United States

Environmental Protection

Agency

Air and Radiation EPA420-R-02-027

October 2002

Methodology for Developing

Modal Emission Rates for

EPA’s Multi-Scale Motor

Vehicle and Equipment

Emission System

 Printed on Recycled Paper
EPA420-R-02-027

October 2002

Methodology for Developing Modal Emission Rates for

EPA’s Multi-Scale Motor Vehicle and

Equipment Emission System

Assessment and Standards Division

Office of Transportation and Air Quality

U.S. Environmental Protection Agency

Prepared for EPA by

Computational Laboratory for Energy, Air, and Risk

Department of Civil Engineering

North Carolina State University

Raleigh, NC

EPA Contract No. PR-CI-02-10493

NOTICE

This technical report does not necessarily represent final EPA decisions or positions.

It is intended to present technical analysis of issues using data that are currently available.

The purpose in the release of such reports is to facilitate the exchange of

technical information and to inform the public of technical developments which

may form the basis for a final EPA decision, position, or regulatory action.
i

TABLE OF CONTENTS

1 INTRODUCTION................................................................................................................... 1

1.1 Objectives of this Project ................................................................................................. 3

1.2 General Technical Approach............................................................................................ 4

1.3 Organization of this Report.............................................................................................. 5

2 DEVELOPMENT OF ANALYSIS DATASET.................................................................... 7

2.1 Development of a Combined Database............................................................................ 7

2.2 Organization of the Data for Analysis.............................................................................. 9

2.3 Summary ........................................................................................................................ 10

3 DEVELOPMENT OF A MODAL EMISSIONS MODELING APPROACH ................ 11

3.1 Statistical Method for Developing Binning Criteria ...................................................... 11

3.2 Development of the VSP-Based Modal Approach ........................................................ 15

3.2.1 Exploratory Analysis.......................................................................................... 15

3.2.2 Considerations in Refinement of the VSP-Based Modal Approach .................. 21

3.2.3 Comparison of Modeling and IM240 Datasets .................................................. 30

3.3 NCSU Modal Approach: Idle, Acceleration, Deceleration, and Cruise........................ 38

3.4 Selection of a Binning Method....................................................................................... 53

4 SELECTION OF AN AVERAGING TIME FOR MODEL DEVELOPMENT............. 55

4.1 Methodological Approach.............................................................................................. 55

4.2 Results for Five and Ten Second Averaging Times....................................................... 55

4.3 Evaluation of Different Averaging Times and Recommendations ................................ 63

5 COMPARISON OF EMISSION FACTOR APPROACHES AND

EVALUATION OF THE ROLE OF REMOTE SENSING DATA ................................. 65

5.1 Background Regarding Emission Factor Units.............................................................. 65

5.2 Background Regarding Remote Sensing Data............................................................... 66

5.3 Comparison of Emission Factors and Emission Ratios Based Upon the NCSU

Modal Approach............................................................................................................. 68

5.4 Comparison of Emission Factors and Emission Ratios Based Upon the VSP

Modal Approach............................................................................................................. 71

5.5 Comparison of Variability in Emission Ratios for Selected VSP Bins for the

Modeling and RSD Data Sets......................................................................................... 75

5.6 Comparison of Vehicle Activity in the RSD and Modeling Databases ......................... 77

5.7 Comparison of Emissions Ratios and Vehicle Activity Between the RSD and

IM240 Databases............................................................................................................ 82

5.8 Summary and Recommendations................................................................................... 88

6 COMPARISON AND EVALUATION OF DATA WEIGHTING

APPROACHES ..................................................................................................................... 91

6.1 Methodological Considerations...................................................................................... 91

6.2 Comparison of Weighting Approaches.......................................................................... 92

6.3 Summary and Recommendation .................................................................................. 114
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7 QUANTIFICATION OF VARIABILITY AND UNCERTAINTY................................ 115

7.1 Methodological Considerations.................................................................................... 115

7.1.1 Variability and Uncertainty.............................................................................. 116

7.1.2 Empirical Distributions .................................................................................... 116

7.1.3 Parametric Distributions................................................................................... 117

7.1.4 Averaging Time................................................................................................ 117

7.1.5 Normal and High Emitters ............................................................................... 118

7.1.6 Uncertainty Estimates for Final Model Results ............................................... 119

7.1.7 Bottom-Up and Top-Down Approaches .......................................................... 121

7.1.8 Summary of Methodological Considerations................................................... 121

7.2 Quantification of Variability ........................................................................................ 121

7.3 Quantification of Uncertainty in Mean Emission Rates............................................... 145

7.4 Uncertainty Correction Factor for Averaging Time..................................................... 156

7.5 Estimation of Uncertainty in Model Results................................................................ 167

7.5.1 Estimation of Uncertainty in Total Emissions Based Upon the IM240

Driving Cycle: Comparison of Monte Carlo Simulation and Analytical

Approaches....................................................................................................... 167

7.5.2 Estimation of Uncertainty in Total Emissions of Selected Driving Cycles ..... 172

7.5.3 Estimation of Uncertainty in Total Emissions for Different Numbers of

Vehicles............................................................................................................ 176

7.6 Summary and Recommendations................................................................................. 176

8 FEASIBILITY OF ESTIMATING MODAL EMISSIONS FROM

AGGREGATE BAG DATA............................................................................................... 183

8.1 Methodological Overview............................................................................................ 183

8.2 Bag-Based Modal Emissions Estimation for Four Modes (Idle, Acceleration,

Cruise, Deceleration) and for 14 VSP Modes.............................................................. 184

8.3 Bag-Based Modal Emissions Estimation for the "56-bin" VSP-based Approach ....... 195

8.4 Characterization of Uncertainty in Predicted Modal Emissions .................................. 211

8.5 Summary and Conclusions........................................................................................... 214

9 VALIDATION OF THE CONCEPTUAL MODEL........................................................ 217

9.1 Validation Case Study 1............................................................................................... 217

9.2 Validation Case Study 2............................................................................................... 222

9.3 Validation Case Study 3............................................................................................... 227

9.4 Preliminary Exploration of Refinements to the Modal Modeling Approach............... 233

9.5 Summary and Recommendations................................................................................. 234

10 RECOMMENDATIONS FOR METHODOLOGY FOR MODAL MODEL

DEVELOPMENT................................................................................................................ 235

11 REFERENCES.................................................................................................................... 241

12 APPENDIX A ...................................................................................................................... 244
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LIST OF FIGURES

Figure 1-1. Simplified Schematic of Project Tasks and Their Inter-Relationships...................... 4

FIGURE 3-1. AVERAGE MODAL EMISSION RATES FOR LDGVS (SOURCE: FREY ET AL., 2002) ........................ 13

FIGURE 3-2. SAMPLE REGRESSION TREE DIAGRAM (NUMBERS REPRESENT NODE NUMBERS OF THE TREE)........ 14

FIGURE 3-3. EXAMPLE OF AVERAGE DISTRIBUTION OF TIME AND EMISSIONS WITH RESPECT TO MODES

(SOURCE: FREY ET AL., 2002).......................................................................................... 15

FIGURE 3-4. EXPLORATORY ANALYSIS OF AVERAGE EMISSIONS OF CO2, NOX, HC, AND CO VERSUS

VEHICLE SPECIFIC POWER (VSP) BASED UPON THE MODELING DATABASE. .............................. 16

FIGURE 3-5. EXAMPLE OF UNSUPERVISED HTBR TREE RESULTS FOR THE MODELING DATA SET FOR

NOX EMISSIONS (G/SEC) ................................................................................................. 19

FIGURE 3-6. AVERAGE MODAL EMISSION RATES (G/SEC) FOR VSP BINS FOR CO, HC, CO2, AND NOX

BASED UPON THE MODELING DATASET.............................................................................. 20

FIGURE 3-7. PERCENT OF TIME SPENT IN VSP MODES AND PERCENTAGE OF TOTAL CO, NOX, CO2, AND

HC EMISSIONS ATTRIBUTABLE TO EACH VSP MODE, BASED UPON THE MODELING DATA

SET............................................................................................................................. 22

FIGURE 3-8. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES FOR 14 VSP

BINS FOR VEHICLES WITH NET WEIGHT < 4,000 LB TO VEHICLES WITH NET WEIGHT > 4,000

LB............................................................................................................................... 26

FIGURE 3-9. COMAPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES FOR 14

VSP BINS FOR VEHICLES WITH ENGINE DISPLACEMENT < 3.5 LITERS TO VEHICLES WITH

ENGINE DISPLACEMENT > 3.5 LITERS................................................................................. 27

FIGURE 3-10. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES FOR 14 VSP

BINS STRATIFIED BY ENGINE DISPLACEMENT AND ODOMETER READING................................... 28

FIGURE 3-11. SAMPLE SIZES FOR EACH VSP MODE FOR EACH ODOMETER READING AND ENGINE

DISPLACEMENT STRATA.................................................................................................. 29

FIGURE 3-12. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES BASED

UPON THE MODELING DATA VERSUS IM240 DATA FOR 14 VSP BINS FOR NET VEHICLE

WEIGHT < 4,000 LB........................................................................................................ 31

FIGURE 3-13. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES BASED

UPON THE MODELING DATA VERSUS IM240 DATA FOR 14 VSP BINS FOR NET VEHICLE

WEIGHT > 4,000 LB........................................................................................................ 33

FIGURE 3-14. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES FOR ENGINE

DISPLACEMENT < 3.5 LITERS AND ODOMETER READING < 50,000 MILES FOR EPA

DYNAMOMETER, EPA ON-BOARD, NCHRP, AND IM240 DATABASES....................................... 34

FIGURE 3-15. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES FOR ENGINE

DISPLACEMENT > 3.5 LITERS AND ODOMETER READING < 50,000 MILES FOR EPA

DYNAMOMETER, EPA ON-BOARD, NCHRP, AND IM240 DATABASES....................................... 35

FIGURE 3-16. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES FOR ENGINE

DISPLACEMENT < 3.5 LITERS AND ODOMETER READING > 50,000 MILES FOR EPA

DYNAMOMETER AND NCHRP DATABASES.......................................................................... 36

FIGURE 3-17. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOX EMISSIONS RATES FOR ENGINE

DISPLACEMENT > 3.5 LITERS AND ODOMETER READING > 50,000 MILES FOR IM240 AND

NCHRP DATABASES...................................................................................................... 37
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FIGURE 3-18. UNSUPERVISED HBTR RESULTS FOR NCSU ACCELERATION MODE FOR NOX EMISSIONS

(G/SEC). ....................................................................................................................... 39

FIGURE 3-19. UNSUPERVISED HBTR RESULTS FOR NCSU CRUISE MODE FOR NOX EMISSIONS (G/SEC)............. 39

FIGURE 3-20. PERCENT OF TIME SPENT IN NCSU MODES AND PERCENTAGE OF TOTAL CO, NOX, CO2,

AND HC EMISSIONS ATTRIBUTABLE TO EACH NCSU MODE, BASED UPON THE MODELING

DATA SET. ................................................................................................................... 42

FIGURE 3-21. AVERAGE MODAL EMISSION RATES (G/SEC) FOR NCSU MODES FOR CO, HC, CO2, AND

NOX BASED UPON THE MODELING DATASET ...................................................................... 43

FIGURE 3-22. SAMPLE SIZES FOR EACH NCSU MODE FOR EACH ODOMETER READING AND ENGINE

DISPLACEMENT STRATA.................................................................................................. 44

FIGURE 3-23. AVERAGE CO EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,

AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE

MODELING DATABASE.................................................................................................... 49

FIGURE 3-24. AVERAGE HC EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,

AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE

MODELING DATABASE.................................................................................................... 50

FIGURE 3-25. AVERAGE NOX EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,

AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE

MODELING DATABASE.................................................................................................... 51

FIGURE 3-26. AVERAGE CO2 EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,

AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE

MODELING DATABASE.................................................................................................... 52

FIGURE 3-27. COMPARISON OF VSP AND NCSU APPROACH-BASED PREDICTIONS OF AVERAGE EMISSIONS

OF CO2, CO, HC, AND NOX FOR SELECTED DRIVING CYCLES FOR VEHICLES IN THE

MODELING DATABASE.................................................................................................... 54

FIGURE 4-1. PERCENT OF TIME SPENT IN FIVE SECOND AVERAGING TIME MAXIMUM VSP-BASED MODES

AND PERCENTAGE OF TOTAL CO, NOX, CO2, AND HC EMISSIONS ATTRIBUTABLE TO EACH

MODE, BASED UPON THE MODELING DATA SET................................................................... 58

FIGURE 4-2. FIVE SECOND AVERAGING TIME MODAL EMISSION RATES (G/SEC) FOR MAXIMUM VSP BINS

FOR CO, HC, CO2, AND NOX BASED UPON THE MODELING DATASET...................................... 59

FIGURE 4-3. PERCENT OF TIME SPENT IN TEN SECOND AVERAGING TIME MAXIMUM VSP-BASED MODES

AND PERCENTAGE OF TOTAL CO, NOX, CO2, AND HC EMISSIONS ATTRIBUTABLE TO EACH

MODE, BASED UPON THE MODELING DATA SET................................................................... 60

FIGURE 4-4. TEN SECOND AVERAGING TIME MODAL EMISSION RATES (G/SEC) FOR MAXIMUM VSP BINS

FOR CO, HC, CO2, AND NOX BASED UPON THE MODELING DATASET...................................... 61

FIGURE 4-5. COMPARISON OF SAMPLE SIZES FOR 1 SECOND, 5 SECOND, AND 10 SECOND AVERAGING

TIME-BASED MODES ESTIMATED FROM THE MODELING DATA SET.......................................... 62

FIGURE 4-6. COMPARISON OF PREDICTED AVERAGE EMISSIONS OF CO2, CO, HC, AND NOX FOR

SELECTED DRIVING CYCLES BASED UPON 1 SECOND, 5 SECOND, AND 10 SECOND

AVERAGING TIME VSP BINNING APPROACHES FOR THE MODELING DATABASE.......................... 64

FIGURE 5-1. AVERAGE MODAL RATES FOR ABSOLUTE AND NORMALIZED NO EMISSIONS FOR A 1999

FORD TAURUS DRIVEN ON CHAPEL HILL ROAD IN CARY, NC (SOURCE: NCSU)........................ 66

FIGURE 5-2. AVERAGE MODAL RATES FOR ABSOLUTE FUEL CONSUMPTION FOR 1999 FORD TAURUS

DRIVEN ON CHAPEL HILL ROAD (SOURCE: NCSU) .............................................................. 68
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FIGURE 5-3. AVERAGE MODAL EMISSION RATIOS FOR CO/CO2, HC/CO2, AND NOX/CO2 BASED UPON

NCSU MODES FOR THE MODELING DATA AND REMOTE SENSING DATA ................................... 69

FIGURE 5-4. AVERAGE MODAL EMISSION RATIOS FOR CO/CO2, HC/CO2, AND NOX/CO2 BASED UPON

VSP MODES FOR THE MODELING DATA AND REMOTE SENSING DATA FOR VEHICLES WITH

ENGINE DISPLACEMENT OF LESS THAN 3.5 LITERS................................................................ 72

FIGURE 5-5. AVERAGE MODAL EMISSION RATIOS FOR CO/CO2, HC/CO2, AND NOX/CO2 BASED UPON

VSP BINS FOR THE MODELING DATA AND REMOTE SENSING DATA FOR VEHICLES WITH

ENGINE DISPLACEMENT OF GREATER THAN 3.5 LITERS ......................................................... 73

FIGURE 5-6. COMPARISON OF VARIABILITY FOR CO/CO2, HC/CO2, AND NOX/CO2 RATIOS FOR

MODELING DATA AND REMOTE SENSING DATA FOR VSP MODE 1 WITH ENGINE SIZE LESS

THAN 3.5 LITERS ........................................................................................................... 75

FIGURE 5-7. COMPARISON OF VARIABILITY FOR CO/CO2, HC/CO2, AND NOX/CO2 RATIOS FOR

MODELING DATA AND REMOTE SENSING DATA FOR VSP MODE 7 WITH ENGINE SIZE LESS

THAN 3.5 LITERS ........................................................................................................... 76

FIGURE 5-8. COMPARISON OF VARIABILITY FOR CO/CO2, HC/CO2, AND NOX/CO2 RATIOS FOR

MODELING DATA AND REMOTE SENSING DATA FOR VSP MODE 12 WITH ENGINE SIZE LESS

THAN 3.5 LITERS ........................................................................................................... 77

FIGURE 5-9. COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE

REMOTE SENSING AND MODELING DATA SETS, FOR VSP MODE 1 FOR VEHICLES WITH

ENGINE DISPLACEMENT LESS THAN 3.5 LITERS.................................................................... 79

FIGURE 5-10. COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE

REMOTE SENSING AND MODELING DATA SETS, FOR VSP MODE 7 FOR VEHICLES WITH

ENGINE DISPLACEMENT LESS THAN 3.5 LITERS. .................................................................. 80

FIGURE 5-11. COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE

REMOTE SENSING AND MODELING DATA SETS, FOR VSP MODE 12 FOR VEHICLES WITH

ENGINE DISPLACEMENT LESS THAN 3.5 LITERS. .................................................................. 81

FIGURE 5-12. AVERAGE MODAL CO/CO2, HC/CO2, AND NOX/CO2 EMISSION RATIOS BASED UPON VSP

BINS FOR THE MODELING DATA AND IM240 DRIVING CYCLE DATA FOR VEHICLES WITH

ENGINE DISPLACEMENT OF LESS THAN 3.5 LITERS. .............................................................. 83

FIGURE 5-13. AVERAGE MODAL CO/CO2, HC/CO2, AND NOX/CO2 EMISSION RATIOS BASED UPON VSP

BINS FOR THE MODELING DATA AND IM240 DRIVING CYCLE DATA FOR VEHICLES WITH

ENGINE DISPLACEMENT OF GREATER THAN 3.5 LITERS. ........................................................ 84

FIGURE 5-14. COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE

REMOTE SENSING AND IM240 DRIVING CYCLE DATA SETS, FOR VSP MODE 1 FOR

VEHICLES WITH ENGINE DISPLACEMENT LESS THAN 3.5 LITERS.............................................. 85

FIGURE 5-15. COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE

REMOTE SENSING AND IM240 DRIVING CYCLE DATA SETS, FOR VSP MODE 7 FOR

VEHICLES WITH ENGINE DISPLACEMENT LESS THAN 3.5 LITERS.............................................. 86

FIGURE 5-16. COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE

REMOTE SENSING AND IM240 DRIVING CYCLE DATA SETS, FOR VSP MODE 12 FOR

VEHICLES WITH ENGINE DISPLACEMENT LESS THAN 3.5 LITERS.............................................. 87

FIGURE 6-1. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #1

CHARACTERIZED BY EMPIRICAL AND FITTED PARAMETRIC PROBABILITY DISTRIBUTION

MODELS FOR SECOND-BY-SECOND DATA. .......................................................................... 94
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FIGURE 6-2. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #7

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR SECOND-BY-SECOND DATA. ................................................ 95

FIGURE 6-3. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #14

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR SECOND-BY-SECOND DATA. ................................................ 96

FIGURE 6-4. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #1

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR TRIP AVERAGE MEANS....................................................... 97

FIGURE 6-5. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #7

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR TRIP AVERAGE MEANS. ...................................................... 98

FIGURE 6-6. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #14

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR TRIP AVERAGE MEANS. ...................................................... 99

FIGURE 6-7. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #1

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR VEHICLE AVERAGE MEANS. .............................................. 100

FIGURE 6-8. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #7

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR VEHICLE AVERAGE MEANS. .............................................. 101

FIGURE 6-9. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #14

CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC

PROBABILITY DISTRIBUTION FOR VEHICLE AVERAGE MEANS. .............................................. 102

FIGURE 6-10. COMPARISON OF VARIABILITY IN NOX EMISSIONS FOR TIME-AVERAGE, TRIP-AVERAGE,

AND VEHICLE-AVERAGE APPROACHES, CHARACTERIZED BY PARAMETRIC PROBABILITY

DISTRIBUTIONS, FOR VSP MODES #1, #7 AND #14.............................................................. 105

FIGURE 6-11. COMPARISON OF VARIABILITY IN HC EMISSIONS FOR TIME-AVERAGE, TRIP-AVERAGE, AND

VEHICLE-AVERAGE APPROACHES, CHARACTERIZED BY PARAMETRIC PROBABILITY

DISTRIBUTIONS, FOR VSP MODES #1, #7 AND #14.............................................................. 106

FIGURE 6-12. COMPARISON OF QUANTIFIED UNCERTAINTY IN THE MEAN EMISSIONS OF NOX, HC, CO2,

AND CO FOR VSP BINS: TIME-AVERAGE, TRIP-AVERAGE, AND VEHICLE-AVERAGE

APPROACHES. ............................................................................................................. 113

FIGURE 7-1. EXAMPLE OF A STEPWISE EMPIRICAL CUMULATIVE DISTRIBUTION FUNCTION.......................... 116

FIGURE 7-1. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS FOR VSP MODE #1 CHARACTERIZED

BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY

DISTRIBUTION, TIME AVERAGE, ODOMETER READING < 50,000 MILES, ENGINE

DISPLACEMENT < 3.5 LITERS.......................................................................................... 123

FIGURE 7-2. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS FOR VSP MODE #4 CHARACTERIZED

BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY

DISTRIBUTION, TIME AVERAGE, ODOMETER READING < 50,000 MILES, ENGINE

DISPLACEMENT > 3.5 LITERS.......................................................................................... 124

FIGURE 7-3. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS FOR VSP MODE #8 CHARACTERIZED

BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY

DISTRIBUTION, TIME AVERAGE, ODOMETER READING > 50,000 MILES, ENGINE

DISPLACEMENT < 3.5 LITERS.......................................................................................... 125
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FIGURE 7-4. VARIABILITY IN NOX, HC, CO2, AND CO EMISSIONS FOR VSP MODE #12 CHARACTERIZED

BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY

DISTRIBUTION, TIME AVERAGE, ODOMETER READING > 50,000 MILES, ENGINE

DISPLACEMENT > 3.5 LITERS.......................................................................................... 126

FIGURE 7-5. COMPARISON OF FITTED PARAMETRIC DISTRIBUTION BASED UPON METHOD OF MATCHING

MOMENT AND MAXIMUM LIKELIHOOD ESTIMATION, MODE 14 CO EMISSIONS, ODOMETER

READING < 50,000 MILES, ENGINE DISPLACEMENT < 3.5 LITERS............................................ 138

FIGURE 7-6. COMPARISON OF FITTED PARAMETRIC DISTRIBUTION BASED UPON METHOD OF MATCHING

MOMENT AND MAXIMUM LIKELIHOOD ESTIMATION, MODE 13 CO EMISSIONS, ODOMETER

READING < 50,000 MILES, ENGINE DISPLACEMENT < 3.5 LITERS............................................ 138

FIGURE 7-7. MIXTURE DISTRIBUTION COMPRISED OF TWO LOGNORMAL COMPONENTS FITTED TO DATA

FOR MODE 14 CO EMISSIONS FOR ODOMETER READING < 50,000 MILES AND ENGINE

DISPLACEMENT < 3.5 LITERS. ........................................................................................ 139

FIGURE 7-8. MIXTURE DISTRIBUTION COMPRISED OF TWO LOGNORMAL COMPONENTS FITTED TO DATA

FOR MODE 13 CO EMISSIONS FOR ODOMETER READING < 50,000 MILES AND ENGINE

DISPLACEMENT < 3.5 LITERS. ........................................................................................ 139

FIGURE 7-9. QUANTIFIED UNCERTAINTY IN THE NOX AND HC MEAN EMISSIONS (G/SEC) OF VSP MODES. ..... 147

FIGURE 7-10. QUANTIFIED UNCERTAINTY IN THE CO2 AND CO MEAN EMISSIONS (G/SEC) OF VSP MODES ...... 148

FIGURE 7-11. EMPIRICAL DISTRIBUTION OF BOOTSTRAP REPLICATIONS OF MEAN VALUES AND FITTED

BETA DISTRIBUTION FOR UNCERTAINTY IN THE MEAN FOR NOX EMISSIONS (G/SEC) OF

MODE 12, ODOMETER READING < 50,000 MILES, ENGINE DISPLACEMENT > 3.5 LITERS............. 155

FIGURE 7-12. ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN

(SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10 SECONDS FOR NOX, HC, CO2,

AND CO EMISSIONS (G/SEC) FOR ODOMETER READING < 50,000 MILES AND ENGINE

DISPLACEMENT < 3.5 LITERS. ........................................................................................ 157

FIGURE 7-13. ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN

(SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10 SECONDS FOR NOX, HC, CO2,

AND CO EMISSIONS (G/SEC) FOR ODOMETER READING < 50,000 MILES AND ENGINE

DISPLACEMENT > 3.5 LITERS. ........................................................................................ 158

FIGURE 7-14. ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN

(SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10 SECONDS FOR NOX, HC, CO2,

AND CO EMISSIONS (G/SEC) FOR ODOMETER READING > 50,000 MILES AND ENGINE

DISPLACEMENT < 3.5 LITERS. ........................................................................................ 159

FIGURE 7-15. ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN

(SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10 SECONDS FOR NOX, HC, CO2,

AND CO EMISSIONS (G/SEC) FOR ODOMETER READING > 50,000 MILES AND ENGINE

DISPLACEMENT > 3.5 LITERS. ........................................................................................ 160

FIGURE 7-16. BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT “ 

SECONDS” OF NOX, HC, CO2, AND CO FOR ODOMETER READING < 50,000 MILES AND

ENGINE DISPLACEMENT < 3.5 LITERS. ............................................................................. 163

FIGURE 7-17. BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT “ 

SECONDS” OF NOX, HC, CO2, AND CO FOR ODOMETER READING < 50,000 MILES AND

ENGINE DISPLACEMENT > 3.5 LITERS. ............................................................................. 164

FIGURE 7-18. BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT “ 

SECONDS” OF NOX, HC, CO2, AND CO FOR ODOMETER READING > 50,000 MILES AND

ENGINE DISPLACEMENT < 3.5 LITERS. ............................................................................. 165
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FIGURE 7-19. BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT “ 

SECONDS” OF NOX, HC, CO2, AND CO FOR ODOMETER READING >50,000 MILES AND

ENGINE DISPLACEMENT > 3.5 LITERS. ............................................................................. 166

FIGURE 7-20. QUANTIFIED UNCERTAINTY IN TOTAL NOX EMISSIONS FROM THE IM240 CYCLE FOR

VEHICLES WITH ODOMETER READING < 50,000 MILES AND ENGINE DISPLACEMENT < 3.5

LITERS BASED UPON MONTE CARLO SIMULATION. ............................................................. 171

FIGURE 7-21. QUANTIFICATION OF UNCERTAINTY BASED UPON MONTE CARLO SIMULATION FOR TOTAL

NOX EMISSION FROM 13 VEHICLES TESTED ON THE ART-EF CYCLE. .................................... 177

FIGURE 8-1. PREDICTED VERSUS OBSERVED NOX NCSU MODAL EMISSION RATES ESTIMATED FROM

NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH. ............................................... 188

FIGURE 8-2. PREDICTED VERSUS OBSERVED HC NCSU MODAL EMISSION RATES ESTIMATED FROM

NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH. ............................................... 188

FIGURE 8-3. PREDICTED VERSUS OBSERVED CO NCSU MODAL EMISSION RATES ESTIMATED FROM

NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH. ............................................... 189

FIGURE 8-4. PREDICTED VERSUS OBSERVED CO2 NCSU MODAL EMISSION RATES ESTIMATED FROM

NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH. ............................................... 189

FIGURE 8-5. PREDICTED VERSUS OBSERVED NOX MODAL EMISSION RATES BASED UPON THE 14 MODE

VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS

APPROACH. ................................................................................................................ 193

FIGURE 8-6. PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES BASED UPON THE 14 MODE

VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS

APPROACH. ................................................................................................................ 193

FIGURE 8-7. PREDICTED VERSUS OBSERVED CO MODAL EMISSION RATES BASED UPON THE 14 MODE

VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS

APPROACH. ................................................................................................................ 194

FIGURE 8-8. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES BASED UPON THE 14 MODE

VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS

APPROACH. ................................................................................................................ 194

FIGURE 8-9. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

MODELING DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 204

FIGURE 8-10. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 204

FIGURE 8-11. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 205

FIGURE 8-12. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 205

FIGURE 8-13. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
ix

MODELING DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 206

FIGURE 8-14. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 206

FIGURE 8-15. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 207

FIGURE 8-16. PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 207

FIGURE 8-17. PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 208

FIGURE 8-18. PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 208

FIGURE 8-19. PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 209

FIGURE 8-20. PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 209

FIGURE 8-21. PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 210

FIGURE 8-22. PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES

ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE

NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 210

FIGURE 9-1. COMPARISON OF OBSERVED AND PREDICTED AVERAGE TOTAL EMISSIONS OF CO2, CO, HC,

AND NOX FOR THREE DRIVING CYCLES AND FOR ON-BOARD DATA FOR VALIDATION

DATASET I.................................................................................................................. 219

FIGURE 9-2. COMPARISON OF OBSERVED AND PREDICTED AVERAGE TOTAL EMISSIONS OF CO2, CO, HC,

AND NOX FOR THE FTP75 AND US06 DRIVING CYCLES AND FOR ON-BOARD

MEASUREMENTS FOR VALIDATION DATASET II.................................................................. 224

FIGURE 9-3. COMPARISON OF OBSERVED AND PREDICTED AVERAGE TOTAL EMISSIONS OF CO2, CO, HC,

AND NOX FOR EIGHT UCC DRIVING CYCLES FOR VALIDATION DATASET III............................ 229
x

FIGURE A-1. RELATIONSHIP BETWEEN AIR CONDITION USE AND EMISSIONS ............................................. 244

FIGURE A-2. RELATIONSHIP BETWEEN RELATIVE HUMIDITY AND EMISSIONS............................................. 245

FIGURE A-3. RELATIONSHIP BETWEEN AMBIENT TEMPERATURE AND EMISSIONS........................................ 246

FIGURE A-4. COMPARISON OF VARIABILITY FOR MODELING DATA AND REMOTE SENSING DATA FOR VSP

MODE 7 WITH ENGINE SIZE LESS THAN 3.5 LITERS AND MODEL YEAR AT 1996........................ 247

FIGURE A-5. AVERAGE MODAL EMISSION RATES FOR VEHICLES WITH ODOMETER READINGS LESS THAN

50,000 MILES BASED UPON VSP BINS ............................................................................. 248

FIGURE A-6. AVERAGE MODAL EMISSION RATES FOR VEHICLES WITH ODOMETER READINGS GREATER

THAN 50,000 MILES BASED UPON VSP BINS ..................................................................... 249

FIGURE A-7. EVALUATION OF AVERAGE CO EMISSION RATES FOR 14 VSP BINS WITH RESPECT TO

ACCELERATION (LEFT PANEL) AND SPEED (RIGHT PANEL). ................................................... 250

FIGURE A-8. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT < 3.5 LITER

AND ODOMETER READING < 50K MILES FOR TWO DIFFERENT SPEED STRATA.......................... 251

FIGURE A-9. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT > 3.5 LITER

AND ODOMETER READING < 50K MILES FOR TWO DIFFERENT SPEED STRATA.......................... 252

FIGURE A-10. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT < 3.5 LITER

AND ODOMETER READING > 50K MILES FOR TWO DIFFERENT SPEED STRATA.......................... 253

FIGURE A-11. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT > 3.5 LITER

AND ODOMETER READING > 50K MILES FOR TWO DIFFERENT SPEED STRATA.......................... 254
xi

LIST OF TABLES

Table 3-1. Definitions for VSP Modes...................................................................................... 18

TABLE 3-2. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR CO FOR EACH OF 14 VSP MODES .......... 23

TABLE 3-3. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR CO2 FOR EACH OF 14 VSP MODES......... 23

TABLE 3-4. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR HC FOR EACH OF 14 VSP MODES .......... 24

TABLE 3-5. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR NOX FOR EACH OF 14 VSP MODES ........ 24

TABLE 3-6. DEFINITION OF NCSU DRIVING MODES ............................................................................. 40

TABLE 3-7. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR CO EMISSIONS BASED UPON THE

NCSU MODAL APPROACH............................................................................................... 46

TABLE 3-8. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR NOX EMISSIONS BASED UPON THE

NCSU MODAL APPROACH............................................................................................... 46

TABLE 3-9. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR HC EMISSIONS BASED UPON THE

NCSU MODAL APPROACH............................................................................................... 47

TABLE 3-10. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR CO2 EMISSIONS BASED UPON THE

NCSU MODAL APPROACH............................................................................................... 47

TABLE 4-1. KEY EXPLANATORY VARIABLES FOR CO, NOX, HC, AND CO2 EMISSIONS (G/SEC)

IDENTIFIED USING UNSUPERVISED HBTR FOR FIVE AND TEN SECOND-AVERAGED DATA............. 56

TABLE 4-2. MAXIMUM VSP-BASED MODE DEFINITIONS FOR FIVE SECOND-AVERAGED DATA...................... 57

TABLE 4-3. MAXIMUM VSP-BASED MODE DEFINITIONS FOR TEN SECOND-AVERAGED DATA....................... 57

TABLE 6-1. SUMMARY OF FITTED PARAMETRIC PROBABILITY DISTRIBUTIONS FOR VARIABILITY IN NOX,

HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP BINS FOR TRIP AVERAGE MEANS ................... 103

TABLE 6-2. SUMMARY OF FITTED PARAMETRIC PROBABILITY DISTRIBUTIONS FOR VARIABILITY IN NOX,

HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP BINS FOR VEHICLE AVERAGE MEANS.............. 104

TABLE 6-3. COMPARISON OF MEAN EMISSIONS OF NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR

VSP BINS: TIME-AVERAGE, TRIP-AVERAGE, AND VEHICLE-AVERAGE APPROACHES................ 108

TABLE 6-4. COMPARISON OF STANDARD DEVIATIONS OF VARIABILITY IN NOX, HC, CO2, AND CO

EMISSIONS (G/SEC) FOR VSP BINS: TIME-AVERAGE, TRIP-AVERAGE, AND VEHICLEAVERAGE APPROACHES. ............................................................................................... 109

TABLE 6-5. SUMMARY OF RELATIVE 95% CONFIDENCE INTERVALS FOR NOX, HC, CO2, AND CO MEAN

EMISSIONS FOR VSP BINS FOR THE TIME-AVERAGE APPROACH ............................................ 110

TABLE 6-6. SUMMARY OF RELATIVE 95% CONFIDENCE INTERVALS FOR NOX, HC, CO2, AND CO MEAN

EMISSIONS FOR VSP BINS FOR THE TRIP-AVERAGE APPROACH. ............................................ 111

TABLE 6-7. SUMMARY OF RELATIVE 95% CONFIDENCE INTERVALS FOR NOX, HC, CO2, AND CO MEAN

EMISSIONS FOR VSP BINS FOR THE VEHICLE-AVERAGE APPROACH ....................................... 112

TABLE 7-1. COMPARISON OF MEAN BETWEEN EMPIRICAL DATA SET AND FITTED PARAMETRIC

DISTRIBUTIONS, ABSOLUTE BASIS................................................................................... 128

TABLE 7-2. COMPARISON OF STANDARD DEVIATION BETWEEN EMPIRICAL DATA SET AND FITTED

PARAMETRIC DISTRIBUTIONS, ABSOLUTE BASIS ................................................................ 132
xii

TABLE 7-3. COMPARISONS OF EMPIRICAL DATA SET AND FITTED PARAMETRIC DISTRIBUTIONS,

AVERAGE DIFFERENCE FOR GOOD FITS, FITTING BASED UPON MLE ...................................... 136

TABLE 7-4. COMPARISONS OF EMPIRICAL DATA SET, FITTED LOGNORMAL DISTRIBUTIONS BASED UPON

MLE, AND FITTED LOGNORMAL DISTRIBUTIONS BASED UPON MOMM, FOR THE TWO

WORST MLE FITS FOR CO............................................................................................. 136

TABLE 7-5. RECOMMENDATION OF MIXTURE DISTRIBUTIONS FOR TWO WORST FITS ................................. 137

TABLE 7-6. SUMMARY OF SINGLE COMPONENT PARAMETRIC PROBABILITY DISTRIBUTIONS FITTED

USING MLE FOR VARIABILITY IN VSP MODES FOR NOX, HC, CO2, AND CO FOR VEHICLES

OF DIFFERENT ENGINE DISPLACEMENT AND ODOMETER READING. ........................................ 140

TABLE 7-7. VSP MODES FOR WHICH UNCERTAINTY IN THE MEAN WAS QUANTIFIED BY BOOTSTRAP

SIMULATION. .............................................................................................................. 145

TABLE 7-8. SUMMARY OF MEAN VALUES AND RELATIVE 95% CONFIDENCE INTERVALS IN THE MEAN

FOR NOX, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODES FOR VEHICLES OF

DIFFERENT ODOMETER READING AND ENGINE DISPLACEMENT. ............................................ 149

TABLE 7-9. PARAMETERS OF PARAMETRIC PROBABILITY DISTRIBUTION FIT TO THE BOOTSTRAP

REPLICATIONS OF THE MEANS FOR SELECTED MODES, STRATA, AND POLLUTANTS, BASED

UPON EMPIRICAL BOOTSTRAP SIMULATION....................................................................... 155

TABLE 7-10. AVERAGING TIME CORRECTION FACTORS FOR UNCERTAINTY IN VSP BINS FOR NOX, HC,

CO2, AND CO EMISSIONS (G/SEC) FOR FOUR STRATA WITH RESPECT TO ODOMETER

READING AND ENGINE DISPLACEMENT............................................................................. 162

TABLE 7-11. BIN ADJUSTMENT FACTORS FOR CORRECTION FACTOR OF TIME ADJUSTMENT AT “ 

SECONDS” FOR NOX, HC, CO2, AND CO AND FOR FOUR ODOMETER READING AND ENGINE

DISPLACEMENT STRATA................................................................................................ 168

TABLE 7-12. ALLOCATION OF THE STANDARD IM240 DRIVING CYCLE INTO VSP MODES WITH RESPECT

TO TIME SPENT IN EACH MODE....................................................................................... 168

TABLE 7-13. INPUT ASSUMPTIONS FOR PREDICTION OF UNCERTAINTY IN TOTAL NOX EMISSIONS FOR A

CAST STUDY OF THE IM240 CYCLE, FOR VEHICLES WITH ODOMETER READING < 50,000

MILES AND ENGINE DISPLACEMENT < 3.5 LITERS............................................................... 170

TABLE 7-14. EXAMPLE PREDICTION OF UNCERTAINTY IN TOTAL EMISSIONS FOR NOX EMISSIONS FROM

THE IM240 CYCLE FOR VEHICLES WITH ODOMETER READING < 50,000 MILES AND ENGINE

DISPLACEMENT < 3.5 LITERS BASED UPON MONTE CARLO SIMULATION ................................. 170

TABLE 7-15. ALLOCATION OF THE ART-EF, IM240, FTP (BAGS 2 AND 3) AND US06 DRIVING CYCLES

INTO VSP MODES WITH RESPECT TO TIME SPENT IN EACH MODE. ........................................ 172

TABLE 7-16. ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF

NOX, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER

1 VEHICLE STRATA FOR THE IM240 CYCLE....................................................................... 173

TABLE 7-17. ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF

NOX, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER

1 VEHICLE STRATA FOR THE ART-EF CYCLE. ................................................................... 173

TABLE 7-18. ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF

NOX, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER

1 VEHICLE STRATA FOR THE FTP (BAGS 2 AND 3) CYCLE. ................................................... 174

TABLE 7-19. ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF

NOX, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER

1 VEHICLE STRATA FOR THE US06 CYCLE. ....................................................................... 174
xiii

TABLE 7-20. ALLOCATION OF THE ACTUAL ART-EF DRIVING CYCLE SPEED TRACES INTO VSP MODES

WITH RESPECT TO TIME SPENT IN EACH MODE FOR 13 DIFFERENT VEHICLES .......................... 177

TABLE 8-1. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA

FOR FOUR NCSU DRIVING MODES FOR NOX: COMPARISON OF NO CONSTRAINT, BASIC

CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS. .......................................................... 187

TABLE 8-2. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA

FOR FOUR NCSU DRIVING MODES FOR HC: COMPARISON OF NO CONSTRAINT, BASIC

CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS. .......................................................... 187

TABLE 8-3. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA

FOR FOUR NCSU DRIVING MODES FOR CO: COMPARISON OF NO CONSTRAINT, BASIC

CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS. .......................................................... 187

TABLE 8-4. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (G/SEC) FROM AGGREGATE DATA FOR

FOUR NCSU DRIVING MODES FOR CO2: COMPARISON OF NO CONSTRAINT, BASIC

CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS. .......................................................... 187

TABLE 8-5. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA

FOR 14 VSP MODES FOR NOX: COMPARISON OF NO CONSTRAINT, BASIC CONSTRAINT,

AND STRICT CONSTRAINT SOLUTIONS. ............................................................................. 191

TABLE 8-6. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA

FOR 14 VSP MODES FOR HC: COMPARISON OF NO CONSTRAINT, BASIC CONSTRAINT, AND

STRICT CONSTRAINT SOLUTIONS..................................................................................... 191

TABLE 8-7. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA

FOR 14 VSP MODES FOR CO: COMPARISON OF NO CONSTRAINT, BASIC CONSTRAINT, AND

STRICT CONSTRAINT SOLUTIONS..................................................................................... 192

TABLE 8-8. RESULTS OF ESTIMATION OF MODAL EMISSION RATES (G/SEC) FROM AGGREGATE DATA FOR

14 VSP MODES FOR CO2: COMPARISON OF NO CONSTRAINT, BASIC CONSTRAINT, AND

STRICT CONSTRAINT SOLUTIONS..................................................................................... 192

TABLE 8-9. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER

READING < 50,000 MILES.............................................................................................. 196

TABLE 8-10. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER

READING < 50,000 MILES.............................................................................................. 196

TABLE 8-11. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER

READING > 50,000 MILES.............................................................................................. 197

TABLE 8-12. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER

READING > 50,000 MILES.............................................................................................. 197

TABLE 8-13. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 198
xiv

TABLE 8-14. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 198

TABLE 8-15. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 199

TABLE 8-16. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 199

TABLE 8-17. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: CO

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 200

TABLE 8-18. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: CO

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING <

50,000 MILES. ............................................................................................................ 200

TABLE 8-19. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: CO

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING

>50,000 MILES............................................................................................................ 201

TABLE 8-20. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: CO

EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING >

50,000 MILES. ............................................................................................................ 201

TABLE 8-21. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

NOX EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER

READING < 50,000 MILES.............................................................................................. 202

TABLE 8-22. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

NOX EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER

READING < 50,000 MILES.............................................................................................. 202

TABLE 8-23. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

NOX EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER

READING > 50,000 MILES.............................................................................................. 203

TABLE 8-24. COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT

CONSTRAINTS APPROACH FOR TWO DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:

NOX EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER

READING > 50,000 MILES.............................................................................................. 203
xv

TABLE 8-25. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE NOX

MODAL EMISSION RATES (MG/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE

VSP-BASED APPROACH. ............................................................................................... 212

TABLE 8-26. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE HC MODAL

EMISSION RATES (MG/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE VSPBASED APPROACH. ...................................................................................................... 212

TABLE 8-27. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE CO MODAL

EMISSION RATES (MG/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE VSPBASED APPROACH. ...................................................................................................... 213

TABLE 8-28. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE CO2 MODAL

EMISSION RATES (G/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE VSPBASED APPROACH. ...................................................................................................... 213

TABLE 9-1. SUMMARY OF VALIDATION DATASET I............................................................................. 218

TABLE 9-2. KEY CHARACTERISTICS OF THE ACTIVITY PATTERN OF THE ART-EF, FTP75 AND US06

CYCLES AND OF THE ON-BOARD MEASUREMENTS USED IN VALIDATION DATASET I.................. 218

TABLE 9-3. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET I FOR CO2.............................................................. 221

TABLE 9-4. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET I FOR CO ............................................................... 221

TABLE 9-5. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET I FOR HC ............................................................... 221

TABLE 9-6. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET I FOR NOX............................................................. 221

TABLE 9-7. SUMMARY OF DRIVING CYCLES, NUMBER OF VEHICLES, NUMBER OF TRIPS, AND SAMPLES

SIZE FOR VALIDATION DATASET II .................................................................................. 223

TABLE 9-8. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET II FOR CO2............................................................. 225

TABLE 9-9. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET II FOR CO .............................................................. 225

TABLE 9-10. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET II FOR HC .............................................................. 225

TABLE 9-11. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET II FOR NOX............................................................ 225

TABLE 9-12. SUMMARY OF DRIVING CYCLES, NUMBER OF VEHICLES, NUMBER OF TESTS, AND SAMPLE

SIZE FOR VALIDATION DATASET III................................................................................. 228

TABLE 9-13. KEY CHARACTERISTICS OF THE ACTIVITY PATTERNS OF THE DRIVING CYCLES IN

VALIDATION DATASET III.............................................................................................. 228

TABLE 9-14. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET III FOR CO2............................................................ 230

TABLE 9-15. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET III FOR CO ............................................................. 230

TABLE 9-16. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET III FOR HC ............................................................. 231
xvi

TABLE 9-17. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL

EMISSIONS FOR VALIDATION DATASET III FOR NOX........................................................... 231

TABLE A-1. CORRELATION AMONG PARAMETERS............................................................................... 255

TABLE A-2. SUMMARY OF VEHICLES IN VALIDATION DATASET  ........................................................... 255

TABLE A-3. SUMMARY OF VEHICLES IN VALIDATION DATASET .......................................................... 258

Table A-3. 	





..................................................... 259
1

1 INTRODUCTION

EPA is undertaking an effort to develop a new set of modeling tools for the estimation of

emissions produced by on-road and off-road mobile sources. The product of this effort will be

the Multi-scale mOtor Vehicle & equipment Emission System, referred to as MOVES. The

design of MOVES is guided by the following four considerations:

1) the model should encompass all pollutants (e.g., HC, CO, NOx, particulate matter, air

toxics, and greenhouse gases) and all mobile sources at the levels of resolution needed for

the diverse applications of the system;

2) the model should be developed according to principles of sound science;

3) the software design of the model should be efficient and flexible; and

4) the model should be implemented in a coordinated, clear, and consistent manner.

A critical element of MOVES is the use of data gathered using on-board emissions measurement

devices. To explore this issue, in Fall 2001 EPA issued an on-board emission analysis

“shootout” contract in order to solicit several approaches for incorporating on-board emissions

into moves. Three shootout contracts were issued to three organizations that worked

independently on the same general statement of work. These organizations were NCSU,

University of California at Riverside (UCR), and Environ. Each contractor had the flexibility to

choose any approach they preferred. NCSU pursued a modal “binning” approach in which

operational bins were defined based on speed, acceleration, and power demand, and refined the

estimates within each modal bin using regression analysis. UCR pursued a database approach,

deriving separate emissions for macroscale, mesoscale and microscale based on a database

lookup of individual vehicle and trip results. Environ based their approach on a calculation of

vehicle specific power (power per unit mass, or vehicle specific power - VSP), aggregating

results over “microtrips” (20 or more seconds, defined by endpoints of stable operation). EPA

also developed a conceptual approach based upon binning of data with respect to VSP bins.

The shootout results from NCSU, UCR, Environ, and EPA, revealed several promising

approaches for using on-board data in the development of MOVES exhaust emission rates. In

particular, the development of modal emission rates using a “binning” approach was successfully

demonstrated by NCSU and EPA in the shootout analysis. NCSU directly tackled the time series

nature of the on-board data and illustrated methods for dealing with the data to reduce the

influence of the time series. The work by Environ illustrated potential benefits to averaging or

smoothing the data. As a result of this work, the proposed design of MOVES is predicated on

emission rates defined by vehicle and modal operation “bins,” and the development of emission

rates for these bins in MOVES is the ultimate purpose of the methodology that will be developed

in this project.

The philosophy for MOVES is that it should be as directly data-driven as possible. The

advantages of a data driven methodology are manifold and include the following:

• Emission rates can be developed from raw data

• Emissions estimates can be developed based upon summaries of actual data within given

bins
2

• Emissions estimates from multiple bins can be weighted to represent any combination of

trip and vehicle characteristics.

• Inter-vehicle variability and fleet average uncertainty can be easily estimated based upon

appropriate averaging times

• Similar conceptual approaches can be used for different types of vehicles (e.g., on-road

gasoline and diesel, nonroad gasoline and diesel)

• Similar conceptual approaches can be used for different pollutants (i.e. HC, CO, NOx,

particulate matter, air toxics, and greenhouse gases)

• The development of bins can be based upon empirical evidence regarding combinations

of factors that have the most influence on aggregate emissions

• A modal/binning approach can easily support meso-scale and macro-scale analysis, and

can also support micro-scale analysis depending on how the approach is actually

implemented.

• A modal/binning approach for light duty gasoline vehicles (LDGV), heavy duty diesel

vehicles (HDDV) and nonroad diesel vehicles has been demonstrated by NCSU and EPA

• The NCSU approach for on-road vehicles is an intuitive and easy to explain one based

upon bins that correspond to idle, acceleration, cruise, and deceleration behaviors for

onroad vehicles. The ability to easily explain the approach to policy makers and the

public is an important consideration in gaining acceptance for a new modeling approach.

• A statistical data-driven statistical approach for developing bins, using Hierarchical TreeBased Regression (HTBR) has been demonstrated and proven by NCSU and can be used

in the identification of appropriate binning criteria.

• Methods have been demonstrated by NCSU for handling cold start emissions as part of

the modal/binning approach.

• Methods have been explored and recommended by NCSU regarding estimation of modal

emission rates from aggregate data (e.g., dynamometer driving cycle data).

• The modal/binning approaches have been evaluated by validating the approaches in

comparison to real-world emission measurements.

• Time series analysis already performed by NCSU as part of the shoot-out establish a

credible scientific basis for determining appropriate averaging times for the

modal/binning approach to be developed in this project.

• The general framework for developing databases, analyzing the data, and developing

modal models has already been established at NCSU, both as part of the shootout project

and in other previous work.

A key goal of the binning methodology is to develop modal emission rates in a manner that does

not require additional modeling analysis, such as regression modeling, and that eliminates the

need for many correction factors common to existing models such as Mobile5 and Mobile6.

Ideally, the emission rates estimated for a specific bin should be based directly on the sample of

raw data falling into that bin.

On-board data is a promising means for developing tailpipe emissions estimates. However, as

noted by EPA and as explained in the NCSU final report from the shootout (Frey, Unal, and

Chen, 2002), in the short-term other sources of data will continue to play an important role in

populating or evaluating MOVES. Thus, an important step in the development of MOVES is to

evaluate the feasibility of techniques for applying the modal binning approach to data from other
3

sources, such as driving cycle dynamometer data and remote sensing device (RSD) data. For

example, Frey et al. (2002) demonstrated an approach for estimating modal emission rates from

aggregate data.

The key purpose of this project is to evaluate methods for developing modal emission rates from

disparate data sources (e.g., on-board data, laboratory second-by-second data, aggregate driving

cycle data, I/M data, and RSD data) for a relatively small “pilot” dataset of light duty vehicles.

In the shootout, NCSU demonstrated that similar approaches can be applied to HDDV and to

nonroad diesel vehicles; therefore, it is reasonable to focus resources on the example of LDGVs

in this project. Furthermore, in previous work, NCSU demonstrated how to develop a bin for

cold starts. Therefore, this project will focus on hot stabilized tailpipe emissions. This project

will demonstrate at the proof-of-concept level the methodology for developing modal emission

rates in MOVES using a wide variety of data sources, including an evaluation of the applicability

of aggregate (bag) data and RSD data.

An important element of MOVES is the incorporation of uncertainty analysis as part of the

emission estimation process. EPA has proposed to characterize emission rates for each

vehicle/operating bin with a mean value, a distribution form, and standard deviation, to allow for

the development of a utility in MOVES which would apply Monte Carlo analysis to generate

uncertainty estimates of model final results. Moreover, this approach enables a change in how

normal and high emitters are characterized. In previous models, EPA has stratified data into

normal and high emitter categories. In the new approach, EPA proposes to treat all vehicles

within a bin as a continuous distribution. Thus, for a given vehicle/operating bin, the distribution

of emissions will reflect the variability of emissions among all vehicles within the bin, including

what are now referred to as normal and high emitters. This approach sets the stage for estimation

of the effect of I/M programs with respect to the characteristics of the distribution of intervehicle variability in emissions. For example, an I/M program would be expected to identify

some portion of the vehicles with emissions above some value and to repair/modify the vehicles

so as to reduce their emission rates. This, in turn, would change the distribution of inter-vehicle

variability in emissions.

1.1 Objectives of this Project

The objectives of this project are as follows:

• Develop, demonstrate, and report an analytical approach for producing exhaust modal

emission rates and emission rate disitributions for MOVES from a variety of data

sources, possibly including aggregate (bag) data and RSD data.

• Develop, demonstrate, and report a methodology for estimation of model uncertainty and

variability in emissions estimates

• Validate the developed approach against an independent dataset

• Develop a recommended step-by-step methodology for generating modal emission rates

in MOVES.
4

Figure 1-1. Simplified Schematic of Project Tasks and Their Inter-Relationships

1.2 General Technical Approach

In this section, an overview is provided of the technical approach of this project. This project

was organized based upon three major tasks:

• Task 1. Develop Pilot Modal Emission Rates From Multiple Data Sources

• Task 2. Perform Validation of Developed Model Against Independent Dataset

• Task 3. Summarize Specific Methodologies for Developing Modal Emission Rates for

MOVES

The first task is comprised of many specific subtasks. We subdivided Task 1 into subtasks as

follows:

• Task 1a: Development of Analysis Dataset

• Task 1b: Development of Binning Methodology

• Task 1c: Characterization of Uncertainty

• Task 1d: Applicability to Bag Data

• Task 1e: Applicability to RSD Data

The relationship among the three major tasks, and among the subtasks of Task 1, is illustrated in

Figure 1. The key starting point of the work was the development of an analysis data set in

subtask 1a. The other subtasks in Task 1, including subtasks 1b, 1c, 1d, and 1e, were dependent

upon the availability of the analysis data set, which included on-board data, second-by-second

laboratory data, IM240 data, aggregate (bag) data, and RSD data. Task 1b included several

Task 1a: Development of

Analysis Data Set

Task 1b: Development

of Binning Methodology

Task 1c: Characterization of Uncertainty

Task 1d: Applicability to

Bag Data

Task 1e: Applicability to

RSD Data

VSP Approach

NCSU Modal Approach

Averaging (1, 5, 10 seconds)

Units (g/sec or ratios)

Weighting (time, vehicle, trip)

Task 2: Validation

Task 3: Recommend

Methodology
5

considerations that are illustrated by the tie-line to a box listing the binning approaches that were

evaluated, the averaging times that were compared, the emission factor units that were compared,

and the method for weighting of data. The uncertainty analysis method in Subtask 1c depended

upon the binning approach selected as a result of Subtask 1b. However, a two-way arrow is

shown between Subtasks 1b and 1c to illustrate the iterative nature of the selection of a binning

approach and an uncertainty analysis approach. For example, the choice of averaging time and

of weighting method in Subtask 1b influenced the results obtained for the uncertainty analysis

method in Subtask 1c, and the availability of uncertainty analysis methods in Subtask 1c has

implications regarding which types of weighting methods were chosen as preferred in Subask 1b.

The applicability of bag and RSD data to the binning approach methodology also impact the

uncertainty characterization. The specifics of these kinds of interactions among subtasks and

trade-offs are addressed in more detail in the discussion of each specific subtask.

In the process of developing the tasks during the course of the project, the following key

questions emerged and were addressed:

1. What dataset should be used for the final version of the conceptual model? (Task 1a,

Chapter 2)

2. Which binning approach should be used? (Task 1b, Chapter 3)

3. How much detail should be included in the binning approach, in terms of how many

explanatory variables and how many strata for each variable? (Task 1b, Chapter 3)

4. What averaging time is preferred as a basis for model development? (Task 1b, Chapter 4)

5. What emission factor units should be used? (Task 1b, Chapter 5)

6. What weighting approach should be used, when comparing time-weighted, vehicle

weighted, and trip weighted? (Task 1b, Chapter 6)

7. How should variability and uncertainty be characterized? (Task 1c, Chapter 7)

8. How should aggregate bag data be analyzed to derive estimates of modal emission rates?

(Task 1d, Chapter 8)

9. What is the potential role and feasibility of incorporating RSD data into the conceptual

modeling approach? (Task 1e, Chapter 5)

10. How should the conceptual model be validated and what are the results of validation

exercises? (Task 2, Chapter 9)

1.3 Organization of this Report

This report is organized on the basis of the ten motivating questions of the previous section. The

development of an analysis data set is addressed in Chapter 2. Chapter 3 presents the empirical

and statistical basis for development of modal emissions modeling approaches. The selection of
6

a preferred averaging time for model development is discussed in Chapter 4. Two major topics

are addressed in Chapter 5: (1) what emission factor units should be used; and (2) evaluation of

the role of RSD data with respect to model development or model validation. Three different

data weighting approaches based upon time, trip, and vehicle averaging are compared in Chapter

6. Methods for quantifying variability and uncertainty are presented and compared in Chapter 7.

Methods for estimating modal emission rates from aggregate driving cycle data are presented

and evaluated in Chapter 8. The conceptual modal emissions model developed in this work is

verified and validated in Chapter 9. Chapter 10 provides a brief summary of the specific

methodology for developing modal emission rates that are recommended for future work.
7

2 DEVELOPMENT OF ANALYSIS DATASET

The objective of Subtask 1a is to develop a combined data set for running exhaust emission rates

for LDGV based upon data provided by EPA. The dataset included the following data:

• Approximately 100,000 seconds of data from 17 on-board vehicles from the “shootout”

analysis;

• Approximately 75,000 seconds of data on 25 vehicles tested at EPA’s lab for the Mobile6

facility-specific driving cycles and other standard cycles;

• 82,800 seconds on 311 vehicles tested on the IM240 as part of the Colorado IM program;

• Bag-only and second-by-second data on 74 vehicles tested over FTP (i.e., Bag 2 and Bag

3) and US06 for development of UC Riverside’s Comprehensive Modal Emission Model;

and

• RSD data on 200,966 Tier 1 LDGVs collected as part of a Missouri’s Gateway Clean Air

Program.

The data sets typically contained the following information:

• The second-by-second datasets typically had the following data fields: time; vehicle

speed; fuel consumption; HC, CO, NOx, and CO2 emissions; vehicle engine size; vehicle

weight; vehicle age; vehicle technology; vehicle mileage; road grade (for on-board data);

ambient temperature; and ambient humidity. Some datasets, such as from on-board data,

typically also had data for more variables such as: engine RPM; latitude; longitude;

altitude; mass air flow; intake air temperature; engine load; and other engine related

variables.

• Bag data sets included total emissions for CO, HC, NOx, and CO2. The bag data were

typically from standard driving cycles for which either the standardized or actual test

second-by-second speed trace was available. Vehicle-related variables such as vehicle

engine size, vehicle mileage, vehicle age, vehicle technology, and vehicle weight were

available for “bag” data sets. Additional data were available for some “bag” data sets

such as a/c usage, ambient temperature, and relative humidity.

• RSD data included instantaneous vehicle speed and emission rates for pollutants

normalized to CO2 emissions, such as the ratios of CO/CO2, HC/CO2, and NOx/CO2. In

addition, vehicle-related data such as engine size and model year based upon the license

plate number that was observed during data collection, identification of the VIN based

upon registration data, and decoding of the VIN. However, information regarding

vehicle mileage accumulation was not available. Additional variables such as road grade,

ambient temperature, and relative humidity were available.

2.1 Development of a Combined Database

In performing the work for this study, our general philosophy was to make use of readily

available software tools where possible. Therefore, we made use of Visual Basic, Excel, and

SAS to a significant extent, consistent with our previous experience in working with similar

datasets.

The combined second-by-second dataset, including on-board data, laboratory dynamometer data,

and IM240 data, was created using programs written in Visual Basic and SAS. For this purpose,
8

Visual Basic programs that were prepared in previous studies (Frey et al., 2001; Frey et al.,

2002) were utilized. The first step in developing a combined dataset was to make sure that each

data file has the same data fields. Each data file represents a vehicle or a trip. A Visual Basic

code was utilized to process the data and arrange the data fields such that each file has the same

format. Formatting of the fields was conducted with Visual Basic programs that were written for

this purpose in previous studies. After completing the processing of all data files, all of the data

was in Excel with the same format. The Excel files were first exported to SAS and combined

together in SAS using codes written specifically for this purpose.

For quality assurance purposes, the data were screened to check for errors or possible problems.

A notable issue was that there were zero and negative numbers in the second-by-second

emissions data. Specifically, 13 percent of the data were comprised of zero or negative values

for CO, 12 percent for HC, 22 percent for NOx, and 0.8 percent for CO2. Since measurements

errors could result in negative values that are not statistically significantly different from zero or

a small positive value, the data were retained as is.

Several post-processing steps were applied to the dataset. The post processing steps included:

(1) humidity corrections for NOx emissions for the on-board data; (2) adjustments to the HC data

for the on-board data; and (3) calculation of derived variables such as acceleration, power

demand, and vehicle specific power. Since the dynamometer data was already corrected for

humidity, a humidity correction was also applied to the on-board data. For this purpose, a

humidity correction factor that was reported in the on-board dataset was utilized. The on-board

measurements of HC emissions were made using NDIR, whereas the dynamometer

measurements were made using FID. In other work, the measurements of the on-board

instrument developed by Sensors that was used to collect the EPA on-board data were compared

with measurements made with a laboratory dynamometer. By comparing the total HC emissions

for specific vehicles and driving cycles, it was observed that the NDIR measurements resulted in

lower values than did the FID measurements. Based upon the available comparison data, a

correction factor of,1.65 was utilized to adjust the on-board HC measurements to an approximate

equivalent basis. Because the adjustment factor was based upon an average of total trip

emissions, the adjustment factor does not take into account possible variability in the ratio of FID

to NDIR measurements on a second-by-second basis.

Variables such as acceleration, power demand and VSP were estimated from other variables such

as vehicle speed. Acceleration is estimated from the observed speed by taking second-by-second

differences in speed. However, to account for the effects of road grade, the estimate of

acceleration was modified. As indicated by Bachman (1999), gravity exerts a force on a vehicle

that must be counteracted. Therefore, the acceleration effect of road grade should be included in

order to estimate the effective acceleration. The effect of road grade on acceleration can be

quantified as:

Acceleration (mph/sec) = 22.15 (mph/sec)× Gradient (%) (2-1)

Power demand was estimated using the following equation:

 = × (2-2)

where:
9

P = Power Demand (mph2/sec)

v = Vehicle speed (mph)

a = Vehicle acceleration (mph/sec)

Vehicle Specific Power (VSP) was estimated using an equation given by EPA, which is:

[ ] ( ) ( ) ( ) 3 VSP (kW/ton) = v 1.1a + 9.81 a tan sin grade + 0.132 + 0.000302v (2-3)

The coefficients given in Equation (2-3) are specific for on-board data. However, coefficients for

dynamometer measurements were not available in this study, therefore, the same coefficients

were used for dynamometer data as well. While it is recognized that the specific estimate of

VSP is a function of vehicle weight and of the specific values of the parameters for each

individual vehicle, it was beyond the scope of this study to develop detailed vehicle-specific

estimates of VSP.

2.2 Organization of the Data for Analysis

The combined database was used to create specific databases for different analyses throughout

the project. These databases included the following:

• A “Modeling” or “Calibration” database comprised of data for most of the on-board

measurements, most of the EPA dynamometer data, and most of the NCHRP data. This

database was also used as “Validation Data Set 1”

• “Validation Data Set 2” was comprised of a small sample of vehicles from the EPA onboard, EPA dynamometer, and NCHRP data that were excluded from the modeling

database.

• IM240 data were used separately from the other data

• The NCHRP data were used in the analysis of methods for developing modal emission

rates from aggregate bag data

• “Validation Data Set 3” was comprised of data obtained from the California Air

Resources Board, and are also referred to as “ARB data.”

• RSD data included approximately 2,000,000 seconds of data. Of this dataset, 200,966

data points were selected randomly for analysis, where each point represents

measurement for one vehicle.

The data from on-board, EPA dynamometer and NCHRP dynamometer measurements were

combined into the modeling data set, and included:

• 71,699 seconds of data from 13 on-board vehicles from the “shootout” analysis;

• 68,482 seconds of data on 33 vehicles tested at EPA’s lab for the Mobile6 facilityspecific driving cycles and other standard cycles; and

• 92,000 seconds of data on 49 vehicles tested over FTP and US06 for development of UC

Riverside’s Comprehensive Modal Emission Model.

Therefore, the combined database for modeling has a total of 232,181 seconds of data. The

combined database has the following data fields: source for data (e.g., EPA dynamometer);

vehicle make; vehicle model; VIN; number of vehicle tested; number of trip tested; speed;

acceleration; ambient temperature; ambient humidity; road grade; power estimate, positive

power estimate; Vehicle Specific Power (VSP) estimate; positive VSP estimate; CO, CO2, HC,
10

NOx emissions; vehicle model year; vehicle engine displacement; number of cylinders; air

condition use; and vehicle net weight.

Validation Data Set 2 included the following data:

• 3 vehicles from EPA dynamometer data

• 3 vehicles from EPA On-board data

• 25 vehicles from NCHRP data

The validation dataset included 83,183 seconds of data. The data fields for this dataset were the

same as for the Modeling dataset.

The NCHRP dataset included 8 high-emitter vehicles as reported in a User’s Manual prepared by

University of California at Riverside. In preparing Validation Dataset 1 and 2, data were selected

randomly from NCHRP data. Six of the high emitter vehicles were included in Validation

Dataset 1, and two of them were included in Validation Dataset 2.

Validation Data Set 3 included data for 17 vehicles from 11 different UCC cycles. The

validation dataset included nominal speed profiles and total emissions for 15 of the vehicles, and

actual speed profiles and second-by-second emissions for two of the vehicles. Detailed

information regarding the Validation Datasets is given in the Appendix.

Data for IM240 were utilized for comparative purposes, as described in this report, including

comparing average emission rates for the developed modes with respect to those obtained from

the calibration data. The IM240 dataset included 311 vehicles tested on the IM240 cycle, for a

total of 82,800 seconds of data. The data fields for this data set were the same as for the

Modeling dataset.

EPA obtained an RSD database from the state of Missouri that contained approximately 2

million records. Of this dataset, 200,966 data points were selected randomly for analysis. This

dataset included data fields similar to the modeling database. However, vehicle net weight was

not available and engine displacement was only available for part of the dataset. Each data point

in the RSD database used for analysis represents a unique vehicle.

2.3 Summary

Data from a variety of sources were reviewed and used to develop data bases for different

components of this project. A modeling database comprised of approximately 232,000 seconds

of data from on-board and laboratory dynamometer measurements was compiled for use in

developing a conceptual modeling approach. A separate IM240 database was developed for

comparison to the modeling data. A database comprised of RSD data was developed in order to

answer key questions regarding the potential role of RSD data in model development or model

interpretation. A database comprised of NCHRP dynamometer data was developed in order to

evaluate methods for estimating modal emissions from aggregate driving cycle data. In addition

to the modeling data set, two other databases were developed for model validation purposes,

including an independent sample of on-board and dynamometer measurements for vehicles

similar to those used in the modeling data base and a separate database obtained from CARB.
11

3 DEVELOPMENT OF A MODAL EMISSIONS MODELING APPROACH

The objective of this section is to demonstrate the modal “bin” approach on data for “running”

hot-stabilized exhaust emission rates, and to determine the best binning approach based upon

evaluation of alternative approaches. This chapter focuses upon the use of one second data in

units of mass per time. Chapter 4 compare different averaging times and Chapter 5 compares

different emission factor units. The two most promising binning approaches identified in the

“shootout” were the VSP-based approach evaluated by EPA and the driving mode-based

approach evaluated by NCSU. These two approaches were compared in this project. A key

methodological component of this work was the use of Hierarchical Tree-Based Regression

(HTBR), using S-Plus software. This chapter focuses on answering the second and third key

questions of this project: (1) which binning approach should be used?; and (2) how much detail

should be included in the binning approach, in terms of how many explanatory variables and

how many strata for each variable? First, the methodology for developing bins based upon

statistical methods is presented. Results of analysis of the modeling data set based upon each of

the NCSU and VSP based approaches are presented. An evaluation of each approach is made,

followed by a selection of a preferred approach.

3.1 Statistical Method for Developing Binning Criteria

HBTR is a forward step-wise variable selection method, similar to forward stepwise regression.

This method is also known as Classification and Regression Trees (CARTs). Conceptually,

HTBR seeks to divide a data set into subsets, each of which is more homogeneous compared to

the total data set. At a given level of division, each of the subsets is intended to be different in

terms of the mean value. Thus, HTBR is a statistical approach for binning data. More

specifically, the method is based upon iteratively asking and answering the following questions:

(1) which variable of all of the variables ‘offered’ in the model should be selected to produce the

maximum reduction in variability (also referred to as deviance in HTBR methodology) of the

response?; and (2) which value of the selected variable (discrete or continuous) results in the

maximum reduction in variability (i.e., deviance) of the response? The method uses numerical

search procedures to answer these questions. The HTBR terminology is similar to that of a tree;

there are branches, branch splits or internal nodes, and leaves or terminal nodes (Washington et

al., 1997).

The iterative partitioning process is continued at each node until one of the following conditions

is met: (1) the node of a tree has met minimum population criteria which is the minimum sample

size at which the last split is performed; or (2) minimum deviance criteria at a node have been

met (Frey et al., 2002; and Unal 1999).

In developing bins, vehicle-based variables such as vehicle class, mileage, age, engine size,

vehicle weight, and technology were utilized. Vehicle operation variables such as vehicle speed,

acceleration, and surrogate for power demand (i.e., Vehicle Specific Power) were included in

this analysis. Based upon the availability of the data, external parameters such as road grade, air

condition usage, ambient temperature, relative humidity were incorporated during HTBR

analysis. S-Plus scripts that were written in previous studies were used in this study.
12

In developing bins both “unsupervised” and “supervised” techniques were utilized. In the

“unsupervised” technique, data is provided to the HTBR with no prior specification of branches

or nodes of the regression tree. In this situation, HBTR is allowed to create whatever bins result

from direct application of HBTR. In contrast, for the “supervised” technique, HTBR is forced to

start with pre-determined modes. A partially supervised technique can often be a better approach

than a purely unsupervised technique. This is because HTBR can be sensitive to artifacts of

variability in the data that may not be important from a practical perspective, and HBTR may

give unexpected or difficult to interpret results if the unsupervised technique is used. Sometimes

HBTR will repeatedly “split” on the same subset of variables (e.g., speed and acceleration)

which may indicate the need for a new explanatory variable that is a function of the subset of

variables. For example, if HBTR splits repeatedly on speed and acceleration, it may be better to

remove speed and acceleration as criteria for creating bins and instead offer some variable that is

a combination of both speed and acceleration, such as VSP or power demand.

The two binning approaches that were evaluated are the VSP approach demonstrated by EPA

and the driving mode approach demonstrated by NCSU (Frey et al., 2002). VSP is a surrogate

for power demand and is a function of vehicle speed, road grade, and acceleration. In an

unsupervised approach, the selection of bins would be determined by the results of application of

HBTR, rather than based upon arbitrary bin assignments, such as those made by EPA as part of

the shootout (e.g., 1 kw/ton bins from –15 to +30).

The HBTR-based approach was also applied to the driving mode definitions developed by

NCSU. As part of previous work (Frey et al., 2001; 2002), NCSU developed a priori driving

mode definitions. Idle is defined as based upon zero speed and zero acceleration. The definition

of the acceleration mode includes several considerations. First, the vehicle must be moving and

increasing in speed. Therefore, speed must be greater than zero and the acceleration must be

greater than zero. However, vehicle speed can vary slightly during events that would typically be

judged as cruising. Therefore, in most instances, the acceleration mode is based upon a minimum

acceleration of two mph/sec. However, in some cases, a vehicle may accelerate slowly.

Therefore, if the vehicle has a sustained acceleration rate averaging at least one mph/sec for three

seconds or more, that is also considered acceleration. Deceleration is defined in a similar manner

as acceleration, except that the criteria for deceleration are based upon negative acceleration

rates. All other events not classified as idle, acceleration, or decelerations are classified as

cruising. Thus, cruising is approximately steady speed driving but some drifting of speed is

allowed. It was shown by NCSU in previous studies (Frey et al., 2001; 2002) that emission

estimates for these driving modes are statistically significantly different from each other. An

example comparison of modal emission rates for hot stabilized driving is given in Figure 3-1.

In working with the NCSU-based approach, two specific applications of HBTR were made. In

the first, the data set was modified to include a bin category for each data point. Unsupervised

HBTR was applied to the modified database to determine whether HBTR will subdivide the data

based upon the NCSU modal definitions preferentially compared to other possible binning

criteria. Additional bins were developed using HBTR in order to further refine the binning

approach. This type of approach was demonstrated briefly in the previous shootout project (Frey

et al., 2002) and was expanded in its application in this project.
13

0.1

1

10

100

1000

Average Pollutant Emission Estimate (mg/sec)

HC (mg/sec) CO (mg/sec) NO (mg/sec) CO2 (g/sec)

Idle Acceleration Deceleration Cruise

Figure 3-1. Average Modal Emission Rates for LDGVs (Source: Frey et al., 2002)

In developing modal “bins” in HTBR it should be kept in mind that there is a trade-off between

the number of bins and the usefulness of the empirical model based upon the bins. While it is

possible to obtain additional explanatory power by increasing the number of bins, there are

diminishing returns associated with creation of an increasing number of bins. Furthermore, the

HBTR determines bins based upon whether there are differences in the average emissions among

the possible bins. It does not determine bins based upon what portion of trip or total emissions

are explained by each bin. Therefore, it is possible to obtain a potentially large number of bins

that do not help explain a significant portion of total trip or aggregate emissions. Supervised

techniques are sometimes more useful than unsupervised techniques in helping to avoid a

proliferation of relatively useless bins. Another method for dealing with the possible

combinatorial explosion of bins is to “prune” a tree created using HBTR. For example, HBTR

could be allowed to develop a large number of bins for purposes of determining a practical upper

limit on the amount of deviance in the data set that can be explained by the bins. Then, the

number of bins can be reduced to a point where there is still good explanatory power of the

binning approach with a much smaller number of bins. This process requires some judgment and

therefore would be considered to be a supervised technique. This approach has been

demonstrated previously (e.g., Rouphail et al., 2000; Frey et al., 2002).

Another important issue regarding bin development is that bins that are formed under different

branches of the tree (see Figure 3-2) may not be statistically significantly different from each

other
14

Figure 3-2. Sample Regression Tree Diagram (Numbers represent Node Numbers of the Tree)

when the number of bins increases. All of the data are “fed” into the HBTR process as Node 1.

HBTR will divide into separate data sets at each branch in the tree. Thus, the first split of the

data is into bins represented by Nodes 2 and 3. Then, another split is made in which the data are

further subdivided into four nodes, Nodes 4, 5, 6, and 7. A third split results in eight modes,

which are Nodes 8 through 15. Each time a split is made, the two nodes that are subdivided

based upon a higher level node are statistically significantly different from each other with

respect to the mean value. Thus, for example, Nodes 8 and 9 will have significantly different

mean values. However, Nodes 9 and 10, which result from different branches, are not

guaranteed to have significantly different means. Thus, it is possible that a larger number of

nodes could result in some overlap with respect to mean values. In other words, the creation of a

large number of bins or nodes may not substantially increase explanatory power compared to a

smaller number of bins or nodes. We evaluated the statistical significance of differences in the

average value of emissions associated with different bins and considered lack of statistical

significance of average values as a stopping criteria pertaining to the creation of additional

branches of the regression tree.

Not all modes are equally important. Some modes are more important than others since they

represent a larger share of total emissions than others. For example, in a previous study by

NCSU it was found that acceleration and cruise modes are the most important modes in terms of

total trip emissions. Figure 3-3 illustrates the distribution of time spent in each driving modes

(i.e., cold-start, idle, acceleration, deceleration, and cruise) and the corresponding percentage

contribution of each mode to total trip emissions for each of four pollutants. One key finding is

that the idle and deceleration modes contribute relatively little to total emissions for any of the

1

2 3

4 5 6 7

8 9 10 11 12 13 14 15
15

Figure 3-3. Example of Average Distribution of Time and Emissions with Respect to Modes

(Source: Frey et al., 2002)

four pollutants compared to cruise, acceleration, and cold start emissions. Therefore, there is

likely to be little to be gained by spending resources to improve the explanatory power of the idle

and deceleration modes. In contrast, cruising, acceleration, and cold start, in a general

descending order, are the most important contributors to total emissions. Therefore, an iterative

approach was taken to develop bins. First bins were developed using the HTBR method. The

percent contribution of each mode total emissions was estimated. Based upon these results, the

definitions of the modes were revised so that no single mode contributes disproportionately to

the total emissions represented in the database.

3.2 Development of the VSP-Based Modal Approach

In developing bins based upon VSP, first step was to explore the relationship between VSP and

emissions with the help of scatter plots. Based upon exploratory analysis of the sensitivity of

emissions to VSP and other explanatory variables, a recommended approach was developed for a

modal model.

3.2.1 Exploratory Analysis

Figure 3-4 shows the relation between VSP and emissions for HC, NO, CO, and CO2. VSP data

were binned into 1kw/ton bins from -50 to +50 and the average within each bin is shown.

It is observed from these scatter plots that there is an approximately monotonic increase in

emissions for all four pollutants for positive VSP. Emissions tend to be very low for negative

VSP bins and tend to increase as VSP increases above zero. For very high values of VSP (i.e.,

VSP bins higher than 45) there is an apparent decrease for CO2 and NOx especially. The number

of data points in these bins are small, typically less than 100. Thus, the reliability of the

estimates for the very high VSP bins in question. However, one reviewer of this work indicated

that there is the possibility that emissions may actually decrease on average in the very high VSP

range.
16

86420

141210

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Vehicle Specific Power (VSP)

d) O2 (grams/seconC

0

0.005

0.01

0.015

0.02

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Vehicle Specific Power (VSP)

d) C (grams/seconH

0

0.005

0.01

0.015

0.02

0.025

0.03

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Vehicle Specific Power

d) Ox (grams/seconN

0

0.80.60.40.2

1

1.61.41.2

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Vehicle Specific Power

d) O (grams/seconC

Figure 3-4. Exploratory Analysis of Average Emissions of CO2, NOx, HC, and CO versus Vehicle Specific Power (VSP) Based Upon

the Modeling Database.
17

HBTR was applied to the modeling dataset in order to see whether VSP would be selected by

HTBR as the mot important explanatory variable. An example for this analysis is given for NO

emissions in Figure 3-5. Vehicle operating parameters as well as vehicle technology parameters

were used as possible explanatory variables. These parameters are: speed; acceleration; VSP;

temperature; engine displacement; number of cylinders; a/c usage; temperature, odometer

reading; model year; and net weight. Of all these parameters VSP was selected as the first split

by HTBR. The vertical distance depicted for each branch is proportional to the reduction in

deviance associated with each explanatory variability. In this specific case, splitting the data set

into two strata based upon a VSP criteria of 13.2 lead to a substantial reduction in deviance.

Under the second branch of the tree, a second split was made based upon vehicle net weight.

However, the reduction in deviance based upon further stratification by net weight is less than

the reduction in deviance from the first split based upon VSP. At the lowest portion of the tree, a

second split based upon VSP is observed for the smaller net weight category of data. When a

variable occurs repeatedly in the tree, such as VSP does in this case, that is evidence that the

variable plays an important role. In this case, VSP alone helps explain a substantial portion of

deviance in the data. When the data are further stratified, VSP explains additional deviance for

vehicles with a net weight less than 4,400 pounds. This result illustrates that VSP is the most

important variable and therefore could be selected as the first criteria for developing bin

definitions. Qualitatively similar results were obtained for other pollutants.

A judgment was made that it would be useful to separately analysis the role of vehicle operating

parameters (e.g., VSP) as distinct from vehicle characteristics (e.g., net weight, odometer

reading, engine size). When only vehicle operating parameters were utilized in HTBR, VSP was

again found to be the most important explanatory variable.

Because VSP was consistently identified as the most important explanatory variable, modal bins

were developed using VSP. HBTR was not used to develop the actual definitions of the bins.

While useful in identifying which variables offer the most capability to explain deviance in the

data set, an “unsupervised” approach to HBTR does not provide optimal bin definitions. For

example, it is possible that nodes that occur under different branches of the tree may have similar

average emission rates. From a practical perspective, it is not useful to have bins with similar

average emission rates, since the objective is to explain variability in emissions. Therefore, a

“supervised” approach was adopted. In the supervised approach, two key considerations were

taken into account. The first is that ideally each mode should have a statistically significantly

different average emission rate than any other mode. The second is that no single mode should

dominate the estimate of total emissions for a typical trip as represented by the database.

Therefore, to guide the selection of modal definitions, it was decided that no mode should

explain more than approximately 10 percent of total emissions. Based upon these two

considerations, VSP modes were defined. It should be noted that same modes were defined for

all the pollutants. Table 3-1 gives the VSP modal definitions.

Figure 3-6 shows average modal rates for these bins for all four pollutants. The average modal

rates are significantly different from each other for all four pollutants. In all four pollutants the

average modal rates for the first two modes, Modes 1 and 2, are higher than average rate for

Mode 3. There is an increasing trend in emissions with increase in VSP bins for Modes 4
18

Table 3-1. Definitions for VSP Modes

VSP Mode Definition

1 VSP<-2

2 -2<=VSP<0

3 0<=VSP<1

4 1<=VSP<4

5 4<=VSP<7

6 7<=VSP<10

7 10<=VSP<13

8 13<=VSP<16

9 16<=VSP<19

10 19<=VSP<23

11 23<=VSP<28

12 28<=VSP<33

13 33<=VSP<39

14 39<=VSP
19

Figure 3-5. Example of Unsupervised HTBR Tree Results for the Modeling Data Set for NOx Emissions (g/sec)

Note: The vertical distance of each branch indicates the proportional explanatory benefit of each particular split, and the numbers at

the bottom of the branches are the average emission rates for the stratified data.
20

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec O Emissions Estimate (g/C

1

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec O2 Emissions Estimate (g/C

0.0001

0.001

0.01

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec C Emissions Estimate (g/H

0.0001

0.001

0.01

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec O Emissions Estimate (g/N

Figure 3-6. Average Modal Emission Rates (g/sec) for VSP Bins for CO, HC, CO2, and NOx Based Upon the Modeling Dataset.
21

through 14 for all of the pollutants. For CO, the range in average modal emissions is more than

two orders-of-magnitude, when comparing Mode 3 and Mode 15. A similar comparison for

NOx, HC, and CO2 implies a range of approximately one to two orders-of-magnitude.

Because each pollutant has a different sensitivity to the modal definitions, there are some cases

in which a mode may contribute approximately 10 percent to the total emissions of one pollutant

but a far lower percentage of total emissions for another pollutant, as shown in Figure 3-7. For

example, for the high VSP bins, such as Modes 12, 13, and 14, approximately 10 percent of the

total CO emissions in the calibration data set are accounted for, for a total of over 30 percent of

the total CO emissions. These four modes account for less than three percent of total travel time

in the database. Furthermore, these modes account for only approximately 15 percent or less of

total NOx, HC, and CO2 emissions. The implication is that high VSP has a more substantial

impact upon CO emissions than for the other pollutants. This seems plausible, in that high VSP

is likely to be associated with an increased frequency and duration of command

enrichment, which tends to have more effect on CO emissions than, for example, NOx emissions.

Because pollutants respond differently to activity captured by each mode, it was necessary to

have 14 modes in order that no individual mode represent more than approximately 10 percent of

the emissions of any single pollutant. Of course, the proportion of emissions in each mode is

conditional on the database used to estimate the modal emission rates.

3.2.2 Considerations in Refinement of the VSP-Based Modal Approach

In order to further improve modal definitions, parameters related to vehicle technology were

included in an analysis to determine which ones are most useful in further explaining variability

in emissions. These parameters included were: engine displacement; number of cylinders;

odometer reading; model year; and net weight. Some of these parameters are correlated with

each other. For example, odometer reading and model year tend to have a positive dependence,

and engine displacement, number of cylinders, and net weight tend to have a positive

dependence. The correlation analysis for these parameters is given in Appendix. Therefore, in the

final model, it is not expected to be necessary to include all of these. Separate HTBR trees were

fit to data in each mode for each pollutant separately. Tables 3-2 through 3-5 summarize the

results of these analyses for CO, CO2, HC, and NOx respectively.

One of the observations from Tables 3-2 through 3-5 is that both net weight and engine

displacement are important variables for all of the pollutants for most of the modes. Engine

displacement is an important variable especially for CO and CO2, whereas odometer reading is

important especially for HC. Based upon the results given in Tables 3-2 through 3-5,

improvements in the VSP modal definitions were considered based upon comparison of based

upon net weight or engine displacement. In addition, the effect of stratification of VSP bins with

respect to odometer reading was also considered.
22

Percent of Emissions and Time Spent in VSP Modes

0

302010

1 2 3 4 5 6 7 8 9 10 11 12 13 14

TimeCONOCO2HC

Figure 3-7. Percent of Time Spent in VSP Modes and Percentage of Total CO, NOx, CO2, and HC Emissions Attributable to Each

VSP Mode, Based Upon the Modeling Data Set.
23

Table 3-2. Unsupervised HBTR Regression Tree Results for CO for Each of 14 VSP Modes

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 E* 5.3 NW 4400 NW 3600

2 E 5.3 

3 E 5.3 

4 E 5.3 

5 E 5.3 NW 3600

6 NW** 4400 O 15000 

7 NW 4400 NW 3600 

8 NW 4200 O 15000 O 24000

9 NW 4200 C  5 

10 NW 4200 C 5 

11 NW 4200 C 5 

12 NW 3800 NW 3200 

13 O** * 15000 O 79000

14 NW 3300 O 45000 O 79000

Table 3-3. Unsupervised HBTR Regression Tree Results for CO2 for Each of 14 VSP Modes

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 NW 3200 C 5 O 25000

2 NW 3200 

3 C 5 NW 3200 

4 C 5 NW 2700 NW 3600

5 E 2.3 NW 2800 NW 3700

6 E 2.3 E 1.95 C> 7

7 NW 3700 E 1.95 E 3.9

8 NW 3700 E 1.95 E 3.5

9 E 3.5 O 46000 

10 E 3.5 O 44000 

11 E 3.5 O 46000 

12 E 3.5 O 37000 

13 E 3.5 O 23000 

14 E 3.5 O 60000

Note: “NW” means “Net Vehicle Weight (lbs)”, “O” means “Odometer Reading (miles)”,

“C” means “Number of cylinders”, “E” means “Engine Displacement (liters)”. The number

following the variables is the value of the cut point.

Results are not shown in cases where sample size was small
24

Table 3-4. Unsupervised HBTR Regression Tree Results for HC for Each of 14 VSP Modes

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 O 77000 

2 O 77000 O 98000

3 O 79000 

4 O 79000 O 98000

5 O 78000 O 98000

6 O 78000 O 98000

7 O 78000 O 30000 O 98000

8 O 78000 O 26000 

9 O 78000 O 33000 O 95000

10 O 78000 O 32000 

11 O 43000 O 95000

12 O 43000 NW 2800

13 O 43000 O 15000 NW 3000

14 O 46000 NW 3000

Table 3-5. Unsupervised HBTR Regression Tree Results for NOx for Each of 14 VSP Modes

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 NW 3600 O 23000 NW 3800

2 O 66000 O 83000

3 O 30000 O 43000

4 NW 4400 O 66000 

5 NW 4400 O 66000 

6 NW 4400 O 66000 

7 NW 4400 O 66000 

8 O 70000 NW 2800 NW 3800

9 NW 4200 O 38000 

10 NW 4200 O 38000 

11 NW 4200 O 38000 

12 O 13000 

13 O 14000 O 95000

14 NW 3800 NW 3600 NW 2800

Note: “NW” means “Net Vehicle Weight (lbs)”, “O” means “Odometer Reading (miles)”,

“C” means “Number of cylinders”, “E” means “Engine Displacement (liters)”. The number

following the variables is the value of the cut point.

Results are not shown in cases where sample size was small
25

Figures 3-8 and 3-9 present the effect of net weight and engine displacement, respectively, on

emissions as applied to the VSP modal bins. For Figure 3-8, the data were stratified based upon

a vehicle weight of 4,000 pounds, and for Figure 3-9, the data were stratified based upon an

engine displacement of 3.5 liters. These cut-offs were chosen based upon the results of Tables 3-

2 through 3-5 and were intended to be representative values. Although for some pollutant/mode

combinations there is no significant or substantial difference in average emissions, for other

combinations there are statistically significant differences based upon either net weight or engine

displacement. For example, for the higher VSP modes (e.g., Modes 10 to 14), average emissions

are larger for all four pollutants for the larger weight category. In the case of CO2, the trend of

higher emissions for heavier vehicles is systematic among all of the positive VSP modes (i.e.

Modes 3 to 14); this difference is expected since heavier vehicles typically have lower fuel

economy and, hence, higher CO2 emissions than lighter vehicles. For CO and NOx, for the most

part emissions of heavier vehicles are higher for the positive VSP modes. For HC, the trend is

slightly different than other pollutants. For the first eight modes, lighter vehicles have higher

emissions; however, for Modes 10 to 14, heavier vehicles have significantly higher emissions.

These results confirm that vehicle net weight is an important variable. The differences in

emissions between the weight categories is on the order of a factor of two to five in most cases.

The relationship between emissions and engine displacement is shown for all pollutants and

modes in Figure 3-9. Although there are some exceptions, particularly for the negative VSP

modes (e.g., Modes 1 and 2), typically vehicles with larger engine size have significantly higher

emissions by a factor of two to five. Thus, engine displacement is also shown to be a

potentially important explanatory variable. Since engine displacement and net vehicle weight

are highly correlated, there is little benefit to including both as criteria for stratification of the

data. Engine displacement was selected as the criteria for further model development, although

it is likely that similar results would be obtained if net vehicle weight were selected instead.

Aside from either engine displacement or vehicle weight, it is clear from the results of Tables 3-2

through 3-5 that odometer reading is also an important explanatory variable. The range of

cutpoints for odometer reading obtained from HBTR varies substantially from one pollutant to

another, and in some cases multiple cutpoints for odometer reading were obtained from the

analysis. However, for simplicity and for consistency with other models and analyses, a single

cutpoint of 50,000 miles was selected. This cutpoint is within the range of values obtained from

HBTR.

The average modal emission rates, and the 95 percent confidence intervals for the averages, are

shown in Figure 3-10 for the 14 VSP modes stratified with respect to two engine displacement

categories and two odometer reading categories. The sample sizes for each mode for each strata

of engine displacement and odometer reading are shown in Figure 3-11.

For the lower engine displacement category of less than 3.5 liters, represented by Strata 1 and

Strata 3 in Figure 3-10, respectively, it is typically the case that the higher mileage vehicles have

higher emissions of HC and NO, only marginally higher emissions of CO, and comparable

emissions for CO2. Similarly, for the larger engine displacement category of greater than 3.5

liters, the higher mileage vehicles have substantially higher HC and NOx emissions, marginally
26

0.001

0.01

0.1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O Emissions EstimatC

NW < 4000NW > 4000

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

te O2 Emissions EstimaC

NW < 4000NW > 4000

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e C Emissions EstimatH

NW < 4000NW > 4000

0.0001

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

te O Emissions EstimaN

NW < 4000NW > 4000

Figure 3-8. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates for 14 VSP Bins for Vehicles with Net Weight <

4,000 lb to Vehicles with Net Weight > 4,000 lb.
27

0.001

0.01

0.1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O Emissions EstimatC

E < 3.5E > 3.5

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O2 Emissions EstimatC

E < 3.5E > 3.5

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e C Emissions EstimatH

E < 3.5E > 3.5

0.0001

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O Emissions EstimatN

E < 3.5E > 3.5

Figure 3-9. Comaparison of Average Modal CO, HC, CO2, and NOx Emissions Rates for 14 VSP Bins for Vehicles with Engine

Displacement < 3.5 liters to Vehicles with Engine Displacement > 3.5 liters.
28

0.0001

0.001

0.01

0.1

1

1 0

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

te C O E m ission s E stim a

S1S2S3S4

1

1 0

100

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

te C O 2 E m ission s E stim a

S1S2S3S4

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

te H C E m ission s E stim a

S1S2S3S4

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

ate N O E m ission s E stim

S1S2S3S4

Figure 3-10. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates for 14 VSP Bins Stratified by Engine

Displacement and Odometer Reading.

S1: Engine Displacement <3.5 liters and Odometer < 50K miles; S2: Engine Displacement >3.5 liters and Odometer < 50K miles;S3: Engine Displacement <3.5 liters and Odometer > 50K miles; S4: Engine Displacement >3.5 liters and Odometer > 50K miles.
29

0

5000

350003000025000200001500010000

123456789

1 0

1 1

1 2

1 3

1 4123456789

1 0

1 1

1 2

1 3

1 4123456789

1 0

1 1

1 2

1 3

1 4123456789

1 0

1 1

1 2

1 3

1 4

VSP Mode

e Sample Siz

Odom eter Readings < 50,000 M ilesEngine Displacem ent < 3.5 Liters

Odom eter Readings < 50,000 M ilesEngine Displacem ent > 3.5 Liters

Odom eter Readings > 50,000 M ilesEngine Displacem ent < 3.5 Liters

Odom eter Readings > 50,000 M ilesEngine Displacem ent > 3.5 Liters

Figure 3-11. Sample Sizes for Each VSP Mode for Each Odometer Reading and Engine Displacement Strata.
30

higher CO emissions, and comparable CO2 emissions for most modes. Thus, it is clearly

important to compare emissions for different odometer reading categories, especially for HC and

NOx.

When comparing engine displacement categories for a given odometer category, it is typically

the case that the larger engine size category has higher CO2, CO, HC, and NOx emissions than

the lower engine size category. However, there are some exceptions to this trend. For example,

the lower mileage vehicles with larger engines tend to have lower NOx emissions for Modes 1

through 7 compared to any other strata, and for the higher VSP modes, the NOx emissions for the

larger engines are not substantially higher than that for the smaller engines for lower mileage

vehicles. However, among the higher mileage vehicles, those with larger engines have

substantially higher NOx emissions than those with smaller engines.

The fact that there are important differences in emissions based upon engine size and odometer

reading for many modes for each of the pollutants confirms that engine size and odometer

reading are useful explanatory variables. Therefore, the modal approach based upon 14 VSP

bins, each divided into four strata representing two engine size and two odometer reading

categories, was adopted for further analysis. This approach is referred to as the “56-bin”

approach because of the 56 bins required (14 VSP bins x 2 engine displacement strata x 2

odometer reading strata = 56 bins in total).

3.2.3 Comparison of Modeling and IM240 Datasets

In this section comparison of modal results based upon the calibration dataset and the IM240

dataset is given based upon the preliminary VSP approach. For this purpose, the VSP bins that

were segregated via net weight are given. The IM240 data were not used in the initial calibration

activity because IM240 data are for a smaller range of VSP than the calibration data and because

of concern that there may be significant differences in fuel characteristics. An objective in

comparing the two data sets is to determine whether the results obtained based upon the

modeling data set are robust when the same binning criteria are applied to a different data set. In

order to make this comparison, it is important to first stratify both datasets as much as possible to

correct for variability in key factors. Based upon appropriate stratification, a more direct

comparison can be made between the data sets.

Figure 3-12 presents a comparison of modeling data and IM240 data based upon VSP bins where

vehicle net weight is less than 4,000lb. For CO2, the results from the modeling data set and the

IM240 data are very similar, both in terms of general trends among all modes and in terms of

comparisons of mean emission rates for individual modes. The only exception is an apparent

anomaly for Mode 1. Aside from the anomaly, the comparison suggests that on average the

vehicles in the two data sets have similar CO2 emission rates, which also indicates that they have

similar fuel economy, since the vast majority of carbon in the fuel is emitted as CO2. For the

other three pollutants, there are similarities in average emission rates for the highest VSP modes,

such as Modes 10 to 14, especially for CO and HC emissions. For NOx, the emissions appear to

differ by a factor of approximately two for these modes. The similarities for the higher modes

for CO and HC may suggest that vehicles emit similarly for these two pollutants under

conditions of high power demand and, presumably, increased occurrence and frequency of
31

0.001

0.01

0.1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O Emissions EstimatC

NW < 4000IM240 NW < 4000

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O2 Emissions EstimatC

NW < 4000IM240 NW < 4000

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e C Emissions EstimatH

NW < 4000IM240 NW < 4000

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O Emissions EstimatN

NW < 4000IM240 NW < 4000

Figure 3-12. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates based upon the Modeling Data versus IM240

Data for 14 VSP Bins for Net Vehicle Weight < 4,000 lb.
32

enrichment. For all other modes, it is generally the case that the IM240 database reveals higher

average emission rates than does the calibration database. This could be perhaps because there is

a higher proportion of high emitting vehicles, a different activity pattern of the vehicles, or

perhaps different fuel or ambient characteristics.

Figure 3-13 shows the comparison between the IM240 and the calibration data for net weight

greater than 4000lb. There are not many data points in several of the VSP bins for the IM240

data. For Modes 11 and 12 there are less than 20 data points and for Modes 13 and 14 there are

no data points. Thus, the results for Modes 11 and 12 are subject to considerable random

sampling error. Similar to the case for the lower weight vehicles, for CO2 there are generally not

significant differences between average modal rates for the IM240 and calibration datasets. For

other pollutants, the IM240 database tends to have higher average modal rates than the

calibration data, especially for the first seven modes.

Overall, these comparisons suggest important similarities between the modeling and the IM240

datasets. The general trend of an increase in emissions from Modes 3 to 14 is common to all

pollutants and for both vehicle size categories. The results for CO2 agree very well, especially

for the smaller vehicle size category for which there is more IM240 data. The results for NOx

are comparable in terms of general trend and relative variation in emissions among the modes,

but the average emissions are systematically higher for the IM240 data than for the modeling

data. For HC, the average modal emissions from the IM240 data are substantially higher than for

the modeling data for Modes 1 through 7, but are statistically similar for the highest VSP modes.

For CO, the average modal emissions based upon the IM240 data are higher than those based

upon the modeling data set for the lower VSP modes for both vehicle size categories. For the

smaller vehicle size category, for which there are more data, the CO emissions are similar for the

higher VSP modes. Since the IM240 is based upon potentially different fuel than the modeling

data set, it is possible that differences in fuel may be important. However, it is also likely that

the IM240 data set contains high emitting vehicles, and that the lower VSP modes may be more

susceptible to differences between normal and high emitting vehicles than the higher VSP

modes, which also typically represent higher emissions.

A more thorough comparison of different data sets is shown in Figures 3-14 through 3-17 for the

four engine displacement and odometer reading strata, respectively. The data sets compared

include the EPA on-board data, the EPA dynamometer data, NCHRP data, and the IM240 data.

The first three are the constituent data of the modeling database. Not all databases could be

compared for all four strata because of lack of data in some of the strata. Generally, the CO2

results are comparable among the databases, although it appears that the NCHRP database

represents higher average CO2 emissions than does the IM240 database for higher mileage

vehicles with larger engines. There tends to be more agreement regarding NOx emissions

estimates compared to CO and HC. Both the on-board and dynamometer data from EPA tend to

be similar. For example, for the smaller engines and lower mileage vehicles, the CO emissions

agree well for most of the modes, and for NOx the trends are very similar even though the

averages are similar primarily only for the lower VSP modes. The on-board hydrocarbon

emissions values tend to be much higher than those of the other data sets except for the high VSP

modes, although the difference is not as pronounced for the larger engine size range. Even

though emissions are not similar when comparing some of the datasets, a likely reason for such
33

0.001

0.01

0.1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O Emissions EstimatC

NW > 4000IM240 NW >4000

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O2 Emissions EstimatC

NW > 4000IM240 NW >4000

0.00001

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e C Emissions EstimatH

NW > 4000IM240 NW > 4000

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

VSP Bins

e O Emissions EstimatN

NW > 4000IM240 NW > 4000

Figure 3-13. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates based upon the Modeling Data versus IM240

Data for 14 VSP Bins for Net Vehicle Weight > 4,000 lb.
34

0.0001

0.001

0.01

0.1

1

1 0

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

te C O Em iss ions Estim a EPA OEM

NCHRPIM 240

E < 3.5O < 50 K

0.1

1

1 0

100

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

te C O 2 Em issions Estim a

EPAOEMNCHRPIM 240

E < 3.5O < 50 K

0.00001

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

te H C Em iss ions Estim a

EPAOEMNCHRPIM 240

E < 3.5O < 50 K

0.00001

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

te N O Em is sions Es tim a EPA OEM

NCHRPIM 240

E < 3.5O < 50 K

Figure 3-14. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates for Engine Displacement < 3.5 Liters and

Odometer Reading < 50,000 miles for EPA dynamometer, EPA on-board, NCHRP, and IM240 Databases.
35

0.0001

0.001

0.01

0.1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te CO Emissions Estima EPA OEM

NCHRPIM240

E > 3.5O < 50 K

0.1

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te CO2 Emissions Estima EPA OEM

NCHRPIM240

E > 3.5O < 50 K

0.00001

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te HC Emissions Estima EPA OEM

NCHRPIM240

E > 3.5O < 50 K

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te NO Emissions Estima EPA OEM

NCHRPIM240

E > 3.5O < 50 K

Figure 3-15. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates for Engine Displacement > 3.5 Liters and

Odometer Reading < 50,000 miles for EPA dynamometer, EPA on-board, NCHRP, and IM240 Databases.
36

0.0001

0.001

0.01

0.1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te CO Emissions Estima EPA

NCHRP

E < 3.5O > 50 K

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te CO2 Emissions EstimaEPA NCHRP

E < 3.5O > 50 K

0.00001

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te HC Emissions Estima

EPANCHRP

E < 3.5O > 50 K

0.00001

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te NO Emissions Estima

EPANCHRP

E < 3.5O > 50 K

Figure 3-16. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates for Engine Displacement < 3.5 Liters and

Odometer Reading > 50,000 miles for EPA dynamometer and NCHRP Databases.
37

0.0001

0.001

0.01

0.1

1

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te CO Emissions Estima NCHRP

IM240

E > 3.5O > 50 K

1

10

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te CO2 Emissions EstimaNCHRP

E > 3.5O

IM240

 > 50 K

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te HC Emissions Estima

NCHRPIM240

E > 3.5O > 50 K

0.0001

0.001

0.01

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

te NO Emissions Estima

NCHRPIM240

E > 3.5O > 50 K

Figure 3-17. Comparison of Average Modal CO, HC, CO2, and NOx Emissions Rates for Engine Displacement > 3.5 Liters and

Odometer Reading > 50,000 miles for IM240 and NCHRP Databases.
38

differences is a different mix of vehicles. The differences among the data sets suggest that it is

important to obtain a good representative sample of vehicles so that the combined database will

adequately capture and represent variability in emissions. The comparison also suggests that the

VSP definitions are useful in explaining variability in emissions within any of the data sets

individually.

3.3 NCSU Modal Approach: Idle, Acceleration, Deceleration, and Cruise

This approach is based on the NCSU modal definitions that are given in previous reports.

The vehicle operating conditions were categorized into NCSU modes, which are idle,

acceleration, deceleration and cruise. In order to refine the NCSU modes, HBTR was run for

each of the NCSU modes for all pollutants. When both operating and vehicle technology

parameters were included in HBTR, VSP was typically selected as the most important

explanatory variable, except as noted below. In a refined HBTR analysis based upon only

operating parameters of speed, acceleration and VSP, VSP was again selected as the most

important explanatory variable in most cases.

It was found that for the acceleration mode, VSP is most powerful in explaining the variability in

the emission rate. For example, Figure 3-18 shows the HBTR results for the acceleration mode

for NO. The first cut point is VSP, and it accounts for a large portion of the reduction of

deviance. VSP also is used for some additional stratification, along with speed. However, the

portion of deviance explained by speed is very small compared to that explained by VSP. Thus,

VSP is identified as the single most important variable to further improve the NCSU

Acceleration mode. Therefore, data within the acceleration mode were subdivided into addition

modes based upon VSP cut-offs. The cut-offs were selected based upon the same criteria as

described for the VSP approach: (1) ideally, each newly defined mode should have a

significantly different average emission rate compared to other modes; and (2) each mode should

account for not more than approximately 10 percent of the total emissions of a single pollutant.

Based upon these criteria, six modes were defined, as summarized in Table 3-6.

For the NCSU Cruise mode, it was found that VSP and Speed are both important variables that

are picked by HBTR. For example, Figure 3-19 shows the regression tree cruise mode results for

NO. The data are first stratified with respect to VSP, resulting in a large reduction in deviance,

as indicated by the vertical length of the branches under the first split. For the high VSP data,

the data are further stratified into smaller VSP categories, suggesting that VSP alone is useful in

explaining emissions as long as the VSP is above a cut-off (in the example, the cut-off is

approximately VSP=12). For the lower VSP data, speed was found to be the most important

variable for further stratification of the data. Therefore, in defining new modes within the cruise

mode, consideration was giving to using speed to stratify data for low VSP cases, and VSP alone

was used to discriminate among the high VSP data. The specific criteria for the bins shown in

Table 3-6 were developed based upon judgment after reviewing HBTR results for all pollutants.
39

|

VSP<20.3884

Speed.mph<36.1904

VSP<12.605

VSP<25.6607

Speed.mph<32.3896

0.001956 0.005092

0.010230

0.011510 0.014280 0.021250

Figure 3-18: Unsupervised HBTR Results for NCSU Acceleration Mode for NOx Emissions

(g/sec).

Figure 3-19. Unsupervised HBTR Results for NCSU Cruise Mode for NOx Emissions (g/sec).

Notes for Figures 3-17 and 3-18: The vertical distance of each branch indicates the proportional

explanatory benefit of each particular split, and the numbers at the bottom of the branches are the

average emission rates for the stratified data
40

Table 3-6. Definition of NCSU Driving Modes

ID Definition

1 NCSU Idle

3 NCSU Deceleration

21 NCSU Acceleration & VSP<8

22 NCSU Acceleration & 8

23 NCSU Acceleration & 15

24 NCSU Acceleration & 25		

25 NCSU Acceleration & 33


26 NCSU Acceleration & VSP


41 NCSU Cruise & VSP

	

42 NCSU Cruise & VSP

	

43 NCSU Cruise & VSP



44 NCSU Cruise & 12<VSP

45 NCSU Cruise & 16<VSP

46 NCSU Cruise & VSP>22
41

For the deceleration mode, speed was the most important explanatory variable picked by HBTR

analysis. However, considering that the total emission contributed by the deceleration mode is

less than 10 percent for all four of the pollutants, it was deemed not necessary to further divide

deceleration into submodes. The idle mode was also not further refined, since idle contributes

only a small portion of total emissions.

In total, 14 modes were identified, including one idle mode, one deceleration mode, six

acceleration modes, and six cruise modes. The definition of these modes is given in Table 3-6.

The time spent in each of the 14 modes, and the emissions contributed by these 14 modes is

shown in Figure 3-20. The average emission values for each of the 14 modes for the four

pollutants are given in Figure 3-21,and the sample size for each mode is shown in Figure 3-22.

Figure 3-20 indicates that CO emissions were the binding consideration in determining the need

for six acceleration modes. Specifically, the high VSP acceleration modes (i.e. Modes 24, 25,

and 26) each represent approximately 10 percent of the total CO emissions in the database, but a

far smaller percentage of emissions of the other three pollutants. On the other hand, NOx

emissions were the binding constraint on determining the need for six cruise bins, since NOx

contributes approximately 10 percent to total NOx emissions for the high VSP cruise modes

(Modes 44, 45, and 46) and other pollutants contribute less than this percentage to their

respective totals.

The comparison of average emission rates in Figure 3-21 reveals that the lowest emission rates

for a given pollutant typically occur for idle, deceleration, and low speed cruising. As cruising

speed increases for low VSP values, as represented by Modes 41, 42, and 43, the average

emission rate increases for all pollutants. High VSP cruising results in higher average emissions

than low VSP cruising. These results tend to confirm intuitive a priori assumptions that

emissions during cruising will typically be higher at higher speeds or under conditions of higher

engine load. The ability to distinguish emissions for different types of cruising illustrates the

intuitive appeal of this particular modal binning approach: it is relatively easy to explain the

relationship between vehicle activity and emissions with this approach.

For the acceleration mode, emissions for any of the pollutants increase with VSP, as illustrated

by comparing Modes 21, 22, 23, 24, 25, and 26. For CO and HC, there is a significant increase

in emissions when comparing one mode with the next mode that has higher VSP. For both NOx

and CO2 emissions, the average emissions increase substantially with VSP for the lower VSP

modes (i.e. Modes 21, 22, 23). For Modes 24, 25, and 26, there are small increases in average

emissions as VSP increases. These results suggest that CO and HC emissions are very sensitive

to VSP throughout the entire range of acceleration events, whereas NOx and CO2 emissions are

sensitive to lower ranges of VSP of less than about 25. Above VSP=25, NOx and CO2 emissions

are less sensitive to VSP. Thus, it appears to be the case that once a VSP threshold is reached,

NOx and CO2 emissions will not change much, but that CO and HC emission rates are more

sensitive to high (or perhaps aggressive) accelerations.
42

0

302010

1 3 21 22 23 24 25 26 41 42 43 44 45 46

TimeCONOCO2HC

Figure 3-20. Percent of Time Spent in NCSU Modes and Percentage of Total CO, NOx, CO2, and HC Emissions Attributable to Each

NCSU Mode, Based Upon the Modeling Data Set.
43

0.001

0.01

0.1

1

10

1 3 21 22 23 24 25 26 41 42 43 44 45 46

CO Emissions Estimate (g/sec)

0.0001

0.001

0.01

0.1

1

1 3 21 22 23 24 25 26 41 42 43 44 45 46

C Emissions Estimate (g/sec)H

0.1

1

10

100

1 3 21 22 23 24 25 26 41 42 43 44 45 46

CO2 Emissions Estimate (g/sec)

0.0001

0.001

0.01

0.1

1

1 3 21 22 23 24 25 26 41 42 43 44 45 46

NO Em issions Estimate (g/sec)

Figure 3-21. Average Modal Emission Rates (g/sec) for NCSU Modes for CO, HC, CO2, and NOx Based Upon the Modeling Dataset
44

0

40000300002000010000

13

2 1

2 2

2 3

2 4

2 5

2 6

4 1

4 2

4 3

4 4

4 5

4 613

2 1

2 2

2 3

2 4

2 5

2 6

4 1

4 2

4 3

4 4

4 5

4 613

2 1

2 2

2 3

2 4

2 5

2 6

4 1

4 2

4 3

4 4

4 5

4 613

2 1

2 2

2 3

2 4

2 5

2 6

4 1

4 2

4 3

4 4

4 5

4 6

NCSU Mode

e Sample Siz

Odom eter Readings < 50,000 M ilesEngine Displacem ent < 3.5 Liters

Odom eter Readings < 50,000 M ilesEngine Displacem ent < 3.5 Liters

Odom eter Readings < 50,000 M ilesEngine Displacem ent < 3.5 Liters

Odom eter Readings < 50,000 M ilesEngine Displacem ent < 3.5 Liters

Figure 3-22. Sample Sizes for Each NCSU Mode for Each Odometer Reading and Engine Displacement Strata.

Mode Definitions:1 = idle3 = deceleration21-26 = acceleration

41-46 = cruise
45

After defining the 14 modes shown in Table 3-6, unsupervised HBTR was applied to data for

each pollutant and each mode to identify vehicle characteristics useful in further explaining the

variability in the emission rate. The vehicle characteristics considered included net weight,

number of cylinders, odometer readings and engine displacement. Tables 3-7 through 3-10

summarize which variable was chosen for the first, second, and third cut-points in the regression

tree and also display the numerical values of the cut-offs.

There is variation regarding which variables were selected for the first stratification of the data,

implying that the choice of a preferred explanatory variable is conditional on the mode.

However, since the objective of this work is to develop modes that are both technically rigorous

but also sufficiently simple for practical application, it is preferred to identify one explanatory

variable that works well for all modes. In reviewing the results of Tables 3-7 through 3-10, it is

apparent that the odometer reading is typically the most frequently selected variable for use in

the first stratification of the data. The second most frequently selected variable for the first cutpoint is the net vehicle weight. Odometer reading and net vehicle weight are also frequently

selected as the basis for the second and third cut-points. These results suggest that both

odometer reading and net vehicle weight are important variables. Therefore, both variables were

selected as the basis for further refinement of the modal definitions.

The selection of specific cutpoint values for odometer reading and net vehicle weight was made

based upon judgment. The specific cutoffs from the HBTR analysis are different for different

modes and pollutants. However, in order to keep the modal definitions as simple as possible,

only one representative cutpoint was selected for each variable. The cutpoints for odometer

readings obtained from HBTR range from typically 12,000 to 80,000 miles. However, many

values are within a range of plus or minus 15,000 miles compared to a chosen cutpoint of 50,000

miles. The cutpoint of 50,000 miles was selected because it is representative of results from the

statistical analysis and is consistent with previous cutpoints used in other modeling work. For

net vehicle weight, a representative cutpoint of 3,500 pounds was selected, which is

representative of many of the cutpoints in the range of 3,300 to 3,800 pounds identified in the

statistical analysis.

Using the same modal definitions as given in Table 3-6, the data were further binned into four

categories:

Net Weight <= 3,500 pounds AND Odometer Reading <= 50,000 miles

Net Weight <= 3,500 pounds AND Odometer Reading > 50,000 miles

Net Weight > 3,500 pounds AND Odometer Reading <= 50,000 miles

Net Weight > 3,500 pounds AND Odometer Reading > 50,000 miles

A comparison of average modal emission rates for these four categories is given in Figures 3-23,

3-24, 3-25, and 3-26 for CO, HC, NOx, and CO2 emissions, respectively. The figures suggest

that at least for some pollutant/mode combinations that average emissions for these four

categories are statistically significantly different from each other (e.g., NO emissions for

acceleration modes 21, 22, 23, 24, and 25). In some cases, there is more sensitivity to odometer
46

Table 3-7. Unsupervised HTBR Regression Tree Results for CO Emissions Based Upon the

NCSU Modal Approach.

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 (Idle) Net 3328 O 79901 Net 3482

3 (Deceleration) E 4.1 N 5 O 17783

21 (Acceleration) O 75432 O 15210 O 12325

22 O 66163 O 15210

23 O 43433 O 15251 O 71964

24 E 3.9

25 Net 3587

26 O 43433

41 (Cruise) O 15210 O 12798 O 75432

42 O 15215 O 12789 O 56637

43 E 3.45 N 5 O 20892

44 E 3.45 N 5 Net 2862

45 Net 3659 N 5

46 O 79022 O 50177

Table 3-8. Unsupervised HTBR Regression Tree Results for NOx Emissions Based Upon the

NCSU Modal Approach.

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 (Idle) N 5 O 60158 E 3.45

3 (Deceleration) O 8785 E 3.45

21 (Acceleration) O 58057 O 29057 E 2.75

22 O 66163 O 38353 O 45900

23 O 63341 O 22195 O 43433

24 O 58560 O 12800 Net 3486

25 O 58057 Net 2813 E 2.3

26 O 58057 Net 2550

41 (Cruise) O 71964 E 0.75 Net 3754

42 Net 3611 O 57695 E 4.45

43 O 17220 E 3.05

44 O 17220 O 11493 Net 2531

45 O 38353 E 3 O 83491

46 O 83490 O 61024

Note: “Net” means “Net Vehicle Weight (lbs)”, “O” means “Odometer Reading (miles)”,

“N” means “Number of cylinders”, “E” means “Engine Displacement (liters)”. The number

following the variables is the value of the cut point.

Results are not shown in cases where sample size was small
47

Table 3-9. Unsupervised HTBR Regression Tree Results for HC Emissions Based Upon the

NCSU Modal Approach.

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 (Idle) O 79022 O 48626 O 98129

3 (Deceleration) O 74867 E 5.3 Net 3613

21 (Acceleration) O 79022 O 37236 O 48465

22 O 74867 O 37238 O 48465

23 O 77495 O 37326

24 O 43437 Net 2586

25 O 43433 Net 2967

26 O 45900 E 2.75

41 (Cruise) O 79022 E 5.3 O 10110

42 O 77495 Net 3611 E 4.9

43 O 77495 O 29949

44 O 77495 O 79022

45 O 77495 O 26082

46 Net 4375 O 43433 O 90660

Table 3-10. Unsupervised HTBR Regression Tree Results for CO2 Emissions Based Upon the

NCSU Modal Approach.

Mode 1st Cut point 2nd Cut point 3rd Cut point

1 (Idle) N 5 Net 2454

3 (Deceleration) Net 3264 O 25347 E 3.45

21 (Acceleration) O 43433 E 3.45 N 5

22 O 43433 E 1.55 Net 3284

23 Net 3724 O 44035 Net 3568

24 Net 3724 E 1.95 Net 2688

25 Net 3724 E 2.1 O 22358

26 E 2.1 O 55582

41 (Cruise) Net 3034 Net 2246 E 1

42 Net 3551 Net 2788 E 2.5

43 E 2.45 Net 2983 Net 3626

44 Net 3724 E 1.95 O 45900

45 Net 3724 O 45900 O 37236

46 Net 3724 Net 2446

Note: “Net” means “Net Vehicle Weight (lbs)”, “O” means “Odometer Reading (miles)”,

“N” means “Number of cylinders”, “E” means “Engine Displacement (liters)”. The number

following the variables is the value of the cut point.

Results are not shown in cases where sample size was small

.

49

0.001

0.01

0.1

1

1 0

1 3 2 1 2 2 2 3 2 4 2 5 2 6 4 1 4 2 4 3 4 4 4 5 4 6

NCSU_Mode

n O emissioC

Net_W eight<=3500 & Odom eter<=50000Net_W eight>3500 & Odom eter<=50000Net_W eight<=3500 & Odom eter>50000Net_W eight>3500 & Odom eter>50000

Figure 3-23. Average CO Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight

and Odometer Reading Based Upon the Modeling Database.

Mode 1: IdleMode 2: DecelerationModes 21-26: Acceleration

Modes 41-46: Cruise
50

0.0001

0.001

0.01

0.1

1

1 3 2 1 2 2 2 3 2 4 2 5 2 6 4 1 4 2 4 3 4 4 4 5 4 6

NCSU_Mode

n C emissioH

Net_W eight<=3500 & Odom eter<=50000Net_W eight>3500 & Odom eter<=50000Net_W eight<=3500 & Odom eter>50000Net_W eight>3500 & Odom eter>50000

Figure 3-24. Average HC Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight

and Odometer Reading Based Upon the Modeling Database.

Mode 1: IdleMode 2: DecelerationModes 21-26: Acceleration

Modes 41-46: Cruise
51

0.00001

0.0001

0.001

0.01

0.1

1

1 3 2 1 2 2 2 3 2 4 2 5 2 6 4 1 4 2 4 3 4 4 4 5 4 6

NCSU_Mode

n O emissioN

Net_W eight<=3500 & Odom eter<=50000Net_W eight>3500 & Odom eter<=50000Net_W eight<=3500 & Odom eter>50000Net_W eight>3500 & Odom eter>50000

Figure 3-25. Average NOx Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight

and Odometer Reading Based Upon the Modeling Database.

Mode 1: IdleMode 2: DecelerationModes 21-26: Acceleration

Modes 41-46: Cruise
52

0.1

1

1 0

100

1 3 2 1 2 2 2 3 2 4 2 5 2 6 4 1 4 2 4 3 4 4 4 5 4 6

NCSU_Mode

on O2 emissiC

Net_W eight<=3500 & Odom eter<=50000Net_W eight>3500 & Odom eter<=50000Net_W eight<=3500 & Odom eter>50000Net_W eight>3500 & Odom eter>50000

Figure 3-26. Average CO2 Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight

and Odometer Reading Based Upon the Modeling Database.

Mode 1: IdleMode 2: DecelerationModes 21-26: Acceleration

Modes 41-46: Cruise
53

reading than vehicle weight. For example, for HC cruise modes, vehicles with higher odometer

readings have higher emissions than those with lower odometer readings, and average emissions

for a given odometer reading are similar for the two net weight categories. In contrast, for NOx

emissions, it appears that older higher mileage vehicles generally have higher modal emission

rates than for the other three categories. However, there are also many specific comparisons that

are not statistically significantly different from each other. For example, for CO emissions the

average acceleration modal emissions rates for higher mileage vehicles are similar regardless of

vehicle weight. Thus, although the specific trends are different for different pollutants, and

although in some cases there are not significant differences among the two or more of the four

categories for a given pollutant/mode, the results suggest that there are observable differences for

many pollutant/mode combinations. Therefore, these categories may be useful in explaining

variability in emissions.

3.4 Selection of a Binning Method

The VSP and NCSU binning approaches were compared and evaluated. The criteria for

evaluating the two approaches included the utility of each method to explain variability in

emissions, the ease of development of the bins, the interpretation of the bins, the ability to

explain the approach to model developers and users, and design issues for future model

development. The choice of a preferred binning approach was made based upon the application

of both approaches to the same data sets.

A comparison of predictions made with both the NCSU-based and VSP-based approaches was

developed by using both approaches to predict the average emissions for driving cycles in the

modeling database for which there were ten or more vehicles. The comparison is shown in

Figure 3-27. The average prediction and the 95 percent confidence interval for the average

prediction is shown for each method and for each driving cycle. The 95 percent confidence

intervals of the mean predictions overlap for all of the cycles and for all pollutants, indicating

that there is no statistically significant difference in predictions for the two methods.

The development of the bins is similar for both methods. The interpretation of bins is different

for the two methods, with the NCSU approach being more intuitive to a lay person and the VSP

approach being consistent with approaches used in a variety of analyses of vehicle emissions.

The NCSU approach produces some bins that have similar average emission rates, even though

they represent different activities. For example, the lower emission acceleration and cruise

modes have similar emissions. Although neither method clearly stands out when compared to

each other, the VSP approach was selected as the basis for further analysis.
54

1

10

100

1000

ARTEF FWY-F FWY- HI NYCC F505 IM240 FTP75 US06 On- Board

Average CO Emissions (g)

VSP ApproachNCSU Approach

100

1000

10000

100000

ARTEF FWY-F FWY- HI NYCC F505 IM240 FTP75 US06 On- Board

g) verage CO2 Emissions (A

VSP ApproachNCSU Approach

0.1

1

10

100

ART-EF FWY-F FWYHI NYCC F505 IM240 FTP75 US06 On- Board

(g) verage HC Emissions A

VSP ApproachNCSU Approach

0.1

1

10

100

ARTEF FWY-F FWY- HI NYCC F505 IM240 FTP75 US06 On- Board

(g) verage NOx Emissions A

VSP ApproachNCSU Approach

Figure 3-27. Comparison of VSP and NCSU Approach-Based Predictions of Average Emissions of CO2, CO, HC, and NOx for

Selected Driving Cycles for Vehicles in the Modeling Database.
55

4 SELECTION OF AN AVERAGING TIME FOR MODEL DEVELOPMENT

The objective of this chapter is to evaluate the potential benefits of working with data that have

been averaged over time when developing bins/modes. The effect of data smoothing on binning

was determined by comparing the bins developed with data averaged over one second to those of

longer periods. For this purpose consecutive averaging of 5 and 10 seconds was utilized and

compared with each other and with the use of 1 second data.

4.1 Methodological Approach

As part of the shootout, NCSU found that there is autocorrelation in the second-by-second onboard tailpipe emissions data (Frey et al., 2002). In most cases, the autocorrelation was found to

be represented by a lag of up to four or five seconds. Therefore, an averaging time of five

seconds should be sufficient to decrease the autocorrelation in the data by smoothing with

consecutive averaging. However, to provide some margin for variability in the autocorrelation,

an averaging time of 10 seconds was also evaluated. It was hypothesized that this longer

averaging time should further smooth the data and remove some of the high frequency variability

in the data.

In order to determine 5 and 10 second averages based upon the second-by-second data, a

program was written in Visual Basic. This program estimated 5 and 10 second consecutive

averages for emissions, as well as vehicle activity data, such as vehicle speed and acceleration.

In addition to estimating average vehicle activity during each activity period, peak values of

vehicle activity were estimated. For example, it was hypothesized that emissions are more

sensitive to peak accelerations or peak VSP within an averaging period than they would be to

average acceleration or average VSP.

The use of averaging times requires reconsideration of the approach for developing bins. For

example, data can be binned by average VSP or by peak VSP during the 5 or 10 second

averaging time. It is possible, for example, for a 10 second period to have an average

acceleration of, say, only 1 mph/sec but to have a peak acceleration of, say, 5 mph/sec that took

place for a short duration. The short duration, high acceleration that took place within the 10

second averaging period may in fact be associated with the largest share of emissions that took

place during the averaging time. Therefore, it may be more effective to use the peak values of

key variables, such as VSP or power demand, as a basis for binning the data, rather than using

average values of these.

The basis for selection of a preferred averaging time was based upon the presence of statistically

significant differences in average emissions among modal bins and explanatory power of the

overall modal model. In addition, approaches that resulted in less variability in emissions within

a bin would typically be preferred over approaches that have more variability in emissions within

a bin.

4.2 Results for Five and Ten Second Averaging Times

The assessment of different averaging times was performed for the VSP-based approach

identified as the preferred modeling approach in Chapter 3. For the five and ten second-averaged

data, unsupervised HBTR was applied to the data sets for each pollutant. The variables used in
56

the regression tree include mean speed, maximum speed, standard deviation of the speed, mean

acceleration, maximum acceleration, standard deviation of the acceleration, mean VSP,

maximum VSP, standard deviation of VSP, mean power, maximum power and standard

deviation of power. It should be noted that there is positive dependence between VSP and power.

Table 4-1 summarizes the variables that were picked during the unsupervised application of

HBTR for the first three cut points. Maximum VSP and maximum power were frequently

selected as the most important variables. Since VSP includes power as part of the estimate, these

two variables are closely related to each other. Therefore, for simplicity and consistency with

the one second averaging time analysis, VSP was chosen as the representative variable for

developing modes, and maximum VSP was selected as the specific criteria to use in defining

modes. The approach for defining modes using a supervised technique is the same as previously

described, based upon seeking modes with average emission rates that differ from each other and

that do not contribute more than about 10 percent to total emissions for any individual pollutant.

A total of 14 modes were defined for both 5 and 10 second-averaged data, as given in Tables 4-2

and 4-3, respectively. The time spent in each mode and the percentage of total database

emissions contributed by each mode for 5 and 10 second-averaged data are given in Figures 4-1

and 4-3, respectively. Similarly, the average modal emission rates for each mode for all four

pollutants are given in Figure 4-2 for the 5-second average data and in Figure 4-4 for the 10-

second average data.

The sample sizes for the 1-second, 5-second, and 10-second averaging times for each of the 14

modes are compared in Figure 4-5. Because the modal definitions are different for each of the

three approaches, it is not expected that there is a proportional distribution of data among the

modes when comparing the approaches. However, it is the case that the total sample size

summed over all 14 modes for the 5-second averaging time is approximately one-fifth that of the

1-second averaging time, and similarly for the 10-second averaging time the overall sample size

is approximately one-tenth that of the 1-second averaging time.

Table 4-1. Key Explanatory Variables for CO, NOx, HC, and CO2 Emissions (g/sec) Identified

Using Unsupervised HBTR for Five and Ten Second-Averaged Data

1st Cut Point 2nd Cut Point 3rd Cut Point

5 Seconds Average for CO Maximum Power Maximum VSP Mean VSP

10 Seconds Average for CO Maximum Power Maximum VSP Maximum Speed

5 Seconds Average for NOx Maximum VSP Maximum VSP Mean Power

10 Seconds Average for NOx Mean VSP Maximum VSP Maximum Power

5 Seconds Average for HC Maximum Power Maximum VSP Maximum Power

10 Seconds Average for HC Maximum Power Maximum VSP Mean Power

5 Seconds Average for CO2 Mean VSP Maximum VSP Mean VSP

10 Seconds Average for CO2 Mean VSP Maximum VSP Mean VSP
57

Table 4-2. Maximum VSP-Based Mode Definitions For Five Second-Averaged Data

ID Definition

1 MaxVSP <0

2 0 	

3 2 	

4 6 	

5 9 	



6 12 	


7 15 	


8 18 	


9 21 	

10 25 	

11 29 	

12 34 	

13 38 	


14 MaxVSP 


Table 4-3. Maximum VSP-Based Mode Definitions For Ten Second-Averaged Data

ID Definition

1 MaxVSP < 1

2 1 	

3 6 	

4 9 	



5 12 	


6 15 	


7 18 	


8 21 	

9 24 	

10 27 	


11 31 	

12 35 	

13 39 	

14 MaxVSP 
58

0

302010

1 2 3 4 5 6 7 8 9 10 11 12 13 14

TimeCONOCO2HC

Figure 4-1. Percent of Time Spent in Five Second Averaging Time Maximum VSP-Based Modes and Percentage of Total CO, NOx,

CO2, and HC Emissions Attributable to Each Mode, Based Upon the Modeling Data Set.
59

Figure 4-2. Five Second Averaging Time Modal Emission Rates (g/sec) for Maximum VSP Bins for CO, HC, CO2, and NOx Based

Upon the Modeling Dataset.

0.0001

0.001

0.01

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

ec HC Emissions Estimate (g/s

0.0001

0.001

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

ec NO Emissions Estimate (g/s

0.001

0.01

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

ec CO Emissions Estimate (g/s

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

ec CO2 Emissions Estimate (g/s
60

0

302010

1 2 3 4 5 6 7 8 9 10 11 12 13 14

TimeCONOCO2HC

Figure 4-3. Percent of Time Spent in Ten Second Averaging Time Maximum VSP-Based Modes and Percentage of Total CO, NOx,

CO2, and HC Emissions Attributable to Each Mode, Based Upon the Modeling Data Set.
61

Figure 4-4. Ten Second Averaging Time Modal Emission Rates (g/sec) for Maximum VSP Bins for CO, HC, CO2, and NOx Based

Upon the Modeling Dataset.

0.0001

0.001

0.01

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

ec HC Emissions Estimate (g/s

0.0001

0.001

0.01

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) NO Emissions Estimate (g/se

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

se CO Emissions Estimate (g/

1

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14

ec CO 2 Em issions Estim ate (g/s
62

0

5000

500004500040000350003000025000200001500010000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Mode

ize ample SS

1 Second5 Second10 Second

Figure 4-5. Comparison of Sample Sizes for 1 Second, 5 Second, and 10 Second Averaging Time-Based Modes Estimated From the

Modeling Data Set.
63

The results share many qualitative similarities compared to the analysis of 1-second data shown

previously. For example, the contribution to total CO emissions is larger for the high maximum

VSP modes (e.g., Modes 10, 11, 12, 13, and 14) than the contribution to total emissions of other

pollutants. For modes that are based only upon positive maximum VSP, the average emission

rates increase from one mode to the next as average VSP increases, for all pollutants and for both

averaging times. The range of variability when comparing the mode with the largest average

emission rate to that with the lowest average emission rate is similar for all of the averaging

times for a given pollutant. Some of the differences that are apparent as the averaging time is

increased is that there is less specific treatment of negative VSP cases and that the average

emissions for Mode 14 for either the 5-second or 10-second averaging times are typically the

same as or perhaps even a little less than that for Mode 13. The lack of a monotonic increase

when comparing Modes 13 and 14 could be attributable in part to small sample sizes for these

two modes, but also could be attributable to the effects of averaging – for example, perhaps there

is less homogeneity in the data of Mode 14 than for other modes.

4.3 Evaluation of Different Averaging Times and Recommendations

Predicted versus actual emissions for individual trips/cycles in the modeling database were

evaluated for each of the three averaging times as a consideration to help in selecting a preferred

averaging time. For that purpose predictions for Modeling dataset are compared for the three

averaging time methods. As seen in Figure 4-6, predictions with all three averaging methods are

similar. The 95 percent confidence intervals overlap for almost all of the cycles, for all

pollutants. Overall, all three averaging times yield qualitatively similar results. Thus, it is not

readily evident that one is clearly superior to another.

The five and ten second averaging times were found to offer no advantage over the one second

averaging time in terms of predictive ability with respect to total emissions for a trip. Because it

is easier to work directly with the one second average data, the one second averaging time

approach was selected.
64

1

10

100

1000

ARTEF FWY-F FWY- HI NYCC F505 IM240 FTP75 US06 On- Board

Average CO Emissions (g)

1 Second5 Seconds 10 Seconds

100

1000

10000

100000

ARTEF FWY-F FWY- HI NYCC F505 IM240 FTP75 US06 On- Board

Average CO2 Emissions (g)

1 Second5 Seconds10 Seconds

0.1

1

10

100

ARTEF FWY-F FWY- HI NYCC F505 IM240 FTP75 US06 On- Board

verage HC Emissions (g) A

1 Second5 Seconds 10 Seconds

0.1

1

10

100

ARTEF FWY-F FWY- HI NYCC F505 IM240 FTP75 US06 On- Board

verage NOx Emissions (g) A

1 Second5 Seconds10 Seconds

Figure 4-6. Comparison of Predicted Average Emissions of CO2, CO, HC, and NOx for Selected Driving Cycles Based Upon 1

Second, 5 Second, and 10 Second Averaging Time VSP Binning Approaches for the Modeling Database.
65

5 COMPARISON OF EMISSION FACTOR APPROACHES AND EVALUATION OF

THE ROLE OF REMOTE SENSING DATA

In this chapter, two different approaches to developing emission factors are compared and

evaluated. The objective of this chapter is to develop a recommendation for a preferred emission

factor approach, in response to the fifth key question of: what emission factor units should be

used?. The two approaches evaluated include mass per time emission factors (e.g., gram/second)

and the ratio of emissions of CO, HC, and NOx with respect to CO2. The latter was based upon

evaluation of the molar ratio of CO/CO2, HC/CO2, and NOx/CO2. Since most of the carbon in

the fuel is emitted in the form of CO2, the ratio approach is approximately equivalent to a gram

per gallon emission factor approach. Previous studies by others (e.g,. Singer and Harley, 1996)

have touted the potential benefits of a fuel-based approach to development of area-wide emission

inventories. However, such inventories are macro-scale in nature and would require a

representative average gram per gallon emission factor combined with good estimates of total

area wide fuel consumption. For meso-scale or micro-scale predictions, it will be necessary to

estimate emissions at a more local scale. In such instances, an understanding of the influence of

different driving modes on emission ratios is critically important. Furthermore, in order to

predict mass emissions using emission ratios, it is necessary to be able to predict mass per time

CO2 emission rates or mass per time fuel consumption.

Since one motivation for considering emission factors is potentially to facilitate accommodation

of remote sensing data, this chapter also deals with an evaluation of the relevance of remote

sensing data for model development. The evaluation is based upon comparison of modal

emission rates calculated based upon remote sensing data and compared with those calculated

from on-board measurements and dynamometer tests. Therefore, this chapter also addresses the

motivating question: What is the potential role and feasibility of incorporating RSD into the

conceptual modeling approach?

5.1 Background Regarding Emission Factor Units

Some investigators hypothesize that gram/gallon emission factors have less inherent variability

than do mass per time or mass per distance emission factors. NCSU is currently conducting an

independent study of this hypothesis, based upon analysis of on-board second-by-second data

collected as part of a previous study (Frey et al., 2001). Our preliminary findings do not fully

support the hypothesis. As an example, we illustrate results for modal analysis of gram per

second and gram per gallon emission factors for NO for a 1999 Ford Taurus in Figure 5-1. The

gram per gallon emission factors are approximately equivalent to the ratio of NO to CO2

emissions, since CO2 emissions are linearly proportional to fuel consumption to a very good

approximation. In this case, there is significant variability in emissions among the four driving

modes considered regardless of the emission factor units employed. For example, as shown in

Figure 5-1, the average acceleration emission rates are approximately a factor of 10 or more

greater than average idle emission rates for both emission factor units. Thus, it is clearly not the

case in this instance that emission ratios or g/gallon
66

0.01

0.1

1

10

Average NO Modal Emission

s

Idle Acceleration Deceleration Cruise

Milligrams/Second Grams/Gallon

Site: Chapel Hill Rd.

Vehicle: 1999 Ford 

 Taurus

n: 141

Figure 5-1. Average Modal Rates for Absolute and Normalized NO Emissions for a 1999 Ford

Taurus Driven on Chapel Hill Road in Cary, NC (Source: NCSU)

emission factors have substantially less variability from one mode to another than do mass per

time emission factors. The results tend to vary for different vehicles and for different pollutants

based upon our preliminary study. For example, the g/gallon emission factors for HC may be

more nearly similar for different driving modes than the g/gallon emission factors for CO or NO.

CO2 emissions are almost constant regardless of the driving mode; however, this is because the

vast majority of carbon in the fuel is emitted as CO2. Thus, a g CO2/gallon emission factor is

essentially a surrogate for the carbon content of the fuel.

Even if g/gallon emission factors are the same for different driving modes, the fuel consumption

rate is not. Figure 5-2 illustrates the variability in fuel consumption rate on a mass per time basis

as a function of different driving modes. For example, the average fuel consumption rate during

acceleration mode is approximately a factor of five times greater than that during the idle mode,

and the average differences in fuel consumption rate among the modes are statistically

significant.

5.2 Background Regarding Remote Sensing Data

There are two critically important limitations of RSD data that must be acknowledged: (1) RSD

data are for a very short averaging time of approximately 1 second, with no information

regarding vehicle activity and emissions either before or after the “snapshot” of the

measurement; and (2) RSD data support estimation of relative emission rates (e.g., ratios of

HC/CO2 and NO/CO2 or similar), or fuel-based emission rates (e.g., g/gallon), but cannot

directly provide g/mile or g/sec emission rates. Secondly, one would need to estimate fuel

consumption or CO2 emissions on a mass per time basis in order to convert all other g/gallon or
67

ratio emission estimates to a mass per time basis. RSD data will not provide a basis for

estimating CO2 emissions on a mass per time basis or for estimating fuel economy in order to

estimate gallon/sec fuel consumption.

Before combining RSD data with second-by-second data, it is first important to determine

whether RSD data and the second-by-second data are sufficiently consistent that a combination

of the two would be meaningful. This comparison is possible if the second-by-second data are

converted to the same basis as the RSD data. Therefore, as part of the evaluation of RSD data,

modal emission rates were calculated based upon RSD data using the modal definitions that were

applied to the modeling dataset, but taking into account the inability to stratify RSD data with

respect to odometer reading. We hypothesize that relative differences in average emission rates

among the RSD-derived estimates should be similar to those observed based upon the secondby-second data sources. If not, then there may be some significant discrepancy in the data

sources that would caution against combining the RSD data into the model development process.

A key limitation of RSD data is that it is essentially a one second (or shorter) snapshot of

emissions at a specific location. Therefore, there is no vehicle history available from which to

estimate modal emission rates for an averaging time greater than one second. The range of intervehicle variability and the range of uncertainty in average modal emissions estimated based upon

RSD data were also evaluated. For example, if the RSD data were excessively noisy (high

variability) then it may not be useful as a supplement to other data sources in developing the

modal.

The appropriateness of using RSD data for developing the model depends on what type of

weighting scheme is preferable. If a time-based weighting scheme is selected, then RSD data

will likely contribute only modestly to the estimation of average emissions within a bin, because

of the short duration of the RSD measurements. If a vehicle weighted approach is selected, then

RSD data will contribute disproportionately to the estimation of average emissions, because it is

possible to obtain measurements on thousands of vehicles per day using RSDs, but each

measurement is for less than one second (typically).

The two emission factor approaches were compared and evaluated based upon the following

criteria: (1) which approach results in a “simpler” model; (2) which approach is best able to

explain variability in emissions; (3) which approach has the least amount of residual error; (4)

which approach can best support model verification or validation; and (5) which approach offers

the most flexibility. The comparison of mass per time factors versus ratios was performed for

both the NCSU and VSP based approaches, and results for both approaches are presented. In

addition, the modal emission rates of both approaches were compared with those estimated from

RSD data. Because RSD data are based upon measurements made during less than one second,

the comparison of mass per time emission factors and emission ratios was done based only upon

the one second averaging time for the modeling database.
68

0.1

1

10

Average Modal Fuel Consumption 

Idle Acceleration Deceleration Cruise

Grams/Second

Site: Chapel Hill Rd.

Vehicle: 1999 Ford 

 Taurus

n: 141

Figure 5-2. Average Modal Rates for Absolute Fuel Consumption for 1999 Ford Taurus Driven

on Chapel Hill Road (Source: NCSU)

5.3 Comparison of Emission Factors and Emission Ratios Based Upon the NCSU Modal

Approach

The NCSU modal definitions were applied to emission ratios calculated from the modeling

dataset. The results when applied to mass per time emission factors were previously described.

To compare with remote sensing data, the emission rates in the modeling dataset were converted

to molar ratios with respect to CO2. Specifically, the emission rate in g/sec was divided by the

molecule weight of the pollutant to get the emission rate in mole/sec, and was further divided by

the CO2 emission rate in mole/sec. The molecular weight used for the HC emission rate is

assumed to be as hexane (C6H14). Figure 5-3 gives the comparison between the modeling dataset

and remote sensing data for each NCSU mode for each pollutant.
69

Figure 5-3. Average Modal Emission Ratios for CO/CO2, HC/CO2, and NOx/CO2 Based Upon NCSU Modes for the Modeling Data

and Remote Sensing Data

0

0.160.120.080.04

0.2

3 21 22 23 24 25 26 41 42 43 44 45 46

tio O/CO2 RaC

Modeling DatasetRemote Sensing

0

0.00080.00060.00040.0002

0.001

3 21 22 23 24 25 26 41 42 43 44 45 46

tio C/CO2 RaH

Modeling DatasetRemote Sensing

0

0.0060.0050.0040.0030.0020.001

3 21 22 23 24 25 26 41 42 43 44 45 46

tio Ox/CO2 RaN

Modeling DatasetRemote Sensing
70

The average emission rates for the NCSU modal bins have a different sensitivity when evaluated

in terms of emission ratios compared to the previously described analysis in terms of grams per

second. For example, for the CO/CO2 ratio, there is relatively little sensitivity to the mode

definitions applied to the calibration data set when comparing the deceleration and cruise modes.

Idle is not shown because idle cannot be observed with the RSD database. However, for the

acceleration modes, and particularly Modes 23, 24, 25, and 26, there is a substantial increase in

the CO/CO2 ratio as VSP increases. Similar results are observed for the HC/CO2 ratios based

upon the calibration data set. However, for the NO/CO2 ratio, the results for the calibration data

set are qualitatively similar to those obtained for the gram/second emission factor units.

Specifically, emissions for deceleration (Mode 3) are comparatively low. Within the

acceleration mode, the emissions ratio increases as VSP increases, when comparing Modes 21

through 26. For the cruise mode, the emissions ratio increases with average speed among the

three low VSP modes (Modes 41, 42, and 43) and with VSP for the three high VSP modes

(Modes 44, 45, and 46). The results obtained with the second-by-second data help set

expectations for trends that would be expected in the RSD data set.

The results from analysis of the RSD data are qualitatively different from those obtained with the

calibration database, in at least two key respects. First, the trend for inter-modal variability in

emissions is very different for the RSD data than for the calibration database for both NOx and

HC. Specifically, there is much less variability when comparing the lowest and highest average

modal rates and the trends when comparing modes are either not as strong or are not apparent at

all. For example, for the RSD HC/CO2 ratios, there is little apparent sensitivity to VSP among

the acceleration modes, in contrast to the observation based upon the calibration database. The

average NOx/CO2 ratios estimated based upon RSD data are less sensitive to changes in VSP for

the acceleration modes, and to changes in speed and VSP for the cruise modes, than the

calibration data. Because RSDs measure HC using NDIR, it may be the case that the RSD

measurements are not responding to total HC and that the ratio of measurable HC to total HC

might vary depending on the mode. For the NOx/CO2 ratio, there has been discussion in the

literature and elsewhere to the effect that RSDs have less sensitivity to NOx than to

measurements for other pollutants; however, it is not known if this is an important factor in this

particular case.

The trends for the CO/CO2 ratio from the RSD data are more comparable to those from the

calibration data compared to the other two pollutants; however, the magnitude of the average

CO/CO2 emission estimates for the three highest VSP acceleration modes is substantially less

than that for calibration data set. This might be because of differences in the vehicle mix;

however, the RSD data used for this analysis is based upon Tier 1 vehicles, as is the calibration

data set. It is possible, perhaps, that there is a different mix of mileage accumulation or other

factors; however, since the average emission rates differ by a factor of two, and each average is

based upon a fairly large sample size, it could be the case that there are differences in the

estimates because of differences in the measurement techniques. It is possible that the RSD data

may contain a better representation of high emitting vehicles, or of high emissions episodes for

normal emitting vehicles, than does the modeling data set. These questions are revisited in the

next sections based upon comparison of emission ratios for the VSP-based approach using both

the modeling data set and the RSD data.
71

5.4 Comparison of Emission Factors and Emission Ratios Based Upon the VSP Modal

Approach

Emission ratios were estimated for the 14 VSP modes based upon the modeling data set and were

compared with modal emission ratios estimated from the RSD data, as shown in Figure 5-4.

The results for the emission ratios estimated based upon the modeling data set indicate that for

the CO/CO2 ratio there is relatively little sensitivity of the ratios for the low VSP modes,

including Modes 1 through 10. However, for the high VSP modes, the emission ratios increase

substantially with VSP. An almost similar trend is observed for the HC/CO2 ratio, with the

exception that Mode 3 has a higher average emission rate than the other low VSP modes. For

the NOx/CO2 ratio, the relative trend among the average emission ratios for each mode is very

similar to that observed for the mass per time emission rates. For example, there is a monotonic

increase in the average NOx/CO2 emissions ratio from Mode 3 through Mode 14. These results

illustrate that in order to capture variability in NOx emissions with a model, it would be

necessary to retain approximately the same number of modes as for the mass per time emission

factor approach. Because the implementation of a modal modeling approach is simpler from a

software design and data management perspective if the same modal definitions are used for all

pollutants, the ability to capture variability in NOx emissions would be binding constraint

regarding a lower bound for the number of modes needed. Thus, even though it might be

possible to have far fewer than 14 modes to adequately capture variability in CO and HC

emissions, a reduction in the number of modes applied to all pollutants would result in loss of

explanatory power for NOx.

The comparison of RSD data with the results from the modeling data set illustrates important

similarities and important differences. The key similarities are the following: (1) the average

CO/CO2 ratios are relatively small for the 10 lowest VSP modes; (2) the average CO/CO2 ratios

increase monotonically for the four highest VSP modes; and (3) the average emission ratios

agree well between the two data sources for both NOx/CO2 and HC/CO2 for Modes 12 and 13.

The key differences are: (1) there is generally less variability among the average modal emission

ratios for the RSD data than for the modeling data set; (2) the RSD data produces lower average

ratios for CO/CO2 for Modes 13 and 14; and (3) the RSD data produces much higher average

ratio estimates for both HC/CO2 and NOx/CO2 for the low VSP modes. These differences could

be because of a different combination of fuel, vehicle characteristics, and odometer reading

(which is unobservable with RSD technology) between the two data sets. Presumably, the RSD

would contain better representation of on-road high emitters, and possibly such vehicles lead to

higher emissions for the lower VSP modes more so than for the higher VSP modes. Thus, at

best, the comparison is inclusive. However, it is not possible to stratify the RSD by odometer

reading, which complicates the ability to refine the comparison.

In the next sections, the activity underlying the RSD data is compared to that of the modeling

data set and of the IM240 data set to obtain additional insights regarding key differences between

the RSD data and the modeling data set.
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Figure 5-4. Average Modal Emission Ratios for CO/CO2, HC/CO2, and NOx/CO2 Based Upon VSP Modes for the Modeling Data and

Remote Sensing Data for Vehicles with Engine Displacement of Less than 3.5 Liters

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Figure 5-5. Average Modal Emission Ratios for CO/CO2, HC/CO2, and NOx/CO2 Based Upon VSP Bins for the Modeling Data and

Remote Sensing Data for Vehicles with Engine Displacement of Greater than 3.5 Liters

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5.5 Comparison of Variability in Emission Ratios for Selected VSP Bins for the

Modeling and RSD Data Sets

In this section, the variability in emission ratios for selected modes is compared for both the

modeling and RSD data sets in order to evaluate the characteristics of the RSD data. Since

odometer reading is not given in the remote sensing data, it is not possible to stratify the data by

odometer reading. However, engine displacement is available in the RSD data. Therefore, the

comparison is based upon the 14 VSP modes stratified by two engine displacement categories

with a cutpoint of 3.5 liters. Examples are shown here for three selected modes based upon

engine displacements of less than or equal to 3.5 liters.

For VSP Mode 1, a comparison is shown in Figure 5-6 of the distribution of variability for

second-by-second data of the modeling dataset and of the data in the RSD data set. Mode 1 is

based upon negative values of VSP. For both the CO/CO2 and NOx/CO2 ratios, the RSD data

generally produces higher values than does the modeling data set. Although not shown as data

values in the graphs because a log scale was used for the x-axis, the modeling data set contained

data values of less than zero, which are considered to reflect measurement error and not to be

significantly different than a true value of zero or just slightly greater than zero. For the HC/CO2

ratio, the RSD data produced a distribution with less variability than the modeling data set. Most

of the data in the modeling data set are based upon FID measurements, in comparison to the

NDIR method used in remote sensing. Therefore, the difference in the shape of the distributions

from the two datasets may reflect differences attributable to the measurement methods.

Figure 5-6. Comparison of Variability for CO/CO2, HC/CO2, and NOx/CO2 Ratios for Modeling

Data and Remote Sensing Data for VSP Mode 1 with Engine Size Less Than 3.5 Liters
76

Figure 5-7. Comparison of Variability for CO/CO2, HC/CO2, and NOx/CO2 Ratios for Modeling

Data and Remote Sensing Data for VSP Mode 7 with Engine Size Less Than 3.5 Liters

Figures 5-7 and 5-8 show comparisons of the variability in emission ratios for Modes 7 and 12,

respectively. For the CO/CO2 and NOx/CO2 ratios, the general trends are similar to that for

Mode 1 in that the average value of the RSD data is generally larger than that of the modeling

data set. Furthermore, the entire distribution of ratios for the RSD data is toward larger values

for most of the percentiles of the distribution, when compared to the modeling data set.

However, the modeling data set typically captures a wider range of variability than the RSD data,

as indicated by comparing the range from the lowest to the highest values of the distributions.

For example, the modeling data typically span three to five orders of magnitude, whereas the

RSD data typically span approximately two to three orders of magnitude in most cases. The

upper tails of the emission ratio distributions are comparable for Modes 1 and 7 for both the

CO/CO2 and NOx/CO2 ratios. For Mode 12, the upper tail of the RSD data distributions typically

have larger values than for the modeling data set.

For the HC/CO2 ratio, the results for Mode 7 are qualitatively similar to that for Mode 1. For

Mode 12, the modeling data set produced a higher average value of the HC/CO2 ratio compared

to the RSD data set. Typically, the RSD data produced a narrower range of values and smaller

values at the upper tail of the distribution when compared to the modeling data in the case of the

HC/CO2 ratio.

When comparing the three modes illustrated in Figures 5-6 through 5-8, it should be borne in

mind that the relative difference between the RSD data and the modeling data set decrease as the
77

Figure 5-8. Comparison of Variability for CO/CO2, HC/CO2, and NOx/CO2 Ratios for Modeling

Data and Remote Sensing Data for VSP Mode 12 with Engine Size Less Than 3.5 Liters

VSP increases. For example, the distributions for the NOx/CO2 ratios for Mode 1 are more

separated from each other than is the case for Mode 12.

5.6 Comparison of Vehicle Activity in the RSD and Modeling Databases

For the CO/CO2 and NOx/CO2 ratios when compared for VSP modes, it is typically the case that

the RSD data produces larger average emission estimates and generally has higher emission

ratios than does the modeling data set. In order to gain insight into possible reasons for these

differences, the vehicle activity in the RSD data base was compared with that of the modeling

database. The comparison was done on the basis of the distribution of speed and acceleration

within specific modes. The comparison was done for selected modes for vehicles with engine

displacement less than 3.5 liters. Because odometer reading is unobservable for RSD

measurements, it was not possible to stratify the comparison with respect to odometer reading.

Three modes were selected for the comparison: (1) Mode 1 to represent low VSP values; (2)

Mode 7 to represent moderate VSP values; and (3) Mode 12 to represent large VSP values. The

cumulative distributions of both speed and acceleration, and the joint distributions of speed and

acceleration, are shown for both the modeling data and the RSD data in Figures 5-9, 5-10, and 5-

11 for VSP Modes 1, 7, and 12, respectively, for vehicles with engine displacement less than 3.5

liters.

For Mode 1, it is clear that the RSD data have less variability in speed than the modeling data.

Furthermore, the RSD data have a larger proportion of larger acceleration rates than the
78

modeling data. Mode 1 is based upon VSP values of less than -2 kW/ton. Although the range of

VSP values in any individual bin is constrained by the definition of the mode, there are many

different combinations of speed and acceleration that can produce a narrow range of values of

VSP. For example, large magnitudes of deceleration at low speed can produce the same VSP

estimate as a small magnitude of deceleration at higher speed. When comparing the scatter plots

of acceleration versus speed for the modeling data set and the RSD data set, it is clear that the

modeling data set addresses a much wider range of combinations of acceleration and speed than

does the RSD data. Most of the RSD data are for decelerations of greater than -3 mph/sec and

for speeds between 20 mph and 40 mph, versus decelerations of typically -5 mph/sec or greater

and speeds ranging from approximately zero to greater than 70 mph. For this mode and strata,

the RSD data produced higher average emission ratios for all three pollutants. It is clear that the

range of activity for Mode 1 is very different for the RSD data compared to the remote sensing

data.

For Mode 7, the remote sensing data have a much narrower range of speeds, from approximately

20 mph to 40 mph, compared to the modeling data, for which speed varies from approximately

10 mph to over 80 mph. However, the RSD data typically have much larger values of

acceleration, with a range from approximately 1 mph/sec to as much as approximately 4

mph/sec. The modeling data set has a large proportion of acceleration data of less than 1

mph/sec, although the upper tail of the cumulative distribution of acceleration includes a small

percentage of values greater than 4 mph/sec. When comparing the scatter plots of acceleration

versus speed, it is clear that the modeling data set has a wider range of activity. The larger

average acceleration for the RSD data set is a notable difference compared to the modeling data

set, and may be a key reason as to why the emission ratios for the RSD data tend to be larger

than for the modeling data set.

For Mode 12, the modeling data set has a remarkably wider range of variability in speed than the

RSD data, but also has a noticeably lower average value of acceleration. The RSD data have

speeds ranging typically from approximately 25 mph to 50 mph, versus a range of approximately

20 mph to 80 mph for the modeling data set. The RSD data have accelerations ranging from 2

mph/sec to 4 mph/sec, compared to a range of approximately 0 mph/sec to 4 mph/sec for the

modeling data. A comparison of the scatter plots in Figure 5-11 suggests that the modeling data

capture a wider range of variability in activity, but have a much smaller proportion of activity

associated with larger accelerations when compared to the RSD data. Thus, it is likely that these

differences in activity account for at least some of the differences in emissions.

It should be pointed out that although the statistical analysis presented in Chapter 3 identified

VSP, engine displacement, and odometer reading as the three most important explanatory

variables, there may be opportunities to further disaggregate the data in the future when working

with larger data sets than the one used in this study. For example, as shown in Chapter 9, there

are some differences in average emissions for a VSP mode when taking into account differences

in speed and/or acceleration that might help explain additional variability not captured by the

model developed in Chapter 3.
79

Figure 5-9. Comparison of Vehicle Activity, In Terms of Speed and Acceleration, for the Remote Sensing and Modeling Data Sets,

for VSP Mode 1 for Vehicles with Engine Displacement Less Than 3.5 Liters.
80

Figure 5-10. Comparison of Vehicle Activity, In Terms of Speed and Acceleration, for the Remote Sensing and Modeling Data Sets,

for VSP Mode 7 for Vehicles with Engine Displacement Less Than 3.5 Liters.
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Figure 5-11. Comparison of Vehicle Activity, In Terms of Speed and Acceleration, for the Remote Sensing and Modeling Data Sets,

for VSP Mode 12 for Vehicles with Engine Displacement Less Than 3.5 Liters.
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5.7 Comparison of Emissions Ratios and Vehicle Activity Between the RSD and IM240

Databases

Because the RSD data are based upon observations of a large number of on-road vehicles, and

because the IM240 are based upon a sample of on-road vehicles that is believed to better

represent high emitters than other data sets used in this study, it was hypothesized that there may

be similarities between the IM240 dynamometer data and the RSD data. To explore this

hypothesis, the average modal emission ratios estimated from the two data sets were compared.

The comparison was stratified based upon engine displacement since information was available

in both data sets regarding this explanatory variable. The average emission ratios based upon

both data sets are shown in Figure 5-12 for vehicles with engine displacement of less than 3.5

liters and in Figure 5-13 for vehicles with engine displacement of greater than 3.5 liters.

Figure 5-12 illustrates a general similarity between the emission ratios estimated from the two

different datasets. Particularly in the case of the HC/CO2 ratios, for 9 of the 14 modes there is

not a significant difference in the average ratios when comparing the two datasets. Both datasets

imply high emission ratios for the low VSP modes, slightly lower emission ratios for the

moderate VSP modes, and relatively high values for Mode 13. In the case of the CO/CO2 ratios,

although only 5 of the 14 modes are statistically similar to each other, the qualitative trends for

both data sets are similar. In particular, the emission ratios for Modes 1 through 10 are relatively

constant for a given data set, but the average ratios increase substantially for Modes 11 through

13. Mode 14 tends to have somewhat lower values than does Mode 13. For the NOx/CO2 ratios,

the RSD data tends to have higher average values for the lowest VSP modes, and the IM240 data

tends to have higher average values for Modes 5 to 14.

The comparisons in Figure 5-13 are less clear than those of Figure 5-12 mainly because there are

fewer data, particularly for the IM240 database, that fall into this particular strata, and especially

for the high VSP modes (e.g., Modes 12, 13, and 14). The results suggest that there are

similarities in the two datasets for CO and NOx, except for the highest VSP modes, and that for

HC the RSD data typically have higher ratios than the IM240 data except for Mode 1.

Overall, based upon the results shown in Figures 5-12 and 5-13, there are important qualitative

similarities in the average emission ratios for both data sets. However, a key question is whether

the similarities in emissions are because of similarities in vehicle activity. In order to answer this

question, the distributions of each of speed and acceleration were compared, as were the joint

distributions of both speed and acceleration. These comparisons are shown in Figures 5-14, 5-

15, and 5-16 for Modes 1, 7, and 12 for vehicles with engine displacement of less than 3.5 liters.

For the Mode 1 comparison shown in Figure 5-14, the IM240 data have a wider range of speed,

but it is apparent that the distribution of speeds for the IM240 data are bimodal. Thus, there is a

large proportion of speeds in the range of approximately 10 to 30 mph, as well as a smaller

proportion of speeds in the range of approximately 50 to 60 mph. In contrast, as noted in the

previous section, the distribution of speeds for the RSD data is primarily between 20 mph and 40

mph. The RSD data tend to have a larger proportion of larger acceleration rates than does the

IM240 data. A comparison of the scatter plots for acceleration versus speed indicates that the

IM240 data captures a much wider range of variability in terms of different combinations of
83

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Figure 5-12. Average Modal CO/CO2, HC/CO2, and NOx/CO2 Emission Ratios Based Upon VSP Bins for the Modeling Data and

IM240 Driving Cycle Data for Vehicles with Engine Displacement of Less Than 3.5 Liters.
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Figure 5-13. Average Modal CO/CO2, HC/CO2, and NOx/CO2 Emission Ratios Based Upon VSP Bins for the Modeling Data and

IM240 Driving Cycle Data for Vehicles with Engine Displacement of Greater Than 3.5 Liters.
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Figure 5-14. Comparison of Vehicle Activity, In Terms of Speed and Acceleration, for the Remote Sensing and IM240 Driving Cycle

Data Sets, for VSP Mode 1 for Vehicles with Engine Displacement Less Than 3.5 Liters.
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Figure 5-15. Comparison of Vehicle Activity, In Terms of Speed and Acceleration, for the Remote Sensing and IM240 Driving Cycle

Data Sets, for VSP Mode 7 for Vehicles with Engine Displacement Less Than 3.5 Liters.
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Figure 5-16. Comparison of Vehicle Activity, In Terms of Speed and Acceleration, for the Remote Sensing and IM240 Driving Cycle

Data Sets, for VSP Mode 12 for Vehicles with Engine Displacement Less Than 3.5 Liters.
88

speed and acceleration than does the RSD data. The RSD data had a higher average emission

ratio for NOx but lower ratios for CO and HC for Mode 1 for vehicles with engine displacements

less than 3.5 liters.

For the Mode 7 comparison, the IM240 data are strongly bimodal with respect to both speed and

acceleration. The IM240 data have a wider range of values for speed and acceleration than do

the RSD data. In particular, there is more representation of higher speeds and a similar

representation of the upper tail of the distribution of acceleration when comparing the IM240

data to the RSD data.

For Mode 12, the IM240 data typically represent somewhat higher speeds but also somewhat

smaller accelerations than does the RSD data. However, for Mode 12, there are relatively few

data points for the IM240 data set in comparison to the RSD data.

Overall, although not conclusive, the comparison of vehicle activity in terms of speed and

acceleration between the IM240 and RSD data suggests that there are substantial differences in

activity patterns between the two data sets. Thus, although in some cases both data sets have

similar emission ratios, it is possible that such apparent similarities are actually based upon

differences in the vehicle and in the vehicle activity.

5.8 Summary and Recommendations

The key findings from the comparison of emission factor units and from the evaluation of RSD

data are briefly summarized here, followed by more detailed discussion:

• When comparing RSD to the modeling data:

– There is less variability in emission ratios of CO/CO2 and HC/CO2 for the low

VSP bins

– There is substantial variability in emissions for the high VSP bins

• for NOx, there is a need for a similar number of modes for the emission ratios and for

mass per time units in order to explain variability in emissions.

• Need CO2 (or fuel use) on a mass per time basis anyway, which motivates the need for a

modal approach such as that developed in Chapter 3 on a mass per time basis

• Because of the variability in NOx emissions even when emission ratios are used, and

because of the need to use a mass per time approach to estimate CO2 emissions, the use

of emission ratios instead of mass per time emission factors for only a subset of

pollutants does not offer any significant advantage, especially from a software/model

design perspective.

• RSD data are not a strong candidate for use in model development because some key

variables are not observable, such as odometer reading.

• The HC/CO2 emissions data from RSD do not appear to be comparable to that from the

modeling dataset because of the measurement techniques employed.

The results of the application of the binning methods to the modeling data set suggest that there

is less variability in emission ratios of CO/CO2 and HC/CO2 for the low VSP bins. However,

there is substantial variability in the NOx/CO2 ratio for the low VSP bins, and for all three

pollutants there is substantial variability in emissions among the high VSP bins. Therefore, the
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use of emission ratios instead of mass per time emission factors does not offer any advantage in

terms of reducing the number of modes needed to model emissions, if the same number of modes

are to be applied to all pollutants for simplicity of software design and data management.

The potential role of RSD data was evaluated based upon several comparisons: (1) comparison

of emission ratios for the RSD data versus the modeling data; (2) comparison of vehicle activity

for the RSD data versus the modeling data; (3) comparison of emission ratios for the RSD data

versus IM240 data; and (4) comparison of vehicle activity for the RSD data versus the IM240

data. The RSD data typically lead to higher emission ratios than the modeling data, especially

for lower VSP modes (e.g., Modes 1 through 10), especially for the NOx/CO2 and HC/CO2

ratios. Although it may be tempting to conclude that such differences are because the RSD data

might have a better representation of higher emitting vehicles, or of higher emissions episodes

with normal emitting vehicles, it is important to compare the vehicle activity of both data sets. A

comparison of the speed and acceleration distributions for both data sets revealed that the RSD

data typically had lower average speeds and higher average accelerations than the modeling data

set. As shown in Chapter 9, it can be the case within a VSP mode that some of the variability in

emissions can be explained in terms of speed and/or acceleration. Therefore, although not

conclusive at this time, it is possible that the differences in emissions between the RSD data and

the modeling data may be attributable, at least in part, to differences in activity patterns.

A comparison of the IM240 and RSD data suggests that these two data sets have quantitatively

similar emission ratios in some cases and qualitatively similar emission ratio trends among the

modes in a number of cases. However, a comparison of the speed and acceleration distributions

of the two datasets indicates that there is a substantially different activity pattern for the two data

sets, with the IM240 data based upon bimodal speed distributions with a wider range in

variability in speed, higher average speed, and lower average acceleration, than the RSD data.

Thus, it is possible that the apparent similarities between these two data sets in terms of average

emission ratios may be because of compensating differences in fleet mix and activity patterns, or

it is possible that the emission ratios are robust to the differences in activity patterns.

The key findings regarding the potential role of RSD data are discussed here. RSD data were not

considered to be a strong candidate for use in model development because some key variables,

particularly odometer reading, are not observable. Odometer reading has been shown in earlier

chapters to be an important predictive variable. The HC/CO2 emissions data from RSD do not

appear to be comparable to that from the modeling dataset, which may be because of significant

differences in the measurement technique employed. It is also possible that there are differences

in fuel composition that may cause some of the observed differences. Finally, the differences in

emission ratios for the RSD data versus the modeling data may be attributable in part to

differences in activity patterns not yet captured by the conceptual modeling approach. This latter

issue deserves some exploration as part of future work.

It has been hypothesized that RSD data may be useful in helping to better characterize the

distribution of different emitting vehicles, and particularly high emitting vehicles. It should be

noted that because RSD measurements are a snapshot of typically less than one second, and

because a normal emitting vehicle can have episodes of high emissions depending on the activity

pattern, it is not conclusive that a single high emissions ratio measurement of a vehicle enables
90

identification of such a vehicle as a high emitter. Thus, it is possible that a high emission ratio

may be associated with a high emitting vehicle or it could be associated with a high emissions

episode for a normal emitting vehicle. A comparison of the distribution of emission ratios for

the modeling data set versus that of the RSD data set suggests that the modeling data set captures

a wider relative range of variability than does the RSD data set, while at the same time the RSD

data often had higher average values than did the modeling data set. The upper tails of the

distributions of variability for a given mode for the modeling data set often overlapped

substantially with the upper tails of the distributions for the RSD data, suggesting that the highest

emission ratios in either data set were comparable. Thus, it could be the case that the modeling

dataset does not have the same proportional representation of high emitting vehicles, or of high

emissions episodes for normal emitting vehicles, as does the RSD data. These differences were

typically more pronounced for the low and moderate VSP modes. For the higher VSP modes,

the shapes of the distributions from the modeling data set and the RSD data set were very similar

for both the CO/CO2 and NOx/CO2 ratios.

The siting of the RSD instrument plays an important role in the range of activity that is observed.

It is clear from these data that the RSD sites had a much smaller range of variability in activity

patterns than did the dynamometer data or the onboard data that comprised the modeling data

base and the IM240 database. Since RSD’s are often sited at locations that are expected to have

positive accelerations or situations in which vehicles are under load, it is possible that there is a

bias in the activity pattern of the RSD data that is perhaps in part responsible for the apparent

differences in emissions when compared to the modeling data set. In this particular case,

although the range of speeds was typically less for the RSD data than for the other data sets, the

accelerations tended to be larger on average. Given these differences, it did not seem fruitful to

try to proceed with methods for making adjustments to the modeling data set in order to better

match the emission ratios estimated from the RSD data.

It is possible that RSD data could be used indirectly as a recruiting tool to try to obtain a

representative sample of vehicles for dynamometer and on-board testing, in order to improve the

representation of differently emitting vehicles.

In brief summary, for the purposes of this study, there was no substantial advantage found for

using emission ratios instead of mass per time emission factors. In either case, it is necessary to

estimate CO2 emission in mass per time units. Therefore, for consistency, mass per time units

are recommended for further analysis. Although there were differences in the emission ratios for

the RSD data versus the modeling data, there were also substantial differences in activity

patterns for the two data sets. Therefore, the RSD data were not used as part of model

development, but the comparisons suggest that there may be opportunities to refine the

conceptual modeling approach in the future by considering additional binning criteria based upon

speed and/or acceleration for the VSP modes.
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6 COMPARISON AND EVALUATION OF DATA WEIGHTING APPROACHES

The objective of this chapter is to compare and evaluate three approaches for weighting data: (1)

time-weighted; (2) vehicle weighted; or (3) trip-weighted. Based upon comparison and

evaluation of these three approaches, a preferred approach is recommended.

6.1 Methodological Considerations

In the time-weighted approach, data in each bin are averaged with respect to time. For secondby-second data, each second of data will have equal weight. For five second average data, each

five second time period of data will have equal weight. For ten second average data, each ten

second time period of data will have equal weight. The advantage of this approach is that data

can be combined from any number of vehicles within a vehicle category and the sample sizes

within each bin can become quite large. Furthermore, the time-weighted approach can be used

to support estimation of emissions for any arbitrary averaging time larger than that of the original

data. For example, 10 second average emission estimates can be developed by averaging over

10 seconds of one second data. Therefore, it is possible to consider, for example, how cruise

emissions that take place during a one minute period of freeway cruising might vary from one

time period to another. The inter-vehicle variability and fleet average uncertainty in emission

will be a function of the desired time periods. Another advantage of the time-weighted approach

is that more weight is given to vehicles that have undergone longer periods of testing. For

example, if RSD data were to be included in the development of a model based upon one second

averaging, each vehicle measured by the RSD would typically be represented by only one second

worth of data. In contrast, a vehicle that has undergone substantial on-road emissions

measurement might be represented by tens of thousands of seconds of data. Intuitively, it seems

appropriate to give more weight to vehicles that have undergone more testing time.

In the vehicle-weighted approach, data in each bin are averaged with respect to each vehicle.

Thus, for each vehicle, a single representative estimate of emissions would be developed. For

example, the simplest vehicle-weighted approach would be to calculate an average emission rate

for each vehicle based upon data for that vehicle within a given bin. The average emission rate

for all data in the bin would then be calculated by averaging the emission rates estimated for

each vehicle represented in the bin. This approach will tend to give less weight to vehicles for

which there are many seconds (or other averaging time periods) of data, and will give

disproportionate weight to vehicles for which there are relatively few time periods of data. For

example, if there are 10 seconds of data for vehicle 1, 30 seconds of data for vehicle 2, and 50

seconds of data for vehicle 3, the average emission rate for each vehicle would first be calculated

Then, the three vehicle average values would be given equal weight to determine the average

over all three vehicles. Thus, the average emission rate for Vehicle 1 would have equal weight

to that of Vehicle 2 or Vehicle 3 even though there are three and five times, respectively, as

much data for these latter two vehicles. Of course, a minimum data requirement criterion could

be specified such that a vehicle average would be calculated only for vehicles for which there are

a minimum number of seconds of data. However, there would still be variability in the amount

of testing time for different vehicles in the database, and there would remain a potential problem

that vehicles with less testing time than others would in effect have an influence comparable to

those with more testing time.
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The vehicle weight approach offers some potential disadvantages. One is that the weight given

to different vehicles may be intuitively unappealing. For example, in the extreme case, one

second of RSD data for a vehicle could be equally weighted with many hours of on-board data

for another vehicle. Secondly, the use of a vehicle-weighted approach may complicate the

quantification of variability and uncertainty. The range of inter-vehicle variability and of fleet

average uncertainty is a function of averaging time, with the latter point illustrated quantitatively

in Chapter 7. For example, one second emissions of a vehicle varies much more from one

second to another than 10 second average emissions vary from one 10 second period to another.

With the time-weighted approach, it is possible to combine data to represent any averaging time

of interest, conditioned on assumptions regarding the structure of the database (e.g., statistical

independence). With the vehicle weighted approach, the averaging time of the analysis is

unknown and is itself variable, because the average modal emission rate for one vehicle will

typically be based upon a different time period than that for another vehicle. For example, if

there are five seconds of data in a given bin for one vehicle, and 10 minutes of data in the same

bin for another vehicle, the averages of each of the two vehicles are based upon disparate

averaging times.

The trip-weighted approach was included as an alternative to be evaluated in this study. The

term “trip” essentially refers to an averaging time selected as the basis for aggregate emissions

measurements. For example, data for each vehicle could be divided into segments representing

trips. Each set of data from the same vehicle and “trip” within a bin would be averaged to arrive

at a “trip-average” emission estimate for that vehicle. A vehicle for which there is a large

amount of on-board data might be represented by more than one such “trip”. Therefore, this

approach will tend to give more weight to vehicles for which there are more data, similar to the

time-weighted approach. Unlike the vehicle-weighted approach, there is some attempt in the

trip-weighted approach to have more comparability with respect to the averaging time of the

data. However, there will still be variation in the number of averaging time periods that are the

basis for any trip average emission estimate in any given bin, since the speed profile of any given

trip will differ from any other given trip. Therefore, this approach has the same qualitative

limitations as the vehicle-weighted approach.

In the vehicle weighted and trip-weighted approach, there is no direct way to control for

averaging time. Therefore, the binned data will represent a mixture of unknown averaging times,

and any uncertainty estimate developed from these data will be of unknown pedigree with

respect to averaging time. Thus, we compared the three approaches with respect to the

characterization of uncertainty in average emission rates.

In choosing a preferred weighting method, consideration was given to the following criteria: (1)

technical rigor to support a defensible estimate of variability and uncertainty; (2) flexibility to

estimate variability and uncertainty for different averaging times; (3) practical aspects of the

performance of each method (e.g., tractability, ease of developing estimates); (4) compatibility of

the method with data availability and overall modeling objectives.

6.2 Comparison of Weighting Approaches

A component of this work that is also closely related to the issue of analysis of variability and

uncertainty is comparison of different approaches for weighting data. Specifically, time, trip,
93

and vehicle-weighted approaches were compared. The analysis results reported in this section

are based upon 14 VSP bins without further binning. The quantitative results for comparison of

the three approaches with respect to the 56-bin approach are given in the Appendix.

The empirical distributions of variability and fitted parametric distributions are displayed for the

examples of VSP Modes 1, 7, and 14 for each of the four pollutants considered and for the timeweighted approach in Figures 6-1, 6-2, and 6-3, respectively. For example, for VSP Mode 1, the

Weibull distribution fitted to the NOx data appears to adequately describe the general

characteristics of the data, including the central tendency, the upper tail, and the positive

skewness. However, there are some deviances in the fit that are noticeable, such between the 50th

and 90th percentiles. Similarly, the lognormal distribution fit to the CO2 data offers a

qualitatively good fit, but deviates from the data in some respects, such as near the 20th percentile

and near the 65th percentile. The deviations of the fitted distribution from the data in these two

cases are not large in an absolute sense, and are likely to be acceptable. In contrast, the fitted

distributions for HC and CO for Mode 1 do not appear to offer good fits. For Mode 7, all the

distributions fitted appear to capture the key trends in the data for all four pollutants. For Mode

14, the fits are generally very good for NOx, HC, and CO2, but in the case of CO the fitted

distribution does not agree with the data, especially above the 70th percentile. Overall, in most

cases, the fitted distributions appear to perform well. In the case of CO for Mode 14, the mean

and standard deviation of the fitted distribution are substantially different than that of the data.

In addition to the time-weighted approach, the results shown graphically in Figures 6-4 through

6-6 are for the trip-weighted approach for Modes 1, 7, and 14, respectively. Similar results are

displayed for the vehicle-weighted approach in Figures 6-7, 6-8, and 6-9 for Modes 1, 7, and 14,

respectively. For the trip-weighted approach, the parametric distributions provide a good fit to

the data for Modes 1 and 7. For Mode 14, the fits for HC and CO2 are good. The fits for NOx

and particularly CO are less than ideal, although key qualitative trends are captured by the fits.

Generally, the comparison of the parametric distributions with the data is similar for the vehicleweighted approach: the fits are typically good for Modes 1 and 7; the fits for HC and CO2 for

Mode 14 are good; and the fits for NOx and CO for Mode 14 are not as good. As discussed in

Chaper 7, an alternative to fitting distributions using Maximum Likelihood Estimation (MLE) is

to use the Method of Matching Moments (MoMM). In the latter method, the fitted distribution

such as a lognormal will have a mean and standard deviation the same as that of the data. This

point is further illustrated in Chapter 7.

The selected types of distributions and the parameters of the fitted distributions are summarized

for all modes and pollutants in Table 6-1 for the trip-weighted approach. A similar summary is

given for the vehicle weighted approach in Table 6-2. Similar information regarding the time

weighted approach is given in the chapter on uncertainty analysis.

A direct graphical comparison of the variability associated with the time, trip, and vehicle

weighted approaches is given in Figures 6-10 and 6-11 for NO and HC, respectively, for Modes

1, 7, and 14. It is typically the case that the time-based approach has a longer upper tail to the

right than the other approaches, which involve averaging of the data. Mode 7 for NOx offers the

clearest example of the effects of averaging the data; in this case, the upper tail of the distribution

is substantially smaller than for the time-based approach.
94

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Figure 6-1. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #1

Characterized by Empirical and Fitted Parametric Probability Distribution Models for Secondby-Second Data.

Sec-By-Sec, VSP Bin 1

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona WL L L a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
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Figure 6-2. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #7

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Second-by-Second Data.

Sec-By-Sec, VSP Bin 7

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona WL W L a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
96

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Figure 6-3. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #14

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Second-by-Second Data.

Sec-By-Sec, VSP Bin 14

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona WL W L a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
97

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Figure 6-4. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #1

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Trip Average Means

Trip Average, VSP Bin 1

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona LLL L a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
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Figure 6-5. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #7

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Trip Average Means.

Trip Average, VSP Bin 7

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona WL W L a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
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Figure 6-6. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #14

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Trip Average Means.

Trip Average, VSP Bin 14

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona WWW W a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
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Figure 6-7. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #1

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Vehicle Average Means.

Vehicle Average, VSP Bin 1

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona LLL W a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
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Figure 6-8. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #7

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Vehicle Average Means.

Vehicle Average, VSP Bin 7

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona WL W L a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
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Figure 6-9. Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Mode #14

Characterized by Empirical Probability Distribution and Fitted Parametric Probability

Distribution for Vehicle Average Means.

Vehicle Average, VSP Bin 14

Pollutant NO HC CO2 CO

Fitted Parametric Distributiona WWW W a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
103

Table 6-1. Summary of Fitted Parametric Probability Distributions for Variability in NOx, HC, CO2, and CO Emissions (g/sec) for

VSP Bins for Trip Average Means

NO HC CO2 CO

VSP Bins Fit Para.

Dista para 1 para 2 Fit Para. Dista Fit Para. Dista para 1 para 2 Fit Para. Dista Fit Para. Dista para 1

1 L 1.1746 -7.1968 L 1.4327 -8.4431 L 0.5305 0.5235 L 1.6843 -5.58812 L 1.2133 -7.222 L 1.5103 -8.6318 L 0.5001 0.5467 L 1.6961 -5.83673 L 1.1893 -7.5064 L 1.5108 -8.7568 L 0.4868 0.3599 L 1.5637 -6.16894 W 0.0021 1.0996 L 1.4482 -8.2217 L 0.3563 0.906 L 1.6522 -5.32735 W 0.0025 1.0771 L 1.3764 -8.0443 L 0.3256 1.0988 L 1.5545 -5.12646 W 0.0031 1.039 L 1.3421 -7.9055 W 3.9612 3.798 L 1.5702 -5.00687 W 0.0036 1.0137 L 1.3774 -7.8134 W 4.5374 3.5135 L 1.595 -4.86618 W 0.0046 0.9858 L 1.4163 -7.7013 W 5.1194 3.2378 L 1.6647 -4.77479 W 0.0055 0.9031 L 1.4125 -7.5305 W 5.773 2.9653 L 1.8428 -4.6522

10 W 0.0061 0.8227 L 1.5656 -7.4463 W 6.3325 2.5081 W 0.0283 0.526311 W 0.0072 0.6991 W 0.0018 0.6731 W 7.5883 2.3674 W 0.0518 0.514812 W 0.012 0.8189 W 0.0036 0.733 W 9.0917 2.5755 W 0.1501 0.521813 W 0.0129 0.8494 W 0.005 0.742 W 10.2248 2.679 W 0.2868 0.509214 W 0.0151 0.6942 W 0.0059 0.7189 W 10.925 2.1308 W 0.4011 0.4567

a W = Weibull; para 1 of Weibull is scale parameter and para 2 of Weibull is shape parameter;

 L = lognormal; para 1 of lognormal is φ and para 2 of lognormal is ξ; Parameters were calculated using SAS.
104

Table 6-2. Summary of Fitted Parametric Probability Distributions for Variability in NOx, HC, CO2, and CO Emissions (g/sec) for

VSP Bins for Vehicle Average Means

NO HC CO2 CO

VSP Bins Fit Para.

Dista para 1 para 2 Fit Para. Dista Fit Para. Dista para 1 para 2 Fit Para. Dista Fit Para. Dista para 1

1 L 1.162 -7.4631 L 1.223 -8.3866 L 0.4726 0.2934 W 0.0127 0.91022 W 0.001 0.8876 L 1.3677 -8.7468 L 0.4384 0.3477 L 1.4844 -5.65183 L 1.1366 -7.6305 L 1.313 -8.8287 L 0.3567 0.2279 L 1.3664 -6.07374 W 0.0016 1.1128 L 1.2155 -8.3183 W 2.5339 4.3527 L 1.22 -5.11055 W 0.0023 1.116 L 1.0873 -7.9406 W 3.2985 5.0571 L 1.1426 -4.71036 W 0.0031 1.117 L 1.0185 -7.6843 W 4.0899 4.7385 L 1.1543 -4.30787 W 0.0038 1.0844 L 1.0469 -7.4981 W 4.8834 4.2448 L 1.256 -4.01678 W 0.0048 1.0523 L 1.1083 -7.2772 W 5.6715 3.9835 L 1.4549 -3.79979 W 0.0059 1.0186 L 1.0985 -7.0789 W 6.4881 3.7832 L 1.5313 -3.5608

10 W 0.007 0.9649 L 1.0641 -6.8674 W 7.2909 3.4183 W 0.0886 0.755711 W 0.0098 0.9198 L 1.1483 -6.5547 W 8.7287 3.0995 W 0.1588 0.696912 W 0.0131 0.919 L 1.199 -6.1941 W 10.1588 2.8832 W 0.3065 0.6813 W 0.0143 0.8884 L 1.2823 -5.8853 L 0.3453 2.2655 W 0.5212 0.637314 W 0.0185 0.7472 W 0.0065 0.7644 W 12.7194 2.7592 W 0.7882 0.5785

a W = Weibull; para 1 of Weibull is scale parameter and para 2 of Weibull is shape parameter;

 L = lognormal; para 1 of lognormal is φ and para 2 of lognormal is ξ; Parameters were calculated using SAS.
105

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Figure 6-10. Comparison of Variability in NOx Emissions for Time-Average, Trip-Average, and

Vehicle-Average Approaches, Characterized by Parametric Probability Distributions, for VSP

Modes #1, #7 and #14.
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Figure 6-11. Comparison of Variability in HC Emissions for Time-Average, Trip-Average, and

Vehicle-Average Approaches, Characterized by Parametric Probability Distributions, for VSP

Modes #1, #7 and #14.
107

Because different types of averaging lead to different weighting of information in the database,

the mean and standard deviation will differ depending upon which weighting approach is used.

Table 6-3 summarizes how much the estimate of mean emissions changes within a mode for a

given pollutant depending upon whether a trip-average or vehicle-average approach is used. The

percentage changes shown in the table are with respect to the time-weighted mean values. The

average value for the trip weighted approach can be either larger or smaller than that of the timeweighted approach for a given pollutant when comparing different modes. For example, the tripweighted average for NOx emissions for Mode 1 is 25 percent greater than for the time weighted

approach, but for Mode 8 the trip-weighted average is 20 percent less than that of the timeweighted approach. Both the trip- and vehicle-weighted approaches have substantially different

mean estimates in specific cases compared to the time weighted approach. These differences

range from essentially no difference to an increase of over 100 percent or a decrease of as much

as –42 percent. For NOx, CO, and HC, the differences in means exceed 10 percent in magnitude

for 80 percent of the pollutant/mode combinations. In contrast, for CO2, a difference in mean

values of more than 10 percent in magnitude occurred for only approximately 30 percent of the

modes. Thus, while mean CO2 emission estimates are more robust to the selection of averaging

methods, the average emissions of NOx, CO, and HC are dependent upon what method is

selected.

A similar comparison is shown in Table 6-4 for the difference in standard deviations estimated

based upon the three alternative weighting schemes. The magnitude of the relative differences is

larger for the standard deviation than it is for the mean. However, unlike the differences in mean

values, which may be higher or lower than the time-weighted approach, the standard deviations

based upon either the trip- or vehicle-weighted approaches are generally substantially smaller

than those based upon the time-weighted approach. This result is expected, since averaging will

lead to a reduction in variability in the data. The reduction in the standard deviation is on the

order of 30 to 60 percent. For most pollutant/mode combinations, the vehicle-weighted approach

leads to more reduction in the standard deviation than does the trip weighted approach. This is

because the database includes multiple trips for some vehicles.

The relative range of uncertainty in the mean modal emissions is given in Table 6-5 for timeaverages, in Table 6-6 for trip-averages and in Table 6-7 for vehicle-averages. The relative

ranges of uncertainty in the mean modal emissions for trip-averages and vehicle-averages can be

compared with the time-weighted results. Because the sample size becomes smaller as secondby-second data are averaged, even though the variability in emissions decreases to some extent

(as indicated by the results in Table 6-4), the uncertainty in the average increases when compared

to the time based approach. For example, consider the range of uncertainty in average NOx

emissions for Mode 1. For the time-weighted approach, it is plus or minus 3 percent. For the

trip-weighted approach, it is plus or minus 15 percent. For the vehicle weighted approach, it is

plus or minus 26 percent.

The average emission rates and the 95 percent confidence intervals for the averages are

compared graphically in Figure 6-12 for each of the four pollutants and for each mode.
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Table 6-3. Comparison of Mean Emissions of NOx, HC, CO2, and CO Emissions (g/sec) for VSP Bins: Time-Average, Trip-Average,

and Vehicle-Average Approaches.

NOa HCa CO2a COa

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Bin

mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff.

1 0.0011 0.0014 25 0.0011 -3 0.0007 0.0006 -9 0.0005 -28 1.6337 1.9294 18 1.4894 -9 0.0110 0.0151 37 0.0134 222 0.0009 0.0014 53 0.0010 12 0.0004 0.0006 35 0.0004 -6 1.5254 1.9498 28 1.5461 1 0.0065 0.0141 118 0.0100 543 0.0006 0.0011 91 0.0009 53 0.0007 0.0005 -17 0.0004 -42 1.2050 1.6322 35 1.3391 11 0.0051 0.0088 72 0.0062 224 0.0016 0.0020 21 0.0015 -7 0.0006 0.0008 21 0.0006 -14 2.3308 2.6267 13 2.3142 -1 0.0114 0.0186 64 0.0130 145 0.0025 0.0025 -1 0.0022 -13 0.0008 0.0008 3 0.0007 -16 3.0882 3.1464 2 3.0461 -1 0.0156 0.0217 39 0.0177 136 0.0034 0.0031 -10 0.0029 -14 0.0011 0.0009 -14 0.0008 -22 3.7963 3.5920 -5 3.7772 -1 0.0224 0.0219 -2 0.0263 177 0.0044 0.0036 -19 0.0036 -18 0.0013 0.0010 -21 0.0010 -24 4.4899 4.0968 -9 4.4868 0 0.0287 0.0258 -10 0.0374 308 0.0058 0.0046 -20 0.0047 -18 0.0016 0.0012 -27 0.0013 -20 5.0543 4.6024 -9 5.1861 3 0.0413 0.0333 -20 0.0573 399 0.0070 0.0058 -17 0.0059 -16 0.0019 0.0014 -28 0.0015 -20 5.6496 5.1663 -9 5.9128 5 0.0526 0.0418 -21 0.0766 4610 0.0085 0.0068 -19 0.0071 -16 0.0023 0.0017 -26 0.0018 -20 6.1914 5.6271 -9 6.5947 7 0.0728 0.0553 -24 0.1074 4811 0.0112 0.0092 -18 0.0102 -9 0.0031 0.0025 -19 0.0026 -17 7.1117 6.7425 -5 7.8458 10 0.1304 0.1047 -20 0.2036 5612 0.0144 0.0134 -7 0.0137 -5 0.0045 0.0046 1 0.0039 -13 8.0558 8.0667 0 9.0446 12 0.2712 0.2701 0 0.3922 4513 0.0171 0.0140 -18 0.0152 -11 0.0060 0.0064 6 0.0056 -5 9.2945 9.0835 -2 10.2076 10 0.4878 0.5091 4 0.6891 4114 0.0198 0.0193 -3 0.0225 13 0.0098 0.0074 -25 0.0077 -21 9.9292 9.6832 -2 11.3174 14 0.8101 0.8049 -1 1.1002 36a Unit of mean: g/sec; Unit of diff.: %.
109

Table 6-4. Comparison of Standard Deviations of Variability in NOx, HC, CO2, and CO Emissions (g/sec) for VSP Bins: TimeAverage, Trip-Average, and Vehicle-Average Approaches.

NOa HCa CO2a COa

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Bin

std. dev.

std.dev. diff.

std.dev. diff. mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff.

1 0.0029 0.0016 -44 0.0013 -56 0.0030 0.0013 -58 0.0007 -77 1.2557 1.0260 -18 0.6768 -46 0.0642 0.0389 -39 0.0184 -712 0.0028 0.0018 -37 0.0012 -57 0.0016 0.0014 -11 0.0007 -59 1.1395 1.0169 -11 0.6415 -44 0.0477 0.0457 -4 0.0196 -593 0.0020 0.0020 0 0.0013 -34 0.0024 0.0012 -48 0.0006 -74 0.7727 1.0000 29 0.5182 -33 0.0361 0.0261 -28 0.0121 -674 0.0037 0.0019 -48 0.0014 -62 0.0021 0.0016 -25 0.0009 -57 1.3014 0.9097 -30 0.5896 -55 0.0585 0.0409 -30 0.0254 -575 0.0051 0.0026 -49 0.0023 -54 0.0025 0.0015 -40 0.0010 -60 1.4529 0.9255 -36 0.6721 -54 0.0982 0.0536 -45 0.0300 -696 0.0067 0.0033 -51 0.0032 -53 0.0030 0.0015 -49 0.0012 -60 1.6444 1.0125 -38 0.8341 -49 0.1416 0.0459 -68 0.0453 -687 0.0079 0.0040 -49 0.0040 -49 0.0032 0.0017 -45 0.0014 -55 1.8382 1.2678 -31 1.0729 -42 0.1159 0.0567 -51 0.0667 -428 0.0092 0.0053 -42 0.0053 -43 0.0041 0.0020 -52 0.0019 -54 2.0072 1.5369 -23 1.3394 -33 0.1732 0.0836 -52 0.1086 -379 0.0116 0.0068 -41 0.0064 -45 0.0041 0.0023 -44 0.0020 -51 2.1765 1.8802 -14 1.6092 -26 0.1976 0.1020 -48 0.1446 -2710 0.0135 0.0086 -36 0.0083 -39 0.0049 0.0029 -40 0.0025 -50 2.4519 2.4060 -2 2.0248 -17 0.2841 0.1282 -55 0.1793 -3711 0.0174 0.0130 -25 0.0120 -31 0.0065 0.0048 -27 0.0035 -47 2.9053 3.0212 4 2.6930 -7 0.4291 0.2295 -47 0.3122 -2712 0.0207 0.0168 -19 0.0159 -23 0.0097 0.0093 -5 0.0052 -47 3.2287 3.3547 4 3.4101 6 0.7115 0.4418 -38 0.5094 -2813 0.0251 0.0169 -32 0.0187 -25 0.0118 0.0133 12 0.0074 -37 3.8763 3.6558 -6 3.4751 -10 0.9704 0.7430 -23 0.8259 -1514 0.0278 0.0305 10 0.0357 28 0.0192 0.0113 -41 0.0111 -42 4.8908 4.8015 -2 4.5328 -7 1.4374 1.1124 -23 1.2247 -15a Unit of diff.: %.
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Table 6-5. Summary of Relative 95% Confidence Intervals for NOx, HC, CO2, and CO Mean Emissions for VSP Bins for the TimeAverage Approach

NOa HCa CO2a COa

VSP Bins

mean lower upper mean lower upper mean lower upper mean lower upper

1 0.0011 -3 3 0.0007 -5 5 1.6337 -1 1 0.0110 -6 62 0.0009 -5 5 0.0004 -5 5 1.5254 -1 1 0.0065 -10 103 0.0006 -4 4 0.0007 -4 4 1.2050 -1 1 0.0051 -7 74 0.0016 -3 3 0.0006 -4 4 2.3308 -1 1 0.0114 -6 65 0.0025 -3 3 0.0008 -4 4 3.0882 -1 1 0.0156 -8 86 0.0034 -3 3 0.0011 -4 4 3.7963 -1 1 0.0224 -9 97 0.0044 -3 3 0.0013 -4 4 4.4899 -1 1 0.0287 -7 78 0.0058 -3 3 0.0016 -5 5 5.0543 -1 1 0.0413 -8 89 0.0070 -4 4 0.0019 -5 5 5.6496 -1 1 0.0526 -8 8

10 0.0085 -4 4 0.0023 -5 5 6.1914 -1 1 0.0728 -9 911 0.0112 -5 5 0.0031 -6 6 7.1117 -1 1 0.1304 -10 1012 0.0144 -6 6 0.0045 -9 9 8.0558 -2 2 0.2712 -11 1113 0.0171 -8 8 0.0060 -11 11 9.2945 -2 2 0.4878 -11 1114 0.0198 -9 9 0.0098 -13 13 9.9292 -3 3 0.8101 -12 12

a Unit of mean: g/sec; Unit of lower and upper bound: %.
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Table 6-6. Summary of Relative 95% Confidence Intervals for NOx, HC, CO2, and CO Mean Emissions for VSP Bins for the TripAverage Approach.

NOa HCa CO2a COa

VSP Bins

mean lower upper mean lower upper mean lower upper mean lower upper

1 0.0014 -15 15 0.0006 -25 25 1.9294 -7 7 0.0151 -32 322 0.0014 -16 16 0.0006 -30 30 1.9498 -6 6 0.0141 -39 393 0.0011 -21 21 0.0005 -28 28 1.6322 -7 7 0.0088 -36 364 0.0020 -12 12 0.0008 -25 25 2.6267 -4 4 0.0186 -27 275 0.0025 -13 13 0.0008 -22 22 3.1464 -4 4 0.0217 -30 306 0.0031 -13 13 0.0009 -20 20 3.5920 -3 3 0.0219 -26 267 0.0036 -14 14 0.0010 -20 20 4.0968 -4 4 0.0258 -27 278 0.0046 -14 14 0.0012 -21 21 4.6024 -4 4 0.0333 -31 319 0.0058 -15 15 0.0014 -21 21 5.1663 -5 5 0.0418 -31 31

10 0.0068 -16 16 0.0017 -22 22 5.6271 -5 5 0.0553 -29 2911 0.0092 -20 20 0.0025 -26 26 6.7425 -6 6 0.1047 -30 3012 0.0134 -23 23 0.0046 -36 36 8.0667 -7 7 0.2701 -29 2913 0.0140 -24 24 0.0064 -41 41 9.0835 -8 8 0.5091 -29 2914 0.0193 -32 32 0.0074 -31 31 9.6832 -10 10 0.8049 -28 28

a Unit of mean: g/sec; Unit of lower and upper bound: %.
112

Table 6-7. Summary of Relative 95% Confidence Intervals for NOx, HC, CO2, and CO Mean Emissions for VSP Bins for the VehicleAverage Approach

NOa HCa CO2a COa

VSP Bins

mean lower upper mean lower upper mean lower upper mean lower upper

1 0.0011 -26 26 0.0005 -31 31 1.4894 -10 10 0.0134 -30 302 0.0010 -26 26 0.0004 -35 35 1.5461 -9 9 0.0100 -42 423 0.0009 -31 31 0.0004 -36 36 1.3391 -8 8 0.0062 -42 424 0.0015 -20 20 0.0006 -35 35 2.3142 -6 6 0.0130 -42 425 0.0022 -23 23 0.0007 -31 31 3.0461 -5 5 0.0177 -37 376 0.0029 -23 23 0.0008 -31 31 3.7772 -5 5 0.0263 -37 377 0.0036 -24 24 0.0010 -31 31 4.4868 -5 5 0.0374 -39 398 0.0047 -24 24 0.0013 -32 32 5.1861 -6 6 0.0573 -41 419 0.0059 -24 24 0.0015 -29 29 5.9128 -6 6 0.0766 -41 41

10 0.0071 -25 25 0.0018 -29 29 6.5947 -7 7 0.1074 -36 3611 0.0102 -26 26 0.0026 -29 29 7.8458 -7 7 0.2036 -33 3312 0.0137 -27 27 0.0039 -30 30 9.0446 -9 9 0.3922 -30 3013 0.0152 -30 30 0.0056 -32 32 10.2076 -8 8 0.6891 -29 2914 0.0225 -40 40 0.0077 -37 37 11.3174 -10 10 1.1002 -28 28

a Unit of mean: g/sec; Unit of lower and upper bounds: %.
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Figure 6-12. Comparison of Quantified Uncertainty in the Mean Emissions of NOx, HC, CO2, and CO for VSP Bins: Time-Average,

Trip-Average, and Vehicle-Average Approaches.

0.03500.03000.02500.02000.01500.01000.00500.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) O Emissions Estimate (g/seN

Time-AvgTrip-AvgVehicle-Avg

0.01200.01000.00800.00600.00400.00200.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) HC Emissions Estimate (g/se

Time-AvgTrip-AvgVehicle-Avg

8.00006.00004.00002.00000.0000

14.000012.000010.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) Emissions Estimate (g/se 2 OC

Time-AvgTrip-AvgVehicle-Avg

1.60001.40001.20001.00000.80000.60000.40000.20000.0000

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) O Emissions Estimate (g/seC

Time-AvgTrip-AvgVehicle-Avg
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The results for the “56-bin” approach given in the Appendix for the comparison of the three

weighting approaches are qualitatively similar to those shown in this chapter for the 14 VSP

bins.

6.3 Summary and Recommendation

The main findings from the comparison of the time, trip, and vehicle weighted approaches are as

follows:

• Compared to time-weighted approach, the means for the trip and vehicle weighted

approaches can be either higher or lower.

• The standard deviation decreases for the trip weighted approach, and further for the

vehicle weighted approach, when compared to the time weighted approach.

• Averaging time varies for both the trip and vehicle weighted approaches; there is no

standard averaging time

• The uncertainty in the average typically increases with more averaging over time,

because of smaller sample size.

• The trip and vehicle weighted approaches disproportionately give emphasis to trips or

vehicles with little data

Based upon these main findings, a judgment was made that the time weighted approach is the

preferred basis for development of a conceptual emission estimation model. The time weighted

approach offers flexibility in the future to weight the data by vehicle or trip if so desired. The

time weighted approach is predicated upon the assumption that data for a given vehicle

stratification (e.g., odometer reading and engine displacement) are representative of that strata.

It is easier from a software design and from an analysis perspective to work with time weighted

data, and such an approach will give more weight to vehicles or trips for which there are more

data, which is intuitively appealing.
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7 QUANTIFICATION OF VARIABILITY AND UNCERTAINTY

The estimation of uncertainty in the average emission rate for a mode depends upon the

variability in data for the mode, the variance within the data, and the sample size. Key issues

addressed in the analyses include the adequacy of selected parametric probability distribution

models for representing variability in data, and whether the range of uncertainty in the mean

values is sufficiently small that a normality approximately can be used to represent uncertainty in

the mean. To provide insight into these issues, results are presented of analysis of both

variability and uncertainty based upon the VSP modes for one-second average data. This chapter

includes a review of methodological considerations, quantification of variability for individual

modes, quantification of uncertainty for individual modes, and estimation of uncertainty for

driving cycles or trips.

7.1 Methodological Considerations

In uncertainty analysis, there are several sources of uncertainty that must be considered. The

first is the scenario being modeled. The second is the model itself. The third are the inputs to

the model. In practice, the term “model uncertainty” is typically understood to mean uncertainty

regarding the functional form of the model itself. Cullen and Frey (1999) address sources of

model uncertainty in detail in Chapter 3. Since MOVES is anticipated to be a data-driven model,

the uncertainty associated with model structure will be associated with the definitions of the bins.

For example, suppose that average emissions are sensitive to variation in engine displacement,

but that a bin-based approach is implemented without using engine displacement as one of the

binning criteria. Then the “model” would fail to enable prediction of the sensitivity of average

emissions with respect to different engine displacements. In this case, one could argue that there

is uncertainty associated with an incomplete formulation of the model structure. Once the model

structure is correctly specified, a technique can be applied for propagating uncertainty regarding

emissions in each bin to predict uncertainty of the final model results. This latter approach

addresses uncertainty in the inputs to the model (i.e. the data within each bin) but does not

address uncertainty associated with the model structure. The main objective this task is to focus

on a methodology for propagating uncertainty in the model input data (e.g., the data used in each

bin, and the activity data used to weight the binned data) in order to predict uncertainty in the

estimated emissions. Another consideration is that for the model predictions to be accurate,

which means free of bias when comparing the average model predictions to the true average

emissions in the real world, the model must be developed based upon a representative data set.

There are several key considerations pertaining to this task, which are briefly summarized in the

following list, with more detailed discussion in the following text:

• Variability

• Uncertainty

• Choice of empirical versus parametric probability distribution models

• Averaging Time

• Bottom-Up versus Top-Down Approaches
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7.1.1 Variability and Uncertainty

Variability refers to real differences in emissions, such as from one vehicle to another.

Uncertainty refers to lack of knowledge regarding the true value of a quantity. Sources of

variability include differences in vehicle/engine design, operating conditions, maintenance, fuel

composition, and ambient conditions (as examples). Sources of uncertainty include random

sampling error, measurement error, lack of representativeness, and lack of information. For

emission factor purposes, we are typically interested in average emissions for a particular fleet of

vehicles, rather than in trying to predict emissions for an individual vehicle. Therefore, we are

typically more interested in characterizing uncertainty in the average emission estimate than in

characterizing inter-vehicle variability in the estimate. The distinction between inter-vehicle

variability and fleet average uncertainty has been demonstrated quantitatively in many recent

studies based upon different sources of data, including dynamometer (bag) data, RSD, and onboard data (e.g., Kini and Frey, 1997; Frey, Bharvirkar, and Zheng, 1999; Frey and Zheng, 2002;

Frey, Rouphail, Unal, and Colyar, 2001; Frey, Unal, and Chen, 2002; Frey and Eichenberger,

1997a&b; Frey, Rouphail, Unal, and Dalton, 2000).

7.1.2 Empirical Distributions

EPA has emphasized that it prefers a data-driven approach to development of MOVES.

However, there is a trade-off between a purely data driven approach versus one that includes

some abstraction and aggregation. Specifically, in the context of quantitative analysis of

variability and uncertainty, there is a choice to be made regarding whether to base the analysis

upon empirical distributions or upon parametric distributions. In the former, each data point in

the database, such as for a single bin, is assigned a probability. Typically, data are assumed to be

equally weighted but this need not be the case in all situations. Based upon the data values and

the probability assigned to each data value, a step-wise empirical cumulative distribution

function can be developed. An example of a step-wise empirical cumulative distribution

function is given in Figure 7-1 for a data set with sample size of 10. A dataset such as this might

represent inter-vehicle variability in emissions.

0

0.2

0.4

0.6

0.8

1

02468

Example Data

Cumulative Probability

Figure 7-1. Example of a Stepwise Empirical Cumulative Distribution Function
117

The mean and standard deviation of the empirical distribution are calculated directly from the

data. The empirical distribution has the advantage that it is “true” to the data. However, there

are several important potential disadvantages: (1) there is no interpolation within the range of

observed data (i.e. the distribution has only discrete values corresponding to the original data set,

and there is zero probability of sampling any other value); (2) there is no plausible extrapolation

beyond the range of observed data; and (3) one must retain all of the data in order to characterize

the empirical distribution. Of these three potential disadvantages, the most important are the

second and third ones. The second one is important especially for small data sets. With any data

set, but especially smaller ones, it is unlikely that the observed highest value corresponds to the

true highest value, and that the observed lowest value corresponds to the true lowest value.

Thus, there is a possibility of failing to characterize the full range of variability. The third

potential disadvantage is that one must retain all of the original data. This is not a problem for a

very small data set, but for a very large data set this could be cumbersome.

7.1.3 Parametric Distributions

An alternative to empirical distributions is to use parametric probability distributions to represent

variability. The most commonly used parametric distributions, such as lognormal, gamma, or

Weibull, typically have only two parameters. The parameters are estimated using statistical

estimation approaches such as the method of matching moments or maximum likelihood

estimation. The distribution is fully specified once the values of its parameters are estimated.

Frey and Zheng (2002) give details of these methods, and such methods are incorporated into the

AuvTool software recently developed for EPA/ORD (Zheng and Frey, 2002). Thus, a data set of

any size can be represented based upon the type of distribution selected (i.e. lognormal, gamma,

Weibull) and the numerical values of its parameters.

Compared to empirical distributions, parametric distributions allow for interpolation within the

range of observed data, and for extrapolation to the upper and lower tails of the fitted

distribution. The latter is a potential advantage because it is likely that the observed range of

variability is less than the true range of variability as previously discussed. Because parametric

distributions provide a compact way of storing information regarding variability, the data storage

requirements will be less than if the empirical data set must be retained. However, there are

some key disadvantages to the use of parametric probability distributions in MOVES. If new

data are obtained and must be used to update the distributions for variability, then it will be

necessary to combine the new data with the previous data, and repeat the process of fitting a

parametric distribution to the data. Alternatively, one could fit a distribution to the new data, and

compare the distribution fitted to the new data with the one that was fitted to the previous data.

If the two distributions are not significantly different from each other, then there would be no

compelling need to update the previous distribution. If they are different, then one could create a

new mixture distribution. For example, if the original fitted distribution was based upon 10,000

data values, and if the new distribution was estimated from a new set of 5,000 data values, a

mixture distribution could be defined in which 2/3 weight is given to the first (older) distribution

and 1/3 weight is given to the second (newer) distribution.

7.1.4 Averaging Time

The issue of averaging time must be explicitly considering regardless of the choice of the

empirical or parametric approach to characterizing variability. The issue of averaging time is
118

also closely related to Subtask 1b and is addressed in Chapter 4 and implicitly in Chapter 6. For

example, suppose that the most basic form of data in MOVES is the average over a five second

time period. Any distribution developed directly from the 5-second data would represent

variability in emissions from one 5-second averaging time to another.

The data within a bin may include multiple data values for each of many vehicles. If the

objective is to estimate inter-vehicle variability, then all of the 5-second average data values for a

given vehicle should be averaged to arrive at a best estimate of the average emissions for a 5-

second period for a given bin for that vehicle. This calculation would be repeated for all vehicles

in the bin. Then, the average values for each vehicle would be used to construct a distribution of

inter-vehicle variability within that bin. The range of variability will be influenced by the fact

that the calculations are based upon a 5-second time period. In contrast, if the objective were to

estimate variability in emissions for a 10-second time period, then the range of inter-vehicle

variability would tend to be somewhat smaller. Through simple calculations with the data, as

long as there are sufficient data and as long as the data can reasonably be assumed to be

statistically independent, it is easy to combine data for two or more averaging time periods to

construct estimates of average emissions over longer time periods.

Calculation of inter-vehicle variability for different averaging times is conceptually straightforward when all data are retained within a bin and if empirical distributions are employed. If

parametric distributions are employed, then it is necessary to develop an analytical procedure for

adjusting the distribution based upon different averaging times. As a conceptual example, Frey

and Rhodes (1996) illustrated that the variability in power plant efficiency decreases as the

averaging increases from one hour, to one day, to one week, and so on. By analyzing example

data sets, it is possible to develop an estimate of how the variance of the data is expected to

decrease as the averaging time increases. For example, the variance is a function of averaging

time. The mean would not change. Thus, if a distribution were fitted to 5-second averaging time

data, a new distribution could be estimated for 10-second averaging time assuming the same

mean and using the empirically-derived function of variance versus averaging time. We have

developed a conceptual example of an analytical averaging time adjustment method for the

parametric approach.

7.1.5 Normal and High Emitters

Regardless of whether empirical or parametric distributions are used, all data within a bin

represent the distribution for variability, including both “normal” and “high” emitters whose data

fall into the given bin. Thus, there is no need for a discrete approach for normal and high

emitters as has been used in the past. However, it is important to have a data set that is

representative of both normal and high emitters when developing estimates of average emissions,

of variability in emissions, and of uncertainty in average emissions. The average emission rate is

calculated based upon all of the data within the bin, and therefore takes into account both normal

and high emitters. Similarly, the standard deviation is calculated based upon all of the data

within the bin, and therefore takes into account both normal and high emitters.

EPA implies that as part of future work, the effects of I/M programs on the distribution of

emission will be evaluated, but this is not included as a task in this work. For example, an I/M

program might identify vehicles with emissions above some cut-off, and result in modification or
119

repair of the vehicle so that its emissions are acceptable. The distribution of emissions can be

recalculated using numerical methods by truncating the distribution and by resampling from

within the range of acceptable emissions for those vehicles that successfully undergo repair or

modification. The numerical method can also be developed to take into account repeated failures

of some proportion of the vehicles and other considerations pertaining to IM programs.

7.1.6 Uncertainty Estimates for Final Model Results

A key objective of MOVES is to estimate uncertainty in final model results. To illustrate an

approach for estimating uncertainty in final model results, consider a simple conceptual example.

Suppose that we wish to know the fleet average tailpipe emissions for LDGVs operating on a

particular corridor. As input assumptions, we specify information such as the typical speed

profile (e.g., an average estimate of second-by-second speed), road grade at specific locations

along the corridor, proportions of vehicles in different vehicle type categories, ambient

conditions, and proportion of vehicles in different mileage accumulation categories for each

vehicle type. Based upon this type of information, weights are calculated for each bin in the

MOVES model. If we focus on a specific vehicle type and mileage accumulation category, we

can narrow the discussion to consideration only of factors having to do with the speed profile and

the road grade. For each bin, an average emission rate can be estimated. Suppose that the

emissions are in units of grams per second. In order to estimate the total emissions associated

with a given bin, there must be an estimate of the amount of time that the vehicle spends “in” the

bin (figuratively speaking), which can be obtained based upon the known or assumed speed

profile and based upon the road grade. For example, if a VSP approach is used, the speed profile

and the road grade are used to estimate VSP, and the numerical value of VSP for a given

segment of the trip is used to determine from which bin an emission estimate is needed. Thus, in

this example, an emission estimate is a time-weighted average of the mass per time emission

rates obtained from different bins. The amount of time allocated to each of the bins will differ.

The uncertainty in the average emissions for the trip is based upon the uncertainty in the average

emission rates within each bin. Potentially, there could also be uncertainty regarding the amount

of time (or weight) assigned to each bin.

The uncertainty in the average emission rate is typically influenced by the following key

considerations: (1) random sampling error; (2) measurement error; and (3) lack of

representativeness. The first of these three can be characterized based upon the variance in the

data for variability and upon the sample size. For example, if normality conditions for the

sampling distribution of the mean are satisfied, the standard error of the mean is given the by

standard deviation for variability divided by the square root of the sample size. If normality

conditions are not satisfied, then a more accurate result can be obtained using bootstrap

simulation. For example, Frey and Rhodes (1996, 1998, 1999), Frey and Burmaster (1999),

Frey, Bharvirkar, and Zheng (1999), Frey and Bammi (2002a&b), Frey and Eichenberger

(1997b), and Frey and Zheng (2002a&b) have demonstrated the use of bootstrap simulation to

characterize uncertainty in mean emission rates in situations when data are positively skewed

and, in many cases, for small sample size. The range of uncertainty in the average emissions is

typically asymmetric when there is a large amount of variability in the data and a small sample

size. The use of a normality assumption in such situations can lead to uncertainty estimates for

the mean that predict negative emission rates, which is physically impossible. Therefore, it is
120

important to employ an appropriate approach for quantifying uncertainty associated with random

sampling error. We recommend the use of bootstrap techniques where appropriate, and we will

also explore simplified solutions obtained based upon the results of bootstrap simulation. For

example, we hypothesize that it is possible to develop generic solution algorithms for estimating

asymmetric uncertainty ranges in the mean when the underlying data for variability can be fitted

reasonably well by a standard parametric distribution and when the coefficient of variation

(standard deviation divided by the mean) and the sample size of the original data are known.

Such algorithms could be used to make a rapid estimate of uncertainty in average emissions

without need to run a full bootstrap simulation in every case.

Random sampling error is typically the dominant source of uncertainty in the mean when the

sample sizes are small. Random sampling error in the mean is relatively easy to quantify in

practice because it can be inferred from the standard deviation and the sample size of the data,

which are usually known.

Measurement error is a potentially important source of uncertainty and should be considered in

developing MOVES. One drawback of estimating uncertainty based only upon random

sampling error is that for very large sample sizes, the random sampling error in the mean

becomes very small. If the measurement error has a random component, then the range of

observed variability in the data is larger than the true range of variability in the actual emissions.

Therefore, random measurement errors in the data are reflected in the range of uncertainty in the

mean emission rates estimated using techniques for random sampling error. However, if

measurement error has a systematic component (bias), statistical analysis alone will not detect

this without comparison to some benchmark. Measurement error may not be well known,

however. Therefore, this source of uncertainty can be difficult to quantify in practice. Since the

random component of measurement error influences the estimate of uncertainty in the mean

obtained from random sampling error-based estimated, the primary consideration in

incorporating measurement error more fully into the analysis is to properly distinguish random

measurement error from observed variability (e.g., Zheng, 2002) and to account for biases in

measurements.

Uncertainty because of lack of representativeness cannot be quantified based upon statistical

analysis of variation within a dataset obtained by only one method. In order to quantify

nonrepresentativeness, which relates to bias (also referred to as systematic error or lack of

accuracy), it is necessary to have a benchmark of the true value of the quantity. By using onboard data, a key goal of MOVES is to develop emission estimates based upon real-world onroad data. Thus, the fundamental basis of MOVES is to use representative, real world data. The

validation aspects of this project also aim at testing the representativeness of the data used for

model development. Overall, the focus of this project was on methods for quantifying

uncertainty associated with random sampling error, which also is influenced by random

measurement errors.

Monte Carlo simulation or similar numerical methods (e.g., Latin Hypercube Sampling) can be

used to propagate distributions for uncertainty in average emissions for a bin to arrive at an

estimate of uncertainty in the total emissions (e.g., Frey and Rhodes, 1996; Frey and Zheng,
121

2001; Zheng and Frey, 2002). In cases with linear models in which normality assumptions are

reasonable, analytical solutions can also be used (Cullen and Frey, 1999).

7.1.7 Bottom-Up and Top-Down Approaches

In the shoot-out, NCSU illustrated both a bottom-up and top-down approach for estimating intervehicle variability and fleet average uncertainty in emissions. The bottom-up approach was

based upon estimating variability or uncertainty for individual modes and using statistical

formulas to estimate the variability or uncertainty in the total emissions. The top-down approach

was based upon comparing trip emissions predictions of the model with the actual observed trip

emissions. Based upon statistical analysis of the parity plots of predictions versus observations,

a 95 percent probability prediction interval was estimated for inter-vehicle variability and a 95

percent confidence interval was estimated for uncertainty in the mean.

In principle, the bottom-up approach will be the more flexible and rigorous approach, and it will

also have an advantage of allowing for identification of which bins contributed the most to

uncertainty in the total emissions estimates. The top-down approach will typically be an easier

but less flexible approach, and it will not provide any insight regarding key sources of

uncertainty.

The primary approach explored in this chapter is the bottom-up approach. This approach is more

consistent with the EPA objective of characterizing variability in emissions within bins.

However, the top-down approach is illustrated in the validation comparisons of average driving

cycle emissions, as discussed in Chapter 9.

7.1.8 Summary of Methodological Considerations

The focus here is to demonstrate a methodology for characterizing inter-vehicle variability in the

binned data and uncertainty in the estimate of the final model result. The methodology was

demonstrated for the pilot modal emission rates. The emphasis of the work was on a parametric

distribution-based approach. The parametric approach was selected because of the attractiveness

of compactly representing large data sets within a bin using only a distribution type and a few

parameters. The adequacy of a purely parametric approach is assessed. A method for properly

characterizing the effect of averaging time on variability (and, in turn, on uncertainty) is

demonstrated.

7.2 Quantification of Variability

Parametric probability distribution models that were considered for fit to data include normal,

lognormal and Weibull distributions. These distributions were selected because they often offer

good fits to dataset. In particular, the lognormal distribution is often a good candidate for fitting

to non-negative positively skewed data, and can be theoretically justified as a descriptor of

emissions data because both emissions and the lognormal distribution are based upon

multiplicative processes. The Weibull distribution can also be used to fit to nonnegative

positively skewed data. However, the Weibull distribution has additional flexibility to take on

different shapes and often has a shorter upper tail than the lognormal distribution does, when

viewed as a cumulative distribution function. The less “tail-heavy” nature of the Weibull

distribution often provides an empirically better fit than does the lognormal distribution. The
122

normal distribution often provides a good fit but is appropriate for use with non-negative data

only if the ratio of the standard deviation to the mean is sufficiently small (e.g., around 0.2 or

less). Otherwise, the normal distribution may lead to predictions of negative values with

unacceptable frequency. In general, it is usually not appropriate to use the normal distribution to

represent variability within a bin, but it is often appropriate to use the normal distribution to

describe uncertainty in the average.

The probability density function (PDF) of the normal distribution is:

2

2

2

( )

2

1 ( ) σ

μ

πσ

− −

=

x

f x e − ∞ < x < ∞ (7-1)

The PDF of lognormal distribution:

2

2

2

(ln )

1

2

1 ( ) φ

ξ

πφ

− −

=

x

e

x

f x 0 < x < ∞ (7-2)

The PDF of the Weibull distribution, shape parameter k and scale parameter c:

k

c

x

k

k x e

c

k f x

( ) 1 ( ) − − = 0 ≤ x < ∞ (7-3)

Fitting of parametric distributions to data was conducted using “SAS” software. Criteria for

selecting a best fit are inherently subjective, but can be aided by the use of statistical goodnessof-fit tests (e.g., Cullen and Frey, 1999). Each such test emphasizes a particular criterion for a

good fit, which may or may not be relevant to the needs of a particular analyst or assessment.

Furthermore, with very large sample sizes, which are often the case for data sets based upon

second-by-second data, the goodness-of-fit (GOF) tests are very sensitive and may reject a

distribution that in other respects would be acceptable. For example, a visual comparison of the

distribution and the data may indicate that the distribution provides a “good” fit even though the

fit was rejected by the GOF test.

As examples, results of fitting parametric distributions to VSP mode data are shown for NOx,

HC, CO2, and CO in Figures 7-1, 7-2, 7-3 and 7-4 for VSP Modes 1, 4, 8 and 12, respectively.

The purpose here is to present representative results. Graphical analysis was done, however, for

all bins, even though not all graphs are shown here. The graphs were generated using SAS. For

VSP Mode 1, the Weibull distribution fitted to the NOx data appears to adequately describe the

general characteristics of the data, including the central tendency, the upper tail, and the positive

skewness. However, there are some deviances in the fit that are noticeable, such between the 50th

and 80th percentiles. Similarly, the lognormal distribution fit to the CO2 data offers a

qualitatively good fit, but deviates from the data in some respects. The deviations of the fitted

distribution from the data in these two cases are not large in an absolute sense, and are likely to

be acceptable. In contrast, the fitted distributions for HC and CO for Mode 1 do not appear to

offer good fits. For Mode 4, all the distributions fitted appear to capture the key trends in the

data for all four pollutants. For Mode 8, the fits are generally good for all four pollutants,

especially for NO. For Mode 12, the fitted distributions appear to agree with the data.
123

0.00 0.02 0.04

no_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0.0 0.1 0.2

hc_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0 10

CO2_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0.0 0.5 1.0 1.5

CO_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

Figure 7-1. Variability in NOx, HC, CO2, and CO Emissions for VSP Mode #1 Characterized by

Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time Average,

Odometer reading < 50,000 miles, Engine Displacement < 3.5 liters.

Sec-By-Sec, VSP Bin 1

Pollutant NOx HC CO2 CO

Fitted Parametric Distributiona WLWL a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
124

0.00 0.02 0.04

no_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0.00 0.02 0.04

hc_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0 5 10 15

CO2_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0.0 0.5 1.0

CO_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

Figure 7-2. Variability in NOx, HC, CO2, and CO Emissions for VSP Mode #4 Characterized by

Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time Average,

Odometer reading < 50,000 miles, Engine Displacement > 3.5 liters.

Sec-By-Sec, VSP Bin 4

Pollutant NOx HC CO2 CO

Fitted Parametric Distributiona WLL L a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
125

0.00 0.02 0.04 0.06 0.08

no_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0.00 0.02 0.04 0.06 0.08

hc_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0 5 10 15

CO2_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0.0 0.5 1.0 1.5

CO_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

Figure 7-3. Variability in NOx, HC, CO2, and CO Emissions for VSP Mode #8 Characterized by

Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time Average,

Odometer reading > 50,000 miles, Engine Displacement < 3.5 liters.

Sec-By-Sec, VSP Bin 8

Pollutant NOx HC CO2 CO

Fitted Parametric Distributiona W WW W a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
126

0.0 0.1 0.2

no_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0.00 0.05 0.10

hc_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0 5 10 15 20

CO2_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

0 2 4 6

CO_gpsec

0

0.5

1

C

u

m

u

l

a

t

i

v

e

D

Figure 7-4. Variability in NOx, HC, CO2, and CO Emissions for VSP Mode #12 Characterized

by Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time

Average, Odometer reading > 50,000 miles, Engine Displacement > 3.5 liters.

Sec-By-Sec, VSP Bin 12

Pollutant NOx HC CO2 CO

Fitted Parametric Distributiona W WL W a

 N = normal; L = lognormal; W = Weibull.

Empirical CDF

Fitted Parametric Distribution
127

Overall, in most cases, the fitted distributions appear to compare well with the data. Because

statistical GOF tests are too sensitive, from a practical perspective, when the sample size

becomes large, alternative criteria for evaluating goodness-of-fit were sought. One such criterion

is to evaluate the absolute difference between the mean of the data and the mean of the fitted

distribution. A second criterion is to evaluate the absolute difference of the standard deviation of

the data versus that of the fitted distribution. Therefore, these absolute differences were

calculated for each of the 14 VSP modes, for each of the four strata by engine displacement and

odometer reading reading, and for each of the four pollutants.

The distributions were fitted to the data using Maximum Likelihood Estimation (MLE). The

choice of MLE was made on the basis that MLE is commonly used and is considered to be a

more statistically efficient method than other approaches, such as the Method of Matching

Moments (MoMM) (Cullen and Frey, 2002). However, MLE has a potential disadvantage in

that the central moments of the fitted distribution (e.g., the mean and standard deviation) may not

be the same as those of the data to which the distribution was fit. In contrast, for MoMM

estimates of the distribution parameters, the fitted distribution will have a mean and standard

deviation the same as that of the data. In most cases, the difference of the means and standard

deviations between fitted distributions and the data are not large in an absolute sense, as shown

in Tables 7-1 and 7-2, respectively. For example, for VSP Bins 1101 through 1114, which

represent data for odometer reading < 50,000 miles, and engine displacement < 3.5 liters, the

largest absolute deviation in the mean values for NOx is for Mode 12 of this strata (identified as

VSP Bin 1112 in Table 7-1), with an absolute difference of 0.0004 g/sec. This difference is in

comparison to a mean from the data set of 0.0121 g/sec, and a mean from the fitted distribution

of 0.0125 g/sec. Therefore, on a relative basis, this difference is only approximately three

percent of the mean of the data. For the other 13 modes for this pollutant and strata, the absolute

differences are smaller. However, in some cases, the relative differences are very large. For

example, for Mode 1104, the absolute difference is -0.00028 g/sec compared to a data mean of

0.00117. Thus, the relative difference in this case is -24 percent. However, the absolute

difference in the mean for Mode 1104 is only 70 percent of the absolute difference for Mode

1112. Typically, the largest absolute differences are small compared to the highest average

emission rates among the modes for given pollutant and strata, although there are some

exceptions (e.g., Mode 1211 for CO). The exceptions typically point to situations in which a

single component distribution cannot provide a good fit because the data are inherently some

type of mixture distributions.

Based upon a review of the results in Tables 7-1 and 7-2, criteria for discriminating good and bad

fit were proposed for different pollutants. These criteria are shown in the second column of

Table 7-3. For example, for NOx, if the absolute difference in the mean of the MLE fitted

distribution versus that of the data is larger than the magnitude of the criteria value, which is

0.001 g/sec, the fit is judged not to be good. When the absolute differences in the mean of the

fitted distribution is less than the criteria value, the fit was also judged to be acceptable. Of the

56 modes, 49 of the modes for NOx have differences in the mean between the data and the fitted

distribution of less than the criteria value. For CO, 48 of the modes satisfy the criteria value, for

HC 54 of the modes satisfy the critera, and for CO2 all 56 modes satisfy the criteria value.
128

Table 7-1. Comparison of Mean between Empirical Data Set and Fitted Parametric Distributions, Absolute Basis

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

1101 0.000901 0.000714 -0.000187 0.000450 0.000460 0.0000103 1.67 1.68 0.00901 0.00781 0.00644 -0.001361102 0.000628 0.000554 -0.0000745 0.000257 0.000187 -0.0000701 1.46 1.45 -0.0122 0.00391 0.00248 -0.001431103 0.000346 0.000221 -0.000124 0.000406 0.000290 -0.000116 1.14 1.11 -0.0213 0.00335 0.00232 -0.001031104 0.00117 0.000894 -0.000279 0.000432 0.000357 -0.0000748 2.23 2.26 0.0223 0.00834 0.00877 0.0004371105 0.00171 0.00167 -0.0000384 0.000530 0.000506 -0.0000242 2.92 2.92 0.00448 0.0110 0.00693 -0.004031106 0.00237 0.00234 -0.0000288 0.000705 0.000709 0.00000383 3.53 3.52 -0.00774 0.0170 0.0101 -0.006911107 0.00310 0.00303 -0.0000746 0.000822 0.000947 0.000124 4.11 4.09 -0.0135 0.0200 0.0134 -0.006621108 0.00423 0.00440 0.000162 0.000976 0.00121 0.000235 4.64 4.62 -0.0192 0.0292 0.0182 -0.01101109 0.00507 0.00509 0.0000255 0.00111 0.00137 0.000261 5.16 5.13 -0.0280 0.0355 0.0230 -0.01251110 0.00587 0.00601 0.000146 0.00144 0.00184 0.000396 5.63 5.60 -0.0295 0.0551 0.0823 0.02721111 0.00762 0.00776 0.000135 0.00206 0.00200 -0.0000595 6.53 6.52 -0.0160 0.114 0.177 0.06301112 0.0121 0.0125 0.000398 0.00337 0.00309 -0.000285 7.59 7.58 -0.00516 0.208 0.381 0.1741113 0.0155 0.0152 -0.000267 0.00486 0.00564 0.000787 9.02 9.02 -0.00434 0.442 2.08 1.631114 0.0179 0.0180 0.000167 0.0109 0.0185 0.00759 10.1 10.1 0.00887 0.882 15.8 15.01201 0.000290 0.000176 -0.000113 0.000548 0.000161 -0.000387 1.57 1.56 -0.00525 0.0177 0.00883 -0.008861202 0.000223 0.000112 -0.000111 0.000222 0.0000357 -0.000187 1.44 1.38 -0.0685 0.00861 0.00109 -0.007521203 0.000174 0.0000733 -0.000101 0.000272 0.0000441 -0.000228 1.47 1.43 -0.0426 0.00848 0.00219 -0.006291204 0.000719 0.000682 -0.0000374 0.000472 0.000125 -0.000347 2.61 2.61 -0.00628 0.0145 0.00560 -0.00894

(Continued on next page).
129

 Table 7-1. Continued.

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

1205 0.00114 0.00106 -0.0000757 0.000754 0.000261 -0.000493 3.52 3.49 -0.0305 0.0257 0.0125 -0.01321206 0.00159 0.00140 -0.000185 0.000702 0.000477 -0.000225 4.65 4.62 -0.0306 0.0252 0.0418 0.01661207 0.00237 0.00234 -0.0000344 0.000944 0.00102 0.0000781 5.64 5.57 -0.0612 0.0411 0.0954 0.05431208 0.00410 0.00427 0.000169 0.00144 0.00128 -0.000161 6.60 6.57 -0.0311 0.0766 0.243 0.1661209 0.00612 0.00609 -0.0000310 0.00171 0.00163 -0.0000792 7.65 7.59 -0.0594 0.129 0.280 0.1511210 0.00731 0.00735 0.0000373 0.00261 0.00240 -0.000207 8.81 8.75 -0.0629 0.151 0.210 0.05921211 0.0132 0.0133 0.000155 0.00352 0.00441 0.000884 11.7 11.6 -0.0625 0.355 1.57 1.221212 0.0127 0.0122 -0.000503 0.00765 0.00918 0.00152 14.5 14.5 -0.00549 0.882 0.967 0.08561213 0.0154 0.0175 0.00210 0.00667 0.00664 -0.0000266 15.7 15.6 -0.0425 0.755 0.834 0.07881214 0.0203 0.0277 0.00742 0.00657 0.00658 0.00000652 17.4 17.4 0.00448 0.905 0.930 0.02562101 0.00101 0.000933 -0.0000812 0.000901 0.000827 -0.0000746 1.54 1.54 -0.00782 0.0110 0.00921 -0.001822102 0.00104 0.000888 -0.000154 0.000901 0.000880 -0.0000215 1.60 1.61 0.00584 0.00872 0.0155 0.006802103 0.000423 0.000416 -0.00000691 0.000835 0.000936 0.000100 1.13 1.10 -0.0352 0.00468 0.00459 -0.00009392104 0.00161 0.00171 0.0000994 0.00103 0.00113 0.000103 2.39 2.39 0.00229 0.0122 0.0107 -0.001492105 0.00264 0.00270 0.0000615 0.00125 0.00151 0.000262 3.21 3.21 -0.00404 0.0167 0.0148 -0.001942106 0.00379 0.00386 0.0000704 0.00166 0.00156 -0.000100 3.96 3.94 -0.0216 0.0233 0.0209 -0.002362107 0.00510 0.00514 0.0000440 0.00209 0.00209 -0.0000000742 4.75 4.74 -0.0167 0.0293 0.0275 -0.00179

(Continued on next page)
130

Table 7-1. Continued.

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

2108 0.00637 0.00652 0.000146 0.00233 0.00232 -0.0000162 5.37 5.34 -0.0317 0.0369 0.0344 -0.002552109 0.00766 0.00775 0.0000836 0.00282 0.00280 -0.0000195 5.94 5.92 -0.0168 0.0495 0.0557 0.006172110 0.00991 0.0100 0.000115 0.00298 0.00303 0.0000464 6.43 6.39 -0.0347 0.0638 0.0652 0.001482111 0.0127 0.0130 0.000290 0.00379 0.00380 0.0000159 7.07 7.04 -0.0240 0.105 0.0834 -0.02202112 0.0144 0.0145 0.000105 0.00457 0.00462 0.0000482 7.62 7.60 -0.0149 0.248 0.170 -0.07752113 0.0160 0.0162 0.000209 0.00570 0.00569 -0.0000096 8.32 8.30 -0.0204 0.413 0.375 -0.03812114 0.0167 0.0170 0.000242 0.00716 0.00721 0.0000479 8.48 8.46 -0.0145 0.625 0.701 0.07622201 0.000725 0.000619 -0.000106 0.000863 0.000530 -0.000333 1.65 1.63 -0.0178 0.0203 0.0216 0.001362202 0.000504 0.000489 -0.0000148 0.000300 0.000219 -0.0000813 1.76 1.68 -0.0833 0.00818 0.00332 -0.004862203 0.000661 0.000754 0.0000929 0.000323 0.000266 -0.0000575 1.56 1.48 -0.0815 0.00483 0.00211 -0.002722204 0.00252 0.00292 0.000406 0.000449 0.000409 -0.0000398 2.95 2.94 -0.00368 0.0123 0.0139 0.001572205 0.00585 0.00695 0.00110 0.000818 0.000637 -0.000181 4.13 4.12 -0.00309 0.0220 0.0209 -0.001152206 0.00836 0.00928 0.000919 0.00122 0.00106 -0.000155 5.34 5.34 -0.00370 0.0451 0.0447 -0.0003262207 0.0106 0.0113 0.000694 0.00211 0.00200 -0.000108 6.51 6.50 -0.00441 0.0775 0.0765 -0.001002208 0.0145 0.0155 0.00106 0.00439 0.00453 0.000134 7.60 7.60 -0.00391 0.167 0.152 -0.01442209 0.0164 0.0175 0.00110 0.00464 0.00450 -0.000133 8.77 8.77 -0.00112 0.170 0.167 -0.00262

(Continued on next page).
131

Table 7-1. Continued.

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

2210 0.0198 0.0213 0.00154 0.00496 0.00461 -0.000356 10.4 10.4 -0.00409 0.264 0.248 -0.01532211 0.0305 0.0326 0.00209 0.00663 0.00643 -0.000203 12.8 12.8 -0.00133 0.339 0.363 0.02422212 0.0342 0.0341 -0.0000985 0.0109 0.0107 -0.000221 15.0 15.0 0.00141 0.825 0.823 -0.001412213 0.0434 0.0433 -0.000115 0.0166 0.0166 0.0000243 16.9 16.9 0.00567 1.44 0.242 -1.202214 0.0690 0.0688 -0.000151 0.0271 0.0275 0.000473 18.9 18.9 0.00168 2.18 2.40 0.223

a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <

50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:odometer reading > 50,000 miles and engine displacement > 3.5 liters.

b Unit of mean: g/sec; Unit of diff.: g/sec.
132

Table 7-2. Comparison of Standard Deviation between Empirical Data Set and Fitted Parametric Distributions, Absolute Basis

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

1101 0.00295 0.00181 -0.00114 0.00283 0.00257 -0.000259 1.39 1.27 -0.118 0.0589 0.0873 0.02841102 0.00256 0.00155 -0.00101 0.00112 0.000921 -0.000202 1.21 1.20 -0.0122 0.0367 0.0307 -0.006021103 0.00154 0.000544 -0.00100 0.00150 0.00157 0.0000668 0.816 0.832 0.0155 0.0216 0.0267 0.005091104 0.00343 0.00262 -0.000809 0.00141 0.00170 0.000290 1.38 1.48 0.0925 0.0519 0.164 0.1121105 0.00442 0.00469 0.000269 0.00160 0.00223 0.000630 1.53 1.52 -0.00811 0.0968 0.0195 -0.07741106 0.00567 0.00629 0.000621 0.00237 0.00308 0.000714 1.67 1.68 0.0161 0.155 0.0291 -0.1261107 0.00671 0.00799 0.00128 0.00240 0.00419 0.00179 1.77 1.79 0.0204 0.106 0.0378 -0.06841108 0.00794 0.0109 0.00298 0.00281 0.00542 0.00260 1.94 1.97 0.0319 0.152 0.0536 -0.09871109 0.0101 0.0127 0.00259 0.00267 0.00559 0.00292 2.09 2.13 0.0378 0.165 0.0674 -0.09811110 0.0110 0.0142 0.00318 0.00369 0.00845 0.00477 2.35 2.40 0.0502 0.252 2.40 2.151111 0.0147 0.0166 0.00196 0.00545 0.00335 -0.00210 2.72 2.66 -0.0570 0.396 5.86 5.461112 0.0201 0.0240 0.00394 0.0104 0.00507 -0.00534 2.99 3.00 0.00935 0.571 13.4 12.81113 0.0247 0.0240 -0.000653 0.0133 0.0210 0.00769 3.64 3.64 -0.00180 0.906 173 1721114 0.0277 0.0304 0.00269 0.0249 0.195 0.170 5.37 5.35 -0.0248 1.52 6426 64241201 0.00135 0.000495 -0.000858 0.00246 0.00102 -0.00145 0.752 0.775 0.0226 0.0876 0.240 0.1531202 0.00142 0.000303 -0.00112 0.00177 0.0000879 -0.00169 0.730 0.990 0.260 0.0764 0.00895 -0.06741203 0.00125 0.000185 -0.00107 0.00194 0.000121 -0.00182 0.784 0.862 0.0785 0.0697 0.0296 -0.04011204 0.00228 0.00217 -0.000105 0.00246 0.000475 -0.00199 1.08 0.981 -0.100 0.0803 0.0868 0.00648

(Continued on next page)
133

 Table 7-2. Continued.

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

1205 0.00334 0.00345 0.000116 0.00360 0.00121 -0.00239 1.21 1.32 0.116 0.139 0.260 0.1211206 0.00440 0.00454 0.000145 0.00277 0.00269 -0.0000782 1.79 1.86 0.0780 0.113 1.19 1.081207 0.00552 0.00628 0.000753 0.00278 0.00726 0.00448 2.31 2.44 0.132 0.166 3.05 2.891208 0.00813 0.0104 0.00225 0.00722 0.00729 0.0000726 2.64 2.75 0.110 0.286 15.5 15.21209 0.0140 0.0138 -0.000243 0.00443 0.00691 0.00248 2.51 2.66 0.155 0.411 11.4 11.01210 0.0145 0.0151 0.000630 0.00909 0.0107 0.00159 2.80 2.94 0.138 0.475 3.65 3.181211 0.0245 0.0281 0.00358 0.00699 0.0218 0.0148 3.38 3.45 0.0633 0.934 126 1251212 0.0230 0.0187 -0.00433 0.0117 0.0375 0.0258 2.53 2.36 -0.168 1.45 2.78 1.341213 0.0359 0.0766 0.0408 0.00917 0.00937 0.000205 1.95 2.02 0.0729 1.10 1.75 0.6501214 0.0378 0.122 0.0846 0.00769 0.00744 -0.000244 2.21 2.22 0.0116 1.18 1.41 0.2342101 0.00229 0.00198 -0.000316 0.00225 0.00158 -0.000666 1.11 1.09 -0.0207 0.0471 0.0220 -0.02512102 0.00257 0.00215 -0.000424 0.00228 0.00178 -0.000505 1.11 1.05 -0.0655 0.0371 0.225 0.1882103 0.00168 0.000959 -0.000724 0.00312 0.00689 0.00377 0.713 0.870 0.157 0.0286 0.0477 0.01912104 0.00334 0.00442 0.00108 0.00287 0.00614 0.00327 1.17 1.18 0.00910 0.0501 0.0226 -0.02742105 0.00467 0.00587 0.00120 0.00294 0.00717 0.00423 1.29 1.33 0.0447 0.0669 0.0279 -0.03902106 0.00658 0.00751 0.000929 0.00377 0.00260 -0.00117 1.36 1.44 0.0770 0.0828 0.0353 -0.04752107 0.00802 0.00859 0.000563 0.00403 0.00317 -0.000860 1.50 1.57 0.0697 0.0809 0.0424 -0.0385

(Continued on next page)
134

Table 7-2. Continued.

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

2108 0.00901 0.0101 0.00109 0.00355 0.00323 -0.000321 1.64 1.72 0.0744 0.102 0.0511 -0.05072109 0.0107 0.0114 0.000657 0.00520 0.00390 -0.00130 1.81 1.87 0.0537 0.147 0.177 0.03002110 0.0135 0.0145 0.000959 0.00484 0.00420 -0.000640 1.96 2.05 0.0877 0.209 0.207 -0.001692111 0.0163 0.0182 0.00187 0.00687 0.00513 -0.00175 2.30 2.38 0.0775 0.331 0.242 -0.08962112 0.0166 0.0185 0.00182 0.00707 0.00621 -0.000863 2.45 2.56 0.101 0.665 0.614 -0.05082113 0.0186 0.0214 0.00278 0.00814 0.00765 -0.000490 3.00 3.09 0.0927 0.918 2.27 1.352114 0.0182 0.0213 0.00313 0.0100 0.00945 -0.000532 3.19 3.25 0.0524 1.26 6.02 4.762201 0.00203 0.00142 -0.000610 0.00572 0.00192 -0.00380 0.614 0.685 0.0715 0.114 0.489 0.3752202 0.00137 0.00126 -0.000111 0.00132 0.000455 -0.000860 0.676 0.856 0.181 0.0762 0.0510 -0.02522203 0.00181 0.00161 -0.000202 0.00249 0.000568 -0.00192 0.662 1.13 0.464 0.0835 0.0219 -0.06152204 0.00402 0.00713 0.00311 0.000901 0.000634 -0.000267 0.735 0.676 -0.0582 0.0623 0.163 0.1012205 0.00834 0.0186 0.0102 0.00430 0.00106 -0.00324 0.886 0.836 -0.0500 0.0699 0.0493 -0.02062206 0.0117 0.0206 0.00890 0.00249 0.00211 -0.000377 1.08 1.02 -0.0627 0.120 0.102 -0.01832207 0.0133 0.0211 0.00785 0.00404 0.00531 0.00128 1.35 1.26 -0.0835 0.196 0.157 -0.03962208 0.0178 0.0287 0.0109 0.0111 0.0172 0.00608 1.44 1.36 -0.0803 0.430 0.294 -0.1362209 0.0200 0.0315 0.0115 0.00739 0.00671 -0.000680 1.50 1.47 -0.0298 0.329 0.270 -0.0596

(Continued on next page)
135

Table 7-2. Continued.

NOxb HCb CO2b COb

VSP Bina empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff empirical fitted dist diff

2210 0.0261 0.0422 0.0161 0.00948 0.00751 -0.00196 1.83 1.74 -0.0961 0.651 0.909 0.2572211 0.0330 0.0521 0.0192 0.0106 0.00980 -0.000809 2.14 2.08 -0.0507 0.706 1.28 0.5772212 0.0466 0.0518 0.00521 0.0168 0.0164 -0.000441 1.62 1.65 0.0221 1.29 1.57 0.2722213 0.0493 0.0484 -0.000869 0.0179 0.0202 0.00228 2.39 2.44 0.0568 1.43 0.369 -1.062214 0.0572 0.0630 0.00582 0.0327 0.0406 0.00795 2.10 2.07 -0.0313 2.05 3.80 1.75

a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <

50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:odometer reading > 50,000 miles and engine displacement > 3.5 liters.

b Unit of mean: g/sec; Unit of diff.: g/sec.
136

Table 7-3. Comparisons of Empirical Data Set and Fitted Parametric Distributions, Average

Difference for Good Fits, Fitting Based upon MLE

Mean Standard deviation

Pollutant Criteria

(g/sec)a

No.

of

good

fits

Empirical

(g/sec)

Abs. diff

(g/sec)

Rel.

diff

(%)

Empirical

(g/sec)

Abs. diff

(g/sec)

Rel.

diff

(%)

NOx 0.001 49 0.00812 0.0000404 0.50 0.0116 0.00119 10

HC 0.001 54 0.00302 -0.0000192 -0.64 0.00570 0.000611 11

CO2 0.1 56 6.27 -0.0186 -0.30 1.81 0.0372 2.1

CO 0.1 48 0.140 0.00511 3.6 0.304 0.500 160 a

 A fit is good when its absolute difference in the mean is smaller than criteria value.

Table 7-4. Comparisons of Empirical Data Set, Fitted Lognormal Distributions Based upon

MLE, and Fitted Lognormal Distributions Based upon MoMM, for the Two Worst

MLE Fits for CO.

MLE MoMM

Mean Standard Deviation Mean Standard Deviation

VSP

Bina

empirical fitted

dist diff empirical fitteddist diff empirical fitteddist diff empirical fitteddist diff

1113 0.442 2.08 1.63 0.906 173 172 0.442 0.442 0 0.906 0.906 0

1114 0.882 15.8 15.0 1.52 6426 6424 0.882 0.882 0 1.52 1.52 0

a

 First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement <

3.5 liters.

From Table 7-3, it is apparent that the relative difference in the mean values of the fitted

distribution and the data is less than one percent for NOx, HC, and CO2 for the vast majority of

the modes, and less than four percent for the majority of the modes in the case of CO. The

estimated standard deviation tends to be more sensitive to deviations of the fitted distribution

from the data than does the estimated mean. For most of the modes and pollutants, the relative

difference between the standard deviation of the fitted distribution versus that of the data is less

than 10 percent, but there are some examples for CO in which the difference is substantially

larger.

In this study, MLE was used to estimate parameters of fitted parametric distributions for

representing variability in population. If MoMM was used, there would have been no difference

in the mean and standard deviation between the empirical sample data and fitted distribution, as

shown for selected examples in Table 7-4. In these two examples, which represent the worst fits

of parametric distributions to modal data for CO, the MoMM fitted distribution is confirmed to

have the same mean and standard deviation as the original data, whereas both the mean and

standard deviations of the distribution fitted using MLE are substantially different than the

values estimated directly from the data. However, it is not likely that the mean and the standard

deviation of population will be exactly the same as those of sample. The basis for fitting a

distribution using MLE is to estimate a distribution from which the data were most likely to have

been a sample, which is a different criterion than that for estimating a distribution using MoMM.
137

Table 7-5. Recommendation of Mixture Distributions for Two Worst Fits

Dist. 1b Dist. 2b

Bina Pollutant Dist. 1 Dist. 2 Weight Para 1 Para 2 Para 1 Para 2

1113 CO Lognormal Lognormal 0.7878 2.3619 -4.7782 0.6782 0.329

1114 CO Lognormal Lognormal 0.6367 2.1368 -5.4363 0.7358 0.6043 a

 First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement <

3.5 liters.

b

 Para 1 of lognormal is φ and Para 2 of lognormal is ξ.

Even though MoMM results in the same estimates of the mean and standard deviation as the

original data set, MoMM does not always provide a good fit. For example, distributions fitted

using both MLE and MoMM for the case of CO emissions for odometer reading < 50,000 miles,

and engine displacement < 3.5 Liters, are shown in comparison to the empirical distribution of

the data for VSP Mode 14 in Figure 7-5. A similar example is given for Mode 13, for CO for the

same odometer reading and engine displacement category in Figure 7-6. Figures 7-5 and 7-6

suggest that neither MLE nor MoMM provides an ideal fit compared to the data. When

comparing MLE and MoMM fits for these two cases, it appears that MLE provides a better fit

for the lower percentiles of the distribution and MoMM provides a better fit for the upper tail of

the distribution. However, it is also clear in these examples that the data are not well represented

by a single component parametric distribution, especially in the central portion of the

distribution. A key question is whether occasional disagreements between fitted distributions

and data, such as these, can be tolerated in the model. Alternatively, either mixture distributions

or empirical distributions can be used to represent data such as these. For the same data as

shown in Figure 7-5, an illustration of the use of a fitted mixture distribution is shown in Figure

7-7. Similarly, for the same data as shown in Figure 7-6, an illustration of the use of a fitted

mixture distribution is given in Figure 7-8. The parameters of the mixture distributions shown in

Figures 7-7 and 7-8 are given in Table 7-5. The mixture distributions comprised of only two

lognormal components are shown to agree very well with the empirical data in both cases. The

mixture distributions were estimated using MLE as described by Zheng (2002) using a modified

version of AuvTool. These example case studies illustrate that mixture distributions can be an

effective approach for achieving a good fit when a single component distribution is not adequate.

These case studies also suggest that the data in these modes may be comprised of two or more

subpopulations that might reflect different activity patterns or different vehicle characteristics.

Table 7-6 summarizes the type of parametric distribution and the parameters of the distribution

fitted to the data for each pollutant and mode based upon MLE approach.
138

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

CO (g/sec)

Cumulative Probability

Empirical

MoMM

MLE

Figure 7-5. Comparison of Fitted Parametric Distribution Based upon Method of Matching

Moment and Maximum Likelihood Estimation, Mode 14 CO Emissions, Odometer reading <

50,000 miles, Engine Displacement < 3.5 liters.

0

0.2

0.4

0.6

0.8

1

0246

CO (g/sec)

Cumulative Probability

Empirical

MoMM

MLE

Figure 7-6. Comparison of Fitted Parametric Distribution Based upon Method of Matching

Moment and Maximum Likelihood Estimation, Mode 13 CO Emissions, Odometer reading <

50,000 miles, Engine Displacement < 3.5 liters
139

Figure 7-7. Mixture Distribution Comprised of Two Lognormal Components Fitted to Data for

Mode 14 CO Emissions for Odometer Reading < 50,000 miles and Engine Displacement < 3.5

Liters.

Figure 7-8. Mixture Distribution Comprised of Two Lognormal Components Fitted to Data for

Mode 13 CO Emissions for Odometer Reading < 50,000 miles and Engine Displacement < 3.5

Liters.

Fitting a Distribution for

Data

(n=344)

Cumulative Probability

0.0

0.2

0.4

0.6

0.8

1.0

0.0 3.4 6.9 10.3 13.7 17.1

Lognormal + Lognormal, Weight = 0.6367

CO (g/sec)

Mixture Distribution

Fitting a Distribution for

Data

(n=648)

Cumulative Probability

0.0

0.2

0.4

0.6

0.8

1.0

0.0 2.2 4.4 6.6 8.7 10.9

Lognormal + Lognormal, Weight = 0.7878

CO (g/sec)

Mixture Distribution
140

Table 7-6. Summary of Single Component Parametric Probability Distributions Fitted Using MLE for Variability in VSP Modes for

NO

x, HC, CO2, and CO for Vehicles of Different Engine Displacement and Odometer Reading.

NOx HC CO2 CO

VSP Bina

Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2

1101 W 3.00E-04 4.58E-01 L 1.86E+00 -9.42E+00 W 1.83E+00 1.34E+00 L 2.28E+00 -7.65E+001102 W 2.00E-04 4.29E-01 L 1.80E+00 -1.02E+01 W 1.54E+00 1.21E+00 L 2.24E+00 -8.52E+001103 W 9.74E-05 4.68E-01 L 1.85E+00 -9.85E+00 W 1.22E+00 1.35E+00 L 2.21E+00 -8.52E+001104 W 3.00E-04 4.17E-01 L 1.78E+00 -9.52E+00 L 5.97E-01 6.35E-01 L 2.42E+00 -7.66E+001105 W 6.00E-04 4.29E-01 L 1.74E+00 -9.10E+00 W 3.30E+00 2.01E+00 W 2.50E-03 4.29E-011106 W 9.00E-04 4.41E-01 L 1.73E+00 -8.75E+00 W 3.97E+00 2.21E+00 W 3.50E-03 4.22E-011107 W 1.20E-03 4.46E-01 L 1.74E+00 -8.47E+00 W 4.62E+00 2.43E+00 W 4.80E-03 4.28E-011108 W 1.90E-03 4.65E-01 L 1.74E+00 -8.24E+00 W 5.20E+00 2.51E+00 W 6.10E-03 4.16E-011109 W 2.20E-03 4.64E-01 L 1.69E+00 -8.02E+00 W 5.78E+00 2.59E+00 W 7.80E-03 4.18E-011110 W 2.80E-03 4.82E-01 L 1.76E+00 -7.85E+00 W 6.32E+00 2.49E+00 L 2.60E+00 -5.87E+001111 W 4.10E-03 5.16E-01 W 1.40E-03 6.25E-01 W 7.34E+00 2.63E+00 L 2.65E+00 -5.23E+001112 W 7.60E-03 5.61E-01 W 2.20E-03 6.35E-01 W 8.52E+00 2.73E+00 L 2.67E+00 -4.52E+001113 W 1.12E-02 6.54E-01 L 1.64E+00 -6.52E+00 W 1.01E+01 2.67E+00 L 2.97E+00 -3.69E+00

(Continued on next page).
141

Table 7-6. Continued.

NOx HC CO2 CO

VSP Bina

Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2

1114 W 1.25E-02 6.20E-01 L 2.17E+00 -6.35E+00 W 1.14E+01 1.97E+00 L 3.47E+00 -3.24E+001201 W 6.36E-05 4.29E-01 L 1.93E+00 -1.06E+01 W 1.76E+00 2.12E+00 L 2.57E+00 -8.03E+001202 W 4.28E-05 4.39E-01 L 1.40E+00 -1.12E+01 W 1.51E+00 1.41E+00 L 2.06E+00 -8.94E+001203 W 3.10E-05 4.60E-01 L 1.46E+00 -1.11E+01 W 1.60E+00 1.71E+00 L 2.28E+00 -8.73E+001204 W 2.00E-04 3.96E-01 L 1.65E+00 -1.04E+01 L 3.64E-01 8.91E-01 L 2.34E+00 -7.93E+001205 W 3.00E-04 3.91E-01 L 1.76E+00 -9.81E+00 W 3.92E+00 2.87E+00 L 2.46E+00 -7.42E+001206 W 4.00E-04 3.93E-01 L 1.87E+00 -9.39E+00 W 5.20E+00 2.67E+00 L 2.59E+00 -6.52E+001207 W 9.00E-04 4.41E-01 L 1.99E+00 -8.86E+00 W 6.29E+00 2.44E+00 L 2.63E+00 -5.82E+001208 W 1.90E-03 4.71E-01 L 1.87E+00 -8.41E+00 W 7.40E+00 2.57E+00 L 2.88E+00 -5.57E+001209 W 3.00E-03 4.96E-01 L 1.72E+00 -7.89E+00 W 8.48E+00 3.12E+00 L 2.72E+00 -4.98E+001210 W 4.10E-03 5.32E-01 L 1.74E+00 -7.55E+00 W 9.75E+00 3.28E+00 L 2.39E+00 -4.42E+001211 W 7.20E-03 5.22E-01 L 1.80E+00 -7.04E+00 W 1.29E+01 3.76E+00 L 2.96E+00 -3.93E+001212 W 9.20E-03 6.70E-01 L 1.70E+00 -6.13E+00 L 1.62E-01 2.66E+00 W 3.36E-01 4.22E-01

(Continued on next page).
142

Table 7-6. Continued.

NOx HC CO2 CO

VSP Bina

Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2

1213 L 1.73E+00 -5.55E+00 W 5.40E-03 7.22E-01 W 1.65E+01 9.25E+00 W 4.52E-01 5.23E-011214 L 1.74E+00 -5.10E+00 W 6.20E-03 8.86E-01 L 1.27E-01 2.85E+00 W 7.13E-01 6.78E-012101 W 5.00E-04 5.20E-01 W 5.00E-04 5.61E-01 W 1.69E+00 1.43E+00 W 4.20E-03 4.77E-012102 W 4.00E-04 4.74E-01 W 5.00E-04 5.39E-01 W 1.79E+00 1.57E+00 L 2.31E+00 -6.84E+002103 W 2.00E-04 4.90E-01 L 2.00E+00 -8.98E+00 W 1.18E+00 1.27E+00 L 2.17E+00 -7.73E+002104 W 7.00E-04 4.53E-01 L 1.85E+00 -8.49E+00 W 2.70E+00 2.13E+00 W 5.70E-03 5.19E-012105 W 1.40E-03 5.10E-01 L 1.78E+00 -8.07E+00 W 3.61E+00 2.58E+00 W 9.10E-03 5.67E-012106 W 2.30E-03 5.55E-01 W 1.10E-03 6.28E-01 W 4.41E+00 2.98E+00 W 1.45E-02 6.21E-012107 W 3.60E-03 6.26E-01 W 1.60E-03 6.78E-01 W 5.28E+00 3.33E+00 W 2.08E-02 6.70E-012108 W 4.90E-03 6.66E-01 W 1.90E-03 7.30E-01 W 5.94E+00 3.44E+00 W 2.68E-02 6.90E-012109 W 6.10E-03 6.98E-01 W 2.30E-03 7.31E-01 W 6.58E+00 3.52E+00 L 1.55E+00 -4.09E+002110 W 8.00E-03 7.07E-01 W 2.50E-03 7.34E-01 W 7.11E+00 3.45E+00 L 1.55E+00 -3.93E+002111 W 1.06E-02 7.26E-01 W 3.20E-03 7.52E-01 W 7.86E+00 3.25E+00 L 1.50E+00 -3.60E+00

(Continued on next page).
143

Table 7-6. Continued.

NOx HC CO2 CO

VSP Bina

Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2

2112 W 1.27E-02 7.92E-01 W 3.90E-03 7.54E-01 W 8.48E+00 3.27E+00 L 1.62E+00 -3.09E+002113 W 1.38E-02 7.65E-01 W 4.80E-03 7.54E-01 W 9.31E+00 2.92E+00 L 1.91E+00 -2.80E+002114 W 1.50E-02 8.02E-01 W 6.20E-03 7.72E-01 W 9.50E+00 2.82E+00 L 2.08E+00 -2.51E+002201 W 3.00E-04 4.92E-01 L 1.63E+00 -8.87E+00 W 1.84E+00 2.55E+00 L 2.50E+00 -6.95E+002202 W 2.00E-04 4.53E-01 L 1.29E+00 -9.27E+00 W 1.90E+00 2.06E+00 L 2.34E+00 -8.44E+002203 W 4.00E-04 5.17E-01 L 1.31E+00 -9.09E+00 W 1.60E+00 1.32E+00 L 2.17E+00 -8.50E+002204 W 1.30E-03 4.71E-01 L 1.11E+00 -8.41E+00 L 2.27E-01 1.05E+00 L 2.22E+00 -6.75E+002205 W 2.70E-03 4.43E-01 L 1.15E+00 -8.02E+00 L 2.01E-01 1.40E+00 W 9.70E-03 4.81E-012206 W 4.70E-03 5.04E-01 L 1.26E+00 -7.65E+00 L 1.89E-01 1.66E+00 W 2.18E-02 4.93E-012207 W 7.00E-03 5.71E-01 L 1.44E+00 -7.26E+00 L 1.93E-01 1.85E+00 W 4.28E-02 5.33E-012208 W 9.80E-03 5.77E-01 L 1.65E+00 -6.76E+00 L 1.78E-01 2.01E+00 W 9.13E-02 5.58E-012209 W 1.13E-02 5.88E-01 W 3.50E-03 6.89E-01 L 1.66E-01 2.16E+00 W 1.21E-01 6.44E-012210 W 1.24E-02 5.47E-01 W 3.30E-03 6.38E-01 L 1.66E-01 2.32E+00 L 1.63E+00 -2.73E+00

(Continued on next page).
144

Table 7-6. Continued.

NOx HC CO2 CO

VSP Bina

Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2 Distb para 1 para 2

2211 W 2.38E-02 6.49E-01 W 4.90E-03 6.75E-01 L 1.61E-01 2.54E+00 L 1.61E+00 -2.31E+002212 W 2.61E-02 6.78E-01 W 8.10E-03 6.72E-01 L 1.09E-01 2.70E+00 W 5.02E-01 5.64E-012213 W 4.10E-02 8.95E-01 W 1.50E-02 8.28E-01 L 1.44E-01 2.82E+00 W 1.85E-01 6.76E-012214 W 7.12E-02 1.09E+00 W 2.16E-02 6.95E-01 L 1.09E-01 2.94E+00 W 1.77E+00 6.53E-01

a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <

50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:odometer reading > 50,000 miles and engine displacement > 3.5 liters.

b W = Weibull; para 1 of Weibull is scale parameter and para 2 of Weibull is shape parameter; L = lognormal; para 1 of lognormal is φand para 2 of lognormal is ξ; Parameters were calculated using SAS.
145

7.3 Quantification of Uncertainty in Mean Emission Rates

A particular concern in this study is whether a normality approximation can be used to represent

uncertainty in the mean. A normality assumption is convenient because it is easy to calculate the

range of uncertainty in the mean in such situations. When a normality assumption is not

applicable, a numerical method, known as bootstrap simulation, was used to quantify uncertainty

in the mean. Typically, the normality assumption is influenced by the sample size, sample mean,

and standard error of mean (SEM). When either sample size n < 40 , or when the SEM divided

by the mean was greater than 20, then bootstrap simulation was done to estimate the sampling

distribution of the mean. Overall, in most cases, a normality assumption was applicable. Table

7-7 indicates situations for which a normality assumption was suspected to be inadequate. These

situations include VSP Modes 12 (NOx), 13 (NOx and CO), and 14 (All Pollutants) for odometer

reading < 50,000 miles and engine displacement > 3.5 liters, and Mode 14 (All Pollutants) for

odometer reading > 50,000 miles and engine displacement > 3.5 liters. In each of these cases,

either the sample size is less than 40 or the relative standard error of the mean is greater than 0.2.

Therefore, in these cases, bootstrap simulation was used to quantify uncertainty in the mean.

Uncertainty estimates for all other modes and strata were based upon application of the normality

assumption.

Table 7-7. VSP Modes for Which Uncertainty in the Mean Was Quantified by Bootstrap

Simulation.

Bina NO HC CO2 CO

1212 = 0.21

mean

SEM ,

n = 77

n/a n/a n/a

1213 = 0.32

mean

SEM ,

n = 52

n/a n/a = 0.20

mean

SEM ,

n = 52

1214 = 0.30

mean

SEM ,

n = 39

= 0.19

mean

SEM ,

n = 39

= 0.020

mean

SEM ,

n = 39

= 0.21

mean

SEM ,

n = 39

2214 = 0.14

mean

SEM ,

n = 34

= 0.21

mean

SEM ,

n = 34

= 0.019

mean

SEM ,

n = 34

= 0.16

mean

SEM ,

n = 34

a

 First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement <

3.5 liters; 12: odometer reading < 50,000 miles and engine displacement > 3.5 liters; 21:

odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometer reading >

50,000 miles and engine displacement > 3.5 liters.
146

The absolute range of uncertainty in the mean values for each pollutant and VSP-based mode is

given in Figure 7-9 for NOx and HC and in Figure 7-10 for CO and CO2. The relative range of

uncertainty in the mean values for each pollutant and VSP-based mode is given in Table 7-8.

The relative range of uncertainty is typically less than plus or minus 50 percent for most cases.

For CO2, the range of uncertainty is less than plus or minus 5 percent in nearly all cases. The

relative range of uncertainty is generally smaller for the strata which have larger sample sizes.

For example, for vehicles with engine displacement less than 3.5 liters and odometer reading less

than 50,000 miles, the typical range of uncertainty is less than plus or minus 10 percent for 12 of

14 modes for modal NOx emissions, less than plus or minus 10 percent for 10 of 14 modes for

HC, less than plus or minus three percent for CO2 for all modes, and less than plus or minus 20

percent for all modes for CO. However, for vehicles with engine displacement greater than 3.5

liters in the same odometer reading category, the typical range of uncertainty is plus or minus 30

percent for NOx, 40 percent for HC, 7 percent for CO2, and 40 percent for CO. The latter

category has a much smaller sample size than the former.

In the several cases identified in Table 7-7 for which the normality assumption was suspected to

be inapplicable, it was confirmed based upon the results of bootstrap simulation that the

sampling distributions of the means were not normal. For example, for NOx emissions for Mode

13 for odometer reading < 50,000 miles and engine displacement > 3.5 liters, uncertainty in the

mean was quantified by bootstrap simulation based upon the empirical distribution of data. The

relative 95 percent confidence interval was found to be minus 48 percent to plus 73 percent. The

confidence interval is positively skewed and the wide range of uncertainty in this case is

attributed to a large SEM relative to the mean. In Table 7-8, uncertainty estimates based upon

bootstrap simulation are highlighted in bold. For the cases in which uncertainties in the means

were quantified by bootstrap simulation, parametric distributions were fit to the sampling

distributions of the means using the AuvTool software. As an example, a graphical comparison

is given in Figure 7-11 of the empirical distribution of the bootstrap replications of the mean and

a fitted parametric distribution is given for NOx emission of Mode 12 based upon an odometer

reading < 50,000 miles and engine displacement > 3.5 liters. A summary of parameters for

parametric distributions fitted to the bootstrap replications of the means is given in Table 7-9.

Normal, lognormal, Weibull, beta and gamma distributions were considered as possible fits for

the sampling distributions. The PDFs of the normal, lognormal, and Weibull distributions have

previously been given in Equations (7-1), (7-2), and (7-3), respectively. The PDF of the beta

distribution is:

1 1 (1 ) ( , )

1 ( ) − − = − α β

α β

x x

B f x( )

( ) ( ) ( , )

α β

α β α β Γ +

Γ Γ

B = (7-4)

The PDF of gamma distribution is:

( ) ( )

1

r

x e f x

r r x

Γ =

− −λ λ Γ = ∫

∞ − −

0

1 (r) x e dx r x 0 ≤ x < ∞ (7-5)
147

0.0001

0.001

0.01

0.1

1

1101110311051107110911111113120112031205120712091211121321012103210521072109211121132201220322052207220922112213

c) O Emissions Estimate (g/seN

0.0001

0.001

0.01

0.1

1

1101110311051107110911111113120112031205120712091211121321012103210521072109211121132201220322052207220922112213

c) C Emissions Estimate (g/seH

Figure 7-9. Quantified Uncertainty in the NOx and HC Mean Emissions (g/sec) of VSP Modes.

First two digit of VSP Bins: 11: odometerreading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading < 50,000

miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometer

reading > 50,000 miles and engine displacement > 3.5 liters.

Odometer Reading < 50,000 miles

Engine Displacement < 3.5 Liters

Odometer Reading < 50,000 miles

Engine Displacement > 3.5 Liters Odometer Reading > 50,000 miles

Engine Displacement < 3.5 Liters

Odometer Reading > 50,000 miles

Engine Displacement > 3.5 Liters
148

1

10

100

1101110311051107110911111113120112031205120712091211121321012103210521072109211121132201220322052207220922112213

c) O2 Emissions Estimate (g/seC

0.0001

0.001

0.01

0.1

1

10

1101110311051107110911111113120112031205120712091211121321012103210521072109211121132201220322052207220922112213

c) O Emissions Estimate (g/seC

Figure 7-10. Quantified Uncertainty in the CO2 and CO Mean Emissions (g/sec) of VSP Modes

First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading < 50,000miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometerreading > 50,000 miles and engine displacement > 3.5 liters.)

Odometer Reading < 50,000 miles

Engine Displacement < 3.5 Liters

Odometer Reading < 50,000 miles

Engine Displacement > 3.5 Liters Odometer Reading > 50,000 miles

Engine Displacement < 3.5 Liters

Odometer Reading > 50,000 miles

Engine Displacement > 3.5 Liters
149

Table 7-8. Summary of Mean Values and Relative 95% Confidence Intervals in the Mean for NOx, HC, CO2, and CO Emissions

(g/sec) for VSP Modes for Vehicles of Different Odometer Reading and Engine Displacement.

NOxb HCb CO2b COb

VSP Bina

mean lower upper mean lower upper mean lower upper mean lower upper

1101 0.000901 -4 4 0.000450 -8 8 1.671078 -1 1 0.007807 -10 101102 0.000628 -6 6 0.000257 -7 7 1.457983 -1 1 0.003908 -15 151103 0.000346 -5 5 0.000406 -4 4 1.135362 -1 1 0.003347 -8 81104 0.001173 -4 4 0.000432 -5 5 2.233264 -1 1 0.008335 -9 91105 0.001706 -4 4 0.000530 -5 5 2.919890 -1 1 0.010959 -14 141106 0.002368 -4 4 0.000705 -6 6 3.525303 -1 1 0.017013 -16 161107 0.003103 -4 4 0.000822 -6 6 4.107483 -1 1 0.020026 -11 111108 0.004234 -4 4 0.000976 -7 7 4.635048 -1 1 0.029222 -12 121109 0.005069 -5 5 0.001112 -7 7 5.160731 -1 1 0.035531 -13 131110 0.005865 -6 6 0.001443 -8 8 5.632545 -1 1 0.055068 -14 141111 0.007623 -8 8 0.002061 -11 11 6.534780 -2 2 0.113824 -14 141112 0.012149 -10 10 0.003373 -18 18 7.585213 -2 2 0.207586 -16 161113 0.015456 -12 12 0.004857 -21 21 9.024217 -3 3 0.441775 -16 16

(Continued on next page)
150

Table 7-8. Continued

NOxb HCb CO2b COb

VSP Bina

mean lower upper mean lower upper mean lower upper mean lower upper

1114 0.017863 -16 16 0.010948 -24 24 10.088390 -6 6 0.882300 -18 181201 0.000290 -19 19 0.000548 -19 19 1.566819 -2 2 0.017699 -21 211202 0.000223 -28 28 0.000222 -35 35 1.443564 -2 2 0.008608 -39 391203 0.000174 -27 27 0.000272 -27 27 1.470553 -2 2 0.008479 -31 311204 0.000719 -12 12 0.000472 -20 20 2.611318 -2 2 0.014548 -22 221205 0.001136 -13 13 0.000754 -22 22 3.523681 -2 2 0.025709 -25 251206 0.001587 -13 13 0.000702 -19 19 4.650741 -2 2 0.025212 -22 221207 0.002370 -13 13 0.000944 -16 16 5.635386 -2 2 0.041130 -22 221208 0.004098 -15 15 0.001443 -38 38 6.599677 -3 3 0.076601 -28 281209 0.006124 -21 21 0.001708 -24 24 7.647334 -3 3 0.129248 -29 291210 0.007313 -22 22 0.002605 -39 39 8.808448 -4 4 0.150578 -35 351211 0.013178 -27 27 0.003523 -29 29 11.670609 -4 4 0.355223 -39 391212 0.012179 -38 46 0.007653 -34 34 14.520355 -4 4 0.881642 -37 37

(Continued on next page)
151

Table 7-8. Continued

NOxb HCb CO2b COb

VSP Bina

mean lower upper mean lower upper mean lower upper mean lower upper

1213 0.016506 -48 73 0.006667 -37 37 15.653272 -3 3 1.059857 -25 271214 0.027225 -36 49 0.006593 -33 39 17.35699 -7 5 0.934715 -36 442101 0.001014 -4 4 0.000901 -5 5 1.543686 -1 1 0.011030 -8 82102 0.001042 -7 7 0.000901 -7 7 1.604406 -2 2 0.008723 -13 132103 0.000423 -7 7 0.000835 -6 6 1.130833 -1 1 0.004682 -10 102104 0.001613 -5 5 0.001027 -6 6 2.386260 -1 1 0.012154 -9 92105 0.002638 -4 4 0.001253 -6 6 3.210249 -1 1 0.016731 -10 102106 0.003793 -5 5 0.001664 -6 6 3.957732 -1 1 0.023269 -10 102107 0.005098 -5 5 0.002089 -6 6 4.752012 -1 1 0.029322 -8 82108 0.006373 -5 5 0.002332 -5 5 5.374221 -1 1 0.036942 -9 92109 0.007664 -5 5 0.002818 -7 7 5.940051 -1 1 0.049513 -11 112110 0.009913 -5 5 0.002985 -6 6 6.427506 -1 1 0.063759 -13 132111 0.012685 -6 6 0.003786 -8 8 7.065985 -2 2 0.105380 -15 15

(Continued on next page)
152

Table 7-8. Continued

NOxb HCb CO2b COb

VSP Bina

mean lower upper mean lower upper mean lower upper mean lower upper

2112 0.014384 -7 7 0.004573 -9 9 7.617703 -2 2 0.247810 -16 162113 0.015967 -10 10 0.005700 -12 12 8.322442 -3 3 0.413069 -18 182114 0.016717 -10 10 0.007164 -13 13 8.475028 -3 3 0.624663 -19 192201 0.000725 -15 15 0.000863 -36 36 1.649427 -2 2 0.020282 -31 312202 0.000504 -20 20 0.000300 -32 32 1.762407 -3 3 0.008183 -68 682203 0.000661 -14 14 0.000323 -39 39 1.557773 -2 2 0.004830 -87 872204 0.002518 -9 9 0.000449 -11 11 2.946419 -1 1 0.012308 -28 282205 0.005847 -9 9 0.000818 -34 34 4.127492 -1 1 0.022033 -20 202206 0.008361 -11 11 0.001216 -16 16 5.343656 -2 2 0.045073 -20 202207 0.010582 -11 11 0.002110 -16 16 6.507179 -2 2 0.077496 -22 222208 0.014473 -14 14 0.004394 -28 28 7.602431 -2 2 0.166593 -28 282209 0.016372 -15 15 0.004635 -19 19 8.773093 -2 2 0.170018 -24 242210 0.019758 -17 17 0.004961 -25 25 10.365910 -2 2 0.263544 -33 33

(Continued on next page)
153

Table 7-8. Continued

NOxb HCb CO2b COb

VSP Bina

mean lower upper mean lower upper mean lower upper mean lower upper

2211 0.030507 -20 20 0.006631 -30 30 12.849389 -3 3 0.338962 -39 392212 0.034219 -32 32 0.010900 -36 36 15.030303 -3 3 0.824829 -36 362213 0.043387 -31 31 0.016573 -30 30 16.861726 -4 4 1.444311 -27 272214 0.068743 -27 27 0.027174 -35 36 18.92916 -13 10 2.420786 -27 28

a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <

50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:odometer reading > 50,000 miles and engine displacement > 3.5 liters.

b Unit of mean: g/sec; Unit of lower and upper bound: %.

155

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025

NOx Emission (g/sec)

Cumulative Probability

Empirical

Beta

Figure 7-11. Empirical Distribution of Bootstrap Replications of Mean Values and Fitted Beta

Distribution for Uncertainty in the Mean for NOx Emissions (g/sec) of Mode 12, Odometer

Reading < 50,000 miles, Engine Displacement > 3.5 Liters.

Table 7-9. Parameters of Parametric Probability Distribution Fit to the Bootstrap Replications of

the Means for Selected Modes, Strata, and Pollutants, Based upon Empirical Bootstrap

Simulation

VSP

Bin

Odometer

reading (miles)

Engine

displacement

(liters)

Pollutant Distributiona First

Para.

Second

Para

12 < 50,000 > 3.5 NOx Beta 22.275 1761.856

13 < 50,000 > 3.5 NOx Beta 3.431 96.093

13 < 50,000 > 3.5 CO Gamma 25.328 0.029

14 < 50,000 > 3.5 NOx Beta 10.482 511.286

14 < 50,000 > 3.5 HC Beta 25.413 3911.552

14 < 50,000 > 3.5 CO2 Weibull 17.169 39.735

14 < 50,000 > 3.5 CO Normal 0.895 0.191

14 > 50,000 > 3.5 NOx Beta 42.992 595.202

14 > 50,000 > 3.5 HC Beta 21.873 805.28

14 > 50,000 > 3.5 CO2 Weibull 18.658 33.446

14 > 50,000 > 3.5 CO Gamma 36.591 0.058 a

	
		


		
	
		


		


	
		


		
		
		




		

156

The parametric distributions fit to the bootstrap replications of the means generally offered an

excellent fit. The use of parametric distributions to describe uncertainty in the mean offers the

key advantage of compactness and eliminates the requirement to save the bootstrap replications

of the mean. There was one case shown in Table 7-9 for which a normal distribution was found

to provide the best fit. However, for the other 10 cases shown, beta, gamma, or Weibull

distributions offered the best fit and captured the skewness in the sampling distributions of the

mean.

7.4 Uncertainty Correction Factor for Averaging Time

Uncertainty in the mean emission rate based upon a 1-second time period was quantified for each

bin. However, the range of uncertainty varies depending upon the averaging time of the data.

The objective of this section is to demonstrate how the range of uncertainty varies with

averaging time and to demonstrate an approach for adjusting estimates of uncertainty in the mean

emission rates for a one second averaging time to other averaging times.

Uncertainty in the mean is related to the Standard Error of Mean (SEM). Therefore, it is

convenient to develop a correction factor to adjust the SEM for different averaging times. To

evaluate the relative change of the SEM, a correction factor for a t-second time period was

defined as Equation (7-6):

1 sec

sec

sec

−

−

− = SEM

SEM CF t

t (7-6)

where: CFt-sec: correction factor for t-second time period, no unit

SEMt-sec: standard error of mean for t-second time period, g/sec

SEM1-sec: standard error of mean for 1-second time period, g/sec

Using a relative correction factor enables a straight-forward adjustment of the uncertainty range

for different time periods. For example, if the absolute 95 percent confidence interval of mean

for a 1-second period is minus 0.1 gram/sec to plus 0.1 gram/sec, then the absolute 95 percent

confidence interval of mean for 5-second period can be calculated as minus 0.1CF5-sec gram/sec

to plus 0.1CF5-sec gram/sec. If the correction factor has a value of 2, then the uncertainty in the

mean for the 5-second averaging time would be from minus 0.2 g/sec to plus 0.2 g/sec in this

example..

In Figures 7-12 to 7-15, for each of four vehicle strata (combinations of odometer reading

reading and engine displacement categories), respectively, the relative standard error of the mean

(or correction factor defined in Equation 7-6) is plotted with respect to averaging time. The data

for this analysis was obtained from the data set used to evaluate 10-second consecutive averages

as a basis for model development. For each 10-second averaging time, there are two five-second

averages and ten 1-second averages that can be compared in order to evaluate the range of

uncertainty for each of these three averaging times. Each graph in each figure displays the

standard error of the mean for the five-second averaging time divided by that for the 1-second

averaging time, for each of 14 VSP modes. Similar data are shown for the 10-second averaging

time. A simplified correction factor was estimated by fitting a polynomial regression through the

data in the graphs. Although the analysis could be extended to averaging times longer than 10
157

y = -0.0154x2 + 0.3326x + 0.6829

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

NOOdometer < 50,000 milesEngine size < 3.5 

y = -0.0167x2 + 0.3638x + 0.653

3.503.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

HCOdometer < 50,000 milesEngine size < 3.5 

y = -0.0186x2 + 0.3608x + 0.6578

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

CO2Odometer < 50,000 milesEngine size < 3.5 

y = -0.0158x2 + 0.3441x + 0.6717

3.503.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

COOdometer < 50,000 milesEngine size < 3.5 

Figure 7-12. Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of

1, 5, and 10 seconds for NOx, HC, CO2, and CO Emissions (g/sec) for Odometer Reading < 50,000 Miles and Engine Displacement <

3.5 Liters.
158

y = -0.0152x2 + 0.2935x + 0.7217

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

NOOdometer < 50,000 milesEngine size > 3.5 

y = -0.0181x2 + 0.3654x + 0.6527

3.503.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

HCOdometer < 50,000 milesEngine size > 3.5 

y = -0.0246x2 + 0.3802x + 0.6443

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

CO2Odometer < 50,000 milesEngine size > 3.5 

y = -0.0167x2 + 0.3948x + 0.6219

8.006.004.002.000.00

10.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

COOdometer < 50,000 milesEngine size > 3.5 

Figure 7-13. Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of

1, 5, and 10 seconds for NOx, HC, CO2, and CO Emissions (g/sec) for Odometer Reading < 50,000 Miles and Engine Displacement >

3.5 Liters.
159

y = -0.0163x2 + 0.3479x + 0.6684

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

NOOdometer > 50,000 milesEngine size < 3.5 

y = -0.0157x2 + 0.3607x + 0.6549

3.503.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

HCOdometer > 50,000 milesEngine size < 3.5 

y = -0.019x2 + 0.3682x + 0.6508

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

CO2Odometer > 50,000 milesEngine size < 3.5 

y = -0.017x2 + 0.3371x + 0.6799

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

COOdometer > 50,000 milesEngine size < 3.5 

Figure 7-14. Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of

1, 5, and 10 seconds for NOx, HC, CO2, and CO Emissions (g/sec) for Odometer Reading > 50,000 Miles and Engine Displacement <

3.5 Liters.
160

y = -0.017x2 + 0.3496x + 0.6674

3.503.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

NOOdometer > 50,000 milesEngine size > 3.5 

y = -0.0168x2 + 0.3687x + 0.6481

3.503.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

HCOdometer > 50,000 milesEngine size > 3.5 

y = -0.0266x2 + 0.398x + 0.6286

3.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

CO2Odometer > 50,000 milesEngine size > 3.5 

y = -0.0191x2 + 0.3619x + 0.6572

3.503.002.502.001.501.000.500.00

0 2 4 6 8 10 12

Averaging Time (seconds)

or orrection FactC

COOdometer > 50,000 milesEngine size > 3.5 

Figure 7-15. Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of

1, 5, and 10 seconds for NOx, HC, CO2, and CO Emissions (g/sec) for Odometer Reading > 50,000 Miles and Engine Displacement >

3.5 Liters.
161

seconds, as the averaging time increases, the sample size decreases. Therefore, for

demonstration purposes, the largest averaging time considered was ten seconds. As an example,

Figure 7-11 shows that the correction factor increases as the averaging time increases. However,

the marginal change becomes smaller as the averaging time increases. We hypothesize that the

correction factor may reach a plateau or a maximum at some averaging time larger than 10-

seconds; however, we also hypothesize that such a plateau or maximum may not be much larger

than the correction factor estimated at 10-seconds. Therefore, as an initial estimate pending

further analysis in future studies, we suggest that the correction factor applied to averaging times

greater than 10-seconds be the same as that for 10 seconds.

Of the 16 graphs shown in Figures 7-12 through 7-15, 14 of them display the same general

characteristic of a reduction in the marginal increase in the correction factor as the averaging

time increases. For only two cases, which are both for CO2 emissions for odometer reading and

engine displacement strata for which the sample size is relatively small, the correction factor

appears to reach a peak at approximately 8 seconds averaging time and decreases from 8 seconds

to 10 seconds averaging times. Thus, for these two case, shown in Figures 7-13 and 7-15, the

correction factor for the 10 second averaging time is not substantially different from the

correction factor for the 5 second averaging time. Although it is possible that the correction

factor for these two cases might decrease as averaging time increases beyond 10 seconds, as a

conservative assumption the value of the correction factor at 10 seconds is suggested for use for

averaging times longer than 10 seconds. For CO as shown in Figure 7-13, there appears to be

some data that may represent outliers, leading to an estimate of the correction factor for an

individual mode as large as approximately 9.0 for the 10 second averaging time. This potential

outlier may be because of a small sample size for that particular mode.

Table 7-10 summarizes the polynomial regression models fit to the data shown in Figures 7-12

through 7-15. Also shown in the table is the value of the correction factor at the 10 second

averaging time for each pollutant and each odometer reading and engine displacement strata.

These values are recommended for use for averaging times greater than 10 seconds. For NOx,

the correction factors for 10 seconds or greater averaging time range from 2.14 to 2.54 among

the four strata. The corresponding ranges for HC, CO2, and CO are 2.50 to 2.70, 1.99 to 2.43,

and 2.35 to 2.90. Thus, a typical value of these correction factors at 10 seconds or greater

averaging time is approximately 2.5, implying that the range of uncertainty for averaging times

of 10 seconds or more is a factor of approximately 2.5 greater than that at 1 second. This

difference is substantial and illustrates the importance of properly accounting for averaging time

when performing uncertainty analysis.

As observed in Figures 7-12 through 7-15, there is variability in the value of the correction factor

at the 10 second averaging time when comparing results for each of the 14 modes. It was

hypothesized that perhaps a portion of the inter-mode variability in the correction factor for a

given averaging time could be explained based upon VSP. Therefore, the values of the

correction factors at 10 seconds were normalized with respect to the average correction factor at

10 seconds (as shown in the last four columns of Table 7-10), and the normalized correction

factors, which are described here as “bin adjustment factors,” were plotted versus mode as shown

in Figures 7-16 through 7-19 for four different odometer reading and engine displacement strata.
162

Table 7-10. Averaging Time Correction Factors for Uncertainty in VSP Bins for NOx, HC, CO2, and CO Emissions (g/sec) for Four

Strata With Respect to Odometer Reading and Engine Displacement.

< 10 secondsb > 10 seconds

Strataa

NOx HC CO2 CO NOx HC CO2 CO

11 y = -0.0154x2 + 0.3326x + 0.6829 y = -0.0167x2 + 0.3638x + 0.653 y = -0.0186x2 + 0.3608x + 0.6578 y = -0.0158x2 + 0.3441x + 0.6717 2.47 2.62 2.40 2.5312 y = -0.0152x2 + 0.2935x + 0.7217 y = -0.0181x2 + 0.3654x + 0.6527 y = -0.0246x2 + 0.3802x + 0.6443 y = -0.0167x2 + 0.3948x + 0.6219 2.14 2.50 1.99 2.9021 y = -0.0163x2 + 0.3479x + 0.6684 y = -0.0157x2 + 0.3607x + 0.6549 y = -0.019x2 + 0.3682x + 0.6508 y = -0.017x2 + 0.3371x + 0.6799 2.52 2.70 2.43 2.3522 y = -0.017x2 + 0.3496x + 0.6674 y = -0.0168x2 + 0.3687x + 0.6481 y = -0.0266x2 + 0.398x + 0.6286 y = -0.0191x2 + 0.3619x + 0.6572 2.46 2.65 1.95 2.37

a 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading < 50,000 miles and engine

displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometer reading > 50,000

miles and engine displacement > 3.5 liters.

b y, correction factor (no unit), x, time (second)
163

y = -0.0084x + 1.0634

1.081.061.041.021.000.980.960.940.920.90

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

NOOdometer < 50,000 milesEngine size < 3.5

y = -0.0121x + 1.0907

1.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

HCOdometer < 50,000 milesEngine size < 3.5

y = -0.0074x + 1.0553

1.151.101.051.000.950.90

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

CO2Odometer < 50,000 milesEngine size < 3.5

y = -0.0169x + 1.127

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

COOdometer < 50,000 milesEngine size < 3.5

Figure 7-16. Bin Adjustment Factors for the Uncertainty Correction Factor at “ 10 seconds” of NOx, HC, CO2, and CO for

Odometer Reading < 50,000 miles and Engine Displacement < 3.5 Liters.
164

y = -0.033x + 1.1125

1.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

r Bin Adjustment Facto COOdometer < 50,000 miles Engine size > 3.5 

y = -0.001x + 1.0078

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

r Bin Adjustment Facto NOOdometer < 50,000 miles Engine size > 3.5 y = -0.0394x + 1.2954

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

r Bin Adjustment Facto HCOdometer < 50,000 miles Engine size > 3.5 

y = -0.04x + 1.3001

1.601.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

r Bin Adjustment Facto CO2 Odometer < 50,000 miles Engine size > 3.5 

Figure 7-17. Bin Adjustment Factors for the Uncertainty Correction Factor at “ 10 seconds” of NOx, HC, CO2, and CO for

Odometer Reading < 50,000 miles and Engine Displacement > 3.5 Liters.
165

y = 0.0073x + 0.9453

1.101.051.000.950.900.85

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

NOOdometer > 50,000 milesEngine size < 3.5

y = -0.0062x + 1.0467

1.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

HCOdometer > 50,000 milesEngine size < 3.5

y = -0.0006x + 1.0047

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

CO2Odometer > 50,000 milesEngine size < 3.5 y = 0.003x + 0.9775

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

COOdometer > 50,000 milesEngine size < 3.5

Figure 7-18. Bin Adjustment Factors for the Uncertainty Correction Factor at “ 10 seconds” of NOx, HC, CO2, and CO for

Odometer Reading > 50,000 miles and Engine Displacement < 3.5 Liters.
166

y = 0.0074x + 0.9448

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

NOOdometer > 50,000 milesEngine size > 3.5

y = -0.0099x + 1.0742

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

HCOdometer > 50,000 milesEngine size > 3.5

y = -0.0425x + 1.3186

1.601.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

CO2Odometer > 50,000 milesEngine size > 3.5 y = -0.0129x + 1.097

1.401.201.000.800.600.400.200.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bin

or in Adjustment FactB

COOdometer > 50,000 milesEngine size > 3.5

Figure 7-19. Bin Adjustment Factors for the Uncertainty Correction Factor at “ 10 seconds” of NOx, HC, CO2, and CO for

Odometer Reading >50,000 miles and Engine Displacement > 3.5 Liters.
167

The bin adjustment factor (BAF) for a given bin is given by:

10 sec

10 sec,

−

− = ACF

CF

BAF k

k (7-7)

Where:

BAFk, Bin Adjustment Factor for Bin k at 10 second;

CF10-sec,k, Correction Factor for Bin t at 10 second;

ACF10-sec, Average Correction Factor for Bin 1 to Bin 14 at 10 second.

The data shown in Figures 7-16 through 7-19 indicate that typically the bin correction factor is

smaller for the larger VSP modes than for the lower VSP modes, although there are exceptions.

For example, for NOx emissions for higher mileage vehicles, it appears that the bin correction

factor increases as VSP increases. For 13 of the 16 graphs shown in the four figures, the typical

range of variation of the bin adjustment factor is approximately plus or minus five percent or

less. For vehicles with larger engine displacement, there are three cases in which the range of

variation of the bin adjustment factor is approximately plus or minus 20 percent or more,

including HC and CO2 emissions for vehicles with odometer reading less than 50,000 miles and

CO2 for vehicles with odometer reading greater than 50,000 miles. It is possible that this

apparent difference for the larger engine vehicles compared to the smaller engine vehicles

represents a real difference or possibly it could be an artifact of having smaller sample sizes for

the larger engine vehicles. In general, while the linear curve fits capture the overall trends of the

data among the 14 modes, it is clear that the variation of the bin adjustment factor with respect to

VSP mode is not truly linear in all cases. In future work, it may be worth exploring other curve

fits to these data and/or exploring the use of other explanatory variables, such as the mid point

value of VSP for each mode instead of the mode number, in order to improve the estimation of

the bin adjustment factor.

A summary of the Bin Adjustment Factors developed based upon the data and curve fits shown

in Figures 7-16 through 7-19 is given in Table 7-11.

7.5 Estimation of Uncertainty in Model Results

In this section, two methods are evaluated and compared for estimating uncertainty in the total

emissions for a trip or driving cycle. These methods include the numerical method of Monte

Carlo simulation and an analytical method based upon a linear model and normality assumptions

for uncertainty in individual modes. These two methods are illustrated for a case study example

of predicting uncertainty in total trip emissions for the IM240 driving cycle. This case study is

followed by case studies for uncertainty in total emissions for several different driving cycles and

then by a case study for multiple vehicles on a selected driving cycle.

7.5.1 Estimation of Uncertainty in Total Emissions Based Upon the IM240 Driving

Cycle: Comparison of Monte Carlo Simulation and Analytical Approaches

This example demonstrates the prediction of total emissions from IM240 cycle. The prediction

was based upon quantified uncertainty in VSP modes in which the uncertainty was adjusted for
168

Table 7-11. Bin Adjustment Factors for Correction Factor of Time Adjustment at “ 10 seconds”

for NOx, HC, CO2, and CO and for Four Odometer Reading and Engine Displacement

Strata.

Odometer

reading

(mile)

Engine

displacement

(liters)

NOx

a HCa CO2a COa

< 50,000 < 3.5 y = -

0.0084x +

1.0634

y = -

0.0121x +

1.0907

y = -

0.0074x +

1.0553

y = -

0.0169x +

1.127

< 50,000 > 3.5 y = -0.001x

+ 1.0078

y = -

0.0394x +

1.2954

y = -0.04x +

1.3001

y = -0.033x

+ 1.1125

> 50,000 < 3.5 y = 0.0073x

+ 0.9453

y = -

0.0062x +

1.0467

y = -

0.0006x +

1.0047

y = 0.003x

+ 0.9775

> 50,000 > 3.5 y = 0.0074x

+ 0.9448

y = -

0.0099x +

1.0742

y = -

0.0425x +

1.3186

y = -

0.0129x +

1.097 a

 y: bin adjustment factor (no unit); x, bin number (from 1 to 14)

averaging time using the correction factors for averaging time adjustment. The standard IM240

cycle contains 240 seconds. The temporal allocation of the IM240 cycle into VSP modes is

given in Table 7-12. Most of the time spend in the IM240 cycle is represented by VSP modes 1

through 8. Only 10 seconds are spent in Modes 9 through 11, combined, and no time is spent in

the highest VSP modes 12, 13, or 14.

Table 7-12. Allocation of the Standard IM240 Driving Cycle Into VSP Modes With Respect to

Time Spent in Each Mode.

VSP Mode Number Total Seconds

1 41

2 24

3 16

4 37

5 47

6 19

7 29

8 17

9 4

10 3

11 3

12 None

13 None

14 None
169

Thus, total emissions from IM240 cycle are calculated based upon a sum of emission from each

bin, based upon summing the products of the time spent in each mode multiplied by the

respective mode average emission rate:

TE = 41EFmode1 + 24EFmode2 + 16EFmode3 + 37EFmode4 +

47EFmode5 + 19EFmode6 + 29EFmode7 + 17EFmode8 +

4EFmode9 + 3EFmode10 + 3EFmode11 (7-8)

where:

TE: total emissions, g

EF: 1-second based emission factor for each VSP mode (g/sec)

As an illustrative example, uncertainty in total NOx emissions from the IM240 cycle for a vehicle

with odometer reading < 50,000 miles and engine displacement < 3.5 liters was predicted. For

Modes 1 through 11 applied to the IM240 cycle for this particular pollutant and vehicle strata,

the quantified uncertainty in the 1-second average modal emissions can reasonably be based

upon a normality assumption. To estimate uncertainty in total emissions, the quantified

uncertainty in the 1-second average emissions of each mode was adjusted based upon the total

amount of time spent in the mode using the averaging time correction factor previously

described. The input assumptions for prediction of uncertainty in total emissions are given in

Table 7-13. These assumptions include the probability distribution assumed for uncertainty in

the mean for each mode, the mean modal emission rate, the standard deviation of the distribution

for uncertainty in the mean (i.e. the standard error of the mean), the numerical value of the

correction factor applied, and the numerical value of the bin adjustment factor applied. For

Modes 1 through 8, 10 or more seconds were spent in each mode. Therefore, the correction

factor applicable to 10 or more seconds is used for these modes. For Modes 9, 10 and 11, less

than 10 seconds were spent in each mode. Therefore, the correction factor was estimated from

the polynomial curve fits presented in Table 7-10. For cases in which the averaging time was

less than 10 seconds, a bin adjustment factor was not applied. The correction factor and bin

adjustment factor were multiplied with the standard deviation of the modal emission rate to

arrive at a new standard deviation for the modal emission rate appropriate for the particular

averaging time of each mode. For example, for Mode 1, the corrected standard deviation was

(1.97x10-5 g/sec) x (2.47) x (1.0248) = 4.99x10-5 g/sec.

Monte Carlo simulation was used to propagate uncertainty in each modal emission rate, using

Equation (7-8), in order to estimate uncertainty in total emissions. For the Monte Carlo

simulation, a sample size of 10,000 was selected. When performing Monte Carlo simulation, the

selection of sample size is typically based upon a compromise between the precision of the

estimated uncertainty for the model output versus the computational burden. A sample size of

10,000 is not necessary in every case. Smaller sample sizes may provide adequate results.

Moreover, other methods aside from Monte Carlo simulation, such as Latin Hypercube

Sampling, can be used to obtain precise estimates of the distribution of a model output using

smaller sample sizes than required for Monte Carlo simulation. Cullen and Frey (1999) and

Morgan and Henrion (1990) provide more discussion on criteria and methods for selecting

sample sizes for Monte Carlo simulation and for Latin Hypercube Sampling. The results from

Monte Carlo simulation are shown in Table 7-14 and in Figure 7-20.
170

Table 7-13. Input Assumptions for Prediction of Uncertainty in Total NOx Emissions for a Cast

Study of the IM240 cycle, for Vehicles with Odometer Reading < 50,000 Miles and

Engine Displacement < 3.5 Liters.

NOx Emission Factor

Mode

Number

Input

Distribution

Mean Modal

Emission Rate

(g/sec)

Standard Deviation of

Mean Modal

Emission Rate (g/sec)

Correction

Factor

Bin

Adjustment

Factor

1 Normal 0.000901 1.97E-05 2.47 1.025

2 Normal 0.000628 2.04E-05 2.47 1.03

3 Normal 0.000346 9.26E-06 2.47 1.033

4 Normal 0.001173 2.46E-05 2.47 1.033

5 Normal 0.001706 3.56E-05 2.47 1.031

6 Normal 0.002368 5.12E-05 2.47 1.027

7 Normal 0.003103 6.86E-05 2.47 1.02

8 Normal 0.004234 9.44E-05 2.47 1.011

9 Normal 0.005069 0.000141 1.77 Nonea

10 Normal 0.005865 0.00017 1.54 Nonea

11 Normal 0.007623 0.000301 1.54 Nonea

a

 no Bin Adjustment Factor is needed because time period is smaller than 10 seconds.

Table 7-14. Example Prediction of Uncertainty in Total Emissions for NOx Emissions From the

IM240 Cycle for Vehicles with Odometer Reading < 50,000 Miles and Engine

Displacement < 3.5 Liters Based upon Monte Carlo Simulation

Cycle IM240

Vehicle Odometer reading < 50,000 miles, engine displacement < 3.5 liters

Pollutant NOx

meana, b 0.45 g

Lower -0.02 g Absolute 95% CIa, b

Upper 0.02 g

Lower -4.4 %

Relative 95% CIa, c

Upper 4.4 % a

 based upon Monte Carlo Simulation results of 10,000 runs

b unit: gram

c

 unit: %
171

Cumulativ e Chart

Certainty is 95.00% from 0.43 to 0.47 gram

.000

.250

.500

.750

1.000

0

10000

0.43 0.44 0.45 0.46 0.48

10,000 Trials 56 Outliers

Forecast: NO, IM240

Figure 7-20. Quantified Uncertainty in Total NOx Emissions from the IM240 Cycle for Vehicles

with Odometer Reading < 50,000 Miles and Engine Displacement < 3.5 Liters Based upon

Monte Carlo Simulation.

The results from the Monte Carlo simulation are a total NOx emissions mean estimate of 0.45

grams with a 95 percent range of uncertainty of plus or minus 0.02 grams, or plus or minus 4.4

percent of the mean. In this particular case, even with the correction factor for averaging time

adjustment and the bin adjustment factor applied to each mode, the range of uncertainty in the

estimated average total emissions was sufficiently narrow that a normality assumption would be

justifiable.

As an alternative to Monte Carlo simulation, an analytical solution was developed. For a linear

model and for an assumption of normality for uncertainty in each modal emission rate, the

uncertainty in the total emissions can be estimated as follows:

= ∑ ×

n

i

Utotal Ui Wi

2 ( (7-9) )

Where:

Utotal: Uncertainty in the sum of the quantities (i.e. half the 95% CI)

Ui: Uncertainties associated with each quantity, (i.e. half the 95% CI)

Wi: Weight associated with each quantity

The weight is the fraction of total time spent in each mode. The analytical solution for the

IM240 cycle is that the average total emissions are 0.45 grams and the uncertainty is

approximate minus or plus 0.018 grams for a 95% confidence interval, corresponding a relative

range of minus or plus 4 percent, which is similar to numerical simulation results.

The analytical method offers the advantage of reduced computing resources required to estimate

total uncertainty in emissions, when compared to the Monte Carlo simulation approach.

However, the analytical method is limited to situations in which there are a linear combination of

normal distributions. Therefore, if in the future there was a need to include uncertainty in not
172

Table 7-15. Allocation of the ART-EF, IM240, FTP (Bags 2 and 3) and US06 Driving Cycles

Into VSP Modes With Respect to Time Spent in Each Mode.

Seconds Spent in Each Mode by Driving Cycle VSP Mode ART-EF IM240 FTP US06

1 85 41 201 113

2 51 24 119 19

3 196 16 336 69

4 66 37 294 26

5 40 47 212 40

6 31 19 105 55

7 18 29 60 64

8 10 17 27 61

9 5 4 8 45

10 2 3 5 56

11 3 3 32

12 9

13 21

14 11

only the modal emission rate but also in the fraction of time spent it each mode, the analytical

method presented here would not be applicable. Cullen and Frey (1999) provide an overview of

approximate analytical methods for propagating the standard deviation of distributions for model

inputs through a model in order to estimate the standard deviation of the model output.

7.5.2 Estimation of Uncertainty in Total Emissions of Selected Driving Cycles

In this section, uncertainty estimates are developed for total emissions of NOx, HC, CO2, and CO

for four selected driving cycles, including ART-EF, IM240, FTP, and US06. These four cycles

represent different ranges of VSP and of total emissions. The uncertainty in total emissions was

quantified using the analytical method explained in the previous section. The distribution of the

total time of each cycle by VSP mode is given in Table 7-15. For the ART-EF cycle, over 90

percent of the total cycle time is spent in Modes 1 through 6, and there is no representation of

Modes 11 through 14. As previously discussed, for the IM240 cycle most of the activity occurs

in Modes 1 through 8. The FTP is similar to the IM240 cycle in that most of the time is spent in

Modes 1 through 8. The US06 cycle is more widely distributed over the 14 modes compared to

the other three cycles.

The results of the uncertainty analysis for the IM240, ART-EF, FTP, and US06 cycles are shown

in Tables 7-16 through 7-19, respectively. Each table shows results for the mean total emissions,

absolute uncertainty, and relative uncertainty for NOx, HC, CO2, and CO and for four strata

based upon odometer reading and engine displacement.
173

Table 7-16. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOx, HC, CO2, and CO for Four Odometer

Reading and Engine Displacement Tier 1 Vehicle Strata for the IM240 Cycle.

NOx HC CO2 CO Odometer

reading

(mile)

Engine

displacement

(liters)

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

< 50,000 < 3.5 0.45 0.018 4.0 0.14 0.0079 5.6 660 5.3 0.79 3.3 0.35 11< 50,000 > 3.5 0.35 0.042 12 0.24 0.061 25 841 14 1.6 7.9 1.9 24> 50,000 < 3.5 0.68 0.030 4.3 0.33 0.018 5.5 728 6.8 0.93 4.6 0.35 7.7> 50,000 > 3.5 1.3 0.15 11 0.32 0.083 26 962 12 1.3 11 2.7 25

a total emissions, gramsb absolute upper and lower limits, gramsc relative upper and lower limits, %

Table 7-17. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOx, HC, CO2, and CO for Four Odometer

Reading and Engine Displacement Tier 1 Vehicle Strata for the ART-EF Cycle.

NOx HC CO2 CO Odometer

reading

(mile)

Engine

displacement

(liters)

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

< 50,000 < 3.5 0.53 0.021 3.9 0.24 0.015 6.3 969 8.2 0.85 4.0 0.41 10< 50,000 > 3.5 0.34 0.040 12 0.18 0.040 23 1176 19 1.7 8.8 2.3 26> 50,000 < 3.5 0.77 0.032 4.2 0.54 0.037 6.9 1025 11 1.0 5.8 0.44 7.7> 50,000 > 3.5 1.3 0.13 9.8 0.37 0.12 31 1318 21 1.6 11 3.1 30

a total emissions, gramsb absolute upper and lower limits, gramsc relative upper and lower limits, %
174

Table 7-18. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOx, HC, CO2, and CO for Four Odometer

Reading and Engine Displacement Tier 1 Vehicle Strata for the FTP (Bags 2 and 3) Cycle.

NOx HC CO2 CO Odometer

reading

(mile)

Engine

displacement

(liters)

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

< 50,000 < 3.5 1.7 0.069 4.0 0.67 0.038 5.7 2997 25 0.84 13 1.4 11< 50,000 > 3.5 1.1 0.13 11 0.73 0.17 23 3640 55 1.5 27 6.5 24> 50,000 < 3.5 2.5 0.11 4.3 1.5 0.097 6.2 3209 33 1.0 18 1.5 8.0> 50,000 > 3.5 4.6 0.46 9.9 1.1 0.30 27 4123 56 1.4 33 7.8 24

a total emissions, gramsb absolute upper and lower limits, gramsc relative upper and lower limits, %

Table 7-19. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOx, HC, CO2, and CO for Four Odometer

Reading and Engine Displacement Tier 1 Vehicle Strata for the US06 Cycle.

NOx HC CO2 CO Odometer

reading

(mile)

Engine

displacement

(liters)

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

Total

Emis.a

Abs.

Lmt.b

Rel.

Lmt.c

< 50,000 < 3.5 2.3 0.15 6.5 0.72 0.094 13 2334 27 1.2 35 5.6 16< 50,000 > 3.5 2.4 0.63 27 0.93 0.22 24 3395 60 1.8 72 20 28> 50,000 < 3.5 3.2 0.16 5.1 1.3 0.076 5.9 2512 26 1.0 35 5.3 15> 50,000 > 3.5 7.3 1.3 17 2.1 0.54 26 3827 51 1.3 117 30 26

a total emissions, gramsb absolute upper and lower limits, gramsc relative upper and lower limits, %
175

The relative range of uncertainty, on a percentage basis in comparison to the mean total

emissions, is similar for the four cycles for a given pollutant and strata in most cases. For

example, for vehicles with odometer reading less than 50,000 miles and engine displacement less

than 3.5 liters, the relative uncertainty range is approximately 4 to 7 percent for NOx, 6 to 13

percent for HC, one percent for CO2 and 10 to 16 percent for CO when comparing all four

driving cycles. Within these ranges, the US06 cycle tends to have larger relative uncertainty

compared to the other three cycles. For example, for the same vehicle strata, the uncertainty in

NOx emissions for the US06 cycle is plus or minus 7 percent compared to only plus or minus 4

percent for the IM240, ART-EF, and FTP cycles. The uncertainty estimates for the US06 cycle

are larger than for the other three cycles for NOx for all strata and for CO for strata 11 (<50,000

miles, < 3.5 liters) and 21 (>50,000 miles, <3.5 liters).

Setting aside the differences between the US06 and the other cycles, the typical ranges of

uncertainty also vary by strata, with smaller ranges of uncertainty for those strata for which there

are more data. These include the strata for engine displacement less than 3.5 liters for both

odometer reading ranges. For these two strata, a typical range of uncertainty is plus or minus 4

percent for NOx, plus or minus 6 percent for HC, plus or minus 1 percent for CO2, and plus or

minus 10 percent for CO. For the larger engine displacement strata for both odometer reading

ranges, the typical ranges of uncertainty are plus or minus 10 percent for NOx, plus or minus 25

percent for HC, plus or minus 2 percent for CO2, and plus or minus 25 percent for CO. The

uncertainty ranges are typically narrowest for CO2.

The relative uncertainty ranges in NOx emissions are typically larger than that for CO2 but less

than that for HC and CO. The relative uncertainty ranges for HC and CO are comparable to each

other in most cases. Thus, the key insights are that: (1) the amount of uncertainty appears to

increase as the average VSP or range of VSP of a cycle increases; (2) the amount of uncertainty

is a function of sample size; and (3) the relative amount of uncertainty is smallest for CO2,

largest for both HC and CO, and in between for NOx. Furthermore, the relative range of

uncertainty for these particular cycles is as small as only one or two percent for CO2 and as large

as 30 percent or more for HC and CO. Thus, in some cases, the range of uncertainty in total

emissions is substantial.

The uncertainty estimates presented in this section represent uncertainty in total emissions for a

single vehicle of a given odometer reading and engine displacement. In order to estimate

uncertainty in total emissions for a fleet of vehicles, these estimates can be multiplied by the total

number of vehicles operated on each activity pattern for each strata. For example, suppose that

100 vehicles of odometer reading less than 50,000 miles and engine displacement less than 3.5

liters were operated on an activity pattern similar to the US06 cycle. The total emissions and the

relative range of uncertainty would be 230 g ± 6.5% for NOx, 72 g ± 13% for HC, 233,400 g

±1.2% for CO2, and 3,500 g ± 16% for CO. Suppose in addition that there were 100 vehicles in

each of the other three odometer reading and engine displacement strata. In this case, the results

would be be 1,520 g ± 9.6% for NOx, 505 g ± 12% for HC, 1,207,000 g ±0.7% for CO2, and

25,900 g ± 14% for CO. Of course, the method for estimating uncertainty in total emissions can

be expanded to account for the sum of total emissions and uncertainty in total emissions when

different vehicles are operating on different activity patterns.
176

7.5.3 Estimation of Uncertainty in Total Emissions for Different Numbers of

Vehicles

The purpose of this section is to illustrate that the relative range of uncertainty in total emissions

for a particular activity pattern is not a function of the number of vehicles operating on that

pattern for a given strata. As a case study, the mean total emissions and the uncertainty in the

mean total emissions was estimated for 13 vehicles operating on the ART-EF cycle. In this case

study, the inter-vehicle variability in the speed traces for each test is taken into account. The

allocation of the second-by-second emission data from the driving cycle tests into VSP modes is

summarized in Table 7-20. Although on average the distribution of modes among the 13

vehicles is similar to the distribution of modes for the standard ART-EF cycle as shown in Table

Table 7-15, there is variability in the amount of time spent in each mode from one test to another.

For example, for 12 of the tests the amount of time spent in Mode 3 varied from 191 seconds to

211 seconds, while for another test the amount of time spent in this mode was 253 seconds. For

comparison, the standard ART-EF speed trace has 196 seconds in Mode 3. Thus, it is the case

that individual tests do not exactly reproduce the standard speed trace.

As an example, the uncertainty in total NOx emissions were quantified for the 13 vehicles taking

into account inter-vehicle variability in the speed traces and uncertainty in the emission rate for

each individual mode. The average estimate of mean total NOx emission from the 13 vehicles,

based upon Monte Carlo simulation with 10,000 replications, is 7.11 grams. The quantified

absolute 95% confidence interval is from 6.84 gram to 7.38 gram, corresponding to a relative

range of minus 3.8 percent to plus 3.8 percent. The CDF of the quantified uncertainty in the

mean total emissions is shown in Figure 7-21.

The relative range of uncertainty of plus or minus 3.8 percent is influenced in part by the

variability in the distribution of the modes among the 13 vehicles because of the variability in the

speed traces for each test. From the previous section, the uncertainty estimated based upon the

standard speed trace for the same strata of vehicles was plus or minus 3.9 percent. The

difference in the relative range of uncertainty of 0.1 percent is most likely attributable to the role

of inter-vehicle variability in the speed traces. Therefore, these results illustrate that the relative

range of uncertainty in mean total emissions is relatively insensitive to the number of vehicles

tested or for which predictions are being made, even though there may be some inter-vehicle

variability in the speed traces.

7.6 Summary and Recommendations

This chapter has demonstrated several key issues pertaining to quantification of variability and

uncertainty in vehicle emissions estimates. With regard to characterization of variability, the key

points addressed in this work include the following:

• Single component distributions are often useful and reasonably accurate for estimating

inter-vehicle variability in emissions for most modes and vehicle strata, but they do not

work well for all modes and vehicle strata;

• Single component distributions whose parameters are estimated using Maximum

Likelihoood Estimation (MLE) can have means and standard deviations that are

substantially different from that of the data;
177

Table 7-20. Allocation of the Actual ART-EF Driving Cycle Speed Traces Into VSP Modes

With Respect to Time Spent in Each Mode for 13 Different Vehicles

VSP Vehicle ID

bina #7 #10 #11 #15 #18 #21 #22 #26 #27 #39 #42 #48 #50

1101 74 64 74 75 68 71 73 71 67 54 72 73 61

1102 54 67 55 45 51 53 59 57 62 50 56 56 69

1103 206 198 200 202 211 206 202 200 202 253 202 199 191

1104 42 66 51 62 56 52 50 56 60 55 56 54 99

1105 43 33 41 50 38 47 34 45 36 40 42 39 47

1106 42 35 38 31 36 34 42 29 32 24 38 40 16

1107 19 17 20 16 18 19 24 19 22 4 15 22 10

1108 8 10 12 8 10 8 7 12 9 11 9 8 5

1109 8677957862642

1110 6436574542662

1111 21 24 1

1112 2

1113 2

1114 a

 First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement <

3.5 liters

Cumulativ e Chart

Certainty is 95.00% from 6.84 to 7.38 g

.000

.250

.500

.750

1.000

0

10000

6.70 6.90 7.10 7.30 7.50

10,000 Trials 44 Outliers

Forecast: NO, ART

Figure 7-21. Quantification of Uncertainty Based upon Monte Carlo Simulation for Total NOx

Emission from 13 Vehicles Tested on the ART-EF Cycle.
178

• The mean and standard deviations of fitted distribution can be forced to match those of

the data if the Method of Matching Moments (MoMM) is used instead of MLE;

• In specific examples evaluated here, distributions fitted using MoMM appeared to better

represent the upper tail of the distribution of emissions for a given mode than did

distributions fitted using MLE;

• The distribution of emissions within any given mode is typically positively skewed and

for most modes either a lognormal or a Weibull distribution could provide an adequate fit

to the data;

• There were a few modes out of 56 for which single component distributions (e.g.,

lognormal, Weibull) could not provide a good fit to the data;

• Case studies were developed illustrating that two component mixtures of lognormal

distributions could be fit to data sets for which a single component distribution was a

poor fit, and that the mixture distribution provided an excellent fit to the data.

• For mixture distributions, MLE is a more readily available and easily applied parameter

estimation method than MoMM; however, the differences between these two techniques

become less important when the fit of the distribution to the data is very good.

• The use of parametric distributions, whether single component or mixtures, was shown to

be a feasible approach for characterizing variability.

With regarding to the characterization of uncertainty in mean emissions for specific modes, the

main findings of this work are as follows:

• The sample sizes are sufficiently large and/or the relative standard error of the means are

sufficiently small, in most cases, so that a normality assumption can be applied for most

modes when estimating uncertainty in the mean emission rates;

• The estimation of uncertainty in the mean emission rates can be based directly upon the

data and need not be based upon the distributions fitted to the data to represent

variability; therefore, any discrepancies between the fitted distributions for variability and

the data need not influence the uncertainty analysis;

• For situations in which the sample size is less than 40 or the relative standard error of the

mean is greater than 0.2, a more detailed assessment is necessary regarding whether a

normality assumption is appropriate for estimating uncertainty in mean modal emission

rates;

• The numerical method of bootstrap simulation can be used to estimate the sampling

distribution of the mean for situations in which a normality assumptions is suspected to

be inaccurate;

• The results of bootstrap simulation may sometimes confirm that a normality assumption

is appropriate, or may provide a strong indication that a normality assumption is not

appropriate;

• Parametric distributions, such as beta, Weibull, gamma, and lognormal, can be fit well to

the distributions of bootstrap replications of the mean in order to compactly represent

uncertainty in mean modal emissions even for cases in which a normality assumption is

not valid;

• The range of uncertainty in mean modal emission rates is a function of averaging time;

therefore, it was necessary to develop an averaging time correction factor in order to
179

adjust uncertainty estimates developed based upon one second averages to uncertainty

estimates applicable for other averaging times;

• When comparing a 10 second average to a 1 second average, the range of uncertainty

increases by a factor of approximately 2.5;

• A method was demonstrated for estimating averaging time correction factors; the results

of analysis of data from the modeling database suggest that the rate of increase of the

correction factor becomes small for an averaging time of 10 seconds; therefore, the

correction factor values estimated for the 10 second averaging time are suggested for use

for averaging times longer than 10 seconds.

• The averaging time correction factor has some sensitivity to average VSP within a mode;

therefore, a “bin adjustment factor” was developed in order to produce a mode-specific

refined estimate of the correction factor.

With respect to the estimation of uncertainty in total emissions, the key findings of this work are

as follows:

• Monte Carlo simulation is a flexible method for accounting for uncertainty in not just the

modal emission rates but also in activity data, such as the percentage of time spent in

each mode;

• The computational burden of Monte Carlo simulation depends on the selected sample

size for the numerical simulation of uncertainty; the choice of sample size can be made

taking into account trade-offs between the precision of the estimate of uncertainty in the

model output versus computational time. Furthermore, techniques such as Latin

Hypercube Sampling can be used to reduce the sample size for a given level of precision

in the estimated distribution for a model output;

• For simple models involving linear combinations of normal distributions, an analytical

approach will give an exact solution with relatively little computational burden; however,

in order to include uncertainty from activity data in addition to uncertainty in modal

emission rates, the analytical approach must be modified to an approximate approach;

• The results obtained from Monte Carlo simulation and from the analytical solution for

linear models based upon normality were shown to be equivalent for a case study of

estimating uncertainty in total emissions for a standard driving cycle;

• Based upon case studies for four driving cycles, four pollutants, and four vehicle strata,

the key insights are that: (1) the amount of uncertainty appears to increase as the average

VSP or range of VSP of a cycle increases; (2) the amount of uncertainty is a function of

sample size; and (3) the relative amount of uncertainty is smallest for CO2, largest for

both HC and CO, and in between for NOx. For the specific case studies, the uncertainty

range was as narrow as plus or minus 1 percent for CO2 and as large as plus or minus 30

percent for HC and CO;

• Uncertainty estimates for total emissions of individual vehicles can be aggregated to

make estimates of uncertainty in total emissions for a fleet of vehicles;

• Inter-vehicle variability in speed traces for a standardized driving cycle had little

influence on the uncertainty estimates for multiple vehicles for the case study of the

ART-EF cycle;
180

• The relative range of uncertainty in total emissions for multiple vehicles is relatively

insensitive to the number of vehicles even when there is inter-vehicle variability with

respect to a standard speed trace, for the example of the ART-EF cycle.

The recommendations based upon this work include the following with respect to quantification

of variability:

• It is feasible to use parametric distributions to represent variability in emissions for

specific modes and the use of parametric distributions is preferred over empirical

distributions because they represent a more compact method of summarizing variability.

• The Method of Matching Moments appears to be a preferred method for fitting

distributions to data because the mean and standard deviation of the fitted distribution

will be the same as that of the data and because distributions fitted using MoMM appear

to provide a better fit to the upper tail of the distribution, compared to MLE. Therefore,

the use of MoMM is recommended for additional evaluation and application.

• Single component distributions such as lognormal and Weibull distributions will typically

be able to adequately describe variability for most modes.

• In cases where single component distributions fail to provide an adequate fit, a two

component lognormal mixture distribution is recommended as a strong candidate for

substantially improving the fit.

• It is not necessary for the uncertainty analysis to be conditioned on the distributions fitted

to represent variability within modes; therefore, if there are discrepancies between the

fitted distributions and the data, such discrepancies need not introduce any error into the

uncertainty analysis.

With respect to quantification of uncertainty in mean modal emission rates, the recommendations

based upon this work include the following:

• The development of uncertainty estimates for mean emissions should be based directly

upon the data if there are problems in fitting distributions for variability to the data;

however, if the fits of the distributions for variability are good, then the uncertainty

analysis can be based either upon the data or upon the fitted distributions for variability;

• A normality assumption will typically be adequate for most modal emission rates as long

as there are sufficient data;

• For modes for which the sample size is less than 40 and/or the relative standard error of

the mean is greater than 0.2, the assumption of normality should be tested by developing

a sampling distribution of uncertainty in the mean based upon bootstrap simulation;

• For cases in which a normality assumption is not valid, bootstrap simulation can be used

to estimate a distribution of bootstrap replications of the mean, and a parametric

distribution such as beta, Weibull, gamma, or lognormal can be fit to the distribution of

the means;

• The range of uncertainty in modal emission rates must be adjusted for different averaging

times using an approach such as the correction factor and bin adjustment factor approach

demonstrated here.
181

With respect to the quantification of uncertainty in total emissions, the recommendations based

upon this work include the following:

• A simple analytical approach for estimating uncertainty in total emissions is adequate as

long as the uncertainty in modal emission estimates are normal or approximately normal

for most or all of the modes and as long as there is no need to include uncertainty in

vehicle activity in the estimate;

• An analytical calculation method based upon normality can be included for comparison

purposes even if a Monte Carlo method is also used; for example, results from the

analytical method could be used as a quality assurance check on the Monte Carlo

simulation results;

• A Monte Carlo simulation-based methods, including variants based upon Latin

Hypercube Sampling, is recommended if the objective is to include uncertainty in activity

as an input to the estimation of uncertainty in total emissions;

• In situations for which the sample sizes are small and/or the variability in data is large,

normality assumptions will not be valid. For such situations, a Monte Carlo-based

method is preferable.

• The range of uncertainty is sufficiently large in many cases that a quantitative uncertainty

analysis is well-justified.

183

8 FEASIBILITY OF ESTIMATING MODAL EMISSIONS FROM AGGREGATE

BAG DATA

The objective of this task is to evaluate a methodology for deriving modal emission rates from

data in which only aggregate emission results are available, in order to answer the key question:

How should aggregate bag data be analyzed to derive estimates of modal emission rates? The

first section provides background and theory, upon which the analyses in the later sections are

based.

8.1 Methodological Overview

In order to estimate modal emission rates, the fraction of time spent in each mode for a driving

cycle is estimated based upon the second-by-second speed trace used for the bag measurements

(preferably the actual speed trace for the test, as opposed to the nominal speed trace), and any

other available information regarding simulation of loads with the dynamometer. A system of

equations for the unknown modal emissions, the fraction of time in each mode, and the total

(agrgretage) emissions is developed since the average emission rate for each trip can be

represented by the fraction of time spent in each mode multiplied by modal emission rate. For

example for four different modes for running exhaust emissions, as was the case for the shootout

project that was conducted by NCSU, the following equation was specified (Frey, Unal, and

Chen, 2002):

ERcs x ftcs + ERidle x ftidle + ERaccel x ftaccel + ERdecel x ftdecel + ERcruise x ftcruise = ERave (8-1)

 where,

ERi = emission rate for mode i (g/sec)

fti = fraction of time spent in mode i

Subscripts

cs = cold start mode

idle = idle mode

accel = acceleration mode

decel = deceleration mode

cruise = cruise mode

ave = average of all modes

From the bag data, the average emission rate for the entire bag (or trip) can be estimated. From

the speed trace, the fraction of time in each mode can be estimated. Therefore, the unknowns are

the modal emission rates.

In order to solve systems of equations such as the one given in Equation (8-1), there are different

methods. A system where the number of equations used is the same as the number of unknowns

is identified as a “square” system, and has unique solutions (Kress, 1998). For “square” systems,

an exact solution is sought by using methods such as Gaussian Elimination.

Systems which have a number of equations less than the number of unknowns are identified as

“underdetermined” systems, and the solutions of these systems of equations are not unique.
184

Such systems can be converted to "square" systems by adding additional equations, such as an

assumption regarding the ratio of the g/sec emission rate for one mode with respect to another.

Conditions where there are more equations than unknowns are identified as “overdetermined”

cases. In these cases, which are likely to be common with respect to the use of existing vehicle

emissions bag data, least-squares methods can be used to find solutions (Kress, 1998).

According to Kress (1998), in order to be able to solve linear systems directly, the system should

be “well-conditioned”, rather than “ill-conditioned”. “Ill-conditioned” systems occur when small

errors in the data of a linear system cause large errors in the solution (Kress, 1998; Hildebrand,

1987). The minimum number of equations (i.e., one equation represents one measurement of

bag data) that are desirable in order to have a well-conditioned system will depend on number of

unknowns, which is the number of modal “bins” in this case. Techniques for solving wellconditioned over-determined systems include least-squares regression and constrained leastsquares. In the latter method, constraints can be included. For example, if it is known that

emissions in one mode should be less than that of other modes, this can be added as a constraint

in the system. Further, a non-negativity constraint can be included. In this study, both LeastSquares and Constrained Least-Squares were investigated. From the previous study it was

observed that Constrained Least-Squares produced good results.

The performance of the modal emission estimation approach based upon aggregate data was

evaluated based upon application of the method to second-by-second data. Specifically, the

second-by-second data were used to estimate the fraction of time spent in each mode and the

total (or trip average) emission rate. The calculation procedure described above was applied to

estimate the modal emission rates. The estimated modal emission rates were compared to the

actual modal emission rates. Uncertainty in the predictions of the solution technique were

characterized by evaluating the distribution of the differences between the predicted modal

emission rates and the actual modal emission rates. Ideally, if the solution method is unbiased,

the average difference between the predicted and actual modal emission rates will be zero. If the

average difference is not zero, then there is a bias. The magnitude of the bias was evaluated to

determine whether it was significant. The uncertainty in the modal emission estimates obtained

from the bag (aggregate) data must be considered in the uncertainty analysis of the emissions

model if these modal emission estimates are used in the model.

8.2 Bag-Based Modal Emissions Estimation for Four Modes (Idle, Acceleration, Cruise,

Deceleration) and for 14 VSP Modes

The objective of this portion of the work was to develop a methodology for deriving modal

emission rates from data in which only aggregate emission results are available. The method

was first applied to relatively simple modal emission models, including the four basic modes of

idle, acceleration, cruise, and deceleration defined by NCSU in previous work and the 14 VSP

modes defined in this project. The generic equation underlying the estimation process can be

specified as:

ER1* ft1 + ...+ ERi* fti +... + ERn* ftn = ERavg (8-2)

Where,
185

ERi : emission rate for mode I (g/sec)

 fti : fraction of time spent in mode i

Subscripts:

 i: mode i

 n: total number of modes

 avg: average of all modes

From the bag data, the average emission rate for the entire bag (or trip) can be estimated. From

the speed trace, the fraction of time in each mode can be estimated. Therefore, the unknowns are

the modal emission rates.

Initially, tests of the method were done on two preliminary versions of modal definitions,

including the four original NCSU based bins and the 14 VSP based bins developed in this

project. The NCSU approach is comprised of four driving modes: idle, acceleration,

deceleration, cruise, which are assigned mode numbers from 1 to 4 sequentially for purposes of

this analysis.

Because the equation above corresponds to one trip and there are hundreds of trips in the data

set, the equation is an “overdetermined” square system in which there are more equations than

unknown variables. The techniques for solving such systems include least-squares and

constrained least-squares as previously discussed. We used both of them and compared their

applicability.

The basic assumption of the least squares method is to find a curve that has the minimal sum of

the deviations squared (least square error) from a given set of data:

Min y = f1(x)* f1(x) + ...+ fi(x)* fi(x) +... + fm(x)* fm(x) (8-3)

Where

 fi(x) = fti1* x1 +...+ ftij* xj +...+ ftin* xn avgi

 xj: the emission rate of mode j

 m: number of trips

 n: number of modes

 ERavgi : aggregated emission rate for all modes in trip i(g/sec)

 Ftij : fraction of time spent in mode j in trip i

For the constrained least square method, the approach is to solve the above least squares problem

additionally with some constraints which may be linear or non-linear equations or inequalities.

For example, it is known that emission rates in the acceleration mode should be larger than that

in the idle modes, from which, we can assume: xaccel > xidle . The constrained least squares

problem is a special form of Nonlinear Programming, which is one of the classic topics in

Operations Research. In the NLP terminology, the previous equation is an objective function

which is nonlinear and quadratic.

At first, only simple constraints were used, but results with these were not promising, so strict

constraints were created. Hence, there are 3 tests conducted respectively on each pollutant for

each binning approach: unconstrained, basic constraints, and strict constraints. The basic
186

constraints just consider the order of emission rates of all the modes and their non-negative

characteristic. For example, the following is the set of basic constraints set for the NCSU

approach used in the test:

 X2 > X4 > X3 > X1 > 0 (8-4)

 Where X2: emission rate of acceleration mode

 X4: emission rate of cruise mode

 X3: emission rate of deceleration mode

 X2: emission rate of idle mode

If the space of the control variables X is not sufficiently focused, it is possible that the estimated

optimal value of X* might lie in an area that is infeasible, such as negative values. Thus, the

more concentrated the effective space of X is, the more accurate the test results would typically

be. Based on this, strict constraints were developed. To develop the strict constraints, the

emission rates of each mode for each trip were calculated as ratios with respect to the smallest

emission rate among all the modes, which is idle in the case of the NCSU approach, and then

statistically summarized over the all the trips to get the means and confidence limits of those

ratios. These ratios were used to develop the strict constraints.. The strict constraints also

include either explicitly or implicitly the basic constraints set. Since the form of the latter was

shown above, here just the additional strict constraints are displayed:

 a * X1 < Xi < b* X1 (8-5)

 where X1: the lowest emission rate among all the modes

 a: the low bound of confidence limits for ratio Xi/ X1 (confidence=0.05)

 b: the high bound of confidence limits of ratio Xi/ X1 (confidence=0.05)

Below is an example of complete strict constraints set for HC emissions based upon NCHRP

data under the NCSU bin approach:

 X2 > X4 > X3 > X1 > 0 (8-6)

 56.5 * X1 < X2 < 73.4* X1

 1.8 * X1 < X3 < 7.1* X1

 3.6 * X1 < X3 < 13.3* X1

 Where X2: emission rate of acceleration mode

 X4: emission rate of cruise mode

 X3: emission rate of deceleration mode

 X2: emission rate of idle mode

The SAS mathematical programming software was used to solve the above NLP problem. The

test was done based upon the NCHRP data set, which has more than one hundred trips and

92,000 observations. The results are shown in Tables 8-1 through 8-4 for NOx, HC, CO, and

CO2, respectively. The results are summarized graphically in Figures 8-1 through 8-4 for the

same four respective pollutants. The results indicate that for the analysis of only four modes, the

accuracy of estimating the average modal emission rates is less than desirable. For example, the
187

Table 8-1. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for

Four NCSU Driving Modes for NOx: Comparison of No Constraint, Basic Constraint,

and Strict Constraint Solutions.

Mode Actual NCa ERRORd Cb ERRORd SCc ERRORd

Er1 2.84 -12.3 -5.35 0 -1 0.78 -0.72

Er2 65.5 -285 -5.35 28.44 -0.57 34.05 -0.48

Er3 3.18 972.02 304.94 28.44 7.95 3.49 0.1

Er4 22.76 -148.98 -7.54 28.44 0.25 31.81 0.4

Avg. Error 131.4 2.44 0.43

Table 8-2. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for

Four NCSU Driving Modes for HC: Comparison of No Constraint, Basic Constraint,

and Strict Constraint Solutions.

Mode Actual NCa ERRORd Cb ERRORd SCc ERRORd

Er1 1.18 28.69 -23.36 0 1 0.49 0.59

Er2 19.7 -207.09 11.51 8.38 0.57 27.54 -0.4

Er3 2.8 295.24 -104.39 8.38 -1.99 3.46 -0.23

Er4 6.58 -12.31 2.87 8.38 -0.27 4.05 0.38

Avg. Error 35.53 0.96 0.4

Table 8-3. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for

Four NCSU Driving Modes for CO: Comparison of No Constraint, Basic Constraint,

and Strict Constraint Solutions.

Mode Actual NCa ERRORd Cb ERRORd SCc ERRORd

Er1 20.04 -3561.8 178.74 0 1 1.02 0.95

Er2 2013.96 -3957.6 2.97 688.62 0.66 1345.18 0.33

Er3 77.15 31522 -407.57 688.62 -7.93 152.54 -0.98

Er4 447.11 -6407.3 15.33 688.62 -0.54 636.76 -0.42

Avg. Error 151.15 2.53 0.67

Table 8-4. Results of Estimation of Modal Emission Rates (g/sec) from Aggregate Data for Four

NCSU Driving Modes for CO2: Comparison of No Constraint, Basic Constraint, and

Strict Constraint Solutions.

Mode Actual NCa ERRORd Cb ERRORd SCc ERRORd

Er1 0.89 1.67 0.87 0 -1 0.96 0.07

Er2 5.76 -45.07 -8.82 3.4 -0.41 4.61 -0.2

Er3 0.98 84.78 85.14 3.4 2.46 1.01 0.02

Er4 3.29 -5.87 -2.78 3.4 0.03 3.65 0.11

Avg. Error 24.4 0.97 0.1

Notes for Tables 8-1 through 8-4:

a

 NC: No Constraint

b

 C: Constraint

c

 SC: Strict Constraint

d Error: (Predicted-Actual)/Actual
188

y = 0.5048x + 0.5634

R2 = 0.6952

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6 7

Observed Modal Rate (mg/sec)

Predicted Modal Rate (mg/sec)

Figure 8-1. Predicted versus Observed NOx NCSU Modal Emission Rates Estimated From

NCHRP Data Using the Strict Constraints Approach.

y = 1.4671x - 0.2214

R2 = 0.9669

-0.5

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5

Observed Modal Rate (mg/sec)

Predicted Modal Rate (mg/sec)

Figure 8-2. Predicted versus Observed HC NCSU Modal Emission Rates Estimated From

NCHRP Data Using the Strict Constraints Approach.
189

y = 0.6244x + 13.451

R2 = 0.9324

0

20

40

60

80

100

120

140

160

0 50 100 150 200 250

Observed Modal Rate (mg/sec)

Predicted Modal Rate (mg/sec)

Figure 8-3. Predicted versus Observed CO NCSU Modal Emission Rates Estimated From

NCHRP Data Using the Strict Constraints Approach.

y = 0.7827x + 0.4207

R2 = 0.9434

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Observed Modal Rate (g/sec)

Predicted Modal Rate (g/sec)

Figure 8-4. Predicted versus Observed CO2 NCSU Modal Emission Rates Estimated From

NCHRP Data Using the Strict Constraints Approach.
190

slopes of the best fit lines in the parity plots deviate substantially from an ideal value of 1 for all

four pollutants. However, the strict constraints do produce modal estimates that qualitatively

preserve the relative ordering among modes and that yield an acceleration mode with an

emission rate substantially higher than for the other modes.

The results based upon application to the 14 VSP-based modes are shown in Tables 8-5 through

8-8 and Figures 8-5 through 8-8 for NOx, HC, CO, and CO2, respectively. These results are

generally more promising, with the slope of the best fit line in the parity plots closer to one than

was the case for the analysis based upon only four modes, and with coefficients of determination

for the parity plots in excess of 0.80. The results are especially promising for CO2.

As exspected, among three types of test, the test based on strict constraints gave the best

performance, which confirms that the focus on the effective area of the control variables X will

improve the predication accuracy.

Comparing the differences among the four pollutants, only the results for CO2 are satisfying,

with a predication error of approximately 10% or less. A possible reason for the superior results

with CO2 but not for the other pollutants is that is CO2 has small inter-trip and inter-vehicle

variance of the modal emission rates. Too much variability in modal emission rates from one

vehicle to another may be the source of difficulties in estimation of modal rates for the other

pollutants.
191

Table 8-5. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for 14

VSP Modes for NOx: Comparison of No Constraint, Basic Constraint, and Strict

Constraint Solutions.

NOx Actual NCa ERRORd Cb ERRORd SCc ERRORd

ER1 4.54 357.88 77.82 11.23 1.47 2.53 -0.44

ER2 4.66 109.4 22.48 0 -1 2.47 -0.47

ER3 4.27 154.63 35.18 11.23 1.63 1.24 -0.71

ER4 13.71 -83.57 -7.09 11.23 -0.18 8.12 -0.41

ER5 20.26 -10.52 -1.52 11.23 -0.45 11.52 -0.43

ER6 25.97 -583.9 -23.48 11.23 -0.57 12.14 -0.53

ER7 34.1 -423.49 -13.42 11.23 -0.67 12.14 -0.64

ER8 48.69 -533.89 -11.97 11.23 -0.77 29.89 -0.39

ER9 61.91 260.33 3.21 11.23 -0.82 48.79 -0.21

ER10 86.39 515.21 4.96 95.29 0.1 66.9 -0.23

ER11 123.44 576.05 3.67 95.29 -0.23 80.16 -0.35

ER12 173.84 295.88 0.7 95.29 -0.45 93.48 -0.46

ER13 176.49 908.56 4.15 381.74 1.16 118.5 -0.33

ER14 201.72 849.94 3.21 1283.26 5.36 211.03 0.05

Avg. Error 15.2 1.06 0.4

a

 NC: No Constraint

b

 C: Constraint

c

 SC: Strict Constraint

d Error: (Predicted-Actual)/Actual

Table 8-6. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for 14

VSP Modes for HC: Comparison of No Constraint, Basic Constraint, and Strict

Constraint Solutions.

HC Actual NCa ERRORd Cb ERRORd SCc ERRORd

ER1 3.69 130.98 34.51 0 -1 2.25 -0.39

ER2 2.27 0.84 56.12 0 -1.63 1.41 -0.63

ER3 1.92 23.35 66.48 5.52 -1.93 1.16 -0.75

ER4 4.02 2.09 31.65 0 -0.92 3.01 -0.36

ER5 5.97 -61.98 21.34 5.52 -0.62 4.04 -0.24

ER6 6.07 -177.83 20.96 5.52 -0.61 4.96 -0.24

ER7 7.57 49.79 16.82 5.52 -0.49 8.87 -0.19

ER8 11.15 -16.64 11.41 5.52 -0.33 8.87 -0.13

ER9 13.71 215.81 9.28 35.33 -0.27 22.33 -0.1

ER10 17.22 -169.45 7.39 35.33 -0.21 22.33 -0.08

ER11 28.09 110.83 4.53 35.33 -0.13 39.42 -0.05

ER12 50.43 -98.42 2.52 35.33 -0.07 39.42 -0.03

ER13 73.6 -180.59 1.73 35.33 -0.05 50.35 -0.02

ER14 98.75 146.08 1.29 211.99 -0.04 248.96 -0.01

AvgError 20.43 0.59 0.23

a

 NC: No Constraint

b

 C: Constraint

c

 SC: Strict Constraint

d Error: (Predicted-Actual)/Actual
192

Table 8-7. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for 14

VSP Modes for CO: Comparison of No Constraint, Basic Constraint, and Strict

Constraint Solutions.

CO Actual NCa ERRORd Cb ERRORd SCc ERRORd

ER1 149.59 23220 154.22 0 -1 121.22 -0.19

ER2 124.14 -2308 -19.6 0 -1 0 -1

ER3 83.59 -2028 -25.27 0 -1 36.62 -0.56

ER4 273.76 -2467 -10.01 0 -1 179.45 -0.34

ER5 338.76 -13068 -39.58 0 -1 179.45 -0.47

ER6 307.11 -2760 -9.99 0 -1 310.19 0.01

ER7 393.27 -1282 -4.26 1716 3.36 595.48 0.51

ER8 608.03 7636 11.56 1716 1.82 1114.42 0.83

ER9 755.63 17311 21.91 3403.35 3.5 1722.36 1.28

ER10 1015.26 -21646 -22.32 3403.35 2.35 1722.36 0.7

ER11 2063.31 -7639 -4.7 3403.35 0.65 4262.86 1.07

ER12 5530.73 -17753 -4.21 3403.35 -0.39 7571.34 0.37

ER13 10336.3 -31840 -4.08 3403.35 -0.67 7571.34 -0.27

ER14 16338.64 -39599 -3.42 3403.35 -0.79 13287 -0.19

AvgError 23.94 1.4 0.56

a

 NC: No Constraint

b

 C: Constraint

c

 SC: Strict Constraint

d Error: (Predicted-Actual)/Actual

Table 8-8. Results of Estimation of Modal Emission Rates (g/sec) from Aggregate Data for 14

VSP Modes for CO2: Comparison of No Constraint, Basic Constraint, and Strict

Constraint Solutions.

CO2 Actual NCa ERRORd Cb ERRORd SCc ERRORd

ER1 1.09 14.78 12.52 1.28 0.17 1.04 -0.05

ER2 1.26 4.43 2.5 1.28 0.01 1.19 -0.06

ER3 1.26 3.83 2.05 1.15 -0.08 1.23 -0.02

ER4 2.46 -4.37 -2.78 1.28 -0.48 2.32 -0.06

ER5 3.2 -9.19 -3.87 1.28 -0.6 3.07 -0.04

ER6 3.95 9.73 1.46 6.18 0.56 3.81 -0.04

ER7 4.69 -2.04 -1.44 6.18 0.32 4.95 0.05

ER8 5.52 -3.63 -1.66 6.18 0.12 5.81 0.05

ER9 6.41 9.47 0.48 6.18 -0.04 6.77 0.06

ER10 7.42 -8.69 -2.17 6.18 -0.17 7.82 0.05

ER11 8.89 17.11 0.93 7.04 -0.21 9.27 0.04

ER12 10.61 6.73 -0.37 7.04 -0.34 10.49 -0.01

ER13 11.87 9.74 -0.18 7.39 -0.38 11.75 -0.01

ER14 13.34 33.77 1.53 43.5 2.26 13.03 -0.02

AvgError 2.42 0.08 0.04

a

 NC: No Constraint

b

 C: Constraint

c

 SC: Strict Constraint

d Error: (Predicted-Actual)/Actual
193

y = 0.8027x - 6.2648

R2 = 0.8871

0

50

100

150

200

250

0 50 100 150 200 250

Observed NOx Emissions (mg/sec)

Predicted NOx Emissions (mg/sec)

Figure 8-5. Predicted versus Observed NOx Modal Emission Rates Based upon the 14 Mode

VSP Approach Estimated From NCHRP Data Using the Strict Constraints Approach.

y = 0.7346x + 3.2797

R2 = 0.861

0

10

20

30

40

50

60

70

80

0 20 40 60 80

Observed HC Emissions (mg/sec)

Predicted HC Emissions (mg/sec)

Figure 8-6. Predicted versus Observed HC Modal Emission Rates Based upon the 14 Mode VSP

Approach Estimated From NCHRP Data Using the Strict Constraints Approach.
194

y = 0.798x + 578.3

R2 = 0.9275

0

5000

10000

15000

20000

0 5000 10000 15000 20000

Observed CO Emissions (mg/sec)

Predicted CO Emissions (mg/sec)

Figure 8-7. Predicted versus Observed CO Modal Emission Rates Based upon the 14 Mode VSP

Approach Estimated From NCHRP Data Using the Strict Constraints Approach.

y = 0.9986x + 0.0482

R2 = 0.9965

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-8. Predicted versus Observed CO2 Modal Emission Rates Based upon the 14 Mode

VSP Approach Estimated From NCHRP Data Using the Strict Constraints Approach.
195

8.3 Bag-Based Modal Emissions Estimation for the "56-bin" VSP-based Approach

In this section, evaluation of the modal estimation method for bag data was applied to the

stratified bin approach. The original NCHRP data set was divided into 4 subsets of data in terms

of odometer reading and engine displacement, based upon cut points of 50K miles and 3.5 liters,

respectively. For each of the four subsets, the 14 VSP modes were applied. From the previous

section, a key conclusion was that the strict-constraint method is more effective than the

unconstrained and basic-constraint methods. Thus, the focus in this section was upon the strict

constraint method. In the previous section, the strict constraints were developed based upon

analysis of the NCHRP data set. In this section, the ranges for the strict constraints were

developed based upon the NCHRP data set and, alternatively, based upon the modeling data set.

The results of the predicted modal emission rates estimated from the aggregate data, and the

observed values, are shown in Tables 8-9 through 8-24. There are four tables for each pollutant,

with each of the four tables representing a different vehicle strata with respect to odometer

reading and engine displacement. All of the results for CO2 based upon the strict constraints

cases are shown in Figures 8-9 through 8-16. Selected results for the modal emissions estimated

for HC are shown in Figures 8-17 through 8-22.

The results for CO2 were generally very good, especially for the case in which the range of

values for the constraints were estimated from data in the NCHRP database. For all four vehicle

strata, the average relative error in the predicted versus observed modal emission rates was less

than 10 percent, except for the first strata (odometer reading < 50,000 miles, engine displacement

< 3.5 liters) when constraints were developed based upon the modeling database. These results

imply that when the constraints are more representative of the data from which the modes are

being estimated, the results will tend to be better. Figure 8-11 and 8-12 illustrate that the modal

emission rates for CO2 estimated using the constraints estimated from the NCHRP data are

better than those estimated using the constraints based upon the modeling database. In

particular, the slope of the trend line for the predicted versus observed modes is closer to one,

indicating a more accurate result. A similar comparison can be observed for Figures 8-13 and 8-

14.

The results for HC were generally not as good as those for CO2. The average relative errors for

the modal estimates, as indicated in Tables 8-13 through 8-16, were typically 0.37 to 0.64 for the

six cases in which results could be obtained. In two cases, it was not possible to get a solution.

The predicted modal emissions tend to be low for the higher VSP modes, as illustrated in Figures

8-17 through 8-19, although there are examples in Figures 8-20 through 8-22 in which the

predictions for the higher VSP modes are relatively more accurate.

For both NOx and CO, the estimation method failed for most cases. For NOx, it was possible to

get results in only three of eight cases, and the errors in these cases ranged from 0.24 to 0.55.

For CO, it was possible to get results in only two of eight cases, with errors of 0.48 and 0.94.

Overall, the key findings of the attempts to estimate modal emission rates for the 56-bin

approach based upon NCHRP data were: (1) the method worked well only for CO2; the method

worked for HC for most cases but the accuracy of the predictions was less than desirable; and (3)
196

Table 8-9. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO2 Emissions (g/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 0.94 1.58 0.68 0.91 -0.03

ER2 1.06 1.51 0.42 0.95 -0.10

ER3 1.2 1.26 0.05 1.08 -0.10

ER4 2.21 2.16 -0.022 2 -0.10

ER5 2.86 2.62 -0.084 2.63 -0.08

ER6 3.53 3.03 -0.14 3.25 -0.08

ER7 4.19 4.25 0.014 4.51 0.08

ER8 4.92 4.82 -0.02 5.31 0.08

ER9 5.74 5.51 -0.04 6.18 0.08

ER10 6.67 6.18 -0.07 7.13 0.07

ER11 7.82 7.34 -0.06 8.65 0.11

ER12 9.49 9.2 -0.03 9.9 0.04

ER13 10.89 11.61 0.066 11.48 0.05

ER14 12.08 12.29 0.017 12.18 0.01

Avg. Error 0.122 0.072

a Error: (Predicted-Actual)/Actual

Table 8-10. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO2 Emissions (g/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 1.03 1.24 -0.20 1.01 0.019

ER2 1.31 1.4 -0.07 1.18 0.099

ER3 1.07 1.08 -0.01 1 0.065

ER4 2.4 2.29 0.05 2.17 0.096

ER5 3.15 2.85 0.10 2.9 0.079

ER6 3.84 3.46 0.10 3.58 0.068

ER7 4.55 5.07 -0.11 4.86 -0.068

ER8 5.32 5.81 -0.09 5.68 -0.068

ER9 6.16 6.56 -0.06 6.6 -0.071

ER10 7 7.55 -0.08 7.54 -0.077

ER11 8.43 8.66 -0.03 9.07 -0.076

ER12 9.91 8.66 0.13 10.54 -0.064

ER13 10.54 9.15 0.13 11.27 -0.069

ER14 11.92 9.9 0.17 11.27 0.055

Avg. Error 0.09 0.070

a Error: (Predicted-Actual)/Actual
197

Table 8-11. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO2 Emissions (g/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading > 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 1.5 1.56 -0.04 1.55 -0.033

ER2 1.53 1.66 -0.08 1.41 0.078

ER3 1.66 1.33 0.20 1.52 0.084

ER4 2.93 2.36 0.19 2.63 0.102

ER5 3.88 2.93 0.24 3.7 0.046

ER6 4.94 5.46 -0.11 4.75 0.038

ER7 5.95 6.55 -0.10 6.67 -0.121

ER8 7.05 7.95 -0.13 7.9 -0.121

ER9 8.23 7.95 0.03 9.28 -0.128

ER10 9.64 7.95 0.18 9.28 0.037

ER11 11.13 12.94 -0.16 12.25 -0.101

ER12 14.24 18.87 -0.33 15.19 -0.067

ER13 15.84 18.87 -0.19 15.25 0.037

ER14 17.47 18.87 -0.08 15.25 0.127

Avg. Error 0.15 0.080

a Error: (Predicted-Actual)/Actual

Table 8-12. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO2 Emissions (g/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 1.67 1.64 0.018 1.64 0.02

ER2 1.97 2.15 -0.091 2.15 -0.09

ER3 1.69 1.54 0.089 1.54 0.09

ER4 3.5 3 0.143 3 0.14

ER5 4.48 4.07 0.092 4.07 0.09

ER6 5.46 5.1 0.066 5.1 0.07

ER7 6.48 6.74 -0.040 6.74 -0.04

ER8 7.64 6.97 0.088 6.97 0.09

ER9 8.83 9.42 -0.067 9.42 -0.07

ER10 10.3 11.36 -0.103 11.36 -0.10

ER11 12.54 13.41 -0.069 13.41 -0.07

ER12 14.75 13.41 0.091 13.41 0.09

ER13 16.96 20.25 -0.194 20.25 -0.19

ER14 18.76 21.42 -0.142 21.42 -0.14

Avg. Error 0.092 0.09

a Error: (Predicted-Actual)/Actual
198

Table 8-13. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 2.18 0 3.26 -0.50

ER2 1.67 0 0.93 0.44

ER3 1.82 0 1.16 0.36

ER4 4.11 0 2.75 0.33

ER5 4.16 0 3.26 0.22

ER6 5.37 0 7.09 -0.32

ER7 6.56 0 7.79 -0.19

ER8 8.82 0 7.79 0.12

ER9 10.52 0 7.91 0.25

ER10 13.25 0 26.16 -0.97

ER11 24.06 0 27.79 -0.16

ER12 31.79 0 27.79 0.13

ER13 59.91 0 27.79 0.54

ER14 70.41 0 27.79 0.61

Avg. Error 0.37

a Error: (Predicted-Actual)/Actual

Table 8-14. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 4.98 2.52 0.494 2.37 0.52

ER2 2.06 1.73 0.160 1.27 0.38

ER3 0.95 1.33 -0.400 0.91 0.04

ER4 3.11 2.79 0.103 2.18 0.30

ER5 5.15 3.19 0.381 2.73 0.47

ER6 5.17 4.38 0.153 3.73 0.28

ER7 6.17 11.42 -0.851 11.65 -0.89

ER8 7.67 13.01 -0.696 11.65 -0.52

ER9 13.26 13.01 0.019 11.65 0.12

ER10 15.18 27.09 -0.785 28.75 -0.89

ER11 24.58 42.49 -0.729 46.4 -0.89

ER12 44.64 42.49 0.048 46.4 -0.04

ER13 70.17 42.49 0.394 46.4 0.34

ER14 116.55 42.49 0.635 46.4 0.60

Avg. Error 0.418 0.45

a Error: (Predicted-Actual)/Actual
199

Table 8-15. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading > 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 1.58 0 0.94 0.41

ER2 1.45 0 0.75 0.48

ER3 1.84 0 2.48 -0.35

ER4 2.39 0 2.01 0.16

ER5 9.17 0 4.4 0.52

ER6 4.72 0 5.42 -0.15

ER7 5.48 0 5.42 0.01

ER8 11.3 0 27.42 -1.43

ER9 12.66 0 27.42 -1.17

ER10 20.14 0 27.42 -0.36

ER11 20.14 0 42.75 -1.12

ER12 71.33 0 91.07 -0.28

ER13 70.54 0 91.07 -0.29

ER14 77.97 0 91.07 -0.17

Avg. Error 0.49

a Error: (Predicted-Actual)/Actual

Table 8-16. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 10.75 1.59 0.852 1.59 0.85

ER2 7.39 1.78 0.759 1.78 0.76

ER3 5.71 3.8 0.335 3.8 0.33

ER4 8.51 0 1.000 0 1.00

ER5 15 7.29 0.514 7.29 0.51

ER6 14.76 8.35 0.434 8.35 0.43

ER7 20.53 9.15 0.554 9.15 0.55

ER8 35.71 44.64 -0.250 44.64 -0.25

ER9 34.84 86.61 -1.486 86.61 -1.49

ER10 43.06 86.61 -1.011 86.61 -1.01

ER11 64.77 122.99 -0.899 122.99 -0.90

ER12 137.02 122.99 0.102 122.99 0.10

ER13 161.42 122.99 0.238 122.99 0.24

ER14 209.61 315.45 -0.505 315.45 -0.50

Avg. Error 0.639 0.64

a Error: (Predicted-Actual)/Actual
200

Table 8-17. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 144.4 0 116.78 0.19

ER2 86.18 0 35.4 0.59

ER3 82.35 0 45.98 0.44

ER4 284.3 0 179.31 0.37

ER5 283.62 0 210.11 0.26

ER6 300.11 0 279.07 0.07

ER7 393.08 0 479.53 -0.22

ER8 625.93 0 479.53 0.23

ER9 749.09 0 2438.1 -2.25

ER10 1033.99 0 2684.08 -1.60

ER11 2576.85 0 2684.08 -0.04

ER12 3944.7 0 3204.4 0.19

ER13 8785.4 0 8891.55 -0.01

ER14 12567.67 0 8891.55 0.29

Avg. Error 0.48

a Error: (Predicted-Actual)/Actual

Table 8-18. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 150.28 0 63.17 0.58

ER2 130 0 0 1.00

ER3 48.96 0 30.66 0.37

ER4 221.4 0 111.62 0.50

ER5 285.13 0 111.62 0.61

ER6 241.95 0 252.67 -0.04

ER7 277.95 0 340.68 -0.23

ER8 327.58 0 430.83 -0.32

ER9 519.72 0 2103.27 -3.05

ER10 651.3 0 2225.11 -2.42

ER11 1249.86 0 5239.32 -3.19

ER12 6740.72 0 5239.32 0.22

ER13 12956.1 0 5239.32 0.60

ER14 23713.22 0 22508 0.05

Avg. Error 0.94

a Error: (Predicted-Actual)/Actual
201

Table 8-19. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading >50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 80.7 0 0

ER2 129.75 0 0

ER3 130.09 0 0

ER4 227.75 0 0

ER5 637.64 0 0

ER6 280.52 0 0

ER7 416.31 0 0

ER8 696.73 0 0

ER9 1094.9 0 0

ER10 1253.14 0 0

ER11 2031.25 0 0

ER12 8029.59 0 0

ER13 8933.28 0 0

ER14 12979.73 0 0

Avg. Error 

a Error: (Predicted-Actual)/Actual

Table 8-20. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 263.35 0 0

ER2 316.27 0 0

ER3 145.17 0 0

ER4 440.86 0 0

ER5 456.54 0 0

ER6 592.43 0 0

ER7 740.36 0 0

ER8 1305.73 0 0

ER9 1135.74 0 0

ER10 1793.1 0 0

ER11 2394.7 0 0

ER12 8240.6 0 0

ER13 13064.57 0 0

ER14 19173.19 0 0

Avg. Error 

a Error: (Predicted-Actual)/Actual
202

Table 8-21. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: NOx Emissions (mg/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 4.4 6.61 -0.502 0

ER2 3.85 5.82 -0.512 0

ER3 4.41 3.77 0.145 0

ER4 11.8 9.85 0.165 0

ER5 15.52 9.85 0.365 0

ER6 18.17 18.71 -0.030 0

ER7 22.95 18.71 0.185 0

ER8 33.86 45.54 -0.345 0

ER9 47.21 45.54 0.035 0

ER10 65.22 89.59 -0.374 0

ER11 78.39 89.59 -0.143 0

ER12 137.34 121.26 0.117 0

ER13 141.33 121.26 0.142 0

ER14 183.97 121.26 0.341 0

Avg. Error 0.243 

a Error: (Predicted-Actual)/Actual

Table 8-22. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: NOx Emissions (mg/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 2.66 0 0

ER2 1.39 0 0

ER3 1.75 0 0

ER4 7.56 0 0

ER5 11.67 0 0

ER6 18.45 0 0

ER7 26.75 0 0

ER8 37.46 0 0

ER9 53.37 0 0

ER10 68.14 0 0

ER11 65.56 0 0

ER12 125.35 0 0

ER13 141.54 0 0

ER14 120.47 0 0

Avg. Error 

a Error: (Predicted-Actual)/Actual
203

Table 8-23. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: NOx Emissions (mg/sec)

for Engine Displacement < 3.5 Liters and Odometer Reading > 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 1.58 0 0

ER2 1.45 0 0

ER3 1.84 0 0

ER4 2.39 0 0

ER5 9.17 0 0

ER6 4.72 0 0

ER7 5.48 0 0

ER8 11.3 0 0

ER9 12.66 0 0

ER10 20.14 0 0

ER11 20.14 0 0

ER12 71.33 0 0

ER13 70.54 0 0

ER14 77.97 0 0

Avg. Error 

a Error: (Predicted-Actual)/Actual

Table 8-24. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints

Approach for Two Different Constraints Versus Actual Rates: NOx Emissions (mg/sec)

for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.

Mode Actual CONSTRAINT_ALLDATA Error a CONSTRAINT_NCHRP Error a

ER1 8.2 19.68 -1.400 19.68 -1.40

ER2 9.36 13.18 -0.408 13.18 -0.41

ER3 8.1 8.46 -0.044 8.46 -0.04

ER4 32.86 41.91 -0.275 41.91 -0.28

ER5 57.24 47.23 0.175 47.23 0.17

ER6 82.87 78.71 0.050 78.71 0.05

ER7 109.92 86.39 0.214 86.39 0.21

ER8 155.13 137.75 0.112 137.75 0.11

ER9 173.28 177.1 -0.022 177.1 -0.02

ER10 229.28 177.1 0.228 177.1 0.23

ER11 362.89 177.1 0.512 177.1 0.51

ER12 490.97 177.1 0.639 177.1 0.64

ER13 485 214.1 0.559 214.1 0.56

ER14 543.47 2172.47 -2.997 2172.47 -3.00

Avg. Error 0.545 0.55

a Error: (Predicted-Actual)/Actual
204

y = 0.9939x + 0.0154

R2 = 0.9881

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-9. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes Estimated

From NCHRP Data Using Strict Constraints Estimated From the Modeling Database: Engine

Displacement < 3.5 liter and Odometer Reading < 50,000 Miles.

y = 1.062x - 0.1424

R2 = 0.9954

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-10. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement < 3.5 liter and Odometer Reading < 50,000 Miles.
205

y = 0.8613x + 0.5484

R2 = 0.9629

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-11. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:

Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.

y = 1.0443x - 0.0958

R2 = 0.9892

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-12. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.
206

y = 1.2017x - 0.8651

R2 = 0.9648

0

5

10

15

20

25

0 5 10 15 20 25

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-13. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:

Engine Displacement < 3.5 liter and Odometer Reading > 50,000 Miles.

y = 0.9628x + 0.3257

R2 = 0.9737

0

5

10

15

20

25

0 5 10 15 20 25

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-14. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement < 3.5 liter and Odometer Reading > 50,000 Miles.
207

y = 1.1389x - 0.751

R2 = 0.9776

0

5

10

15

20

25

0 5 10 15 20 25

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-15. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:

Engine Displacement > 3.5 liter and Odometer Reading > 50,000 Miles.

y = 1.1389x - 0.751

R2 = 0.9776

0

5

10

15

20

25

0 5 10 15 20 25

Observed CO2 Emissions (g/sec)

Predicted CO2 Emissions (g/sec)

Figure 8-16. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement > 3.5 liter and Odometer Reading > 50,000 Miles.
208

y = 0.4202x + 5.4632

R2 = 0.6422

0

20

40

60

80

0 20 40 60 80

Observed HC Emissions (mg/sec)

Predicted HC Emissions (mg/sec)

Figure 8-17. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement < 3.5 liter and Odometer Reading < 50,000 Miles.

y = 0.415x + 8.4139

R2 = 0.621

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140

Observed HC Emissions (mg/sec)

Predicted HC Emissions (mg/sec)

Figure 8-18. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:

Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.
209

y = 0.4381x + 10.16

R2 = 0.6052

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Observed HC Emissions (mg/sec)

Predicted HC Emissions (mg/sec)

Figure 8-19. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.

y = 1.2275x + 2.7305

R2 = 0.96

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Observed HC Emissions (mg/sec)

Predicted HC Emissions (mg/sec)

Figure 8-20. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement < 3.5 liter and Odometer Reading > 50,000 Miles.
210

y = 1.2151x - 0.0221

R2 = 0.8317

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

Observed HC Emissions (mg/sec)

Predicted HC Emissions (mg/sec)

Figure 8-21. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:

Engine Displacement > 3.5 liter and Odometer Reading > 50,000 Miles.

y = 1.2151x - 0.0221

R2 = 0.8317

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

Observed HC Emissions (mg/sec)

Predicted HC Emissions (mg/sec)

Figure 8-22. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

Engine Displacement > 3.5 liter and Odometer Reading > 50,000 Miles.
211

the method failed in most cases for NOx and CO. A likely reason for the failure to obtain results

in many cases for the 56-bin approach is that the sample sizes for the stratified data sets are

smaller than for the case of the 14-mode approach in the previous section. An implication is that

it may be necessary to have a sufficient large data set in order to estimate modal emission rates

from aggregate data. It is also apparent that the strict constraint approach produces better results

when the bounds of the constraints are derived from data similar to that being analyzed.

8.4 Characterization of Uncertainty in Predicted Modal Emissions

The objective of this part of work is to characterize the distribution of errors in the predicted

modal emissions in order to identify whether biases in the modal estimates are statistically

significant. Because the results from the 56 bin approach were not satisfying, this work was

based upon the results obtained with the 14 VSP bin approach.

In order to characterize uncertainty in the predictions, the distribution of the error of each modal

prediction, based upon the difference between the actual value for each vehicle minus the

predicted value, was estimated. These distributions are summarized by presenting the mean,

standard deviation, 95 percent confidence interval on the mean, and skewness. The results are

presented for NOx, HC, CO, and CO2 in Tables 8-25 through 8-28, respectively. The

predictions are based upon the strict constraint method. The average observed and predicted rates

are given in Tables 8-5 through 8-8, respectively, for these same pollutants.

Table 8-25 summarizes the analysis of the distribution of prediction errors among all the vehicles

and cycles in the database for predictions of modal emissions for NOx emissions. The mean

prediction error is given for each VSP mode along with the standard deviation, lower and upper

limit for the 95 percent confidence interval on the mean, number of data points, and skewness

estimate. The average prediction error for each mode is slightly different than zero, indicating the

possibility that the modal predictions are biased. For example, for VSP mode 11, average

prediction error is -0.0008. However, 95 percent confidence interval on the mean includes zero,

which indicates that at a significance level of 0.05, the mean prediction error is not statistically

significantly different from zero. Furthermore, the average prediction error is not statistically

significantly different from zero for all VSP modes for NOx as well as for all other pollutants.

Thus, the results indicate that there are no statistically significant biases in the mean estimates of

the prediction error.

However, the range of the prediction error is substantial in many cases. For example, for NOx,

the standard deviation of the prediction error is 5.1 mg/sec for Mode 1, compared to an observed

emission rate of 4.5 mg/sec. Similarly, the standard deviation is 276 mg/sec versus an average

observed emission rate of 202 mg/sec for Mode 14. For NOx, HC, and CO, the standard

deviation of the prediction error is comparable to the average emission rate for each mode. In

contrast, the standard deviation of the prediction error for CO2 is approximately one third of the

mean observed emission rate for CO2. When the standard deviation of the prediction error is

large relative to the mean emission rate, the distribution of the prediction error tends to be

positively skewed. For example, the range of skewness of the prediction errors among the 14

VSP modes is 2.7 to 4.4 for NOx, 2.0 to 5.2 for HC, and 1.0 to 4.3 for CO. In contrast, the

distributions of the prediction errors for CO2 tend to have only slight skewness, ranging from a
212

Table 8-25. Summary of Analysis of Uncertainty in the Prediction Error for the NOx Modal

Emission Rates (mg/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based

Approach.

VSP bin Mean Std Dev N

Lower

Limit

(95%)

Upper

Limit

(95%) Skewness

1 0.0005 5.09 90 -1.05 1.05 2.77

2 -0.0017 5.71 90 -1.18 1.18 2.99

3 0.0043 4.73 90 -0.97 0.98 2.69

4 0.0027 18.64 90 -3.85 3.85 3.25

5 0.0013 28.68 90 -5.92 5.93 3.56

6 0.0019 37.30 90 -7.70 7.71 4.40

7 -0.0046 48.75 90 -10.08 10.07 4.38

8 -0.0017 65.79 90 -13.59 13.59 4.03

9 -0.0012 79.83 90 -16.49 16.49 3.76

10 -0.0018 104.07 90 -21.50 21.50 2.82

11 -0.0008 165.71 77 -37.01 37.01 2.66

12 0.0038 220.48 45 -64.42 64.42 2.72

13 -0.0054 215.91 41 -66.09 66.08 2.98

14 -0.0016 276.33 37 -89.04 89.04 2.74

Table 8-26. Summary of Analysis of Uncertainty in the Prediction Error for the HC Modal

Emission Rates (mg/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based

Approach.

VSP bin Mean

Std

Dev N

Lower

Limit

(95%)

Upper

Limit

(95%) Skewness

1 -0.00188 8.41 90 -1.740 1.736 4.45

2 -0.00173 5.03 90 -1.041 1.038 4.38

3 -0.00532 4.07 90 -0.847 0.837 4.54

4 0.00137 6.75 90 -1.394 1.396 4.23

5 -0.00490 10.49 90 -2.171 2.162 3.48

6 0.00329 10.98 90 -2.265 2.271 5.15

7 -0.00247 14.32 90 -2.961 2.956 4.90

8 0.00304 20.38 90 -4.207 4.213 4.10

9 0.00077 21.18 90 -4.375 4.376 3.67

10 0.00335 26.06 90 -5.381 5.388 3.62

11 -0.00135 41.84 77 -9.348 9.345 3.00

12 -0.00331 64.50 45 -18.84 18.84 2.38

13 0.00126 85.35 41 -26.12 26.12 2.03

14 -0.00448 123.3 37 -39.73 39.72 2.49
213

Table 8-27. Summary of Analysis of Uncertainty in the Prediction Error for the CO Modal

Emission Rates (mg/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based

Approach.

VSP

bin Mean Std Dev N

Lower

Limit

(95%)

Upper

Limit

(95%) Skewness

1 0.0028 233 90 -48.04 48.04 2.3

2 -0.0055 241 90 -49.88 49.87 2.5

3 0.0024 186 90 -38.49 38.50 3.4

4 0.0021 428 90 -88.51 88.52 2.1

5 0.0025 686 90 -141.8 141.8 4.0

6 0.0044 529 90 -109.3 109.3 3.4

7 -0.0005 747 90 -154.3 154.3 4.2

8 0.0042 1250 90 -258.2 258.2 3.7

9 0.0008 1472 90 -304.1 304.1 4.3

10 0.0031 1818 90 -375.5 375.5 4.1

11 0.0036 3324 78 -737.6 737.6 2.8

12 0.0021 190 45 -3859 3859 1.6

13 -0.0001 8622 41 -2639 2639 1.3

14 -0.0044 12297 37 -3962 3962 1.0

Table 8-28. Summary of Analysis of Uncertainty in the Prediction Error for the CO2 Modal

Emission Rates (g/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based

Approach.

VSP bin Mean

Std

Dev N

Lower

Limit

(95%)

Upper

Limit

(95%) Skewness

1 0.00336 0.34 90 -0.068 0.075 0.37

2 0.00340 0.45 90 -0.089 0.096 0.53

3 -0.00466 0.39 90 -0.086 0.076 0.37

4 -0.00046 0.80 90 -0.165 0.164 0.49

5 0.00007 0.89 90 -0.184 0.184 0.28

6 -0.00262 1.02 90 -0.213 0.207 0.17

7 0.00366 1.20 90 -0.245 0.253 0.24

8 -0.00207 1.39 90 -0.289 0.285 0.15

9 0.00160 1.65 90 -0.340 0.343 0.10

10 -0.00313 1.94 90 -0.405 0.398 0.04

11 0.00202 2.49 77 -0.553 0.557 -0.11

12 -0.00189 2.67 45 -0.782 0.779 0.45

13 -0.00017 2.98 41 -0.911 0.911 0.56

14 0.00237 3.25 37 -1.044 1.049 0.46

magnitude of 0.04 to 0.56 among the 14 modes. These results illustrate that the predictions for

CO2 are generally substantially better than those for the other three pollutants.
214

The range of uncertainty in the mean prediction error is typically a factor of approximately five

less than the standard deviation of the prediction error, because the 95 percent confidence

interval of the uncertainty in the mean is estimated based upon a factor of 1.96 multiplied by the

standard error of the mean, which in turn is estimated based upon the standard deviation of the

data divided by the square root of sample size. For a sample size of 90, which is typical of many

of the estimates, this amounts to a factor of 0.207 multiplier of the standard deviation to arrive at

the upper and lower ranges of the 95 percent confidence interval. Thus, the range of uncertainty

in the mean error is comparable in many cases to a range of approximately plus or minus 25 to

50 percent of the mean observed emission rate for NOx, HC, and CO, and approximately plus or

minus 7 percent of the mean observed emission rate for CO2. These ranges of uncertainty are

larger than the ranges of uncertainty estimated based upon the modeling database in Chapter 7.

Thus, it would be the case that incorporation of emissions estimates obtained from aggregate

data would entail additional uncertainty than estimates obtained from second-by-second data.

8.5 Summary and Conclusions

The key findings from this analysis include:

• The strict constraint method gave the best results.

• The least squares optimization method with strict constraints worked for all of the cases

for the four driving cycle approach (idle, deceleration, acceleration, and cruise) and for

the 14 mode VSP-based approach.

• The method worked for the VSP 56 mode approach for CO2 for all four vehicle strata, but

success was more limited with the other three pollutants.

• The failures to obtain solutions or to obtain sufficiently accurate solutions for HC, CO,

and NOx with the 56-bin approach may be attributable to small sample sizes.

• The analysis of uncertainty in modal predictions for the 14 Mode VSP-based approach

clearly illustrates that the quality of the predictions are substantially better for CO2 than

for the other pollutants.

• The standard deviation of prediction errors for a given mode for NOx, HC, and CO based

upon the 14-mode VSP approach is typically of the same order of magnitude as the

observed mean emission rate, implying that the distribution of prediction errors are

positively skewed.

• The standard deviation of prediction errors for a given mode for CO2 based upon the 14

mode VSP approach are approximately one third of the observed mean emission rate,

implying that the distribution of prediction errors are relatively symmetric.

• The range of uncertainty in modal estimates obtained from aggregate bag data are

substantially larger than those obtained from second-by-second data

The key recommendations from this work are that the constrained least squares optimization

method can be effective at estimating modal emission rates from aggregate data as long as there

is a sufficiently large sample size of data. The method worked well for the 14-mode VSP case

compared to the 4-mode NCSU case. Thus, the method appears capable of handling a relatively

large number of modes for a given data set. The predictions are generally much better for CO2

than for the other pollutants. Thus, this technique works well for CO2 even for cases in which

solutions could not be obtained for other pollutants. For future work, it may be worth exploring

other types of constraints than those addressed in this project. For example, the “strict
215

constraints” employed in this work allowed for considerable variability in the ratio of the

emission rate for a particular mode with respect to another mode. An even stricter constraint

would be to require that these ratios be defined for much narrower ranges or that some or all

combinations of ratios be point estimates. Of course, the more that constraints are imposed upon

the solution, the more critically dependent the solution becomes upon the accuracy of the

constraints themselves. If modal emission estimates are used in a modeling framework such as

moves, the uncertainty in those estimates must be incorporated as well, since the range of

uncertainty in modal emissions rates estimated from aggregate data will typically be much larger

than that when estimated from second-by-second data.

217

9 VALIDATION OF THE CONCEPTUAL MODEL

This report presents three validation studies in which a VSP-based binning approach was used to

estimate hot stabilized tailpipe emissions of CO2, CO, HC, and NOx. The VSP-based approach is

based upon 1 second data in mass per time emission factor units.

The first case study includes the data utilized for model development and is only a consistency

check in response to comments received by EPA from the FACA committee. The second

validation case study is based upon comparisons of the model with EPA dynamometer, EPA onboard, and NCHRP dynamometer data that were withheld from the modeling dataset. The third

validation case study is based upon an independent dataset from the California Air Resources

Board.

9.1 Validation Case Study 1

In this study, internal consistency of the modeling approach was evaluated by: (1) estimating

average modal emission rates for individual driving cycles using data only from the vehicles that

were tested on those cycles based upon data in the modeling database; and (2) making

predictions of average cycle emissions based upon the estimated modal emission rates. The

purpose of this comparison was to demonstrate that the modal emissions approach is internally

consistent in disaggregating and re-aggregating the emission estimates for a driving cycle. For

this purpose, three driving cycles and on-board data were selected for analysis. The three cycles

were: ART-EF; FTP; and US06. These cycles were selected because there were ten or more

vehicles tested on these cycles in the modeling database and these three cycles different ranges

of speeds, VSP, and emissions.

In Table 9-1, number of vehicles, number of trips and number of seconds of data associated with

each of the selected driving cycles are reported. Validation Dataset 1 includes more than 100

vehicles and 169,112 seconds of data. Key characteristics of the cycles utilized for Validation

Dataset 1 are given in Table 9-2, including average speed, maximum speed, minimum speed,

maximum acceleration, average VSP, and Maximum VSP. For the on-board data, for which

there was not a standard cycle, these statistics were calculated based upon all of the available

data for all vehicles and trips. The average speeds for the cycles vary between 12 mph and 47

mph, with the lowest average speed associated with the ART-EF cycle and the highest average

speed associated with the US06 cycle. The average maximum acceleration among all the cycles

is approximately 6 mph/sec. Except for the FTP, all of the cycles have a maximum acceleration

greater than 6 mph/sec. Two cycles, ART-EF and FTP, have an average VSP less than 5

Kw/ton, and two cycles, ART-EF and FTP, have maximum VSP less than 50 Kw/ton.

The predicted vehicle average total emissions and the observed vehicle average total emissions

for the three driving cycles and for the on-board measurements are shown graphically in Figure

9-1. The 95 percent confidence intervals for the means are also shown. Comparisons between

predicted and observed average total vehicle emissions are given in Tables 9-3 through 9-6 for

CO2, CO, HC, and NOx, respectively. These tables present average observed values for each

cycle with 95 percent confidence intervals, average predicted values for each cycle with 95

percent confidence intervals.
218

Table 9-1. Summary of Validation Dataset I

Vehicle Characteristics Cycle Number of vehicles Number of seconds

ART-EF 12 6024

FTP 24 32952

US06 22 13251 Engine Size < 3.5 liter

Odometer < 50,000 On-Board 7 36096

ART-EF 0 0

FTP 6 8238

US06 4 2436 Engine Size 	



Odometer < 50,000 On-Board 6 35603

ART-EF 0 0

FTP 15 20595

US06 11 6010 Engine Size < 3.5 liter

Odometer  On-Board 0 0

ART-EF 0 0

FTP 4 5492

US06 4 2425 Engine Size 	



Odometer  On-Board 0 0

Table 9-2. Key Characteristics of the Activity Pattern of the ART-EF, FTP75 and US06 Cycles

and of the On-Board Measurements Used in Validation Dataset I.

Cycle

Name

Time

(s)

Average

Speed

(mph)

Max

Speed

(mph)

Min

Speed

(mph)

Max

Acceleration

(mph/sec)

Mean

VSP

(Kw/ton)

Max

VSP

(Kw/ton)

Art-EF 504 12 40 0 5.8 0.9 22.8

FTP75 1875 21 57 0 3.3 2.2 25.1

US06 622 47 81 0 7.4 8.3 54.5

On-Board 1525 33 83 0 7.4 4.6 78.3
219

0.1

1

10

100

1000

Art-EF FTP US06 On-Board

Average CO Emissions (g)

ObservedPredicted

1

10

100

1000

10000

100000

Art-EF FTP US06 On-Board

Average CO2 Emissions (g)

ObservedPredicted

0.001

0.01

0.1

1

10

100

Art-EF FTP US06 On-Board

Average HC Emissions (g)

ObservedPredicted

0.1

1

10

100

Art-EF FTP US06 On-Board

Average NOx Emissions (g)

ObservedPredicted

Figure 9-1. Comparison of Observed and Predicted Average Total Emissions of CO2, CO, HC, and NOx for Three Driving Cycles

and for On-Board Data for Validation Dataset I.

221

Table 9-3. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset I for CO2

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

ART-EF 926 800 - 1000 926 900 – 950 0 Y

FTP75 2740 2500 - 2900 2740 2600 – 2900 0 Y

US06 2790 2600 - 3000 2790 2600 - 2900 0 Y

On-Board 16800 11200 - 22000 16800 12000 - 21000 0 Y a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-4. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset I for CO

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

ART-EF 0.49 0.30 - 0.80 0.49 0.47 – 0.51 0 Y

FTP75 11 0.29 - 21 11 9.4 – 12 0 Y

US06 78 60 – 96 78 72 – 84 0 Y

On-Board 120 60 - 170 120 77 - 150 0 Y a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-5. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset I for HC

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

ART-EF 0.033 0.006 - 0.060 0.033 0.032 - 0.035 0 Y

FTP75 0.4 0.13 - 0.67 0.4 0.35 – 0.44 0 Y

US06 0.83 0.55 - 1.1 0.83 0.66 - 1.0 0 Y

On-Board 11 6.4 - 15 11 8.0 – 14 0 Y a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-6. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset I for NOX

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

ART-EF 0.24 0.11 - 0.36 0.24 0.22 - 0.25 0 Y

FTP75 1.4 0.90 – 2.0 1.4 1.1 – 1.7 0 Y

US06 2.6 1.7 - 3.6 2.6 2.2 - 3.0 0 Y

On-Board 21 11 - 31 21 15 - 27 0 Y a

 Diff: ((Predicted-Observed)/Observed)*100
222

The percentage difference in predicted and observed values is presented in Tables 9-3 through 9-

6. An indication is given as to whether the confidence intervals for the predicted and observed

means overlap.

The average total emissions predictions from the model are exactly the same as the observed

values for all the cycles and for the on-board data: in all cases the percentage difference between

the mean prediction and the mean observation is zero percent, and the confidence intervals for

the predicted and observed means overlap. The three cycles and the on-board data differ

substantially in terms of total average emissions. For example, the observed values for CO range

between 0.5 grams to 115 grams when comparing the ART-EF cycle and the on-board data,

respectively. Thus, the performance of the modeling approach is robust over a wide range of

different emissions estimates.

The main findings from Validation Case Study 1 are:

- Percent difference in the predicted versus observed values are all zero

- There was excellent agreement between the predicted and observed CO2, CO, HC, and NOx

emissions over a wide range of emissions

- The methodology for disaggregating driving cycle or trip emissions into driving modes, and

re-aggregating the average modal emissions to make estimates of driving cycle or trip

emissions, is demonstrated to be internally consistent, as is expected.

9.2 Validation Case Study 2

For Validation Case Study 2, model predictions were prepared based upon average modal

emission rates calibrated to the modeling data set for all vehicles, all driving cycles, and all onboard data. Model predictions were made for an independent data set of emissions for vehicles

that were not included in the modeling data set. The independent data set, referred to as

Validation Data Set 2, is summarized in Table 9-7. This data set is comprised of 81,808 seconds

of data from EPA dynamometer, EPA on-board measurement, and NCHRP dynamometer data.

The number of vehicles, number of trips and number of seconds of data associated with each

driving cycle are reported in the table. Validation Data Set 2 includes 78 vehicles, 83 trips, and

16 different cycles, including the on-board data as a lumped category. It should be noted that the

number of vehicles tested on some cycles is very small. Specifically, except for the FTP75 and

US06 cycles, three or fewer vehicles were tested. For validation purposes, comparisons were

made only for FTP75, US06 cycles, and On-Board data for which many vehicles and/or many

seconds of data were available. Key characteristics of the cycles utilized for the Validation

Dataset II are given in Table 9-2. Key characteristics of vehicles in this dataset are shown in

Appendix A.

The predicted and observed average total emissions for specific cycles, and the 95 percent

confidence intervals on the averages, are shown in Figure 9-2 for total emissions of CO2, CO,

HC, and NOx. The comparisons are summarized in Tables 9-8 through 9-11 for CO2, CO, HC,

and NOx emissions, respectively.
223

Table 9-7. Summary of Driving Cycles, Number of Vehicles, Number of Trips, and Samples

Size for Validation Dataset II

Data Source

Cycle

NO. of

Vehicles No. of Trips Total Seconds

EPA Dynamometer ART-AB 2 2 1471

EPA Dynamometer ART-CD 2 2 1255

EPA Dynamometer ART-EF 3 3 1507

EPA Dynamometer FWY-AC 2 2 1029

EPA Dynamometer FWY-D 2 2 809

EPA Dynamometer FWY-E 2 2 909

EPA Dynamometer FWY-F 3 3 1321

EPA Dynamometer FWY-G 2 2 777

EPA Dynamometer FWY-HI 3 3 1825

EPA Dynamometer LOCAL 2 2 1047

EPA Dynamometer NONFWY 2 2 2693

EPA Dynamometer NYCC 3 3 1795

EPA Dynamometer Ramp 2 2 529

NCHRP FTP75 24 24 32950

NCHRP US06 21 21 12648

On-Board Data On-Board 3 18 19243
224

1

10

100

1000

10000

100000

FTP75 US06 On-Board

 (g verage CO2 EmissionsA

ObservedPredicted

0.1

1

10

100

1000

FTP75 US06 On-Board

 (g verage CO EmissionsA

ObservedPredicted

0.1

1

10

100

FTP75 US06 On-Board

 (g verage HC EmissionsA

ObservedPredicted

1

10

100

FTP75 US06 On-Board

 (g verage NOx EmissionsA

ObservedPredicted

Figure 9-2. Comparison of Observed and Predicted Average Total Emissions of CO2, CO, HC, and NOx for the FTP75 and US06

Driving Cycles and for On-Board Measurements for Validation Dataset II.
225

 Table 9-8. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset II for CO2

a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-9. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset II for CO

a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-10. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset II for HC

a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-11. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset II for NOX

a

 Diff: ((Predicted-Observed)/Observed)*100

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

FTP75 2563 2480 - 2645 3195 3164 - 3227 25 N

US06 2596 2505 - 2686 2491 2440 - 2542 -4 Y

On-Board 17775 14367 - 21184 19612 16083 - 23142 10 Y

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

FTP75 10.6 8.3 - 13.0 17.4 16.7 - 18.0 64 N

US06 75.1 67.7 - 82.5 34.9 32.2 - 37.5 -54 N

On-Board 328.4 161.0 - 495.8 199.8 162.7 - 236.9 -39 Y

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

FTP75 0.69 0.49 - 0.89 1.26 1.20 - 1.32 83 N

US06 0.93 0.80 - 1.06 1.08 1.02 - 1.13 16 Y

On-Board 13.17 7.49 - 18.85 9.40 7.02 - 11.78 -29 Y

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

FTP75 2.06 1.61 - 2.51 2.33 2.24 - 2.42 13 Y

US06 2.53 2.09 - 2.97 2.93 2.78 - 3.07 16 Y

On-Board 16.60 11.57 - 21.62 21.05 16.46 - 25.65 27 Y
226

As observed in Figure 9-2, the predicted average total CO2 emissions are close to the observed

average total CO2 emissions, especially for the US06 cycle and the on-board data. In these latter

two cases, the confidence intervals of the predicted and observed means overlap. The predicted

average CO2 emissions are within 25 percent of the observed average values for the FTP75

cycle.

For CO, the qualitative trends of the model predictions are similar to that of the observed data, as

illustrated in Figure 9-2. For example, the on-board data had the highest observed total

emissions and also had the highest predicted total emissions. Both the observed and predicted

emissions decreased when comparing the FTP75 driving cycle to the US06 driving cycle.

Except for the FTP75 cycle, the model underpredicted the observed emissions. The

underprediction is suggestive of a different vehicle mix in Validation Data Set 2 versus the

modeling data set. Validation Data Set 2 contains a larger proportion of smaller engine sizes and

higher mileage than does the modeling data set. Nonetheless, the model predictions were not

statistically significantly different from the observed values for the on-board data, and were

comparable in magnitude to the data from the two driving cycles.

Qualitatively, the model predictions perform well compared to the observations for HC

emissions. Similar to the situation for CO emissions, the model appropriately predicts the

highest emissions for the on-board data, which have the highest observed emissions. The US06

and FTP75 cycles are predicted to have moderate emissions, comparable in magnitude to the

observed values. Furthermore, the predictions of the model were not statistically significantly

different from the observed emissions for the US06 driving cycle and for the on-board data.

For NOx, the model performed well for all three of the comparisons. In particular, the

confidence intervals of the model predictions overlapped with the confidence interval of the

observed emissions. Thus, the model predictions were not statistically significantly different

than the observed values. Therefore, the average error in the model prediction ranging from 13

to 27 percent among the three comparisons are not considered significant and are within the

random error of the data.

The overall findings of this case study are:

- There is good concordance in the model predictions versus the observations in terms of the

ordinal ranking of which cycles have the highest and lowest emissions.

- The predictions for CO, HC, and NOx tend to be better when the prediction for CO2 is also

reasonably close. For example, the predictions for all three pollutants were very good for the

on-board data, and the predictions of two of the three pollutants were very good for the US06

cycle. The CO2 predictions were generally very good for these three data sets. In contrast,

somewhat surprisingly, the predictions were generally not as good as expected for the FTP75

cycle, for which the CO2 average prediction was also different from the average observed

value by 25 percent.

- A comparison of CO2 predicted and observed values may be a good diagnostic tool for

identifying systematic differences between data sets. It appears that the Validation Data Set

2 is more heavily weighted toward vehicles with smaller engines compared to the calibration

data set.
227

- The systematic differences observed here for CO2 suggest that additional refinement may be

warranted for the engine displacement criteria when binning data. For example, rather than

grouping all engine displacements of less than 3.5 liters into a bin for a given VSP, it may be

appropriate to further subdivide this bin into two or more subcategories.

9.3 Validation Case Study 3

Validation Dataset III includes California Air Resources Board (CARB) data provided by the

EPA. This dataset includes data from the following cycles: UCC17; UCC20; UCC25; UCC30;

UCC35; UCC40; UCC45; OLD UCC50; UCC50; Modified Unified Cycle (MUC); and UCC60.

The data provided by EPA did not include second-by-second speed profiles for each test.

However, nominal speed profiles for these cycles were provided. The nominal speed profiles

were used to determine the fraction of time that the vehicle was in each VSP mode. Table 9-12

summarizes Validation Dataset III. A total of 17 vehicles were tested, over 164 tests, on 11

different cycles. However, the number of vehicles tested on some cycles was small. For example,

four or fewer vehicles were tested on the MUC, UCC50, and UCC60 cycles. For comparison

purposes, only cycles for which 10 or more vehicles were tested were utilized in this study.

Key characteristics of the cycles utilized for Validation Dataset III are given in Table 9-13.

Average speeds for the cycles ranges between 13 mph and 53 mph. The lowest average speed

occurred for the UCC17 cycle and the highest average speed occurred for the UCC60 cycle. The

lowest maximum speed of 37 mph occurred for the UCC17 cycle and the highest maximum

speed of 81 mph occurred for the UCC60 cycle. Except for the Old UCC50 and UCC50 cycles,

all cycles have a maximum acceleration of less than 7 mph/sec. Seven of the 11 cycles have an

average VSP of less than 5 Kw/ton. The UCC35, Old UCC50, and UCC60 cycles have a

maximum VSP greater than 50 Kw/ton.

Since engine displacement data were not available for Validation Data Set III, it was assumed

that all vehicles in this dataset have engine displacement less than 3.5 liters based upon

discussion with EPA.

The average predicted and observed emissions, along with 95 percent confidence intervals are

shown in Figure 9-3 for all four pollutants. The comparisons are detailed in Tables 9-14 through

9-17 for CO2, CO, HC, and NOx emissions, respectively. The predictions were made using the

average modal emission rates estimated from the modeling database.

For CO2, the average model predictions are close to the average observed values as indicated by

the fact that for six of the eight cycles for which comparisons were done, the means agreed to

within 10 percent. Furthermore, for seven of the cycles, the confidence intervals of the

predictions overlapped with the confidence intervals of the observations, and for all cycles the

mean predictions were within 15 percent. These findings imply strong agreement between the

model predictions and the observations. The model average predictions vary among the driving

cycles by a factor of approximately 8 for the largest to the smallest prediction compared to a

factor of approximately 10 for the average observations. The model appears to slightly

overpredict for the lower emissions cycles.
228

Table 9-12. Summary of Driving Cycles, Number of Vehicles, Number of Tests, and Sample

Size for Validation Dataset III

Data Source

Cycle

No. of

Vehicles No. of Tests Total Seconds

ARB data UCC17 17 17 7174

ARB data UCC20 17 17 15048

ARB data UCC25 17 17 15372

ARB data UCC30 17 17 17712

ARB data UCC35 17 17 24318

ARB data UCC40 17 17 24012

ARB data UCC45 17 17 23472

ARB data OLD UCC50 15 15 34663

ARB data MUC* 4 20 46760

ARB data UCC50 2 4 8768

ARB data UCC60 2 4 11240

* MUC: Modified Unified Cycle

Table 9-13. Key Characteristics of the Activity Patterns of the Driving Cycles in Validation

Dataset III.

Cycle ID

Time

(s)

Average

Speed

(mph)

Max

Speed

(mph)

Min

Speed

(mph)

Max

Acceleration

(mph/sec)

Mean

VSP

(Kw/ton)

Max

VSP

(Kw/ton)

UCC17 422 13 37 0 4.6 1.4 22.3

UCC20 836 18 44 0 5.7 1.9 25.6

UCC25 854 23 50 0 5.9 2.5 23.1

UCC30 984 27 59 0 5.5 3.1 35.8

UCC35 1351 32 69 0 5.6 4.1 68.2

UCC40 1334 36 72 0 5.5 5.1 48.9

UCC45 1304 45 71 0 5.7 6.5 43.3

OLD

UCC50 2039 48 76 0 8.1 7.8 86.5

MUC* 2338 17 67 0 6.9 2.1 35.1

UCC50 2192 43 72 0 7.5 6.3 28.1

UCC60 2810 53 81 0 6.4 9.2 57.2

* MUC: Modified Unified Cycle
229

Figure 9-3. Comparison of Observed and Predicted Average Total Emissions of CO2, CO, HC, and NOx for Eight UCC Driving

Cycles for Validation Dataset III.

0.1

1

1 0

100

UCC17 UCC20 UCC28 UCC30 UCC35 UCC40 UCC45 Old UCC50

CO Emissions (g)

ObservedPredicted

1

1 0

100

1000

10000

UCC17 UCC20 UCC28 UCC30 UCC35 UCC40 UCC45 Old UCC50

CO2 Emissions (g)

ObservedPredicted

0.01

0.1

1

1 0

UCC17 UCC20 UCC28 UCC30 UCC35 UCC40 UCC45 Old UCC50

HC Emissions (g)

ObservedPredicted

0.1

1

1 0

100

UCC17 UCC20 UCC28 UCC30 UCC35 UCC40 UCC45 Old UCC50

NO Emissions (g)

ObservedPredicted
230

Table 9-14. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset III for CO2

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

UCC17 800 722 - 879 915 902 - 929 14 N

UCC20 1787 1632 - 1941 1975 1941 - 2008 11 Y

UCC25 2050 1888 - 2211 2196 2155 - 2237 7 Y

UCC30 2407 2220 - 2594 2617 2568 - 2666 9 Y

UCC35 3690 3416 - 3963 3849 3771 - 3926 4 Y

UCC40 4078 3799 - 4356 4084 3998 - 4171 0 Y

UCC45 4586 4257 - 4916 4439 4338 - 4540 -3 Y

OLD

UCC50 7856 7235 - 8477 7252 7070 - 7435 -8 Y a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-15. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset III for CO

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

UCC17 2.9 0.8 – 4.9 4.3 3.9 - 4.7 48 Y

UCC20 8.6 3.9 – 13.4 9.8 9.0 - 10.6 14 Y

UCC25 8.3 4.4 – 12.2 11.6 10.7 - 12.6 40 Y

UCC30 12.8 7.6 – 18.0 15.5 14.4 - 16.6 21 Y

UCC35 24.3 11.9 – 36.8 25.1 23.6 - 26.5 3 Y

UCC40 31.2 18.1 – 44.4 29.0 27.4 - 30.5 -7 Y

UCC45 29.5 16.9 – 42.1 34.4 32.9 - 35.9 17 Y

OLD

UCC50 47.7 22.4 – 73.1 54.8 52.2 - 57.4 15 Y a

 Diff: ((Predicted-Observed)/Observed)*100
231

Table 9-16. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset III for HC

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

UCC17 0.08 0.04 - 0.12 0.29 0.23 - 0.36 263 N

UCC20 0.20 0.12 - 0.29 0.62 0.48 - 0.76 210 N

UCC25 0.24 0.16 - 0.31 0.68 0.53 - 0.83 183 N

UCC30 0.34 0.24 - 0.44 0.81 0.63 - 0.99 138 N

UCC35 0.56 0.36 - 0.76 1.20 0.94 - 1.46 114 N

UCC40 0.67 0.45 - 0.89 1.28 1.01 - 1.56 91 N

UCC45 0.71 0.49 - 0.93 1.40 1.10 - 1.69 97 N

OLD

UCC50 1.19 0.74 - 1.63 2.21 1.71 - 2.71 86 N a

 Diff: ((Predicted-Observed)/Observed)*100

Table 9-17. Summary of Comparisons of Predicted versus Observed Vehicle Average Total

Emissions for Validation Dataset III for NOX

Cycles

Mean

Obs.

(g)

95 %

CI

Mean

Pred.

(g)

95 %

CI

Diff. a

(%)

CIs

Overlap

UCC17 0.65 0.29 - 1.00 0.59 0.53 - 0.65 -9 Y

UCC20 1.25 0.54 - 1.96 1.36 1.22 - 1.50 9 Y

UCC25 1.57 0.70 - 2.44 1.62 1.45 - 1.79 3 Y

UCC30 1.98 0.86 - 3.11 2.00 1.79 - 2.21 1 Y

UCC35 3.34 1.22 - 5.46 3.09 2.76 - 3.42 -7 Y

UCC40 4.67 1.34 - 8.00 3.46 3.10 - 3.82 -26 Y

UCC45 4.47 1.64 - 7.30 3.99 3.56 - 4.42 -11 Y

OLD

UCC50 9.41 6.7 - 16 6.54 5.79 - 7.29 -30 Y a

 Diff: ((Predicted-Observed)/Observed)*100
232

For CO and NOx, the confidence intervals overlap for all eight of the driving cycles when

comparing predicted and observed averages. This suggests strong agreement between the model

and the observations for all of the cycles evaluated. The CO predictions typically are larger than

the observed values and the prediction errors are as large as approximately 40 percent for the

lower emission cycles and not larger than approximately 20 percent for the higher emission

cycles. The observed CO emissions vary by a factor of 16 from the smallest to the largest

values, and the predicted CO emissions vary similarly by a factor of 13. For NOx, the prediction

errors were less than plus or minus 10 percent for five of the eight cycles, and were less than or

equal to plus or minus 30 percent for all cycles. The observed NOx emissions varied by a factor

of 15 from the smallest to the highest values, while the predictions varied similarly by a factor of

11.

For HC, the predictions were typically a factor of two to three larger than the observed values.

However, the qualitative trend of the predictions was similar to the observed values when

comparing cycles in terms of rank ordering with respect to emissions. For example, the model

predicted the lowest emission rate for the UCC17 cycle and the highest emission rate for the Old

UCC50 cycle, which is consistent with the observations.

There is some uncertainty regarding the regulations to which some of the vehicles in the CARB

data set are subject. It is possible that some of the vehicles may be TLEV, rather than Tier 1,

vehicles, although specific information regarding this was not available with the data set. TLEV

vehicles are subject to a more stringent HC emission standard but are otherwise the same as Tier

1 vehicles. The comparison suggests that the CARB vehicles have similar CO2, CO, and NOx

emissions but lower HC emissions when compared to the predictions made based upon modal

emissions rates estimated from the modeling data set. An analysis was done for two subsets of

the CARB database: (1) vehicles believed to be subject to Tier 1 standards; and (2) vehicles

believed to be subject to TLEV standards. It turned out that these two subgroups of vehicles did

not have any statistically significant difference in emissions with each other taking into account

all four pollutants and all eight driving cycles. Thus, to the extent that TLEV vehicles may be

present in the CARB database, the specific sample of TLEVs would not appear to have different

average emissions than the specific sample of Tier 1 vehicles. It is possible, therefore, that the

predicted and observed HC emissions may differ for reasons other than emission standards, such

as perhaps because of different fuels. There was also uncertainty as to whether the HC emissions

reported in the CARB database were for total hydrocarbons or for non-methane hydrocarbons

(NMHC). The data were used assuming that they represented total hydrocarbons. However, if

the HC data were actually for NMHC, then it would be necessary to add the estimated methane

emissions in order to calculate the total observed hydrocarbons, in which case the comparison

would improve. Confirmation on this point could not be obtained during the time period of this

study.

The main findings from Validation Case Study 3 are:

- There was excellent agreement between the predicted and observed CO2, CO, and NOx

emissions.

- There appears to be excellent concordance between the predicted and observed HC

emissions.
233

9.4 Preliminary Exploration of Refinements to the Modal Modeling Approach

Validation Case Study II indicated that there was some disagreement between the model

predictions and the observed values particularly for the FTP75 cycle. It was observed that the

validation data set tended to have vehicles with smaller engines than did the modeling dataset.

Therefore, a refinement to the modal modeling approach was explored in which the modeling

database was stratified into more engine displacement categories than was used in the “56-bin”

approach developed in Chapter 3. In addition, a second type of refinement was explored in

which an additional explanatory variable was sought for purposes of disaggregating each VSP

bin. Based upon an analysis of the sensitivity of the average emissions in a VSP bin to

acceleration and to average speed, as illustrated in Appendix A in Figure A-7, either of these two

variables was identified as potentially useful in further disaggregating the modeling database to

create additional bins. Speed was selected as the explanatory variable for further consideration

because speed is directly measured and because speed and acceleration are inversely related to

each other for most of the VSP bins, as illustrated by the scatter plots shown in Chapter 5 in

Figures 5-10 and 5-11. Thus, there is little need to include both speed and acceleration as

additional explanatory variables.

In the case of refinement of the modal modeling approach based upon additional engine

displacement categories, three levels of engine displacement were used, rather than two as in the

original VSP-approach. These levels are: engine displacement less than 2.0 liter; engine

displacement greater than 2.0 liters and less than 3.5 liters; and engine displacement greater than

3.5 liter. In this approach, there are totally 84 bins, (2 odometer reading categories, 3 engine

displacement categories, and 14 VSP modes). The average modal emission rates for this “84-

bin” approach are given in Appendix A in Figures A-5 and A-6 for vehicle with odometer

reading less than 50,000 miles and for vehicles with odometer reading greater than 50,000 miles,

respectively. Using these average modal rates, predictions were made and compared to the

observed values for Validation Dataset II. There was no significant improvement in the

predictions based upon the disaggregating of engine displacement into three instead of two

categories.

In the case of refinement of the modal modeling approach based upon speed, two levels of speed

were defined for each VSP mode based upon a selected cut point of 32 mph. The average

emission rates for each VSP mode for the low and high speed bins are shown in Appendix A in

Figures A-8 through A-11 for vehicles with the following characteristics, respectively: (1)

engine displacement less than 3.5 liters and odometer reading less than 50,000 miles; (2) engine

displacement greater than 3.5 liters and odometer reading less than 50,000 miles; (3) engine

displacement less than 3.5 liters and odometer reading greater than 50,000 miles; and (4) engine

displacement greater than 3.5 liters and odometer reading greater than 50,000 miles. For the

higher speed bins, the average emission rates tend to be higher in many cases, such as for CO2

emissions for the lower VSP modes, for CO for most modes, for HC especially for the lowest

VSP modes, and for NOx for low to moderate VSP modes. The comparison of the average

modal emission rates for the two speed bins for a given VSP mode suggests that there are

opportunities to refine the estimation of emission rates by considering speed as an additional

explanatory variable. A trade-off is that the sample size of each bin becomes smaller, leading to

wider confidence intervals in some cases. When the speed disaggregated VSP modes were used

to make predictions of cycle emissions for Validation Case Study 2, there was not a significant
234

improvement in the prediction of total emissions compared to the predictions from the “56-bin”

approach. Thus, it may be the case that additional levels of detail at the micro scale may not lead

to substantial improvements in predictions at the macro scale. However, it is likely that

disaggregation of VSP bins by speed will lead to more accurate predictions at the micro- or

mesoscale.

Of the two refinements to the modal modeling approach explored here, the refinement based

upon speed appears to offer promise for improving the accuracy of microscale or mesoscale

predictions, even though it may not help substantially in improving macroscale predictions, at

least for the conditions evaluated in this study.

9.5 Summary and Recommendations

The main findings from all three verification and validation case studies are:

- The modal modeling approach is internally consistent, as demonstrated by Validation Case

Study I. Specifically, it is possible to reproduce total trip emissions based upon proper

estimating and combination of average emissions for individual modes.

- The model generally performs well for the higher emission cycles and for cycles or

conditions that are represented by a large portion of the data in the modeling data set.

- The model is highly responsive, predicting a wide range of variability in average emissions.

- Although the model tends to ove-rpredict for low emissions cycles, such cycles may be less

important from an inventory perspective than the high emissions cycles for which the model

performs better.

- The model performance for the low emissions cycles could be improved by working with

modeling datasets that have a larger representation of such cycles, or perhaps by refining the

modal definitions to better represent such cycles.

- A promising approach for refining the modal modeling method is to consider speed as an

additional explanatory variable.

- Comparisons of CO2 emissions appear to be a good method for determine the comparability

of two datasets: in the case of the ARB data sets, there was excellent agreement for CO2 and

this extended to the other pollutants. For Validation Data Set 2, there were systematic

differences in CO2 for one of the driving cycles for which comparisons were done that

appeared to extend to at least some of the other pollutants (e.g., CO, HC).

Overall, the results of the case studies illustrate the flexibility and robustness of a modal-based

approach for making predictions for a wide variety of driving cycles and for on-board data.
235

10 RECOMMENDATIONS FOR METHODOLOGY FOR MODAL MODEL

DEVELOPMENT

This report has explored in detail a number of key issues pertaining to the methodology for

developing a modal emissions model. The main focus of the case studies have been with respect

to hot stabilized tailpipe emissions from Tier 1 vehicles. However, when taking in the context of

recent previous work by NCSU to develop approaches for estimating cold start emissions for

gasoline vehicles, as well as modal emission rates for heavy duty diesel vehicles, this report

combined with the previous efforts clearly demonstrates the feasibility of a modal modeling

approach.

The key questions that were addressed in this work were the following:

1. What dataset should be used for the final version of the conceptual model? (Task 1a,

Chapter 2)

2. Which binning approach should be used? (Task 1b, Chapter 3)

3. How much detail should be included in the binning approach, in terms of how many

explanatory variables and how many strata for each variable? (Task 1b, Chapter 3)

4. What averaging time is preferred as a basis for model development? (Task 1b, Chapter 4)

5. What emission factor units should be used? (Task 1b, Chapter 5)

6. What weighting approach should be used, when comparing time-weighted, vehicle

weighted, and trip weighted? (Task 1b, Chapter 6)

7. How should variability and uncertainty be characterized? (Task 1c, Chapter 7)

8. How should aggregate bag data be analyzed to derive estimates of modal emission rates?

(Task 1d, Chapter 8)

9. What is the potential role and feasibility of incorporating RSD data into the conceptual

modeling approach? (Task 1e, Chapter 5)

10. How should the conceptual model be validated and what are the results of validation

exercises? (Task 2, Chapter 9)

The answers to these questions are briefly summarized here, and are given in more detail in the

respective chapters devoted to each topic.

The data set used for the conceptual model was comprised of EPA dynamometer data, EPA onboard data, and NCHRP dynamometer data. These data comprised the modeling database. The

modeling database was compared to several other databases, including an IM240 database and an

RSD database.
236

The binning approach selected was a 14 mode VSP-based approach. However, it was shown that

an approach based upon driving modes of idle, acceleration, cruise, and deceleration produced

comparable predictions for total emissions. Thus, the 14 mode VSP-based approach is not

unique in its capability to predict emissions, but it is expected to facilitate design of a modeling

system perhaps moreso than the other approach.

There is a trade-off between improving the explanatory power of a model and having a model

that becomes complicated to code or use. Odometer reading and engine displacement were

identified as key explanatory variables. Engine displacement is highly correlated with vehicle

net weight and with the number of cylinders of the engine. Therefore, it is not necessary to

include net vehicle weight or number of cylinders if engine displacement is selected as an

explanatory variable. Odometer reading is weakly correlated with model year. This suggests

that there might be a role for model year in future model development. Because this study

focused upon Tier 1 vehicles, with much of the data spanning only a very limited range of model

years, it is possible that the influence of model year is understated with respect to this analysis

and that it may be more important for other types of vehicles. Ambient parameters such as

humidity were accounted for in correcting NOx emissions. Ambient temperature was not found

to be a significant explanatory variable. On the other hand, as discussed in Chapter 9, there may

be an opportunity to improve the explanatory power of the 14 mode VSP-based approach by

including either speed or acceleration as a criteria for further disaggregating the bins.

The method for selecting the specific definitions of the 14 VSP bins took into account that each

pollutant has a different sensitivity to VSP. Thus, a “supervised” technique was used in which

the contribution of any individual mode to total emissions for a given pollutant was considered

as a key criteria. This approach produced one set of modal definitions that worked well for all

four pollutants.

An approach based upon “56 bins” for which the 14 VSP modes were stratified into two

odometer reading categories and two engine displacement categories performed reasonably well

when predictions were compared to observations for independent data sets, as reported in

Chapter 9. The validation case studies thus emphasize that the modal emissions approach is

feasible. A key benefit of the conceptual modeling approach is that it works for all four

pollutants considered, and it is not necessary to develop a separate approach for each pollutant.

Three averaging times were compared with respect to ability to make predictions of trip

emissions. No substantial difference was found. Thus, for simplicity, the one second averaging

time was recommended for model development and was employed in this work. However,

although the issue of averaging time may not have a significant effect on prediction of average

emissions, there is a significant effect on the prediction of uncertainty in average emissions. As

noted in Chapter 7, the range of uncertainty in the average modal emission rates is a function of

averaging times, and the uncertainty estimates should be adjusted appropriately when making

predictions of uncertainty.

Three weighting approaches were compared, including time, trip, and vehicle weighted

approaches. It is clear that the average emission estimates will differ depending on which

approach is used, because each approach gives a different amount of weight to different
237

subgroups of the data. For example, the time weighted approach gives equal weight to each data

point. The trip weighted approach gives each trip (or driving cycle test) equal weight, even

though trip lengths may differ and even though some vehicles may be represented by many trips

and others may be represented by only one. The vehicle weighted approach gives each vehicle

equal weight regardless of the total testing time or number of trips (or tests). When comparing

time, trip, and vehicle weighted approaches, the standard deviation of the variability in emissions

decreases in the same order because each successive approach involves more averaging.

However, the averaging time is not standardized for the trip and vehicle weighted approaches.

Because averaging time is important to accurate estimation of uncertainty, preference was given

in this work to the time weighted approach.

With regard to emission factor units, there was no clear overall advantage for emission ratios

versus mass per time emission factors for CO, HC, and NOx. Although it is the case that there is

less variability in the averages among many of the modes for CO and HC for emission ratios

when compared to mass per time emission rates, for NOx there is substantial variability across all

modes regardless of the units used. For software design purposes, it is simpler to use the same

approach for all pollutants. Thus, an emission ratio approach would require a similar number of

modes as the mass per time approach. In this regard, there was no clear advantage.

Additionally, it is necessary to estimate mass per time emissions of CO2, or to estimate mass per

time fuel consumption, in order to convert emission ratios for CO, HC, and NOx to mass

emission rates as would be required for an emission inventory model. Although an emission

ratio approach offers some benefits of simplicity when applied to an areawide macroscale

emission inventory based upon information such as fuel sales, an emission ratio approach

nonetheless would require modal estimates of CO2 emissions or fuel use when applied to

mesoscale emission inventories. Thus, for consistency in the modeling approach, the preferred

strategy was to use mass per time emission rates for all pollutants and to apply the same modal

emissions approach for all pollutants.

Considerable attention was devoted in this work to methods for characterizing variability in

emission rates for individual modes, uncertainty in average emissions for individual modes, and

uncertainty in total emissions estimated based upon weighted combinations of modes. The

recommendations regarding these issues are given in more detail in Chapter 7. In brief, the

feasibility of representing variability in modal emission rates with parametric distributions was

demonstrated. In some cases, single component parametric distributions cannot provide a good

fit, but in such cases a two component mixture of lognormal distributions provided an excellent

fit. The Method of Matching Moments is recommended as a preferred parameter estimation

method if the objective is to have the mean and standard deviation of the fitted distributions

match those of the data. For mixture distributions, MoMM is not considered a feasible

parameter estimation method and Maximum Likelihood Estimation is recommended. However,

the differences in results between MoMM and MLE become smaller as the goodness-of-fit

improves. Thus, a well fitting mixture distribution will typically have a mean and standard

deviation similar to that of the data.

The analysis of uncertainty need not be conditioned upon the assumptions made regarding the

characterization of variability based upon parametric distributions. For example, uncertainty in

the mean can be estimated directly based upon the data using analytical or numerical methods. It
238

is recommended that the sample size and the relative standard error of the mean of each bin

quantified. If the sample size is less than 40 and/or if the relative standard error of the mean is

greater than 0.2, then bootstrap simulation is recommended as a technique for quantifying the

sampling distribution of the mean. In all other cases, a normality assumption will typically be

more than adequate. Parametric distributions can be fit to sampling distributions obtained from

bootstrap simulation. Thus, for all modes, it is possible to use parametric distributions to

represent uncertainty in the mean, which will facilitate software design and model applications.

Both numerical and analytical methods for propagating uncertainty through a model were

explored. Numerical methods such as Monte Carlo simulation or Latin Hypercube Sampling

offer the advantage of increased flexibility to accommodate many kinds of distributions and

models, including situations in which uncertainty is quantified not only for modal emission rates

but also for vehicle activity (e.g., percentage of time spent in different modes and trip duration).

In contrast, the analytical approach offers the advantage of less computational burden but is also

less flexible. An exact solution can be obtained for linear combinations of normal distributions,

such as when uncertainty in only modal emission rates is quantified and when all such

uncertainties are assumed to be normally distributed. Approximate analytical solutions can be

developed for other situations, such as when propagating uncertainty in both activity and

emission rates. If this latter approach is to be further considered, the approach should be

evaluated quantitatively in comparison to a Monte Carlo approach to make sure that it will

produce sufficiently accurate results. If a Monte Carlo approach is adopted, consideration should

be given to also including an analytical approach for use as a quality assurance tool.

The range of uncertainty in total emissions estimates was large enough in many cases to justify

the importance of performing an uncertainty analysis. For example, for HC and CO emissions

the range of uncertainty was as large as plus or minus 30 percent for selected vehicle groups and

for four different driving cycles.

With respect to the issue of how to estimate modal emission rates from aggregate dynamometer

data (for which no second-by-second data are available), the results were mixed. It is possible to

develop good modal emission estimates especially for CO2 as long as there is a sufficient sample

size and as long as sufficient constraints are specified in the least squares optimization approach.

However, the range of uncertainty in the predicted modal emission rates can be much larger than

the uncertainty in modal emission rates obtained from second by second data. The results imply

that it is important to develop good estimates of the constraints; however, when applied to

vehicle groups for which there are no or few comparable second-by-second data, such as for

older carbureted vehicles, it may be difficult to develop good estimates of what the constraints

should be. An alternative approach is to arbitrarily specify more stringent constraints, such as

defining ratios to be multiples of each other, in which case the estimation problem becomes

simpler but the answers obtained will be highly conditional upon such constraints.

The most critical issue in the modal modeling approach is to have a representative data set. This

issue cannot be sidestepped regardless of the modeling approach employed. A representative

data set should have proportional representation of vehicle emission rates and activity patterns

similar to that in the real world. The development of such a database is resource limited and

requires considerable judgment. In this particular work, the modeling database used for
239

development and demonstration of the modal emissions concept was compared to other

databases, including IM240 and remote sensing data. It appears to be the case that modeling

database produces lower emissions estimates for some modes and comparable emissions

estimates for others when compared to these other data sources. A possible reason for the

differences could be because of a different representation of high emitting versus normal

emitting vehicles. However, another reason that was explored is that the activity patterns of the

modeling database are generally different than those of the IM240 and RSD data. Thus, a key

question is not only whether the modeling database contains sufficient representation of high

emitting vehicles, but also whether the IM240 and RSD data contain adequate or appropriate

representation of real world activity patterns from which it is useful to make inferences regarding

emissions. The modeling database contained some high emitting vehicles, and it was apparent

that the upper range of emission rates for a given mode of the modeling database were typically

comparable to the upper range of emission rates from these other databases. Thus, the question

is not whether the modeling database represents high emitting vehicles and/or high emitting

episodes. Clearly, it does. The question is whether it contains a sufficient proportional

representation of such situations. The evidence to support an answer to this question is

inconclusive given the different nature of the activity patterns for the IM240 and RSD databases

compared to that of the modeling database, as well as the possibility of other potential

confounding factors, such as fuel effects. From a methodological perspective, the main

implication of these comparisons in terms of future model development is to make sure that the

modeling database for future work is more comprehensive in terms of sample size and coverage

of vehicles considered to be both normal and high emitters.

Three approaches were taking toward validation of the conceptual modeling approach. The first

was to perform a consistency check, which demonstrated that the modal emission approach can

be applied to a dataset to disaggregate emissions into modes, and that it is possible to reaggregate

the model emissions and reproduce the total trip emissions. The second was to compare model

predictions to observed values for a set of vehicles similar to but not identical to those used in the

modeling data base. The comparison demonstrated that differences in vehicle mix between the

modeling database and the validation database can lead to differences when comparing predicted

and observed emissions. However, for cases in which the model and the observed values agreed

well for CO2 emissions, they also tended to agree well for emissions of the other three pollutants.

In the future, it is worthwhile to perform similar validation studies by withholding data from the

modeling database for some of the trips made by a subset of vehicles, rather than to withhold

from the modeling database all data for a particular set of vehicles. Such an approach would

improve the likelihood that the vehicles in the validation data set are similar to those in the

modeling data set. The third validation case study involved prediction of emissions for an

independent set of vehicles based upon data provided by CARB. The comparison of predicted

and observed emissions was generally excellent for CO2, NOx, and CO for eight different driving

cycles. The model overpredicted for HC in all cases; however, it is possible that CARB may

have reported only nonmethane hydrocarbons instead of total hydrocarbons or that there was a

fuel effect. A potential distinction between Tier 1 and TLEV vehicles in the CARB database

was explored. However, no significant difference in emissions was found for vehicles that might

be TLEVs versus those that were Tier 1; therefore, it was not useful to report results separately

for these two possible categories.
240

A key criteria for comparison when performing validation studies is to evaluate the statistical

significance of differences between predicted and observed emissions. Emissions for individual

vehicles can vary by orders of magnitude even for the same driving cycle; therefore,

comparisons based upon a small number of vehicles will typically have wide confidence

intervals for the mean and will be less reliable than those based upon a larger set of vehicles.

Since the objective of an emission inventory model is to make accurate predictions for a fleet of

vehicles, it is important to have a quantitative understanding of the level of uncertainty

associated with mean predictions of the model, as has been demonstrated in this work.

In conclusion, this work has demonstrated the feasibility of an empirically-based method for

modal emissions model. The methods demonstrated in this work can and should be incorporated

or adapted for use in the development of MOVES and other emission estimation systems.
241

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244

12 APPENDIX A

Figure A-1. Relationship between Air Condition Use and Emissions
245

Figure A-2. Relationship between Relative Humidity and Emissions
246

Figure A-3. Relationship between Ambient Temperature and Emissions
247

0

0.90.80.70.60.50.40.30.20.1

1

0.000001 0.00001 0.0001 0.001 0.01 0.1

CO/CO2

y Cumulative Probabilit

 Modeling data Remote Sensing

0

0.90.80.70.60.50.40.30.20.1

1

0.000001 0.00001 0.0001 0.001 0.01 0.1

HC/CO2

y Cumulative Probabilit

 Modeling data Remote Sensing

0

0.90.80.70.60.50.40.30.20.1

11E-08 1E-07 0.000001 0.00001 0.0001 0.001 0.01 0.1

NO/CO2

y Cumulative Probabilit

 Modeling data Remote Sensing

Figure A-4. Comparison of Variability for Modeling Data and Remote Sensing Data for VSP Mode 7 with Engine Size Less Than 3.5

Liters and Model Year at 1996.
248

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) C Emissions (g/seH

Engine Displacement<=2 Liters2 Liters< Engine Displacement <3.5 LitersEngine Displacement >=3.5 Liters

0.1

1

10

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) O2 Emissions (g/seC

Engine Displacement<=2 Liters2 Liters < Engine Displacement < 3.5 Liters Engine Displacement >=3.5 Liters

0.001

0.01

0.1

1

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) O Emissions (g/seC

Engine Displacement <=2 Liters2 Liters< Engine Displacement < 3.5 LitersEngine Displacement >=3.5 Liters

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) Ox Emissions (g/seN

Engine Displacement <=2 Liters2 Liters< Engine Displacement <3.5 LitersEngine Displacement >=3.5 Liters

Figure A-5. Average Modal Emission Rates for Vehicles with Odometer Readings Less than 50,000 miles Based Upon VSP Bins
249

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) C Emissions (g/seH

Engine Displacement<=2 Liters2 Liters< Engine Displacement <3.5 LitersEngine Displacement >=3.5 Liters

0.1

1

10

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) O2 Emissions (g/seC

Engine Displacement<=2 Liters2 Liters < Engine Displacement < 3.5 Liters Engine Displacement >=3.5 Liters

0.001

0.01

0.1

1

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) O Emissions (g/seC

Engine Displacement <=2 Liters2 Liters< Engine Displacement < 3.5 LitersEngine Displacement >=3.5 Liters

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

c) Ox Emissions (g/seN

Engine Displacement <=2 Liters2 Liters< Engine Displacement <3.5 LitersEngine Displacement >=3.5 Liters

Figure A-6. Average Modal Emission Rates for Vehicles with Odometer Readings Greater than 50,000 miles Based Upon VSP Bins
250

Figure A-7. Evaluation of Average CO Emission Rates for 14 VSP Bins with Respect to Acceleration (left panel) and Speed (right

panel).
251

0.001

0.01

0.1

1

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec O Emissions (g/C

Speed > 32 mphSpeed < 32 mph

1

10

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec O2 Emissions (g/C

Speed > 32 mphSpeed < 32 mph

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec C Emissions (g/H

Speed > 32 mphSpeed < 32 mph

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

sec Ox Emissions (g/N

Speed > 32 mphSpeed < 32 mph

Figure A-8. Average Modal Emission Rates for VSP Bins for Engine Displacement < 3.5 liter and Odometer Reading < 50K miles

for Two Different Speed Strata
252

0.001

0.01

0.1

1

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) O Emissions (g/secC

Speed > 32 mphSpeed < 32 mph

1

10

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) O2 Emissions (g/secC

Speed > 32 mphSpeed < 32 mph

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) C Emissions (g/secH

Speed > 32 mphSpeed < 32 mph

0.00001

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) Ox Emissions (g/secN

Speed > 32 mphSpeed < 32 mph

Figure A-9. Average Modal Emission Rates for VSP Bins for Engine Displacement > 3.5 liter and Odometer Reading < 50K miles

for Two Different Speed Strata
253

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) O Emissions (g/secC

Speed > 32 mphSpeed < 32 mph

1

10

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) O2 Emissions (g/secC

Speed > 32 mphSpeed < 32 mph

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) C Emissions (g/secH

Speed > 32 mphSpeed < 32 mph

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) Ox Emissions (g/secN

Speed > 32 mphSpeed < 32 mph

Figure A-10. Average Modal Emission Rates for VSP Bins for Engine Displacement < 3.5 liter and Odometer Reading > 50K miles

for Two Different Speed Strata
254

0.001

0.01

0.1

1

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) O Emissions (g/secC

Speed > 32 mphSpeed < 32 mph

1

10

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) O2 Emissions (g/secC

Speed > 32 mphSpeed < 32 mph

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) C Emissions (g/secH

Speed > 32 mphSpeed < 32 mph

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

) Ox Emissions (g/secN

Speed > 32 mphSpeed < 32 mph

Figure A-11. Average Modal Emission Rates for VSP Bins for Engine Displacement > 3.5 liter and Odometer Reading > 50K miles

for Two Different Speed Strata
255

Table A-1. Correlation Among Parameters

Parameter

Net

Weight Odometer

Number of

Cylinders

Engine

Displacement

Model

Year

Net Weight 1 0.35 0.76 0.78 0.00

Odometer 1 0.18 0.10 0.47

Number of

Cylinders 1 0.93 0.01

Engine

Displacement 1 -0.02

Model Year 1

Table A-2. Summary of Vehicles in Validation Dataset •

Source Vehicle Year

Net

Weight

Engine

Size

Odomet

er

EPA 1 1997 2826 2 15806

EPA 2 1997 3553 3 58197

EPA 3 1996 3633 3 10102

EPA 4 1997 3650 3.1 22549

EPA 5 1996 2966 2.2 68768

EPA 6 1997 3223 2.5 17312

EPA 7 1996 3669 3.1 22000

EPA 8 1996 3279 3.1 23894

EPA 9 1996 3500 2.2 7573

EPA 10 1999 3538 3 19208

EPA 11 1996 3627 3.1 24798

EPA 12 1997 3699 3 12328

EPA 13 1996 2283 1.3 76931

EPA 14 1996 3625 3.1 17233

EPA 15 1997 3598 3.1 15248

EPA 16 1998 4216 4.6 19177

EPA 17 1998 4250 6.2 5098

EPA 18 1996 3625 3 18992

EPA 19 1998 3628 3.1 4983

EPA 20 1999 2827 1.6 10674

EPA 21 1999 2849 1.8 23800

EPA 22 1996 3338 N/A 30418

EPA 23 1997 2826 N/A 15768

EPA 24 1996 3633 N/A 9997

EPA 25 1997 3650 N/A 22093

EPA 26 1997 3223 N/A 17207

EPA 27 1996 3669 N/A 21951

(Continued on next page)
256

Table A-2. (Continued).

Source Vehicle Year

Net

Weight

Engine

Size

Odomet

er

EPA 28 1996 3279 N/A 23799

EPA 29 1996 3627 N/A 24708

EPA 30 1997 3699 N/A 1220

EPA 31 1997 3598 6 15182

EPA 32 1998 4250 8 5038

EPA 33 1998 3628 6 4829

NCHRP 1 1995 2250 1.5 23249

NCHRP 2 1996 4000 4.6 13287

NCHRP 3 1996 3500 3.8 22607

NCHRP 4 1995 3750 4 50541

NCHRP 5 1995 2250 1.6 49814

NCHRP 6 1995 2250 1.5 43708

NCHRP 7 1995 3000 2 21468

NCHRP 8 1996 3000 2 15096

NCHRP 9 1994 4250 4.3 43625

NCHRP 10 1994 2750 1.8 27339

NCHRP 11 1996 4000 4.6 16390

NCHRP 12 1996 2500 2 5312

NCHRP 13 1995 3500 3.8 28905

NCHRP 14 1996 2625 1.9 18000

NCHRP 15 1994 3000 3 49492

NCHRP 16 1995 2750 1.6 35291

NCHRP 17 1996 2625 1.9 7107

NCHRP 18 1996 2875 2.2 5690

NCHRP 19 1995 3500 2.2 29209

NCHRP 20 1996 3625 3.8 25877

NCHRP 21 1995 3375 3 22197

NCHRP 22 1995 3250 2.2 37194

NCHRP 23 1996 2875 1.9 13719

NCHRP 24 1996 3250 2.4 14212

NCHRP 25 1996 2875 1.8 4280

NCHRP 26 1995 2375 1.5 56213

NCHRP 27 1994 3500 2.2 56197

NCHRP 28 1993 2625 1.9 63125

NCHRP 29 1994 3000 2.5 56338

NCHRP 30 1996 2750 1.6 13845

NCHRP 31 1994 3250 2.2 57192

NCHRP 32 1997 2750 2 370

NCHRP 33 1994 4000 4.6 58923

NCHRP 34 1994 3875 3.8 54825

NCHRP 35 1996 2875 1.8 29480

(Continued on next page)
257

Table A-2. (Continued).

Source Vehicle Year

Net

Weight

Engine

Size

Odomet

er

NCHRP 36 1995 4000 3 51286

NCHRP 37 1995 2750 1.6 54843

NCHRP 38 1994 3125 2.5 56936

NCHRP 39 1993 2625 1.9 150139

NCHRP 40 1993 3250 2.2 72804

NCHRP 41 1995 3000 2.2 20606

NCHRP 42 1994 2875 2.5 72483

NCHRP 43 1994 4500 4.3 78060

NCHRP 44 1995 3625 3 63558

NCHRP 45 1994 2750 1.8 28630

NCHRP 46 1996 3250 2 105430

NCHRP 47 1998 2875 2.2 100250

NCHRP 48 1994 4000 3 100160

NCHRP 49 1998 3375 2.2 13247

On-Board 1 1998 3550 3.1 44362

On-Board 2 1997 3508 3 79984

On-Board 3 1996 3464 3 96099

On-Board 4 1996 3464 2.5 96099

On-Board 5 1998 2553 1.9 37278

On-Board 6 1999 3068 3.1 26288

On-Board 7 1999 2392 1.9 43242

On-Board 8 1999 2515 2 39429

On-Board 9 1997 3318 2 71446

On-Board 10 1998 2548 3 47439

On-Board 11 1998 2548 3 47439

On-Board 12 1996 2935 2.2 86999

On-Board 13 1996 3508 3 94321
258

Table A-3. Summary of Vehicles in Validation Dataset •

DATA Vehicle Year GVWR

Engine

Size

Odomet

er

EPA 1 1996 4036 2.4 30669

EPA 2 1996 N/A 3.1 21219

EPA 3 1996 N/A 1.6 9433

NCHRP 1 1996 3500 3.8 22651

NCHRP 2 1996 2625 1.6 20975

NCHRP 3 1997 3625 3 3415

NCHRP 4 1994 3625 3 22258

NCHRP 5 1995 2375 1.5 52111

NCHRP 6 1994 2625 1.5 78056

NCHRP 7 1994 2375 1.5 57742

NCHRP 8 1995 3625 3.3 62007

NCHRP 9 1994 3000 2.5 57407

NCHRP 10 1994 3875 3.8 72691

NCHRP 11 1993 2625 1.6 61032

NCHRP 12 1994 2625 1.9 64967

NCHRP 13 1996 2000 1 32034

NCHRP 14 1993 3500 2.2 97869

NCHRP 15 1994 3500 2.5 61040

NCHRP 16 1994 3250 3.1 80877

NCHRP 17 1993 2750 1.8 102240

NCHRP 18 1994 2625 1.5 91045

NCHRP 19 1997 2625 1.6 6172

NCHRP 20 1997 3375 3.1 3015

NCHRP 21 1997 3250 2 23099

NCHRP 22 1995 2625 1.9 104890

NCHRP 23 1996 2625 1.9 111203

NCHRP 24 1999 2875 3.1 100250

NCHRP 25 1995 2875 2.5 100250

On-Board 1 1998 4721 3 78187

On-Board 2 1998 N/A 2.2 56803

On-Board 3 1998 5166 2 41319
259

Table A-3. Summary of Vehicles in Validation Dataset •I

DATA Vehicle Year

Net

weight Odometer

ARB 2 1994 3500 65294

ARB 5 1997 3250 23503

ARB 24 1995 2750 12698

ARB 33 1996 3375 28454

ARB 36 1993 3250 52196

ARB 41 1995 2250 6181

ARB 49 1993 3500 40626

ARB 59 1993 3250 47368

ARB 77 1993 3125 37353

ARB 79 1994 2875 23730

ARB 84 1995 3125 3188

ARB 187 1994 4000 88592

ARB 216 1993 3375 90080

ARB 258 1995 2750 32015

ARB 315 1993 4000 66932

ARB 341 1995 3500 49437

ARB 342 1995 2750 14904
260

Table A-4. Comparison of Mean Emissions of VSP Bins, Time-Average vs. Trip-Average vs. Vehicle-Average

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Binamean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff.

1101 0.000901 0.001097 22 0.000852 -6 0.00045 0.000391 -13 0.00034 -24 1.671078 2.092668 25 1.780418 7 0.007807 0.010418 33 0.009971 281102 0.000628 0.001017 62 0.000727 16 0.000257 0.000387 51 0.000337 31 1.457983 2.020811 39 1.70965 17 0.003908 0.007937 103 0.007968 1041103 0.000346 0.000742 114 0.000411 19 0.000406 0.00035 -14 0.000274 -33 1.135362 1.667869 47 1.332954 17 0.003347 0.005155 54 0.004262 271104 0.001173 0.001389 18 0.001039 -11 0.000432 0.000528 22 0.000429 -1 2.233264 2.552053 14 2.338717 5 0.008335 0.01246 49 0.010144 221105 0.001706 0.001684 -1 0.00141 -17 0.00053 0.000572 8 0.000515 -3 2.91989 2.98235 2 2.931022 0 0.010959 0.013319 22 0.014101 291106 0.002368 0.002066 -13 0.00198 -16 0.000705 0.00065 -8 0.000666 -6 3.525303 3.327366 -6 3.502494 -1 0.017013 0.014941 -12 0.021879 291107 0.003103 0.002466 -21 0.002489 -20 0.000822 0.00077 -6 0.000804 -2 4.107483 3.739047 -9 4.054487 -1 0.020026 0.017961 -10 0.030889 541108 0.004234 0.003103 -27 0.003235 -24 0.000976 0.000813 -17 0.000946 -3 4.635048 4.121626 -11 4.52942 -2 0.029222 0.022877 -22 0.046249 581109 0.005069 0.004166 -18 0.004544 -10 0.001112 0.000871 -22 0.001097 -1 5.160731 4.606298 -11 5.152217 0 0.035531 0.027536 -23 0.059231 671110 0.005865 0.004178 -29 0.004414 -25 0.001443 0.001096 -24 0.00133 -8 5.632545 4.858016 -14 5.440037 -3 0.055068 0.03832 -30 0.086515 571111 0.007623 0.004979 -35 0.005441 -29 0.002061 0.001673 -19 0.0019 -8 6.53478 5.798515 -11 6.266617 -4 0.113824 0.08035 -29 0.175599 541112 0.012149 0.009459 -22 0.009449 -22 0.003373 0.003284 -3 0.002607 -23 7.585213 7.097114 -6 7.671417 1 0.207586 0.169395 -18 0.253183 221113 0.015456 0.010298 -33 0.010679 -31 0.004857 0.005374 11 0.004349 -10 9.024217 8.439456 -6 9.319705 3 0.441775 0.386715 -12 0.530003 20
261

Table A-4. Continued

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Binamean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff.

1114 0.017863 0.015276 -14 0.018635 4 0.010948 0.005063 -54 0.005851 -47 10.08839 8.611693 -15 9.917922 -2 0.8823 0.574791 -35 0.820496 -71201 0.00029 0.000571 97 0.000767 165 0.000548 0.001243 127 0.000619 13 1.566819 1.742827 11 1.76866 13 0.017699 0.03866 118 0.019879 121202 0.000223 0.000526 136 0.000747 235 0.000222 0.001518 583 0.000704 217 1.443564 1.883233 30 1.812724 26 0.008608 0.055898 549 0.025235 1931203 0.000174 0.000571 227 0.000899 415 0.000272 0.001165 329 0.000395 46 1.470553 1.778044 21 1.767513 20 0.008479 0.034922 312 0.011575 371204 0.000719 0.000938 30 0.001112 55 0.000472 0.001411 199 0.000649 38 2.611318 2.93208 12 2.769411 6 0.014548 0.04941 240 0.019972 371205 0.001136 0.001304 15 0.00152 34 0.000754 0.001704 126 0.000799 6 3.523681 3.620842 3 3.558054 1 0.025709 0.072916 184 0.026876 51206 0.001587 0.001657 4 0.001932 22 0.000702 0.001412 101 0.000809 15 4.650741 4.399458 -5 4.452864 -4 0.025212 0.047817 90 0.026926 71207 0.00237 0.002194 -7 0.002551 8 0.000944 0.001489 58 0.000939 0 5.635386 5.248342 -7 5.270724 -6 0.04113 0.059382 44 0.041535 11208 0.004098 0.002927 -29 0.00348 -15 0.001443 0.001799 25 0.001299 -10 6.599677 6.16888 -7 6.252616 -5 0.076601 0.070431 -8 0.060221 -211209 0.006124 0.004377 -29 0.005834 -5 0.001708 0.002151 26 0.001614 -5 7.647334 7.075418 -7 7.38033 -3 0.129248 0.103004 -20 0.103436 -201210 0.007313 0.00506 -31 0.006455 -12 0.002605 0.002985 15 0.002385 -8 8.808448 8.096559 -8 8.042326 -9 0.150578 0.122169 -19 0.123995 -181211 0.013178 0.00802 -39 0.011761 -11 0.003523 0.003469 -2 0.003386 -4 11.67061 9.372073 -20 9.594158 -18 0.355223 0.168599 -53 0.220936 -381212 0.012663 0.018412 45 0.018412 45 0.007653 0.005327 -30 0.005327 -30 14.52036 14.8929 3 14.8929 3 0.881642 0.546928 -38 0.546928 -38
262

Table A-4. Continued

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Binamean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff.

1213 0.015387 0.020783 35 0.020783 35 0.006667 0.005828 -13 0.005828 -13 15.65327 15.30436 -2 15.30436 -2 0.755155 0.722783 -4 0.722783 -41214 0.020308 0.041798 106 0.041798 106 0.006574 0.006035 -8 0.006035 -8 17.36653 17.66742 2 17.66742 2 0.904851 0.909832 1 0.909832 12101 0.001014 0.001018 0 0.000965 -5 0.000901 0.000926 3 0.000607 -33 1.543686 1.395048 -10 1.330709 -14 0.01103 0.014076 28 0.011779 72102 0.001042 0.001243 19 0.001088 4 0.000901 0.000833 -8 0.000545 -40 1.604406 1.656132 3 1.547675 -4 0.008723 0.013194 51 0.009119 52103 0.000423 0.000793 87 0.000858 103 0.000835 0.000705 -16 0.000486 -42 1.130833 1.266896 12 1.270197 12 0.004682 0.007685 64 0.006283 342104 0.001613 0.002034 26 0.001561 -3 0.001027 0.001237 20 0.000757 -26 2.38626 2.640064 11 2.361957 -1 0.012154 0.021867 80 0.013167 82105 0.002638 0.002791 6 0.002287 -13 0.001253 0.001192 -5 0.000865 -31 3.210249 3.366473 5 3.10974 -3 0.016731 0.025063 50 0.016411 -22106 0.003793 0.003603 -5 0.003145 -17 0.001664 0.00134 -19 0.000994 -40 3.957732 3.973958 0 3.83721 -3 0.023269 0.024633 6 0.02069 -112107 0.005098 0.004579 -10 0.003967 -22 0.002089 0.001472 -30 0.001134 -46 4.752012 4.620807 -3 4.583745 -4 0.029322 0.027876 -5 0.027406 -72108 0.006373 0.005964 -6 0.005095 -20 0.002332 0.001585 -32 0.001232 -47 5.374221 5.332288 -1 5.321404 -1 0.036942 0.033271 -10 0.034868 -62109 0.007664 0.007039 -8 0.006184 -19 0.002818 0.002136 -24 0.001654 -41 5.940051 5.905244 -1 6.043941 2 0.049513 0.046846 -5 0.053282 82110 0.009913 0.01015 2 0.00841 -15 0.002985 0.002352 -21 0.001781 -40 6.427506 6.722447 5 6.755205 5 0.063759 0.060781 -5 0.071075 112111 0.012685 0.013099 3 0.012178 -4 0.003786 0.00317 -16 0.002651 -30 7.065985 7.632773 8 7.972946 13 0.10538 0.10403 -1 0.139503 32
263

Table A-4. Continued

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Binamean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff.

2112 0.014384 0.014329 0 0.01417 -1 0.004573 0.005006 9 0.004808 5 7.617703 8.201694 8 8.694089 14 0.24781 0.367169 48 0.504717 1042113 0.015967 0.01535 -4 0.015462 -3 0.0057 0.006377 12 0.006267 10 8.322442 8.290563 0 9.310727 12 0.413069 0.63355 53 0.884127 1142114 0.016717 0.015747 -6 0.013914 -17 0.007164 0.009796 37 0.009379 31 8.475028 8.780078 4 9.856257 16 0.624663 1.067502 71 1.495996 1392201 0.000725 0.00082 13 0.000717 -1 0.000863 0.001075 25 0.000857 -1 1.649427 1.666261 1 1.637489 -1 0.020282 0.026335 30 0.020063 -12202 0.000504 0.000937 86 0.000607 20 0.0003 0.000739 146 0.000388 29 1.762407 1.971398 12 1.729282 -2 0.008183 0.031627 286 0.009787 202203 0.000661 0.000812 23 0.000619 -6 0.000323 0.000571 77 0.000298 -8 1.557773 1.688165 8 1.594651 2 0.00483 0.014518 201 0.004375 -92204 0.002518 0.003287 31 0.00248 -1 0.000449 0.000851 90 0.000444 -1 2.946419 3.503549 19 2.950934 0 0.012308 0.044087 258 0.012215 -12205 0.005847 0.005724 -2 0.005791 -1 0.000818 0.0015 84 0.000816 0 4.127492 4.476632 8 4.105545 -1 0.022033 0.045654 107 0.021965 02206 0.008361 0.008287 -1 0.008562 2 0.001216 0.001476 21 0.001255 3 5.343656 5.461154 2 5.347669 0 0.045073 0.059244 31 0.046499 32207 0.010582 0.010992 4 0.010822 2 0.00211 0.002053 -3 0.002082 -1 6.507179 6.480357 0 6.513549 0 0.077496 0.074036 -4 0.077436 02208 0.014473 0.015513 7 0.014517 0 0.004394 0.003571 -19 0.004342 -1 7.602431 7.642446 1 7.693818 1 0.166593 0.130573 -22 0.165597 -12209 0.016372 0.017328 6 0.015037 -8 0.004635 0.003484 -25 0.004221 -9 8.773093 8.827697 1 8.848806 1 0.170018 0.113574 -33 0.158411 -72210 0.019758 0.022928 16 0.019472 -1 0.004961 0.004306 -13 0.005332 7 10.36591 10.29987 -1 10.33755 0 0.263544 0.17931 -32 0.271669 3
264

Table A-4. Continued

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Binamean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff. mean mean diff. mean diff.

2211 0.030507 0.036289 19 0.03191 5 0.006631 0.006477 -2 0.006673 1 12.84939 12.53602 -2 12.83404 0 0.338962 0.23947 -29 0.341425 12212 0.034219 0.049097 43 0.037247 9 0.0109 0.013702 26 0.011512 6 15.0303 14.74582 -2 15.13418 1 0.824829 0.82406 0 0.877657 62213 0.043387 0.0485 12 0.0485 12 0.016573 0.016142 -3 0.016142 -3 16.86173 16.96438 1 16.96438 1 1.444311 1.306457 -10 1.306457 -102214 0.068988 0.054347 -21 0.054347 -21 0.027066 0.020961 -23 0.020961 -23 18.94712 18.76208 -1 18.76208 -1 2.175099 1.917319 -12 1.917319 -12a First two digit of VSP Bins: 11: odometer < 50,000 miles and engine size < 3.5 liter; 12: odometer < 50,000 miles and engine size > 3.5

liter; 21: odometer > 50,000 miles and engine size < 3.5 liter; 22: odometer > 50,000 miles and engine size > 3.5 liter.

b Unit of mean: g/sec; Unit of diff.: %.
265

Table A-5. Comparison of Standard Deviations of Variability in Original Emission Data Sets of VSP Bins, Time-Average vs. TripAverage vs. Vehicle-Average

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Bina

std.

dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff.

1101 0.0029

45 0.001611 -45 0.000963 -67 0.002831 0.000566 -80 0.0005 -82 1.385471 1.12253 -19 0.935668 -32 0.058918 0.021028 -64 0.014674 -75

1102 0.0025

6 0.001587 -38 0.000811 -68 0.001123 0.000774 -31 0.000587 -48 1.212863 1.132493 -7 0.866006 -29 0.036678 0.019927 -46 0.018202 -50

1103 0.0015

43 0.001962 27 0.000375 -76 0.001502 0.000801 -47 0.000534 -64 0.816426 1.130622 38 0.61943 -24 0.021594 0.012754 -41 0.010782 -50

1104 0.0034

33 0.001756 -49 0.000878 -74 0.001414 0.000919 -35 0.000777 -45 1.384324 0.955028 -31 0.767325 -45 0.051944 0.028064 -46 0.026506 -49

1105 0.0044

18 0.001999 -55 0.001167 -74 0.001599 0.001047 -35 0.000917 -43 1.529625 0.894469 -42 0.709841 -54 0.096842 0.03279 -66 0.031709 -67

1106 0.0056

74 0.00236 -58 0.001735 -69 0.00237 0.00116 -51 0.001224 -48 1.667104 0.902644 -46 0.775961 -53 0.154603 0.036387 -76 0.049995 -68

1107 0.0067

12 0.002811 -58 0.00242 -64 0.002401 0.001414 -41 0.001481 -38 1.77441 1.1272 -36 0.899522 -49 0.106224 0.048599 -54 0.073973 -30

1108 0.0079

42 0.003529 -56 0.003294 -59 0.002812 0.001523 -46 0.001687 -40 1.938311 1.323727 -32 1.138721 -41 0.15224 0.077492 -49 0.115758 -24

1109 0.0100

76 0.005296 -47 0.005013 -50 0.002673 0.001854 -31 0.001912 -28 2.088216 1.598809 -23 1.322392 -37 0.165469 0.09141 -45 0.150854 -9

1110 0.0109

91 0.005133 -53 0.004874 -56 0.003685 0.002444 -34 0.002394 -35 2.35424 2.112815 -10 1.874281 -20 0.251833 0.11994 -52 0.191922 -24

1111 0.0146

62 0.007957 -46 0.006742 -54 0.005445 0.004588 -16 0.00348 -36 2.720312 2.556017 -6 2.543511 -6 0.396332 0.232956 -41 0.335661 -15

1112 0.0200

7 0.012712 -37 0.011631 -42 0.010402 0.010036 -4 0.003884 -63 2.987478 2.795777 -6 2.773975 -7 0.570599 0.300565 -47 0.334399 -41

1113 0.0246

82 0.013143 -47 0.013583 -45 0.013267 0.015286 15 0.007115 -46 3.637198 3.125796 -14 2.715516 -25 0.906088 0.622866 -31 0.689833 -24

1114 0.0277

26 0.027707 0 0.032729 18 0.024933 0.008866 -64 0.008941 -64 5.372496 4.190774 -22 3.666952 -32 1.521667 0.830872 -45 0.891284 -41
266

Table A-5. Continued

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Bina

std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff.

1201 0.001353 0.001435 6 0.001873 38 0.002465 0.003384 37 0.001711 -31 0.752061 0.664471 -12 0.774477 3 0.087575 0.099099 13 0.049412 -441202 0.001423 0.001521 7 0.002003 41 0.001773 0.004194 137 0.002062 16 0.729907 0.668691 -8 0.77674 6 0.076393 0.141591 85 0.068659 -101203 0.001253 0.001896 51 0.002485 98 0.001936 0.003079 59 0.000929 -52 0.783702 0.697239 -11 0.855793 9 0.069682 0.078986 13 0.023375 -661204 0.002278 0.001665 -27 0.002125 -7 0.002461 0.003694 50 0.001778 -28 1.080752 0.677613 -37 0.628547 -42 0.080298 0.104564 30 0.04997 -381205 0.003336 0.002119 -36 0.002614 -22 0.003597 0.003467 -4 0.001681 -53 1.206617 0.794739 -34 0.714965 -41 0.138754 0.147007 6 0.054372 -611206 0.0044 0.002279 -48 0.002609 -41 0.002765 0.003178 15 0.001488 -46 1.78582 1.112786 -38 0.921626 -48 0.113237 0.093205 -18 0.042388 -631207 0.005525 0.001954 -65 0.002196 -60 0.002781 0.003305 19 0.001768 -36 2.306199 1.366 -41 1.220852 -47 0.16598 0.113099 -32 0.061202 -631208 0.008133 0.002694 -67 0.002807 -65 0.00722 0.003196 -56 0.001831 -75 2.635432 1.781243 -32 1.570403 -40 0.286122 0.111506 -61 0.090063 -691209 0.014025 0.005225 -63 0.006173 -56 0.004432 0.003916 -12 0.001976 -55 2.505814 2.228266 -11 1.895366 -24 0.410763 0.197293 -52 0.188263 -541210 0.014451 0.006155 -57 0.007053 -51 0.009088 0.005182 -43 0.003244 -64 2.799147 2.633155 -6 2.432006 -13 0.474955 0.196622 -59 0.166781 -651211 0.024503 0.014531 -41 0.017887 -27 0.006989 0.006375 -9 0.005167 -26 3.381765 3.876705 15 3.990195 18 0.933668 0.326539 -65 0.370172 -601212 0.023031 0.014183 -38 0.014183 -38 0.011665 0.006219 -47 0.006219 -47 2.530211 1.692154 -33 1.692154 -33 1.445647 0.856243 -41 0.856243 -411213 0.035852 0.020699 -42 0.020699 -42 0.009166 0.005278 -42 0.005278 -42 1.94742 1.40999 -28 1.40999 -28 1.100803 0.76091 -31 0.76091 -311214 0.037826 0.066474 76 0.066474 76 0.007689 0.004986 -35 0.004986 -35 2.208716 1.110591 -50 1.110591 -50 1.17728 0.932473 -21 0.932473 -21
267

Table A-5. Continued

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Bina

std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff.

2101 0.002291 0.001038 -55 0.001092 -52 0.002249 0.001355 -40 0.000609 -73 1.109149 0.522517 -53 0.492078 -56 0.04711 0.017075 -64 0.008651 -822102 0.00257 0.001248 -51 0.001228 -52 0.002282 0.001089 -52 0.000673 -71 1.114641 0.653819 -41 0.596964 -46 0.037055 0.017076 -54 0.007536 -802103 0.001682 0.001174 -30 0.001481 -12 0.003115 0.001064 -66 0.000707 -77 0.713377 0.508459 -29 0.588173 -18 0.028625 0.011217 -61 0.011063 -612104 0.003339 0.00162 -51 0.001267 -62 0.002869 0.001942 -32 0.000965 -66 1.171887 0.711085 -39 0.587889 -50 0.05007 0.026471 -47 0.013628 -732105 0.004665 0.002149 -54 0.001593 -66 0.002939 0.00126 -57 0.000973 -67 1.288537 0.823675 -36 0.613453 -52 0.066924 0.031311 -53 0.012323 -822106 0.006577 0.002846 -57 0.002235 -66 0.003766 0.00141 -63 0.001123 -70 1.360129 0.737997 -46 0.56076 -59 0.082777 0.021256 -74 0.014604 -822107 0.008025 0.003665 -54 0.002943 -63 0.004028 0.001526 -62 0.001221 -70 1.498808 0.809143 -46 0.675402 -55 0.08088 0.023906 -70 0.022786 -722108 0.009009 0.005018 -44 0.003925 -56 0.003551 0.001595 -55 0.001195 -66 1.644394 0.802907 -51 0.725539 -56 0.101806 0.029478 -71 0.028732 -722109 0.01072 0.005428 -49 0.005163 -52 0.0052 0.001935 -63 0.001437 -72 1.811788 1.301192 -28 1.036041 -43 0.146791 0.040071 -73 0.042312 -712110 0.013533 0.008557 -37 0.006739 -50 0.004841 0.002246 -54 0.001466 -70 1.959334 1.247208 -36 1.169198 -40 0.208775 0.055964 -73 0.061325 -712111 0.016326 0.010608 -35 0.008615 -47 0.006874 0.002737 -60 0.002002 -71 2.303041 2.134836 -7 1.86914 -19 0.331085 0.112855 -66 0.128683 -612112 0.016636 0.009201 -45 0.009319 -44 0.007075 0.004083 -42 0.004147 -41 2.454817 2.221742 -9 2.195417 -11 0.664957 0.508908 -23 0.587978 -122113 0.018636 0.009346 -50 0.008606 -54 0.008143 0.005669 -30 0.004974 -39 3.00003 2.826129 -6 2.735825 -9 0.917957 0.906304 -1 1.037041 132114 0.018182 0.012218 -33 0.008621 -53 0.009979 0.012121 21 0.009851 -1 3.192905 3.65873 15 3.427465 7 1.255385 1.425734 14 1.612373 28
268

Table A-5. Continued

NOb HCb CO2b COb

TimeAvg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Time- Avg Trip-Avg Vehicle-Avg Bina

std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff. std. dev. std. dev. diff. std. dev. diff.

2201

0.002025 0.000981 -52 0.000666 -67 0.005724 0.001843 -68 0.001068 -81 0.613904 0.273568 -55 0.263742 -57 0.114323 0.041109 -64 0.018576 -84

2202

0.001373 0.001018 -26 0.000437 -68 0.001315 0.001012 -23 0.000366 -72 0.675646 0.401726 -41 0.118576 -82 0.076183 0.044768 -41 0.007651 -90

2203

0.001812 0.000953 -47 0.000498 -73 0.002487 0.000827 -67 0.000309 -88 0.662243 0.237542 -64 0.22642 -66 0.08347 0.02829 -66 0.005443 -93

2204

0.004017 0.004185 4 0.003048 -24 0.000901 0.001069 19 0.000361 -60 0.7346 0.861998 17 0.345979 -53 0.062257 0.052883 -15 0.009072 -85

2205

0.008341 0.00692 -17 0.007591 -9 0.004297 0.002034 -53 0.00079 -82 0.88572 0.871532 -2 0.460997 -48 0.069947 0.062257 -11 0.02374 -66

2206

0.011656 0.009697 -17 0.0106 -9 0.002485 0.001831 -26 0.001041 -58 1.082677 0.935579 -14 0.745519 -31 0.120335 0.071032 -41 0.040804 -66

2207

0.01327 0.012669 -5 0.013467 1 0.004035 0.002652 -34 0.001958 -51 1.347016 1.10976 -18 1.145355 -15 0.196119 0.092674 -53 0.073024 -63

2208

0.017788 0.01643 -8 0.017134 -4 0.011091 0.00444 -60 0.004399 -60 1.439746 1.04263 -28 1.20379 -16 0.429698 0.191461 -55 0.175101 -59

2209

0.019972 0.020016 0 0.019755 -1 0.00739 0.003756 -49 0.003978 -46 1.495146 1.094696 -27 1.235369 -17 0.329428 0.119911 -64 0.115394 -65

2210

0.026059 0.023848 -8 0.02638 1 0.009476 0.004503 -52 0.004976 -47 1.831227 0.851895 -53 1.134458 -38 0.651197 0.220715 -66 0.250122 -62

2211

0.032955 0.033371 1 0.032509 -1 0.010611 0.007382 -30 0.006424 -39 2.135363 1.230785 -42 1.433405 -33 0.706309 0.266176 -62 0.297055 -58

2212

0.04661 0.04875 5 0.047183 1 0.016814 0.012329 -27 0.012946 -23 1.624249 1.219954 -25 0.913632 -44 1.294249 0.671993 -48 0.717117 -45

2213

0.049311 0.048572 -1 0.048572 -1 0.017884 0.013392 -25 0.013392 -25 2.386484 1.472577 -38 1.472577 -38 1.427208 0.894934 -37 0.894934 -37

2214

0.057202 0.051111 -11 0.051111 -11 0.032672 0.026775 -18 0.026775 -18 2.102866 1.50871 -28 1.50871 -28 2.051322 1.561656 -24 1.561656 -24

a First two digit of VSP Bins: 11: odometer < 50,000 miles and engine size < 3.5 liter; 12: odometer < 50,000 miles and engine size > 3.5 liter; 21: odometer > 50,000 miles and engine size < 3.5 liter; 22:

odometer > 50,000 miles and engine size > 3.5 liter.

b Unit of standard deviation: g/sec; Unit of diff.: %.