under approximate proportional

allocation, using systematic sampling within strata, in accordance with the scheme

determined in Phase 2. This sample was successfully evaluated through a comparison of

aggregated estimates of the mean bext to the actual mean bext, revealing a high level of

agreement, although there was a slight tendency of the aggregation and episode selection

technique to over-estimate the expected mean bext. 

The goal of this research was to categorize many years worth of meteorological patterns into a

few classes. This represents a very ambitious goal, and it should not be surprising that there is

substantial variability associated with the wind vectors assigned to individual clusters. 

Nevertheless, the results described above suggest that the approach achieves a reasonable

characterization of frontal passage scenarios and leads to clusters that explain variation in the

evaluative meteorological parameters used in this analysis (temperature, relative humidity, and
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17-32

visibility), and therefore can be used to achieve improved estimates of these parameters relative

to estimates obtained from simple random sampling. Moreover, the constrained definition of

distinct seasonally-based clusters brings further improvement to the ability of the clusters to

explain the variation in these parameters, and therefore leads to more precise estimates

associated with them. The evaluative parameters were selected for their known associations with

many air quality parameters of interest, thus suggesting that the clusters should also be effective

in defining strata from which events can be selected to estimate those air quality parameters.

17.8 References

Brook, J.R., P.J. Samson, and S. Sillman, 1995a. Aggregation of selected three-day periods to

estimate annual and seasonal wet deposition totals for sulfate, nitrate, and acidity. Part I: A

synoptic and chemical climatology for eastern North America. Journal of Applied Meteorology,

34, 297-325.

Brook, J.R., P.J. Samson, and S. Sillman, 1995b. Aggregation of selected three-day periods to

estimate annual and seasonal wet deposition totals for sulfate, nitrate, and acidity. Part II:

Selection of events, deposition totals, and source-receptor relationships. Journal of Applied

Meteorology , 34, 326-339.

Cochran, W.G., 1977. Sampling Techniques. Wiley & Sons, New York.

Davis, R.E. and L.S. Kalkstein, 1990. Development of an automated spatial synoptic

climatological classification. International Journal of Climatology, 10, 769-794.

Eder, B. K., J. M. Davis and P. Bloomfield, 1994. An automated classification scheme designed

to better elucidate the dependence of ozone on meteorology. Journal of Applied Meteorology,

33, 1182-1199.

Eder, B. K., S.K. LeDuc and F. Vestal, 1996. Aggregation of selected RADM simulations to

estimate annual ambient air concentrations of fine particulate matter. Ninth Joint Conference on

Applications of Air pollution Meteorology with the A&WMA, Jan.28-Feb. 2, Atlanta, GA.

Eder, B. K. and S.K. LeDuc, 1996. Can selected RADM simulations be aggregated to estimate

annual concentrations of fine particulate matter? Proceedings of the International Specialty

Conference on the Measurement of Toxic and Related Air Pollutants, May 7 - 9, Research

Triangle Park, NC.

Fernau, M.E. and P.J. Samson, 1990a. Use of cluster analysis to define periods of similar

meteorology and precipitation chemistry in eastern North America. Part I: Transport patterns.

Journal of Applied Meteorology, 29, 735-750.
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Fernau, M.E. and P.J. Samson, 1990b. Use of cluster analysis to define periods of similar

meteorology and precipitation chemistry in eastern North America. Part II: Precipitation patterns

and pollutant deposition. Journal of Applied Meteorology, 29, 751-761.

Kalnay, E., M. Kanamitsu, R. Kistler, W. Collins, D. Deaven, L. Gandin, M. Iredell, S. Saha, G.

White, J. Woollen, Y. Zhu, M. Chelliah, W. Ebisuzaki, W. Higgins, J. Janowiak, K. Mo, C.

Ropelewski, J. Wang, A. Leetmaa, R. Reynolds, R. Jenne and D. Joseph, 1996. The

NCEP/NCAR 40-year reanalysis project. Bull. Amer. Meteor. Soc., 77, 437-471.

NAPAP, 1991. National Acid Precipitation Assessment Program 1990 Integrated Assessment

Report, National Acid Precipitation Assessment Program, 722 Jackson Place NW, Washington,

D.C.

SAS Institute Inc., 1989. SAS/STAT® User’s Guide, Version 6, Fourth Edition, Volume 1. SAS

Institute Inc., Cary, NC.

Ward, J.H., 1963. Hierarchical grouping to optimize an objective function. Journal of the

American Statistical Association 58, 236-244.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.
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Fig.17.1 (a) Mean wind vectors for day 1 of annually defined cluster

1 (of 30).
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17-35

Fig.17.1 (b) Mean wind vectors for day 3 of annually defined cluster

1 (of 30).

Fig.17.1 (c) Mean wind vectors for day 5 of annually defined cluster

1 (of 30).
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Fig.17.2 (a) Mean wind vectors for day 1 of annually defined cluster

9 (of 30).

Fig.17.2 (b) Mean wind vectors for day 3 of annually defined cluster

9 (of 30).
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Fig.17.2 (c) Mean wind vectors for day 5 of annually defined

cluster 9 (of 30).

Fig. 17.3 (a) Actual wind vectors for 25 January 1986, day 3 of cluster

9 (of 30).
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Fig. 17.3 (b) Actual wind vectors for 13 January 1988, day 3 of cluster

9 (of 30).

Fig. 17.3 (c) Actual wind vectors for 8 January 1990, day 3 of cluster 9

(of 30).
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17-39

Fig. 17.4 (a) Mean and distribution of wind vectors for day 1 of

cluster 9 (of 30).

Fig. 17.4 (b) Mean and distribution of wind vectors for day 3 of

cluster 9 (of 30).
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17-40

Fig. 17.4 (c) Mean and distribution of wind vectors for day 5 of cluster 9 (of 30).
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17-41

Fig. 17.5 (a) Monthly frequencies of annually derived clusters for clusters 1-6.
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17-42

Fig. 17.5 (b) Monthly frequencies of annually derived clusters for clusters 7-12.
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17-43

Fig. 17.5 (c) Monthly frequencies of annually derived clusters for clusters 13-18.
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17-44

Fig. 17.5 (d) Monthly frequencies of annually derived clusters for clusters 19-24.
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17-45

Fig. 17.5 (e) Monthly frequencies of annually derived clusters for clusters 25-30.
EPA/600/R-99/030

17-46

Fig. 17.6 Site locations for 201 meteorological parameters used in the evaluation.
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17-47

Standard Deviation Versus Sample Size: Temperature

Average (Across Stations) Standard Deviation Associated with

Estimation of 1984-1992 Mean from Aggregation of 3-Day Episodes

Sampling Simple Random S ampling

Stra tifie d : P ro po rtio n al Al lo c .

Ac h ie va b le w / 2 0 Stra ta

S

t

a

n

d

a

r

d

D

e

v

.

(

d

e

g

r

e

e

s

C

)

0.0

0.5

1.0

1.5

2.0

2.5

Number of Episodes in Sample

0 50 100 150 200 250 300

Fig. 17.7 (a) Standard deviation of estimated mean temperature

versus sample size.

Standard Deviation Versus Sample Size: Relative Humidity

Average (Across Stations) Standard Deviation Associated with

Estimation of 1984-1992 Mean from Aggregation of 3-Day Episodes

Sampling S imple Random Sampling

Stra ti fie d: Prop ortio na l All oc .

A chievable w / 20 Strata

S

t

a

n

d

a

r

d

D

e

v

.

(

%

)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Number of Episodes in Sample

0 50 100 150 200 250 300

Fig. 17.7 (b) Standard deviation of estimated mean relative

humidity versus sample size.
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17-48

Standard Deviation Versus Sample Size: Temperature

Average (Across Stations) Standard Deviation Associated with Estimation of

1984-1992 Mean & 90th Pctl from Aggregation of 3-Day Episodes in 20 Strata

Estimation of... Mean

90th Pctl

S

t

a

n

d

a

r

d

D

e

v

.

(

d

e

g

r

e

e

s

C

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Number of Episodes in Sample

20 30 40 50 60 70

Fig. 17.8 (a) Standard deviation of estimated mean and 90th

percentile temperature versus sample size.

Standard Deviation Versus Sample Size: RH-Adj Extinction Coeff

Average (Across Stations) Standard Deviation Associated with

Estimation of 1984-1992 Mean from Aggregation of 3-Day Episodes

Sampling Simple Random Sampling

Stratified : Pro po rtio na l A ll oc .

Ac hi ev able w/ 20 S trata

S

t

a

n

d

a

r

d

D

e

v

.

(

k

m

-

1

)

0.000

0.002

0.004

0.006

0.008

0.010

Number of Episodes in Sample

0 50 100 150 200 250 300

Fig. 17.7 (c) Standard deviation of estimated mean extinction

coefficient (adjusted for relative humidity) versus sample size. 
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17-49

Standard Deviation Versus Sample Size: RH-Adj Extinction Coeff

Average (Across Stations) Standard Deviation Associated with Estimation of

1984-1992 Mean & 90th Pctl from Aggregation of 3-Day Episodes in 20 Strata

Estimation of... Mean

90th Pctl

S

t

a

n

d

a

r

d

D

e

v

.

(

k

m

-

1

)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Number of Episodes in Sample

20 30 40 50 60 70

Fig. 17.8 (c) Standard deviation of estimated mean and 90th

percentile extinction coefficient (adjusted for relative humidity)

versus sample size.

Fig. 17.8 (b) Standard deviation of estimated mean and 90th

percentile relative humidity versus sample size.
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17-50

Fig. 17.9 (a) Monthly frequencies of seasonally derived clusters for clusters 1-6.
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17-51

Fig. 17.9 (b) Monthly frequencies of seasonally derived clusters for clusters 7-12.
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17-52

Fig. 17.9 (c) Monthly frequencies of seasonally derived clusters for clusters 13-18.
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17-53

Fig. 17.9 (d) Monthly frequencies of seasonally derived clusters for clusters 19-20.

Fig. 17.10 Mean wind vectors for day 3 of seasonally (Spring) defined

cluster 1 (of 20).
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17-54

Fig. 17.11 Mean wind vectors for day 3 of seasonally (Summer)

defined cluster 2 (of 20).

Fig. 17.12 Mean wind vectors for day 3 of seasonally (Autumn)

defined cluster 3 (of 20).
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Fig. 17.13 Mean wind vectors for day 3 of seasonally (Winter)

defined cluster 4 (of 20).

Fig. 17.14 Mean wind vectors for day 3 of seasonally (Spring) defined

cluster 5 (of 20).
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17-56

Fig. 17.15 Mean wind vectors for day 3 of seasonally (Winter) defined

cluster 6 (of 20).

Fig. 17.16 Mean wind vectors for day 3 of seasonally (Spring) defined

cluster 7 (of 20).
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17-57

Fig. 17.17 Mean wind vectors for day 3 of seasonally (Summer)

defined cluster 8 (of 20).

Fig. 17.18 Mean wind vectors for day 3 of seasonally (Summer)

defined cluster 9 (of 20).
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17-58

Fig. 17.19 Mean wind vectors for day 3 of seasonally (Winter)

defined cluster 10 (of 20).

Fig. 17.20 Mean wind vectors for day 3 of seasonally (Autumn)

defined cluster 11 (of 20).
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17-59

Fig. 17.21 Mean wind vectors for day 3 of seasonally (Autumn)

defined cluster 12 (of 20).

Fig. 17.22 Mean wind vectors for day 3 of seasonally (Winter)

defined cluster 13 (of 20).
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17-60

Fig. 17.23 Mean wind vectors for day 3 of seasonally (Autumn) defined

cluster 14 (of 20).

Fig. 17.24 Mean wind vectors for day 3 of seasonally (Summer)

defined cluster 15 (of 20).
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17-61

Fig. 17.25 Mean wind vectors for day 3 of seasonally (Autumn)

defined cluster 16 (of 20).

Fig. 17.26 Mean wind vectors for day 3 of seasonally (Winter) defined

cluster 17 (of 20).
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Fig. 17.27 Mean wind vectors for day 3 of seasonally (Summer) defined

cluster 18 (of 20).

Fig. 17.28 Mean wind vectors for day 3 of seasonally (Spring) defined

cluster 19 (of 20).
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Fig. 17.29 Mean wind vectors for day 3 of seasonally (Spring)

defined cluster 20 (of 20).

Fig. 17.30 Scatterplot of the observed mean bext (km-1) versus the

aggregated estimate of the mean bext (km-1) for the period 1984-

1992.
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17-64

Fig. 17.31 Spatial variation of the bias of the aggregated estimates of the mean bext

(km-1) for the period 1984-1992. (Deviations (%) are relative to the observed mean:

aggregate-observed/observed). Top figure indicates sites with positive bias, bottom

figure sites with negative bias.

 

 
EPA/600/R-99/030

Chapter 18

INTEGRATION OF SCIENCE CODES INTO MODELS-3

Jeffrey Young*

Atmospheric Modeling Division

National Exposure Research Laboratory

U.S. Environmental Protection Agency

Research Triangle Park, NC 27711

ABSTRACT

A complete group of CMAQ science codes has been integrated into the Models-3 system

following a set of rules to ensure compatibility and compliance with design principles that enable

modularity and flexibility and that allow easy modification and replacement of science process

components. This chapter describes the concept of classes and modules, the Models-3

input/output application programming interface, science code configuration management, and

model building and execution concepts

 

*On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Corresponding author address: Jeffrey Young, MD-80, Research Triangle Park, NC 27711. E-mail:

yoj@hpcc.epa.gov
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18.0 INTEGRATION OF SCIENCE CODES INTO MODELS-3

18.1 Introduction

Integration of the Community Multiscale Air Quality (CMAQ) science into the Models-3 design

paradigm takes place at the level of transforming the science, described by systems of partial

differential equations, into a discretized and parameterized numerical model. The integral parts

that are involved in the process are the coding language (Fortran 77, currently), an operational

design, a set of coding rules, computer platforms, model data access methods and storage

management, and a public code repository. Models-3 is a user interface system designed to

facilitate the development and use of simulation models by scientists, model developers and

regulatory users. The Models-3 framework provides a high-performance computational structure

for a community modeling system that currently contains distinct emissions, meteorological, and

chemical transport air quality models. In this chapter we define a model as a single, complete

executable built from a set of compiled subroutines that define either a core environmental

simulation model or a processing system that provides data to a simulation model. The

framework also links the models to data management tools and analysis/visualization software.

A complete set of CMAQ science codes has been integrated into the Models-3 system. The

development and integration of these codes has followed a set of principles relating to design and

implementation concepts that are discussed in this chapter.

We have promulgated a small set of software requirements and integration rules related to these

concepts so that science codes can be developed that conform to Models-3 requirements. With

this approach, the general user community may readily develop and execute models that use the

rich and growing base of science codes and data that reside in Models-3. A user may contribute

to that base and allow others to integrate his developments by applying these integration rules.

With access to all the released, or publicly available source files, a developer can supplement his

own codes and readily develop and test model versions within a highly modularized building

environment. On the other hand, people whose primary interest is studying the effects of control

strategies or regulatory applications can easily build and execute standard model versions for

different emissions scenarios and modeling domains.

The Models-3 and CMAQ systems have been developed to foster community access, and to

facilitate the improvement of the CMAQ system over time by the easy inclusion of new

scientific models and modules developed by researchers in the larger scientific community.

The CMAQ system contains a number of models needed to carry out an air quality model

application. Defining a “model” to be an executable built for a specific application, the codes

that make up the model are relatively general. To build a specific model, the user selects a set of

fundamental criteria that determine the application, such as the modeling domain, the chemical

mechanism, and physical process solvers. The reader is referred to Chapter 15 for details.

Defining a generic model as the set of codes from which a particular application can be built, the

following generic CMAQ models are currently available in the system:

• ICON provides the required initial conditions for a model simulation as concentrations of

specified individual chemical species for the complete modeling domain.
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18-2

• BCON provides the needed simulation boundary conditions as concentrations of

individual chemical species for the grid cells surrounding the modeling domain.

• Emissions-Chemistry Interface Processor (ECIP) transforms emission files produced

by the Models-3 Emissions Processing and Projection System (MEPPS) into an hourly,

3-D emissions data file for the CMAQ Chemical Transport Model (CCTM). For a

detailed discussion of the MEPPS operations, refer to Chapter 6 of the Models-3 User

Manual [6].

• The Meteorology-Chemistry Interface Processor (MCIP) interprets the output from a

meteorological model, such as the Penn State/NCAR fifth-generation Mesoscale Model

(MM5) [8], and prepares the data for use in the CCTM.

• The Landuse Processor (LUPROC) provides a high-resolution landuse database for the

CMAQ system. For example, MCIP uses the output from LUPROC to obtain surface

characteristics for computing dry deposition and other planetary boundary layer

parameters.

• The photolysis model (JPROC) computes photolytic rate constants (j-values) for the

gas-phase chemistry used in the CCTM.

• The Plume Dynamics Model (PDM) generates plume dimensions and positions along

with other related data for use in applying the plume-in-grid module in a CCTM

simulation.

• The CMAQ Chemical Transport Model (CCTM) simulates the chemical and physical

processes affecting tropospheric pollutants and estimates pollutant concentrations (e.g.,

ozone, particulate matter (PM2.5 and PM10), and carbon monoxide) and acid deposition.

The reader is referred to the Models-3 User Manual [6] for more details and descriptions of the

usage of these models.

Each generic model consists of a complete set of codes that can be compiled and linked into

different model executables by means of specific user-selected options with regard to groups of

code called modules, the horizontal grid and vertical layer domain, the chemical mechanism, the

computer platform, and compiling options.

One of the key issues in modeling is the manner in which developers and users must deal with

reading, writing and using model data. Models-3 provides a user-friendly Input/Output

Applications Programming Interface (I/O API) library [4] that enables a universal approach to

managing data across subroutines, models, platforms, and networks.

The organization of the remainder of this chapter is as follows: We discuss the concepts that lead

to and the implementation of classes and modules in the next section (18.2). We describe I/O

API usage and function in Section 18.3. Code management, an important consideration for

complex models, is discussed in Section 18.4. In Section 18.5 we discuss how a model is

organized and constructed through Models-3. Issues in regards to executing a particular model

are discussed in Section 18.6. Using the Models-3 framework to construct and execute a model
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18-3

is summarized in Section 18.7. Finally in Section 18.8, we discuss concepts and issues that

address Models-3 compliant coding practice and how to ensure code development that is

conformant to the Models-3 system.

18.2 Classes and Modules

18.2.1 Operational Design

The design concept of code classes is used to facilitate the plug&play capability in the Models3/CMAQ system. Science process modules are grouped into classes that are primarily based on

the time-splitting paradigm used in a CMAQ Chemical Transport Model (CCTM). Generally

each class is associated with a particular science process. A module consists of a complete set of

subroutines capable of modifying the concentration field related to the science process associated

with the module’s class. The CCTM is designed so that each module computes the changes in

the concentration field (CGRID) specific to that particular science process. A science module

operates on the entire three-dimensional gridded concentration field for a period of time called

the synchronization time step interval. The module performs whatever looping over that grid

and over whatever internal time steps that are necessary to complete its function.

Table 18-1 lists the classes and associated processes and modules currently available for the

CCTM. In building a particular CCTM, one module is selected from each class.

The other CMAQ models (i.e., those other than the CCTM) do not generally follow the timesplitting science process paradigm. However, for convenience and consistency in model

building, and for code organization, we have extended the concept of classes and modules to

apply to the other CMAQ models. Class and module organizations similar to those in Table 18-1

exist for the other models but are less extensive.
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Table 18-1. The Classes, Processes, and Modules Available in CCTM

CLASS (PROCESS) MODULES

driver (Control Model Execution) ctm

init (Initialize Model) init

hadv (Horizontal Advection) hbot (Bott’s scheme)

hppm (Piecewise Parabolic Method)

hadv_noop (no operation)

vadv (Vertical Advection) vbot (Bott’s scheme)

vppm (Piecewise Parabolic Method)

vadv_noop (no operation)

hdiff (Horizontal Diffusion) unif (Uniform eddy diffusion)

hdiff_noop (no operation)

vdiff (Vertical Diffusion) eddy (eddy diffusion)

vdiff_noop (no operation)

adjcon (Advected Mass Adjustment) denrate

adjcon_noop (no operation)

phot (Photolytic Rate Constants) phot

phot_noop (no operation)

chem (Gas Chemistry Solver) smvgear (SMVGEAR solver)

qssa (Vectorized QSSA solver)

chem_noop (no operation)

aero (Aerosol Solver) aero

aero_noop (no operation)

aero_depv (Aerosol Dry Deposition) aero_depv

aero_depv_noop (no operation)

cloud (Cloud and Aqueous Chemistry) cloud_radm (RADM cloud scheme)

cloud_noop (no operation)

ping (Plume-in-Grid) ping_smvgear (uses SMVGEAR solver)

ping_qssa (uses QSSA solver)

ping_noop (no operation)

procan (Process Analysis) pa

couple (Couple for Transport) gencoor

util (Utility Processing) util

18.2.2 CGRID

To facilitate the science processing for the different chemistries involved in CMAQ, the

concentration field array CGRID, is partitioned into four species classes: gas chemistry, aerosols,

non-reactive, and tracer species. This order is mandatory and maintained throughout the

processing. A subroutine, CGRID_MAP provides the means to correctly index into the CGRID

array for each science process that deals with individual classes of species. The tracer species

group is user-determined and may be empty in CGRID. Aqueous chemistry is dealt with solely

in the cloud processing, and currently aqueous species are not transported outside of the cloud

processing, therefore do not appear explicitly in CGRID. A subroutine call to CGRID_MAP

provides pointers to the locations of the species classes within CGRID. A process that deals only

with one of the classes (e.g. aerosols) can thus determine which part of CGRID it needs to

access.
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18.2.3 Class Driver

Generally, each module within a class requires a “class-driver,” which is the top level subroutine

within the module - it is at the top of the call chain for that module. Exceptions for this paradigm

exist for the util, procan, phot, and aero_depv classes. The class-driver presents a fixed name

and calling interface to the driver class subroutine SCIPROC that calls all the science process

modules. The calling interface consists of a subroutine argument list containing CGRID, the

current scenario data and time, and a time step vector. Each class also contains a “no-operation”

module, if appropriate. The no-op module has the fixed name and call interface for that class,

but performs no calculations. When called, it merely returns control to SCIPROC.

The following algorithm illustrates the processing and call sequence used in a CMAQ model for

fractional time steps processed non-symmetrically with respect to the chemistry processes:

Load CGRID from initial data; set initial Date/Time

Get the TimeStep vector: TimeStep[1] = output time interval

TimeStep[2] = synchronization time interval

TimeStep[3] = horizontal advection time interval

Foreach output_time_step

Call Couple ( CGRID, Date, Time, TimeStep )*

Foreach sync_step [in output time interval]

Call Horizontal_Advection ( CGRID, Date, Time, TimeStep )

Call Vertical_Advection ( CGRID, Date, Time, TimeStep )

Call Mass_Adjustment ( CGRID, Date, Time, TimeStep )

Call Horizontal_diffusion ( CGRID, Date, Time, TimeStep )

Call De-Couple ( CGRID, Date, Time, TimeStep )*

Call Vertical_diffusion ( CGRID, Date, Time, TimeStep )

Call Plume_in_Grid ( CGRID, Date, Time, TimeStep )

Call Gas_Chemistry ( CGRID, Date, Time, TimeStep )

Call Aerosol ( CGRID, Date, Time, TimeStep )

Call Cloud ( CGRID, Date, Time, TimeStep )

Advance Date/Time by synchronization time interval

Call Couple ( CGRID, Date, Time, TimeStep )*

End Foreach sync_step

Call De-Couple ( CGRID, Date, Time, TimeStep )*

Write Concentration File

End Foreach output_time_step

* Couple CGRID concentrations with, or de-couple CGRID from the air density × the

Jacobian of the computational grid. See Chapter 6 for a complete discussion on the

concept.

Not shown in the algorithm are processes that deal with source emissions (in either

Vertical_diffusion or Gas_chemistry), dry deposition (in Vertical_diffusion), and wet deposition

(in Cloud). Also not shown are calls to process analysis routines after each science process,

which compute the integrated process rates for that particular process. Such calls are also

embedded in science process modules that affect CGRID, such as emissions injection in either

the vertical diffusion process or gas chemistry. The Science Process Code Template in Section

18.8.3 below illustrates how these calls can be integrated within a module.
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In order to maintain the Models-3/CMAQ modularity and data-independence, the science

process class-drivers must adhere to coding standards with regard to the calling interface, file

data I/O, and standardized, uniform domain and mechanism data within global include files. See

Section 18.5, below, and Chapter 15 for a more complete discussion on the use of global include

files. These coding standards have not been propagated to the level below the class-driver. At

the sub-module level there are no strict I/O or coding standards, however we offer suggestions to

facilitate the potential incorporation of a module into the Models-3 system in Section 18.8 below.

18.2.4 Synchronization Time Step

There are many different time scales that are important in modeling. The CCTM deals with four

levels of time stepping:

1. Output time step - the time interval for which output data is written to disk.

2. Synchronization time step - the time interval for which the science processes,

represented by science modules, are considered to run independently of the other

processes. This is the time interval during which no interaction with the other time-split

science processes needs to take place.

3. Advection time step - the time interval over which horizontal advection occurs. It may

be less than or the same as the synchronization time interval.

4. Local or internal time looping - a possibly variable time interval that subdivides the

synchronization time step and is dependent on the user’s implementation of a particular

algorithm.

There may also be some science processes that don’t fit into this type of time scale hierarchy.

The sub-grid cloud time step in CCTM for example, has a fixed lifetime that may span the

synchronization time interval.

In the CCTM the synchronization time step is essentially the time interval over which the

chemistry processes are considered to be time-split and independent of the other processes.

The proper relationship between the first three time steps listed above is determined by the

“ADVSTEP” algorithm. Based on a user-supplied output time step interval, and optionally an

upper and lower limit for the synchronization time step interval,1 the algorithm:

• Ensures the synchronization time interval evenly divides the output time interval.

• Ensures the synchronization interval to not be greater than the upper limit.

• Determines a horizontal advection time interval that ensures all horizontal advection

calculations satisfy a Courant condition with respect to the horizontal winds for each

output time step. See Chapter 7 for details about the Courant condition requirement.

 

1

If these limits are not specified, the algorithm uses defaults of 900 and 300 seconds,

respectively.
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• Attempts to establish a horizontal advection time interval as close to the synchronization

interval as possible, but evenly divides the synchronization interval.

• In case the Courant condition restriction forces an advection time interval to be less than

the lower synchronization interval limit, sets advection time intervals to be as close to the

lower limit as possible but still evenly divide2 the lower limit.

• If none of these criteria can be satisfied, reports the issue and aborts the execution.

18.3 Input/Output Applications Programming Interface

A model needs access to external data. Data access, including output to external files, is done at

the module level. The Models-3 I/O API [4] provides a standardized interface to external data

that enables a user to follow the object oriented design concept of encapsulation. For example,

all basic and some derived meteorological data are calculated outside the CCTM (see MCIP

documentation in Chapter 12, e.g.) and available to a module through calls to the Models-3 I/O

API library [4]. Thus the user can avoid the re-calculation of various meteorological variables

within subroutines using different algorithms and parameterizations to re-compute essentially the

same quantities, which may give rise to errors and modeling inconsistencies. It is expected that

the modules treat these I/O API data completely independently, not knowing or caring if files

have been opened or read by any other module. In particular, any subroutine within a module

can open an I/O API file. It is recommended that at least one routine within a module, preferably

the class-driver, should open any I/O API files that are required in the module.

In general, the I/O API provides the Models-3 user with a library containing both Fortran and C

routines, which manage all the necessary file manipulations for data storage and access. The

main requirement is that the user follows the I/O API conventions for data structures, naming

conventions, and representations of scenario date and time. The I/O API routines manage access

to the files in such a manner that data can be read or written flexibly, virtually in any order, and

freeing the user from being concerned with low level file manipulation details, such as the order

or format of file variables.

In addition, the I/O API routines can be used for both file storage and cross-media model

coupling using Parallel Virtual Machine (PVM) mailboxes.

For file storage and access, the I/O API, which is the standard data access library for Models-3,

is built on top of NCAR’s netCDF files [5]. NetCDF (network Common Data Form) is a library

that provides an interface for array-oriented data access. The netCDF library also defines a

machine-independent format for representing scientific data. Together, the interface, library, and

format support the creation, access, and sharing of scientific data. The netCDF software was

developed at the Unidata Program Center in Boulder, Colorado. The freely available source can

be obtained by anonymous FTP [5].

The I/O API provides a variety of data structure types for organizing the data, and a set of access

routines that offer selective direct access to the data in terms meaningful to the user.

 

2

Strictly speaking, this means divides without remainder, not by a factor of two.
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Since they are netCDF files, I/O API files share the following characteristics:

1. They are machine-independent and network-transparent. Files created on a Cray

Supercomputer can be read on a desktop workstation (or vice versa) either via NFS

mounting or FTP, with no data format translation necessary;

2. They are self-describing. That is, they contain headers that provide a complete set of

information necessary to use and interpret the data they contain;

3. They are direct access. A small subset of a large dataset may be accessed efficiently

without first reading through all the preceding data. This feature is mandatory in

visualization requiring rapid access of large datasets;

4. They are appendable. Data can be appended to a netCDF dataset along one dimension

without copying the dataset or redefining its structure. For example, the I/O API can add

more time step data to a previously created file; and

5. They are sharable. One writer and multiple readers may simultaneously access the same

netCDF file. This means, for example, that visualization tools can access the file and

display data while the file is being created by the model.

The I/O API has been designed to support a variety of data types used in the environmental

sciences, among them:

• Gridded data (e.g., concentration or meteorological fields);

• Grid-boundary data (for model boundary conditions);

• Scattered data (e.g., meteorology observations or source level emissions); and

• Sparse matrix data (a specialized data type used in an emissions model).

I/O API files support three different time step structures:

1. Time-stepped with regular time steps (e.g. hourly model output concentration fields or

twice-daily upper air meteorology observation profiles);

2. Time-independent (e.g. terrain height); and

3. Restart, which always maintains the last two time step records of output from a running

process as “even” and “odd.” The “odd” is available for restart in case of a crash while

the “even” step is being written, and vice versa. Restart data does not consume an

inordinate amount of disk space with only two time steps worth of data at all times.

The I/O API provides automated built-in mechanisms to support production and application

requirements for dataset histories and audit trails:

• Identifiers of the program execution that produced the file.
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• Description of the study scenario in which the file was generated.

The I/O API also contains an extensive set of utility routines for manipulating dates and times,

performing coordinate conversions, storing and recalling grid definitions, sparse matrix

arithmetic, etc. There are a variety of related programs that perform various analysis or datamanipulation tasks, including statistical analysis, file comparison, and data extraction. Section

18.8.3 below illustrates the use of some of these utilities in coding practice, and the web site [5]

provides background materials, a user manual, and a tutorial.

18.4 Code Configuration Management

18.4.1 The Need

Faced with a large and growing community that uses and develops a wide variety of programs,

modules and codes, it is imperative to systematically manage the cross-community access to this

software. Typically, successful management of software involves:

• A repository - a place where all of the public code resides;

• The concept of archived code - codes that have been deposited into the repository in such

a manner that anyone can extract the exact code at a later time. This involves some kind

of transformation program to maintain master copies of the codes with embedded change

tables;

• The concept of revision control - archiving codes results in modifying the tags or unique

revision identifiers in the change tables in the master copies in order to recover the exact

code at a later date; and

• The concept of released code - codes that have reached some state of maturity and have

been designated with some kind of “released” status. They can be used with reasonable

expectation of reliability.

The paradigm used employs the following scenario.

1. A user modifies or develops code. The code may be one subroutine or many, possibly

comprising whole science models. The code may originate from “scratch,” or be

extracted from the repository and modified.

2. After testing or reaching a point of being satisfied with his/her results, he/she decides to

save it in the repository so that others can have access to it.

3. Some archived codes may still be in an experimental, or development, state while others

may be reasonably stable and more completely tested. The latter may be designated as

“released.” There is no enforceable means to control access based on an experimental or

released state. The community will have and should have access indiscriminately, well

aware that using development state code is risky.
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4. As the user continues to work with the codes, he/she may make enhancements or

discover and fix errors. The upgrades are then installed in the repository, which

automatically assigns unique revision identifiers.

5. The repository is located where it is conveniently accessible to all pertinent users, and it

is maintained by an administrator who sets and enforces general access rules.

18.4.2 The Tool

There are many configuration management tools both free and commercially available. We

chose The Concurrent Versions System (CVS) [1] mainly because of its versatility. CVS

controls the concurrent editing of sources by several users working on releases built from a

hierarchical set of directories. CVS uses the Revision Control System (RCS) [2] as the base

system. Other reasons that CVS was an attractive choice include:

• It works on virtually all UNIX platforms and many PCs;

• It is publicly available and free;

• CVS is a state-of-the-art system, constantly being improved; and

• MM5 codes are managed by CVS, and MM5 is a primary meteorology model for the

CMAQ system.

From the UNIX man pages (online manual):

CVS is a front end to the Revision Control System (RCS) that extends the notion

of revision control from a collection of files in a single directory to a hierarchical

collection of directories consisting of revision controlled files. These directories

and files can be combined together to form a software release. CVS provides the

functions necessary to manage these software releases and to control the

concurrent editing of source files among multiple software developers [emphasis

added].

The Revision Control System (RCS) manages multiple revisions of files. RCS

automates the storing, retrieval, logging, identification, and merging of revisions.

Another widely used source code management system is the Source Code Control System

(SCCS), which is usually distributed with UNIX systems. The main note is that RCS and SCCS

act on files only, while CVS operates on projects. Working with entire projects works better and

easier with CVS. Multi-developer project development works better with CVS as well. CVS

supports a client/server mode of operation that can be very useful. CVS also allows

customization by adding hooks so that local scripts or programs can be called when executing

various CVS commands. This can be useful to force naming conventions of tags, or reference to

bug-tracking software, etc. Thus CVS adds power and features that are attractive for the

ModelsS-3/CMAQ system.
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18.4.3 The Repository

The repository structure, that is, the UNIX directory hierarchy, follows the class/module

organization discussed above in Section 18.2. The repository is actually divided into many

repositories, one for each generic model. This division makes it easier to maintain the

class/module organization that is important for the model building operation described below in

Section 18.5.

CVS allows for the use of a “modules” file3, which enables a user to easily check out or extract a

complete CMAQ module. For example, a module might be checked out by a user to make code

modifications, and complete modules are checked out during the model building operation.

The following shows a symbolic CVS UNIX directory tree that represents the current structure

for the CCTM:

 

3

The terminology is unfortunate. The CVS modules file has no intrinsic relationship with the

CMAQ classes/module design implementation.
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...CCTM -+-> CVSROOT ---+-> CVS administrative files

 | |

 \-> src -------+-> driver --+-------> ctm ------+-> RCS files

 |

 +-> hadv ---+---> hadv_noop ---+-> RCS files

 | +---> hbot --------+-> RCS files

 | +---> hppm --------+-> RCS files

 |

 +-> vadv ---+---> vadv_noop ---+-> RCS files

 | +---> vbot --------+-> RCS files

 | +---> vppm --------+-> RCS files

 |

 +-> vdiff --+---> vdiff_noop --+-> RCS files

 | +---> eddy --------+-> RCS files

 |

 +-> chem ---+---> chem_noop ---+-> RCS files

 | +---> smvgear -----+-> RCS files

 | +---> qssa --------+-> RCS files

 |

 +-> phot ---+---> phot_noop ---+-> RCS files

 | +---> phot --------+-> RCS files

 |

 +-> aero ---+---> aero_noop ---+-> RCS files

 | +---> aero --------+-> RCS files

 |

 +-> couple -+---> gencoor -----+-> RCS files

 |

 +-> cloud --+---> cloud_noop --+-> RCS files

 | +---> cloud_radm --+-> RCS files

 |

 +-> procan -+---> pa ----------+-> RCS files

 |

 +-> hdiff --+---> hdiff_noop --+-> RCS files

 | +---> unif --------+-> RCS files

 |

 +-> init ---+---> init --------+-> RCS files

 |

 +-> util ---+---> util --------+-> RCS files

 |

 +-> aero_depv +-> aero_depv_noop +-> RCS files

 | +-> aero_depv -+-> RCS files

 |

 +-> adjcon -+---> adjcon_noop -+-> RCS files

 | \---> denrate -----+-> RCS files

 |

 \-> ping ---+---> ping_noop ---+-> RCS files

 +---> ping_qssa ---+-> RCS files

 \---> ping_smvgear +-> RCS files

The symbolic tree is shown relative to the subdirectory in the repository named for the CCTM

model. Similar trees exist for each of the generic models. The RCS files are the revision control

history files that contain the change tables to reconstruct the actual source code according to a

specific revision identifier. Also note that the tree closely follows the organization of classes and

modules for the CCTM described in Table 18-1, and contains alternate modules within the

classes. In particular, most classes contain a “no-operation” (_noop) module that allows a user to

essentially turn off that particular science process modeling. This is useful, for example in

debugging, where rapid turn-around is important, and a computationally demanding module that

is not needed can be bypassed.
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18.5 How a Model is Constructed

18.5.1 Object Oriented Concepts

To make the Models-3/CMAQ system robust and flexible, object oriented concepts were

incorporated into the design of the CMAQ system. Incorporating these ideas into the design

helps avoid introducing errors when code modifications are necessary. Additionally, the system

is capable of easy and efficient modification, allowing the user to quickly make models for

different applications.

The implementation language for CMAQ is Fortran 77, which imposes limits on how far one can

go in terms of object oriented design. In particular, since Fortran is a static language, objects

cannot be instantiated dynamically; they must be declared explicitly in the source code to be

created at compile time. However, to encourage a user community that will be contributing code

for future enhancements, every attempt has been made to adhere to the Fortran 77 standard. In

the future, the use of other implementation languages such as Fortran 90 will be considered.

18.5.2 Global Name Table Data

In order to implement modularity and data-independence, we have employed design ideas that

draw heavily from the object-oriented concept of inheritance and code re-use. The data

structures in the codes that deal with the domain sizes, chemical mechanism, I/O API, logical file

names, general constants, and CGRID pointers are determined by Fortran declarations in data

and parameter statements that are created through the Models-3 system. These data structures

pertain to a particular application (domain, mechanism, etc.) and are meant to apply globally, not

only to one particular CCTM through all its subroutines, but also to all the models that supply

data to the CCTM for that application. These data structures are contained in Fortran INCLUDE

files, which are essentially header files, included in the declaration sections near the top of the

Fortran code source files. The inclusion of these source files is made automatic by using a

generic string that represents the include file and which is parsed and expanded to the actual

include file during a pre-processing stage in the compilation. The Fortran global include files

contain name tables that define:

1. The computational grid domain;

2. The chemical mechanism;

3. The I/O API interface, including logical file names;

4. The global modeling constants; and

5. Other constants or parameters that apply across the model.

In order to effect the implementation of the include files into the code, a special compiling

system, m3bld, has been developed [3], which reads a configuration file that, based on the

application, completely determines the model executable to be built. The ASCII configuration

file can be generated either by the Models-3 system or by the user following a few, simple

syntactical rules illustrated below. For additional details, the reader is referred to Chapter 15.
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In addition to the global include files, the configuration file contains module commands that tell

m3bld to extract the codes for that module from the model code repository for compilation.

18.5.3 Build Template

The following exhibit is an example of a configuration file that m3bld would use to build a

model executable: (The numerals at the left-hand margin are labels for the legend and are not

part of the configuration file. The “//” represents a non-parsed, comment line.)

Example Configuration File

(1) model TUTO_r4y;

(2) cpp_flags “-Demis_vdif “;

(2) f77_flags “-e -fast -O4 -xtarget=ultra2 -xcache=16/32/1:1024/64/1”;

(2) link_flags “-e -fast -O4 -xtarget=ultra2”;

(3) libraries “-L/home/models3/tools/IOAPI/release/m3io/lib/SunOS5 -lm3io

 -L/home/models3/tools/netCDF/SunOS5 -lnetcdf”;

(4) global verbose;

(5) include SUBST_BLKPRM /work/rep/include/release/BLKPRM_500.EXT;

(5) include SUBST_CONST /work/rep/include/release/CONST3_RADM.EXT;

(5) include SUBST_FILES_ID /work/rep/include/release/FILES_CTM.EXT;

(5) include SUBST_EMPR_VD /work/rep/include/release/EMISPRM.vdif.EXT;

(5) include SUBST_EMPR_CH /work/rep/include/release/EMISPRM.chem.EXT;

(5) include SUBST_IOPARMS /work/rep/include/release/PARMS3.EXT;

(5) include SUBST_IOFDESC /work/rep/include/release/FDESC3.EXT;

(5) include SUBST_IODECL /work/rep/include/release/IODECL3.EXT;

(5) include SUBST_XSTAT /work/rep/include/release/XSTAT3.EXT;

(6) include SUBST_COORD_ID /work/yoj/tgt/BLD/COORD.EXT;

(6) include SUBST_HGRD_ID /work/yoj/tgt/BLD/HGRD.EXT;

(6) include SUBST_VGRD_ID /work/yoj/tgt/BLD/VGRD.EXT;

(6) include SUBST_RXCMMN /work/yoj/tgt/BLD/RXCM.EXT;

(6) include SUBST_RXDATA /work/yoj/tgt/BLD/RXDT.EXT;

(6) include SUBST_GC_SPC /work/yoj/tgt/BLD/GC_SPC.EXT;

(6) include SUBST_GC_EMIS /work/yoj/tgt/BLD/GC_EMIS.EXT;

(6) include SUBST_GC_ICBC /work/yoj/tgt/BLD/GC_ICBC.EXT;

(6) include SUBST_GC_DIFF /work/yoj/tgt/BLD/GC_DIFF.EXT;

(6) include SUBST_GC_DDEP /work/yoj/tgt/BLD/GC_DDEP.EXT;

(6) include SUBST_GC_DEPV /work/yoj/tgt/BLD/GC_DEPV.EXT;

(6) include SUBST_GC_ADV /work/yoj/tgt/BLD/GC_ADV.EXT;

(6) include SUBST_GC_CONC /work/yoj/tgt/BLD/GC_CONC.EXT;

(6) include SUBST_GC_G2AE /work/yoj/tgt/BLD/GC_G2AE.EXT;

(6) include SUBST_GC_G2AQ /work/yoj/tgt/BLD/GC_G2AQ.EXT;

(6) include SUBST_GC_SCAV /work/yoj/tgt/BLD/GC_SCAV.EXT;

(6) include SUBST_GC_WDEP /work/yoj/tgt/BLD/GC_WDEP.EXT;

(6) include SUBST_AE_SPC /work/yoj/tgt/BLD/AE_SPC.EXT;

(6) include SUBST_AE_EMIS /work/yoj/tgt/BLD/AE_EMIS.EXT;

(6) include SUBST_AE_ICBC /work/yoj/tgt/BLD/AE_ICBC.EXT;

(6) include SUBST_AE_DIFF /work/yoj/tgt/BLD/AE_DIFF.EXT;

(6) include SUBST_AE_DDEP /work/yoj/tgt/BLD/AE_DDEP.EXT;

(6) include SUBST_AE_DEPV /work/yoj/tgt/BLD/AE_DEPV.EXT;

(6) include SUBST_AE_ADV /work/yoj/tgt/BLD/AE_ADV.EXT;

(6) include SUBST_AE_CONC /work/yoj/tgt/BLD/AE_CONC.EXT;
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Example Configuration File

(6) include SUBST_AE_A2AQ /work/yoj/tgt/BLD/AE_A2AQ.EXT;

(6) include SUBST_AE_SCAV /work/yoj/tgt/BLD/AE_SCAV.EXT;

(6) include SUBST_AE_WDEP /work/yoj/tgt/BLD/AE_WDEP.EXT;

(6) include SUBST_NR_SPC /work/yoj/tgt/BLD/NR_SPC.EXT;

(6) include SUBST_NR_EMIS /work/yoj/tgt/BLD/NR_EMIS.EXT;

(6) include SUBST_NR_ICBC /work/yoj/tgt/BLD/NR_ICBC.EXT;

(6) include SUBST_NR_DIFF /work/yoj/tgt/BLD/NR_DIFF.EXT;

(6) include SUBST_NR_DDEP /work/yoj/tgt/BLD/NR_DDEP.EXT;

(6) include SUBST_NR_DEPV /work/yoj/tgt/BLD/NR_DEPV.EXT;

(6) include SUBST_NR_ADV /work/yoj/tgt/BLD/NR_ADV.EXT;

(6) include SUBST_NR_N2AE /work/yoj/tgt/BLD/NR_N2AE.EXT;

(6) include SUBST_NR_N2AQ /work/yoj/tgt/BLD/NR_N2AQ.EXT;

(6) include SUBST_NR_SCAV /work/yoj/tgt/BLD/NR_SCAV.EXT;

(6) include SUBST_NR_WDEP /work/yoj/tgt/BLD/NR_WDEP.EXT;

(6) include SUBST_TR_SPC /work/yoj/tgt/BLD/TR_SPC.EXT;

(6) include SUBST_TR_EMIS /work/yoj/tgt/BLD/TR_EMIS.EXT;

(6) include SUBST_TR_ICBC /work/yoj/tgt/BLD/TR_ICBC.EXT;

(6) include SUBST_TR_DIFF /work/yoj/tgt/BLD/TR_DIFF.EXT;

(6) include SUBST_TR_DDEP /work/yoj/tgt/BLD/TR_DDEP.EXT;

(6) include SUBST_TR_DEPV /work/yoj/tgt/BLD/TR_DEPV.EXT;

(6) include SUBST_TR_ADV /work/yoj/tgt/BLD/TR_ADV.EXT;

(6) include SUBST_TR_T2AQ /work/yoj/tgt/BLD/TR_T2AQ.EXT;

(6) include SUBST_TR_SCAV /work/yoj/tgt/BLD/TR_SCAV.EXT;

(6) include SUBST_TR_WDEP /work/yoj/tgt/BLD/TR_WDEP.EXT;

 // Process Analysis / Integrated Reaction Rates processing

(6) include SUBST_PACTL_ID /work/yoj/tgt/BLD/PA_CTL.EXT;

(6) include SUBST_PACMN_ID /work/yoj/tgt/BLD/PA_CMN.EXT;

(6) include SUBST_PADAT_ID /work/yoj/tgt/BLD/PA_DAT.EXT;

(7) module ctm release ;

(7) module init release ;

 // options are denrate and adjcon_noop

(7) module denrate release ;

(7) module gencoor release ;

 // options are hbot and hadv_noop

(7) module hppm release ;

 // options are vbot and vadv_noop

(7) module vppm release ;

 // options are phot and phot_noop

(7) module phot release ;

 // options are ping_qssa, ping_smvgear and ping_noop

 (7) module ping_qssa release ;

 // options are qssa, smvgear and chem_noop

(7) module qssa release ;

 // aerosols
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Example Configuration File

(7) module aero release ;

 // aerosol dep vel

(7) module aero_depv release ;

 // options are eddy and vdiff_noop

(7) module eddy release ;

 // options are const and hdiff_noop

(7) module unif release ;

 // options are cloud_radm and cloud_noop

(7) module cloud_radm release ;

 // options are pa and pa_noop, which requires the replacment of the three

 // global include files with their pa_noop counterparts

(7) module pa release ;

(7) module util release ;

Legend:

(1) - Model name definition. This string is what the model executable will

be named.

(2) - The C pre-processor, Fortran compiler and link flags. The flags

specified indicate that the model is to be compiled with the option to input

emissions in the vertical diffusion processing, and to compile and link on a

Sun Sparc, Ultra-30 workstation.

(3) - I/O API and netCDF object libraries to be linked. The format is

virtually identical to that of a UNIX make command.

(4) - m3bld flag: one of many options. verbose indicates report all actions.

Other options are:

• compile_all - force compile, even if object files are current

• clean_up - remove all source files upon successful completion

• no_compile - do everything except compile

• no_link - do everything except link

• one_step - compile and link in one step

• parse_only - checks config file syntax

• show_only - show requested commands but doesn’t execute them

(5), (6) - global include files. The syntax is:

 include internal-string full-path-name.

Every routine that requires a specific include file must contain a Fortran

include statement using the internal-string (see Section 18.3 for examples).

 (5) - “fixed” global include files. The fixed include files have been

constructed outside of the Models-3 framework and contain global data not

directly related to the domain or chemical mechanism such as modeling

constants and file logical names.

(6) - The Models-3 framework automatically generates all the include files

labeled (6). The user supplies information through the Models-3 Science

Manager that determines the data in these include files. These data define

the complete problem domain for a particular CMAQ application. See Chapter

15 for a complete discussion.

(7) - The module name to extract from the model code repository and an

optional revision flag to select a particular module version. The syntax is:

 module module name revision flag.
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Example Configuration File

For additional information on this implementation, the reader is referred to the Model Building

Tool described in Fine et al. [3].

18.6 How a Model is Executed

In order to run a model executable, various UNIX environment variables must be set in the shell

that invokes the execute command. Generally, these involve the modeling scenario start date and

time, the run duration, the output time step interval, various internal code flags that differ among

the models, and all the input and output logical, or symbolic file names (see Section 15.4.3 in

Chapter 15). There are various ways by which external file names can be referenced in the code,

but the most general across all UNIX platforms is to link them by means of environment

variables. There are I/O API utility functions that allow a user easy access to these variables

within the code, making such accesses generic and portable.

An additional feature that is provided through the I/O API is to declare a file “volatile” by

appending a -v flag in the shell’s declaration for the environment variable. By doing this, the I/O

API will cause the netCDF file to update (sync) its disk copy after every write and thereby

update the netCDF header. Otherwise, netCDF file headers are not updated until the files are

closed. This is useful, for example, to allow a user to analyze an open netCDF file using

visualization tools while the model is executing. It is also useful in case of a system crash. A

CCTM model can be restarted at the scenario time step after the last successful write using the

aborted output file as the input initial data.

18.7 Using the Models-3 Framework

The Models-3 framework simplifies the model building and model execution tasks, especially if

key objects have been pre-defined. Thus if a user is conducting a study that uses the same

domain or chemical mechanism, but uses different code options, e.g., then rebuilding and reexecuting using the framework makes conducting the study very straightforward. Other

examples where the framework greatly simplifies operational tasks would be where a model is to

be applied on different domains, or for control strategies in which the only thing that changes are

the emissions input files. A knowledgeable user is still able to build and execute model

applications outside the framework. In fact, one can easily run model applications using

executables and UNIX scripts generated by the framework.

In general, in order to build a model within the framework, the coordinate system, horizontal grid

and vertical layer definitions, and chemical mechanism must be specified. This is done within

the Models-3 Science Manager component. If objects required for a particular application, such

as a coordinate system specification, are already defined, then the user needs only to select those

objects. The Configuration File Manager, an additional subcomponent within the Science

Manager, allows a user to control the module definitions and fixed 4

 include files that go into the

 

4

not generated by the framework
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configuration file used to build the model. Also the user can specify compiling and linking flags

related to a specific platform on which the model is to be executed.

With all required Models-3 objects defined, the task of building a model is made simple using

the Models-3 component, Model Builder. It’s important to note that as users develop models, the

set of objects will grow to become a rich pool from which to select for a particular application.

The Models-3 framework was designed to allow extensive re-use of objects. Model Builder

generates all the “non-fixed” include files, then builds a model, linking in the include files

including the user-specified fixed ones. See the section above for the include file definitions.

Perhaps one of the most useful features of the Models-3 framework is the ability to graphically

set up and execute single or multiple model executions with automatic data registration. This

allows a user to carefully control the order of model executions and the management of all the

input and output data. The Models-3 component that performs this function is the Study Planner.

Study Planner allows a user to specify input data sets, executables, and UNIX environment

variables, and to initiate (possibly multiple) model runs.

18.8 Conformant Code

18.8.1 Thin Interface

As mentioned above in section 18.5.1 , the Models-3/CMAQ system was designed to be robust

and flexible with respect to the interchange of modules and the elimination of cross-module data

dependencies. Consequently, the concept of a “thin interface” has been employed in the design,

which applies principally to the class-drivers. At the least, the thin interface implementation

implies the following requirements:

• Eliminate global memory references (across modules). This implies no common blocks

across modules, no hidden data paths, no “back doors”;

• Each module reads and interpolates its required data independently. The I/O API helps to

ensure this kind of data independence; and

• Standardized argument list (CGRID, Date, Time, TimeStep) for the class-driver, as

described in the section above.

These requirements attempt to incorporate the object-oriented idea of encapsulation in the

Models-3/CMAQ design. The following quotation is from Rumbaugh et al. [7]:

Encapsulation (also information hiding) consists of separating the external aspects

of an object, which are accessible to other objects, from the internal

implementation details of the object, which are hidden from other objects.

Encapsulation prevents a program from becoming so interdependent that a small

change has massive ripple effects. The implementation of an object can be

changed without affecting the applications that use it [emphasis added].

The encapsulation design makes the CMAQ system safer and enables the transaction processing,

plug&play capability. This design also makes it easier for a user to trace data and usage within a

module, particularly at the class-driver level.
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18.8.2 Coding Rules

In order to maintain the object oriented concepts implemented in the CMAQ system design, we

have established a small set of coding rules that apply for those that develop CMAQ science and

affect the low-level design of the models. We have developed standards to control data

dependencies at the class-driver level, but we have not propagated these coding standards to the

sub-module level.

1. The models are generally coded in Fortran (Fortran-77 conventions are used). It is

possible to link in subroutines written in the C language, although this has not been done

within the current CMAQ implementation.

2. The modules must be controlled by a top-level class-driver routine, whose calling

arguments must be the computational concentration grid array, CGRID, the current

scenario data and time, and the controlling time step vector. See the section above.

3. The class-driver is also responsible for any temporal integration required within the

module. (The time steps for process integration at the module level are usually shorter

than those of the CCTM synchronization time step.)

4. Any reads and writes for the module should be done at the level of the class-driver

routine. Although not absolutely necessary, this is strongly suggested because it is

usually much easier to control the timing of the data accesses at the highest level of the

module where the current scenario date and time are known.

5. Use the IMPLICIT NONE Fortran declaration to maintain some control on typographic

errors and undefined variables. Although not standard Fortran-77, the use of IMPLICIT

NONE forces the developer to declare all internal variables.

6. Use the global include files for domain definitions, chemical mechanism data, and other

data where available.

7. Use the I/O API for external data references where appropriate. For an illustration of

these rules, the reader is referred to the code template below.

At the sub-module level there are no strict I/O or coding standards. Here it is envisioned that

individual researchers/programmers use their own coding styles for their algorithms. However

the following suggestions are offered to facilitate the potential incorporation of a module into the

CMAQ system:

• It is expected that MKS units are used for input and output variables, as these units have

been standardized throughout the CMAQ system. Within a sub-module subroutine

whatever units are most convenient can be used. However, the developer must be

responsible for any unit conversions to MKS for input and output, and thus avoid any

potential errors.

• For efficiency and performance considerations, operations may need to be done on

groups of grid cells (a block of cells) at a time. If there are N cells in the block and the
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entire domain contains M cells, then the entire domain can be decomposed into M/N

blocks. We have used N=500. For operations in the horizontal (x,y), the cell constraint

becomes X × Y ≤ N, where X= number of cells in the x-direction, and Y= number of cells

in the y-direction. For operations in both the horizontal and vertical, the constraint

becomes X × Y × Z ≤ N, where Z= number of cells in the z-direction. There may be some

operations, such as for some horizontal advection schemes, where this decomposition

into blocks becomes more difficult or impossible.

18.8.3 Science Process Code Template

The following demonstrates what a science process class-driver Fortran 77 subroutine might look

like. We recommend that a code developer follows this template, where appropriate, to get

maximum benefit from the design concepts implemented in the Models-3/CMAQ system. This

template is generic and attempts to show most, if not all the features available. Some classdrivers and most other sub-programs within a module may not have, nor require, most or any of

these features. (The numerals at the left-hand margin are for the legend and are not part of the

text, and the text within “< >“ indicates code not included.)

Example of Science Process Class-driver

( 1) SUBROUTINE VDIFF SUBST_GRID_ID ( CGRID, JDATE, JTIME, TSTEP )

( 2) C------------------------------------

( 2) C Function:

( 2)

( 2) C Preconditions:

( 2)

( 2) C Subroutines and Functions Called:

( 2)

( 2) C Revision History:

( 2) C------------------------------------

( 3) IMPLICIT NONE

( 4) INCLUDE SUBST_HGRD_ID ! horizontal dimensioning parameters

( 4) INCLUDE SUBST_VGRD_ID ! vertical dimensioning parameters

( 5) INCLUDE SUBST_GC_SPC ! gas chemistry species table

( 5) INCLUDE SUBST_GC_EMIS ! gas chem emis surrogate names and map table

( 5) INCLUDE SUBST_GC_DEPV ! gas chem dep vel surrogate names and map table

( 5) INCLUDE SUBST_GC_DDEP ! gas chem dry dep species and map table

( 5) INCLUDE SUBST_GC_DIFF ! gas chem diffusion species and map table

( 5) INCLUDE SUBST_AE_SPC ! aerosol species table

( 5) INCLUDE SUBST_AE_DEPV ! aerosol dep vel surrogate names and map table

( 5) INCLUDE SUBST_AE_DDEP ! aerosol dry dep species and map table

( 5) INCLUDE SUBST_AE_DIFF ! aerosol diffusion species and map table

( 5) INCLUDE SUBST_NR_SPC ! non-reactive species table

( 5) INCLUDE SUBST_NR_EMIS ! non-react emis surrogate names and map table

( 5) INCLUDE SUBST_NR_DEPV ! non-react dep vel surrogate names and map table

( 5) INCLUDE SUBST_NR_DDEP ! non-react dry dep species and map table

( 5) INCLUDE SUBST_NR_DIFF ! non-react diffusion species and map table

( 5) INCLUDE SUBST_TR_SPC ! tracer species table

( 5) INCLUDE SUBST_TR_EMIS ! tracer emis surrogate names and map table

( 5) INCLUDE SUBST_TR_DEPV ! tracer dep vel surrogate names and map table

( 5) INCLUDE SUBST_TR_DDEP ! tracer dry dep species and map table

( 5) INCLUDE SUBST_TR_DIFF ! tracer diffusion species and map table

( 6) #ifdef emis_vdif

( 6) INCLUDE SUBST_EMPR_VD ! emissions processing in vdif

( 6) #else

( 6) INCLUDE SUBST_EMPR_CH ! emissions processing in chem
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Example of Science Process Class-driver

( 6) #endif

( 7) INCLUDE SUBST_PACTL_ID ! PA control parameters

( 7) INCLUDE SUBST_CONST ! constants

( 7) INCLUDE SUBST_FILES_ID ! file name parameters

( 7) INCLUDE SUBST_IOPARMS ! I/O parameters definitions

( 7) INCLUDE SUBST_IOFDESC ! file header data structure

( 7) INCLUDE SUBST_IODECL ! I/O definitions and declarations

( 7) INCLUDE SUBST_XSTAT ! M3EXIT status codes

( 4) INCLUDE SUBST_COORD_ID ! coordinate and domain definitions (req IOPARMS)

( 8) C Arguments:

( 8)

( 8) REAL CGRID( NCOLS,NROWS,NLAYS,* ) ! concentrations

( 8) INTEGER JDATE ! current model date, coded YYYYDDD

( 8) INTEGER JTIME ! current model time, coded HHMMSS

( 8) INTEGER TSTEP( 3 ) ! time step vector (HHMMSS)

( 8) ! TSTEP(1) = local output step

( 8) ! TSTEP(2) = sciproc sync. step (chem)

( 8) ! TSTEP(3) = advection time step

( 9) C Parameters:

( 9) < >

(10) C External Functions not previously declared in IODECL3.EXT:

(10)

(10) INTEGER SECSDIFF, SEC2TIME, TIME2SEC

(10) EXTERNAL SECSDIFF, SEC2TIME, TIME2SEC

(11) C File variables:

(11) < >

(12) C Local variables:

(12) < >

(13) IF ( FIRSTIME ) THEN

(13)

(13) FIRSTIME = .FALSE.

(13)

(13) LOGDEV = INIT3()

(13)

(13) C Open the met files:

(13)

(13) IF ( .NOT. OPEN3( MET_CRO_3D, FSREAD3, PNAME ) ) THEN

(13) XMSG = ‘Could not open ‘// MET_CRO_3D // ‘ file’

(13) CALL M3EXIT( PNAME, JDATE, JTIME, XMSG, XSTAT1 )

(13) END IF

(13)

(13) < open other met files >

(13)

(13) C Open Emissions files:

(13)

(13) < do other intialization or operations that need be done only once >

(13)

(13) END IF ! if firstime

(14) C set file interpolation to middle of time step

(14)

(14) MDATE = JDATE

(14) MTIME = JTIME

(14) MSTEP = TIME2SEC( TSTEP( 2 ) )

(14) CALL NEXTIME ( MDATE, MTIME, SEC2TIME( MSTEP / 2 ) )

(15) C read&interpolate met data

(15)

(15) VNAME = ‘DENSA_J’

(15) IF ( .NOT. INTERP3( MET_CRO_3D, VNAME, PNAME,

(15) & MDATE, MTIME, NCOLS*NROWS*NLAYS,

(15) & RRHOJ ) ) THEN

(15) XMSG = ‘Could not interpolate DENSA_J from ‘ // MET_CRO_3D

(15) CALL M3EXIT( PNAME, MDATE, MTIME, XMSG, XSTAT1 )

(15) END IF

(15)
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Example of Science Process Class-driver

(15) < do other reads >

(15)

(15) C read&interpolate deposition velocities

(15)

(15) < do operations >

(15)

(15) C read&interpolate emissions

(15)

(15) CALL RDEMIS ( MDATE, MTIME, NCOLS, NROWS, EMISLYRS, NEMIS, EM_TRAC,

(15) & VDEMIS )

(15)

(16) IF (LIPR) CALL PA_UPDATE_EMIS ( ‘VDIF’, VDEMIS, JDATE, JTIME, TSTEP )

 < do other operations >

(17) CALL EDYINTB SUBST_GRID_ID ( EDDYV, DT, JDATE, JTIME, TSTEP( 2 ) )

(18) DO 345 R = 1, NROWS

(18) DO 344 C = 1, NCOLS

 < do operations >

(19) DO 301 N = 1, NSTEPS( C,R )

 < do operations >

(19) 301 CONTINUE ! end time steps loop

(18) 344 CONTINUE ! end loop on col C

(18) 345 CONTINUE ! end loop on row R

(20) C If last call this hour: write accumulated depositions:

(20)

(20) WSTEP = WSTEP + TIME2SEC( TSTEP( 2 ) )

(20) IF ( WSTEP .GE. TIME2SEC( TSTEP( 1 ) ) ) THEN

(20) MDATE = JDATE

(20) MTIME = JTIME

(20) CALL NEXTIME( MDATE, MTIME, TSTEP( 2 ) )

(20) WSTEP = 0

(20)

(20) IF ( .NOT. WRITE3( CTM_DRY_DEP_1,

(20) & ALLVAR3, MDATE, MTIME, DDEP ) ) THEN

(20) XMSG = ‘Could not write ‘ // CTM_DRY_DEP_1 // ‘ file’

(20) CALL M3EXIT( PNAME, MDATE, MTIME, XMSG, XSTAT1 )

(20) END IF

(20)

(20) WRITE( LOGDEV, ‘( /5X, 3( A, :, 1X ), I8, “:”, I6.6 )’ )

(20) & ’Timestep written to’, CTM_DRY_DEP_1,

(20) & ’for date and time’, MDATE, MTIME

(20)

(16) IF (LIPR) CALL PA_UPDATE_DDEP ( ‘VDIF’, DDEP, JDATE, JTIME, TSTEP )

(20)

(20) < do other operations >

(20)

(20) END IF

(21) RETURN

(21) END

 Legend:

( 1) - Class-driver subroutine internal name. Note the calling argument list. It is fixed for

class-drivers. The string “SUBST_GRID_ID” is used for developing run-time nesting applications,

which has not been fully implemented in the current version. By specifying subroutine names

associated with a particular nest and using corresponding domain include files for that

subroutine, it is possible to set up a multi-nest application. The details have not been

discussed because this kind of nesting has not been implemented in the current release of the

Models-3/CMAQ system.

( 2) - Header comments. Highly recommended for internal documentation.

( 3) - Highly recommended for Fortran. IMPLICIT NONE will catch typo’s and other undeclared
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Example of Science Process Class-driver

variable errors at compile time.

( 4) - Domain array dimensioning and looping global variables, e.g. NCOLS, NROWS, NLAYS.

( 5) - Chemical mechanism array dimensioning and looping global variables.

( 6) - C Preprocessor flags that determine which emissions control dimensioning and looping

variables are compiled.

( 7) - Other global array dimensioning and looping global variables including those for the I/O

API. The logical variable LIPR is defined in the SUBST_PACTL_ID include file for use at lines

labeled (16).

( 8) - Declarations for the argument list (standardized).

( 9) - Declarations and PARAMETER statements for local Fortran parameters.

(10) - Declarations for external functions not previously declared.

(11) - Declarations for arrays to hold external file data.

(12) - Declarations for local variables.

(13) - Code section for subroutine initialization and for any local data that need not be set at

every entry into the subroutine. Such data would require a SAVE statement in the declarations.

For example FIRSTIME is initialized to .TRUE. in the local variables section (12).

(14) - Illustrates using an I/O API function to set file interpolation time.

(15) - Read accesses from I/O API files using the I/O API time-interpolation function.

(16) - Call to process analysis routine to obtain data for the optional integrated process rates

function.

(17) - Illustrates call to another science process within the module.

(18) - Main computational loop over the horizontal grid.

(19) - Time step loop over sub-synchronization time step intervals.

(20) - Illustrates writing to an I/O API file within a module.

(21) - Subroutine end

18.8.4 Robustness and Computational Efficiency

Scientists, while working in their discipline, are generally not interested in the physical situations

that don’t significantly affect the phenomena they are studying and modeling. Typically, the

scientist works with box models, and uses specialized data to test hypotheses, parameterizations

and numerical schemes. The focus is to generate new results based on output from these

relatively simple models. In trying to integrate these codes into a more general grid model,

problems may arise when modeling simulations carry their formulations into regimes not

explored in initial studies, therefore not properly accounted for in the grid model. The scientist

who is developing codes that may go into a grid model should be cognizant of these issues and

should make every effort to make the codes robust.

Another issue is code efficiency. In order to handle the pathological situations, codes like these

may become inefficient, spending many cycles dealing with the “off-problem” cases. A good

example is solving for the roots of a cubic polynomial whose coefficients, depending closely on

the locally modeled physics, may range over broad values. So, in addition to robustness,

attention should be paid to code performance. As the science improves in environmental

modeling, this usually translates into increased computational complexity. Although hardware

performance is continually improving, it cannot keep pace with the computational demands of

new science developments. Not typically the main interest of the science developer, software

performance is nevertheless a critical issue and must be addressed. Otherwise scientifically

sound models will not be of much general use if they take an inordinate amount of time to

execute.
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18.9 Conclusion

The CMAQ system has been designed and implemented in such a way that its integration into

Models-3 allows access to the extensive functionality of the Models-3 framework. Users can

easily select important model options and can readily develop and execute models that apply to

their requirements.

We have integrated the CMAQ codes into the Models-3 system by following the basic set of

guidelines and rules presented in this chapter.

18.10 References

[1] http://interactivate.com/public/cvswebsites/cvs_toc.html, http://www.cyclic.com/cvs/, and

the UNIX man pages

[2] http://www.cs.cmu.edu/People/vaschelp/Archiving/Rcs/, and the UNIX man pages

[3] Fine, S. S., W. T. Smith, D. Hwang, T. L. Turner, 1998: Improving model development

with configuration management, IEEE Computational Science and Engineering, 5(1, Ja-Mr), 56-

65. and http://envpro.ncsc.org/pub_files/fine1998b.html

[4] http://sage.mcnc.org/products/ioapi/

[5] ftp://ftp.unidata.ucar.edu/pub/netcdf/

[6] EPA Third-Generation Air Quality Modeling System, Models-3 Volume 9b, User Manual,

Appendices, June 1998, EPA-600/R-98/069(b)

[7] J. Rumbaugh, M. Blaha, W. Premerlani, F. Eddy, and W. Lorensen, 1991: Object-Oriented

Modeling and Design, Prentice Hall

[8] Grell, G. A., J. Dudhia and D. R. Stauffer, 1994: A description of the fifth-generation Penn

State/NCAR mesoscale model (MM5). NCAR Technical Note, NCAR/TN-398+STR, 122 pp.

This chapter is taken from Science Algorithms of the EPA Models-3 Community

Multiscale Air Quality (CMAQ) Modeling System, edited by D. W. Byun and J. K. S.

Ching, 1999.