Click here for 

DISCLAIMER

Document starts on next page 

TITLE: Technical Guidance Manual for Performing Wasteload Allocations, 

Book III: Estuaries – 

Part 2: Application of Estuarine Waste Load Allocation Models 

EPA DOCUMENT NUMBER: DATE: May 1990 

ABSTRACT 

As part of ongoing efforts to keep EPA’s technical guidance readily accessible to 

water quality practitioners, selected publications on Water Quality Modeling and 

TMDL Guidance available at http://www.epa.gov/waterscience/pc/watqual.html 

have been enhanced for easier access. 

This document is part of a series of manuals that provides technical information 

related to the preparation of technically sound wasteload allocations (WLAs) that 

ensure that acceptable water quality conditions are achieved to support 

designated beneficial uses. The document provides a guide to monitoring and 

model calibration and testing, and a case study tutorial on simulation of waste 

load allocation problems in simplified estuarine systems. 

Book III Part 2 presents information on the monitoring protocols to be used for 

collection of data to support calibration and validation of estuarine WLA models, 

and discusses how to use this data in calibration and validation steps to 

determine the predictive capability of the model. It also explains how to use the 

calibrated and validated model to establish load allocations that result in 

acceptable water quality even under critical conditions. Simplified examples of 

estuarine modeling are included to illustrate both simple screening procedures 

and application of the WASP4 water quality model. 

This document should be used in conjunction with “Part 1: Estuaries and Waste 

Load Allocation Models” which provides technical and policy guidance on 

estuarine WLAs as well as summarizing estuarine characteristics, water quality 

problems, and processes along with available simulation models. 

KEYWORDS: Wasteload Allocations, Estuaries, Modeling, Water Quality 

Criteria, Calibration, Validation 

EPA 823/R-92-003
United States

Environmental Protection

Agency

Office of Water

Washington, DC 20460

EPA-823-R-92-003

May 1990

Technical Guidance

Manual for Performing

Waste Load Allocations

Book III

Estuaries

Part 2

Application of Estuarine

Waste Load Allocation Models
TECHNICAL GUIDANCE MANUAL

FOR PERFORMING WASTE LOAD ALLOCATIONS

BOOK III: ESTUARIES

Part 2: Application of Estuarine Waste Load Allocation Models

Project Officer

Hiranmay Biswas, Ph.D.

Edited by

James L. Martin, Ph.D.,P.E.2

Robert B. Ambrose, Jr. P.E.1

Steve C. McCutcheon, Ph.D., P.E.1

Sections written by

Robert B. Ambrose, Jr., P.E.1

James L. Martin, Ph.D., P.E.2

Steve C. McCutcheon, Ph.D., P.E.1

Zhu Dongwei1

Sandra Bird1

John F. Paul, Ph.D.3

David W. Dilks, Ph.D.4

Scott C. Hinz4

Paul L. Freedman, P.E.4

1. Center for Exposure Assessment Modeling,

Environmental Research Laboratory, U.S. EPA, Athens, GA

2. AScI Corp., at the

Environmental Research Laboratory, U.S. EPA, Athens, GA

3. Environmental Research Laboratory,

U.S. EPA, Narragansett, RI

4. Limno-Tech, Inc. (LTI), Ann Arbor, Michigan

Prepared for

U.S. ENVIRONMENTAL PROTECTION AGENCY

401 M Street, S.W.

Washington, DC 20460

Table of Contents

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

PART I: Estuaries and Waste Load Allocation Models . . . . . . . . . . . . . . xxiii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

Overview of Processes Affecting Estuarine Water Quality . . . . . . . . . . . . xxiii

Model Identification and Selection . . . . . . . . . . . . . . . . . . . . . . . . xxiv

PART II: Application of Estuarine Waste Load Allocation Models . . . . . . . . . xxv

Monitoring Protocols for Calibration and Validation of Estuarine WLA Models . . xxv

Model Calibration, Validation, and Use . . . . . . . . . . . . . . . . . . . . . . xxvi

Simplified Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxix

4. Monitoring Protocols for Calibration and Validation of Estuarine WLA Models . . . . 4-1

4.1. General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

4.2. Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2

4.3. Frequency of Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3

4.4. Spatial Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4

4.5. Model Data Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5

4.6. Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8

4.7. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12

5. Model Calibration, Validation, and Use . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.1. Introduction And Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

5.2. Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4

5.3. Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-11

5.4. Model Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-11

Example 5.1. Calibration of Hydrodynamics, Mass Transport, and Toxic

Chemical Model for the Delaware Estuary . . . . . . . . 5-18

5.6 Application of The Calibrated Model In Waste Load Allocations . . . . . . 5-23

Example 5.2. Component Analysis of Dissolved Oxygen Balance in the

Wicomico Estuary, Maryland . . . . . . . . . . . . . . . 5-26
SUPPLEMENT I: Selection of Manning n Values . . . . . . . . . . . . . . 5-29

EXAMPLE 5.3. Initial Selection of the Manning n for a Hypothetical Estuary . . 5-35

EXAMPLE 5.4. Selection of the Manning n for the Delaware Estuary . . . . . . 5-36

SUPPLEMENT II: Selection of Surface Drag Coefficients . . . . . . . . . . 5-37

SUPPLEMENT III: Selection of Eddy Viscosity Values . . . . . . . . . . . . 5-38

SUPPLEMENT IV: Brief Review of Turbulence Closure Models . . . . . . . 5-45

SUPPLEMENT V: Selection of Dispersion Coefficients . . . . . . . . . . . . 5-46

SUPPLEMENT VI: Selection of Wind Speed Functions: . . . . . . . . . . . 5-52

SUPPLEMENT VII: Selection of Bacteria Die-off Coefficients . . . . . . . . . 5-54

SUPPLEMENT VIII: Calibrating Simple Sediment Models . . . . . . . . . . . 5-58

SUPPLEMENT IX: Selection of CBOD Coefficients . . . . . . . . . . . . . . 5-59

SUPPLEMENT X: Selection of NBOD Coefficients . . . . . . . . . . . . . . 5-61

SUPPLEMENT XI: Calibrating Nitrogen Cycle Models . . . . . . . . . . . . 5-63

SUPPLEMENT XII: Phosphorus Cycle Coefficients . . . . . . . . . . . . . . 5-64

SUPPLEMENT XIII: Selection of Reaeration Coefficients . . . . . . . . . . . 5-65

SUPPLEMENT XIV: Program of O’Connor’s Method to Compute K2 In Wind

Dominated Estuaries . . . . . . . . . . . . . . . . . . . 5-69

SUPPLEMENT XV: Selection of SOD Rates . . . . . . . . . . . . . . . . . . 5-70

5.5. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-71

6. SIMPLIFIED ILLUSTRATIVE EXAMPLES . . . . . . . . . . . . . . . . . . . . . . 6-1

6.1. Screening Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2

6.2. Screening Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5

6.3. WASP4 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-11

6.4. WASP4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-13

6.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-47
List of Figures

Figure 4-1. Illustration of use of log probability plot to estimate statistics for data

including non-detects. . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11

Figure 5-1. Model calibration and verification procedure. . . . . . . . . . . . . . . . 5-4

Figure 5-2. Relationship between data collection, model calibration, validation, and

waste load allocation procedures. . . . . . . . . . . . . . . . . . . . . . 5-4

Figure 5-3. Relationship between data set components, water quality model, and set

of model coefficients for model calibration. . . . . . . . . . . . . . . . . 5-5

Figure 5-4. Phased calibration procedure. . . . . . . . . . . . . . . . . . . . . . . . 5-6

Figure 5-5. Example showing that calibration is not unique unless material

transformation rates are specified and that validation should be

performed with significantly different data sets [Wlonsinski (1984)]. . . . 5-10

Figure 5-6. Cumulative frequency diagram. . . . . . . . . . . . . . . . . . . . . . 5-12

Figure 5-7. Types of bias and systematic error determined by regression analysis

[(O’Connor (1979), Thomann (1982), and NCASI (1982)]. . . . . . . . 5-13

Figure 5-8. Upper Delaware Estuary [Ambrose (1987)]. . . . . . . . . . . . . . . . 5-18

Figure 5-9. Observed and predicted tidal ranges in the Delaware Estuary

[Ambrose (1987)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-19

Figure 5-10. Observed and predicted dye concentrations [Ambrose (1987)]. . . . . . 5-20

Figure 5-11. Northeast Water Pollution Control Plant Effluent Concentrations,

October 2-3, 1983 [Ambrose (1987)]. . . . . . . . . . . . . . . . . . . 5-21

Figure 5-12. Observed and predicted DCP concentrations [Ambrose (1987)]. . . . . 5-22

Figure 5-13. Observed and predicted DMM concentrations [Ambrose (1987)]. . . . . 5-22

Figure 5-14. Observed and predicted DCE concentrations [Ambrose (1987)]. . . . . 5-22

Figure 5-15. Observed and predicted PCE concentrations [Ambrose (1987)]. . . . . 5-22

Figure 5-16. Components of the waste load allocation procedure. . . . . . . . . . . 5-23

Figure 5-17. General waste load allocation procedure. . . . . . . . . . . . . . . . . 5-23

Figure 5-18 Model segmentation - Wicomico River, Maryland. . . . . . . . . . . . . 5-27

v
Figure 5-19. Component deficits for July 1971 dissolved oxygen verification

[Robert Thomann in review]. . . . . . . . . . . . . . . . . . . . . . . . 5-28

Figure 5-20. Modified Moody diagram relating the Manning n to Reynolds number. . 5-30

Figure 5-21. Longitudinal distribution of Manning n values in the Delaware Estuary

[Thatcher and Harleman (1981)]. . . . . . . . . . . . . . . . . . . . . 5-36

Figure 5-22. Hydraulic calibration to tidal range and high and low water planes for

mean conditions in the Delaware Estuary

[Thatcher and Harleman (1981)]. . . . . . . . . . . . . . . . . . . . . 5-36

Figure 5-23. Water surface drag coefficient as a function of wind speed measured

at a 10-m height [O’Connor (1983)] . . . . . . . . . . . . . . . . . . . 5-37

Figure 5-24. Diffusion coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-46

Figure 5-25. Relationship between horizontal diffusion coefficient and horizontal

length scale [Thibodeaux (1979), Fan and Koh, Orlob (1959),

Okuba]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-47

Figure 5-26. Relationship between longitudinal dispersion coefficient and discharge

in a Scottish estuary [West and Williams (1972)]. . . . . . . . . . . . . 5-50

Figure 5-27. Relationship between longitudinal dispersion coefficient in the Potomac

Estuary and distance downestuary from the Chain Bridge in

Washington, D.C. [Hetling and O’Connell (1966)]. . . . . . . . . . . . . 5-50

Figure 5-28. Sources and sinks of carbonaceous BOD in the aquatic environment

[Bowie et al. (1985)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-59

Figure 5-29. Effect of pH and temperature on unionized ammonia

[Willingham (1976)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-63

Figure 5-30. Reaeration coefficient (day-1 versus depth and velocity using the

suggested method of Covar (1976) [Bowie et al. (1985)]. . . . . . . . . 5-65

Figure 6-1. Schematic of tidal tributary for analytical equation example. . . . . . . . 6-5

Figure 6-2. Determination of tidal dispersion from salinity data. . . . . . . . . . . . . 6-6

Figure 6-3. Calibration of TRC decay rate. . . . . . . . . . . . . . . . . . . . . . . . 6-7

Figure 6-4. Estuary TRC concentration in response to two discharges. . . . . . . . . 6-8

Figure 6-5. Schematic for illustrative vertically stratified estuary. . . . . . . . . . . . 6-9

Figure 6-6. The Trinity Estuary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-14

Figure 6-7. Average monthly river flow at the Highway 64 USGS gauge. . . . . . . 6-14

vi
Figure 6-8. Mean monthly temperatures at the Highway 64 USGS gauge. . . . . . 6-15

Figure 6-9a. Variations in water surface elevations at the mouth of the Trinity

Estuary during March, 1989 . . . . . . . . . . . . . . . . . . . . . . . 6-15

Figure 6-9b. Model network for the Trinity Estuary. . . . . . . . . . . . . . . . . . . 6-16

Figure 6-10. Predicted variations in volumes near the mouth, near the midpoint, and

at the upper extremity of the Trinity Estuary. . . . . . . . . . . . . . . . 6-17

Figure 6-11. Monthly averaged salinities in the Trinity Estuary versus distance

upstream from its mouth. . . . . . . . . . . . . . . . . . . . . . . . . . 6-18

Figure 6-12. Predicted variations in salinity during March, 1989, near the mouth of

the Trinity Estuary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-18

Figure 6-13. Predicted variations in salinity during March, 1989, near the mid-point of

the Trinity Estuary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-18

Figure 6-14. Neap tide dye simulations for the Trinity Estuary. . . . . . . . . . . . . 6-19

Figure 6-15. Spring Tide dye simulations for the Trinity Estuary. . . . . . . . . . . . 6-19

Figure 6-16. Predicted average, minimum and maximum bacterial concentrations for

March versus distance from the mouth of the Trinity Estuary assuming

no die-off. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-20

Figure 6-17. Predicted average bacterial concentrations during March, with standard

deviations, versus distance from the mouth of the Trinity Estuary

assuming no die-off. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-20

Figure 6-18. Predicted average, maximum and minimum bacterial concentrations

during March versus distance from the mouth of the Trinity Estuary

assuming a bacterial die-off rate of 1.0 day -1. . . . . . . . . . . . . . . 6-21

Figure 6-19. Predicted average bacterial concentrations, with their standard

deviations, for March versus distance from the mouth of the Trinity

Estuary, assuming a bacterial die-off rate of 1.0 day-1. . . . . . . . . . 6-21

Figure 6-20. Comparison of predicted bacterial concentrations for different die-off

rates versus distance from the mouth of the Trinity Estuary. . . . . . . 6-22

Figure 6-21. Morphometry of the Rhode Estuary. . . . . . . . . . . . . . . . . . . . 6-23

Figure 6-22. Mean salinity profile for the Rhode Estuary. . . . . . . . . . . . . . . . 6-23

Figure 6-23. Results of the Rhode Estuary tracer study. . . . . . . . . . . . . . . . 6-24

Figure 6-24. Average monthy flow at the Highway 64 USGS gauge . . . . . . . . . 6-24

vii
Figure 6-25. Mean monthly temperatures at the Highway 64 Gauge . . . . . . . . . 6-24

Figure 6-26. Mean depths for the Rhode Estuary versus distance upestuary from its

mouth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25

Figure 6-27. Mean widths of the Rhode Estuary versus distance upestuary from its

mouth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25

Figure 6-28. Mean depths of Holcomb Creek versus distance upstream from its

mouth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26

Figure 6-29. Mean widths for Holcomb Creek versus distance upstream from its

mouth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26

Figure 6-30. Model segmentation for the Rhode Estuary. . . . . . . . . . . . . . . . 6-28

Figure 6-31. Comparison of predicted and observed salinities for different values of

the dispersion coefficient (m2

/s). . . . . . . . . . . . . . . . . . . . . . 6-28

Figure 6-32. Comparison of measured and observed dye concentrations. . . . . . . 6-29

Figure 6-33. Measured and predicted DO concentrations in the Rhode Estuary

versus distance upestuary from its mouth. . . . . . . . . . . . . . . . . 6-30

Figure 6-34. Predicted and observed NBOD and CBOD concentrations in the Rhode

Estuary versus distance upestuary from its mouth. . . . . . . . . . . . 6-30

Figure 6-35. Predicted and observed NBOD and CBOD concentrations in the Rhode

Estuary versus distance upestuary from its mouth. . . . . . . . . . . . 6-31

Figure 6-36. Measured and predicted DO concentrations in Holcomb Creek versus

distance upstream from its mouth. . . . . . . . . . . . . . . . . . . . . 6-31

Figure 6-37. Comparison of DO predictions under existing and proposed conditions

for the Rhode City WWTP. . . . . . . . . . . . . . . . . . . . . . . . 6-32

Figure 6-38. Deep Bay location map. . . . . . . . . . . . . . . . . . . . . . . . . . 6-33

Figure 6-39. Deep Bay navigation chart. . . . . . . . . . . . . . . . . . . . . . . . 6-34

Figure 6-40. Deep Bay model segmentation. . . . . . . . . . . . . . . . . . . . . . 6-35

Figure 6-41. Deep Bay salinity Apr-Aug mean response. . . . . . . . . . . . . . . . 6-36

Figure 6-42. Deep Bay dye study June 15, surface. . . . . . . . . . . . . . . . . . . 6-37

Figure 6-43. Deep Bay dye study center channel, surface and bottom. . . . . . . . . 6-38

Figure 6-44. Deep Bay dye study center channel, surface. . . . . . . . . . . . . . . 6-38

viii
Figure 6-45. Deep Bay total N and P - August 11, surface and bottom. . . . . . . . 6-39

Figure 6-46. Deep Bay dissolved oxygen - June-Sept, surface and bottom. . . . . . 6-40

Figure 6-47. Deep Bay phytoplankton - June-Sept, surface. . . . . . . . . . . . . . 6-40

Figure 6-49. Boatwona Estuary depth chart. . . . . . . . . . . . . . . . . . . . . . 6-43

Figure 6-48. City of Boatwona waste water treatment plant location. . . . . . . . . . 6-43

Figure 6-50. Boatwona Estuary flow pattern. . . . . . . . . . . . . . . . . . . . . . 6-44

Figure 6-51. Ammonia simulation results. . . . . . . . . . . . . . . . . . . . . . . . 6-45

Figure 6-52. Hydrophobic (Alachlor) chemical simulation for example 6. . . . . . . . 6-46

ix

List of Tables

Table 4-1. Estuarine Transport Data . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5

Table 4-2. Water Quality Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9

Table 5-1. Guidance Manuals for Rates, Constants, and Kinetics Formulations for

Conventional and Toxic Pollutants . . . . . . . . . . . . . . . . . . . . . 5-5

Table 5-2. Outline of a General Calibration Procedure for Water Quality Models for

Conventional Pollutants when Baroclinic Circulation Effects are

Unimportant [McCutcheon, (1989)] . . . . . . . . . . . . . . . . . . . . . 5-5

Table 5-3. Guidance on the Selection of Model Coefficients and Parameters -

Phase I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6

Table 5-4. Guidance on the Selection of Model Coefficients and Parameters -

Phase II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7

Table 5-5. Guidance on the Selection of Model Coefficients and Parameters -

Phase III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8

Table 5-6. Relative Error in a Number of Estuarine Model Calibrations for Dissolved

Oxygen. [Thomann (1982) and Ambrose and Roesch (1982)] . . . . . . 5-13

Table 5-7. Hydrodynamic Model Error Statistics for the Delaware Estuary

[Ambrose and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . 5-14

Table 5-8. Hydrodynamic Model Error Statistics for the Potomac Estuary

[Ambrose and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . 5-14

Table 5-9. Transport Model Error Statistics for the Delaware Estuary

[Ambrose and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . 5-15

Table 5-10. Transport Model Error Statistics for the Potomac Estuary

[Ambrose and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . 5-15

Table 5-11. Water Quality Model Error Statistics for the Delaware Estuary [Ambrose

and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16

Table 5-12. Water Quality Model Error Statistics for the Potomac Estuary, 1965-1975

[Amborose and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . 5-16

Table 5-13. Chlorophyll-a Model Error Statistics for the Potomac Estuary, 1977-78

[Ambrose and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . 5-17

Table 5-14. Water Quality Model Error Statistics for the Potomac Estuary, 1977-1978

[Ambrose and Roesch (1982)] . . . . . . . . . . . . . . . . . . . . . . 5-17

xi
Table 5-15. Preliminary Guidance on Error Statistic Criteria for Calibrating Estuarine

Water Quality Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18

Table 5-16. Environmental Properties Affecting Interphase Transport and

Transformation Processes [Ambrose (1987)] . . . . . . . . . . . . . . . 5-19

Table 5-17. Chemical Properties Affecting Interphase Transport and

Transformation Processes [Ambrose (1987)] . . . . . . . . . . . . . . . 5-20

Table 5-18. Predicted Chemical Loss Rate Constants in the Delaware River near

Philadelphia [Ambrose (1987)] . . . . . . . . . . . . . . . . . . . . . . 5-21

Table 5-19. Observed and Predicted High Slack Concentrations at Baxter

[Ambrose (1987)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-21

Table 5-20. Main Sources of Criteria to Protect Designated Water Uses . . . . . . . 5-24

Table 5-21. Relationship between Various Friction Factors used to Quantify Friction

Loss in Estuaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-29

Table 5-22. Values of the Manning n for Different Types of Vegetation in Wetland

Areas [Chow (1959) and Jarrett (1985)] . . . . . . . . . . . . . . . . . 5-31

Table 5-23. Manning n Corrections for Ripples and Dunes . . . . . . . . . . . . . . 5-32

Table 5-24. Manning n Corrections for the Relative Effect of Obstructions . . . . . . 5-32

Table 5-25. Manning n Corrections for Changes in Channel Depth and Width . . . . 5-32

Table 5-26. Adjustments for the Manning n due to Vegetation [Jarret (1985)] . . . . 5-32

Table 5-27. Reach Characteristics for a Hypothetical Estuary and Calculation of the

Manning n Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-35

Table 5-28. Vertical Eddy Viscosity Formulations for Flow in Estuaries . . . . . . . . 5-41

Table 5-29. Observed Values of the Constants in Various Forms of the

Munk-Anderson Stability Function . . . . . . . . . . . . . . . . . . . . 5-43

Table 5-30a.Various Means of Representing the Stability of Stratification and the

Relationship between Various Parameters . . . . . . . . . . . . . . . . 5-44

Table 5-30b. Tidally Averaged Longitudinal Dispersion Coefficients Observed in

Selected One Dimensional Estuaries [Hydroscience (1971), Officer

(1976) and Bowie et al. (1985)] . . . . . . . . . . . . . . . . . . . . . . 5-49

Table 5-31. Longitudinal Dispersion Coefficients Observed in Selected Two

Dimensional Estuarine and Coastal Water Studies

[Hydroscience (1971), Officer (1976) and Bowie et al. (1985)] . . . . . . 5-50

xii
Table 5-32. Lateral Dispersion Coefficients in Estuaries and Coastal Waters

[Officer (1976)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-51

Table 5-33. Evaporation Formula for Lakes and Reservoirs

[Ryan and Harleman (1973)] . . . . . . . . . . . . . . . . . . . . . . . 5-52

Table 5-34. Evaporation Formulas [Wunderlich (1972) and McCutcheon (1989)] . . 5-53

Table 5-35. Reported Decay Rate Coefficients for Bacteria and Viruses in

Seawater and Brackish Water [Thomann and Mueller (1987),

Bowie et al. (1985), and Velz (1984)] . . . . . . . . . . . . . . . . . . . 5-55

Table 5-36. Reported Decay Rate Coefficients for Bacteria and Viruses in

Freshwater and Stormwater [Thomann and Mueller (1987),

Bowie et al. (1985), and Velz (1984)] . . . . . . . . . . . . . . . . . . . 5-56

Table 5-37. Settling Velocities in m/day at 20 o

C for Inorganic Particles

[Ambrose et al. (1987)] . . . . . . . . . . . . . . . . . . . . . . . . . . 5-58

Table 5-38. Settling Velocities for Phytoplankton . . . . . . . . . . . . . . . . . . . 5-58

Table 5-39. First-Order Nitrification Rate Constants Observed in Estuaries

[Bowie et al. (1985)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-61

Table 5-40. Rate Coefficients for Nitrogen Transformations [Bowie et al. (1985)] . . 5-62

Table 5-41. Rate Coefficients for Denitrification [Bowie et al. (1985)] . . . . . . . . . 5-63

Table 5-42. Rate Coefficients for Phosphorus Transformations

[Bowie et al. (1985)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-64

Table 5-43. Formulas to Estimate Reaeration Coefficients for Deeper, Bottom

Boundary Generated Shear Flows [Bowie et al. (1985), Rathbun

(1977), Gromiec et al. (1983), and McCutcheon (1989)] . . . . . . . . . 5-66

Table 5-44. Constant Values of Surface Mass Transfer Coefficients Applied in the

Modeling of Estuaries, Coastal Waters, and Lakes

[Bowie et al. (1985)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-68

Table 5-45. Empirical Wind Speed Relationships for Mass Transfer and Reaeration

Coefficients [Bowie et al. (1985)] . . . . . . . . . . . . . . . . . . . . . 5-68

Table 5-46. Transfer-Wind Correlations [O’Connor (1983)] . . . . . . . . . . . . . . 5-69

Table 5-47. Measured Values of Sediment Oxygen Demand in Estuaries

and Marine Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-70

Table 6-1. Observed Conditions During Survey . . . . . . . . . . . . . . . . . . . . 6-5

xiii
Table 6-2. Predicted Concentrations Throughout Estuary Under Observed

Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6

Table 6-3. Predicted Concentrations Throughout Estuary for Multiple Discharge

Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-7

Table 6-4. Calculation Table for Conservative Pollutant by Fraction of Freshwater

Method [Millls et al. (1985)] . . . . . . . . . . . . . . . . . . . . . . . . . 6-9

Table 6-5. Completed Calculation Table for Fraction of Freshwater Method . . . . . 6-9

Table 6-6. Calculation Table for Non-Conservative Pollutant by Modified Tidal Prism

Method [Mills et al. (1985)] . . . . . . . . . . . . . . . . . . . . . . . . 6-10

Table 6-7. Completed Calculation Table for Non-Conservative Pollutant by Modified

Tidal Prism Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-11

Table 6-8. Treatment Plant Effluent Characteristics . . . . . . . . . . . . . . . . . 6-14

Table 6-9. Tidal Periods, Amplitudes and Phases for the Trinity Estuary during

March, 1989 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-15

Table 6-10. Treatment Plant Effluent Characteristics . . . . . . . . . . . . . . . . . 6-27

Table 6-11. Summary of Deep Bay Tidal Monitoring Data . . . . . . . . . . . . . . 6-33

Table 6-12. Summary of Deep Bay Estuarine Data . . . . . . . . . . . . . . . . . . 6-34

Table 6-13. Deep River Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-34

Table 6-14. Summary of Athens POTW Effluent Data . . . . . . . . . . . . . . . . 6-34

Table 6-15. Boatwona Estuary Survey Data . . . . . . . . . . . . . . . . . . . . . 6-43

Table 6-16. Boatwona River Survey Data . . . . . . . . . . . . . . . . . . . . . . . 6-43

xiv
Glossary

Acute Toxicity1 - Any toxic effect that is produced

within a short period of time, usually 24-96 hours.

Although the effect most frequently considered is

mortality, the end result of acute toxicity is not necessarily death. Any harmful biological effect may be the

result.

Aerobic1 - Refers to life or processes occurring only

in the presence of free oxygen; refers to a condition

characterized by an excess of free oxygen in the

aquatic environment.

Algae (Alga)1 - Simple plants, many microscopic,

containing chlorophyll. Algae form the base of the

food chain in aquatic environments. Some species

may create a nuisance when environmental conditions are suitable for prolific growth.

Allochthonous1

- Pertaining to those substances, materials or organisms in a waterway which originate

outside and are brought into the waterway.

Anaerobic2 - Refers to life or processes occurring in

the absence of free oxygen; refers to conditions characterized by the absence of free oxygen.

Autochthonous1 - Pertaining to those substances,

materials, or organisms originating within a particular

waterway and remaining in that waterway.

Autotrophic1 - Self nourishing; denoting those organisms that do not require an external source of organic

material but can utilize light energy and manufacture

their own food from inorganic materials; e.g., green

plants, pigmented flagellates.

Bacteria1

- Microscopic, single-celled or noncellular

plants, usually saprophytic or parasitic.

Benthal Deposit2 - Accumulation on the bed of a

watercourse of deposits containing organic matter

arising from natural erosion or discharges of wastewaters.

Benthic Region1 - The bottom of a waterway; the

substratum that supports the benthos.

Benthal Demand2 - The demand on dissolved oxygen

of water overlying benthal deposits that results from

the upward diffusion of decomposition products of the

deposits.

Benthos1 - Organisms growing on or associated principally with the bottom of waterways. These include:

(1) sessile animals such as sponges, barnacles, mussels, oysters, worms, and attached algae; (2) creeping forms such as snails, worms, and insects; (3)

burrowing forms, which include clams, worms, and

some insects; and (4) fish whose habits are more

closely associated with the benthic region than other

zones; e.g., flounders.

Biochemical Oxygen Demand2 - A measure of the

quantity of oxygen utilized in the biochemical oxidation of organic matter in a specified time and at a

specific temperature. It is not related to the oxygen

requirements in chemical combustion, being determined entirely by the availability of the material as a

biological food and by the amount of oxygen utilized

by the microorganisms during oxidation. Abbreviated

BOD.

Biological Magnification1 - The ability of certain organisms to remove from the environment and store in

their tissues substances present at nontoxic levels in

the surrounding water. The concentration of these

substances becomes greater each higher step in the

food chain.

Bloom1 - A readily visible concentrated growth or

aggregation of minute organisms, usually algae, in

bodies of water.

Brackish Waters1 - Those areas where there is a

mixture of fresh and salt water; or, the salt content is

greater than fresh water but less than sea water; or,

the salt content is greater than in sea water.

Channel Roughness2 - That roughness of a channel,

including the extra roughness due to local expansion

or contraction and obstacles, as well as the roughness

of the stream bed proper; that is, friction offered to the

flow by the surface of the bed of the channel in contact

with the water. It is expressed as roughness coefficient in the velocity formulas.

Chlorophyll1 - Green photosynthetic pigment present

in many plant and some bacterial cells. There are

seven known types of chlorophyll; their presence and

abundance vary from one group of photosynthetic

organisms to another.

Chronic Toxicity1 - Toxicity, marked by a long duration, that produces an adverse effect on organisms.

The end result of chronic toxicity can be death although the usual effects are sublethal; e.g., inhibits

reproduction, reduces growth, etc. These effects are

reflected by changes in the productivity and population structure of the community.

xv
Coastal Waters1 - Those waters surrounding the continent which exert a measurable influence on uses of

the land and on its ecology. The Great Lakes and the

waters to the edge of the continental shelf.

Component Tide2 - Each of the simple tides into

which the tide of nature is resolved. There are five

principal components; principal lunar, principal solar,

N2, K, and O. There are between 20 and 30 components which are used in accurate predictions of tides.

Coriolis Effect2

- The deflection force of the earth’s

rotation. Moving bodies are deflected to the right in

the northern hemisphere and to the left in the southern

hemisphere.

Datum2 - An agreed standard point or plane of state

elevation, noted by permanent bench marks on some

solid immovable structure, from which elevations are

measured or to which they are referred.

Density Current2 - A flow of water through a larger

body of water, retaining its unmixed identity because

of a difference in density.

Deoxygenation2 - The depletion of the dissolved oxygen in a liquid either under natural conditions associated with the biochemical oxidation of organic matter

present or by addition of chemical reducing agents.

Diagenetic Reaction - Chemical and physical

changes that alter the characteristics of bottom sediments. Examples of chemical reactions include oxidation of organic materials while compaction is an

example of a physical change.

Dispersion2 - (1) Scattering and mixing. (2) The mixing of polluted fluids with a large volume of water in a

stream or other body of water.

Dissolved Oxygen2 - The oxygen dissolved in water,

wastewater, or other liquid, usually expressed in milligrams per liter, or percent of saturation. Abbreviated

DO.

Diurnal2 - (1) Occurring during a 24-hr period; diurnal

variation. (2) Occurring during the day time (as opposed to night time). (3) In tidal hydraulics, having a

period or cycle of approximately one tidal day.

Drought2 - In general, an extended period of dry

weather, or a period of deficient rainfall that may

extend over an indefinite number of days, without any

quantitative standard by which to determine the degree of deficiency needed to constitute a drought.

Qualitatively, it may be defined by its effects as a dry

period sufficient in length and severity to cause at

least partial crop failure or impair the ability to meet a

normal water demand.

Ebb Tide1

- That period of tide between a high water

and the succeeding low water; falling tide.

Enrichment1 - An increase in the quantity of nutrients

available to aquatic organisms for their growth.

Epilimnion1 - The water mass extending from the

surface to the thermocline in a stratified body of water;

the epilimnion is less dense that the lower waters and

is wind-circulated and essentially homothermous.

Estuary1 - That portion of a coastal stream influenced

by the tide of the body of water into which it flows; a

bay, at the mouth of a river, where the tide meets the

river current; an area where fresh and marine water

mix.

Euphotic Zone1 - The lighted region of a body of water

that extends vertically from the water surface to the

depth at which photosynthesis fails to occur because

of insufficient light penetration.

Eutrophication1 - The natural process of the maturing

(aging) of a lake; the process of enrichment with

nutrients, especially nitrogen and phosphorus, leading to increased production of organic matter.

Firth1 - A narrow arm of the sea; also the opening of

a river into the sea.

Fjord (Fiord)1 - A narrow arm of the sea between

highlands.

Food Chain1 - Dependence of a series of organisms,

one upon the other, for food. The chain begins with

plants and ends with the largest carnivores.

Flood Tide2 - A term indiscriminately used for rising

tide or landward current. Technically, flood refers to

current. The use of the terms “ebb” and “flood” to

include the vertical movement (tide) leads to uncertainty. The terms should be applied only to the horizontal movement (current).

Froude’s Number2 - A numerical quantity used as an

index to characterize the type of flow in a hydraulic

structure that has the force of gravity (as the only force

producing motion) acting in conjunction with the resisting force of inertia. It is equal to the square of

characteristic velocity (the mean, surface, or maximum velocity) of the system, divided by the product

of a characteristic linear dimension, such as diameter

or expressed in consistent units so that the combinations will be dimensionaless. The number is used in

xvi
open-channel flow studies or in cases in which the free

surface plays an essential role in influencing motion.

Heavy Metals2 - Metals that can be precipitated by

hydrogen sulfide in acid solution, for example, lead,

silver, gold, mercury, bismuth, copper.

Heterotrophic1 - Pertaining to organisms that are

dependent on organic material for food.

Hydraulic Radius2 - The right cross-sectional area of

a stream of water divided by the length of that part of

its periphery in contact with its containing conduit; the

ratio of area to wetted perimeter. Also called hydraulic

mean depth.

Hydrodynamics2 - The study of the motion of, and the

forces acting on, fluids.

Hydrographic Survey2 - An instrumental survey

made to measure and record physical characteristics

of streams and other bodies of water within an area,

including such things as location, areal extent and

depth, positions and locations of high-water marks,

and locations and depths of wells.

Inlet1 - A short, narrow waterway connecting a bay,

lagoon, or similar body of water with a large parent

body of water; an arm of the sea, or other body of

water, that is long compared to its width, and that may

extend a considerable distance inland.

Inorganic Matter2 - Mineral-type compounds that are

generally non-volatile, not combustible, and not biodegradable. Most inorganic-type compounds, or reactions, are ionic in nature, and therefore, rapid

reactions are characteristic.

Lagoon1 - A shallow sound, pond, or channel near or

communicating with a larger body of water.

Limiting Factor1 - A factor whose absence, or excessive concentration, exerts some restraining influence

upon a population through incompatibility with species requirements or tolerance.

Manning Formula2 - A formula for open-channel flow,

published by Manning in 1890, which gives the value

of c in the Chezy formula.

Manning Roughness Coefficient2 - The roughness

coefficient in the Manning formula for determination

of the discharge coefficient in the Chezy formula.

Marsh1 - Periodically wet or continually flooded area

with the surface not deeply submerged. Covered

dominantly with emersed aquatic plants; e.g., sedges,

cattails, rushes.

Mean Sea Level2 - The mean plane about which the

tide oscillates; the average height of the sea for all

stages of the tide.

Michaelis-Menton Equation2 - A mathematical expression to describe an enzyme-catalyzed biological

reaction in which the products of a reaction are described as a function of the reactants.

Mineralization2 - The process by which elements

combined in organic form in living or dead organisms

are eventually reconverted into inorganic forms to be

made available for a fresh cycle of plant growth. The

mineralization of organic compounds occurs through

combustion and through metabolism by living animals. Microorganisms are ubiquitous, possess extremely high growth rates and have the ability to

degrade all naturally occurring organic compounds.

Modeling2 - The simulation of some physical or abstract phenomenon or system with another system

believed to obey the same physical laws or abstract

rules of logic, in order to predict the behavior of the

former (main system) by experimenting with latter

(analogous system).

Monitoring2 - Routine observation, sampling and testing of designated locations or parameters to determine efficiency of treatment or compliance with

standards or requirements.

Mouth2 - The exit or point of discharge of a stream into

another stream or a lake, or the sea.

Nautical Mile2 - A unit of distance used in ocean

navigation. The United States nautical mile is defined

as equal to one-sixteenth of a degree of a great circle

on a sphere with a surface equal to the surface of the

earth. Its value, computed for the Clarke spheroid of

1866, is 1,853.248 m (6,080.20ft). The International

nautical mile is 1,852 m (6,070.10 ft).

Nanoplankton2 - Very minute plankton not retained in

a plankton net equipped with no. 25 silk bolting cloth

(mesh, 0.03 to 0.04 mm.).

Neap Tides1 - Exceptionally low tides which occur

twice each month when the earth, sun and moon are

at right angles to each other; these usually occur

during the moon’s first and third quarters.

Neuston2 - Organisms associated with, or dependent

upon, the surface film (air-water) interface of bodies

of water.

Nitrogenous Oxygen Demand (NOD)2 - A quantitative measure of the amount of oxygen required for the

biological oxidation of nitrogenous material, such as

xvii
ammonia nitrogen and organic nitrogen, in wastewater; usually measured after the carbonaceous oxygen

demand has been satisfied.

Nutrients1 - Elements, or compounds, essential as

raw materials for organism growth and development;

e.g., carbon, oxygen, nitrogen, phosphorus, etc.

Organic1 - Refers to volatile, combustible, and sometimes biodegradable chemical compounds containing

carbon atoms (carbonaceous) bonded together and

with other elements. The principal groups of organic

substances found in wastewater are proteins, carbohydrates, and fats and oils.

Oxygen Deficit1 - The difference between observed

oxygen concentration and the amount that would

theoretically be present at 100% saturation for existing conditions of temperature and pressure.

Pathogen1 - An organism or virus that causes a disease.

Periphyton (Aufwuchs)1 - Attached microscopic organisms growing on the bottom, or other submersed

substrates, in a waterway.

Photosynthesis1 - The metabolic process by which

simple sugars are manufactured from carbon dioxide

and water by plant cells using light as an energy

source.

Phytoplankton1 - Plankton consisting of plant life.

Unattached microscopic plants subject to movement

by wave or current action.

Plankton1 - Suspended microorganisms that have

relatively low powers of locomotion, or that drift in the

water subject to the action of waves and currents.

Quality2 - A term to describe the composite chemical,

physical, and biological characteristics of a water with

respect to it’s suitability for a particular use.

Reaeration2 - The absorption of oxygen into water

under conditions of oxygen deficiency.

Respiration1 - The complex series of chemical and

physical reactions in all living organisms by which the

energy and nutrients in foods is made available for

use. Oxygen is used and carbon dioxide released

during this process.

Roughness Coefficient2 - A factor, in the Chezy,

Darcy-Weisbach, Hazen-Williams, Kutter, Manning,

and other formulas for computing the average velocity

of flow of water in a conduit or channel, which represents the effect of roughness of the confining material

on the energy losses in the flowing water.

Seiche1 - Periodic oscillations in the water level of a

lake or other landlocked body of water due to unequal

atmospheric pressure, wind, or other cause, which

sets the surface in motion. These oscillations take

place when a temporary local depression or elevation

of the water level occurs.

Semidiurnal2 - Having a period or cycle of approximately one half of a tidal day. The predominating type

of tide throughout the world is semidiurnal, with two

high waters and two low waters each tidal day.

Slack Water2 - In tidal waters, the state of a tidal

current when its velocity is at a minimum, especially

the moment when a reversing current changes direction and its velocity is zero. Also, the entire period of

low velocity near the time of the turning of the current

when it is too weak to be of any practical importance

in navigation. The relation of the time of slack water

to the tidal phases varies in different localities. In

some cases slack water occurs near the times of high

and low water, while in other localities the slack water

may occur midway between high and low water.

Spring Tide1 - Exceptionally high tide which occurs

twice per lunar month when there is a new or full

moon, and the earth, sun, and moon are in a straight

line.

Stratification (Density Stratification)1 -Arrangement of water masses into separate, distinct, horizontal layers as a result of differences in density; may be

caused by differences in temperature, dissolved or

suspended solids.

Tidal Flat1 - The sea bottom, usually wide, flat, muddy

and nonproductive, which is exposed at low tide. A

marshy or muddy area that is covered and uncovered

by the rise and fall of the tide.

Tidal Prism2 - (1) The volume of water contained in a

tidal basin between the elevations of high and low

water. (2) The total amount of water that flows into a

tidal basin or estuary and out again with movement of

the tide, excluding any fresh-water flows.

Tidal Range2 - The difference in elevation between

high and low tide at any point or locality.

Tidal Zone (Eulittoral Zone, Intertidal Zone)1 - The

area of shore between the limits of water level fluctuation; the area between the levels of high and low tides.

Tide1 - The alternate rising and falling of water levels,

twice in each lunar day, due to gravitational attraction

xviii
of the moon and sun in conjunction with the earth’s

rotational force.

Tide Gage2 - (1) A staff gage that indicates the height

of the tide. (2) An instrument that automatically registers the rise and fall of the tide. In some instruments,

the registration is accomplished by printing the heights

at regular intervals; in others by a continuous graph in

which the height of the tide is represented by ordinates

of the curve and the corresponding time by the abscissae.

Toxicant1 - A substance that through its chemical or

physical action kills, injures, or impairs an organism;

any environmental factor which, when altered, produces a harmful biological effect.

Water Pollution1 - Alteration of the aquatic environment in such a way as to interfere with a designated

beneficial use.

Water Quality Criteria1 - A scientific requirement on

which a decision or judgement may be based concerning the suitability of water quality to support a designated use.

Water Quality Standard1 - A plan that is established

by governmental authority as a program for water

pollution prevention and abatement.

Zooplankton2 - Plankton consisting of animal life.

Unattached microscopic animals having minimal capability for locomotion.

1Rogers, B.G., Ingram, W.T., Pearl, E.H., Welter, L.W.

(Editors). 1981, Glossary, Water and Wastewater

Control Engineering, Third Edition, American Public

Health Association, American Society of Civil Engineers, American Water Works Association, Water

Pollution Control Federation.

2

Matthews, J.E., 1972, Glossary of Aquatic Ecological

Terms, Manpower Development Branch, Air and

Water Programs Division, EPA, Oklahoma.

xix

Acknowledgements

The contents of this section have been removed to

comply with current EPA practice.

xxi

Executive Summary

The Technical Guidance Manual for Performing Waste

Load Allocations, Book III: Estuaries is the third in a

series of manuals providing technical information and

policy guidance for the preparation of waste load allocations (WLAs) that are as technically sound as current state of the art permits. The objective of such load

allocations is to ensure that water quality conditions

that protect designated beneficial uses are achieved.

This book provides technical guidance for performing

waste load allocations in estuaries.

PART I: ESTUARIES AND WASTE LOAD

ALLOCATION MODELS

Introduction

Estuaries are coastal bodies of water where fresh

water meets the sea. Most rivers and their associated

pollutant loads eventually flow into estuaries. The complex loading, circulation, and sedimentation processes

make water quality assessment and waste load allocation in estuaries difficult. Transport and circulation

processes in estuaries are driven primarily by river flow

and tidal action. As a consequence of its complex

transport processes, estuaries cannot be treated as

simple advective systems such as many rivers.

Wastewater discharges into estuaries can affect water

quality in several ways, both directly and indirectly. In

setting limits on wastewater quantity and quality, the

following potential problems should be assessed: salinity, sediment, pathogenic bacteria, dissolved oxygen

depletion, nutrient enrichment and overproduction,

aquatic toxicity, toxic pollutants and bioaccumulation

and human exposure.

A WLA provides a quantitative relationship between

the waste load and the instream concentrations or

effects of concern as represented by water quality

standards. During the development of a WLA, the user

combines data and model first to describe present

conditions and then to extrapolate to possible future

conditions. The WLA process sequentially addresses

the topics of hydrodynamics, mass transport, water

quality kinetics, and for some problems, bioaccumulation and toxicity.

For each of the topics addressed in a modeling study,

several steps are applied in an iterative process: problem identification, model identification, initial model

calibration, sensitivity analysis, model testing, refinement, and validation.

After the WLAs have been put into effect, continued

monitoring, post-audit modeling and refinement should

lead to more informed future WLAs.

Overview of Processes Affecting Estuarine

Water Quality

The estuarine waste load allocation process requires

a fundamental understanding of the factors affecting

water quality and the representation of those processes in whatever type of model is applied (conceptual

or mathematical) in order to determine the appropriate

allocation of load. Insight into processes affecting

water quality may be obtained through examination of

the schemes available for their classification. Estuaries

have typically been classified based on their geomorphology and patterns of stratification and mixing. However, each estuary is to some degree unique and it is

often necessary to consider the fundamental processes impacting water quality.

To determine the fate and affects of water quality

constituents it is necessary first to determine processes impacting their transport. That transport is affected by tides, fresh water inflow, friction at the fluid

boundaries and its resulting turbulence, wind and atmospheric pressure, and to a lesser degree (for some

estuaries) the effects of the earth’s rotation (Coriolis

force). The resulting transportation patterns may be

described (determined from field studies) in waste load

allocation studies, or, as is becoming more frequently

the case, estimated using hydrodynamic models. Hydrodynamic models are based on descriptions of the

processes affecting circulation and mixing using equations based on laws of conservation of mass and

momentum. The fundamental equations generally include: (A) the conservation of water mass (continuity),

(B) conservation of momentum, and (C) conservation

of constituent mass.

An important aspect of estuarine WLA modeling often

is the capability to simulate sediment transport and

sediment/water interactions. Sediments not only affect

water transparency, but can carry chemicals such as

nutrients and toxic substances into receiving waters.

Unlike rivers, which have reasonably constant water

quality conditions, the large changes in salinity and pH

in an estuary directly affect the transport behavior of

many suspended solids. Many colloidal particles agglomerate and settle in areas of significant salinity

gradients. Processes impacting sediment transport

include settling, resuspension, scour and erosion, coagulation and flocculation.

xxiii
The water quality parameters of interest vary with the

objectives of the waste load allocation study, from

“conventional pollutants” (e.g. organic waste, dissolved oxygen and nutrients) to toxic organics and

trace metals.

The focus of WLA models of conventional pollutants is

often DO and biochemical oxygen demand (BOD) as

a general measure of the health of the system, or the

focus can be primary productivity when eutrophication

is the major concern. Conventional WLA models usually include temperature, major nutrients, chemical

characteristics, detritus, bacteria, and primary producers. WLA models may include higher trophic levels (i.e.

zooplankton and fish) because of higher trophic level

effects on other more important variables, such as

phytoplankton, BOD and DO. Synthetic organic chemicals include a wide variety of toxic materials whose

waste loads are allocated based upon threshold concentrations as well as tolerable durations and frequencies of exposure. These pollutants may ionize and

different forms may have differing toxicological affects.

The transport of the materials also may be affected by

sorption and they can degrade through such processes as volatilization, biodegradation, hydrolysis, and

photolysis.

Trace metals may be of concern in many estuaries due

to their toxicological effects. The toxicity of trace metals

and their transport is affected by their form. Upon entry

to a surface water body, metal speciation may change

due to complexation, precipitation, sorption, and redox

reactions. Metals concentrations are diluted further by

additional stream flow and mixing. Physical loss can

be caused by settling and sedimentation, whereas a

physical gain may be caused by resuspension.

Model Identification and Selection

The first steps in the modeling process are model

identification and selection. The goals are to identify

the simplest conceptual model that includes all the

important estuarine phenomena affecting the water

quality problems, and to select the most useful analytical formula or computer model for calculating waste

load allocations. During model identification, available

information is gathered and organized to construct a

coherent picture of the water quality problem. There

are four basic steps in model identification: establish

study objectives and constraints, determine water

quality pollutant interactions, determine spatial extent

and resolution, and determine temporal extent and

resolution. Following model identification, another important step is advised: perform rapid, simple screening calculations to gain a better understanding of

expected pollutant levels and the spatial extent of

water quality problems.

The first step in identifying an appropriate WLA model

for a particular site is to review the applicable water

quality standards and the beneficial uses of the estuary

to be protected. Local, state, and federal regulations

may contribute to a set of objectives and constraints.

The final result of this step should be a clear understanding of the pollutants and water quality indicators,

the areas, and the time scales of interest.

After the pollutants and water quality indicators are

identified, the significant water quality reactions must

be determined. These reactions must directly or indirectly link the pollutants to be controlled with the primary water quality indicators. All other interacting

water quality constituents thought to be significant

should be included at this point. This can best be done

in a diagram or flow chart representing the mass

transport and transformations of water quality constituents in a defined segment of water. The final result of

this step should be the assimilation of all the available

knowledge of a system in a way that major water

quality processes and ecological relationships can be

evaluated for inclusion in the numerical model description.

The next step is to specify the spatial extent, dimensionality, and scale (or computational resolution) of the

WLA model. This may be accomplished by determining the effective dimensionality of the estuary as a

whole, defining the boundaries of the study area, then

specifying the required dimensionality and spatial

resolution within the study area. The effective dimensionality of an estuary includes only those dimensions

over which hydrodynamic and water quality gradients

significantly affect the WLA analysis. Classification

and analysis techniques are available. Specific

boundaries of the study area must be established, in

general, beyond the influence of the discharge(s) being evaluated. Data describing the spatial gradients of

important water quality constituents within the study

area should be examined. Dye studies can give important information on the speed and extent of lateral and

vertical mixing. It is clear that choice of spatial scale

and layout of the model network requires considerable

judgment.

The final step in model identification is to specify the

duration and temporal resolution of the WLA model.

The duration of WLA simulations can range from days

to years, depending upon the size and transport characteristics of the study area, the reaction kinetics and

forcing functions of the water quality constituents, and

the strategy for relating simulation results to the regulatory requirements. One basic guideline applies in all

cases - the simulations should be long enough to

eliminate the effect of initial conditions on important

water quality constituents at critical locations.

xxiv
The temporal resolution of WLA simulations falls into

one of three categories - dynamic, quasi-dynamic, and

steady state. Dynamic simulations predict hour to hour

variations caused by tidal transport. Quasidynamic

simulations predict variations on the order of days to

months. The effects of tidal transport are time-averaged. Other forcing functions such as freshwater inflow, pollutant loading, temperature, and sunlight may

vary from daily to monthly. Steady state simulations

predict monthly to seasonal averages. All inputs are

time-averaged. Two schools of thought have persisted

regarding the utility of dynamic versus quasidynamic

and steady state simulations. For some problems the

choice is reasonably clear.

In general, if the regulatory need or kinetic response is

on the order of hours, then dynamic simulations are

required; if regulatory needs are long term averages

and the kinetic response is on the order of seasons to

years, then quasidynamic or steady simulations are

indicated.

The goal of model selection is to obtain a simulation

model that effectively implements the conceptual

model identified for the WLA. Models selected for

discussion here are general purpose, in the public

domain, and available from or supported by public

agencies. The selection of an estuarine WLA model

need not be limited to the models discussed in this

document. Other models that are available to a project

or organization should also be considered. The models

summarized in this report represent the typical range

of capabilities currently available. Estuarine WLA models can be classified as Level I to Level IV according

to the temporal and spatial complexity of the hydrodynamic component of the model. Level I includes desktop screening methodologies that calculate seasonal

or annual mean pollutant concentrations based on

steady state conditions and simplified flushing time

estimates. These models are designed to examine an

estuary rapidly to isolate trouble spots for more detailed analyses.

Level II includes computerized steady state or tidally

averaged quasidynamic simulation models, which

generally use a box or compartment-type network to

solve finite difference approximations to the basic partial differential equations. Level II models can predict

slowly changing seasonal water quality with an effective time resolution of 2 weeks to 1 month. Level III

includes computerized one-dimensional (1-d) and

quasi two-dimensional (2-d), dynamic simulation models. These real time models simulate variations in tidal

heights and velocities throughout each tidal cycle.

Their effective time resolution is usually limited to

average variability over one week because tidal input

parameters generally consist of only average or slowly

varying values. The effective time resolution could be

reduced to under 1 day given good representation of

diurnal water quality kinetics and precise tidal input

parameters. The required data and modeling effort are

usually not mobilized in standard WLAs. Level IV

consists of computerized 2-d and 3-d dynamic simulation models. Dispersive mixing and seaward boundary

exchanges are treated more realistically than in the

Level III 1-d models. These models are almost never

used for routine WLAs.

The effective time resolution of the Level IV models

can be less than 1 day with a good representation of

diurnal water quality and intratidal variations.

The advantages of Level I and II models lie in their

comparatively low cost and ease of application. The

disadvantages lie in their steady state or tidally averaged temporal scale. When hydrodynamics and pollutant inputs are rapidly varying, steady state models

are difficult to properly calibrate.

The dynamic models (Levels III and IV) have advantages over steady state and tidally averaged models

in representing mixing in partially mixed estuaries because advection is so much better represented. The

success with which these models can predict transient

violations depends upon both the accuracy and resolution of the loading and environmental data, and the

model’s treatment of short time scale kinetics such as

desorption or diurnal fluctuations in temperature, pH,

or sunlight. While dynamic models are capable of

predicting diurnal and transient fluctuations in water

quality parameters, the input data requirements are

much greater.

PART II: APPLICATION OF ESTUARINE

WASTE LOAD ALLOCATION MODELS

Monitoring Protocols for Calibration and

Validation of Estuarine Waste Load

Allocation Models

The monitoring data collected in support of a modeling

study is used to: (1) determine the type of model

application required (e.g. dimensionality, state variables); (2) perturb the model (e.g. loadings, flows); (3)

provide a basis for assigning rate coefficients and

model input parameters (model calibration); and (4)

determine if the model adequately describes the system (model evaluation).

The specific types of data and quantity required will

vary with the objectives of the WLA modeling study and

the characteristics of the estuary. Data are always

required to determine model morphometry, such as

depths and volumes (e.g. available from sounding data

xxv
or navigation charts). Data are also required for transport. Transport within the modeled system may either

be specified (measured, e.g. current meters) or computed from hydrodynamic models. Flows into the system must be measured, or in the case of the open

boundary, water surface elevations must be determined.

The water quality data required, beyond that needed

to quantify transport, will vary depending on how the

variables will be used and their anticipated impact on

the system. Data requirements will differ if the WLA

modeling study is intended for dissolved oxygen, eutrophication or toxics. Concentrations for all pertinent

water quality variables should be provided at the model

boundaries, providing the perturbation for model predictions, as well as at points within the waterbody to

provide a basis for estimating model parameters and

evaluating model predictions. Data should be available

to determine variations in water quality parameters

over space and time.

Planning monitoring studies should be a collaborative

effort of participants involved in budgeting, field collection, analysis and processing of data, quality assurance, data management and modeling activities.

Collaboration insures that fundamental design questions are properly stated so that the available resources are used in the most efficient manner possible

and that all critical data for modeling are collected. The

use of monitoring and modeling in an iterative fashion,

wherever possible, is often the most efficient means of

insuring that critical data are identified and collected.

A rigorous, well documented, quality assurance, quality control (QA/QC) plan should be an integral part of

any waste load allocation program.

Model Calibration, Validation, and Use

While models can be run with minimal data, their

predictions are subject to large uncertainty. Models are

best operated to interpolate between existing conditions or to extrapolate from existing to future conditions, such as in the projection of conditions under

anticipated waste loads. The confidence that can be

placed on those projections is dependent upon the

integrity of the model, and how well the model is

calibrated to that particular estuary, and how well the

model compares when evaluated against an independent data set (to that used for calibration).

Model calibration is necessary because of the semiempirical nature of present day (1989) water quality

models. Although the waste load allocation models

used in estuary studies are formulated from the mass

balance and, in many cases, from conservation of

momentum principles, most of the kinetic descriptions

in the models that describe the change in water quality

are empirically derived. These empirical derivations

contain a number of coefficients and parameters that

are usually determined by calibration using data collected in the estuary of interest.

Calibration alone is not adequate to determine the

predictive capability of a model for a particular estuary.

To map out the range of conditions over which the

model can be used to determine cause and effect

relationships, one or more additional independent sets

of data are required to determine whether the model is

predictively valid. This testing exercise, which also is

referred to as confirmation testing, defines the limits of

usefulness of the calibrated model. Without validation

testing, the calibrated model remains a description of

the conditions defined by the calibration data set. The

uncertainty of any projection or extrapolation of a

calibrated model would be unknown unless this is

estimated during the validation procedure.

In addition, the final validation is limited to the range of

conditions defined by the calibration and validation

data sets. The uncertainty of any projection or extrapolation outside this range also remains unknown. The

validation of a calibrated model, therefore, should not

be taken to infer that the model is predictively valid over

the full range of conditions that can occur in an estuary.

For example, a model validated over the range of

typical tides and low freshwater inflow may not describe conditions that occur when large inflows and

atypical tides occur.

This is especially true when processes such as sediment transport and benthic exchange occur during

atypical events but not during the normal, river flow and

tidal events typically used to calibrate and validate the

model.

Following model calibration and validation, several

types of analyses of model performance are of importance. First, a sensitivity analysis provides a method

to determine which parameters and coefficients have

the greatest impact on model predictions. Second,

there are a number of statistical tests that are useful

for defining when adequate agreement has been obtained between model simulations and measured conditions in order to estimate the confidence that may be

assigned to model predictions. Finally, a components

analysis indicates the relative contribution of processes to variations in predicted concentrations. For

example, the cause of violations of a dissolved oxygen

standard can be determined from the relative contribution of various loads and the effect of sediment oxygen

demand, BOD decay, nitrification, photosynthesis, and

reaeration.

xxvi
Once the model is calibrated and validated, it is then

used to investigate causes of existing problems or to

simulate future conditions to determine effects of

changes in waste loads as part of the waste load

allocation procedure. Once critical water quality conditions are defined for the estuary, harbor or coastal

area of concern, determining the waste assimilative

capacity is relatively straightforward. Models are available to relate critical water quality responses to the

loads for most problems. However, the definition of

critical conditions for estuaries is not straightforward.

For streams receiving organic loads, this is a straightforward matter of determining the low flow and high

temperature conditions. In estuaries, fresh water,

tides, wind, complex sediment transport, and other

factors can be important to determining the critical

conditions. As of yet, there are no clear methods of

establishing critical conditions, especially in terms of

the probability of occurrence. The analyst must use

considerable judgement in selecting critical conditions

for the particular system. Once loads and either critical

conditions or estimated future conditions are specified,

the calibrated model can be used to predict the water

quality response. The investigation may involve study

of extreme hydrological, meteorological, or hydrographic events that affect mixing; waste loadings from

point and non-point sources; and changes in benthic

demands.

Simplified Illustrative Examples

This section presents illustrative examples of estuarine

modeling using both simple screening procedures and

the water quality model WASP4. The screening procedures are based upon simple analytical equations and

the more detailed guidance provided in “Water Quality

Assessment: A Screening Procedure for Toxic and

Conventional Pollutants - Part 2.” WASP4 examples

demonstrate model based estuarine WLA application.

WASP4 is a general multi-dimensional compartment

model supported and available through the U.S. EPA

Center for Exposure Assessment Modeling.

The examples provided consider eight water quality

concerns in three basic types of estuaries. A one

dimensional estuary is analyzed by screening methods for conservative and nonconservative toxicants

and chlorine residual. Bacteria and DO depletion are

simulated. Nutrient enrichment, phytoplankton production, and DO depletion in a vertically stratified estuary

are simulated. Finally, ammonia toxicity and a toxicant

in a wide, laterally variant estuary are simulated.

The screening procedures can be applied using calculator or spreadsheet. While they may not be suitable

as the sole justification for a WLA, they can be valuable

for initial problem assessment. Three screening methods are presented for estimating estuarine water quality impacts: analytical equations for an idealized

estuary, the fraction of freshwater method, and the

modified tidal prism method. These example procedures are only applicable to steady state, one-dimensional estuary problems.

Deterministic water quality modeling of estuarine systems can be divided into two separate tasks: description of hydrodynamics, and description of water

quality. The WASP4 model was designed to simulate

water quality processes, but requires hydrodynamic

information as input. Hydrodynamic data may be directly specified in an input dataset, or may be read from

the output of a separate hydrodynamic model. The

examples here illustrate tidal-averaged modeling with

user-specified hydrodynamics. Both the eutrophication and toxicant programs are described and used.

For the six examples using WASP4, background information is provided, the required input data are summarized, selected model results are shown, and

certain WLA issues are briefly described.

xxvii

Preface

The document is the third of a series of manuals

providing information and guidance for the preparation

of waste load allocations. The first documents provided general guidance for performing waste load

allocation (Book I), as well as guidance specifically

directed toward streams and rivers (Book II). This

document provides technical information and guidance for the preparation of waste load allocations in

estuaries. The document is divided into four parts:

Part 1 of this document provides technical information

and policy guidance for the preparation of estuarine

waste load allocations. It summarizes the important

water quality problems, estuarine characteristics and

processes affecting those problems, and the simulation models available for addressing these problems.

This part, “Part 2: Application of Estuarine Waste Load

Allocation Models,” provides a guide to monitoring and

model calibration and testing, and a case study tutorial

on simulation of waste load allocation problems in

simplified estuarine systems. The third part summarizes initial dilution and mixing zone processes, available models, and their application in waste load

allocation. Finally, the fourth part summarizes several

historical case studies, with critical reviews by noted

experts.

Organization: “Technical Guidance Manual for Performing Waste Load Allocations. Book III:

Estuaries”

Part Title

1 Estuaries and Waste Load Allocation Models

2 Application of Estuarine Waste Load Allocation Models

3 Use of Mixing Zone Models in Estuarine Waste Load Allocation Modeling

4 Critical Review of Estuarine Waste Load Allocation Modeling

xxix

4. Monitoring Protocols for Calibration and Validation of

Estuarine Waste Load Allocation Models

James L. Martin, Ph.D., P.E.

AScI Corp., at the

Center for Exposure Assessment Modeling

Environmental Research Laboratory, U.S. EPA, Athens, GA

4.1. General Considerations

This section addresses data needs for the calibration

and validation of estuarine waste load allocation models. The type and amount of data will depend on: (1)

the study objectives, (2) system characteristics, (3)

data presently available, (4) modeling approach selected, (5) the degree of confidence required for the

modeling results, and (6) project resources. Each of

these factors should be considered in the planning

stage of the monitoring effort in order to formulate

fundamental questions that can be used in sample

design.

Quantitative estimates should be made, wherever possible, of the gains or losses in model accuracy and

precision due to different monitoring plans or modeled

processes in order to provide a rational aid for making

decisions governing the monitoring plan. For example, if study objectives require that boundary loads

must be sampled with 95 percent confidence, then

there are established quantitative methods available

to estimate the sampling effort required (e.g. Cochran

1977, Whitfield 1982). The feasibility of study objectives can then be evaluated in terms of available

resources and other study requirements.

Planning monitoring studies should be a collaborative

effort of participants involved in budgeting, field collection, analysis and processing of data, quality assurance, data management and modeling activities.

Collaboration insures that fundamental design questions are properly stated so that the available resources are used in the most efficient manner possible

and that all critical data for modeling are collected. The

use of monitoring and modeling in an iterative fashion,

wherever possible, is often the most efficient means of

insuring that critical data are identified and collected.

4.1.1. Study Objectives

The study objectives will often determine the degree

of effort required for the monitoring study. The objectives should be clearly stated and well known prior to

the planning of any monitoring study. Obviously, the

purpose of such a study will be the allocation of waste

loads for the water quality constituent of interest. However, the effort expended and the acceptable uncertainty in study results will depend largely upon the

study objectives. For example, the monitoring program

must be of much higher resolution if the main objective

is to define hourly variations as compared to one where

the objective is to determine the mean or overall effect

of a waste load on an estuary. Until all objectives are

defined it will be difficult to establish the basic criteria for

a monitoring study.

4.1.2. System Characteristics

Each estuary is unique, and the scope of the monitoring

study should be related to the problems and characteristics of that particular system. The kind of data

required is determined by the characteristics of the

system, the dominant processes controlling the constituent, and the time and space scales of interest. The

same factors that control selection of modeled processes and resolution will be integral in determination of

the monitoring required. A model can only describe the

system, and that description can be no better than the

data which determines how it is applied, drives it, and is

used to evaluate its predictions. The particular advantages of models are that they can be used to interpolate

between known events and extrapolate or project to

conditions for which, for whatever reason, data are not

available.

4.1.3. Data Availability

Some data have to be available in order to make initial

judgments as to the location and frequency of samples

as well as to make decisions concerning the selection

and application of the waste load allocation model.

Where data are not available for the constituents of

interest then it may be necessary to use some alternative or surrogate parameters for these initial judgments.

For example, suspended solids may be used in some

situations as a surrogate for strongly sorbed constituents. Reconnaissance or preliminary surveys may be

required to provide a sufficient data base for planning

where only limited data are available.

4-1
4.1.4. Model Selection

A preliminary modeling approach should be selected

prior to the monitoring study based on historical data

and reconnaissance or preliminary surveys. Ideally,

preliminary model applications should be conducted to

assess the available data and provide guidance on

monitoring requirements. Critical examination of the

models input data requirements and studies of its

sensitivity to parameters and processes should aid in

the development of monitoring strategies. Several

iterative cycles of data collection and model application

serve to optimize both monitoring and modeling efforts.

4.1.5. Confidence

To a large degree the quantity and quality of the data

determine the confidence that can be placed on the

model application. Without data, it is impossible to

determine the uncertainty associated with model predictions. Uncertainties in the determination or estimation of driving forces for the model (e.g. loadings, wind)

will be propagated in model predictions. The greater

the uncertainty (spatial, temporal or analytical) associated with data used in model forcing functions, estimation of model parameters, or evaluation of model

predictions, the greater the resulting uncertainty associated with those predictions. One fundamental issue

that may impact monitoring studies is the acceptable

degree of uncertainty in both data and model projections.

4.1.6. Resources

All waste load allocation studies will be limited to some

degree by budgetary, manpower, laboratory, or other

constraints. The limited resources will probably require that the number of stations and/or the frequency

of sampling be restricted. The planning of the data

collection program should involve analysis of various

sampling strategies and their associated cost. The

planning should include factors such as the logistics

and scheduling of crews, boats, equipment, meals,

sample storage and preservation, acceptable holding

times, laboratory preparation, communications,

backup for equipment failure, quality assurance and

other resource intensive factors that affect the successful completion of data collection efforts. An objective of any such planning study then is to maximize the

information obtained for the given project resources.

For major studies, the time and effort for this planning

effort should be carefully considered and included in

project plans.

4.2. Types of Data

The data collected in support of an estuarine waste

load allocation study will be used to (1) determine the

type of model application required, (2) drive the model,

(3) provide a basis for assigning rate coefficients and

critical model input parameters, and (4) determine if

the model is adequately describing the system. The

methods for using this data in the calibration and validation of models is the topic of Section 5.0. The general

types of data required are described below.

4.2.1. Reconnaissance and/or Historical Data

Data are required initially to define the problem and

determine the type of model solution required. For

example, determination of appropriate model resolution

must be based on available data. Historical data should

always be surveyed. Historical data should be verified

to insure that sampling techniques and laboratory analysis procedures have not changed which might make the

historical data unsuitable for comparative purposes.

Where historical data are not available it may be necessary to perform reconnaissance studies to obtain sufficient data for planning. A reconnaissance study as

defined here is a survey of the site to obtain sufficient

data to make preliminary judgments. Additional reconnaissance studies may be required particularly in areas

where the greatest uncertainties exist. The reconnaissance level data is important not only in defining the

more intensive monitoring effort but also in determining

the modeling approach and resolution.

4.2.2. Boundary Conditions

Boundary condition data are external to the model domain and are driving forces for model simulations. For

example, atmospheric temperature, solar radiation and

wind speeds are not modeled but are specified to the

model as boundary conditions and drive modeled processes such as mixing, heat transfer, algal growth,

reaeration, photolysis, volatilization, etc. Nonpoint and

point source loadings as well as inflow water volumes

are model boundary input. The boundaries at the upstream end of the estuary and the open boundary at the

ocean provide major driving forces for change. Models

do not make predictions for the boundary conditions but

are affected by them.

4.2.3. Initial Conditions

Generally, initial conditions are not required for internal

flows or velocities. However, for water quality constituents initial conditions are required where the period of

interest in simulations is less than the time required for

these initial conditions to be “flushed out”. For example,

if the model is to be run to steady-state, then by definition

initial conditions are not required. However, if simulations are to be conducted over “short” (in relation to the

flushing time) periods of time, then initial conditions may

be critical. Where changes

4-2
are small, the initial conditions may dominant projections making it difficult to determine sources of error,

such as in modeling approaches.

4.2.4. Calibration

Most estuarine hydrodynamic and water quality models are general in that they can be applied to a variety

of sites and situations. However, the values of model

parameters may be selected on a site specific basis,

within some acceptable range. The process of adjusting model parameters to fit site specific information is

known as model calibration, and requires that sufficient

data be available for parameter estimation. The data

base should include not only information on concentrations for the parameters of interest but on processes

affecting those concentrations, such as sediment oxygen demand, settling and resuspension velocities, etc.

While resources often limit the extent of the calibration

data, more than one set describing a range of conditions is desirable.

4.2.5. Validation/Evaluation

It is always wise to test the calibration with one or more

independent data sets in order to insure (or validate)

that the model accurately describes the system. Validation conditions should be sufficiently different from

calibration conditions to test model assumptions without violating them (where the assumptions are considered reasonable). For example, if the rate of sediment

oxygen demand is assumed not to change (i.e. is

specified as a zero order rate), then the model obviously would not predict well under situations where the

sediment oxygen demand was drastically different due

to some event. A second example is that an application assuming constant morphometry could not be

expected to perform well after flood events, dredging,

or construction resulted in variations in that morphometry. Discussions of the procedures for model

validation/evaluation are provided in Chapra and

Reckhow (1983) and Thomann and Mueller (1987).

4.2.6. Post Audit Data

One type of data that is often ignored is post-audit data.

Generally, models will be calibrated and validated and

then applied to make some projection about conditions, such as the effects of waste loads. The projections are often then used as an aid in making regulatory

decision. This is often the end of most modeling and

monitoring studies. There are relatively few cases

where studies are conducted after the implementation

of those decisions to determine if the model projections

were accurate and management decisions appropriate. However, without this type of data the overall

success or failure of modeling studies often can not be

accurately assessed.

4.3. Frequency Of Collection

The frequency of data collection depends on all the

factors mentioned in part 4.1. However, two general

types of studies can be defined - those used to identify

short term variations in water quality and those used to

estimate trends or mean values.

4.3.1. Intensive Surveys

Intensive surveys are intended to identify intra-tidal

variations or variations that may occur due to a particular

event in order to make short-term forecasts. Intensive

surveys should encompass at least two full tidal cycles

of approximately 25 hours duration (Brown and Ecker

1978). Intensive surveys should usually be conducted

regardless of the type of modeling study being conducted.

Wherever possible, all stations and depths should be

sampled synoptically. For estuaries that are stationary

wave systems (high water slack occurs nearly simultaneously everywhere), this goal may be difficult to

achieve due to the logistics and manpower required.

Synoptic sampling schemes are constrained by distance between stations, resources in terms of manpower and equipment, and other factors which may limit

their applicability. Where it is not possible to sample

synoptically, careful attention should be given to the

time of collection. For some estuaries, where movement of the tidal wave is progressive up the channel,

sampling the estuary at the same stage of the tide may

be possible by moving upstream with the tide to obtain

a synoptic picture of the water quality variations at a

fixed tide stage, that is a lagrangian type of sampling

scheme (Thomann and Mueller 1987). Sampling

should not be conducted during unusual climatic conditions in order to insure that the data is representative of

normal low flow, tidal cycle and ambient conditions.

Boundary conditions must be measured concurrently

with monitoring of the estuary. In addition, a record of

waste loads during the week prior to the survey may be

critical. It is necessary to identify all of the waste discharging facilities prior to the survey so that all waste

discharged can be characterized. Estimates of nonpoint loads are also required.

Where project resources limit the number of samples,

an alternative may be to temporally integrate the samples during collection or prior to analysis. This will,

however, not provide information on the variability associated with those measurements.

4-3
4.3.2. Trend Monitoring

Trend monitoring is conducted to establish seasonal

and long term trends in water quality. Intensive data

is not sufficient to calibrate and validate a model which

will be used to make long-term projections, due to

differences in the time scales of processes affecting

those projections. Trend sampling may take place on

a bi-weekly or monthly basis. Stations should be

sampled at a consistent phase of the tide and time of

day to minimize tidal and diurnal influences on water

quality variations (Ambrose 1983). Diurnal variations

must still be considered, however, tidal effects may be

less important in wind dominated estuarine systems.

Care should be exercised to sample during representative conditions and not during unusual climatic

events in order to allow comparison between sampling

times. Some stations may be selected for more detailed evaluation. Intensive surveys, spaced over the

period of monitoring, should also be considered where

the trend monitoring will be used to track changes in

parameters between intensive surveys (Brown and

Ecker 1978).

Boundary data should generally be measured at a

greater frequency than estuarine stations used for

monitoring trends. Boundary conditions are critical in

that they will drive the model used for waste load

allocation. The rate at which the boundary conditions

are expected to change will indicate the time scale

required for boundary sampling. Tiered or stratified

sampling programs may be required which include

different sampling strategies, such as between low and

high flow periods. The more intensive boundary data

will provide an estimate of the mean driving forces for

the model as well as their associated variability.

The type of boundary data required is discussed in the

next section. Generally, data on flows, meteorology

and water level variations may be available more

frequently than necessary for water quality parameters. The variability associated with the observations

can be used to estimate the sampling effort required

for a given acceptable degree of confidence using well

established methods (see Cochran 1977, Gilbert

1987, Elliott 1977 or others). For example, where the

mean and standard error of a constituent have been

estimated from reconnaissance studies and the error

is simply inversely proportional to the sample size, the

sample size required to obtain an acceptable error rate

can easily be determined. The frequency required for

water quality parameters for tributaries may be estimated using ratio and regression methods to determine the uncertainty associated with loading estimates

for various sampling designs (see for example Cochran 1977; Dolan, Yui and Geist 1981; Heidtke,

DePinto and Young 1986).

4.4. Spatial Coverage

An intensive spatial coverage of the estuary for some

indicator or surrogate water quality parameter, such as

salinity or turbidity, is generally needed in order to

estimate spatial variability, as well as determine the

model type and segmentation required.

Generally, the spatial grid for an estuarine model should

extend from above the fall line, or zone of tidal influence,

to the open boundary of the estuary. The last USGS

gauging station is often a good upper boundary since

they are typically placed outside of the region of tidal

influence. In some cases the ocean boundary will extend beyond the estuary into the ocean to insure a

representative boundary condition or to allow use of tidal

gauge information collected at some point away from

the estuary.

Where simple waste load allocation studies are planned

on a portion of an estuary, and it is unrealistic to model

the entire estuary, then the spatial grid may be delimited

by some natural change in depth or width, such as a

restriction in the channel or regions where the velocity

and water quality gradients are small. The spatial grid

must encompass the discharges of interest in all cases.

Sampling stations should generally be located along the

length of the estuary within the region of the model grid,

with stations in the main channel and along the channel

margins and subtidal flats for the intensive surveys.

Lateral and longitudinal data should be collected, including all major embayments. The spatial coverage required is governed by the gradients in velocities and

water quality constituents. Where no gradients exist,

then a single sample is sufficient. Some caution should

be exercised in the selection of the indicator parameter

for this decision. For example, strong vertical dissolved

oxygen gradients may occur in the absence of velocity,

thermal or salinity gradients. Two areas where crosschannel transects are generally required are the upper

and lower boundaries of the system. Additional sampling stations may also be selected so that poorly mixed

discharges can be adequately detected and accounted

for.

The spatial coverage should consider the type of model

network to be used. For model networks with few, large

segments, several stations (e.g. 3-6) should be located

in each model segment in order to estimate spatial

variability. For detailed models with many segments it

may not be possible to determine the parameters for

each segment. For initial conditions and model evaluation, sufficient samples should be collected to estimate

missing data by interpolation.

4-4
Where resources are limited, one possible monitoring

strategy is to spatially integrate samples, such as over

depth or width depending on the modeling approach

used. Careful consideration will need to be given to

the integration scheme for this type of monitoring. For

example, a flow weighted integration scheme would

require some a priori knowledge of the fraction of the

total flows associated with all sampling stations.

4.5. Model Data Requirements

4.5.1. Estuary Bathymetry

Data are always required to determine model morphometry. Morphometry affects the characterization

of the estuary and the type of modeling approach

required. Estuarine depth controls propagation of the

tidal wave. Shallow channels and sills increase vertical mixing while deep channels are more likely to be

stratified with greater upstream intrusion. Deep fjords

with shallow sills usually have little circulation and

flushing in bottom waters. The length of the estuary

determines the type of tidal wave, phase between

current velocities and tidal heights. The width effects

velocities (narrow constrictions increase vertical mixing and narrow inlets restrict tidal action). Wind-induced circulation is transient and interacts with

channel geometry to produce various circulation patterns and affects vertical mixing and sediment transport.

Bathymetric data are available for most estuaries from

U.S. Coastal and Geodetic Navigation Charts and

Boat Sheets or from sounding studies conducted by

the U.S. Army Corps of Engineers. The National

Oceanographic Survey can provide data on computer

tapes. The charts tend to slightly underestimate

depths in navigation channels to allow for siltation.

Alternatively, a vessel traveling along established transects can measure depth profiles with a high frequency

fathometer connected to a continuous strip-chart recorder. Depths must be corrected to mean tide level

at the time of measurement (Kuo et al. 1979). Slopes

of the water surface should also be considered in data

reduction. Fathometer frequencies used in measuring

bottom depths should be between 15 and 210 KHz

(wavelengths between 85 and 6 mm). Short wavelengths are most useful for measuring soft, muddy

bottoms, while long wavelengths are used with a hard,

firm bottom (Ambrose 1983).

For certain estuaries, such as many of those along the

Gulf of Mexico, the affects of tidal marshes can dramatically effect estuarine circulation and water quality.

These are generally some of the more difficult systems

to model. An initial decision may be whether to measure flows and quality and provide information to the

model as boundary conditions or to attempt to model

them. Where modeling is required then the corresponding bathymetry data must be collected.

4.5.2. Transport

Either description or prediction of transport is essential

to all waste load allocation studies. All mechanistic

waste load allocation models are based on mass balance principles, and both concentrations and flows are

required to compute mass rates of change. For example, a loading to the system is expressed in units of

mass/time, not concentration. Essential physical data

required for prediction or description of transport are

listed in Table 4-1.

The type of data used to quantify transport depends

upon the model application and the characteristics of

the system (i.e. well mixed, partially mixed or highly

stratified estuary). Estuarine geometry, river flow and

tidal range, and salinity distribution (internal, inflow and

boundary concentrations representative of conditions

being analyzed) may be sufficient for applications involving fraction of freshwater, modified tidal prism methods, or Pritchard’s methods (as described in Mills et al.

1985). Models such as QUAL2E (Brown and Barnwell

1987) can also be applied to estuaries using this data

where vertical resolution is not a concern, using net

flows and a tidal dispersion coefficient.

For complex estuaries, time varying flows, depths, and

cross sections will make estimation of flows and dispersion from field data difficult. Then the flows have to be

measured, estimated from dye studies, estimated by

trial and error methods, or obtained from hydrodynamic

studies. However these parameters are determined

they must adequately reflect the flushing characteristics

of the system. Data requirements for

Morphometry Data: Channel Geometry, “roughness” or bottom type

Hydrodynamic Data: Water surface elevations

Velocity and direction

Incoming flow

Point and distributed flows

Meteorological Data: Solar radiation

Air temperature

Precipitation

Wind speed and direction

Wave height, period and direction

Relative humidity

Cloud cover

Water Quality Data: Salinity

Water temperatures

Suspended sediments

Dye studies

Table 4-1. Estuarine Transport Data

4-5
flow measurement and hydrodynamic modeling are

discussed below.

4.5.2.1. Flow Measurement

Flow measurements can be used directly in waste load

allocation models or be used to aid in the calibration

and validation of hydrodynamic models, as discussed

below. Tidal current is determined by placing a network of current meters at selected stations and depths

throughout the estuary and measuring velocities over

time. A tidal velocity curve can then be constructed.

The data measured at different points can be integrated over space (i.e. laterally or vertically) and/or

time depending on the needs of the water quality

model. Data from the flow measurements should be

evaluated when incorporated into models to insure that

continuity is maintained and that constituents are properly transported.

Freshwater inflow measurements are often available

for major tributaries from USGS records or from state

agencies. Daily records are normally available and

hourly or 15 minute records can often be obtained.

The frequency at which data are required must be

assessed in the context of how rapidly flows are changing. Generally, hourly and often daily data are sufficient. Flows must be estimated for ungauged

tributaries, and where the influence of ungauged tributaries is appreciable, a flow monitoring program initiated. Groundwater inflows or flows from direct runoff

may be estimated from flow gauges available in the

fluvial portion of most large drainage basins. Inflows

from point source dischargers, including municipal and

industrial sources and combined sewer overflows are

essential input to any model.

4.5.2.2. Dye Studies

Dye and time of travel studies are often one of the

better sources of data for estimating dispersion coefficients, computing transport or for calibration and confirmation data for hydrodynamic models. Dye studies

can be conducted with injections toward the mouth of

the estuary or in areas where there is the greatest

uncertainty in model predictions. For example, dye

studies can be used to estimate mixing in the freshwater portion of a tidal river where no salinity gradients

occur.

The type of dye study conducted varies with the study

objectives. Studies may involve continuous or slug

releases of the tracer dye. Continuous discharges are

particularly useful in estimating steady-state dilution

levels while slug studies are often useful for estimating

dispersion coefficients or for calibrating and testing

hydrodynamic models.

Continuous tracer studies generally release dye over

one or more tidal cycles or discharge periods, which is

then monitored within the estuary at selected locations

over a series of tidal cycles. Monitoring of continuous

dye releases may be continuous or concentrate on initial

dilution and successive slack tides to obtain wastewater

dilution levels for initial dilution, high and low slack tides

or tidally averaged conditions. The superposition principal developed by the U.S. Geological Survey (Yotsakura and Kilpatric 1973) can be used to develop

wastewater dilutions.

A slug of dye may be injected into the system and then

the dye cloud is tracked over several tidal cycles. The

spread of the dye and/or attenuation of the dye peak will

aid in estimation dispersion coefficients, and the movement of the dye centroid will give an estimate of net

flows. The computations usually involve solving the

transport equation in some form where the known quantities are geometry and time varying dye concentrations

and the unknowns are advection and dispersion.

Diachishin (1963) provides guidance on estimating longitudinal, lateral and vertical dispersion coefficients from

dye studies. Fischer (1968) described methods for

predicting dispersion in applications to the lower Green

and Duwamish Rivers, estuaries of Puget Sound. Carter and Okubo (1972) described a technique to estimate

a longitudinal dispersion coefficient from peak dye concentrations and describe the slug release method used

in Chesapeake Bay. Thomann and Meuller (1987) provided an example of computing tidal dispersion coefficients from a slug release of dye into the Wicomico

River, an estuary of Chesapeake Bay. Some caution

should be exercised in that dyes injected at a point will

have different travel times from those mixed over the

modeled dimensions. For example, for a one-dimensional (longitudinal) model it may be preferable to distribute the dye as a vertically mixed band across the

estuary.

A variety of dye types have been used in the past, and

a comparison of tracer dyes was provided by Wilson

(1968) as well as an overview of fluorometric principals.

The most common dye presently in use is Rhodamine

WT. The U.S. Geological Survey (Hubbard et al. 1982)

provides information on planning dye studies which has

applicability to estuaries. Generally boat mounted continuous flow fluorometers can be best used to locate and

track a dye cloud or to obtain dye concentrations at

discrete stations. Some consideration should be given

to the toxicity of the dye as well as to its degradation by

chlorine in studies of treatment facilities or its absorption

onto particulates and macrophytes. Rhodamine WT is

also slightly more dense than water and may require

adjustment to obtain neutral buoyancy. The background florescence

4-6
should be determined to aid in determining quantities

of dye to be released and subtracted from field measurements. Care should also be exercised to schedule

dye studies to avoid non-representative meteorological conditions. Some of the considerations for planning and conducting dye studies in estuaries were

discussed by Story et al. (1974).

4.5.2.3. Hydrodynamic Models

Hydrodynamic models may be used to generate flow

fields for waste load allocation models. Major processes impacting transport in estuaries incorporated in

hydrodynamic models include river flow, tidal action,

fresh and salt water mixing, salinity gradients and

stratification, wind stress, coriolis force, channel geometry and bottom friction. Data required to drive the

hydrodynamic models includes initial and boundary

conditions as well as calibration and validation data.

Generally, unknowns solved for in hydrodynamic models include velocities and water surface elevations.

However, most hydrodynamic models applicable to

estuaries include forces due to changes in density and,

as such, include transport of salinity and possibly

temperature to be coupled with the hydrodynamic

equations at the intra-tidal time scale. The accurate

prediction of water surface elevations or velocities is

not sufficient to test the model application for waste

load allocation purposes, but the models must also

accurately transport materials as well. Therefore, data

requirements as discussed below will include constituents such as salinity, temperature, and other tracers

which can be used to evaluate hydrodynamic predictions. An intensive data sampling program which includes concurrent water surface elevation, velocity

and dye/dispersion studies or salinity profiles provides

the best assessment of the hydrodynamic model application.

A. Initial conditions

Initial conditions are generally not required for flows in

hydrodynamic models. Generally, velocity fields are

set up within relatively few model time steps. Initial

conditions are required for materials such as tracers,

salinity or temperature used to validate transport predictions. An exception is where the initial conditions

are rapidly flushed, or the flushing period is short in

comparison to the simulation period. For rapid flushing

it is often reasonable to run the model to a steady-state

using the initial boundary conditions and use the results of steady-state simulations as the initial conditions for subsequent simulations. Where initial

conditions are required, data will generally not be

available for all model segments, due to the fine spatial

resolution required in hydrodynamic models. Where

data are not available it may be possible to estimate

missing data by interpolation.

B. Boundary conditions

Hydrodynamic boundary conditions consist of flows or

heads. Head refers to the elevation of the water surface

above some datum. Generally, flow information is provided for tributary and point sources and water surface

elevations provided for the open (ocean) boundary(ies).

Salinity, and often temperature, conditions may be required at the boundaries in order to estimate density

effects on circulation (baroclinic effects).

Water surface elevation information is often available

for major estuaries from tide gauge records such as the

Coast and Geodetic Survey Tide Tables published annually by NOAA. These records may be processed into

tidal constituents. Records are often available for time

periods of 15 minutes which is usually sufficient for

model application. These tide tables do not include the

day-to-day variations in sea level caused by changes in

winds or barometric conditions, nor do they account for

unusual changes in freshwater conditions. All of these

conditions will cause the tide to be higher or lower than

predicted in the tables. The data can however be used

to determine if the data collected in the sampling period

is “typical (Brown and Ecker 1978). Where possible,

water surface elevation gauges should be placed at the

model boundaries as part of the monitoring program.

Meteorological data, including precipitation, wind speed

and direction are required to compute surface shear,

vertical mixing and pressure gradients. Meteorological

data are often available for nearby National Weather

Service stations from the National Climatic Center in

Asheville, North Carolina. However, the class of the

stations should be identified to determine if all the required data are available. If the estuary is large or

nearby stations are unavailable then either the use of

several stations or field monitoring of meteorological

conditions may be required. If temperature is to be

simulated, as part of the hydrodynamic model evaluation or for water quality modeling purposes, then data

on air temperature, cloud cover, humidity and precipitation must be available. Evaporation data should also be

evaluated. Solar radiation and the effects of coriolis

forces can be computed from the location of the estuary

and time of the year.

Boundary data are required for water quality constituents used to calibrate and validate transport predictions,

such as salinity and temperature. The

4-7
frequency of data collection for tributaries and point

sources was discussed previously (see section 4.3).

The sampling stations for tributaries should generally

be above the fall line, or region of tidal influence. The

open, or ocean boundary, is generally specified as

either constant or time-varying conditions which are

not impacted by interactions with the estuary. In some

cases this may require that the model and its boundary

be extended into the ocean to a point where this

assumption is valid or to where data are available. The

station(s) used for open boundary should be determined with careful consideration of the model application.

C. Calibration and validation data

Calibration and validation of hydrodynamic predictions

can consist of comparison of model predictions to

measured velocities or water surface elevations.

Measurements of water surface elevations and current

velocities at critical sampling locations should be included as part of the monitoring effort. The placement

of the current meters should be based, at least in part,

by the model application. For example, a single continuous monitor placed at the edge of a channel would

provide little usable information for a laterally averaged

model, where laterally averaged velocities at a given

depth are required for comparison.

As stated previously, the accurate predictions of water

surface elevations and velocities are not sufficient for

testing the application of a hydrodynamic model where

those velocities will be used to determine constituent

transport. Additional testing must be conducted to

determine if the transport is reasonable and if known

water quality gradients can be maintained. For example, the effects of an overestimation of vertical velocities, which are often too small to be accurately

measured in the field, may only become apparent

when the transport model is unable to maintain known

vertical profiles.

The calibration of the hydrodynamic model may require an iterative effort in conjunction with the application of the water quality models for the constituents of

interest (i.e. dissolved oxygen). However, initial calibration is usually conducted against materials such as

conservative tracers, salinity, or temperature. Salinity,

temperature and suspended solids concentrations will

impact density which will in turn affect computed velocity distributions. The transport of at least salinity,

and possibly temperature and suspended solids,

should generally be directly linked to hydrodynamic

predictions for estuaries (i.e. their effects are considered in density terms).

4.5.3. Water Quality

The water quality data required, beyond that needed

to quantify transport as described above, will vary

depending on how the variables will be used and their

anticipated impacts on the waste load allocation analysis. In addition, the water quality data required will vary

depending on the anticipated response time of the

system to changes in the value of the variable. For

example, processes that vary over long time scales, in

relation to the period of modeling, are often assumed to

have a constant effect over the period of simulation

(treated as zeroth order processes). Sediment oxygen

demand and sediment release rates are often treated in

this way.

Data requirements will vary if the waste load allocation

is intended for dissolved oxygen, eutrophication or toxics. Variables critical for an analysis of toxicity, such as

pH for ammonia and metals, may not be required if the

parameter of interest is DO. If the waste load is not

expected to impact particular variables, such as pH,

then it may be sufficient to use available data to determine their effects. If however, data are not available for

conditions of interest, or if the variable is expected to

change, either directly or indirectly, in response to the

loading, then modeling may be required as well as

collection of additional supporting data.

Table 4-2 provides an overview of some commonly

measured water quality variables, their problem contexts, and an indication of the processes they impact.

Some variables, such as dissolved oxygen (DO) are

suggested for all studies. DO can provide general

information about the estuaries capacity to assimilate

polluting materials and support aquatic life (MacDonald

and Weisman 1977). The specific type of data for a

particular application will vary depending on the factors

listed in section 4.1. Concentrations for all pertinent

water quality variables should be provided at the model

boundaries, providing the driving forces for model predictions, as well as at stations within the model system

to provide a basis for estimating model parameters and

evaluating model predictions.

Measurements of processes impacting water quality

may be required in addition to concentration measurements. For example, strongly sorbed contaminants are

strongly affected by sediment interactions, including

resuspension, settling, and sedimentation. Some independent measurement of these processes may be required to reduce model uncertainty. Modeled

processes for a variety of water quality constituents and

the data requirements for those process descriptions

are provided by Ambrose et al. (1988a,b).

4-8
4.6. Quality Assurance

A rigorous, well documented, quality assurance (QA)

plan should be an integral part of any waste load

allocation program. The QA plan should include descriptions of sampling collection, preservation, handling, analysis, analytical detection limits, and data

management. The implemented plan should provide

a well documented record of all stages of the project,

extending from sampling and transferring custody of

samples, to modeling. The development of the plan

should be completed prior to the initiation of any monitoring activities and a quality assurance coordinator

assigned to implement and coordinate QA activities.

There are a variety of documents which describe procedures for quality assurance, and a complete description of a quality assurance plan is beyond the scope of

this report. Additional information is provided in:

Guidelines and Specifications for Preparing Quality Assurance Project Plans. USEPA Office of Research and

Development, Municipal Environmental Research

Laboratory. 1980.

Standard Methods for the Examination of Water and

Wastewater, 15th Edition. American Public Health Association. 1980.

Methods for the Chemical Analysis of Water and

Wastes. EPA-600/4-79-020. USEPA Environmental

Support Laboratory. 1979.

Constituent Problem Context Effects

Salinity or Conductivity All Transport, dissolved oxygen

Temperature All Transport, kinetics, dissolved oxygen, toxicity

Suspended Solids All Transport, light extinction, sorption

UV Light Eutrophication, Toxics Heat, algal growth, photolysis

Light Extinction Eutrophication, Toxics Heat, algal growth, photolysis

Dissolved Oxygen All Indicator, toxicity, sediment release

BOD-5 DO Dissolved Oxygen

Long Term CBOD DO DIssolved Oxygen

Carbon Dioxide Toxics, Eutrophication

NBOD DO Dissolved Oxygen

Bottom Demand Eutrophication DO Dissolved Oxygen, nutrient release

Total phosphorus Eutrophication DO Algae

Soluble reactive phosphorus Eutrophication DO Algae

Total kjeldahl nitrogen Eutrophication DO Dissolved oxygen, algae

Ammonia-nitrogen Eutrophication DO, Toxicity Dissolved oxygen, toxicity, algae

Nitrate-nitrogen Eutrophication DO Dissolved oxygen, algae

Nitrite-nitrogen Eutrophication DO Dissolved oxygen, algae

Dissolved available silica Eutrophication DO Algae

Chlorophyll-a and Phaeophyton Eutrophication DO Algal indicator

Phytoplankton (major groups) Eutrophication DO Dissolved oxygen, nutrient cycles, pH

Alkalinity Toxics pH, carbonate species, metals

Total inorganic carbon Toxics pH, carbonate species, metals

pH Toxics Speciation, ionization, toxicity

Contaminant (dissolved particulate, total) Toxics Allocation

Dissolved organic carbon Toxics Sorption, activity

Total organic carbon Toxics Sorption, activity

Porosity Sediments Pore water movement, toxicity

Grain size Sediments Settling, sorption, sediments

Percent solids Sediments Sorption, sediments

Eh Toxics, DO Indicator, speciation

Biomass Toxics Biouptake

Meteorologic Data All Gas transfer, reaction rates

wind, temperature, etc.

Toxicity (cereodaphnia toxic units, etc.) Toxicity Toxicity

Coliform Bacteria (Fecal, Total, Streptococci) Human Health Human Health

Table 4-2. Water Quality Variables

4-9
Handbook for Analytical Quality Control in Water

and Wastewater Laboratories. EPA-600/4-79-

019. USEPA Environmental Support Laboratory.

1979.

Discussion is provided below of some suggested elements of a QA plan.

4.6.1. Data Collection

All stations for data collection should be well described

and documented in order to insure that they are reestablished during subsequent sampling periods. Stations can be established using an easily determined

distance from some permanent structure or landmark.

However, care should be exercised to insure that the

stations are not located near some structure which

would make them unrepresentative. For example,

velocity measurements should not be made immediately downstream of a bridge or piling no matter how

convenient it may be. Stations can be relocated using

electronic positioning equipment such as range instruments, radar or Loran if they are sufficiently accurate

to allow relocation within an acceptable distance.

Methods should be established for maintaining positions at stations during sampling. Records of arrival

and departure times for each site as well as surface

observations should be made during each sampling

period.

Instruments for electronic in situ determination of water

quality parameters should be calibrated at least before

and after each sampling trip. For example, samples

should be collected for salinity to verify field measurements and samples fixed in the field for dissolved

oxygen to verify dissolved oxygen probes.

All field collection equipment should be listed and

prepared before each sampling trip, insuring that all

collection containers are clean and proper log forms

and labeling equipment available. Different containers

should be available for metals, nutrients, organics,

dissolved oxygen, etc. due to their cleaning and preservation requirements. The QA plan should contain a

detailed description of techniques for samples requiring special handling, such as toxics and anaerobic

samples.

An established sequence of collection should be developed and maintained throughout the monitoring

effort, insuring that new personnel are trained in the

proper methods and sequence of data collection. All

samples should be logged and sample log sheets

should include station location, time, depth, results of

in situ sampling, and container numbers for each type

of sample. Datum should always be clearly specified

(e.g. time of day standard, datum for water surface

elevations).

All samples should be preserved on board, where the

preservation technique will vary with the type of analysis

required, but may involve icing, acidification, organic

extraction, etc. The preservation techniques should be

documented prior to implementation of the monitoring

study. For some samples that do not preserve well it

may be necessary to either conduct analyses on board

or quickly transfer them to nearby on-shore facilities.

Additional samples should be collected to determine

sampling variability and individual samples may be split

prior to analysis to determine analytical variability. The

number of replicate samples should be established as

part of the planning for the monitoring effort. Field

samples may also be spiked with a known amount of a

standard prior to analysis. The identity of the spiked,

split and duplicate samples should be kept on separate

logs and the analyst should not be aware of their identity.

The samples should be transferred from the field to the

laboratory in a timely manner. The field logs should be

recorded and a laboratory log kept of the samples and

their arrival. Custody sheets may be kept to further

document the transferral of samples.

4.6.2. Data Analysis and Release

Samples should be transferred from the field to laboratory personnel, and the laboratory personnel should log

samples into the laboratory, noting the time and date

received, sample identities and other pertinent information from the field logs. The samples should be checked

for proper preservation and transferred to proper storage facilities prior to analysis. The laboratory QA plan

should include timelines indicating time limits for the

analysis, descriptions of the analytical tests, sample

preparation or extraction methods, detection limits, and

methods for evaluating the quality of the analytical results. Methods should be included to describe handling

of samples where their chemical matrix may cause

analytical problems, such as toxicity for BOD samples,

matrix problems for metals, or oils in organic analyses.

Methods should be outlined describing archiving techniques for samples and analytical data.

An analytical log should be maintained for each type of

analysis, providing information on the sample identity,

analyst, date and time of analysis, and where applicable, information on standard curves, blanks or baseline

information, peak heights or meter readings, dilutions or

concentrating methods, and computed concentrations.

Observations should be included on any noted interferences or conditions which could effect the analysis.

Strip chart or electronically produced information on the

analysis should be ar4-10
chived. Generally, the results of each analysis should

be recorded on prepared forms for each sample containing information on the results of all analysis performed.

After completion of the analysis, the analytical results

should be reviewed by the laboratory’s quality assurance team to determine if the analytical results are

acceptable. Methods should be established prior to

implementation of the monitoring plan to check and

identify the quality of the analytical results, insure the

correct transferal of information and describe follow up

procedures and corrective actions. The results should

include indications of the analytical variability, as indicated by analysis of split samples, recovery of spikes,

periodic laboratory audits and other methods. Wherever possible, questionable samples should be rerun.

In some cases additional analysis may be included

beyond the requirements of the modeling activities to

insure the quality of the analytical results, such as to

perform a dissolved solids or anion-cation balances

where applicable.

Analytical results have little utility in mass balance

calculations if those results are below, or clustered

near, analytical detection limits. However, methods

are available to estimate values where the statistical

distribution of the samples are known or assumed. A

method suggested by Thomann (R.V., pers. comm.)

to analyze data including non-detects is to plot the data

on log normal probability paper with a ranking of the

data that includes those values below the detection

limit (Figure 4-1). If the data are log normally distributed, the median and log standard deviation can be

estimated from the plots and can then be used to

estimate the mean using standard statistical transformations. This allows the estimation of statistics for

data with values below the analytical detection limit.

Where data are not sufficient to estimate statistics,

based on assumptions regarding the statistical distribution of samples, it may be necessary to explore

alternative analytical methods. Where more than one

technique is used for a particular analysis care should

be exercised to insure each sample is identified as to

the type of analysis performed and its associated analytical variability.

The laboratory supervisors should maintain tracking

records indicating the samples received, source, time of

collection and their stage in the analytical process. This

tracking record can be used to insure that samples are

analyzed within preset time frames, aid in setting priorities, and inform data users of the status of the information they require. A common conflict occurs between

laboratories wanting to prevent release of information

until all possible checks are completed for all samples

collected and data users who want any data they can

obtain as quickly as possible. If preliminary or partial

results are released, they should be properly identified

indicating their status and updated when new information becomes available.

4.6.3. Data Management

QA plans should also extend to data management,

insuring that data storage and retrieval mechanisms are

established and that information on the identity and

quality of the analytical results is maintained for each

record. Care should be exercised to insure that the

identity of the sample is preserved. Data should include

time and location of collection, value, units, variability

and information on significant figures and rounding procedures, and status as perhaps indicated by analytical

codes. Checks should be established to insure that all

data are recorded and that accurate transfer of information occurs between different media (such as between

laboratory forms and data bases).

Modeling activities should be performed in a stepwise

manner with testing at all stages in the application to

insure that predictions are accurate and reasonable.

The degree of model testing will be determined to some

degree by the model’s complexity and its previous history of testing and applications. However, a healthy

skepticism is often the best method of avoiding errors

and improper applications. All assumptions should be

clearly stated and supported for independent review.

The QA for modeling activities should include, but not

be limited to validation against independent data sets to

insure that concentrations are accurately predicted.

The QA activities should include calculations to insure

that mass is properly conserved, numerical stability is

maintained, and that model parameters are within reasonable ranges as reported in the literature. Analyses

should be conducted of the confidence associated with

the predicted results.

Figure 4-1. Illustration of use of log probability plot to

estimate statistics for data including non-detects.

4-11
Wherever available, model testing should not be limited to comparisons with concentrations but model

components should be compared to available data to

insure that they are reasonable. For example, productivity data for a system could be computed for eutrophication models and compared to field data. A

component, or mass balance, analysis will also provide

information on the dominant factors affecting predictions (see Thomann and Meuller 1987).

A model application should be most accurate in estimating conditions that occur between those measured

for calibration and validation, analogous to interpolation. However, model applications often require projection or extrapolation to conditions outside of the range

of available data, such as to “pristine” conditions or to

determine recovery times after a particular source has

been eliminated. The variability associated with the

projections can be determined to some degree by

evaluation of the historical variability in forcing functions. However, testing of the model assumptions can

often be determined only through comparisons with

similar previous applications or with data collected

after implementation of strategies based on those

model projections. Wherever possible, such postaudit studies should be considered as part of the

monitoring and modeling plans. The QA plan for

modeling should also include methods to insure that,

at a minimum, the input data used to drive the model

in final calibration and validation simulations and copies of the computer codes and their users manuals

used for prediction and manipulation are archived for

later use. The archived files should contain a description of all of the files necessary to do the analysis and

sufficient information to allow duplication of the reported results.

4.7. References

Ambrose, R.B. 1983. Introduction to Estuary Studies,

Prepared for the Federal Department of Housing and

Environment, Nigeria, Environmental Research Laboratory, Athens, GA.

Ambrose, R.B., Wool, T.A., Connolly, J.P., and

Schanz, R.W. 1988a. WASP4, A Hydrodynamic and

Water Quality Model—Model Theory, User’s Manual,

and Programmers Guide, EPA/600/3-87/039, Environmental Research Laboratory, Athens, GA.

Ambrose, R.B., Connoly, J.P., Southerland, E., Barnwell, T.O., and Schnoor, J.L. 1988b. Waste Load

Allocation Models, J. Water Poll. Cntrl. Fed. 60(9). pp.

1646-1656.

Brown, L.C. and Barnwell, T.O. 1987. The Enhanced

Stream Water Quality Models QUAL2E and QUAL2-

UNCAS: Documentation and User Manual,

EPA/600/3-87-007. Environmental Research Laboratory, Athens, GA.

Brown, S.M. and Ecker, R.M. 1978. Water Quality

Monitoring Programs for Selected Subestuaries of the

Chesapeake Bay, Batelle Pacific Northwest Laboratories. Prepared for the USEPA Environmental Research

Laboratory, Athens, GA.

Carter, H.H. and Okubo, A. 1972. Longitudinal Dispersion in Nonuniform Flow, Water Resources Research,

8(3), pp. 648-660.

Chapra, S.C. and Reckhow, K.H. 1983. Engineering

Approaches for Lake Management, Vol. 2: Mechanistic

Modeling, Butterworth Publishers, Boston, Mass.

Cochran, W.G. 1977. Sampling Techniques, 3rd ed., J.

Wiley and Sons, New York.

Diachishin, A.N. 1963. Dye Dispersion Studies, ASCE

J. Sanitary Engr. Div. 89(SA1), pp. 29-49.

Dolan, D.M., Yui, A.K., and Geist, R.D. 1981. Evaluation of River Load Estimation Methods for Total Phosphorus, J. Great Lakes Res. 7(3), pp. 207-214.

Elliot, J.M. 1977. Some Methods for the Statistical

Analysis of Samples of Benthic Invertebrates. Freshwater Biological Association, The Ferry House, Ambleside,

Cumbria, England.

Fischer, H.B. 1968. Methods for Predicting Dispersion

Coefficients in Natural Streams, with Applications to

Lower Reaches of the Green and Duwamish Rivers

Washington, U.S. Geological Survey Professional Paper 582-A.

Gilbert, R.O. 1987. Statistical Methods for Environmental Pollution Modeling, Van Nostrand, Reinholt,

New York.

Heidtke, T.M., DePinto, J.V., and Young, T.C. 1986.

Assessment of Annual Total Phosphorus Tributary

Loading Estimates: Application to the Saginaw River,

Environ. Engr. Rept. 86-9-1, Dept. of Civil and Environ.

Engr., Clarkson Univ., Potsdam, N.Y.

Hubbard, E.F., Kilpatrick, F.A., Martens, L.A., and Wilson, J.F. Jr. 1982. Measurement of Time of Travel and

Dispersion in Streams by Dye Tracing, TWI 3-A9, U.S.

Geological Survey, Washington, D.C.

Kuo, A.Y, Heyer, P.V., and Fang, C.S. 1979. Manual

of Water Quality Models for Virginia Estuaries, Special

Report No. 214, Virginia Institute of Marine Science,

Gloucester Point, VA.

4-12
MacDonald, G.J. and Weisman, R.N. 1977. OxygenSag in a Tidal River, ASCE J. Environ. Engr. Div., 103

(EE3).

Mills, W.B. et al. 1985. Water Quality Assessment: A

Screening Procedure for Toxic and Conventional Pollutants in Surface and Ground Water - Part II,

EPA/600/002b/ Environmental Research Laboratory,

Athens, Ga.

Som, R.J. 1973. A Manual of Sampling Techniques.

Crane, Russak and Co., New York, New York.

Story, A.H., McPhearson, R.L., and Gaines, J.L. 1974.

Use of Fluorescent Dye Tracers in Mobile Bay,: J.

Water Poll. Cntr. Fed., 46(4), pp. 657-665.

Thomann, R.V. and Mueller, J.A. 1987. Principles of

Surface Water Quality Modeling and Control. Harper

& Row, New York, N.Y.pp. 91-172.

Whitfield, P.H. 1982. Selecting a Method for Estimating Substance Loadings, Water Resourc. Bull. 18(2),

203-210.

Wilson, J.F. 1968. Fluorometric Procedures for Dye

Tracing, TWI 3-A12, U.S. Geological Survey, Washington, D.C.

Yotsukura, N. and Kilpatrick, F.A. 1973. Tracer Similation of Soluble Waste Concentration, ASCE J. Environmental Engr. Div. Vol. 99, EE4, pp. 499-515.

4-13

5. Model Calibration, Validation, and Use

Steve C. McCutcheon, Ph.D., P.E.

Center for Exposure Assessment Modeling

Environmental Research Laboratory, U.S. EPA, Athens, GA

Zhu Dongwei

Research Fellow from Nanjing University, P.R.C.

with Center for Exposure Assessment Modeling

Sandra Bird

Center for Exposure Assessment Modeling

Environmental Research Laboratory, U.S. EPA, Athens, GA

5.1. Introduction And Terminology

This section describes procedures for selecting model

parameters and coefficients that result in a calibrated

model of the estuary of interest. Also described are

procedures necessary to ensure that the calibrated

model is validated for an appropriate range of conditions. Third, model testing procedures needed to calibrate and validate models are reviewed and assessed.

Finally, guidance on how the calibrated model can be

utilized in a waste load allocation to describe existing

conditions and project the effects of reducing or increasing loads into the estuary, is provided.

Section 5.2 reviews a general procedure for calibrating

models of the dissolved oxygen balance, of the nutrients that cause eutrophication problems, and of toxic

chemicals and sediment. A comprehensive listing in a

series of Supplements assists in defining the set of

potential model coefficients and parameters that may

be required to calibrate a model for waste load allocation. The Supplements are provided for each of the

important coefficients and give specific guidance on

how these parameters can be selected.

Section 5.3 briefly describes the validation procedure

that is intended to estimate the uncertainty of the

calibrated model and help establish that the model

formulation chosen is at least useful over the limited

range of conditions defined by the calibration and

validation data sets. Section 5.4 reviews important

statistical methods for testing the calibrated model.

These methods are useful to aid in the various calibration phases and in the validation phase to measure

how well model predictions and measurements of

water quality agree.

Section 5.5 provides limited guidance on the utilization

of a calibrated model for waste load allocation. Methods to determine causes of existing conditions and to

project effects of changes in waste loads are discussed. Presently, methods to modify model coefficients such as sediment oxygen demand rates and

deoxygenation rate coefficients are not well developed.

Model calibration is necessary because of the semiempirical nature of present day (1989) water quality

models. Although the waste load allocation models

used in estuary studies are formulated from the mass

balance and, in many cases, from conservation of

momentum principles, most of the kinetic descriptions

in the models that describe the change in water quality

are empirically derived. These empirical derivations

contain a number of coefficients and parameters that

are usually determined by calibration using data collected in the estuary of interest. Occasionally, all important coefficients can be measured or estimated. In

this case, the calibration procedure simplifies to a

validation to confirm that the measurements of the

inflows, the seaward conditions, and the conditions in

the estuary are consistent according to the model

formulation chosen to represent the water quality relationships. More often than not, it is not possible to

directly measure all the necessary coefficients and

parameters.

In general, coefficients must be chosen by what is in

essence a trial and error procedure to calibrate a

model. There is guidance on the appropriate range for

coefficients but because each estuary is unique, there

is always a chance that coefficients will be different

from any other observed condition and fall outside the

range. Because unique coefficients outside the normal

ranges can also result if inappropriate model formulations are used, it becomes necessary to adopt, as much

as possible, well accepted model formulations and to

use standardized methods of testing the adequacy of

calibration and validation. Also very important is the

experience required to be able to determine when

model formulations are not quite adequate. In this

5-1
regard, it remains difficult to say how much experience

is enough but this should not prevent the inexperienced

from attempting this type of analysis. Many studies are

straightforward enough so that extensive experience

is not always mandatory.

If one accepts that calibration is basically a trial and

error procedure, it can be quickly recognized that the

methods involved should be as efficient as possible.

To achieve some efficiency, there are two similar principles that should be applied. These are:

1. The universal caveat that the simplest model

formulation should be used to solve the problem at

hand, and

2. Principle of Parsimony.

The first caveat probably originated soon after the wide

spread use of water quality models began in the 1960s

(Schnelle et al. 1975). The use of simpler models

remains a useful goal, but it should not be pursued

zealously. For example, it should be kept in mind that

the complete solution of the modeling problem may

involve simulation and prediction of effects on constituents that are unimportant during the calibration phase.

The benthic flux of nutrients may become more important when point sources are cleaned up and may need

to be included in any long term projection. Also, modelers should use codes with which they have the most

experience and confidence in, as long as this does not

complicate the analysis or avoid including important

elements of the water quality processes. Finally,

NCASI (1982) demonstrates that for stream water

quality modeling, that overly simplistic models can be

calibrated (due to the flexibility built into general purpose models) and unless rigorous validation procedures are followed, the errors involved will not be

obvious. Since some estuarine conditions are quite

similar to riverine conditions, these conclusions are

also valid for estuarine modeling. Therefore, reasonably simple models should be used, but the effects of

the approximations involved must be investigated.

The Principle of Parsimony (terminology suggested by

Robert V. Thomann in review) is similar to the caveat

that the simplest model should be employed but is

more comprehensive in concept. Also included is the

idea that model coefficients and parameters should be

spatially and temporally uniform unless there is specific

data or information demonstrating that the coefficients

change. For example, it is very poor practice to vary

coefficients from one model segment to the next unless

there are well defined changes in the physical, chemical, or biological characteristics. When parameters

are allowed to vary from one segment to the next to

cause an exact match between predictions and measurements, the selected coefficients are contaminated

with an accumulation of measurement errors from the

field data and approximation error for the model formulations chosen. This assumes that water quality model

equations are exact descriptions of the physical,

chemical, and biological processes. This is never true

for the currently available models (1989). Typically, this

contamination causes rapid variation of coefficients

from segment to segment when few data are available

and the data are error prone. Values occasionally fall

outside normal or typical ranges. In essence, this poor

practice avoids the necessary use of engineering or

scientific judgement in evaluating the limitations of the

model chosen and in evaluating uncertainty in field

data. It reduces the procedure to a grossly empirical

curve fitting exercise. Since statistical curve fitting

analysis has not been employed for the analysis of

most water quality parameters of interest for several

decades, this indicates that the model user is not

sufficiently experienced in most cases to perform a

waste load allocation.

The calibration procedure also involves investigation of

the measurements that define the boundary conditions.

In many cases, it is never clear that all loads can be

adequately measured until the model is calibrated.

Strictly speaking, it is not correct to use a calibration

procedure to investigate measurements of loads and

to define kinetic rates, parameters, and formulations.

In general, this is a poor way to confirm that load

measurements are adequate and when some loads are

missed or over estimated, the optimum coefficients are

error prone. When significant calibration errors occur,

the calibrated model has very little predictive validity

(i.e., the predictions are expected to be inaccurate) and

the description of causes of water quality problems can

be misleading.

In practice, however, there are no alternatives except

to collect selected concentration data that can be used

to indicate if loads are adequately measured. Other

measurements of water quality concentration can be

oriented to providing optimum calibration data to aid in

the selection of accurate parameters. This practice

requires some artful selection of parameters to be

measured and of measurement locations and frequency. For example, dissolved solids and other conservative constituents should be simulated, especially

those natural tracers occurring in point and non-point

sources. Where undocumented sources are suspected, curtains of stations or upstream and downstream stations can be used to perform localized mass

balances in portions of the estuary to indicate if any

loads are not measured. (Here we use upstream and

downstream

to imply a localized mass balance in the riverine sections of the estuary.)

5-2
Other types of concentration measurements can be

performed to better calibrate water quality kinetics.

These measurements should be focused in areas

some distance from suspected loads but where large

water quality gradients are suspected. This may involve measurements away from shorelines and areas

with contaminated sediments.

Unfortunately, these selective types of measurements

can not be made in all cases and the calibration can

be error prone. However, if proper validation procedures are followed, it should be possible to detect

unreliable results in most cases. Nevertheless, a paucity of post-audit studies makes it impossible to ensure

that unreliable or error prone results will be detected in

all cases.

In addition to the selective concentration measurements to aid calibration, there are calibration procedures designed to aid in investigating loading data and

avoid calibration errors. These procedures generally

follow a phased approach that is described in the

section on calibration procedures.

Finally, embarrassing errors can occur in the formulation of model data sets. To avoid these calibration

errors, there are two methods that should be employed. First, conservation of mass should always be

checked. This is done by simulating a conservative

constituent such as dissolved solids or by using a

hypothetical unit loading of 1, 10, or 100 concentration

units to be sure that dilution, transport, and mixing are

properly quantified. Second, the calibration should be

compared to any analytical or simpler solution available. Section 6 provides some simple formulations

that may be useful and Thomann and Mueller (1987)

provide a wealth of additional information. When simple calculations are not possible, selective hand calculations using the more elaborate equations in critical

areas are recommended to be sure that the modeler

understands the data sets that have been formulated.

A sensitivity analysis to indicate critical locations and

important processes that should be checked, is suggested.

Calibration alone is not adequate to determine the

predictive capability of a model for a particular estuary.

To map out the range of conditions over which the

model can be used to determine cause and effect

relationships, one or more additional independent sets

of data are required to determine whether the model is

predictively valid. This testing exercise, which also is

referred to as confirmation testing (Reckhow and

Chapra 1983), defines the limits of usefulness of the

calibrated model. Without validation testing, the calibrated model remains a description of the conditions

defined by the calibration data set. The uncertainty of

any projection or extrapolation of a calibrated model

would be unknown unless this is estimated during the

validation procedure.

In addition, the final validation is limited to the range of

conditions defined by the calibration and validation

data sets. The uncertainty of any projection or extrapolation outside this range also remains unknown. The

validation of a calibrated model, therefore, should not

be taken to infer that the model is predictively valid over

the full range of conditions that can occur in an estuary.

For example, a model validated over the range of

typical tides and low freshwater inflow may not describe

conditions that occur when large inflows and atypical

tides occur. This is especially true when processes

such as sediment transport and benthic exchange occur during atypical events but not during the normal,

river flow and tidal events typically used to calibrate and

validate the model.

To stress the limited nature of a calibrated model,

validation testing is used here in place of the frequently

used terminology “model verification.” Strictly speaking, verification implies a comparison between model

predictions and the true state of an estuary. Because

the true state can only be measured and thus known

only approximately, validation is a better description of

what is actually done. Furthermore, many diverse

modeling fields seem to refer to the procedure of initially testing a computer model on different computer

systems using a benchmark set of input data as verification. In this latter case, the term verification is more

appropriate because model simulations on a different

computer are being compared with an exact benchmark condition derived by the developer on his original

computer. For engineering purposes, these calculations are “precise enough” to serve as exact definitions.

In the past, the adequacy of model calibration and

validation generally has been evaluated by visually

comparing model predictions and measured data.

There are statistical criteria, as well, that should be

used in testing the adequacy of a calibration or validation. These will be critically reviewed in the final part of

this section.

Figures 5.1 and 5.2 describe, in general terms, the

calibration and validation procedure. As noted in the

introductory section of this manual, waste load allocation modeling is an iterative process of collecting data,

calibrating a model, collecting additional data, and

attempting to validate the model. In some critically

important estuaries, such as Chesapeake Bay, the

Delaware Estuary, New York Harbor, and San Francisco Bay, it is necessary to continually update assessments and waste load allocation studies. It is possible,

however, to adequately validate a model and set reasonable waste loads in a short period of study (i.e., 6

5-3
to 12 months) for most smaller estuaries or for smaller

sections of larger estuaries.

5.2. Model Calibration

As illustrated in Figure 5.3, sets of data are collected to

define the loads and flows entering and leaving an

estuary and to characterize the receiving water quality

for comparison to conditions simulated by the waste

load allocation model. The appropriate data collection

procedures, which are equally important to developing

a well calibrated model, are described in Section 4.0.

The inflows, outflows, and loads entering and leaving

the estuary are used to specify the model boundary

conditions. These inputs to the model, along with

specified model coefficients, control the simulation of

receiving water quality. Calibration of the model involves a comparison of the measured and simulated

receiving water quality conditions. Model coefficients

are modified by trial and error until the measurements

and simulations agree reasonably well (e.g., see

McCutcheon 1989, Thomann and Mueller 1987). Ideally, agreement should be evaluated in terms of

prespecified criteria. Very little guidance is available,

however, to make this fully feasible.

Figure 5-2. Relationship between data collection, model calibration, validation, and waste load allocation procedures.

Figure 5-1. Model calibration and verification procedure.

5-4
Occasionally, the trial and error procedure reduces to

one trial of a coefficient either estimated by empirical

formulations or measured. Typically this occurs when

model results are not sensitive to a particular coefficient.

A number of methods (e.g., least squares and maximum likelihood) can and should be used to guide the

subsequent trials of coefficients. Various statistical

criteria such as least squares have been selected as

the basis for schemes to select optimum sets of model

coefficients. Unfortunately, use of optimization

schemes still require expert judgement to weigh the

importance of subsets of data being used for calibration and to establish ranges of coefficients from which

to select from a given estuary. A critical limitation

seems to involve a lack of knowledge about correlations between parameters that influence the selection

of an optimum set. As a result, calibration by optimization is not frequently used unless extremely complex

models are employed where significant time savings

may be achieved.

The most useful compilations of these model formulations and range of coefficients are published in the EPA

guidance manuals for conventional and toxic pollutants

given in Table 5.1. In addition, guidance is available

from a number of reference books (e.g., Thomann and

Mueller 1987, Krenkel and Novotny 1980, McCutcheon 1989, 1990, and Rich 1973).

In general, models are calibrated in phases beginning

with the selection of the model parameters and coefficients that are independent (or assumed to be independent in the formulation of the model) as shown in

Table 5.2 for conventional pollutants when baroclinic

circulation is not important. The final phases focus on

the least independent parameters as illustrated in Figure 5.4. Typically, as many as three distinct phases

are involved and each phase involves the selection of

a number of critical parameters and coefficients as

shown in Tables 5.3, 5.4, and 5.5.

5.2.1. Phase I of Calibration

Phase I concentrates on the calibration of the hydrodynamic and mass transport models. In general, there is

a complex interaction between circulation and density

differences caused by gradients of salinity and temperature that must be taken into account in stratified

estuaries. In vertically mixed estuaries, the

Step Procedure

1 Calibrate hydraulics or hydrodynamics model by

reproducing measurements of discharge, velocity, or

stage (depth of flow) at selected sensitive locations.

This involves modification of the Manning roughness

coefficient, eddy viscosity coefficients, or empirical

flow versus stage coefficients to predict the proper

residence time through the reach of interest. Dye

studies to determine time of travel or average velocity

may be used in place of hydraulic measurements for

some simpler models.

2 Select dispersion or mixing coefficients (or eddy

diffusivities) to reproduce any dispersive mixing that

may be important. Natural tracers or injected dye

clouds may be monitored for this purpose.

3 Calibrate any process models such as water

temperature that are not affected by any other water

quality constituent.

4 Calibrate any process model affected by the

processes first calibrated. In conventional models,

this may include biochemical oxygen demand (BOD),

fecal coliform bacteria, and nitrification.

5 Finally, calibrate all constituents or material cycles

affected by any other process. In conventional

models this usually means that the dissolved oxygen

balance is calibrated last after biochemical oxygen

demand, nitrification and photosynthesis sub-models

are calibrated.

Table 5-2. Outline of a General Calibration Procedure for

Water Quality Models for Conventional Pollutants when

Baroclinic Circulation Effects are Unimportant [McCutcheon, (1989)]

1. Bowie, G.L., Mills, W.B., Porcella, D.B., Campbell, C.L.,

Pagenkopf, J.R., Rupp, G.L., Johnson, K.M., Chan, P.W.H.,

and Gherini, S.A., Rates, Constants, and Kinetics Formulations in Surface Water Quality Modeling, 2nd ed., EPA

600/3-85/040, U.S. Environmental Protection Agency, Athens,

Georgia, 1985.

2. Schnoor, J.L., Sato, C., McKechnie, D., and Sahoo, D., Processes, Coefficients, and Models for Simulating Toxic Organics and Heavy Metals in Surface Waters,

EPA/600/3-87/015, U.S. Environmental Protection Agency,

Athens, Georgia, 1987

Table 5-1. Guidance Manuals for Rates, Constants, and

Kinetics Formulations for Conventional and

Toxic Pollutants

Figure 5-3. Relationship between data set components,

water quality model, and set of model coefficients for model

calibration.

5-5
interaction among salinity, temperature and circulation

is usually not significant. When vertical salinity gradients are not present, vertically mixed one-and two-dimensional models are employed and these are

relatively easy to calibrate. In these cases, circulation

in the estuary is not as strongly controlled by changes

in salinity and temperature. As a result, the hydrodynamic model can first be calibrated and then the salinity and temperature models calibrated afterwards.

Model calibration for stratified estuaries involves determining bottom and surface friction coefficients (see

Supplements I and II) and vertical, lateral, and horizontal eddy viscosity coefficients for the hydrodynamic

model (see Supplements III and IV). The calibration of

the mass transport model is achieved by properly

selecting the vertical, lateral, and horizontal mass

transfer coefficients (see Supplement V). The calibration of the temperature model is accomplished by

selection of the proper wind speed coefficients (see

Supplement VI). See Table 5.3 for a listing of the

coefficients that must be selected for the most general

case.

Under the simplest and best conditions, however, it is

possible to calibrate the circulation model and mass

transport model with tracer or salinity measurements

and ignore any variation in temperature. Typically, this

sort of indirect calibration works well when the estuary

can be simulated with a one-dimensional model but it

is also the method most frequently attempted for all

types of flows including complex stratified flows.

Whether the indirect method is useful or not depends

on the expertise of the model user and whether the

waste load allocation is very sensitive to circulation

patterns in the estuary. At the very least, this method

should be attempted and used in preliminary model

setup when simulating the estuary with whatever historic data are available to assist in planning data

collection studies.

Generally, calibration procedures for hydrodynamic

models are not well developed. In fact, it is not clear

that the full resolution available from two- and three-dimensional models are fully useful to inexperienced

modelers. As a result, precise calibrations are rarely

attempted for routine waste load allocation studies.

When it is necessary to precisely define complex circulation patterns due to the dynamic action of tides and

wind, stratification, or coriolis effects, the modeling is

usually left to experts (e.g., HYDROQUAL 1987). In

part, precise calibrations are not attempted because

critical circulation conditions for estuaries analogous

to the critical low flow case found in streams have not

been defined. For example, it is rarely obvious what

Calibration Parameters for

Complex Model Simple Model Range of Values Guidance Documents and References

Bottom roughness coefficient 0.010 to 0.120 Hydrodynamic model documentation

[i.e. Ambrose et al. (1988)], Chow

(1959), Frecnh (1985), Barnes (1972)

Eddy Viscosity: Hydrodynamic model documentation.

Assumed to be the same order as the

dispersion coefficient. Bowie et al.

(1985), NAS (1977), Officer (1979), and

Dyer (1973)

Vertical1 10-2 to 100

 cm s

-1

Lateral1 102 to 106

 cm s

-1

Horizontal 10

2

 to 106 cm s

-1

Dispersion Coefficient: Dispersion Coefficient: Bowie et al. (1985), Fisher et al.(1979),

Thomann and Mueller (1987), NAS

(1977), and Officer (1976)

Vertical Vertical 10-2 to 100

 cm s

-1

Lateral1 Lateral1 102

 to 106 cm s

-1

Horizontal1 Horizontal1 102

 to 106 cm s

-1

Wind speed function See Supplement VI Bowie et al. (1985), Ryan and

Harleman (1973), Brutsaert (1982), and

McCutcheon (1989)

Surface drag coefficient 0.001 to 0.0025 O’Connor (1983)

1 Harleman, in review, notes that these ranges are too large to be fully useful. However, the data does reflect the approximate nature of

these types of models and shows the extreme variability to be expected.

Table 5-3. Guidance on the Selection of Model Coefficients and Parameters - Phase I

Figure 5-4. Phased calibration procedure.

5-6
Ca

batoaaetes o

Complex Model Simple Model Range of Values Guidance Documents and References

CBOD: CBOD: Bowie et al. (1985)

Deoxygenation rate

coefficient

Deoxygenation rate

coefficient

0.05 to 0.4 d -1 (20oC)

Decay rate coefficient Decay rate coefficient 0.05 to 0.4 d-1 (20o

C)

Settling coefficient Settling coefficient approximately 0.0

NBOD decay rate

 coefficient

0.1 to 0.5 d-1 (20oC) Bowie et al. (1985), Thomann and Mueller (1987)

Nitrogen transformations: Bowie et al. (1985)

ON hydrolysis rate

coefficient

0.001 to 0.14 in d-1 (20oC)

Ammonification rate

coefficient

0.02 to 1.3 in d-1 (20oC)

Nitrification rate

coefficient

0.1 to 20 in d-1 (20oC)

Phosphorus transformations Bowie et al. (1985)

OP→PO4 0.001 to 0.2 d-1 (20o

C)

Biomass coefficients: Bowie et al. (1985)

Ammonia preference factor 0 to 1.0

N half sat. constant 0.001 to 0.4 mg L-1

P half sat. constant 0.0005 to 0.08 mg L-1 Thomann (1972) - Delaware

Estuary

Light half sat. constant 0.1 x 10-5 to 20.5 x 10-5 W m-2

Light ext. coefficient 2.3 to 6.9 in m-1

Max growth rate coeff. 0.2 to 5 d-1 (20o

C)

Respiration rate coeff. 0.05 to 0.15 d-1 (20o

C)

Settling rate 0.05 to 0.6 m d-1

Non-predatory mortality rate 0.003 to 0.17 d-1

Zooplankton grazing rate 0.35 to 0.8 d-1

Phytoplankton stochiometry: (% dry weight biomass) Bowie et al. (1985) - see their table of values for

various species.

Carbon 10 to 70

Nitrogen 0.6 to 16

Phosphorus 0.16 to 5

Silica 20 to 50

Net photsynthesis rate 0.5 to 5 g O2 m

-2 d-1 Thomann (1972), Mills et al. (1985)

Net respiration rate same order of magnitude as

photosynthesis rate

Mills et al. (1985)

Coliform die-off rate

coefficient

Coliform die-off rate

coefficient

0 to 84 d-1 Bowie et al. (1985), Thomann and Mueller (1987)

Settling velocity 1 to 100 m d-1 Thomann in review

Resuspension velocity 0.1 to 50 m yr-1 Thomann in review

Net settling velocity 0.1 to 50 cm yr-1 Thomann in review

Definition of symbols and explanation of terms:

ON = organic nitrogen ON hydrolysis = degradation of organic nitrogen to ammonia

Ammonification = oxidation of ammonia to nitrate Nitrification = oxidation of nitrite to nitrate

5-7
combination of freshwater inflow, wind conditions, tidal

conditions, and storm effects represent a critical circulation condition on which the design of a sewage

treatment plant should be based to provide adequate

protection of water quality. Therefore, calibrations are

usually based on uniformly constant roughness coefficients and literature estimates of eddy viscosity values that only attempt to capture estimates of gross

circulation patterns for selected conditions. The few

readily available studies (many are published in “grey

literature” reports) that have explored circulation in

detail, did not include sensitivity. Typically, this sort of

indirect calibration works well when the estuary can be

simulated with a one-dimensional model, but it is also

the method most frequently attempted for all types of

flow analyses to establish what combinations of conditions lead to a reasonable worst case design standard. Similarly, the sensitivity of water quality to

hydrodynamic conditions has not been explored in any

study that leading experts are aware of. (conclusion of

the January 1988 Workshop 3: Hydrodynamic and

Water Quality Model Interfacing and Workshop 4:

Long Term Modeling of Chesapeake Bay, Baltimore,

Maryland, U.S. Army Corps of Engineers and U.S.

Environmental Protection Agency).

The best studies attempt to collect current velocity data

for calibration but questions remain about the appropriate procedure for averaging data for comparison

with model results. As a result, opportunities remain

for the development of innovative approaches to data

collection and interpretation for comparison with model

simulations. Generally, water elevations measured at

a very few locations (one to three) are the only data

readily available for direct calibration (e.g., Thatcher

and Harleman 1981). Typically, circulation models are

indirectly calibrated from salinity or conservative tracer

measurements that also must be used to calibrate the

mass transport model as mentioned above. Indirect

calibration can result in an imprecise calibration of both

the circulation and mass transport algorithms but this

is not a severe drawback unless the critical water

quality components of the waste load allocation model

are sensitive to small changes in circulation and mass

transport. In addition, hydrodynamic models are more

firmly based on first principles than other water quality

model components. As a result, there is a greater

possibility of making valid hydrodynamic predictions

without extensive calibration.

In contrast with two- and three-dimensional models, a

number of one-dimensional hydrodynamic models

have been determined to be generally useful (e.g.,

Ambrose et al. 1988, Ambrose and Roesch 1982, and

Thatcher and Harleman 1981). These one-dimensional models are occasionally calibrated with current

velocity and water surface elevation data but more

Calibration Parameters for

Complex Model Simple Model Range of Values Guidance Documents and

References

Sediment oxygen demand rate Sediment oxygen

demand rate

0.0 to 11 in g O2 m

-2 d-1 Bowie et al. (1985), Krenkel and

Novotny (1980)

Rearation rate coefficient Rearation rate

coefficient

order of 0.001 to 0.1 d-1or

K2 = (depth)-1d

-1, depth in m

 Bowie et al. (1985), Kim and Holley

(1988), Thomann and Mueller (1987)

 Toxics 1st order decay

coefficient

Not well defined

Toxicant Fate Processes: See range for each individual

chemical

Schnoor et al. (1987), Mills et al. (1985)

Volatilization rate coeffiient

Biodegradation rate coefficient

Photolysis rate coefficient

Hydrolysis rate coefficient

Acid

Neutral

Base

Partitioning coefficient Thomann and Mueller (1987)

Conservative heavy

metals with settling

Thomann in review

Metals Fate Processes: See data bases in MINTEQA2 model

[Brown and Allison (1987)] and other

geochemical speciation models, and

Stumm and Morgan (1981), Schnoor et

al. (1987)

Solubility constants

Chemical equilibrium constants

Definition: K2 = reaeration coefficient.

Table 5-5. Guidance on the Selection of Model Coefficients and Parameters - Phase III

5-8
often are calibrated by indirect means. The dominant

calibration parameter for a one-dimensional model is

the roughness coefficient (the Manning n or Chezy C),

which is relatively easy to select. Supplement I also

reviews the selection procedure for the Manning n that

is used in simpler one-dimensional models.

5.2.2. Phase II of Calibration

Phase II involves the selection of coliform die-off coefficients, settling and re-suspension velocities for suspended sediment, BOD coefficients, and the set of

coefficients describing the nutrient cycles and photosynthesis. The selection of die-off coefficients is relatively straightforward compared with other phases of

the calibration (see Supplement VII, and Thomann and

Mueller 1987, and Bowie et al. 1985). Derivation of

parameters describing sediment transport and BOD is

somewhat more involved. The calibration of nutrient

and phytoplankton models requires some skill and

expertise because of the complexity of the potential

interactions between a number of the components of

the cycles involved.

Suspended sediment and BOD models are somewhat

more difficult to calibrate because the processes can

not be fully defined by measurement techniques readily available for the collection of calibration data. Suspended sediment is continually exchanged with

bottom deposits and this exchange can be relatively

important in tracing the fate of nutrients and sorbed

contaminants. Unfortunately, it is only feasible at present to measure changes in suspended sediment at

various locations over time and to measure long term

net deposition or erosion of sediments. The limited

guidance available for calibrating simple sediment

transport models is presented in Supplement VIII.

The calibration of a model for BOD is complicated if

settling and sorption to organic material is occurring

along with biodegradation. If only water column BOD

measurements are available, it is difficult to determine

the relative importance of deoxygenation, settling, and

adsorption of dissolved BOD on the dissolved oxygen

balance. Settling is usually not important, however,

because of recent advances (since the late 1960s) in

regulating organic solids in waste effluents. This is

especially true away from a localized mixing zone at

the point of discharge where some flocculation and

settling may occur. In addition, the relatively large

depths of estuaries preclude rapid adsorption of dissolved BOD like that observed in streams because of

the limited surface area available. Also, brackish waters tend to slow biotic reactions and growth which

should slow the uptake of dissolved organic carbon.

Therefore, calibration of BOD models frequently can

be a simple matter of accounting for the decay of BOD

measured in the water column. Recommendations for

calibration of a BOD model are given in Supplement

IX.

The effect of nitrification can be modeled in two ways.

First, simple nitrogenous BOD (NBOD) models have

been utilized. Second, and most useful, are nitrification models of organic nitrogen, ammonia, nitrite, and

nitrate. NBOD models are typically only useful when

nitrification is relatively unimportant in the dissolved

oxygen balance. Supplement X gives useful guidance

for the implementation of an NBOD model. Supplement XI gives guidance on the selection of nitrification

rate constants and parameters. The nitrification model

is more complex but this complexity is well justified by

the existence of well defined measurement techniques

and calibration procedures. Nutrient and phytoplankton models typically involve several separate major

components and a number of minor components that

are frequently ignored or lumped in with the major

components. The most difficult problem faced in the

calibration process is that a unique set of coefficients

is difficult to derive. The limited guidance available on

the calibration of nitrogen and phosphorus models is

given in Supplements XI and XII.

Wlosinski (1984) illustrates this problem with a simple

example involving an interactive four component

model shown in Figure 5.5. This example is somewhat

abstract but it shows that exactly the same values of

the state variables can be computed in two cases with

significantly different process rates controlling the

magnitude of mass transfer between environmental

components. In addition, Wlosinski shows that validation testing also can fail to detect a problem unless the

data set is significantly different from the calibration

data. Therefore, he recommends, as we emphasize

in this section, that models be carefully validated and

suggests that as many process rate measurements be

made as possible. These are measurements of gas

transfer, benthic exchange, and degradation rates, to

name a few of the most important. Clearly, it is not

possible to uniquely describe an estuarine water quality system without at least one process rate measurement.

5.2.3. Phase III of Calibration

The final phase of calibration can be either difficult or

extremely easy depending on how well other components have been calibrated and whether process

measurements such as the reaeration rate and sediment oxygen demand rates have been measured as

part of the calibration data collection study. Typically,

this final phase highlights weaknesses in the prior

calibration steps that must be addressed by repeating

some steps to achieve a more consistent overall calibration. In fact, it is more useful to attempt a quick step

through the calibration procedure to obtain a

5-9
preliminary indication of which parameters and coefficients may be the most important. This assessment

can be based on a preliminary sensitivity analysis.

At this stage in the calibration of a eutrophication and

dissolved oxygen model, the available guidance is

relatively straightforward. Supplements XIII, XIV and

XV describe methods of estimating reaeration coefficients and rates of sediment oxygen demand. Once

these values are initially selected, it becomes a matter

of making different trials until model simulations and

measurements are in reasonable agreement.

Available guidance for calibration of toxic chemical

models is not as clear. Generally, it is not always clear

what types of models should be implemented and it is

difficult to ascertain beforehand what measurements

may be required to form a comprehensive data set for

calibration and validation. At this time, the best guidance is contained in Schnoor et al. (1987).

Schnoor et al. (1987) review formulations of the fate

processes for organic chemicals and heavy metals.

They review the effects of biodegradation, hydrolysis,

oxidation, photolysis, volatilization, sorption, and bioconcentration for organic contaminants and compile

rate constants for these processes that can be used in

model calibration.

Schnoor et al. (1987) also review the transformation

and transport mechanisms affecting selected metals.

These include cadium, arsenic, mercury, selenium,

lead, barium, zinc, and copper. In addition, screening

level information can be obtained from metals speciation models (Brown and Allison 1987).

In review, Robert Thomann recommends treating

heavy metals as conservative constituents except for

partitioning with sediments when crude estimates of a

distribution coefficient can be used to estimate dissolved concentrations. Estimates of the distribution

coefficient can be obtained from Schnoor et al. (1987)

or Thomann and Mueller (1987). Geochemical speciation models such as MINTEQA2 (Brown and Allison

1987) can be used to estimate distribution coefficients

(when dissolved solids are not very high — i.e., applicable for fresh or brackish waters but not sea waters)

in addition to being used to determine potential mobility

as indicated above.

Figure 5-5. Example showing that calibration is not unique unless material transformation rates are specified and that validation

should be performed with significantly different data sets [Wlonsinski (1984)].

5-10
5.3. Model Validation

Validation testing is designed to confirm that the calibrated model is useful at least over the limited range

of conditions defined by the calibration and validation

data sets. As indicated earlier in this section, the

procedure is not designed to validate a model as being

generally useful in every estuary or even validate the

model as useful over an extensive range of conditions

found in a single estuary. Validation, as employed

here, is limited strictly to indicating that the calibrated

model is capable of producing predictively valid results

over a limited range of conditions. Those conditions

are defined by the sets of data used to calibrate and

validate the model. As a result, it is important that the

calibration and validation data cover the range of conditions over which predictions are desired.

Validation testing is performed with an independent

data set collected during a second field study. The

field study may occur before or after the collection of

calibration data. For the best results, however, it is

useful to collect the validation data after the model has

been calibrated. This schedule of calibration and validation ensures that the calibration parameters are fully

independent of the validation data. To extend the

range of conditions over which the calibrated model is

valid, however, it may be useful to save the initial study

for validation testing if it is expected that data collected

at a later date will provide a less severe test of the

calibrated model.

At present, it is very difficult to assemble the necessary

resources to conduct the desired number of surveys.

Therefore, it is important that surveys be scheduled in

an innovative manner and the choice of calibration and

validation data sets remain flexible in order to make

the test of the calibrated model as severe as possible.

Many studies are faced with severely limited resources

for sampling and laboratory analysis that preclude

collection of more than one set of data. If this highly

undesirable circumstance occurs, the historic data

should be investigated to determine whether the model

can be calibrated a priori and validated with one set of

data or vice versa. In any event, it is very important

that both calibration and validation data be defined

even if this involves splitting a single data set (a data

set divided into two data sets by assigning every other

datum or set of data in each time series, to separate

data sets or by dividing time series data into sets

covering different time periods as done by Ambrose

and Roesch (1982) for calibration to selective conditions).

If a split data set is used, however, it must be clearly

noted that these types of limited studies are not fully

useful. Wlosinski (1985) shows that the likelihood of

being unable to detect a poorly selected set of coefficients is quite low using split data sets.

Too many times, limited studies only attempt calibration. This, in effect, limits the study to describing the

conditions during the calibration data collection period

and increases the uncertainty associated with the

waste load allocation. In fact, uncertainty can not be

reliably assessed.

Once the validation tests are concluded, Reckhow and

Chapra (1983) recommend that the model be recalibrated to obtain the overall optimum calibration. This

should improve the overall predictions but it should not

be used as a shortcut to avoid rigorous validation

testing. Overall optimum calibration can be achieved

by minimizing the least squares error for all data available in multiple sets or by obtaining the best overall fit

between predictions and measurements from visual

inspection.

5.4. Model Testing

During and after the calibration and validation of a

model, at least two types of testing are important.

First, throughout the calibration procedure, a sensitivity test provides a method to determine which parameters and coefficients are the most important. Second,

there are a number of statistical tests that are useful

for defining when adequate agreement has been obtained between model simulations and measured conditions.

The sensitivity analysis is simply an investigation of

how much influence changes in model coefficients

have on simulated results. Typically, important coefficients, parameters, boundary conditions, and initial

conditions are varied by a positive or negative constant

percentage to see what effect the change has on

critical predictions. Values of ±1, ±10, and ±50 percent

have been used frequently. The coefficients and parameters are changed one at a time and the effects are

typically ranked to show which parameters have the

most influence and which have the least influence.

A sensitivity analysis also is useful when applied to a

preliminary calibration of a model using historic or

estimated conditions. In this case, the ranking can be

used to determine which coefficients and parameters

should be measured and which can be estimated. For

example, if a model is sensitive to SOD rates, these

should be measured rather than estimated. If other

parameters like the wind speed function have little

influence, very little effort should be expended to estimate its exact form.

The second type of testing involves assessment of the

goodness of fit for model simulations compared with

5-11
measurement of important water quality parameters.

In addition to making a visual assessment, a number

of statistical tests have proven useful (Ambrose and

Roesch 1982, Thomann 1982, Beck 1987, Beck 1985,

Southerland et al. 1984). These include:

1. Root mean square error,

2. Relative error,

3. Regression analysis,

4. Comparison of means, and

5. Other techniques.

Recent studies of heuristic methods (e.g., “rules of

thumb”) for the development of expert systems indicate that a visual fit of model predictions to measured

data can quite accurately be used to obtain accurate

calibrations, especially if performed by experts. However, a number of useful statistical criteria can be

employed to obtain an optimum fit and these avoid any

bias that may be introduced by inexperienced modelers.

5.4.1. Root Mean Square Error

The most widely used criterion to evaluate the agreement between model predictions and measurements

is perhaps the root mean square (rms) error or standard error of the estimate (Ambrose and Roesh 1982)

defined as

rms =







Σ(Cm − Cs)

2

N







0.5

(5.1)

where

Cs= simulated concentration or state variable

Cm= measured concentration or state variable

N= number of measurements

The rms error can be used to compute simultaneous

discrepancies at a number of points or it can be used

to compute discrepancies between measurements

and predictions at a single point over time (Thomann

1982). Ensemble or global rms errors can be computed for a series of measurements at multiple points

over time as

rmsg =







Σ (Cm − Cs)

2

Ni







0.5

(5.2)

where

Ni = the total number of measurements at every site

over all periods of time.

Equation (5.2) is frequently useful for obtaining the

best overall fit between a model and a number of

different data sets where each measurement is considered to be equally valid. For example, this statistic

would be useful for obtaining an overall calibration for

two or more sets of data containing different numbers

of measurements that are all equally accurate. Different weighting schemes could be applied if measurements were of differing accuracy (i.e., when a less

accurate dissolved oxygen meter is used in a different

part of the estuary or during a different study). Beck

(1987) discusses these schemes and the elements of

engineering judgement involved.

When the rms error is expressed as a ratio to a spatial

or temporal mean, the resulting statistic, which is the

coefficient of variation (Kennedy and Neville 1976),

represents a second type of relative error that expresses relative discrepancy. This type of relative rms

error can be useful for obtaining an ensemble statistic

to obtain the best overall fit for composite sets of data

where each individual measurement may not be comparable between two or more separate sets of data.

For example, one data set may contain more measurements that document greater dynamic uncertainty

that should not be overweighted.

In general, the use of the rms error assumes that all

discrepancies are of the same order and this is usually

true over a limited range of conditions. However,

calibration over a more extensive range where discrepancies between model predictions and measurements may be proportional to the magnitude of the

measurement, other statistics (e.g., relative error) will

be more appropriate. Finally, the rms error has at least

one disadvantage (Thomann 1982). It is not readily

evident how a pooled statistic for all state variables can

be computed to assess over all model credibility.

5.4.2. Relative Error

When discrepancies between model simulations and

measurements are not uniform over parts of the esFigure 5-6. Cumulative frequency diagram.

5-12
tuary or with time, the relative error may be a more

appropriate statistic for testing calibration or validation.

The relative error is defined as (Thomann 1982)

e =

|Cm

___

− Cs

__

|

Cm

___ (5.3)

where the overbars denote the average measured or

simulated valued. Averages are performed over multiple sites or over time and cumulative frequency of

error can be computed (Thomann 1982). The cumulative frequency (see for example Figure 5.6) can be

used to estimate the median error and various percentiles such as the 10th and 90th exceedance frequencies. Southerland et al. (1984) notes that the 50th

percentile of median error is usually reported in waste

load allocations since this is the most easily understood value. The relative error behaves poorly for

small values of measurements if discrepancies are not

proportional to the magnitude of the measurement

(i.e., small values of Cm magnify discrepancies) and if

Cm>Cs, (since the maximum relative error is usually

taken to be 100 percent). Therefore, the relative error

is best for computing composite statistics when discrepancies are not constant as may occur when calibration over an extensive range is attempted.

Thomann (1982) and Ambrose and Roesch (1982)

seem to offer the best available guidance on what

relative errors may be appropriate to achieve adequate

estuarine dissolved oxygen model calibration. In general, median relative errors should be 15 percent or

less. Values of the relative error obtained for a number

of estuaries by Thomann (1982) and Ambrose and

Roesch (1982) are given in Table 5.6. Note that

Ambrose and Roesch define the relative error without

the absolute brackets as

e =

Cm

___

− Cs

__

Cm

___ (5.4)

so that on average, values of this statistic are smaller

than or equal to the values obtained from Equation

(5.3).

5.4.3. Regression Analysis

A regression analysis is very useful in identifying various types of bias in predictions of dynamic state variables. The regression equation is written as

Cm

___

= a + b Cs

__

+ ε (5.5)

where

a = intercept value

b = slope of the regression line

ε = the error in measurement mean, Cm.

The standard linear regression statistics computed

from Equation (5.5) provide a number of insights into

the goodness of fit for a calibration (Thomann 1982,

Southerland et al. 1984). These include:

1. The square of the correlation coefficient, r2

(measure of the percent of the variance accounted for)

between measured and predicted values,

2. The standard error of estimate (Kennedy and

Neville 1976), representing residual error between

model and data,

3. The slope estimate, b, and intercept, a, and

Relative Error

Estuary

|Cm

___

−Cs

___

|

Cm

___

Cm

___

−Cs

___

Cm

___

New York Harbor 5% to 35 %

Manhasset Bay, NY 5%

Wicomico Estuary, MY 58%

Table 5-6. Relative Error in a Number of Estuarine Model

Calibrations for Dissolved Oxygen. [Thomann

(1982) and Ambrose and Roesch (1982)]

Figure 5-7. Types of bias and systematic error determined

by regression analysis [(O’Connor (1979), Thomann (1982),

and NCASI (1982)].

5-13
4. The test of significance for the slope and intercept.

Figure 5.7 from O’Connor (1979), Thomann (1982),

and NCASI (1982) illustrates the insight available from

a regression analysis. Figure 5.7(a) shows that an

unbiased estimate can result even when a correlation

between measured and predicted data does not exist.

Figure 5.7(b), (c) and (d) show that a very good

correlation can occur when a constant fractional bias

(b > 1 or b < 1) and a constant bias (a > 0) occurs. The

slope of the regression curve indicates how well trends

can be projected with the calibrated model and the

intercept of the regression indicates if any systematic

error is present in the calibrated model. The test of

significance of the slope and intercept to detect the

probable existence of any error in trend or systematic

errors should be based on the null hypothesis that b =

1 and a = 0. The test statistics (b -1/sb) and a/sa are

distributed as the student’s t distribution with n-2 degrees of freedom. See standard texts such as Kennedy and Neville (1976) for formulas to compute the

standard deviation of the slope and intercept, sb and

sa. Thomann recommends a “two-tailed” t test employing a 5 percent level of significance. This yields a

critical t value of approximately 2 for the rejection of

the null hypothesis.

5.4.4. Comparison of Means

A third criterion for agreement between measured and

predicted values can be derived from a simple test of

the difference between the computed and measured

mean values (Thomann 1982). The most general test

statistic for this purpose is based on the Student’s t

probability density function (see Kennedy and Neville

1976)

t =

Cm

___

− Cs

__

− d

sd

(5.6)

where

d = true difference between model predictions and

measurements (normally zero)

sd = the standard deviation of the difference given by a

pooled variance of measured and predicted variability

where if these variances are assumed equal,

sd = (2 sx ′ )

1

⁄2

 (5.7)

where

sx ′ = standard error of estimate of the measured data

given by the standard deviation, sx , divided by the

number of measurements

(sx ′)2= (sx)

2

⁄ N (5.8)

The use of a test like this comparison of means requires that the computed statistic be compared with a

statistic value based on a level of significance or

probability. Typically, a 5 percent level is used. At least

one stream study (NCASI 1982) has required that at

least 95 percent of the data fall within the 95 percent

confidence interval (5 percent level of significance) to

achieve calibration. Less stringent criteria were used

to evaluate the validation of the model for the same

stream. These criteria were that 60 percent of data

had to fall within the 95 percent confidence interval.

Where

Tidal Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

Tidal range (m) 82 -0.001 -0.00 0.036 0.06 0.92 0.046 0.98

High water arrival (min) 82 0.076 0.02 0.27 0.07 0.97 0.03 0.99

Table 5-8. Hydrodynamic Model Error Statistics for the Potomac Estuary [Ambrose and Roesch (1982)]

Tidal Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

Tidal range (m) 15 -0.012 -0.00 0.093 0.02 1.03 -0.06 0.98

High water arrival (min) 15 -18.4 -0.09 19.9 0.10 0.94 -6.69 1.00

Table 5-7. Hydrodynamic Model Error Statistics for the Delaware Estuary [Ambrose and Roesch (1982)]

5-14
a large number of data are available, a statistic based

on the gaussian or normal distribution can be used in

place of the Student’s t distribution.

5.4.5. Other Techniques

Beck (1987) and Southerland et al. (1984) describe

other techniques that can be used to aid in parameter

estimation to calibrate models. Generally, these methods require some knowledge of the distribution of

discrepancies between measurements and predictions or involve tests to determine the distribution.

Methods requiring a priori knowledge of the distributions include: 1) maximum likelihood estimator, and 2)

Bayesian estimator. Southerland et al. (1984) note

that the Kolmogorov-Smirnov one sided test can be

used to evaluate whether a significant difference exists

between an observed distribution and a normal distribution. If the distribution is normal, the F-test (Kennedy and Neville 1976) of the variances of

measurements and predictions is a measure of the

goodness of fit. In addition, the Kolmogorov-Smirnov

two sided test can be used to evaluate goodness of fit.

5.4.6. Guidance on Statistical Criteria for

Calibration and Validation

Few studies have included calculations of statistical

criteria to guide model calibration and validation and

what work that is available in engineering reports has

not been adequately compiled. An exception of note

are the studies of the Potomac and Delaware Estuaries by Ambrose and Roesch (1982).

The work of Ambrose and Roesch (1982) is important

because it presents benchmarks to which other calibrations can be compared and evaluated. In this

regard, these data are very similar to the compilation

of error statistics compiled by Thomann (1982) to

define how well a calibrated model should simulate

dissolved oxygen. Thomann’s guidance only covers

relative error statistics. Ambrose and Roesch define

average errors, relative errors, root mean square errors, coefficient of variation, regression intercept, regression slope, and correlation coefficients but only for

two estuaries. Nevertheless, the Potomac and Delaware Estuaries are among the most important East

Tidal Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

Chloride concentration (mg/L) 37 -85. -0.02 200. 0.05 0.95 300. 1.00

Dye concentration (ug/L)

All data: 189 0.00 0.00 0.12 0.44 0.69 0.08 0.84

Period 1: 50 0.11 0.27 0.18 0.44 0.68 0.05 0.81

Period 2: 139 -0.03 -0.14 0.08 0.37 0.85 0.06 0.85

Peak dye concentration (ug/L) 14 -0.01 -0.01 0.15 0.22 0.96 0.02 0.91

Movement of dye peak (km) 14 -0.9 -0.14 1.4 0.22 0.98 1.0 0.97

Width of 0.1 ug/L dye isocline (km) 10 1.9 0.10 1.3 0.07 0.66 4.5 0.96

Table 5-10. Transport Model Error Statistics for the Potomac Estuary [Ambrose and Roesch (1982)]

Tidal Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

Chloride concentration (mg/L) 35 -140. -0.10 440. 0.31 0.97 -98.0 0.97

Movement of 500 mg/L Isochlor (km) 5 -1.9 -0.22 2.8 0.33 0.78 -0.05 0.99

Peak dye concentration (ug/L)

All data: 14 0.03 0.09 0.10 0.30 0.82 0.09 0.82

Period 1: 7 0.06 0.14 0.14 0.32 0.52 0.27 0.62

Period 2: 7 0.01 0.05 0.03 0.14 0.76 0.07 0.92

Movement of dye peak (km)

All data: 14 3.4 0.26 6.0 0.45 1.12 1.8 0.96

Period 1: 7 1.6 0.54 5.1 1.73 0.15 4.2 0.44

Period 2: 7 5.0 0.21 6.6 0.28 1.26 -1.1 0.98

Width of 0.1 ug/L dye isocline (km)

All data: 14 1.3 0.05 3.2 0.13 0.83 5.5 0.90

Period 1: 7 1.0 0.04 2.3 0.10 0.84 4.5 0.96

Period 2: 7 1.6 0.06 4.0 0.14 0.38 20.0 0.47

Table 5-9. Transport Model Error Statistics for the Delaware Estuary [Ambrose and Roesch (1982)]

5-15
Coast estuaries and seem to be quite representative

of drowned river valley types.

Ambrose and Roesch (1982) give average errors

(E), relative errors (RE) [note that Equation (5.4) and

not Equation (5.3) is used by Ambrose and Roesch],

root mean square errors (SE), coefficient of variation

(CV), regression intercept (a), regression slope (b), and

correlation coefficients (r) in Tables 5.7, 5.8, 5.9, 5.10,

5.11, 5.12, 5.13 and 5.14. Tables 5.7 and 5.8 present

error statistics from the calibration of a hydrodynamics

model for the Delaware and Potomac estuaries. Tables

5.9 and 5.10 present error statistics from the calibration

of a transport model for the Delaware and Potomac

Quality Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

(a) Median Concentrations (mg/L)a

Dissolved Oxygen 36 -0.15 -0.04 0.69 0.18 0.84 0.44 0.93

BOD 8 -0.70 -0.11 0.97 0.15 0.84 0.37 0.93

Ammonia-N 36 0.05 -0.10 0.16 0.33 0.90 0.10 0.91

Nitrate-N 36 -0.11 -0.08 0.24 0.17 0.90 0.04 0.91

Organic-N 36 -0.11 -0.19 0.21 0.37 0.14 0.39 0.27

(b) DO categories

Zone 2 (mg/L) 9 -0.21 -0.04 0.50 0.10 0.78 0.90 0.91

Zone 3 (mg/L) 9 0.13 0.06 0.66 0.28 1.21 -0.38 0.78

Zone 4 (mg/L) 9 -0.10 -0.04 0.82 0.32 0.82 0.35 0.86

Zone 5 (mg/L) 9 -0.41 -0.08 0.73 0.15 0.74 0.87 0.92

Calibration (mg/L) 16 -0.06 -0.02 0.53 0.14 0.88 0.39 0.95

Verification (mg/L) 20 -0.22 -0.06 0.79 0.21 0.81 0.47 0.92

DO Minimumb9 -0.07 -0.05 0.55 0.41 1.54 -0.79 0.78

2 mg/L Reach Length (km)c9 -2.7 -0.13 6.0 0.28 0.90 -0.64 0.89

Table 5-11. Water Quality Model Error Statistics for the Delaware Estuary [Ambrose and Roesch (1982)]

Quality Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

(a) Median Concentrations

DO (mg/L) 32 -0.04 -0.01 1.02 0.17 0.80 1.12 0.86

NH3 (mg/L) 41 0.02 0.02 0.27 0.31 1.01 0.01 0.95

NO3 (mg/L) 39 0.05 0.07 0.18 0.26 0.79 0.21 0.90

TPO (mg/L) (as PO4) 40 0.01 0.01 0.20 0.16 1.03 -0.03 0.98

CHL (ug/L) 31 2.7 0.04 19.3 0.27 0.92 8.70 0.87

(b) Extreme Concentrationb

DO Min. (mg/L) 9 -0.02 -0.01 0.35 0.23 1.08 -0.15 0.93

NH3 Max. (mg/L) 15 -0.02 -0.01 0.20 0.11 0.91 0.15 0.96

NO3 Max. (mg/L) 12 -0.11 -0.09 0.25 0.20 0.85 0.08 0.93

TPO Max. (mg/L, as PO4) 14 -0.15 -0.05 0.30 0.10 1.00 -0.16 0.97

CHL Max. (ug/L) 8 -4.1 0.03 6.1 0.05 1.02 -7.1 0.99

(c) Reach Lengthc

DO < 5 mg/L 9 -2.1 -0.10 4.3 0.20 0.81 2.1 0.78

DO < 3 mg/L 9 -1.1 -0.11 3.2 0.33 0.66 2.2 0.70

NH3 > 1 mg/L 15 1.7 0.08 6.8 0.32 0.93 3.2 0.94

NO3 > 1 mg/L 12 -0.3 -0.02 6.6 0.46 0.91 1.0 0.95

TPO > 1 mg/L (as PO4) 14 0.0 0.0 8.6 0.23 0.80 7.6 0.79

Table 5-12. Water Quality Model Error Statistics for the Potomac Estuary, 1965-1975 [Amborose and Roesch (1982)]

5-16
Estuaries, respectively. Tables 5.11, 5.12, 5.13, and

5.14 provide error statistics from the calibration of

water quality models in the two estuaries. Example

5.1 gives a visual illustration of how well observations and simulations should agree to help put these

statistics into perspective.

From this work by Ambrose and Roesch (1982) and

Thomann (1982) it is possible to develop preliminary

guidance on how well simulations should agree with

measurements to achieve adequate calibration.

Ambrose and Roesch (1982) indicate that the coefficient of variation should be 5 to 10 percent for hydrodynamic variables, less than 45 percent for transport variables, and generally less than 90 percent for water

quality variables. The correlation coefficient should be

greater than 0.94 for hydrodynamic variables, greater

than 0.84 for transport variables, and generally greater

than 0.60 for water quality variables. The general guidance is summarized in Table 5.15.for water quality variables. The general guidance is summarized in Table

5.15.

Quality Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

(a) Median Concentrations (mg/L)

DO 32 -0.20 -0.03 1.15 0.16 0.54 3.00 0.77

CBOD 29 -1.00 -0.31 1.57 0.48 0.25 1.47 0.33

NH3 29 -0.11 -0.45 0.26 1.07 0.38 0.04 0.59

NO3 40 -0.02 -0.03 0.15 0.24 0.85 0.08 0.97

(b) Extreme Concentrationb(mg/L)

DO Min 8 -0.03 -0.01 0.86 0.25 0.70 0.99 0.62

CBOD Max 8 -0.26 -0.04 1.92 0.32 1.30 -2.09 0.66

NH3 Max 10 0.04 0.04 0.14 0.13 0.89 0.15 0.95

NO3 Max 10 -0.08 -0.05 0.18 0.11 0.90 0.10 0.85

(c) Extreme Locationc(km)

DO Min 8 -1.2 -0.10 3.7 0.31 1.02 -1.4 0.99

CBOD Max 8 -6.0 -0.82 10.5 1.45 0.01 1.1 0.04

NH3 Max 10 -1.4 -0.54 6.9 2.67 -0.03 1.2 -0.11

NO3 Max 10 -2.4 -0.31 5.5 0.70 0.71 -0.2 0.89

(d) Reach Lengthd (km)

DO < 5 mg/L 8 -3.2 -0.22 5.4 0.37 0.66 1.7 0.97

Table 5-14. Water Quality Model Error Statistics for the Potomac Estuary, 1977-1978 [Ambrose and Roesch (1982)]

Quality Response Variables

Calculated Errors Regression Statistics

N E RE SE CV a b r

Median concentration (ug/L)a32 12.2 0.16 53.2 0.69 0.82 26.2 0.69

Peak concentration (ug/L) 8 11.3 0.07 35.1 0.23 1.16 -14.2 0.94

Peak Location (km)b8 -4.8 -0.15 17.7 0.55 0.14 22.9 0.09

100 ug/L reach length (km)c8 2.8 0.11 10.9 0.42 0.86 6.5 0.89

a Concentrations are median values by river segment (16-26 km) and survey period.

Table 5-13. Chlorophyll-a Model Error Statistics for the Potomac Estuary, 1977-78 [Ambrose and Roesch (1982)]

5-17
Example 5.1. Calibration of Hydrodynamics, Mass Transport, and Toxic

Chemical Model for the Delaware Estuary

Ambrose (1987) calibrated a tidal transport and volatile chemical model of the Upper Delaware Estuary

(see Figure 5.8) to determine if seven volatile chemicals discharged by the Northeast Philadelphia

Wastewater Pollution Control Plant (NEWPCP) migrate 6 miles (9.7 km) upstream to the Baxter Drinking Water Plant intake. Earlier versions of the WASP

and DYNHYD models (Ambrose et al. 1988) were

calibrated using data collected for conventional pollution studies from the summer of 1968 until July

1976, and from volatile chemical data collected in October 1983. The seven chemicals were:

 1. Chloroform (CF);

 2. 1,2-dichloroethane (DCE);

 3. 1,2- dichloropropane (DCP);

 4. Dimethoxy methane (DMM);

 5. Methylene choloride (MC);

 6. Perchloroethylene (PCE), and

 7. Trichloroethylene (TCE).

Figure 5-8. Upper Delaware Estuary [Ambrose (1987)].

Error Statistics Criteria for Model Variables

Hydrodynamic Transport Water Quality DO Chlorophyll-a

Relative Errora15%

Relative Errorb

±30% ±25% ±45% ±3% ±16%

Cofficient of Variation 10% 45% 90% 17% 70%

Correlation Coefficient 0.94 0.84 0.60 0.80 0.70

a See Equation (5.3)

b See Equation (5.4)

Table 5-15. Preliminary Guidance on Error Statistic Criteria for Calibrating Estuarine Water Quality Models

5-18
DYNHYD is a one-dimensional hydrodynamics

model that is calibrated by selecting appropriate

Manning roughness coefficients and surface drag

coefficients. In this case, calibration was based on

annual average tidal heights where wind shear was

unimportant, leaving only Manning n values to be

selected. As noted later in Example 5.4, values of n

ranged from 0.020 to 0.045 in various areas of the

estuary. Figure 5.9 illustrates the agreement obtained with the selected Manning n values by comparing measured and simulated average spring tide

and mean tide (Ambrose 1987). Also see Table 5.7

for a statistical characterization of how well the

model was calibrated.

Mass transport components of the model were calibrated using Rhodamine WT dye data collected in

July 1974 from a four day steady release from

NEWPCP and slack-water salinity measurements.

The agreement between simulated and measured

slack-water dye concentrations is shown in Figure

5.10. Calibration involved changing the longitudinal

dispersion coefficient until the best agreement was

obtained. See Table 5.9 for the statistical evaluation

of the agreement between measured and simulated

characteristics.

The seven problem chemicals were checked and it

was found that more that 99% of the total chemical

was dissolved in the water column. As a result,

suspended sediment parameters were calibrated in

an approximate manner using average long term settling, scour and sedimentation data.

Chemical rate constants were determined from the literature and by various predictive methods. Volatilization

rate constants were determined from the Whitman two

layer resistance model using relationships between oxygen, water vapor, and the chemicals of concern.

Reaeration was predicted with the O’Connor-Dobbins

(1958) equation (see Supplement XIII). Evaporation

was predicted with the regression

Figure 5-9. Observed and predicted tidal ranges in the

Delaware Estuary [Ambrose (1987)].

Environmental

 Property

Input

Value

Environmental Process

Kp

a

Ks

b

Kv

c

KH

d

Ko

e

KpH

f

Ks

g

Sediment conc.

Suspended (mg/L) 20-50 X X

Benthic (kg/L) 1.35 X X

Organic carbon fraction

Suspended sediment 0.015 X X

Benthic sediment 0.065 X X

Sediment settling velocity

(m/day)

5.0 X

Bed sediment resuspension velocity (cm/yr)5.0 X

Pore water diffusion

(cm2/s)

1.0 x 10-5 X

Benthos mixing factor (0-

1)

0.5 X

Surficial sediment depth

(cm)

6.1 X

Water column depth (m) 3-10 X X X

Water column temp (oC) 25 X X X X X XX

Average water velocity

(m/s)

0.65 X

Wind speed at 10 cm (m/s) 2.0 X

pH and pOH

(standard units)

7.0 X

Concentration of oxidants (moles/L)

1.0 x 10-9 X

Surface light intensity

(Langleys/day)

— X

Cloud cover (fraction) 0.3 X

Light extinction

coefficient (m-1)

3.0 X

Active bacterial

populations

suspended (cells/ml) 1.0 x 104

X

benthic (cells/100g) 2.0 x 106

a

 Sorption e Oxidation

b

Benthos-water column exchange fPhotolysis

c

 Volatilization gBacterial degradation

d

Hydrolysis

Table 5-16. Environmental Properties Affecting Interphase Transport and

Transformation Processes [Ambrose (1987)]

5-19
Figure 5-10. Observed and predicted dye concentrations [Ambrose (1987)].

Chemical Propertiesa

Compund Simulated

DCP DMM DCE PCE TCE MC CF

General molecular weight (g/mole) 113 76.1 99.0 165.8 131.39 84.94 119.38

Solubility (mg/L) 2.7 x 103

3.35 x 103b 8.69 x 103 200 1.1 x 103

2.0 x 1048.2 x 103

Sorption

Octanol-water partition, Kow

(mg/L octanol per mg/L water)

15 1

c

30 759 263 18.2 91

Organic carbon partition, Kα (L/kg) 1 0.4 14 364 126 8.8 44

Volatilization

Henry’s Law constant (m3-atm/mole) 2.31 x 10-3 1.7 x 10-4d 9.4 x 10-3 1.53 x 10-2 9.1 x 10-3 2.03 x 10-3 2.88 x 10-3

Vapor pressure (torr) 2 325e61 14 57.9 362.4 150.5

Volatilization ratio to oxygen 0.53 —- —- 0.51 0.55 0.65 0.58

Hydrolysis

Acid-catalysis rate constant (per molar per

hour)

0 0.12f0 0 0 0 0.23

Base-catalysis rate constant (per molar

per hour)

0 0 0 0 0 0 0

Neutral rate constant (per hour) 7.2x10-4 0 2.0x10-9 0 0 1.15x10-7 2.5x10-9

Photolysis near surface rate constant

(per day)

0 —- 0 0 0 0 0

Oxidation constant (per molar per

hour)

100 —- 100 100 500 100 100

Bacterial degradation second order

rate constant (ml per cell per hour)

1.0x10-9 —- 1.0x10-9 1.0x10-9 1x10-10 —- —-

a

 Values from Mabey et al. (1982) unless otherwise noted c Leo et al. (1971) e Boublik et al. (1984)

b Valvani et at. (1981) d

 Hine and Mookerjee (1975) f Shubert and Brownawell (1982)

Table 5-17. Chemical Properties Affecting Interphase Transport and Transformation Processes [Ambrose (1987)]

5-20
equation of Liss (1973) which ignores the vapor

pressure deficit in the atmosphere

E = 4.46 + 272.7 W(5.9)

The Evaporation rate is in m day-1 and W is wind

speed in m sec-1 at a 10 cm (0.33 ft) height estimated

from 2 m (6.6 ft) measurements in the area and

converted to the 10 cm (0.33 ft) height assuming that

the logarithmic profile is valid and that the roughness

height of the water surface is typically 1 mm (0.0033

ft).

Data defining the environmental properties and

chemical properties are reproduced in Tables 5.16

and 5.17. Table 5.18 gives the computed rate constants for volatilization, hydrolysis, biodegradation,

oxidation, and photolysis plus the total loss rate

constant.

The calibration of the chemical kinetics model is

more of a one step validation process of confirming

that the literature values are correctly applied for the

model and physical conditions at the site. To check

the validity of the model, the loads of chemicals and

the uncertainty associated with the loads were specified as presented in Figure 5.11. Hydrodynamics

and mass transport for the October 1983 period

when the volatile chemical samples were collected,

were assumed (there were no measurements available) to be governed by mean and spring tides

(noted to occur during the study) and a steady freshwater inflow of 3010 ft3

 sec-1 (85.2 m3 sec-1). The

model was used to simulate 30 days with mean tide,

steady freshwater flow, and constant loads of chemicals from NEWPCP so that a dynamic steady state

(i.e., tidal conditions simulated by the model closely

matched the simulations of the preceding tidal cycle)

was achieved. The simulation was continued one

more day to represent the spring tide observed when

the volatile chemical samples were collected. These

simulations of width and depth average concentrations were compared to the median and range of

concentrations obtained from grab samples collected at three locations upstream of the waste inflow.

These results are given in Figures 5.12, 5.13, 5.14, and

5.15 for DCP, DMM, DCE, and PCE. The monitoring

stations, Tacony-Palmyra, Baxter (water intake), and

Logan Point were located at 3, 6, and 11 miles (4.8, 9.7,

and 17.7 km) upstream of the waste inflow, respectively.

Predicted and simulated concentrations of TCE, CF, and

MC were below detection limits (1 μg/L) at the water

intake (see Table 5.19).

Compound

Simulated

Concentrations (g/L)

Error

Factor NEWPCP

 Effluent

Baxter

Observed Predicted

DCP

Median 6,050 66 57 1.2-1

95% Interval 1,360-16,800 56-84 12-138

DMM

Median 591 9.4 6.2 1.5-1

95% Interval 25-2,820 7.7-13.6 0.3-30

DCE

Median 213 2.0 2.1 1.0

95% Interval 67-2,380 1.2-3.0 0.7-24

PCE

Median 54 2.1 0.5 4.2-1

95% Interval 30-85 0.2-2.6 0.3-0.8

TCE

Median 9.3 0.4 0.09 4.4-1

95% Interval 2.0-33 0-2.5 0-0.3

CF

Median 4.4 0.4 0.04 10.0-1

95% Interval 3.2-7.5 0.3-0.9 0.03-0.07

MC

Median 2.5 0.04 0.03 1.3-1

95% Interval 1.7-11 0-0.9 0-0.15

Baxter [Ambrose (1987)]

Figure 5-11. Northeast Water Pollution Control Plant Effluent

Concentrations, October 2-3, 1983

[Ambrose (1987)].

Compound

Simulated

Predicted Rate Constants (day-1)

KV

a

KH

b

KR

c

KO

d

KPH

e

K

f

DCP 0.11 0.02 10-4 10-6 0 0.13

DMM 0.10 10-6 0 — — 0.10

DCE 0.12 10-5 10-4 10-6 0 0.12

PCE 0.11 0 10-4 10-6 0 0.11

TCE 0.12 0 10-5 10-6 0 0.12

MC 0.14 10-6 — 10-6 0 0.14

CF 0.12 10-6 — 10-6 0 0.12

a

 Volatilization c Biodegradation e Photolysis

b

 Hydrolysis d Oxidation f Total

Delaware River near Philadelphia

[Ambrose (1987)]

5-21
Figure 5-12. Observed and predicted DCP concentrations

[Ambrose (1987)]. Figure 5-14. Observed and predicted DCE concentrations

[Ambrose (1987)].

Figure 5-15. Observed and predicted PCE concentrations

[Ambrose (1987)].

Figure 5-13. Observed and predicted DMM concentrations

[Ambrose (1987)].

5-22
At this point, the model is sufficiently calibrated to

establish a link between the high concentrations measured at the water intake and the waste load and

establishes that any other loads are insignificant. Next

the concentrations measured at, and predicted at and

between monitoring locations can be compared to

water quality standards (keeping in mind that this

particular model has a tendency to slightly underpredict because of the coefficients chosen from the literature and only predicts averaged values) to determine

where water quality standards are violated. If standards do not exist or are not adequate, a human and

ecological risk assessment can be performed. If it is

determined that the loads should be reduced, the

model can be used to make a preliminary estimate of

the total load reduction required or after the calibration

is refined somewhat to better predict concentrations at

the water intake or other critical locations, the model

can be used to set loads. To set the final loads, the

calibrated model could be used to investigate the effect

of extremely low flow and extremely high tides as well

as typical conditions.

Jet dilution models can be used to set the mixing zone

limits if any are permitted. See Doneker and Jirka

(1988) for the recommended model.

5.6 Application Of The Calibrated Model In

Waste Load Allocations

Once the model is calibrated and validated, it is then

used to investigate causes of existing problems or to

simulate future conditions to determine effects of

changes in waste loads as part of the waste load

allocation procedure. To understand how the calibrated model is used, it is first necessary to review the

general waste load allocation procedure.

5.6.1 Waste Load Allocation Procedure

There are several components of the waste load allocation procedure as illustrated in Figure 5.16. The

calibration and use of models is only a part of the

overall decision making process that also includes

some analysis of economic and social issues. Many

of the decisions based on economic and social issues

have been already addressed in most estuaries and

coastal waters but as a general practice, these issues

involved in defining water quality standards should be

revisited for each study. Also, in local areas of large

water bodies some refinement of standards may be

necessary, and this should be addressed as part of a

general procedure. Typically, the regulatory agency

Figure 5-16. Componennts of the waste load allocation

procedure.

Figure 5-17. General waste load allocation procedure. Note

WQ = water quality, NPDES = National Pollution Discharge

Eliminiation System, and TMDL = total maximum daily load.

5-23
should determine that the published standards are still

valid and useful.

The general procedure for waste load allocation is

shown in Figure 5.17 and has the following steps

(Thomann and Mueller 1987, Krenkel and Novotny

1980, Driscoll et al. 1983):

1.Designate desirable water uses for the estuary,

coastal area, or harbor of interest. Examples include

maintaining water quality to permit commercial fin and

shell fishing, maintain habitat diversity to protect the

ecological health of the estuary, to allow use of the

water in industrial applications such as process cooling, use of water for drinking in freshwater segments,

recreational boating and fishing, and use of the estuary

for navigation.

2.Investigate criteria available to protect the desired

water uses. See Table 5.20 for the main criteria documents.

3.Select numerical criteria to protect the designated

uses (i.e., 5 mg/L dissolved oxygen to protect certain

fish species).

4.Define waste assimilative capacity. This involves

the use of a water quality model or simplified analysis

to determine the cause and effect relationship between

existing and projected loads, and water quality response of the estuary. The modeling alternative involves calibration and validation of the model with

site-specific data as described in this section. The

simplified analysis (see Mills et al. 1985) involves

analysis of existing data and some engineering judgement (typically from experts). The complexity of estuary problems usually overwhelmingly favors a

modeling approach.

5. Define existing loads. This is done as part of the

calibration of any model used to determine the assimilative capacity but these load measurements may not

provide all the information required. In addition, the

typical loads and maximum loads must be determined

for any sensitivity analysis and projection of critical

effects. When the analysis focuses on point sources

(i.e., when nonpoint sources are unimportant), the

study is termed Waste Load Allocation. When the

analysis focuses on nonpoint sources, the study is

termed a Load Allocation. Total Maximum Daily Loads

are determined from both the Waste Load Allocation

and Load Allocation. The definition of existing and

projected loads are usually best done in cooperation

with the discharger when strict quality assurance of the

data is possible.

6.Project future loads. This step defines future capacity required for continued economic growth in an area

and is done in consultation with the industries and

municipalities involved.

7.Determine a factor of safety or reserve capacity.

This is largely a policy matter involving what degree of

protection will be afforded. This should account for

uncertainty in the calibrated model and projection of

future loading.

8.Determine Total Maximum Daily Loads and individual dischargers waste load allocations (see EPA 1985

for definitions). This includes simulation with existing

and projected loads, and incorporation of reserve capacity to determine what load reductions or projected

loads will allow the water quality to remain at or above

the standards chosen. Decisions on how to allocate

load reductions to various dischargers depends on the

weighting scheme chosen by each state agency and

is typically based on state law and regulation. The

decision should be influenced by economic and social

factors that encompass differences in the ability of

municipalities and industries to

Primary

Documents

EPA’s “Gold Book” - US EPA, Quality Criteria for

Water 1986 (with updates), Rept. EPA 440/5-86-

001, Office of Water Regulations and Standards,

Washington, D.C., U.S. Government Printing

Office, No. 995-002-00000-8.

Any State criteria documents for the water body

of interest.

Secondary

Documents

Any information available in the open literature.

Historical

Documents*

EPA’s “Red Book” - US EPA, Quality Criteria for

Water, Rept. EPA 440/5-86-001, Washington

D.C. (superseded by EPAS’s “Blue Book” -

Environmental Studies Board, National Academy

of Sciences and National Academy of

Engineering, Washington, D.C., Rept. EPA-R3-

73-033, 1973).

“Green Book” - Report of the Committe on Water

Quality Criteria, Federal Water Pollution Control

Administration, U.S. Department of the Interior,

Washington, D.C. 1968.

McKee, J.E., and wolf, H.W., Water Quality

Criteria, 2nd edition, California State Water

Quality Control Board, Sacramento, 1963.

Water Quality Criteria, California State Water

Quality Control Board, Sacramento, 1952.

See p. iii of the Red Book for pre-1950 work in

this area.

 * Useful for tracing the development of criteria and citation of

additional information

Table 5-20. Main Sources of Criteria to Protect Designated

Water Uses

5-24
achieve load reductions (i.e., differences in economic

efficiency). Equity may also be considered to account

for past efforts to voluntarily reduce loads and to

account for differences between the dischargers who

have been located on the estuary for different lengths

of time. A sensitivity analysis, first order error analysis,

and Monte Carlo analysis is used to determine the

uncertainty in the total maximum daily loads selected.

See Brown and Barnwell (1987) for examples of how

uncertainty analysis is applied to streams.

9. For the total maximum daily loads selected, evaluate

the cost-benefit of the standards chosen. This step

may be somewhat controversial and applied in different ways. In general, however, the analysis should

consider:

a. Individual costs to the dischargers

b. Regional costs and the associated benefits of

improved water quality.

In practice it may difficult to separate steps 8 and

9 of the procedure.

10. If the economic analysis is favorable, the full effects

on present and future water quality are examined. If

appropriate, standards may be upgraded if necessary

to prevent degradation of existing water quality

(Krenkel and Novotny 1980). If meeting the standards

represents a significant economic or social impact,

adoption of different standards to forgo some water

uses may be in order.

11. If the standards and waste load allocations are

adequate, the standards are promulgated and the

NPDES (National Pollution Discharge Elimination System) permits are issued.

5.6.2 Critical Water Quality Conditions and

Projections

Once critical water quality conditions are defined for

the estuary, harbor or coastal area of concern, determining the waste assimilative capacity is relatively

straightforward. Models are available to relate critical

water quality responses to the loads for most problems. See Chapter 3 for guidance.

However, the definition of critical conditions for estuaries is not straightforward. For streams receiving organic loads, this is a straightforward matter of

determining the low flow and high temperature conditions. In estuaries, fresh water, tides, wind, complex

sediment transport, and other factors can be important

to determining the critical conditions. As of yet, there

are no clear methods to establish critical conditions,

especially in terms of the probability of occurrence.

The analyst must use considerable judgement in understanding the exact effects of the processes described in Chapter 2.

Once loads are set or if critical conditions or future

conditions are to be simulated, the calibrated model

can be used to predict the response to the different

conditions. The investigation may involve study of

extreme hydrological, meteorological, or hydrographic

events that affect mixing; waste loadings from point

and non-point sources; and changes in benthic demands. If the physical, chemical, and biological characteristics of the estuary or wastes entering the

estuary are changed, then it may be necessary to

modify model coefficients. However, these changes

can not be reliably predicted. As a result, some sensitivity analysis is necessary to assist in selection of

the appropriate safety factor in the total maximum daily

load.

Extreme circulation events can move sludge deposits

out of the estuary or into the estuary. Point source

reduction can cut off the organic deposits that cause

SOD. Nevertheless, it is not presently possible to

make more that crude estimates of the reduced SOD.

Greater degrees of waste treatment can also reduce

deoxygenation coefficients but it is not clear why this

occurs and when it should be expected. As a result,

estimates of the effects of changes in SOD, the deoxygenation coefficient, and other parameters are routinely made to see if a significant effect can occur, but

final calculations may conservatively assume that the

rates remain unchanged.

Occasionally, estimates of the effects on SOD can be

made by experts such as those with EPA Region IV

who have made extensive measurements in polluted

and clean areas and who understand how to conservatively extrapolate to future conditions. In addition, it

is possible to consult the existing data and make

reasonable estimates. See Supplement XV for guidance. Crude estimates of deoxygenation rate coefficients can also be made in a similar manner but with

less certainty. Tabulations of deoxygenation coefficients for different types of conditions may be less

certain because of the errors of calibration contained

in the tabulated estimates. Nevertheless, when some

judgement is employed, the tabulations and guidance

given in Supplement IX is usually adequate.

5.6.3 Component Analysis and Superposition

Applications involving setting total maximum daily

loads and individual waste load allocations for dissolved oxygen problems are conceptually simplified in

many cases by noting that a linear relationship usually

exists between loads and deficits. Only when phytoplankton and second order toxic chemical modeling is

5-25
required, does a nonlinear relationship between deficits or chemical concentrations and load exist. It is

also possible to investigate which components of a

waste load (unoxidized carbon or nitrogen versus nutrients that result in eutrophication), cause a dissolved

oxygen deficit. The linear relationship between waste

load components and deficit or other chemical concentrations (e.g., BOD or ammonia) is also very useful to

investigate the effect of multiple sources. A component analysis can be performed to determine the effect

of each load. For additional information, see Thomann

and Mueller (1987), Krenkel and Novotny (1980), and

Mills et al. (1985).

Investigation of existing problems is best pursued with

a components analysis that indicates those processes

and loads that contribute to the problems. For example, the cause of violations of a dissolved oxygen

standard can be determined from the relative contribution of various loads and the effect of sediment oxygen

demand, BOD decay, nitrification, photosynthesis, and

reaeration. This is illustrated in Example 5.2 from

Robert Thomann in review. Components of the maximum deficit are computed by keeping up with the

deficit calculated in each time step for each process:

reaeration, deoxygenation, nitrification, sediment oxygen demand, net photosynthesis, and by dilution with

other loads and tributaries.

Multiple sources that do not significantly increase estuary flow are usually handled in an additive fashion

according to the principle of superposition (Thomann

and Mueller 1987, Krenkel and Novotny 1980, and

Mills et al. 1985) as indicated above, since all water

quality models are linear except for phytoplankton

kinetics and when toxic chemical kinetics are not first

order. Therefore, a component analysis like that in

Example 5.2 would be performed that would separate

individual loads and the analysis would determine

which loads cause the maximum deficit or any deficit

below standards. Where different point sources contribute to one problem, some arbitrary allocation of

more restrictive treatment requirements based on

state policy will be necessary as discussed above.

The superposition of multiple sources is illustrated in

Examples IV-3, IV-5, IV-6, and IV-8 from Mills et al.

(1985).

Example 5.2 Component Analysis of Dissolved Oxygen Balance in the

Wicomico Estuary, Maryland

The Wicomico Estuary is a small arm of Chesapeake

Bay. Figure 5.18 shows the location of the Salisbury

Sewage Treatment Plant outfall, other tributaries, and

the model segmentation of the estuary. The problem

is to determine the required additional treatment beyond secondary levels at the Salisbury, Maryland Sewage Treatment Plant (Robert Thomann, in review). To

perform the analysis, a one-dimensional model was

calibrated for the estuary and a component analysis of

the dissolved oxygen balance was performed along

the axis of the estuary. The results are given in Figure

5.19. The upper panel gives the dissolved oxygen

deficit along the estuary where a maximum deficit of

almost 4 mg/L occurs near Mile 10 (km 16) down

estuary of the outfall. Near the outfall, the estuary is

supersaturated with oxygen. The component analysis

in the lower three panels shows that the discharge of

carbonaceous and nitrogenous demands from the

sewage treatment plant and the upstream deficit do not

contribute to the maximum deficit. However, the discharge of excess nutrients was a problem. The growth

of phytoplankton due to chlorophyll a levels of 300 ug/L

was stimulated by nutrients in the waste discharge.

The management decision for this waste load was then

to control the level of nutrients rather than increase the

level of carbon or nitrogen treatment (Robert Thomann

in review).

5-26
Figure 5-18 Model segmentation - Wicomico River, Maryland.

5-27
Figure 5-19. Component deficits for July 1971 dissolved oxygen verification [Robert Thomann in Review].

5-28
Manning n Chezy Cz Drag

Coefficient

 Cd = u*2/U2

DarcyWeisbach

 f

Fanning

 ff

Manning n

= n

=

C1

Cz

RH

1 ⁄ 6

=

Cd

1 ⁄ 2C1R1 ⁄ 6

g

1 ⁄ 2

=

C1 RH

1 ⁄ 6

f

1 ⁄ 2

(8g)

1 ⁄ 2

=

C1 RH

1 ⁄ 6

ff

1 ⁄ 2

(2g)

1 ⁄ 2

Chezy Cz

=

C1

n

RH

1 ⁄ 6

= Cz

=

g

1 ⁄ 2

co1

1 ⁄ 2

=

(8g)

1 ⁄ 2

(f )1 ⁄ 2

=

(2g)

1 ⁄ 2

(ff ) 1 ⁄ 2

Drag

Coefficient Cd =

g n

2

C1

2R1 ⁄ 3

=

g

Cz

2

= Cd =

f

8

=

ff

2

DarcyWeisbach f =

8 g n

2

C1

2R1 ⁄ 3

=

8g

Cz

2 = 8 Cd = f = 4 ff

Fanning ff

=

2 g n

2

C1

2R1 ⁄ 3

=

2 g

Cz

2 = 2 Cd

=

f

4 = ff

Notes:

1) C1 = unit conversion factos; equal to 1.0 if the hydraulic radius R is expressed in units of meters and 1.49 if expressed in

units of feet.

2) The Fanning friction factor is typically used in mechanical engineering applications.

3) Reports of values of the drag coefficient should be accompanied by a definition of Cd. Alternatively, Cd has been defined

[Chow (1959), Streeter and Wylie (1975)] as τ0 = (1 ⁄ 2) ρ Cd U

2

 or Cd = 2u∗

2

⁄ U

2

 where bed shear velocity, τ, divided by

water density, ρ, is the shear velocity, u∗ = (g RH S )

1 ⁄ 2

. S is the energy gradient of the flow. U is the average flow velocity.

Table 5-21. Relationship between Various Friction Factors used to Quantify Friction Loss in Estuaries

SUPPLEMENT I: SELECTION OF MANNING n VALUES

The effect of bottom friction on the flow in estuaries is

represented in a variety of ways in flow or hydrodynamic models. The most common method used in the

United States and in many other countries, employs

the Manning roughness coefficient to quantify friction

and turbulent hydraulic losses in the flow. However, a

number of other friction coefficients are used in the

models available. These are given in Table 5.21 along

with the relationship between coefficients.

In models with vertical resolution (i.e., having more

than one layer), the Manning n is used to compute

stress at the bottom boundary in a series of relationships between n, the drag coefficient (Cd), and turbulent mixing. The quadratic stress formulation relates

the eddy viscosity approximation of the vertical

Reynolds stress to a drag coefficient and average

velocities as follows

ρo Ez (∂u ⁄ ∂z ) = ρo Cd (ub

2

+ vb

2

)

0.5 (ub) (5.10)

and

ρo Ez (∂v ⁄ ∂z ) = ρo Cd (ub

2

+ vb

2

)

0.5 (vb) (5.11)

where

ρo = density of water,

∂u ⁄ ∂z , ∂v ⁄ ∂z = the vertical velocity gradient in the x

and y directions, respectively,

ub, vb = horizontal velocities at a point above the

bottom in the x and y directions, respectively, and

Ez = vertical eddy viscosity.

The drag coefficient is related to the Manning n as

shown in Table 5.21

Cd =

g n

2

C1

2

RH

1

⁄3

(5.12)

Also any other friction factor or roughness coefficient

can be used from Table 5.21. Equations (5.10 and

5.11) represent terms in the conservation of momentum equations given in Table 2.1 of the second section

in Part I of this guidance manual. The two- and threedimensional models based on these formulas are calibrated by varying the Manning n until any

measurements of average velocity and tidal amplitude

at a number of sites plus any observations of salinity

intrusion are properly described by the model. When

models discretization elements are reduced to smaller

and smaller scales, the calibration values of the Manning n approach values only controlled by the scale of

roughness on the bottom. In the limiting case where

the bed is flat, the Manning n can be estimated for sand

5-29
and gravel beds using an approximate form of Sticklers

equation (Henderson 1966, Garde and Ranga Raju

1977)

nb = 0.031 d

1

⁄6

(5.13)

where d is the diameter in feet of bed sediments that

are larger than 75 percent of the material present. If

the diameter, d, is expressed in meters

nb = 0.025 d

1

⁄6

(5.14)

These expressions for nb should be valid for many

estuarine flows where rough turbulent flow is expected

to be the predominate flow regime. In general, however, flow resistance is a function of the Reynolds

number of the flow

Re =

4UR

ν

(5.15)

where U is the average flow velocity, R is the hydraulic

radius (cross sectional area divided by wetted perimeter), and ν is the kinematic viscosity of estuarine

waters. Figure 5.20, modified from a Moody diagram

for flow resistance, gives the general relationship between the ratio of the Manning n to depth to the

one-sixth power (hydraulic radius is approximately

equal to depth in wide water bodies) and Reynolds

number. The curves for sand-coated surfaces should

be used to estimate nb for estuaries when sandy

bottoms are observed.

The smooth surface curve shown in Figure 5.20 may

be approached when fluid mud layers are observed on

the bottom. Typically, fluid mud may occur near or just

downestuary of the turbidity maximum where significant deposition is expected. For example, values of n

were found to be approximately 0.018 to 0.020 near

the turbidity maximum in the Delaware Estuary (Ambrose, personal communication, Ambrose 1987, Ambrose and Roesch 1982, Thatcher and Harleman

1981). Occasionally, unrealistically low values of n

(i.e., n = 0.015) normally associated with very smooth

surfaces may be indicated by calibration. These values may not be consistent with Figure 5.20. The

reason is that stratification of the flow near the bed by

fluid mud or suspended sediment significantly decreases the apparent roughness coefficient (McCutcheon 1979, 1981, McDowell and O’Connor 1977).

Where this occurs, the calibrated hydrodynamics

model can be expected to have an extremely limited

range of applicability since the fine scale effects of

sediment stratification are not incorporated into vertically averaged models or models having gross repreFigure 5-20. Modified moody diagram relating the Manning n to Reynolds number. ks is sand grain height and

RH is the hydraulic radius.

5-30
sentation of the vertical structure. When this occurs, it

is important to conduct a sensitivity analysis to determine if the overall calibrated model shows any sensitivity in the important decision variables (i.e., dissolved

oxygen, chlorophyll a, or sedimentary contaminant

concentrations, etc.) to values of n.

There are also effects of vegetation on flow in shallow

parts of estuaries that may need to be taken into

account, especially if the trend to employ natural or

created wetlands to aid wastewater treatment continues. First, sea grass and other vegetation influence

shallow open water flows. Second, emergent vegetation such as cyprus trees, mangroves, bushes, and

marsh grasses may control flow through wetland areas. At present, there do not seem to be many studies

of the effect of sea grass on friction loss (personal

communication, Florida Dept. of Environmental Regulation, 1989). There are, however, investigations of

friction losses in grassed open channels that show that

losses are a complex function of the Reynolds number.

As flow increases, grasses are pushed flatter along the

bottom and less area of grass is in direct contact with

the flow. In effect, the relative roughness decreases

as a function of flow velocity or Reynolds number.

Perhaps the best study of this effect is by Chen and

the US Geological Survey.

In the absence of solid guidance on this topic, it should

be noted that Chow (1959), Jarrett (1985) and others

give guidance on the effect of grass on channel and

overbank flow. Values on the order of 0.025 to 0.050

are reasonable.

In wetlands and other areas of emergent vegetation,

relative roughness is less likely to vary and the Manning n is expected to be constant. The scale of the

roughness is considered to be the trunk diameter that

should not change significantly as depth increases.

Values have not been well defined, but values of river

flow over flood plains is very applicable when the

density and trunk size of the vegetation are similar.

Values as high as 0.20 have been observed, as noted

in Table 5.22.

In addition to the older information in Table 5.22,

Arcement and Schneider (1984) report more recent

information for more tranquil flows in floodplains. However, it is not expected that n can be precisely defined

in any published study. Flow in wetlands occurs in ill

defined channels where the uncertainty in average

velocity, area, depth, and slope make it very difficult to

determine n.

As larger and larger model scales are employed, more

and more large scale turbulent friction losses due to

flow non-uniformity must be included in estimates of

the Manning n to adequately represent losses due to

energy dissipation. Empirical relationships have not

been derived for this purpose but similar corrections of

this nature have been derived for river flows that can

be used as guidance. Guidance for riverine reaches

works well in the upper sections of estuaries where the

transition from riverine conditions occur. The guidance

is less useful downestuary where the scales of flow

may increase by an order of magnitude in some cases.

Conceptually, the riverine estimation procedure can be

formulated as a process of modifying a base value of

the Manning n such that

ncomposite = nb + nf + n1 + n2 + n3 (5.16)

where typical values are on the order of 0.020,

nb = Manning n associated with bottom roughness conditions,

nf = correction related to form roughness or bed

irregularity due to ripples and dunes,

n1 = correction related to the nonuniform depth

of the flow, and

Value of n

Type of Vegetation Minimum Typical Maximum

Grass:

Short 0.025 0.030 0.035

Tall 0.030 0.035 0.050

Brush:

Scattered with Dense

Weeds

0.035 0.050 0.070

Sparse Trees and Brush

in Winter

0.035 0.050 0.060

Sparse Trees and Brush

in Summer

0.040 0.060 0.080

Medium to Dense Brush

in Winter

0.045 0.070 0.110

Medium to Dense Brush

in Summer

0.070 0.100 0.160

Trees:

Dense, Straight Willows 0.110 0.150 0.200

Stumps or Cyprus Knees 0.030 0.040 0.050

Stumps with Dense

Sprouts, Grass and

Weeds

0.050 0.060 0.080

Dense Stand of Trees,

Few Fallen Trees, and no

Branches hanging in

water

0.080 0.100 0.120

 Dense Stand of Trees,

 Some Fallen Trees, or

Branches Hanging in

Water

0.100 0.120 0.160

Table 5-22. Values of the Manning n for Different Types of

Vegetation in Wetland Areas

[Chow (1959) and Jarrett (1985)]

5-31
n2 = correction for the nonuniform width of the

flow.

n3 = correction for effects of vegetation

Alternatively, Chow (1959) notes that a multiplicative

version of Equation (5.16) can be used as well. However, that form is better adopted to meandering channels and is not very suitable for estimates in estuaries.

Values of nf are approximately 0.00 to 0.010 (Chow

1959) as shown in Table 5.23. Values of n1 and n2

can be estimated approximately from the effect of

obstructions and channel cross section variations

given by Chow (1959) in Tables 5.24 and 5.25. Table

5.26 gives corrections for the effect of vegetation. It

should be noted however, that these constant corrections may not be adequate since the correction for

seagrasses and kelp probably vary with flow velocity

or Reynolds number.

In models that assume that the flow field can be

vertically and laterally averaged, the one-dimensional

equations of motion and continuity can be written as

(Thatcher and Harleman 1981, Ambrose et al. 1988)

∂Q

∂t

= −∂ (QU )

∂x

− g A

∂h

∂x

g n

2Q |Q|

AC 1

2

RH

4

⁄3

 − g

Adc

ρ

∂ρ

∂x

+

ACda ρa

RH ρ

W 10

2

 cos α (5.17)

and

b

∂h

∂t

+

∂Q

∂x

− q = 0 (5.18)

where

∂Q

∂t

 = local inertia term,

∂

(QU )

∂x

= force due to advection or momentum

change due to mass transport of water,

gA ∂h

∂x

= force due to potential energy of the fluid

or gravitational body force,

gn

2Q |Q|

AC 1

2

RH

4

⁄3

= force due to bottom shear or frictional resistance (quadratic stress law),

g

Adc ∂ρ

ρ ∂x

= force due to longitudinal pressure difference caused by density differences along the

axis of the estuary,

ACda ρa

RH ρ

W 10

2

 cos α = Force due to wind shear

on the water surface,

Q = Discharge (Q=UA),

U = Longitudinal velocity averaged over the

cross section and averaged over time,

t = time,

x = Longitudinal direction along the axis of the

estuary,

Amount

of Vegetation

Range of n3 Description of Conditions

Small 0.002 to 0.01 Dense growths of grass or

weeds, average depth at least

twice the height of grass, or

supple seedlings where the flow

is at three times the height of

the vegetation.

Medium 0.010 to 0.025 Grass from 1/2 to 1/3 of the

depth; moderately dense large

stem grass, weeds, or tree

seedlings 1/2 to 1/3 the depth of

flow; or moderately dense bushy

trees like 1 to 2 year old willows.

Table 5-26. Adjustments for the Manning n due to Vegetation

[Jarret (1985)]

Relative Effect of Obstructions n1

Negligible 0.00

Minor 0.010 to 0.015

Table 5-24. Manning n Corrections for the Relative Effect of

Obstructions

Variation of Channel Cross Section n2

Gradual 0.00

Alternating occasionally 0.005

Table 5-25. Manning n Corrections for Changes in Channel

Depth and Width

Bed Topography nf

Smooth Bed 0.00

Table 5-23. Manning n Corrections for Ripples and Dunes

5-32
g = Gravitational constant,

A = Cross sectional area,

∂h

∂x

= Slope of the energy gradient or approximately the water surface slope, where h is the

depth of flow to water surface from an arbitary datum,

n = Manning roughness coefficient,

C1 = Units conversion factor (1.0 when RH is expressed in m and 1.49 when RH is expressed in

feet),

RH = Hydraulic radius (cross-sectional area divided by wetted perimeter of the cross section

that is approximately equal the depth in wide estuaries),

dc = Distance from water surface to the centroid

of the cross-section,

Cda = Drag coefficient for air moving over water

surface (typically assumed constant and having a

value of 0.0025 or slightly less),

ρa = The density of air,

ρ = Density of water,

α = Angle of wind direction from the axis of the

estuary,

W10 = Wind speed measured at 10 above the

water surface,

b = Total surface width, and

q = Lateral inflow per unit length.

Equations (5.17) and (5.18) are accurate approximations when lateral and vertical differences are unimportant, which is the case in many estuaries. However, a

more approximate equation has proven almost as

widely applicable. The approximation is the link-node

model that assumes that the one-dimensional estuary

can be divided into a series of uniform channels between nodes. The cross section may vary from one

channel to the next and any flows into the estuary are

assumed to enter at the nodes. It is also assumed that

longitudinal pressure differences due to pressure gradients are small enough to neglect. The best examples of link-node models are the EXPLORE I (Baca et

al. 1973), DEM (Dynamic Estuary Model) (Feigner

and Harris 1970), and the derivations of these models

such as the DYNHYD model used with the WASP

modeling package (Ambrose et al. 1988). The approximate equations are written as

∂U

∂t

= − U

∂U

∂x

− g

∂h

∂x

−

g n

2

C 1

2

RH

4

⁄3

U |U |

+

Cda

RH

ρa

ρ

W 10

2

 cos α (5.19)

and

∂A

∂t

=

−∂Q

∂x

 (5.20)

Since Equations (5.19) and (5.20) have been used

extensively, some care may be necessary to interpret

results relating to selections of the Manning n. Any

effects of neglecting longitudinal, vertical, and lateral

salinity gradients and accelerations due to nonuniform

channels will be lumped into the value of the roughness coefficient used to calibrate the model. Normally,

these effects are minor and relatively reliable guidance

can be formulated.

Guidance on the selection of Manning n values is as

follows:

1. Select initial values based on bed material and

correct for bed variations - Values should be uniform

for areas where bottom topography, channel alignment and sediment size distributions do not vary significantly. Smaller values should be selected for

bottoms covered with fluid mud or other fine-grain

material. Typically a value of 0.02 is appropriate for

reaches with fine grain sediments and 0.025 to 0.030

is appropriate for reaches with sand bottoms. If necessary, a precise initial estimate can be made by

computing the Reynolds number and the relative

roughness (i.e., 2R/ks, where ks is the sand grain

diameter or the height of the ripples and dunes) and

consulting Figure 5.18. If the bed is covered with

vegetation (i.e., none of the sediments are in contact

with the flow) then Table 5.22 should be used to select

an n value and correct for variations in cross section,

bottom topography, and obstructions. If the bed is

partially covered with vegetation, the initial selection

should be based on the bed materials present and

corrections should be made for vegetation, and variations in cross section, bottom topography, and obstructions. Where it is not clear whether exposed bed

materials are important in causing friction losses, both

procedures should be followed to see if any significant

discrepancies exist.

2. Correct for bed roughness - Table 5.23 shows the

corrections that should be added if bed ripples and

dunes are present on the bed. A correction should not

be made if Figure 5.20 is used and the roughness

height is assumed to be the height of ripples and

dunes.

3. Correct for topographic variability - Values may

need to be increased in computational elements or

reaches in which there is a significant change in bottom

5-33
elevation or where channels narrow. Increased n values are required to compensate for friction loss due to

non-uniform flow conditions. Tabulated values of the

Manning n (Chow 1959, French 1985, Henderson

1966, Barnes 1967) do not reflect the increased turbulence due to non-uniform flow. It should be noted that

these corrections can only be approximated because

friction losses in nonuniform flows are dependent on

flow direction. Losses are significantly greater when

the flow speeds up and contracts into a shallower or

narrower channel compared to expansion into a

deeper channel accompanied by a decrease in flow

velocity. Examples where these corrections should be

considered include flows out of deeper navigation

channels onto shallower tidal flats if excess turbulence

is generated. Other examples include narrowing flows

at the mouth of an estuary, at river passes like those

of the Mississippi River, and in flows constricted by a

peninsula. Many times submerged sills that cause

shallower flows at the entrance of a fjord are associated with points of land that extend into the estuary

from both sides. These corrections are obtained from

Table 5.25.

4. Correct for obstructions - Table 5.24 is used for

further correction when large obstructions are contained in the flow (generally expected to cover or

occupy approximately one percent or more of the cross

sectional area). These include submerged rock outcrops, very large boulders, and small islands (friction

losses caused by gradual channel changes around

large islands may be unimportant). Rock outcrops and

small islands are clearly marked on navigation charts.

A very good indication of when corrections are needed

is increased turbulence in the flow near the obstruction. From the air, large turbulent eddies are usually

very evident when the wind speed is not large.

5. Correct for vegetation - If the initial selection

does not fully take the effects of vegetation into account, these corrections should be made using Table

5.26. Where vegetation is sparse or patchy, or only

extends over part of the depth, it is best to select an

initial n value reflective of the sediments in contact with

the flow and correct for effects of vegetation using

Table 5.26. If vegetation dominates roughness in

wetlands and elsewhere, an initial selection from Table

5.22 is best. The initial selection should be compared

with corrections in Table 5.26 but should not be modified unless some large discrepancy is noted.

5-34
.

EXAMPLE 5.3. Initial Selection of the Manning n for a Hypothetical Estuary

Table 5.27 illustrates the Manning n selection procedure. Six segments varying from wetland and marsh

land, to shallow areas with sea grass, to deep channels

with sand, fine grain sediments, and fluid muds were

selected for illustration. For segment 1, the initial value

was selected as 0.10 from Table 5.22 and corrections

were not made for changes in the channel since flow

around trees is very irregular and braided and the

value from Table 5.22 should account for this. Obstructions (there were very few fallen trees) and vegetation

were taken into account in the initial selection. The

selection for segment 2 was governed by the same

procedure. Segment 3 involved selection of a value

representative of flat sandy bottoms and correcting for

the seagrass. The final value should be compared

with Table 5.22 where the value is exactly the same as

the value for flows over tall grass. Segments 4 and 5

involve straight forward selections for sandy and fine

grain materials and minor corrections for changes in

cross section and obstructions. Segment 6 involves

selection of a smaller value to reflect the influence of

fluid mud. The few islands and vegetation on the

shores of a wide channel is probably negligible.

Segment

Number Description

Bed

Material

 Bed

 Topography

 Channel

Change

ObstructionsVegetation nf n1 n2 n3 n

1 Wetland with dense

stand of straight trees,

few fallen trees, very little

brush and no weeds

Fine

grain

Irregular

surface

Meandering.

irregular,

braided and

indistinct

channel in areas

A few fallen

trees

See description

0.01 0 0 0 0.01

2 Wetland with marsh

grass

na na Meandering,

irregular,

braided and

indistinct

channel in areas

None See description

0.035 0 0 0 0.035

3 Shallow area with sea

grass over 70% of the

bottom, extending over

about 50% of the depth

Sandy Flat No significant

change

None See description

0.025 0 0 0.01 0.035

4 Deep well defined

channel

Sandy Dunes Some narrowing

of channel and

bends

Submerg

ed

None 0.025 0.01 0 0 0.035

5 Wide deep channel in the

vicinity of the turbidity

maximum

Fine

grain

Ripples Straight None None 0.02 .005 0 0 0.025

6 Wide deep channel down

estuary of the turbidity

maximum with significant

sediment transport into

the estuary

Fine

grain

Fluid mud

layer over

much of

the

channel

Straight A few small

islands

Minor

vegetat

ion on

the

shores

0.015 0 0 0 0.015

Table 5-27. Reach Characteristics for a Hypothetical Estuary and Calculation of the Manning n Value

5-35
EXAMPLE 5.4. Selection of the Manning n for the Delaware Estuary

Figure 1 from Ambrose and Roesch (1982) and Ambrose (1987) shows five zones for the Upper Delaware

Estuary. Ambrose and Roesch varied the Manning n

in each zone to obtain an optimum fit of predicted water

surface elevation to that measured at selected points.

The timing of high and low water throughout the estuary was also used to calibrate the model. These data

were averaged over a year to filter out the important

short-term effect of wind stress that was not included

in their hydrodynamics model [Equation (5.10) with the

last term for wind stress assumed to be equal to zero

on average]. Annual average tidal conditions and

fresh inflows were employed. A few measurements

of point maximum velocity during ebb and flood tide

were compared to the predicted values after calibration but were not used to recalibrate. The result was

that n varied from about 0.02 in zone 5 to 0.045 in the

riverine dominated zone 1. The value of 0.02 is consistent with a fine grain or sand bed channel with very

limited changes in cross section and meandering. The

turbidity maximum occurs in this zone. A value of

0.045 in the river zone 1 indicates significant changes

in the channel cross section are occurring. Figure 5.8

does not indicate significant meandering. Figure 5.9

shows that excellent agreement was obtained between measured and predicted tidal range for mean

tide and average spring tide events. Table 5.7 indicates that discrepancies (as measured by the coefficient of variation) are less than 10 percent throughout

the estuary. Thatcher and Harleman (1981) also calibrated a similar model based on Equation (5.17) for

the same segments of the Upper Delaware Estuary.

They used the same long term average tidal elevation

data from the National Ocean Survey (NOS) but also

added data from the U.S. Geological Survey (USGS)

not used by Ambrose and Roesch (1982) and gave

greater emphasis to the USGS data. The n values

selected were very similar with one exception in the

upper part of the estuary near Trenton where the

maximum values of n were selected to be 0.032 versus

0.045 chosen by Ambrose and Roesch (1982). The

results from Thatcher and Harleman (1981) are shown

in Figure 5.21. The difference could be due to neglecting effects of the longitudinal salinity gradient and by

assuming the channel is uniform over five segments.

More likely, however, is the emphasis on agreement

with two different data sets that are in some conflict.

In Figure 5.22, the calibration results of Thatcher and

Harleman (1981) for tidal range, and high water and

low water planes are shown. The USGS data indicate

a larger tidal amplitude in the area of the discrepancy

and it is probable that a larger value of n would be

necessary to reproduce the larger tidal range measured by the USGS.

Figure 5-21. Longitudinal distribution of Manning n values in

the Delaware Estuary (1 mile = 1.61 km)

[Thatcher and Harleman (1981)].

Figure 5-22. Hydraulic calibration to tidal range and high and

low water planes for mean conditions (1 ft = 0.035 m; 1 mile =

1.61 km) in the Delaware Estuary [Thatcher and Harleman

(1981)].

5-36
SUPPLEMENT II: SELECTION OF SURFACE DRAG COEFFICIENTS

The final coefficient necessary to solve Equation (5.17)

(hydrodynamics or flow equation) is the water surface

drag coefficient that quantifies the effect of wind shear

on flow and mixing. As noted above, wind shear is not

extremely important for matching predictions with

measurements of water surface elevation averaged

over long periods of up to a year in deeper tidally

controlled estuaries. Ambrose and Roesch (1982),

however, note that over periods of hours or days,

atmospheric storms can significantly effect water surface elevations on a temporary basis. Shallower estuaries with barrier islands, like the

Pamlico-Albermarle Sound, are controlled more by

wind shear than tidal influence. As a result, effects of

wind shear must be incorporated for shallow tidally

damped estuaries when wind driven events cause

critical water quality conditions, or when flows are

significantly effected by wind during calibration data

collection.

For crude estimates, Cda is sometimes taken as a

constant of about 0.0010 to 0.0025 (Amorocho and

DeVries 1980). In general, however, Cda is a function

of surface roughness and Reynolds number. Cda

could be determined from Figure 5.23 or a similar

friction diagram because of the relationship between

various friction factors shown in Table 5.12. But in

practice boundary height and air viscosity do not vary

significantly and the effect of wind shear on water

surface roughness is understood well enough so that

a relationship between Cda and wind speed can be

derived (O’Connor 1983). This relationship is given in

Figure 5.23.

Figure 5-23. Water surface drag coefficient as a function of wind speed measured at a 10-m height [O’Connor (1983)]

5-37
SUPPLEMENT III: SELECTION OF EDDY VISCOSITY VALUES

Mixing coefficients required in a typical hydrodynamic

model cannot be precisely estimated. Mixing is controlled by flow intensity and estuarine morphology as

well as grid resolution and the degree of time averaging

employed in the model chosen. These are effects that

cannot be forecast sufficiently well to aid in the selection of these parameters. However, initial estimates

are needed to begin the calibration procedure. The

best guidance available for making the necessary first

estimates is found in Bowie et al. (1985) and Fischer

et al. (1979). McCutcheon (1983) reviews the commonly used methods of computing vertical mixing.

The initial estimate generally is only required to be

close enough to allow the numerical scheme in the

hydrodynamic model to converge to a stable solution.

Once these estimates are made, fine tuning to achieve

precise, optimum estimates of eddy viscosity is rarely

necessary. At this time (1989), it is not clear that many

simulations of water quality are sensitive to values of

the eddy viscosity.

Hydrodynamic models of the eddy viscosity type are

limited to describing the effects of large scale turbulent

mixing in boundary-layer-like conditions where the turbulence is dissipated under the same conditions in

which it was generated. In other words, the effect of

localized turbulent mixing in the vicinity of outfalls and

associated with diffusers can not be predicted too well

in a far-field eddy viscosity model. These effects can

be described in calibrating a model, but it is difficult to

forecast what eddy viscosity values will be required.

At present, a consistent analysis framework that readily links the near-field dilution and mixing analysis (see

Chapter 10 in Fischer et al. 1979 and Doneker and

Jirka 1988) and the far field eddy viscosity type hydrodynamics models, is not available. To fully understand

the basic limitations of the eddy viscosity model and to

fully understand when difficulties in selecting calibration values will occur, one should refer to Rodi (1980).

When it seems that water quality simulations are not

sensitive to hydrodynamic transport and mixing, the

following guidance on the selection of eddy viscosity

values should be useful. In some cases, it is expected

that hydrodynamic simulations will be important and

less approximate methods will be required. In these

special cases, higher-order turbulence modeling will

be necessary. These special studies will, at present,

require expert assistance. To aid in the selection of

correct models and expertise, the next Supplement IV

will briefly review turbulence closure.

To select eddy viscosity values it should be recognized

from inspection of Equations 5.10, 5.11, and 5.12 that

eddy viscosity is directly related to the Manning n for

certain conditions. As a result, it is assumed that

guidance for the selection of eddy viscosity values will

be somewhat similar to that developed for the selection

of roughness coefficients.

First-order Approximation - As a first approximation,

selection of a constant value has proven useful in

some studies (see Rodi 1980 for a review). This

involves assuming that vertical, lateral, and horizontal

eddy viscosities are all equal. From experience with

selection of Mannings n in one-dimensional estuaries,

values can change significantly along the axis of the

estuary. Therefore, this approach should be validated

before the results are used in decision making. First,

a sensitive analysis of the constant eddy viscosity

value on water quality predictions should be performed. Second, validation of the hydrodynamic

model should be accomplished by comparing simulations to water surface and velocity measurements.

The degree of validation should be matched to the

sensitivity of water quality simulations to eddy viscosity

values. It should be noted that the model calibrated

with a constant eddy viscosity may have only very

limited predictive validity outside the range of calibration and validation data.

Typically, a constant eddy viscosity value is only applicable for one-dimensional and two-dimensional depth

averaged models where jets and man-made structures

do not interfer with the flow (ASCE Task Committee

1988). However, significant phase errors can occur in

the prediction of tidal elevations when roughness

changes and differences in friction losses are averaged or ignored. Nevertheless, the approximation

would seem to be quite useful in wide bodies of water

with only limited changes in depth and roughness.

Both the lateral and horizontal eddy viscosity is related

to a length scale that is approximately equal in many

cases.

Constant values have also been applied to models of

stratified flows (laterally averaged two-dimensional

models and three dimensional models), but these are

quite inaccurate. As a matter of practice, constant

eddy viscosity values should be avoided except for use

in depth-averaged models and crude preliminary or

screening level analyses using stratified flow models

where the approximation error is well understood and

taken into account.

Second-order Approximation for One-dimensional

and Depth-averaged Models - To better match tidal

5-38
elevation measurements, eddy viscosity should be

changed in the lateral and horizontal directions to

reflect changes in roughness (i.e., bottom roughness

element effects), differences in turbulent energy

losses (due to “macro-roughness” caused by irregular

shoreline bottom morphology), and different scales of

the model elements. The Principle of Parsimony

should be used, however, to limit changes to those that

are absolutely necessary by virtue of well defined and

documented changes in roughness, turbulence, and

model scale.

When turbulent characteristics of the unstratified estuary do not change extensively, a good depth-averaged

model can be reasonably calibrated and expected to

make predictively valid simulations over a wider range

(compared to the first-order calibration). However,

rigorous calibration and validation are normally necessary, especially when water quality results are sensitive to hydrodynamic variables.

Uniform values of the horizontal and lateral mixing

coefficients are applied to elements of similar depth

and roughness. Values should be increased where

turbulence of the flow increases. This includes increases for elements containing separation zones and

wakes of flow around islands, headlands, and peninsulas.

Second-order Approximation for Stratified Flow

Models - For laterally averaged two dimensional models and three-dimensional models, it is usually possible

to obtain a reasonable calibration with a constant

lateral and vertical eddy viscosity and by relating the

vertical eddy viscosity to a measure of stability such as

the Richardson or Froude numbers so that eddy viscosity varies with depth and degree of stratification.

This works well for cases where the estuary is relatively deep. Vertical mixing coefficients are typically

two or more orders of magnitude smaller than lateral

and horizontal coefficients and can be even smaller

depending on the degree of vertical stratification

(McDowell and O’Connor 1977).

It is especially important that the vertical eddy viscosity

formulation be rigiously calibrated (ASCE Task Committee 1988). Generally, stratified flow models using

eddy viscosity are not predictively valid outside the

range of calibration and validation data. Furthermore,

the eddy viscosity and the similar mixing length formulations are only approximately useful for estuarine

flows when the flows are approximately boundarylayer like. Complex, unsteady, reversing flows can not

be precisely simulated (see Rodi 1980 and ASCE Task

Committee 1988).

Third-order Approximation for Three Dimensional

Models - The best results for three-dimensional models are obtained when lateral and horizontal values are

modified to account for roughness, excessive turbulence production, and model scale, while vertical

changes in eddy viscosity are related to depth and

stratification. Typically, lateral and hortizontal values

are chosen to ensure that changes in tidal elevations

are accurately represented and then the vertical eddy

viscosity is calibrated to reproduce measurements of

vertical velocity and salinity profiles, and longitudinal

salinity profiles.

The results should be carefully validated. The predictive validity is not expected to be very good outside the

range of calibration and validation data. Generally,

eddy viscosity formulations depend upon a critical

assumption that turbulence is dissipated under the

same circumstances under which it was produced.

This is consistently violated in the unsteady salt stratified flows of estuaries and in many cases, more elaborate methods that simulate the generation, transport,

and dissipation (under different conditions) of turbulence are required.

Fourth-order Approximation - In a significant

number of cases, it is expected that an eddy-viscosity

based approach will not be adequate to make predictively valid simulations of critical hydrodynamic conditions nor can eddy viscosity approaches simulate

some complex unsteady flows. This is especially true,

in some of the larger and very important estuaries in

the U.S. These include Cheaspeake Bay and its larger

tribuatary estuaries, Long Island Sound and New York

Harbor areas, Boston Harbor, Tampa Bay, San Francisco Bay, and Puget Sound to name several. In these

cases and others, higher order turbulence closure

methods and the necessary expertise are required.

Supplement IV briefly reviews the general approach.

Procedurally, the following steps seem to offer the best

approach to the calibration of an eddy viscosity type

hydrodynamic model (see model equations in Table

2.1 of Part I of this manual — the values of Ex, Ey, and

Ez are to be determined).

A. One-Dimensional Models: See selection of Manning’s n, Supplement I

B. Depth Averaged Two Dimensional Models:

 1. Estimate a uniform lateral and longitudinal eddy

viscosity coefficient for all computation elements (segments or nodes). At least two approaches have

proven useful.

5-39
a. Empirical length scale formulas (Fischer et al.

1979, Bowie et al., 1985, Bedford 1985) that

approximate eddy diffusivity:

EH = 0.005 L

4

⁄3

(5.21)

where EH is the horizontal eddy viscosity (lateral, Ey, or longitudinal, Ex) for open waters

away from shallow areas and shore and L is

the characteristic length scale in centimeters.

L is typically taken as the grid size in the

model or derived from the physical geometry.

For diffusers, L is taken as the diffuser length,

which is typically on the order of 1 km. In

open estuarine waters, L has been taken as

the length of the tidal excursion.

b. Reports of values from similar water bodies.

In this regard, the case studies by Officer

(1976) provide a useful reference.

 2. Correct horizontal eddy viscosity values for areas

of higher turbulence. These typically occur in the lee

of islands and other shore line irregularities, near the

mouth of the estuary, or where bottom roughness

changes drastically causing increased velocity gradients.

 3. Correct for time averaging. When values from the

literature are used, smaller values should be chosen

for models with shorter times steps. EH should be

chosen as a larger value in models that average over

a tidal period compared to models that average over a

much shorter time step.

C. Select vertical eddy viscosity. Table 5.28 from

McCutcheon (1983), McCutcheon and French (1985),

and others list various formulas that are useful for

estimating vertical momentum transfer. Typically a

formula is selected and coefficients are modified until

calibration is achieved. Predictions of the extent of

salinity intrusion into estuaries the existance and location of a halocline and the residence time of pollutants

can be quite sensitive to the form and exact magnitude

of vertical mixing formulations yet little guidance is

available on how these values can be rationally selected. In addition, it is not yet clear what stability

parameters (i.e., Richardson number) best quantify

the effects of stratification.

 1. As Table 5.28 indicates, a number of vertical eddy

formulations can be chosen. At present only limited

guidance is available to aid in this choice. The formulations listed in Table 5.28 have been used in a number

of modeling studies; some (eg., Munk-Anderson) have

been used frequently while others have only occasionally been applied. Unfortunately, these model applications have only rarely reported on the usefulness of

these formulations. As a result, only crude guidance

is possible and that must be derived from a few studies

that must also include the data from selected atmospheric boundary layer studies where the stratification

effects on mixing are the same in most cases.

 2. From the best data available on the Great Ouse

Estuary in the United Kingdom (Odd and Rodger

1978), it is clear that the formulations of Holzman and

Mamayev are not appropriate for the complete range

of stratification encountered in estuaries. These equations are only valid for slight stratification. Knight et al.

(1980) shows that the Holzman form is quite inaccurate, especially for large values of Ri (e.g., Ri > 3.4).

Also Knight et al. (1980), Nelson (1972) and Delft

(1974) tend to indicate that the Mamayev formula is

inaccurate, the extreme amount of data scatter not

withstanding, and that other forms are better able to

be calibrated to represent the data. These conclusions are most important when the RAND two- and

three-dimensional hydrodynamic model is being applied. The Mamajev formula was used primarily to

provide quick simulated mixing when stratification becomes unstable. As a result, it is not expected that this

model will reproduce the vertical structure in estuaries

as well as could be expected.

 3. Ruling out the Holzman and Mamayev forms

leaves the Munk and Anderson [(Rossby and

Montgomery 1935) where n = 1 and (Kent and

Pritchard 1959) where n = 2)] types of stability functions based on gradient Richardson number as the

most adequate. These are most frequently used

equations in modeling studies (McCutcheon 1983).

However, even these formulations are quite limited

and require calibration in all cases. In addition, there

is some debate regarding whether other stability parameters are more adequate than the gradient

Richardson number. In general, all formulations will

not exactly reproduce vertical stratification. Odd and

Rodger (1978) and others have found that the Munk

and Anderson type formulas only reproduce the general trend of vertical eddy viscosity with changes in

stratification as measured by the gradient Richardson

number. There are typically large discrepancies in

values of β that best fit profiles of Ez measured at

different times at a point in the estuary and Table 5.29

shows that there is a significant variation in values

determined for different estuaries and other stratifiedflows. In addition, Odd and Rodger (1978) show that

highly stratified

5-40
Investigator Formulation for Ez Comments

Munk and Anderson (1948) Ez =

Ezo

[1+β(n) Ri]

n

n = 1 and β(n) = 10, based on oceanic thermocline Anderson measurements

from Jacobsen (1913) for Rander’s Fjord and Schultz’s Grund recognized that a

general empirical equation could be written.

Rossby and

Montgomery

(1935)

Ez =

Ezo

[1+β(n) Ri]

n

n = 1 and β(n) = 40, based on Heywood’s wind profiles at Leafield. Derived

from an energy dissapation per unit volume concept and a flawed assumption

that stratified and unstratified velocity gradients are equivalent.

Sverdrup

(1936) Ez =

Ezo

[1+β(n) Ri]

n

n = 1 and β(n) = 10 to 13, based on wind profiles over Spitzbergen snow field.

Holzman

(1943))

Ez = Ezo [1+β(n) Ri] Empirical equation proposed to explain evaporative flux in the atmosphere.

Incorrectly presupposes that a critical Ri of 1/β(n) exists which is quite

inconsistent with the observations of Jacobsen (1913) and others.

Pasquill

(1949) Ez =

Ezo

[1+β(n) Ri]

n

For n = 1, β(n) = 12, and for n = -1 and β(n) = -12. From wind profiles in 2-meter

layer over grass.

Kent and

Pritchard

(1957)

Ez =

Ezo

[1+β(n) Ri]

n

For n = 1, β(n) = 2.4; for n = 2, β(n) = 0.24; and for n = -1, β(n) = 0.06 from

tidally averaged data collected in James River Estuary. The semi- empirical

formulation for n = 2 was derived from an energy dissapation per unit length

(vs. volume) basis with the flawed assumption that stratified and unstratified

velocity gradients are equivalent.

Pritchard

(1960) Ez =

Ezo

[1+β(n) Ri]

n

For n = 2, β(n) = 0.28, based on a re-evaluation of the James River Estuary

data.

Vreugdenhil

(1966) Ez =

Ezo

[1+β(n) Ri]

n

For n = 1, β(n) = 30, data source unknown.

Nelson (1972) Ez =Ezo

[1+β(n) Ri]

n

For n = 1, β(n) = 10; for n = 2, β(n) = 2.5 or 5; and for n = -1, β(n) = -3.3.

Based on data compiled from atmospheric boundary layer including Rider

(1954), and Deacon (1955). Also includes inappropriate data from Ellison and

Turner (1960).

Odd and

Rodger

(1978)

1)

Ez =

Ezo

[1+β(n) Ri]

n

For n = 1, β(n) = 140 to 180 and for n = 2, β(n) = 10 to 15; determined by

minimization of relative error from an excellent data base collected in the Great

Ouse Estuary. Relative error puts more weight on fit to highly stratified data.

Best fit obtained from n = 1 but still the average percentage error in shear stress

exceeded 100% for 35% of the measurements.

2) For Ri continually increasing to over

75% of depth:

Ez =

Ezo

[1+β(n) Ri]

n

 for Ri ≤ 1

Ez =

Ezo

[1+β(n)]

n

 for Ri > 1

For the occurrence of a peak Ri in the

lower 75% of the flow at zo:

Ez =

Ezo

[1+β(n) Ri(zo)]

n

 for Ri(zo) ≤ 1

Ez =

Ezo

[1+β(n)]

n

 for Ri(zo) > 1

Except where Ez > Ezo, then

Ez = Ezo

Better fit to data obtained with a hybrid formula that compensates for the effect

of a strong thermocline that accentuates the error in misapplying the eddy

viscosity model in estuaries where turbulence is dissipated under conditions

different from the conditions generating the turbulence. Best fit is β(1) = 160 or

β(2) = 13. n =1 remaining somewhat better than n = 2. Improves Reynold

stress prediction to + 60 for 60% of the data.

Knight et al.

(1980) Ez =

Ezo

[1+β(n) Ri]

n

Collected additional data in Great Ouse Estuary with less stratification and

found that β(1) = 110 to 160 and β(2) = 13 to 20 consistent with Odd and

Rodger (1978).

Ez = Ezo e

−7.6 R i Formula in poor agreement with Great Ouse Estuary data.

Ez = Ezo [1+β(−1) Ri] Formula in poorest agreement with Great Ouse Estuary data. β(-1)=3.4.

Ueda et al.

(1981) Ez =

Ezo

[1+β(n) Ri]

n

For n = 2, β(n) = 2.5, in the atmospheric boundary layer.

French and

McCutcheon

(1983)

Ez =

Ezo

[1+β(n) Ri]

n

For n=1, β(n) = 30 and for n = 2, β(n) = 10 from Great Ouse Estuary analyzed

by Odd and Rodger (1978) but the root mean square error was minimized

instead of the relative error.

Table 5-28. Vertical Eddy Viscosity Formulations for Flow in Estuaries

5-41
Investigator Formulation for Ez Comments

French and

McCutcheon

(1983)

(continued)

Ez = Ezo (1+αk

2Ro′) Derived from Monin-Obukhov stability function for atmospheric boundary layer.

αk

2

 are empirical coefficients determined from unstratified flows (k = 0.41) and

from the atmospheric boundary layer (α = 5) such that no calibration is required

for estuaries. Limited to small z/L (i.e., z/L≤0.0025); where c= momentum p’w‘

= ck2z

2

(∂u/∂z) where c = ratio of momentum mixing length to mass mixing

length and assumed constant for small z/L; and minimum Δρ is small (i.e., less

than 3 to 5%). This form is generally inaccurate like the Holzman (1943) eq.

because Ro’≤(ακ2) except for small values of Ro’. Does not fit strongest

stratification data from the Great Ouse Estuary at all.

Ez =

Ezo

(1+αk

2Ro′)

Derived from eq. above by noting these eqs. are approximately equal as αk

2Ro’

→ 0 and from agreement with data. This equation fits the Great Ouse Estuary

data as well as any similar form based on Ri with n = 1 or 2 but αk

2

 is known

without data fitting from unstratified flows (k = 0.4) and the atmospheric

boundary layer (α = 5) and Ro’ is less error prone than Ri.

Mamajev

(1958)

Ez = Ezo e

−0.4 R i Based on data of Jacobsen (1913) and reported by author to better fit than

other forms. Knight et al. (1980), Nelson (1972), and Delft (1974) show this is

inaccurate.

French (1979)

Ez = γ







Ezo

1+Ro







Γ Derived from dimensional analysis and calibrated with Great Ouse Estuary

data, γ=0.062 and Γ=0.379. This is a grossly empirical eq. that must be

calibrated for each estuary of interest and it lacks some vertical resolution

because of the definition of Ro.

HendersonSellers (1982) Ez =

Ezo

1+0.74 Ri

Derived from Ueda et al. (1981) atmospheric boundary layer data.

McCutcheon

(1983) Ez =

Ezo

1+α(z ⁄ L)

α = 5 to 7 (wider range reported is 0.6 to 12 but under questionable

experimental conditions.

Notation:

Ezo = Vertical eddy viscosity coefficient for unstratified open channel flow = kzu*(1 - z/D),

k = von Karman’s constant assumed to be 0.41,

z = vertical coordinate axis; distance above bottom boundary,

u* = shear velocity = (gSD)1/2 where S is the slope of the energy gradient (or water surface if the flow is approximately uniform),

D = depth of flow (assumed to equal hydraulic radius),

n = exponent for Munk and Anderson stability function; n = 1 for Rossby and Montgomery (1935) function, and n = 2 for Kent and Pritchard

(1957) formulation, and n = -1 for the Holzman (1943) formulation.

β(n) = constant in the Munk and Anderson stability function for different values of n (i.e., 1,2, and -1) that varies for each estuary and must

be calibrated or estimated from other estuaries.

Ri = gradient Richardson number = −

g

∂ρ

∂z

ρ

_





∂u

∂z







2

Ro’ = Richardson number based on shear velocity = −

gz2

ρ

_

u∗

2

∂ρ

∂z

Ro* = gross Richardson number based on shear velocity =−

gDΔρ

ρ

_

u∗

2

Table 5-28. Vertical Eddy Viscosity Formulations for Flow in Estuaries (continued)

ρ = average density.

g = gravitational constant.

∂ρ ⁄ ∂z= density gradient

∂u ⁄ ∂z= velocity gradient.

α = Monin-Obukhov constant = 5.

Δρ = density difference over the depth

of flow.

conditions are difficult to reproduce as others would

expect (Munk and Anderson 1948, Henderson-Sellers 1982).

Also, in comparing the results of Kent and Pritchard

(1959) based on tidally averaged data, to other studies

using profiles that have not been averaged or at least

not averaged over periods of more than several minutes (Odd and Rodger 1978, French and McCutcheon

1983, Knight et al. 1980), there seems to be an effect

of tidally averaging. If differences between flow conditions in different estuaries are unimportant, the effect

of tidal averaging on modeling vertical structure may

be up to an order of magnitude of difference in the

value of β.

Of the two forms of the Munk-Anderson formula, the

Rossby-Montgomery form seems superior to the KentPritchard. This is clearly demonstrated from the studies by Odd and Rodger (1978) and from French and

McCutcheon (1983). Perhaps tidally averaged data

favors the Kent-Pritchard equation. In addition,

French and McCutcheon demonstrate that the

Rossby-Montgomery form is less error prone.

The poor predictions from an eddy viscosity formulation are expected in highly stratified flows because the

basic concept was developed for uniform flows where

turbulence is dissipated under the conditions under

which in was generated. When a strong halocline

exists in the estuary there is an uncoupling between

flow conditions in the lower layers that generate turbulence and the upper layer conditions where some

5-42
turbulence is dissipated. When the exact stratification

structure must be known to determine a waste load

allocation or a cause and effect, more elaborate turbulence closure schemes may be required (see Rodi

1980, Sheng (1983), and Blumberg 1977). If vertical

structure is repeated during critical conditions, however, it may be possible to calibrate an eddy viscosity

model from measurements using the approach of Odd

and Rodger (1978) or French (1979) and French and

McCutcheon (1983). The choice is governed by

whether prediction of highly stratified conditions is

more feasible than calibrating an eddy viscosity model

with extensive and difficult to collect data.

If calibration is chosen, a number of alternatives are

available. First, a site specific equation like that developed by Odd and Rodger (1978) can be developed.

Odd and Rodger noted that the Munk-Anderson formula shoud be modified if Ri≥1 and a significant peak

in Ri occurred in the lower 75 percent of the depth of

flow. Second, French and McCutcheon (1983) show

that less precise, more empirical approaches may yield

better results. French (1979) shows that a simpler

stability function can be derived by dimensional analysis that uses a gross Richardson number based on

shear velocity. French and McCutcheon (1983) found

that this simpler equation (see Table 5.28) predicted

eddy viscosity better than the complex four equation

hybrid model proposed by Odd and Rodgers (1978)

that is also given in Table 5.28. Unfortunately, the

simplification by French must be calibrated for any use

whereas the Odd and Rodger hybrid equation is a

direct extension of the Munk-Anderson formulation

that may be considered for use without calibration in

screening calculations (or at least the Odd-Rodger

formulation should be considered before the French

equation when calibration is not possible).

The final type of formulation is a class of equations

adapted from work in the atmospheric boundary layer

using different stability parameters. First, McCutcheon (1983) notes that the most direct application of the

atmospheric boundary layer work involves the MoninObukhov stability parameter (see Table 5.28). However, the stability parameter z/L where L is the

Monin-Obukhov scaling length (Monin and Yaglom

1971), is very difficult to numerically compute even

compared to the gradient Richardson number. In addition, there are data (Nelson 1972, Delft 1974) to

show that estuaries and coastal areas stratify to a

greater degree than the atmospheric boundary layer

and strong indications that the layer of constant stress

may be less deep in water flows (see Henderson-Sellers 1982). The result is that only limited direct application of the other data for stratified flows is fully

feasible. Any application of this sort is limited to small

values of Ri.

Second, McCutcheon (French and McCutcheon 1983)

shows that the Monin-Obukhov stability function can

be converted to a Richardson number (based on shear

velocity) function for small z/L. This conversion allows

one to maintain the empirical constants determined

from extensive measurements (i.e. von Karman conSource β(1) β(2) β(−1) Flow condition

Rossby and Montgomery

(1935)

40 — — Heywood’s wind profiles at Leafield

Sverdrup (1936) 10-13 — — Wind profiles over Spitzbergen snow field. From Munk and

Anderson (1948)

Munk and Anderson (1948) 10 — — Oceanic thermocline from Jacobsen (1913) for Randers Fjord

and Schultz’s Grund

Pasquill (1949) 12 — 12 Wind profiles in 2 meter layer over grass. From Nelson

(1972).

Kent and Pritchard (1957) 2.4 0.24 0.06 James River Estuary

Pritchard (1960) — 0.28 — James River Estuary

Pasquill (1962) — — 2.5 Rider’s (1954) wind profiles.

6 Taylor’s (1960) analysis of Rider’s (1954) and eddy flux data

of Swinbank (1955)

Vreugdenhil (1966) 30 — — Data source unknown. From Nelson (1972)

Nelson (1972) 10 2.5,5.0 3.3 Wind profiles Rider (1955) and questionable pipe flow data

from Ellsion and Turner (1960). (1954) and Deacon

Odd and Rodger (1978) 160 13 — Great Ouse Estuary. Fit by minimizing the relative error.

Knight et al. (1980) 110-160 13-20 3.4 Great Ouse Estuary. Visual fit.

Ueda et al. (1981) 2.5 — — Atmospheric boundary layer. From Henderson-Sellers (1982).

Henderson-Sellers (1982) 0.74 — — Rederived from data of Ueda et al (1981)

French and McCutcheon

(1985)

30 10 — Great Ouse Estuary. Fit by minimizing the root mean square

error.

Table 5-29. Observed Values of the Constants in Various Forms of the Munk-Anderson Stability Function

5-43
stant determined in unstatified flows as 0.4 and α determined as 5 to 7). Unfortunately, the resulting form

(see Table 5.28) is of the same inadequate form as the

Holzman type equation and has only a limited range of

applicability. However, comparison with the Great

Ouse data indicates that the proper form should be

similar to the Munk-Anderson form, shown as the third

equation under French and McCutcheon (1983) in

Table 5.28. Further, it can be observed that the constants should retain the same value determined from

other conditions (i.e., k = 0.4 and α = 5). The second

two equations under French and McCutcheon (1983)

in Table 5.28 must be equivalent in the limit

k

2 α Ro ′ → 0 according to the procedures generally

used to investigate stability functions (Monin and

Yaglom 1971). The link between the Monin-Obukhov

stability function and the functions derived by

McCutcheon are theoretically tenuous but the formulations do as well as any others in describing the

vertical mixing in the Great Ouse Estuary and this was

accomplished without the extensive calibration required for all other formulations (French and McCutcheon 1983). It is also notable that the parameter Ro’ is

much less error prone than Ri (e.g., computations of

u∗ are more precise than those for ∂u ⁄ ∂z.

As a result, the best methods to represent Ez seem to

be the third equation from French and McCutcheon in

Table 5.28 or the Rossby-Montgomery equation if the

estuary is not strongly stratified. The McCutcheon

formulation can be used without calibration in some

cases. The value of β(1) in the Rossby-Montgomery

equation should be taken as about 10 to 30 (see Table

5.29) if calibration is not possible but reduced values

of about 2 or 3 may be more useful if tidal averaging is

involved or 100 or more if prediction of sharp haloclines

(Ri>1) is to be attempted. Calibration to determine α

or β for each individual estuary is presently required if

the waste load is sensitive to vertical mixing. Where

Ri>1, higher order turbulence closure modeling is necParameter Ri Ro’ Ro* Ro Fr z/L Rf N

2

Definition

−

g

∂ρ

∂z

ρ

_





∂u

∂z







2

−

gz2∂ρ

ρu∗

2

∂z

gDΔρ

ρU∗

2

gDΔρ

ρU

2

U

2

gDΔρ

ρ

ρu∗

2

kgρ'w'

____

EzRi

Dz

−

g∂ρ

ρ∂z

Gradient

Richardson

number, Ri

=Ri

=

Ro′

k

2

φm

2

— — — =z/L for

small Ri

=Rf φm

=

N

2







∂u

∂z







2

Shear Richardson Number,

Ro’

=Ri(k

2

)φm

2 = Ro’ =Ro* for

z = D and

∂ρ

∂z

= −β

— — — =Rf(k

2

)φm

3 —

Shear Gross

Richardson

number, Ro*

— =Ro’ for

z = D and

∂ρ

∂z

= −β

= Ro* — — — — —

Gross Richardson number, Ro

— —- — =Ro = Fr−2 — — —

Densimetric

Froude number,

Fr

— — — =(Ro)

−2 = Fr — — —

Monin-Obukho

Stability pararmeter, z/L

= Ri for

small z/L

— — — — = z/L — —

Flux Richardson nymber, Rf

=Riφm

−1

= Ro′k

−2

φm

3 — — — — = Rf —

Brunt-Viasala

frequency, N2

= Ri





∂u

∂z







2 — — — — — — =N2

Notation: β=constant density gradient

φm=Monin-Obukhov stability function

Table 5-30a. Various Means of Representing the Stability of Stratification and the Relationship between Various Parameters

5-44
SUPPLEMENT IV: BRIEF REVIEW OF TURBULENCE CLOSURE MODELS

In recent years, 2 and 3 dimensional turbulence closure models have been employed in environmental

problems (e.g., HYDROQUAL 1987). ASCE Task

Committee (1988) gives a good review and assessment of various types of turbulence closure models.

The starting point of all turbulence closure models are

Navier-Stokes equations (see Hinze 1975, Rouse

1976, Monin and Yaglom 1971). These equations

include all details of turbulence fluctuations, but can

only be solved, at present, by introducing time averaged mean quantities. Turbulent quantities are averaged over a time step that is large compared with the

time scale of turbulent motion. The equations in Table

2.1 are the result. Averaging and relating the resulting

turbulent fluxes to mean flow properties introduces

eddy viscosity and eddy diffusivity parameters into the

flow and mass transport equations. These coefficients

are not related to fluid properties, but are controlled by

flow intensity and estuary morphology as well as grid

resolution and other factors. The critical steps in turbulence modeling is to relate these turbulent coefficients to average variables (i.e., velocity, pressure,

and concentration), empirical constants, and functions, so that this set of equations become a closed set

having one more equation than unknown. Turbulence

closure models are classified according to how the

equations are closed.

Prandtl (1925) suggests that eddy viscosity can be

related to the local gradient of mean velocity and a so

called mixing length. This theory has been applied and

modified by many researchers (e.g., Munk-Anderson

1948, Patanker and Spalding 1970) but mainly in

two-dimensional thin-layer flows with only one significant velocity gradient (Rodi 1980). Table 5.28 lists

some empirical formulations developed for this theory.

As ASCE Task Committee(1988) points out, the mixing length theory assumes that the transport and history of eddy effects can be neglected. It is therefore,

not very suitable when these effects are important, as

in many estuaries. In some cases, however, mixing

length models give reasonably good results when

applied to estuaries.

To account for the transport and history of eddy affects,

one-equation models have been developed which relate eddy viscosity to turbulent kinetic energy and a

length scale (Kolmogorov 1942, Prandtl 1945). The

kinetic energy equation (k-equation) was derived from

the Navier-Stokes equations which describes eddy

energy transport and history. So, theoretically, oneequation models are more suitable than mixing length

models when applied in estuaries. But the length scale

in this method is not convenient to determine, and can

only be determined through empirical equations (Launder and Spalding 1972). Two-equation models have

also been develolped and have become more popular

based on their greater utility.

Two-equation turbulence closure models introduce

one more equation (ε-equation) which is used to determine the length scale. Together with the k-equation

(Rodi, 1980), they can account for the transport of

turbulent energy and also the length scale of the turbulent motion. They can be used in the situations where

the length scale can not be prescribed by empirical

equations, and have been applied successfully in many

situations where simpler models failed (Rodi, 1980,

1984). But, the length scale equation has been criticized as not universal enough (e.g., Mellor and

Yamada, 1982). Also, the k-equation assumes a direct

relation between eddy viscosity and eddy diffusivity,

and turbulent kinetic energy (which is a velocity scale).

In some situations, eddy fluctuations, stress, and the

scale used to describe them develop differently. Therefore, more complex stress/flux -equation models have

been developed which abandoned the k-equation used

by the above two methods. These models are promising in the sense of universality, but are still in the stage

of research and have not yet been tested enough (see

Rodi 1980, Launder 1984, Mellor and Yamada 1982,

Gibson and Launder 1978). So far, turbulence closure

models have been employed mainly in the research

programs. Though there have been some notable environmental applications (e.g., HYDROQUAL 1987), it

should be noted that turbulence models can be reasonably applied only when the model assumptions are not

violated, and the extensive requireessary or extensive calibration of the eddy viscosity

model is required if vertical mixing is important.

Finally, these recommendations are specific to the use

of the stability parameters Ri and Ro’. A number of

hydrodynamic models (McCutcheon 1983) use slightly

different forms as given in Table 5.30a. These stability

functions should be converted to the required form or

the constants corrected as necessary. Table 5.30a

gives preliminary guidance on the relationships involved but these have not been thoroughly checked

and tested.

5-45
SUPPLEMENT V. SELECTION OF DISPERSION COEFFICIENTS

Dispersion coefficients are empirical analogs of the

molecular diffusion coefficient defined in the advectivediffusive equation:

∂C

∂t

+

∂(UC )

∂x

+

∂(VC )

∂y

+

∂(WC )

∂z

= Dx

∂

2C

∂x

2

+ Dy

∂

2C

∂y

2

+ Dz

∂

2C

∂z

2

+ ΣS (5.22)

where C is concentration of the constituent being

modeled; U, V, and W are mean water velocities in the

x, y, and z coordinate directions, respectively; and Dx,

Dy, and Dz are the longitudinal, lateral and vertical

dispersion coefficients, respectively. ΣS is the sum of

all sources and sinks of constituent C. Typical values

of longitudinal, lateral, and vertical turbulent dispersion

are much larger than values of thermal and molecular

diffusion as shown in Figure 5.24.

Figure 5-24. Diffusion Coefficients.

ments for expertise, data, and computation facilities

are met. Presently, cost compared with the benefits

might make it unfeasible to employ a turbulence closure model in a particular estuary waste load allocation

study. Hopefully, this will change the near future. For

more detailed turbulence model descriptions, one can

consult ASCE Task Committee (1988), and Rodi

(1980).

It is a good suggestion that one use one-dimensional

hydrodynamic models, which lump turbulence effects

into a simple roughness coefficient discussed in Supplement I and are throughly tested, much easier to

implement and well documented, whenever possible.

If it is decided that a turbulence model should be used,

one should be fully aware of the expertise and cost

required.

5-46
Figure 5-25. Relationship between horizontal diffusion coefficient and horizontal length scale

[Thibodeaux (1979), Fan and Koh, Orlob (1959), Okuba].

5-47
The dispersion coefficients can not be defined in terms

of physical properties of the water. These represent

coefficients of proportionality relating velocity gradients (∂U/∂x, ∂V/∂y, and ∂W/∂z) to correlations of turbulent fluctuations of concentration, c’, and velocity (u’,

v’, and z’) written as: u’c’, v’c‘, and w’c’ (McCutcheon

1989). As such, the coefficients of proportionality represent a method of simplifying the transport equation

so that it may be reasonably solved. The dispersion

coefficients are therefore, functions of turbulence (u’c’,

v’c’, w’c’), which in turn are related to flow conditions

in the estuary, and the method of averaging over time

or space. Greater numerical dispersion and thus lower

actual specified dispersion results when the equations

are solved over greater element distances or averaged

over longer time periods. The coefficients can not be

predicted but a number of empirical relationships have

been observed that can be used to estimate initial

values. In addition, there are a number of case studies

that establish representative values. These initial values are then modified as necessary to calibrate the

model.

When estimating the dispersion coefficients, it should

be noted that these are empirical factors that are not

only related to the turbulence in the flow but that these

values are also influenced by the way in which Equation 5.22 is solved. Therefore, at least minor differences are expected to be found if different numerical

schemes, with differing degrees of numerical dispersion are employed, or if different length and time scales

are used in solving the equations. As a result, any

observational experience obtained from similar estuaries or from predictive equations based on past experience, are useful as initial guidance but may not be

adequately related to the conditions in the estuary

being simulated with the form of Equation 5.22 in the

model being used. This includes use of eddy viscosity

values obtained from prior calibrations of different

models in the estuary of interest where some difference may occur between the final calibrated values

and the previous estimates. In addition, the use of case

studies from other estuaries must be carefully considered to be sure that the calibrated model was sensitive

to the dispersion coefficients. If the calibrated model

was not sensitive to the dispersion coefficients, the

final values may not be estimated precisely.

Generally, concentration distributions in estuaries and

streams are not sensitive to dispersion coefficients

(Krenkel and Novotny 1980). Therefore, precise calibration usually is not critical.

The general guidance is somewhat similar to that

used for the selection of eddy viscosity values and is

as follows:

1. Qualitatively estimate relative importance of mixing

by various mechanisms. These mechanisms include

shear flows set up by tides and river flow, mixing by

wind shear, and mixing by internal density differences.

The importance of these mechanisms indicates how

best to select dispersion coefficients. Various methods include:

a. Estimation of shear flow dispersion. Fischer

et al. (1979) notes that dispersion can be reasonably estimated in estuaries that are long

and narrow, or wide. Shear flow dispersion,

usually acting along the longitudinal axis of

the estuary, is most important when mixing

times across the estuary are approximately

equivalent to times required to mix along the

axis of the estuary (Fischer et al. 1979). Fischer et al. (1979) note that the maximum longitudinal dispersion due to shear is

approximately

Kx = 0.1(0.2 U

2

)T (0.8) (5.23)

 Where Kx is expressed in m2 s-1, (0.2U) is assumed to approximate the deviation of the velocity in a cross section from the cross

sectional average, T is the tidal period in seconds, and the constant 0.8 is derived by Fischer et al. (1979, see their Figure 7.4). U is

the mean tidal velocity. Fischer et al. (1979), illustrates this method of estimation.

b. Fraction of freshwater method. Officer (1976)

describes how freshwater and observed longitudinal salinity gradients can be used to estimate longitudinal dispersion.

c. 4/3’s law. It has been widely observed that

lateral dispersion can be estimated from the

empirical formula:

Ky = constant (length scale)

4

⁄3

 (5.24)

See Bowie et al. (1985), Officer (1976), and Figure 5.25.

2. Compare estimates with published values. Tables

5.30b, 5.31, and 5.32 compile the readily available

estimates of tidally averaged longitudinal coefficients,

longitudinal dispersion coefficients observed in two-dimensional estuaries and coastal waters, and lateral

dispersion coefficients. These values should be used

to confirm the reasonableness of estimates made with

Equations 5.23 and 5.24 or to provide preliminary

estimates for the water body of interest. See Officer

(1976).

5-48
Freshwater Inflow

Low Flow Net

Non-tidal Velocity

Longitudinal Dispersion

Coefficient

Estuary (m3s

-1) (ft3

s

-1) (ms-1) (fts-1) (m2

s

-1) (ft2

s

-1) Comments

North America

Hudson River

Mouth

106 to 637 3,750 to

22,500

— __ 450 to 1,500 4,840 to

16,133

From O’Conner (1962). Found

correlation between flow and Kx

Potomac 56 2000 __ __ 6 to 59 65 to 635 Estimated from the fraction

freshwater method and dye

studies by Hetling and O’Connell

(1965, 1966). A very consistent

relationship between Kx and

distance downstream of Chain

Bridge observed

San Francisco Bay

Suison Bay __ __ __ __ 600 to 1,400 600 to 15,000 Determined by Bailey (1966) from

dye studies of one to a few days

in duration.

Sacramento and

San Joaquin

Rivers

__ __ __ __ 9 to 90 100 to 1,000

Northern Arm __ __ __ __ 30 to 1,770 320 to 19,000 Determined with the fraction of

freshwater method by Glenne and

Selleck (1969) from

measurements over 3 stages of

the tidal cycle at 2 or more

depths. Glenne and Bailey also

used silica as a conservative

tracer and confirmed that values

of Kx were accurate.

Southern Arm __ __ __ __ 10 to 100 190 to 1,900

Yaquina 17 __ __ __ 60 to 853 650 to 9,180 Burt and Marriage (1957)

determined these values by

fraction of freshwater method.

High flow Kx significantly higher

than low flow Kx.

low flow __ __ __ 14 to 99 140 to 1,066

United Kingdom

Narrows of Mersey 25.7 907.6 __ __ 161 1,733 Estimates based on the fraction

freshwater method measured at

various locations along with

salinity concentrations averaged

over tidal cycles.

103 3,637 __ __ 359 3,864

Severn __ __ __ __ 54 to 174 581 to 1,873 Kx values recomputed by Bowden

(1963) from estimates of Stommel

(1953). Bowden included the

freshwater inflow from tributaries

in the fraction of freshwater

method and derived significantly

larger values. The higher values

are representative of a section

with a tidal bore.

Southampton 158 1700 Kx computed by fraction

freshwater method by Dyer

(1973).

Thames low flow __ __ ___ 53 570 At 16 Km (10 miles) and 40 Km

(25 miles) downestuary of London

Bridge.

84 904

high flow __ __ 338 3,638 At 48 Km (30 miles) downestuary

of London Bridge.

Tay 50 1,766 __ __ 50 to 135 540 to 1,453 Estimates by the fraction

freshwater method. Estimated by

the fraction freshwater method.

Kx varies at each location as a

function of freshwater discharge.

100 3,531 70 to 210 750 to 2,260

200 7,063 30 to 470 320 to 5,060

300 10,600 70 to 700 750 to 7,530

Japan

Ariake Bay __ __ __ __ 670 7,212 Derived by Higuchi (1967) from

an observed longitudal salinity

profile caused by freshwater

inflow of the Chikugo River.

Diffusion of small dye patches

were found to follow the 4/3’s law.

Table 5-30b. Tidally Averaged Longitudinal Dispersion Coefficients Observed in Selected One Dimensional Estuaries

[Hydroscience (1971), Officer (1976) and Bowie et al. (1985)]

5-49
Freshwater Inflow

Low Flow Net

Non-tidal Velocity

Longitudinal Dispersion

Coefficient

Estuary (m3s

-1) (ft3

s

-1) (ms-1) (fts-1) (m2

s

-1) (ft2

s

-1) Comments

United Kingdom

Irish Sea __ __ 0.0035 0.0115 500 to 900 5,380 to

9,690

Estimated from the longitudinal salinity

gradiental across a section between Lands

End and Cape Clear and between St.

Davids Head and Carnsore Point using the

simplified continuity relationships known as

Knudsen’s relations. Large values

attributable to large depths and extremely

large horizontal length scales.

North Sea __ __ __ __ 21.7 to 9.6 234 to 103 Estimated from dye spreading experiments

with instanteous point injections tracked for

up to 60 hr. Kx = σx ⁄ 2t.

Firth of Fal __ __ __ __ 0.4 to 3.6 4.3 to 38.9 Estimated from dye spreading experiments

with instanteous point injections tracked for

up to 7 hr. Kx = σx ⁄ 2t.

Blackwater __ __ __ __ 13 to 27 140 to 291 Estimated from dye spreading experiments

with instanteous point injections tracked for

up to 12 hrs.Kx = σx ⁄ 2t.

Japan

Osaka Bay and

Mizushima Bay

__ __ __ __ 0.5 5.4 Determined by calibration of a heat balance

model for thermal plume injected into the

bay from a power plant.

Ariake Bay __ __ __ __ 0.25 to 5 2.7 to 53.8 Determined by Higuchi (1967) from

diffusion of small dye patches in the bay.

The data follows the 4/3’s law.

Table 5-31. Longitudinal Dispersion Coefficients Observed in Selected Two Dimensional Estuarine and Coastal Water Studies

[Hydroscience (1971), Officer (1976) and Bowie et al. (1985)]

Figure 5-26. Relationship between longitudinal dispersion

coefficient and discharge in a Scottish estuary

[West and Williams (1972)].

Figure 5-27. Relationship between longitudinal dispersion

coefficient in the Potomac Estuary and distance

downestuary from the Chain Bridge in Washington, D.C.

 [Hetling and O’Connell (1966)].

5-50
Lateral Dispersion Coefficient

Estuary (m3s

-1) (ft3

s

-1) Comments

United Kingdom

Severn Estuary 2 22 Estimated by de Turville and Jarman (1965) from the mixing of the thermal

plume entering the estuary with the River Usk into the Bristol Channel using

observed temperature distributions, cooling water flow rates, river flow rates, and

assumptions about the distribution of the sources at the outfall. Ky was related

to the lateral dimensions of the river.

Fal Estuary 1.5 16 Estimated from dye spreading perpendicular to the axis of longitudinal spreading

of an instanteous point injection. Spreading occurred over periods of up to 7 hrs.

Ky = σy/2t.

Blackwater Estuary 3 to 9 32 to 97 Estimated from dye spreading perpendicular to the axis of longitudinal spreading

of an instantaneous point injection. Spreading occurred over periods of up to 12

hrs. Ky = σy/2t.

North Sea (between

U.K. and Europe)

1.4 to 6.0 15 to 65 Estimated from dye spreading perpendicular to the axis of longitudinal spreading

of an instanteous point injection. Spreading occurred over periods of up to 12

hrs. Ky = σy/2t.

Irish Sea (between

U.K. and Ireland)

110 to 1,480 1,184 to 15,930 Based on a simple heat balance by Bowden (1948).

25 270 Based on a steady-state salt balance and assumptions that the longitudinal

salinity gradient through the Sea is linear, the lateral gradient is parabolic, the

vertical salt balance terms are negligible, lateral advection can be neglected,

and the horizontal advective velocities are on the order of 0.005 m s-1

(0.016 ft s-1).

Japan

Osaka Bay and

Mizushima Bay

0.5 5.4 Determined by calibration of a heat balance model for a thermal plume injected

into the bay from a power plant.

Table 5-32. Lateral Dispersion Coefficients in Estuaries and Coastal Waters [Officer (1976)]

3. Correct for areas of higher turbulence. These

areas typically occur in the lee of islands and other

shore line irregularities or where bottom roughness

or topography changes drastically.

4. Relate dispersion coefficient to freshwater discharge. If the waste load allocation covers more

than a single freshwater discharge condition, longitudinal dispersion coefficients are typically related

to changing freshwater discharge as illustrated in

Figure 5.26.

5. Relate dispersion coefficient to location. The longitudinal dispersion coefficient tends to increase in

the downestuary direction. See Figure 5.27 for an

illustration of the expected behavior.

6. Select vertical dispersion coefficients. McCutcheon (1983) lists various formulas that are useful.

Typically a formula is selected and modified if necessary during calibration. See guidance on the

selection of vertical eddy viscosity.

5-51
Investigator

Evaporation Rate

Expression

in Original Form

Units* for

E, u, and

E*

Observation

Levels

Time

Scale

Incremen

ts

Water

Body

Formula at

Sea Level**

Remarks

Marcians

and Harbeck (1954)

E=6.25x10-4u8(eo-e8) cm(3 hr)-1

knots

mb

8m-wind

8m-ea

3 hrs

Day

Lake

Hefner,

Oklahoma

2587 acres

12.4u8(eo-e8)

17.2u2(eo-e2)

Good agreement with

Lake Mead, Lake

Eucumbene and

Russian Lake data.

Kohler

(1954)

E=0.00304u4(eo-e2) in.(day)-1

miles(day)-1

in. Hg

4m-wind

2m-ea

Day Lake

Hefner,

Oklahoma

2587 acres

15.9u4(eo-e2)

17.5u2(eo-e2)

Essentially the same as

the Lake Hefner

Formula.

Zaykov

(1949)

E=[.15+.108u2](eo-e2) mm(day)-1

ms-1, mb

2m-wind

2m-ea

Ponds and

small

reservoirs

(43+14u2)(eo-e2) Based on Russian

experience.

Recommended by

Shulyakovskiy.

Meyer

(1942)

E=10(1+0.1u8)(eo-e8) in.(month)-1

 25 ft-wind

mph

in. Hg

25 ft - wind

25 ft-ea

Monthly Small

lakes and

reservoirs

(73+7.3u3)(eo-e8)

(80+10u2)(eo-e2)

ea is obtained daily from

mean morning and

evening measurements

of Ta, and relative

humidity. Increase

constants by 10% if

average of maximum

and minimum used

Morton

(1976)

E=(300+50u8)(eo-ea)/p in.(month)-1

mph

in. Hg

8m-wind

2m-ea

Monthly Class A

pan

(73.5+12.2u8)(eo-e2)

(73.5+14.7u2)(eo-e2)

Data from

meteorological stations.

Measurement heights

assumed.

Rohwer

(1931)

E=0.771[1.465-.0186B]x

[0.44+0.118u](eo-ea)

where B = atmos. press

in.(day)-1

mph

in. Hg

0.5-1 ft-wind

1 inch-ea

Daily Pans

85 ft

diamter

tank

1300 acre

reservoir

(67+10u2)(eo-e2) Extensive pan

measurements using

several types of pans

Correlated with tank and

reservoir data.

Table 5-33. Evaporation Formula for Lakes and Reservoirs [Ryan and Harleman (1973)]

* For each formula, the units are for evaporation rate, wind speed, and vapor pressure (i.e., in Meyer’s formula evaporation rate is in

inches month -1, wind speed is in miles per hour (mph) measured 25 feet above the water surface, and vapor pressure is in inches of

mercury also measured at 25 feet).

** Measurement heights are specified as subscripts to wind speed, u, and vapor pressure, e. The units for evaporation rate, E; wind

speed; and vapor pressure or saturation vapor pressure (ea and eo) are BTU ft-2day-1, miles hr.-1, and mm Hg, respectively

SUPPLEMENT VI: SELECTION OF WIND SPEED FUNCTIONS:

All mechanistic temperature models have at least one

empirical function, known as the wind speed function,

that must be specified during the calibration procedure.

Even equilibrium temperature approximations have

the wind speed function embedded in the first-order

heat transfer coefficient (McCutcheon 1989). The

wind speed function is typically expressed in Stelling’s

form (Brutsaert 1982) as:

E = (a + buw ) (eo − ea ) (5.25)

where E is the heat flux due to evaporation, (a + buw)

is the wind speed function to be specified as part of the

calibration procedure, and eo - ea is the difference

between the saturation vapor pressure of the atmosphere at the ambient temperature (eo) and the measured vapor pressure (ea).

Whether the waste load allocation is sensitive to the

choice of wind speed coefficients or not determines

how precise the calibration must be. Generally, the

final results are not expected to be overly sensitive to

temperature predictions. Temperature gradients are

normally not as strong as salinity gradients and

changes in temperature over the estuary do not seem

likely to cause large differences in biochemical reactions. The wind speed function, therefore, is expected

to be most important when simulations extend over

seasonal changes (i.e., spring into summer) and when

5-52
the evaporative heat flux is a significant part of the

estuary heat balance.

Typically, a wind speed function is selected from the

compilations of available functions given in Tables

5.33 and 5.34. The best choice from the compiled

values is one that has been developed for a water body

of similar size at approximately the same latitude.

Shore line conditions that influence aerodynamic

roughness and the atmospheric boundary layer over

the estuary should be similar if possible. When the

wind speed function is modified during calibration, it is

usually best to change the function by a constant

multiplier rather than arbitrarily changing the coefficients a and b (McCutcheon 1989) by disproportionate

amounts unless the physical meaning of the two coefficients is well understood (e.g., see Wunderlich 1972,

Ryan and Harleman 1973).

Investigator

Evaporation Rate Expression

 E=f(u, eo, e, etc.)

 Units for E, u, & e Time

Scale

Type of Water Body

Penman (1956) 0.35(0.5+0.01u2)(eo-e2) mm day-1

mi/day @ 2m

 mm Hg

— Lake, meteorological data collected on land

Meyer (1942) 0.36(1+0.1u7.6)(eo-e7.6) in. month-1

mph @ 7.6m

 in. Hg

Daily Small lakes, reservoirs, and pan evaporation

Harbeck et al.

(1958)

0.078u2(eo-e2) in. day-1

mph @ 2m

 in. Hg

Daily Lake Mead, NV

Turner (1966) 0.00030u2(eo-e2) ft. day-1

mph @ 2m

 in.Hg

— Lake Michie, NC

Fry 0.0001291u2(eo-e2) cm. day -1

km. day-1 @ 2m

 mb

— —

Easterbrook

(1969)

0.000302 u2(Co-C2) g cm

-2

 s

-1

 ft. s-1

— Lake Hefner, mid-lake

0.000001942 u2(Co-C2)

C is relative humidity, unitless

Lake Hefner combined data

Jobson (1980) (3.01 + 1.13u2)(e0-e2) mm day -1

ms

-1 @ 2m

 kilopascals

— San Diego Aqueduct, CA. Energy balance.

Faye et al. (1979) 0.70(3.01 + 1.13u2)(eo-e2) mm day -1

ms

-1 @ 2m

 kilopascals

— Chattahoochee River, GA.

McCutcheon

(1982)

0.45(3.01 + 1.13u2)(eo-e2) mm day -1

ms

-1 @ 2m

 kilopascals

15 min West Fork Trinity River, TX.

Table 5-34. Evaporation Formulas [Wunderlich (1972) and McCutcheon (1989)]

5-53
SUPPLEMENT VII: SELECTION OF BACTERIA DIE-OFF COEFFICIENTS

Traditionally, the bacteria die-off process is considered

as a simple first-order decay, such that

dN

dt = − KB N (5.26)

where N = bacteria concentration {num/L3}

 KB = die-off or decay rate {1/T}

The resulting distribution downstream is

N = N0 e

−KB t

where

No = initial concentration of bacteria {num/L3}

In some cases, bacteria resuspension from the bottom

can be important, so, a resuspension term is added

dN

dt = − KB N +

Vu

H

Ms RN (5.27)

where

Vu = resuspension velocity {L/T}

H = water column depth {L}

Ms = solids concentration in the sediment {Ms/L3}

RN = bacteria concentrations based on solids

{num/Ms}

The solution of equation 5.21 is

N = No ext (−KB t ) +

VuMsRN

HKB

 [1−e

−KB t

] (5.28)

For bacteria analysis and modeling, the order of magnitude is often considered precise enough, so, steady

state modeling is often employed. On the other hand,

the fate of bacteria in natural waters is assumed to be

a first-order decay, therefore all modeling procedures

for other contaminants with a first-order decay are

applicable to bacteria.

Table 5.35 and 5.36 compile the bacteria decay rates

from studies involving salty and fresh waters, respectively. They can be used as a guidence to select initial

rates for a particular study. Generally, the decay rates

for coliforms are on the order of 1 per day, but can be

as high as 48/day for marine outfalls. Virus decay

rates are usually one order of magnitude lower than

that of bacteria.

In estuaries and other natural water bodies, the fate of

bacteria is affected by many site-specific factors, such

as (Thomann and Mueller 1987, Bowie, et.al., 1985)

temperature, sunlight, salinity, settling, resuspension,

aftergrowth, nutrient difficiencies, predation, and toxic

substances. After selecting a initial value for the decay

rate, adjustment should be made to fit the prediction

results to actual measurement by trial and error.

Often, the actual bacteria decay is not exactly first-order. Under these situations, the decaying process is

divided into different stages. Each stage can be described reasonably well by first-order decay and a

different decay rate (Thomann and Mueller 1987).

An alternative way of selecting the initial bacteria decay rate is described in Thomann and Mueller (1987).

They recommend an empirical equation which includes the effects of salinity, temperature, sunlight and

settling of bacteria.

KB = [0.8 + 0.006(%seawater)] 1.07T−20

+

αIo (t )

KeH

 [1−e

−KeH

] +

Vs

H

(5.29)

where

% sea water = percent of salinity compared to

sea water

1.07 = temperature correction coefficient

T = temperature in oC

α = constant coefficient in light correction function

Io = surface solar radiation, Cal/m2hr

Ke = vertical light extinction coefficient in water

column, 1/m

Vs = settling velocity of particulate bacteria in

m/day. Precisely, Vs should not include resuspension, which is already accounted for with a resuspension term in Eq. 5-22. But, lumping

resuspension into Vs is also feasible; then Vs becomes net settling rate.

 H = water column depth, m.

Following is a simple example to calculate bacteria

transport.

T = 25oC

Q = 200 m3/sec

u = 0.01 m/sec

E = 50 m2/sec

Discharge: 0.5 m3/sec, 4 x 106 FC/100ml

x = 5 km to bathing area

So = 7 PPT

Where PPT = part per thousand and FC is the number

of fecal coliform bacteria. The problem is the water

quality standard requires the fecal coliform bacteria

concentrations in a bathing area to be less than

200/100 ml. If an effective aftergrowth factor is as5-54
sumed to be 2, what percent of fecal coliform bacteria

in the downstream discharge should be cut off to meet

the standard?

Calculation of fecal coliform bacteria decay rate:

a) the salinity of bathing area

S = So e

ux ⁄ E

= 7e

0.01(−5000 ) ⁄ 50

= 2.6 PPT

b) the average salinity between the outlet and bathing

area

S

_

= (2.6 + 7.0 ) ⁄ 2 = 4.8 PPT

c)Take 35 PPT as 100% sea water salinity, then

% seawater = 4.8 ⁄ 35 = 14 %

d) Decay rate estimation

Kb (25oC ) = [0.8 + (0.006 ⋅ 14)] 1.4 = 1.24 day−1

This decay rate will be used without the calibration or adjustment that is needed in a real problem.

e) Concentration and Bathing Area with no disinfection:

N = No e

jx

j =

u

2E (1+√ 1+4EKB ⁄ u

2

)

=

0.01

2(50)

(1+√ 1+4(50)1.24 ⁄ 0.012)=6.4 x 10−4 1 ⁄ m

No =

(4x 106) 0.5

200+0.5

= 104⁄ 100 ml

N = 104⋅e

6.4x 10−4(−5000)

= 400 ⁄ 100 ml

Organism

Dieoff Rate

 Coefficient *

 (d-1 base e)

Temperature

(

o

C) Reference Comments

Coliforms:

Total coliform 1.4 20 Mancini (1978) Seawater

 (0.7 to 3.0)

48. __ Mitchell and

Chamberlain (1978)

Collected from 14 ocean outfalls, variable temp.

 (8. to 84)

Total or fecal coliform

 0.0 to 2.4 __ Hydroscience (1977b)New York Harbor Salinity: 2 to 18 o/oo. Sample kept in

darkness

 2.5 to 6.1 __ Hydroscience (1976b)New York Harbor Salinity: 15 o/oo. Sample kept in

sunlight

0.48 20 Chen (1970) Derived from the calibration of a model for San

Francisco Bay

0.48 to 8.00 20 Tetra Tech (1976) Derived from model calibration for Long Island, New

York Estuaries

1.0 __ Velz (1984) Observed in New York Harbor

(summer)

0.60 __ Velz (1984) Moracaibo Strait, Venezula; from observations by Parra

(summer) Pardi.

Fecal coliform 37 to 110 __ Fujioka et al. (1981) Seawater kept in sunlight

E. coli 0.08 to 2.0 __ Anderson et al. (1979)Seawater, 10 to 30 o/oo

Fecal streptococci 18 to 55 __ Fujioka et al. (1981) Seawater kept in sunlight

Viruses:

Coxsackie 0.12 25 Colwell and Hetrick

(1975)

Marine waters

0.03 4

Echo 6 0.08 25 Colwell and Hetrick

(1975)

Marine waters

0.03 4

Polio type I 0.16 25 Colwell and Hetrick

(1975)

Marine waters

0.05 4

Enteric (polio,

Echo, and coxsackie)

 1.1 to 2.3 24 Fujioka et al. (1980) Seawater collected off Hawaii

*Range of values or time of year in parenthesis.

Table 5-35. Reported Decay Rate Coefficients for Bacteria and Viruses in Seawater and Brackish Water [Thomann and Mueller

(1987), Bowie et al. (1985), and Veiz (1984)]

5-55
Organism Dieoff

RateCoefficient

 (d-1 base e)

Temperature

(

o

C)

Reference Comments

Coliforms:

Total coliforms 0.8 20 Mancini (1978) Average freshwater

Total or fecal

coliforms

.2 (summer) 20 Frost and Streeter

(1924)

From observed disappearance rates in the Ohio River.

1.1 (winter) 5

2.0 (Jn/Sept) __ Hoskins et al. (1927) From observed disappearance rates in the Upper Illinois

River.

2.5 (Oct/May) __

0.58 (Dec/Mar)__

1.0 (Apr/Nov) __

2.0 (Jn/Sept) __ Hoskins et al. (1927) From observed disappearance rates in the lower Illinois

River

0.9 (Oct/May) __

0.62 (Dec/Mar)__

0.7 (Apr/Nov) __

15.1 __ Kittrell and Kochtitzky

(1947)

From observed disappearance rates in a shallow turbulent

stream

0.48 (winter) __ Kittrell and Furfari

(1963)

From observed disappearance rates in the Miissouri River

downstream of Kansas City, Missouri

1.03 (summer)__ Kittrell and Furfari

(1963)

From observed disappearance rates in the Tennessee River

at Knoxville.

0.12 (summer)__ Kittrell and Furfari

(1963)

From observed disappearance rates in the Tennessee River

at Chattanooga.

1.73 (summer)__ Kittrell and Furfari

(1963)

From observed disappearance rates in the Sacramento

River downstream of Sacramento, California

5.5 (summer) __ Kittrell and Furfari

(1963)

From observed disappearance rates in the Cumberland

River in Tennessee.

2.2 (summer) __ Velz (1970) From observed disappearance rates in the Scoito River,

Ohio. Original data from Kehr et al.

1.1 (winter) __

1.84 (summer)__ Velz (1984) From observed disappearance rates in the Upper Miami

River, Ohio. Original data from Velz et al.

1.84 (summer)__ Velz (1984) From observed disappearance rates in the Hudson

River,downstream of Albany, New York. Original data from

Hall et al.

26.4 __ Wasser et al. (1934) From observed disappearance rates in the Glatt River

0.5 10 Wuhrmann (1972) From observed disappearance rates in a groundwater fed

stream

0.41 __ Mahlock (1974) From observed disappearance rates in the Leaf River,

Mississippi

1.51 (summer)__ Velz (1984) From observed disappearance rate in Yaracuy River,

Venezula by Parra Pardi.

0.2 to 0.7 7.9 to 25.5 Klock (1971) From observed disappearance rates in a wastewater lagoon.

2.0 __ Marais (1974) From observed disappearance rates in maturation ponds

1.7 19

Table 5-36. Reported Decay Rate Coefficients for Bacteria and Viruses in Freshwater and Stormwater

[Thomann and Mueller (1987), Bowie et al. (1985), and Velz (1984)]

5-56
Organism Dieoff

RateCoefficient

 (d-1 base e)

Temperature

(

o

C)

Reference Comments

2.6(1.19)T-20

__ Marais (1974) From observed disappearance rates in oxidation ponds

8.64 10 to 17 Zanoni et al. (1978) From observed disappearance rates in Lake Michigan

9.6 (August) __ Gannon et al. (1983) From observed disappearance rates in FordLake, Ypsilanti,

Michigan

1.25 15 Thornton et al. (1980) October 1976, March 1977, June 1977. From observed

disappearance rates in DeGray Reservoir, Arkansas.

2.62 to 0.384 10

3.3 to 2.7 20

1.0 20 Chen et al. Derived from model calibration(1976)

0.01 to 3.5 20 Baca and Arnett (1976) Derived from model calibration for various streams.

0.48 to 2.0 20 U.S. Army Corps of

Engineers (1974)

Derived from model calibration for Lake Ontario.

0.48 20 Chen and Orlob (1975) Derived from model calibration for Lake Washington.

1.0 to 3.0 20 Hydroscience (1971) Derived from model calibration for various streams.

0.48 20 Chen and Wells (1975) Derived from model calibration for Boise River, Idaho.

Fecal streptococci:

S.faecalis 0.4 to 0.9 20 USEPA (1974) Freshwater

0.1 to 0.4 4

0 to 0.8 20 Kenner (1978) Kanawha River

0.3 20 Geldrich and Kenner

(1969)

Stormwater, observed from 0 to 3rd day

0.1 20 Observed from 3rd to the 14th day.

1.0 to 3.0 18 Dutka and Kwan (1980) Hamilton Bay, Lake Ontario observed from 0 to 10th day.

0.05 to 0.1 __ Observed from 10th to 28th day.

S. bovis 1.5 20 Geldrich and Kenner

(1969)

Stormwater

Pathogens:

Salmonella typhinurium1.1 20 Geldrich and Kenner

(1969)

Stormwater, observed from 0 to 3rd day.

0.1 20 Observed from 3rd to 14th day

Salmonella

thompson

0.5 to 3 18 Dutka and Kwan (1980) Hamilton Bay, Lake Ontario observed from 0 to 10th days

0.1 18 Observed from 10th to 28th day

Viruses:

Coxsackie 0.77 21 to 23 Herrmann et al. (1974) Lake Wingra

Table 5-36. Reported Decay Rate Coefficients for Bacteria and Viruses in Freshwater and Stormwater

[Thomann and Mueller (1987), Bowie et al. (1985), and Velz (1984)]

Fecal Coliform Bacteria Reduction percent with a

growth factor of 2

2(400)−200

2(400)

= 75%

If there is no background concentration of fecal coliform bacteria in the bathing area, reducing the 75%

concentration in the fecal coliform bacteria load will

result in 200/100 ml fecal coliform bacteria concentration in the bathing area.

5-57
SUPPLEMENT VIII: CALIBRATING SIMPLE SEDIMENT MODELS

Section 2.4 and Supplement I of Section 2 introduced

the important processes concerning sediment transport in estuaries. Settling is always an important potential factor to water quality problems and a careful

analysis and calibration of settling coefficients is always necessary. Limited guidance in the calibration

of simple sediment transport models includes:

1. Select initial settling values from Table 5.37 for

inorganic particles and Table 5.38 for algae modeling.

2. Adjust settling velocity by trial and error for calibration.

It’s important to note that the initial values selected at

step 1 do not include the effects of resuspension which

can be extremely important to understand the special

characteristics of sediment movement in estuaries. During every tidal cycle, particle settling attains a

maximum during the slack tides. Later, the sediments

on the bottom can be resuspended and carried upstream with flood tide and settle to the bottom there.

They can also be carried downstream with ebb flow.

For most estuaries, sediments settled onto the bottom

layer near the mouth are often carried back into the

estuary rather than into the open sea. Usually, at the

head of the saline intrusion wedge of a stratified estuary, this upstream transport is balanced by the downstream transport. This point is called the null zone.

In a steady state model a net settling velocity is usually

adopted, which equals the gross settling velocity minus resuspension. This net settling can be arrived at

by calibrating the model against the suspended solid

balance. But, in some situations, this net settling

velocity can not be used in describing the pollutant

transport. For example, the concentrations of pollutant adsorbed on solids might be appreciably different

between the solids settling from the water column and

the solids resuspending into the same water due to the

sediment movement in the estuary. Also, if a pollutant

is newly introduced into an estuary which did not have

it before, the gross settling velocity should probably be

used to describe the pollutant transport instead of the

Particle Diameter,

mm

Particle Density, g cm-3

1.8 2.0 2.5 2.7

Fine Sand

0.3 300 400 710 800

0.05 94 120 180 200

Silt

0.05 94 120 180 200

0.02 15 19 28 32

0.01 3.8 4.7 7.1 8.0

0.005 0.94 1.2 1.8 2.0

0.002 0.15 0.19 0.28 0.32

Clay

0.002 0.15 0.19 0.28 0.32

Table 5-37. Settling Velocities in m/day at 20 oC for Inorganic

Particles [Ambrose et al. (1987)]

Algal Type Settling

Velocity

(m/day)

References

Total Phytoplankton0.05 - 0.5 Chen & Orlob (1975), Tetra Tech (1976), Chen

(1970), Chen & Wells (1975,1976)

0.05 - 0.2 O’Connor et al.(1975,1981) Thomann et al.

(1974,1975,1979), Di Toro & Matystik (1980), Di

Toro & Connolly (1980), Thomann & Fitzpatrick

(1982)

0.02 - 0.05 Canale et al. (1976)

0.4 Lombardo (1972)

0.03 - 0.05 Scavia (1980)

0.05 Bierman et al. (1980)

0.2 - 0.25 Youngberg (1977)

0.04 - 0.6 Jorgensen (1976)

Diatoms 0.05 - 0.4 Bierman (1976), Bierman et al. (1980)

0.1 - 0.2 Thomann et al. (1979), Di Toro & Connolly (1980)

0.1 - 0.25 Tetra Tech (1980), Porcella et al. (1983)

0.03 - 0.05 Canale et al. (1976)

0.3 - 0.5 Smayda & Boleyn (1965)

2.5 Lehman et al. (1975)

Green Algae 0.05 - 0.19 Jorgensen et al. (1978)

0.05 - 0.4 Bierman (1976), Bierman et al. (1980)

0.02 Canale et al. (1976)

0.8 Lehman et al. (1975)

0.1 - 0.25 Tetra Tech (1980), Porcella et al. (1983)

0.3 DePinto et al. (1976)

Blue-green Algae0.05 - 0.15 Bierman (1976), Bierman et al. (1980)

0. Canale et al. (1976)

0.2 Lehman et al. (1975)

0.1 DePinto et al. (1976)

0.08 - 0.2 Tetra Tech (1980), Porcella et al. (1983)

Flagellates 0.5 Lehman et al. (1975)

0.05 Bierman et al. (1980)

0.09 - 0.2 Tetra Tech (1980), Porcella et al. (1983)

Dinoflagellates 8.0 O’Connor et al. (1981)

Chrysophytes 0.5 Lehman et al. (1975)

Coccolithophores0.25 - 13.6 Collins & Wlosinski (1983)

Table 5-38. Settling Velocities for Phytoplankton

5-58
SUPPLEMENT IX: SELECTION OF CBOD COEFFICIENTS

Carbonaceous biochemical oxygen demand (CBOD) is

the utilization of oxygen by aquatic microorganisms to

metabolize organic matter and the oxidation of any

reduced minerals such as ferrous iron, methane, and

hydrogen sulfide that may leach out or be transported

from the anaerobic layers in bottom sediments. In

addition, there are usually significant amounts of unoxidized nitrogen in the form of ammonia and organic

nitrogen that must be taken into account. To improve

the chances for describing the oxygen balance, however, nitrogenous BOD (NBOD) is generally simulated

separately as will be discussed in Supplement VIII. The

total effect of CBOD and NBOD has been modeled on

occasion as total BOD (= CBOD + NBOD) but this is

not recommended for waste load allocations because

of the difficulty in forecasting total BOD. Occasionally,

total BOD is used in screening-level models where

adequate data are not available, but these types of

studies should not be confused with a more precise

waste load allocation model study. Figure 5.28 shows

the major sources and sinks of CBOD in surface waters

including estuaries. Point sources are usually the most

important source of CBOD and because these are the

most controllable sources, they are typically the focus

of the waste load allocation. However, nonpoint

sources, autochthonous sources due to the recycling

of organic carbon in dead organisms and excreted

materials, the benthic release of reduced minerals and

scour and leaching of organic carbon, can be quite

Figure 5-28. Sources and sinks of carbonaceous BOD in the aquatic environment [Bowie et al. (1985)].

5-59
important as well. In fact, many point sources already

have been controlled to the point that any further

improvements in water quality may require waste load

allocation of the diffuse and less readily controlled

nonpoint sources. For example, the continued anoxia

in Chesapeake Bay seems to indicate as much. In any

event, it is important that background sources of

CBOD be adequately quantified to determine the relative importance compared to point sources. If other

sources are relatively important, they too must be

included in the CBOD mass balance or the calibrated

model will be inadequate for aiding waste load allocation.

CBOD is removed from the water column by three

processes. First, carbonaceous material is oxidized

by microbes causing a reduction in CBOD. Typically,

this is the dominant process that must be taken into

account. Second, CBOD can settle out of the water

column. This occurs in two ways. Particulates immediately begin to settle unless sufficient turbulence is

present to maintain the suspension. This is aided by

the tendency of saline water to stabilize freshwater

particulates and assist in flocculation and increased

settling. In addition, dissolved CBOD can be adsorbed

and assimilated by bacteria cell synthesis without immediate oxidation. These bacteria also can settle,

especially as part of any floc generated as a result of

the stabilization of freshwater particles. Third, dissolved CBOD can be adsorbed by benthic biota, especially by filamentous growth on surfaces, and

benthic plants can filter particulate material. However,

there is usually limited contact between benthic bacteria and plants, and the water column with the result that

only oxidation and, occasionally, settling are the important processes to describe in calibrating a model.

Exceptions to the general expectations occur when

significant interactions occur with tidal flats and adjoining wetlands. Also in brackish and saline waters, metabolism is slower (Krenkel and Novotny 1980)

compared to freshwater so there is also less of a

tendency for organic carbon to be assimilated for cell

synthesis. As a result, the CBOD mass balance is

usually quite simple except near the outfall and at the

interface or mixing zone between saline and freshwater where settling is more likely. In general, the CBOD

mass balance is expressed as:

dL

dt = −Kr L + La (5.30)

where L is ultimate CBOD in mg L-1, t is time, Kr is the

first order rate constant describing the reduction in

CBOD, and La is the zero order CBOD resuspension

or reentrainment rate in mg L-1 d-1. Kd is actually a

combination of the coefficient for oxidation, settling and

adsorption:

Kr = Kd + Ks + Ku (5.31)

where Kd is the water column deoxygenation rate

coefficient (i.e., oxidation rate) in d-1, Ks is the settling

rate coefficient in d-1, and Ku is the sorption rate

coefficient in d-1. Unexplainable discrepancies occasionally are observed (see Krenkel and Novotny

1980), but in general, Kd can be estimated from the

bottle deoxygenation rate coefficient, K1, determined

from long term CBOD tests (see Whittemore et al.

1989, Stamer et al. 1979, or McCutcheon et al. 1985

for a description of the test and data analysis procedures). This seems to be especially true for samples

collected from larger bodies of water like large rivers

(Mackenzie et al. 1979), lakes, and estuaries where

suspended bacteria are more important than attached

bacteria in oxidizing organic matter and the samples

are not diluted. Ks can be estimated from settling

velocity tests like those involving the Imhoff cone

(Standard Methods 1985), where

Ks =

Vs

D

(5.32)

Vs is the settling velocity measured in m d-1 and D is

depth of flow in m. Unfortunately, Equation (5.32) is

only useful in describing the settling of discrete particles. When flocculation or disaggregation occurs, Vs

typically changes by orders of magnitude at times. At

present, the effect of flocculation and disaggregation

can not be described. As a result, Ks can not be readily

estimated. In addition, Ku can not be readily estimated

for typical field studies. Therefore, a calibration parameter, K3 = Ks + Ku, is defined and selected by trial

and error. Generally, it is possible to locate large areas

where K3 = 0 so that Kd can be selected. If Kd is not

approximately equal to the bottle coefficient, K1, additional investigation is required to re-evaluate Kd and

determine whether the initial calibration value may

actually be Kd + Ks + Ku. Once Kd is properly selected,

K3 can be determined in other parts of the estuary

where settling and sorption are occurring by selecting

Kd + K3 so that model predictions agree with measurements. Likewise, La can be determined in other areas

where re-entrainment of organic materials or leaching

of reduced materials occur. Typically, scour of organic

particles is expected when velocities near the bed

exceed 0.2 to 0.3 m s-1 (0.6 to 1 ft s-1). Any zones

with high near bed velocities approaching these velocities should be investigated. Because estuaries are

normally a net depositional regime, however, La can

probably be ignored as a first approximation unless

extensive organic deposits are evident (e.g., like the

tidally affected reaches of the Willamette River where

recent uncontrolled point source discharges of wood

fibers caused long-lasting organic deposits). Therefore, sludge and organic deposits should be mapped

if possible to show where La may exceed zero.

5-60
SUPPLEMENT X: SELECTION OF NBOD COEFFICIENTS

There are two usual approaches to describe the transformation of oxidizable nitrogen. One is to consider

the actual process of transformation: from organic

nitrogen, through nitrite to nitrate, where oxygen consumption is involved in the process. This will be discussed in Supplement XI. The other approach that will

be discussed here simply lumps the organic and ammonia nitrogen together (called total kjeldahl nitrogen,

TKN). This total kjeldahl nitrogen will be oxidized

through a first-order decay. The oxidation of TKN is

NBOD.

Decay of NBOD is written as

dt =

dN

−KN N

(5.33)

Where

N = NBOD concentrations, mg/L.

NBOD = 4.57(No+Ni)+1.14N2 can be used as the upper limit of NBOD (see Bowie et al. 1985)

No = organic nitrogen concentrations, mg/L

Ni = ammonia nitrogen concentration, mg/L

N2 = nitrite-nitrogen concentration, mg/L

KN = overall NBOD reaction rate, 1/day

According to Thomann and Mueller (1987), the range

of KN values is close to the deoxygenation rate of

CBOD, and for large water bodies, the typical range is

0.1-0.5/day at 20oc; but for small streams, it can often

be expected to be greater than 1/day. Table 5.39

compiles the available first-order NBOD decay rates in

estuaries that can be helpful in selecting initial NBOD

decay rates. The effects of temperature on KN can be

estimated by

(KN )T = (KN )20 ⋅1.08T−20 (5-34)

for 10<T<30oC

Where 1.08 = average temperature correction coefficient (see Bowie et al. 1985)

When temperature goes higher than 30oC, the nitrification rate is inhibited by the high temperature and the

relationship is no longer valid. When temperature is

below 10oC, the nitrifying bacteria do not multiply very

well and the above equation will give a KN that is too

high. So, when temperature is below 5-10oC, KN is

usually set to zero (Thomann and Mueller 1987).

pH is also an important factor to the nitrification rate

(Bowie et al. 1985). The optimal pH for nitrification is

about 8.5. When pH is outside the range of 7.0 to 9.8,

the nitrification rate can be reduced significantly. If pH

is lower than 6.0, no nitrification is expected.

Estuary Maximum Average Minimum Reference Comment

Potomac 0.14 — 0.10 Slayton and Trovato (1978, 1979) Measured by BOD bottle tests; data fit

with Thomas Graphical Method

Potomac — 0.09 to 0.13 — Thomann and Fitzpatrick (1982) Derived from model calibration

Delaware 0.54 0.3 0.09 Bansal (1976)

New York

Bight

— 0.09 — O’Connor et al. (1981)

Table 5-39. First-Order Nitrification Rate Constants Observed in Estuaries (constants are in d-1) [Bowie et al. (1985)]

5-61
PONa→DON DON→NH3 PON→NH3 NH3→NO2 NH3→NO3 NO2→NO3 SEDN→NH3 References

K θ K θ K q K θ K θ K θ K θ

Calibration values derived from field data

0.035 linear 0.04 linear Thomann et al. (1976)

0.03b1.08 Thomann et al. (1979)

0.03c1.08 0.12b1.08 0.0025 1.08 DiToro and Conolly (1980)

0.03c1.08 0.20 1.08 DiToro and Matystik (1980)

0.075 1.08 0.09-

0.13c

1.08 0.004 1.08 Thomann & Fitzpatrick (1982)

0.025c1.08 O’Connor et al. (1981)

0.14 linear Salas and Thomann (1973)

0.001 1.02 0.003-

0.03

1.02 0.09 1.02 0.001 1.02 Chen & Orlob (1972, 1975)

0.020 linear 0.020 linear 0.060 linear Scavia et al. (1976)

0.020 linear 0.020 linear 0.1 linear Scavia (1980)

0.02 1.020 0.02 1.020 0.1 1.020 Bowie et al. (1980)

0.02 linear 0.024 linear 0.16 linear Canale et al. (1976)

0.003 1.020 0.02 1.047 0.25 1.047 .0015 1.047 Tetra Tech (1980)

0.1 1.047 0.02 1.047 0.25 1.047 .0015 1.047 Porcella et al. (1983)

0.01b NI 0.95-

1.8c

1.14 Nyholm (1978)

.005b1.08 Bierman et al. (1980)

0.1b1.02 Jorgensen (1976)

0.2b1.072 Jorgensen et al. (1978)

Recommendations from Model Documentation

.1-.4 NI .1-.5 NI 5.-10. NI Baca et al. (1973)

0.02-

0.04

1.02-

1.09

.1-.5 1.02-

1.09

3.-10. 1.02-

1.09

.01-.1 1.02-

1.09

Baca and Arnett (1976)

.1-.5 1.047 0.5-

2.0

1.047 Duke and Marsh (1973)

.1-.5 1.047 0.5-

2.0

1.047 Roesner et al. (1978)

.005-

.05

1.02-

1.04

.05-.2 1.02-

1.03

0.2-

0.5

1.02-

1.03

.001-

.01

1.02-

1.04

Smith (1979)

.001-

.02

1.045 .05-.2 1.02 0.2-

0.5

1.02 .001-

.02

1.040 Brandes (1976)

0.04-

3.0

logistic Granney and Krassenski

(1981)

0.001-

1.3d

NI Collins and Wlosinski (1983)

a Abbreviations are defined as follows:

NI - no information

PON - Particulate Organic Nitrogen

DON - Dissolved Organic Nitrogen

SEDN - Sediment Organic Nitrogen

Linear refers to linear temperature correction.

Logistic refers to logistic theory of growth parameters.

b Unavailable nitrogen decaying to algal-available nitrogen.

c DiToro & Connolly (1980) & Di Toro & Matystik (1980) multiply the PON-NH3 rate by a chlorophyll limitation factor, Chl a/K1+Chl a,

where K1 is a half-saturation constant = 5.0 mg Chl a/L.

DiToro & Connoly (1980) and Thomann & Fitzpatrick (1982) multiply the NH3-NO3 rate by an oxygen limitation factor, O2/K2+O2, where

K2 is a half-saturation constant = 2.0 mg O2/L.

O’Connor et al. (1981) multiply the NH3-NO3 rate by an oxygen limitation factor, O2/K3+O2, where K3 is a half-saturation constant = 0.5

mg O2/L.

Nyholm (1978) used a sediment release constant which is multiplied by the total sedimentation rate of algae and detritus.

d

Literature value.

Table 5-40. Rate Coefficients for Nitrogen Transformations [Bowie et al. (1985)]

5-62
SUPPLEMENT XI: CALIBRATING NITROGEN CYCLE MODELS

The nitrogen cycle plays an important role in water

quality problems through its biochemical effects and

oxygen consumption. Table 5.40 compiles the available values of rate coefficients for some important

nitrogen transformations, including ammonification

and nitrification. The coefficients for ammonification,

which means the release of ammonia due to the decay

of organic nitrogen in the water column and sediments,

are very site dependent and not as well documented

as the coefficients of nitrification, which means the

oxidation of ammonia through nitrite to nitrate consuming dissolved oxygen at the same time.

Table 5.41 lists the coefficients for the denitrification

process which reduce the nitrate of N2 under anaerobic conditions.

Values in the above two tables can be used as a

guidance for selecting initial values of these coefficients. Models should be calibrated for the specific

problem later on.

Another important phenomenon that needs to be mentioned is the toxity of un-ionized ammonia to aquatic

life. The ionization equibrum is

NH3⋅nH2O <−above→ NH4

+

+OH −+(n−1)⋅H2O(5.35)

Equibrum is reached rapidly, and is largely controlled

by pH and temperature. Figure 5.29 gives the percentage of un-ionized ammonia under different pH and

temperature conditions. Usually, water quality models

predict ammonium concentration, which can be related to the total concentration in Fig. 5.29. Additional

guidance on processes affecting ammonia toxicity

may be found in U.S. EPA (1985b and 1989).

Nitrate → Nitrogen Gas

K θ References

0.1* 1.045 Di Toro and Connolly (1980)

0.1** 1.045 Di Toro and Connolly (1980)

0.09* 1.045 Thomann and Fitzpatrick (1982)

0.1* 1.045 O’Connor et al. (1981)

0.002 No information Jorgensen (1976)

0.02-0.03 No information Jorgensen et al. (1978)

0.0-1.0*** 1.02-1.09*** Baca and Arnett (1976)

*This rate is multiplied by an oxygen limitation factor, K1/[K1+O2],

where K1 is a half-saturation constant = 0.1 mg O2/L.

** The same rate applies to sediment NO3 denitirfication

*** Model documentation values

Table 5-41. Rate Coefficients for Denitrification

[Bowie et al. (1985)]

Figure 5-29. Effect of pH and temperature on un-ionized

ammonia [Willingham (1976)].

5-63
SUPPLEMENT XII: PHOSPHORUS CYCLE COEFFICIENTS

Guidance on the selection of phosphorus cycle model

coefficients is given in Table 5.42.

POP→DOP POP→PO4 DOP→PO4 SEDP→DOP SEDP→PO4

K θ K θ K q K θ K θ References

0.14 linear Thomann et al. (1975)

0.03 1.08 Thomann et al. (1975)

0.03b1.08 DiToro and Conolly (1980)

DiToro and Matysik (1980)

Salsbury et al. (1983)

0.22b1.08 0.22b1.08 0.0004 1.08 0.0004 1.08 Thomann & Fitzpatrick

(1982)

0.14 linear Salas and Thomann

(1978)

0.001 1.02 0.001 1.02 Chen & Orlob (1972,

1976)

0.02 linear Scavia et al. (1976)

Scavia (1980)

0.22blinear Connie et al. (1976)

0.003 1.020 0.0015 1.047 Tetra Tech (1980)

0.02 1.020 0.001 1.020 Bowie et al. (1980)

0.1 1.047 0.0015 1.047 Porcalia et al. (1983)

0.1 1.14 1.04147 1.14b Nyholm (1978)

0.005 1.08 Bierman et al. (1980)

0.1 1.02 0.0018 1.02 Jorgensen (1976)

0.5-0.6 1.072 Jorgensen et al. (1978)

0.1-0.7c 1.02-1.09c0.1-0.7c 1.02-1.09c Baca et al. (1973)

0.1-0.7c 1.02-1.09c Baca and Arnett (1976)

0.005-0.05c1.02-1.04c0.004-0.04c1.02-1.04c Smith (1976)

0.001-0.02c1.040c Brandes (1976)

Sediment

References DOP→PO4 SA→DOP SA→PO4

K θ K θ K θ

0.0004 1.08 0.02 1.08 0.02 1.08 Thomann & Fitzpatrick (1982)

Abbreviations are defined as follows:

POP - Particulate Organic Phosphorus

DOP - Dissolved Organic Phosphorus

SEDP - Sediment Organic Phosphorus

PO4 - Phosphate

SA - Settled Algae

Linear - linear temperature correction assumed.

b DiToro & Connolly (1980), DiToro & Matystik(1980) and Salsibury et al. (1980) multiply this rate by a chlorophyll limitation factor, Chl

a/K1+Chl a, where K1 is a half-saturation constant = 5.0 mg Chl a/L. Thomann & Fitzpatrick (1982) multiply this rate by an algal carbon

limitation factor, Algal-C/K2+Algal-C, where K2 is a half-saturation constant = 1.0 mg C/L. Nyholm (1978) uses a sediment release constant which is multiplied by the total sedimentation of algae and detrirus.

c Model documentation values.

Table 5-42. Rate Coefficients for Phosphorus Transformations [Bowie et al. (1985)]

(K = 1st order rate coefficient in d-1 and θ = temperature correction factor)

5-64
SUPPLEMENT XIII: SELECTION OF REAERATION COEFFICIENTS

Three methods are used to select reaeration coefficients:

1. Reaeration coefficients are computed by various

empirical and semi-empirical equations that relate

K2 to water velocity, depth, wind speed and other

characteristics of the estuary.

2. Reaeration occasionally is determined by calibration

of the model involved.

3. Reaeration is measured using tracer techniques on

rare occasions.

In most cases, K2 is computed by a formula that is

included in the model being applied. Only a very few

models (see Bowie et al. 1985 for example) force the

user to specify values of K2, the reaeration rate coefficient, or KL, the surface mass transfer coefficient. Also

infrequently applied, but expected to be of increasing

importance, is the measurement of gas transfer.

Whether a study should concentrate on estimation of

K2 or KL depends on the nature of the flow. When water

surface turbulence is caused by bottom shear and the

flow is vertically unstratified, formulations for K2, similar

to those used in streams are the most useful. When

the flow is vertically stratified and wind shear dominates

water turbulence at the surface, KL is typically specified.

The values of K2 and KL are related according to:

K2 =

KL

H

(5.36)

where H is the average depth with the units of meters

when KL is expressed in units of m d-1. In effect, K2 is

the depth-averaged value of KL when the depth is equal

to the volume of the water body or segment divided by

the area of the water surface.

When reaeration is dominated by the shear of flow on

the bottom boundary, the O’Connor-Dobbins equation

(see O’Connor and Dobbins 1958, Table 5.43) has

been used almost exclusively to estimate K2. The

reason for this is that the equation is derived from the

film penetration theory, which seems to be applicable

for most of the conditions found in estuaries except

those related to wind-generated turbulence (i.e. flows

are deep to moderately deep and rarely very shallow,

and velocities range from zero to moderately fast but

never extremely fast). Covar (1976) defines, in more

precise terms, what are thought to be the limitations of

the O’Connor-Dobbins equation. Generally, flows

should be deeper than approximately 0.6 m (2 ft) and

velocities should not exceed 0.5 m s-1 (1.5 ft s-1) at

depths of 0.6 m (2 ft) or exceed 1.5 m s-1 (5 ft s-1) at

depths of 15 m (50 ft) as illustrated in Figure 5.30.

Estimation errors are expected to be small, however, if

velocities only occasionally exceed 0.5 m s-1 to 1.5 m

s

-1 (1.5 ft s-1 to 5 ft s-1) as noted in Figure 5.30.

If alternative formulations seem necessary, it may be

useful to examine those in Table 5.43. Following the

O’Connor-Dobbins equation, the Hirsh equation

(McCutcheon and Jennings 1981), the Dobbins equation, and the Churchill et al. equations may be most

useful. The Hirsh equation is derived from the Velz

iterative method using the surface renewal theory that

has been used extensively in estuaries and deeper

streams. Experience indicates that this equation may

be most appropriate for deeper, stagnant bodies of

water that are more sheltered. This equation seems to

provide a minimum estimate of K2 not related to velocity. Alternatively, expert practitioners (personal communication, Thomas Barnwell, Jr., U.S. EPA Center for

Exposure Assessment Modeling) use a minimum estimate on the order of 0.6/D where depth is in meters. The equations by Churchill et al. (1962) are

included because of the applicability at higher velocities

in deeper flows. The complex equation by Dobbins is Figure 5-30. Reaeration Coefficient (day-1 versus depth and

velocity using the suggested method of Covar (1976) [Bowie

et al. (1985)].

5-65
Citation K2 (base e, 20oC, day-1) Units Applicability

 Derived from Conceptual Models

O’Connor and

Dobbins (1958)

12.8u

1 ⁄ 2

D

1.5

U: ft/s

D: ft

U:m/s

D:m

Conceptual model based on the film penetration

theory for moderately deep to deep rivers;1

ft≤D≤30 ft (0.3 m≤D≤9.1 m), 0.5 ft/s≤U≤1.6 ft/s

(0.15 m/s≤U≤0.49 m/s), 0.005/d≤K2≤ 12.2/d.

O’Connor and Dobbins developed a second

formula but O’Connor (1960) noted that the

difference between the two formulas was

insignificant and recommended the use of this

form.

Dobbins (1964) C1[1+F

2

(US )0.375]

(0.9+F )1.5D

 coth







4.10(US )0.125

(0.9+F )0.5







coth [ ] is the hyperbolic contangent

for C1=117

U:ft /s

D:ft

S:ft/ft

for C1=62.4

U:m/s

D:m

S:m/m

Based on film penetration model combined with

data from natural streams and the flume data of

Krenkel and Orlob (1963)

 Semi-Empirical Models

Krenkel and Orlob (1962, 1963)

C2 (US )0.408

D

0.660

or

8.4(Dx )1.321

D

2.32

or

0.0024(Dx )1.321

D

2.32

2.6(Dy )1.237

D

2.087

C2=234

U:ft/s

S:ft/ft

D:ft

C2=174

U:m/s

D:m

S:m/m

Dx:ft2/s

D:ft

Dx:m

2

/min

D:m

Dy:m

2

/s

D:m

Energy dissipation model calibrated by multiple

correlation analysis using 1-ft (0.3-m) wide flume

data; 0.08 ft≤D≤0.2 ft (0.02 m≤D≤0.06 m). Based

on correlation with longitudinal and vertical

disperson and calibration with data from 1-ft (0.3-

m) wide flume with deoxygenated water. Other

similar forms were also reported. The flume Dx

was less than that typically encountered in

streams.

Thackston and

Krenkel (1969)

C3(1+F

1 ⁄ 2

)u

∗

D

or

C3=24.9

u*:ft/s

D:ft

C3=24.9

u*:m/s

D:m

Calibrated with measurements of deoxygenated

water in a 2-ft (0.61-m) wide flume; 0.05 ft≤D≤

0.23 ft (0.015 m≤D≤0.091 m).

A4Q

B

, where A4 and B = constants Derived from the original equation given above.

Tivoglou and

Wallace (1972)

(4700 )US or 0.054(Δh ⁄ Δt ) at 25oC

(15,300 )US or 0.18(Δh ⁄ Δt ) at 25oC

U:ft/s

S:ft/ft

Δh:ft

Δt:d

U:m/s

S:m/m

Δh:m

Δt:d

Energy dissipation model calibrated from

radioactive tracer measurements in five rivers.

Table 5-43. Formulas to Estimate Reaeration Coefficients for Deeper, Bottom Boundary Generated Shear Flows

[Bowie et al. (1985), Rathbun (1977), Gromiec et al. (1983), and McCutcheon (1989)]

5-66
Notation:

U = averaged velocity or tidal velocity [Harleman (1977)]

D = average depth of flow.

F = U/(gD)1/2 = Froude number.

g = gravitational constant.

S = slope of water surface.

Dx = longitudinal dispersion coefficient.

Dy = averaged vertical eddy diffusivity.

u* = (gDS)1/2 = shear velocity.

Q = stream discharge.

h = change in water surface elevation in a reach (between two points).

t = time of travel in the reach over which change in elevation is measured.

Dm = molecular diffusion coefficient for oxygen in water.

T = water temperature

I = mix interval.

W = top width of estuary.

A = cross sectional area.

Citation K2 (base e, 20oC, day-1) Units Applicability

Semi-Empricial Models (continued)

McCutcheon

and Jennings

(1982)

−ln[1−2







Dm I 24

π(30.48D )2







1 ⁄ 2

 ]

I

Dm = 1.42(1.1)

T−20

[I = 0.0016+0.0005 D ] D ≤ 2.26 ft

[I = 0.0097 ln(D ) − 0.0052] D >2.26 ft

D:ft

T:oC

Originally derived by Hirsch (1972) to replace the

Velz (1984) interative method. Expressions for

the mix interval, I are derived from the extensive

experience in applying the interative method.

The underlying concept is similar to the surfacerenewal theory.

Churchill et al.

(1962)

0.035U

2.695

D

3.085S0.823

0.746U

2.695

D

3.085S0.823

U:ft/s

D:ft

U:m/s

D:m

Based on dimensional analysis. Derived from

data collected in rivers below Tennessee Valley

Authority (U.S.) dams.

Empirical Formulas

Churchill et al.

(1962)

11.6U

0.969

D

1.673

5.01U

0.969

D

1.673 or

6.91U

D

1.67

U:ft/s

D:ft

U:m/s

D:m

See Churchill et al. above. This form almost as

good and is recommended by Churchill et al. 2

ft(0.61 m)≤D≤11 ft (3.35 m) and 1.8 ft/s≤U≤5 ft/s

(0.55 m/s≤U≤1.5 m/s)

Owens et al.

(1964)

21.7U

0.67

D

1.85

5.32U

0.67

D

1.85

U:ft/s

D:ft

U:m/s

D:m

Developed from oxygen recovery data collected

on six English streams following deoxygenation

with sodium sulfide by Gameson et al. (1955)

and Owens et al. (1964) and collected below

TVA dams by Churchhill et al. (1962); 0.1 ft/s≤U

≤5 ft/s (0.03 m/s≤U≤1.5 m/s).

Owens et al.

(1964)

23.3U

0.73

D

1.75

6.92U

0.73

D

1.75

U:ft/s

D:ft

U:m/s

D:m

This second formula was developed for 0.1 ft/s

≤U≤1.8 ft/s (0.03 m/s≤U≤0.55 m/s); 0.4 ft≤ D≤1.5

ft (0.12 m≤D≤0.46 m) from a restricted data set

at the Water Pollution Research Laboratory.

Harleman et al.

(1977) 10.86 U

0.6DW

D

1.4A

U:ft/s

D:ft

W:ft

A:ft2

Equation of unknown original developed for the

MIT Transient Water Quality Model.

Ozturk

4.56U

4 ⁄ 3

D

U:m/s

D:m

Equation developed exclusively for estuaries.

See Bowie et al. (1985)

Table 5-43. Formulas to Estimate Reaeration Coefficients for Deeper, Bottom Boundary Generated Shear Flows

[Bowie et al. (1985), Rathbun (1977), Gromiec e1al. (1983), and McCutcheon (1989)] (concluded)

5-67
KL Location or type of

water body Reference Comment

(m d-1)

1 New York Bught O’Connor et al. (1981)

0.6 Estuaries O’Connor (personal communication)

2 Lake Erie Di Toro and Connolly (1980)

Table 5-44. Constant Values of Surface Mass Transfer Coefficients Applied in the Modeling of Estuaries, Coastal Waters, and

Lakes [Bowie et al. (1985)]

Reference Formulation Comment

 Estuaries

Thomann and Fitzpatrick (1982)K2 = 13 U0.5 + 3.281 (0.728U0.5 - 0.371u + 0.0372U2

 D1.5 D

K2 in d-1, D in ft, U ln t s-1, u ln m s-1

Applied in the Potomac Estuary. Combines

O’Connor-Dobbins and wind speed

formulations.

Lakes

Chen et al. (1975) KL = 86,400Dm Dm in m2s-1, u in m s-1

(200-60u

0.5) x 10-6

Banks (1975) KL = 0.362u

0.5 for 0 < u < 5.5 m s-1

KL = 0.0277u

2 for u > 5.5 m s-1

Table 5-45. Empirical Wind Speed Relationships for Mass Transfer and Reaeration Coefficients [Bowie et al. (1985)]

included because its rational derivation indicates that

it may be occasionally useful. The Krenkel and Orlob

(1962) and Thackston and Krenkel (1969) energy dissipation equations are included for similar reasons,

although these equations are more applicable to shallower depths than the Dobbins equation. The equation

by Ozturk (1979) is included for completeness but little

is known about the limitations of applicability and usefulness. Finally, the Tsivoglou and Wallace (1972)

energy dissipation equation is included because it is

now widely thought to be the best method for predicting

K2 in shallow turace of the Owens et al. (1964) equation given in Figure 5.30 from Covar (1976). When

estimated K2 values are too small, maximum velocities

observed during the tidal cycle or the average of the

absolute velocity are used in place of tidal or average

velocities in the O’Connor-Dobbins (1958) and other

velocity type equations [i.e. Harleman et al. (1977)].

If the estuary is dominated by bottom-shear-generated

turbulence, selection of K2 values seems to best be

guided as follows:

1) Compute K2 from the O’Connor-Dobbins equation

(see Table 5.43 for the equation).

2) Check to be sure that K2 exceeds or equals a

minimum value of approximately 0.6/depth.

3) If K2 seems to be over-predicted, investigate use

of the Hirsh equation (see Table 5.43 for the equation).

4) If K2 seems to be under-predicted, investigate the

use of the maximum tidal velocity or the tidally

averaged absolute velocity or determine if wind

shear may be important.

5) To investigate the importance of wind shear, compute KL from the screening level equations of Kim

and Holley (1988), divide by the depth and compare

with values computed by the O’Connor-Dobbins

equation. If wind shear does seem important, compute KL values from the O’Connor (1983) formulations.

When estuarine reaeration is dominated by wind-generated water turbulence, or the flow is deep and stratified, two approaches have been found to be useful.

First, many studies in open coastal waters and lakes

specify a constant value of KL. Table 5.44 lists some

of the known examples. Second, there are a number

of semi-empirical and empirical formula relatNotation:

K2 = reaeration coefficient (T-1),

KL = surface mass transfer coefficient (LT-1),

U = depth averaged velocity (LT1),

D = Depth (L),

u = wind speed (LT1),

Dm = molecular diffusion coefficient for oxygen in water (L2T1),

a = empirical coefficient, and

b = empirical coefficient.

5-68
SUPPLEMENT XIV: PROGRAM OF O’CONNOR’S METHOD TO COMPUTE K2 IN WIND

DOMINATED ESTUARIES

D.J. O’Connor, (1983) developed a relation between the

transfer coefficient of slightly soluble gases (i.e. reaeration coefficient, KL for oxygen) and wind velocity. This

method assumes that reaeration is a wind dominated

process. The functions relating the viscous sublayer

and roughness height with the wind shear provide the

basis for the development of equations which define the

transfer coefficient.

For hydrodynamically smooth flow, viscous conditions

prevail in the liquid sublayer which controls transfer and

the transfer is effected solely by molecular diffusion. In

fully established rough flow, turbulence extends to the

surface and turbulent transfer processes dominant. In

the transition region between smooth and rough flow

where both transfer mechanisms contribute, O’Connor

envisions the exchange as a transfer in series and the

overall coefficient (1/KL) described by

1

KL

=

1

Kz

+

1

Kτ

(5.37)

where Kτ is the transfer coefficient through the diffusional sublayer and Kz is the surface renewal transfer at

the boundary of the diffusional sublayer.

Based on the physical behavior in the smooth and rough

layers KL is then developed by O’Connor as

1

KL

=

1







D

νw







2

⁄3

κ

1

⁄3

Γ(u∗)

ρa u∗

ρw

+

1







Du∗

κ z0 u∗

Pa νa

ρw νw







1

⁄2

(5.38)

 where

D = molecular diffusivity

νa = kinematic viscosity of air

νw = kinematic viscosity of water

κ = the Von Karmen constant

ρa = density of air

ρw = density of water

u* = shear velocity

zou* = is given as

1

zo u∗

=

1

zc

λ1 u∗

ν

e

−

u∗⁄u∗t

 and

Γ (u∗) = Γo

u∗

u∗c

 exp [ −u∗

u∗c + 1

]

u*c = critical shear stress

u*t = transition shear stress

u∗ = (CD)

1

⁄2 Ua

 where

CD = drag coefficient

Ua = wind speed

The drag coefficient is a non-linear function of wind

speed derived from formulation described in O’Connor

(1983)

1

√CD

=

1

κ

[ln 1000⋅( 1

ze

+

λ1√ CoUA

ν

 exp(−√ CDUA⁄u∗t))]

The quantities λ1, u∗t, Γo, u∗c, and ze are dependent on

the size of the water body and values for these parameters are given in Table 5.46 from O’Connor, 1983);

λ1 u∗t Γo u∗c ze

Small scale 10 9 10 22 0.25

Intermediate 3 10 6.5 11 0.25

Table 5-46. Transfer-Wind Correlations [O’Connor (1983)]

ing K2 or KL to wind speed measurements. These are

listed in Table 5.45.

The selection of KL values seem to be best made

according to the following procedure:

1) Select a constant KL, especially if surface dissolved

oxygen is near saturation (Bowie et al. 1985, Di

Toro and Connolly 1980) and test to see if this

adequately closes the dissolved oxygen balance in

the model employed.

2) If the dissolved oxygen balance is not adequately

closed, compute KL according to the method of

O’Connor (1983).

3) If KL values still do not seem to be correct, determine whether any of the other wind speed relationships in Table 5.33 are useful. The crude

screening approach of Kim and Holley (1988) may

be the next most useful approach

5-69
small scale values are for laboratory studies, intermediate scale values are for small scale field sites and

large scales are for large lake or ocean scales.

A Fortran implementation which calculates drag coefficients and reaeration coefficients using O’Connor’s

method is available for the U.S. EPA Center for Exposure Assessment Modeling in Athens. This program

requires as input; the size scale of the water body, wind

speed at 10 m, (m/sec), air temperature (oC), and

water temperature (oC). Values for the drag coefficient

and reaeration coefficient are calculated by the program. The program is available through the CEAM

bulletin board. A more detailed description of the

equation development may be found in O’Connor

(1983).

SOD

 (g O2/m2 day) Environment Experimental Conditions References

0.10±0.03 (12oC)

0.20±0.05 (20oC)

0.22±0.09 (28oC)

 0.37±0.15 (36oC)

A North Carolina estuary 45 day incubation of 0.6 liters

sediment in 3.85 liters BOD dilution

water, light

NCASI (1981)

2.32±0.16 Buzzards Bay near raw sewage outfall In situ dark respirometers stirred, 1-3

days; temperature unknown

Smith et al. (1973)

1.88±0.018 Buzzards Bay control

0.14-0.68 (5oC)

0.20-0.76 (10oC)

0.30-1.52 (15oC)

Puget Sound sediment cores Laboratory incubations Pamatmat et al. (1973)

0.05-0.10 San Diego Trough

(deep marine sediments)

In situ respirometry for 5-13 hours,

4

oC, light

Smith (1974)

1.25-3.9 Yaquina River Estuary, Oregon Dark laboratory incubators, stirred,

20oC

Martin & Bella (1971)

0.02-0.49 Eastern tropical Pacific Shipboard incubations, 15oC, stirred,

dark

Pamatmat (1971)

0.9-3.0 Baltic Sea In situ light respirometer stirred, 10oC Edberg & Hofsten (1973)

0.4-0.71 Baltic Sea Laboratory incubations, stirred, dark,

10oC

Edberg & Hofsten (1973)

0-10.7 Delaware Estuary (22 stations) In situ dark respirometry, 13-14oC Albert (1983)

0.3-3.0 Fresh and brackish waters, Sweden In situ respirometry, 0-18oC

Laboratory cores, 5-13oC

Edberg & Hofsten (1973)

Table 5-47. Measured Values of Sediment Oxygen Demand in Estuaries and Marine Systems [Bowie et al. (1985)]

SUPPLEMENT XV: SELECTION OF SOD RATES

Guidance on the Selection of Sediment Oxygen Demand Rates is given in Table 5.47.

5-70
5.5. References

Ambrose, R.B., Jr. 1987. Modeling volatile organics

in the Delaware Estuary, Journal of Environmental

Engineering, American Society of Civil Engineers,

113(4), 703-721.

Ambrose, R.B., Jr., and Roesch, S.R. 1982. Dynamic

estuary model performance, Journal of Environmental

Engineering Division, American Society of Civil Engineers, 108, 51-71.

Ambrose, R.B., Jr., Wool, T.A., Connolly, J.P., and

Schanz, R.W. 1988. WASP4, A Hydrodynamic and

Water Quality Model—Model Theory, User’s Manual,

and Programmer’s Guide, U.S. Environmental Protection Agency Report EPA/600/3-87/039, Athens, Ga.

American Public Health Association, Water Pollution

Control Federation, and American Water Works Association.. 1985. Standard Methods for the Examination

of Water and Wastewaters, 16th ed., Washington,

D.C.

Amorochio, J., and DeVries, J.J. 1980. A new Evaluation of wind stress coefficient over water surfaces,

Journal of Geophysical Research, 85(C1).

ASCE Task Committee on Turbulence Models in Hydraulics Computations. 1988. Turbulence modeling

of surface water flow and transport: Parts I to V,

Journal of Hydraulics Engineering, American Society

of Civil Engineering, 114(9), 970-1073.

Arcement, G.J., Jr. and Schneider, V.R. 1984. Guide

for Selecting Manning’s Roughness Coefficients for

Natural Channels and Flood Plains, Report FHSA-TS84-204, U.S. Department of Transportation, Federal

Highway Administration.

Baca, R.G., Waddel, W.W., Cole, C.R., Bradstetter, A.,

and Cearlock, D.B. 1973. EXPLORE-I: A River Basin

Water Quality Model, Pacific Northwest Laboratories

of Battelle Memorial Institute, Richland, Washington,

for the U.S. Environmental Protection Agency, Washington, D.C., Contract 68-01-0056.

Bailey, T.E. 1966. Fluorescent tracer studies of an

estuary, Journal of the Water Pollution Control Federation, 38, 1986-2001.

Barnes, H.H., Jr. 1967. Roughness Characteristics of

Natural Channels, U.S. Geological Survey, Water

Supply Paper 1849, U.S. Government. Printing Office,

Washington, D.C.

Beck, M.B. 1985. Water Quality Management: A Review of the Development and application of Mathematical Models, Lecture Notes in Engineering,

International Institute for Applied Statistical Analysis,

no. 11, Springer-Verlag, New York.

Beck, M.B. 1987. Water Quality Modeling: A review

of the analysis of uncertainty, Water Resources Research, 23(8), 1393-1442.

Bedford, K.W. 1985. Selection of Turbulence and Mixing Parameterizations for Estuary Water Quality Models, U.S. Army Engineer Waterways Experiment

Station, Miscellaneous Paper EL-85-2, Vicksburg,

Miss..

Benson, B.B., and Krause, D. 1984. The concentration

and isotopic fractionation of gases dissolved in fresh

water in equilibrium with the atmosphere: I. oxygen,

Limnol. Oceanogr., 29(3), 620-632.

Blumberg, A.F. 1977. Numerical model of estuarine

circulation, Journal of the Hydraulics Division, American Society of Civil Engineers, 103(HY3), 295-310.

Boublik, T., Fried, V., and Hala, E. 1984. The vapor

pressures of pure substances. Vol. 17, Elsevere Scientific Publications, Amsterdam.

Bowden, K.F. 1963. The mixing processes in a tidal

estuary, International Journal of Air and Water Pollution, 7, 343-356.

Bowie, G.L., Mills, W.B., Porcella, D.B., Campbell,

C.L., Pagenkopf, J.R., Rupp, G.L., Johnson, K.M.,

Chan, P.W.H., and Gherini, S.A. 1985. Rates, Constants, and Kinetics Formulations in Surface Water

Quality Modeling, 2nd Edition, EPA/600/3-85/040,

U.S. Environmental Protection Agency, Athens, Georgia.

Brown, D.S. and Allison, J.D. 1987. MINTEQA1, An

Equilibrium Metal Speciation Model: User’s Manual,

EPA/600/3-87/012, U.S. Environmental Protection

Agency, Athens, Georgia.

Brown, L. and Barnwell, T.O., Jr. 1987. The Enhanced

Stream Water Quality Models QUAL2E and QUAL2EUNCAS: Documentation and User Manual, Report

EPA/600/3-87/007, U.S. Environmental Protection

Agency, Athens, Ga.

Brutsaert, W. 1982. Evaporation into the Atmosphere,

D. Reidel Publishing, Dordrecht, Holland.

Brutsaert, W. and Jirka, G.H., eds. 1984. Gas Transfer

at Water Surfaces, Reidel, Boston.

Brutsaert, W. and Jirka, G.H. 1984. Measurement of

wind effects on water-side controlled gas exchange in

riverine systems, in Gas Transfer at Water Surfaces,

Brutsaert, W. and Jirka, G.H., ed.s, Reidel, Boston.

5-71
Burt, W.V. and Marriage, L.D. 1957. Computation of

pollution in the Yaquina river estuary, Sewage and

Industrial Wastes, 29, 1385-1389.

Chen, C.W. 1970. Concepts and utilities of ecological

model, Journal of the Sanitary Engineering Division,

American Society of Civil Engineers, 96(SA5), 1085-

1097.

Chen, C.W. and Orlob, G.T. 1975. Ecological Simulation of Aquatic Environments, in Systems Analysis and

Simulation in Ecology, Vol. 3B, Pattern, C., ed., Academic Press, New York, N.Y., pp 476-588.

Chen, C.W. and Wells, J. 1975. Boise River Water

Quality-Ecological Model for Urban Planning Study,

Tetra Tech technical report prepared for U.S. Army

Engineering District, Walla Walla, Washington, Idaho

Water Resources Board, and Idaho Dept. of Environmental and Community Services.

Chen C.W., Smith, D.J., and Lee, S.S. 1976. Documentation of Water Quality Models for the Helms

Pumped Storage Project, Prepared for Pacific Gas and

Electric Company, Tetra Tech, Inc. Lafayette, CA.

Chow, V.T. 1959. Open-Channel Hydraulics, McGrawHill, New York, chap. 5.

Covar, A.P. 1976. Selecting the Proper Reaeration

Coefficient for use in Water Quality Models, Proceeding of the U.S. EPA Conference on Environmental

Simulation and Modeling, Cincinnati, Ohio.

Deacon, E.L. 1955. The Turbulent Transfer of Momentum in The Lowest Layers of the Atmosphere, Division

of Meterological Physics, Technical Paper No. 4.,

Commonwealth Scientific and Industrial Research Organization, Australia, Melbourne.

Delft Hydraulics Laboratory. 1974. Momentum and

Mass Transfer in Stratified Flows: Report on Literature

Study, Report R880, Delft, The Netherlands.

Doneker, R.L., and Jirka, G.H. 1988. CORMIX1: An

Expert System for Mixing Zone Analysis of Conventional and Toxic Single Port Aquatic Discharges, U.S.

EPA Report EPA/600/3-88/013, Athens, Georgia.

Driscoll, E.D., Mancini, J.L., and Mangarella, P.A.

1983. Technical Guidance Manual for Performing

Waste Load Allocation, Book II: Biochemical Oxygen

Demand/Dissolved Oxygen, U.S. Environmental Protection Agency, Report 440/4-84/020, Washington,

D.C.

Dyer, K.R. 1973. Estuaries: A Physical Introduction,

John Wiley and Sons, London, Great Britain.

Easterbrook, C.C. 1969. A Study of the Effects of

Waves on Evaporation from Free Water Surfaces,

U.S. Department of Interior, Bureau of Reclamation,

Research Report No. 18, U.S. Government Printing

Office, Washington, D.C.

Edinger, E. and Geyer, J.C. 1965. Heat Exchange in

the Environment, Edison Electric Institute Publication

No. 65-902, The John Hopkins University, Baltimore,

Maryland.

Ellison, T.H. and Turner, J.S. 1960. Mixing of dense

fluid in a turbulent pipe flow, part 2: dependence of

transfer coefficients on local stability, Journal of Fluid

Mechanics, 8, 529-542.

Elmore, H.L., and Hayes, T.W. 1960. Solubility of

atmospheric oxygen in water, Twenty-Ninth Report of

the Committee on Sanitary Engineering Research,

Journal Sanitary Engineering Division, American Society of Civil Engineers, 86(SA4), 41-53.

Faye, R.E., Jr., Jobson, H.E., and Land L.F. 1979.

Impact of Flow Regulations and Power Plant Effluents

on the Flow and Temperature Regimes of the Chattahoochee River-Atlanta to Whitesburg, Georgia, U.S.

Geological Survey, Professional Paper 1108, U.S.

Government Printing Office, Washington, D.C.

Feigner, K. and Harris, H.S. 1970. Documentation

report-FWOA dynamic estuary model. United States

Department of Interior, Federal Water Quality Administration.

Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J.,

and Brooks, N.H. 1979. Mixing In Inland and Coastal

Waters, Academic Press, New York.

French, R.H. 1979. Vertical mixing in stratified flows,

Journal of the Hydraulics Division, American Society

of Civil Engineering, 105(HY9), 1087-110.

French, R.H. 1985. Open-Channel Hydraulics,

McGraw-Hill, New York, 34-37, 328, 330.

French, R. H. and McCutcheon, S.C. 1983. Turbulent

Vertical Momentum Transfer in Stratified Environments, Desert Research Institute Publication No.

41079, Las Vegas, Nevada, March.

Fulford, J.M., and Sturm, T.W. 1984. Evaporation from

flowing channels, Journal of Environmental Engineering, 110(1), 1-9.

Garde, R.J. and Ranga Raju, K.G. 1977. Mechanics

of Sediment Transportation and Alluvial Stream Problems, Wiley, New Delhi, 122.

5-72
Gibson, M., and Launder. B. 1978. Ground effects on

pressure fluctuations in the atmospheric boundary

layer, J. Fluid Mechanics, 86, 491.

Glenne, B. and Selleck, R.E. 1969. Longitudinal estuarine diffusion in San Francisco Bay, California, Water

Research, 3, 1-20.

Harbeck, G.E., Kohler, M.A., Koberg, G.E., and others.

1958. Water-Loss Investigations: Lake Mead Studies, U.S. Geological Survey Professional Paper 298,

U.S. Government Printing Office, Washington, D.C.

Henderson, F.M. 1966. Open Channel Flow, Macmillan, New York, 98.

Henderson-Sellers, B. 1982. A simple formula for vertical eddy diffusion coefficients under conditions of

nonneutral stability, Journal of Geophysical Research,

American Geophysical Union, 87(C8), 5860-5864.

Hetling, L.J., and O’Connell, R.L. 1965. Estimating

diffusion characteristics of tidal waters, Water and

Sewage Works, 110, 378-380.

Hetling, L.J., and O’Connell, R.L. 1966. A study of tidal

dispersion in the Potomac River, Water Resources

Research, 2, 825-841.

Higuchi, H. 1967. Hydraulic model experiment on the

diffusion due to the tidal current, International Association for Hydraulic Research, Proceedings of the

Twelfth Congress, 4, 79-88.

Hine, J., and Mookerjee, P.K. 1975. The intrinsic hydrophilic character or organic compounds; correlations

in terms of structural contributions, J. Organic Chem.,

40, 292-298.

Hinze, J.O. 1959. Turbulence, McGraw-Hill, New York.

Holzman, B. 1943. The influence of stability on evaporation, in Boundary Layer Problems in the Atmosphere

and Ocean, W.G. Valentine, ed., Vol. XLIV, Article 1,

13-18.

HYDROQUAL Inc. 1987. A Steady-State Coupled Hydrodynamic/Water Quality Model of the Eutrophication

and Anoxia Process in Chesapeake Bay, EPA contract

no. 68-03-3319, U.S. EPA, Chesapeake Bay Program,

Annapolis, Maryland.

Hydoscience Inc. 1971. Simplified Mathematical Modeling of Water Quality, U.S. EPA-Water Programs.

Jacobsen, J.P. 1913. Beitrag zur hydrographie der

danischen Gewasser. Medd. Komm. Havundersog.

Kbh., (Hydr.), 2,94 pages.

Jarrett, R.D. 1985. Determination of Roughness Coefficients for Streams in Colorado, Water-Resources

Investigations Report 85-4004, U.S. Geological Survey, Lakewood, Colorado.

Jobson, H.E. 1980. Thermal Modeling of Flow in the

San Diego Aqueduct, California, and Its Relation to

Evaporation, U.S. Geological Survey Professional Paper 1122, U.S. Governement Printing Office, Washington, D.C.

Kennedy, J.B. and Neville, A.M. 1976. Basic Statistical

Methods for Engineers and Scientists, Don Donnelley,

New York.

Kent, R.E. and Pritchard, D.W. 1959. A test of mixing

length theories in a coastal plain estuary. Journal of

Marine Research, 18(1), 62-72.

Kim, J.H., and Holley, E.R. 1988. Literature Survey on

Reaeration in Estuaries, Technical Memorandum 88-

1, Center for Research in Water Resources, Bureau

of Engineering Research, Department of Civil Engineering, University of Texas at Austin, Texas.

Knight, D.W., Roger, J.G., Shiono, K., Waters, C.B.,

and West, J.R. 1980. The measurement of vertical

turbulent exchange in tidal flows, Proc. 2nd Inter.

Sym. on Stratified Flow, Trondheim, Norway, Vol. 2,

722-730.

Kolher, M.A. 1954. Lake and Pan Evaporation, in

Water Loss Investigations, Lake Hefner Studies, U.S.

Geological Survey Professional Paper 269, U.S. Government Printing Office, Washington, DC.

Kolmogorov, A. 1942. Equations of turbulent motion of

an incompressible fluid, Izvestiya AN SSSR, Ser. fiz.,

6, No.s 1-2, 56-58.

Krenkel, P.A. and Novotny, V. 1980. Water Quality

Management, Academic Press, New York.

Launder, B.E. 1984. Second-moment closure: Methodology and practice, in Simulation of Turbulence

Models and their Applications, Vol. 2, Collecting de la

direction des Estudes et Recherches, Electricite de

France, editions Eyrolles, Paris, 1984.

Launder, B.E., and Spalding, D. 1972. Lectures in

Mathmetical Models of Turbulence, Academic Press,

New York.

Leo, A., Hansch, C., and Elkins, D. 1971. Partition

coefficients and their uses, Chem. Reviews, 71(6),

525-616.

Liss, P.S. 1973. Process of gas exchange across an

air-water interface, Deep-Sea Research, 20, 221-238.

5-73
Mabey, W.R., Smith, J.H., Podell, R.T., Johnson, H.L.,

Mill, T., Chou, T.W., Gates, J., Partridge, I.W., Jaber,

J., Vandenberg, D. 1982. Aquatic Fate Process Data

for Organic Priority Pollutants. U.S. Environmental

Protection Agency, EPA 404/4-81-014, Washington,

DC.

Mackenzie, S.W., Hines, W.G., Rickert, D.A., and

Rinella, F.A. 1971. Steady-State Dissolved Oxygen

Model of the Willamette River, Oregon, U.S. Geological Survey, Circular 715-J, Arlington, VA.

Mamajev, O.I. 1958. The influence of stratification on

vertical turbulent mixing in the sea, Izv. Acad. Sci.

USSR, Geoph. Ser., 870-875, (English, version, p.

494-497).

McCutcheon, S.C., Modification of vertical velocity

profiles by density stratification in an open channel

flow, Ph.D. dissertation, Vanderbilt University, Nashville, Tennessee.

McCutcheon, S.C. 1981. Vertical velocity profiles in

stratified flows, Journal of the Hydraulics Division,

American Society of Civil Engineers, 107(HY8), 973.

McCutcheon, S.C. 1983 Vertical mixing in models of

stratified flow, Frontiers in Hydraulic Engineering,

American Society of Civil Engineers, 15-20.

McCutcheon, S.C. and others. 1985. Water Quality

Data for the West Fork Trinity River in Fort Worth,

Texas, U.S. Geological Survey Water Resources Investigations Report 84-4330, NSTL, Mississippi.

McCutcheon, S.C. 1989. Water Quality Modeling: Vol.

I: Transport and Surface Exchange in Rivers, CRC

Press, Boca Raton, Florida.

McCutcheon, S.C. (in press) Water Quality Modeling,

Vol. II: Biogeochemical Cycles in Rivers, CRC Press,

Boca Raton, Florida.

McDowell, D.M. and O’Connor, B.A. 1977. Hydraulic

Behavior of Estuaries, John Wiley and Sons, New

York.

McKee, J.E., and Wolf, H.W. 1963. Water Quality

Criteria, 2nd edition, California State Water Quality

Control Board, Sacramento.

Mellor, G., and Yamada, P. 1982. Development of a

turbulence-closure model for geophysical fluid problems, Reviews of Geophysics and Space Physics,

20(4), 851-875.

Meyer, A.F. 1942. Evaporation from Lakes and Reservoirs, Minnesota Resources Commission, St. Paul,

Minnesota.

Mills, W.B., Porcella, D.B., Ungs, M.J., Gherini, S.A.,

Summers, K.V., Mok, L., Rupp, G.L., and Bowie, G.L.

1985. Water Quality Assessment: A Screening Procedure for Toxic and Conventional Pollutants in Surface

and Ground Water Part 1, (Revised 1985), EPA/600/6-

85/002a, U.S. Environmental Protection Agency, Athens, Georgia.

Monin, A., and Yaglom, A. 1971. Statistical Fluid Mechanics, MIT Press, Cambridge, Mass.

Morgan, D.L., Pruitt, W.O., and Lourence, F.L. 1970.

Radiation Data and Analyses for the 1966 and 1967

Micrometeorological Field Runs at Davis, California,

Department of Water Science and Engineering, University of California, Davis, California, Research and

Development Technical Report ECOM 68-G10-2.

Mortimer, C.H. 1981. The Oxygen Content of Air-Saturated Fresh Waters Over Ranges of Temperature and

Atmospheric Pressure of Limnological Interest, International Association of Theor. and Appl. Limnolo,

Communication Number 22, Stuttgart, Germany.

Morton, F.I. 1976. Climatological estimates of evapotranspiration, Journal of the Hydraulics Division,

American Society of Civil Engineers, 102(HY3), 275-

291.

Munk, W.H. and Anderson, E.R. 1948. J. Marine Research, 7(3), 276-295.

National Academy of Sciences. 1977. Studies in Estuaries, Geophysics, and the Environment, Washington,

D.C.

National Council for Air and Stream Improvement.

1982. A Study of the Selection, Calibration and Verification of Water Quality Models, Tech. Bull. No 367,

New York, New York.

Nelson, E. 1972. Vertical Turbulent Mixing in Stratified

Flow-A Comparison of Previous Experiments, University of California, Berkley, Rept WHM3.

O’Connor, D.J. 1979. Verification Analysis of Lake

Ontario and Rochester Embayment 3D Eutrophication

Model, U.S. Environmental Protection Agency, EPA600/3-79-094.

O’Connor, D.J. 1983. Wind effects on gas-liquid transfer coefficients, Journal of Environmental Engineering,

American Society of Civil Engineers, 9(3), 731-752.

O’Connor, D.J. and Dobbins, W.E. 1958. Mechanism

of reaeration in natural streams, Transactions, American Society of Civil Engineers, paper no. 2934, 641-

684.

5-74
Odd, N.V.M. and Rodger, J.G. 1978. Vertical mixing in

stratified tidal flows, Journal of the Hydraulics Division,

American Society of Civil Engineers, 104 (HY3), 337-

351.

Officer, C.B. 1976. Physical Oceanography of Estuaries (And Associated Coastal Waters), John Wiley and

Sons, New York, New York.

Okubo, A, and R.V. Osmidov. 1970. Empirical dependence of coefficient of horizontal turbulent diffusion in

the ocean on the scale of the phenomenom in question, Izv. Atmospheric and Oceanic Physics, 6(5), 534-

536, (Translated by Allen B. Kaufman).

Okubo, A. 1971. Ocean diffusion diagrams, Deep Sea

Research, 18.

Orlob, G.T. 1959. Eddy diffusion in homogeneous

turbulence, Journal of Hydraulics Division, American

Society of Civil Engineers, 85(HY9).

Pasquill, F. 1949. Eddy diffusion of water vapor and

heat near the ground, Proceedings A Royal Society of

London, 198(1052).

Pasquill, F. 1962. Atmosperhic Diffusion, Van Nostrand, London.

Patankar, S. and Spalding, D. 1970. Heat and Mass

Transfer in Boundary Layers, 2nd ed., Intertext Books

Pub., London.

Prandtl, L. 1925. Bericht uber untersuchungen zur

ausgebildete turbulenz, Zs. Angew. Math. Mech., 5(2),

136-139.

Prandtl, L. 1945. Uber ein neues formelsystem fur die

ausgebildete turbulenz, Nachr. Akad. Wiss., Gottingen, Math. Phys. Klasse, 6, G-19.

Priestly, C.H.B. 1959. Turbulent Transfer in the Lower

Atmosphere, University of Chicago Press.

Pritchard, D.W. 1960. The movement and mixing of

contaminants in tidal estuaries, Proceedings of the

First International Conference on Waste Disposal in

the Marine Environment, University of California at

Berkeley, Pearson, E.A., ed., Pergamon Press, New

York.

Reckhow, K.H. and Chapra, S.C. 1983. Engineering

Approaches for Lake Management, Vol.l: Data Analysis and Empirical Modeling, Butterworth, Boston,

Mass.

Rich, L. 1973. Environmental Systems Engineering,

McGraw-Hill.

Rider, N.E. 1954. Eddy diffusion of momentum, water

vapor, and heat near the ground, Philosophical Transactions, Royal Society of London, 246(918).

Rodi, W. 1980. Turbulence Models and Their Application in Hydraulics, International Assoc. for Hydraulic

Research, Delft, The Netherlands.

Rodi, W. 1984. Examples of turbulence-model applications, in Simulation of Turbulence Models and Their

Applications, Vol. 2, Collection de la Direction des

Estudes et Recherches, Electricite de France, editions

Eyrolles, Paris, France.

Rohwer, C. 1931. Evaporation from Free Water Surfaces, U.S. Department of Agriculture, Washington,

Technical Bulletin Number 271.

Rossby, C.G. and Montgomery, R.B. 1935. The Layer

of Fictional Influence in Wind and Ocean Currents,

Papers in Physical Oceanography and Meterology,

III(3), Massachusetts Institute of Technology.

Rouse, H. 1976. Advanced Mechanics of Fluids,

Robert E. Krieger Publishers, Huntington, New York.

Ryan, P.J., and Harleman, D.R.F. 1973. An Analytical

and Experimental Study of Transient Cooling Pond

Behavior, R.M. Parsons Laboratory, Massachusetts

Institute of Technology, Technical Report No. 161.

Schnelle, K., Parker, F., Thackston, E.L., and Krenkel,

P.A. 1975. personal communication, Vanderbilt University, Nashville, TN. (The Caveat that the simplest

possible model should be used for the problem at

hand, has been learned and re-learned by every experienced modeler, especially in their initial project, until

it is no longer clear who first proposed this idea. It is

now a matter of common sense but it is not clear that

this was so originally).

Schnoor, J.L., Sato, C., McKechnie, D., and Sahoo,

D. 1987. Processes, Coefficients, and Models for

Simulating Toxic Organics and Heavy Metals in Surface Waters, Report EPA/600/3-87/015, U.S. Environmental Protection Agency, Athens, Ga.

Schubert, W.M. and Brownawell, D.W. 1982. Methylal

hydrolsis: reversal reactions under dilatometric conditions and invalidity of the dilatometric method, Journal

of American Chemical Society, 104(12), 3487-3490.

Sheng, Y.P. 1983. Mathematical Modeling of ThreeDimensional Coastal Currents and Sediment Dispersion: Model Development and Application, U.S. Army

Corps of Engineers Waterways Experiment Station

Tech. Rept. CERC-83-2, Vicksburg, Mississippi.

5-75
Southerland, E., Wagner, R., and Metcalfe, J. 1984.

Technical Guidance for Performing Waste Load Allocations, Book III: Estuaries, Draft Rept., U.S. Environmental Protection Agency, Office of Water.

Stamer, J.K., Cherry, R.N., Faye, R.E., and Klechner,

R.L. 1979. Magnitudes, Nature, and Effects of Point

and Nonpoint Discharges in the Chattahoochee River

Basin, Atlanta to West Point Dam, Georgia, U.S. Geological Survey, Water Supply Paper 2059, U.S. Government Printing Office, Washington, DC.

Stommel, H. 1953. Computation of pollution in a vertically mixed estuary, Sewage and Industrial Wastes,

25, 1065-1071.

Streeter V.L., and Wylie, E.B. 1975. Fluid Mechanics,

6th ed., McGraw-Hill, New York.

Stumm, W. and Morgan, J.J. 1981. Aquatic Chemistry:

An Introduction Emphasizing Chemical Equilibria in

Natural Waters, 2nd ed., Wiley-Interscience, New

York.

Sverdrup, H.U. 1936. The eddy conductivity of the air

over a smooth snow field, Geofysiske Publ., 11(7),

1-69.

Tetra Tech Inc. 1976. Estuary Water Quality Models,

Long Island , New York-Users Guide, technical report

prepared for Nassau Suffolk Regional Planning Board,

Hauppauge, New York.

Thackston, E.L. 1974. Effect of Geographical Variation on Performance of Recirculating Cooling Ponds,

U.S. Environmental Protection Agency, Report EPA660/2-74-085, Corvallis, Oregon.

Thatcher, M.L., and Harleman, D.R.F. 1981. Longterm salinity calculation in Delaware Estuary, Journal

of the Hydraulics Division, American Society of Civil

Engineers, 107(EE1), 11-27.

Thibodeaux, L.J. 1979. Chemodynamics: Environmental Movement of Chemicals in Air, Water, and Soil,

Wiley and Sons, New York.

Thomann, R.V. 1972. Systems Analysis and Water

Quality Management, McGraw-Hill, New York.

Thomann, R.V. 1982. Verification of water quality models, Journal of the Environmental Engineering Division,

American Society of Civil Engineers, 108(EE5), 923.

Thomann, R.V., and Mueller, J.A. 1987. Principles of

Surface Water Quality Modelling and Control, Harper

and Row, New York.

Turner, J.F., Jr. 1966. Evaporation Study in a Humid

Region, Lake Michie North Carolina, U.S. Geological

Survey, Professional Paper 272-G, U.S. Government

Printing Office, Washington, DC.

de Turville, C.M. and Jarman, R.T. 1965. The mixing

of warm water from the Uskmonth power station in the

estuary of the River Usk, International Journal of Air

and Water Pollution, 9, 239-251.

Ueda, H., Mitsumoto, S. and Komori, S. 1981. Buoyancy effects on the turbulent transport processes in the

lower atmosphere, Quart. J. Roy. Meteor. Soc., 107,

561-578.

U.S. Environmental Protection Agency. 1985. Technical Support Document for Water Quality-based Toxics

Control, Office of Water, Washington, DC.

U.S. Environmental Protection Agency. 1985b. Ambient Aquatic Life Water Quality Criteria for Ammonia.

EPA 440/5-85-001, NTIS PB85-227114, Office of

Water Regulations and Standards, Washington, D.C.

U.S. Environmental Protection Agency. 1989. Ambient Aquatic Life Water Quality Criteria for Ammonia

(Saltwater)-89. EPA 440/5-88-004, Office of Water

Regulations and Standards, Washington, D.C.

U.S. Geological Survey. 1954. Water Loss Investigations: Lake Hefner Studies, Professional Paper 269,

U.S. Government Printing Office, Washington, D.C.

U.S. Geological Survey. 1981. Quality of Water Branch

Technical Memorandum Number 81.11.

Valvani, S.C., Yalkowsky, S.H., and Rossman, T.J.

1981. Solutility and partitioning, number 4, aqueous

solubility and octanol water partition coefficients of

liquid nonelectrolytes, Pharmacology Sci., 70, 502-

507.

Velz, C.J. 1984. Applied Stream Sanitation, 2nd ed.,

Wiley, New York.

Vreugdenhil, C.B. 1966. Delft Hyd. Lab. Rept.

Weiss, R.F. 1970. The solubility of nitrogen, oxygen

and argon in water and sea water, Deep-Sea Research, 17, 721-735.

West, J.R. and Williams, D.J.A. 1972. An evaluation of

mixing in the Tay Estuary, American Society of Civil

Engineers, Proceedings of the Thirteenth Conference

on Coastal Engineering, pp. 2153-2169.

Wlosinski, J.H. 1985. Flux use for calibrating and

validating models, Journal of Environmental Engineering, American Society of Civil Engineers, 111(3), 272.

5-76
Whittmore, R., et al. 1989. National Council for Air and

Stream Improvement, Tufts University, Medford, Massachusetts.

Wunderlich, W.O. 1972. Heat and Mass Transfer Between A Water Surface and the Atmosphere, Water

Resources Research, Laboratory Report Number 14,

Report no. 0-6803, Tennessee Valley Authority, Norris, Tennessee.

Zaykov, B.D. 1949. Evaporation from the water surface of ponds and small reservoirs in the USSR, Trans.

State Hydrologic Institute (TRUDY GCI), cited by Ryan

and Harleman, 1973.

Zison, S.W., Mills, W.B., Deimer, D., and Chen, C.W.

1978. Rates, Constants, and Kinetics Formulations in

Surface Water Quality Modeling, Report EPA/600/3-

78-105, U.S. Environmental Protection Agency, Athens, Ga.

5-77

6. SIMPLIFIED ILLUSTRATIVE EXAMPLES

David W. Dilks, Ph.D.

Scott C. Hinz,

Paul L. Freedman, P.E.

LTI, Limno-Tech, Inc.

Ann Arbor, Michigan

Robert B. Ambrose, Jr, P.E.

Center for Exposure Assessment Modeling

Environmental Research Laboratory, Athens, GA

James L. Martin, Ph.D.,P.E.

Timothy A. Wool, AScI

AScI Corp., at the

Center for Exposure Assessment Modeling

Environmental Research Laboratory, Athens, GA

This section presents illustrative examples of estuarine

modeling using both simple screening procedures and

the water quality model WASP4. The examples are

provided primarily to serve as templates to facilitate

future estuarine WLA analyses. Sample calculations

and model inputs are provided as well as background

information on the models being used. The reader is

referred to other chapters and other guidance manuals

for detailed technical guidance.

Screening procedures are provided to demonstrate

estuarine analyses conducted without use of computer

models. Screening analyses provided herein are

based upon simple analytical equations and the more

detailed guidance provided in the EPA Report “Water

Quality Assessment: A Screening Procedure for Toxic

and Conventional Pollutants - Part 2" (Mills et al, 1985).

WASP4 examples are provided to demonstrate modelbased estuarine WLA application. WASP4 is a general multi-dimensional model supported and available

through the U.S. EPA Center for Exposure Assessment Modeling, Athens, Georgia (requests require 3

double sided double density diskettes). WASP4, a

general- complexity water quality model, can be used

to simulate a wide range of water quality processes in

different types of estuaries. Depending upon the type

of estuary/water quality processes simulated, the representative WASP4 input file will vary greatly.

This chapter presents a range of hypothetical estuarine

situations designed to be representative examples of

general classes of estuarine WLA analysis. The examples used have been simplified to demonstrate

basic uses of the different approaches. This chapter

does not provide detailed guidance on model selection,

model development, calibration, waste load allocation,

or all-inclusive instructions on WASP4 use.

Model input files for each WASP4 example are provided in an Appendix to this manual which is available

from the Center for Exposure Assessment Modeling on

diskette. These input files can be used as templates in

simulation of water quality. The templates allow estuarine modelers to modify an existing input file to meet

site-specific modeling needs instead of the more time

consuming and difficult task of developing the entire

input file from scratch.

The examples provided herein consider eight water

quality concerns in three basic types of estuarine characterizations:

One-Dimensional Estuary:

— Analytical equation for non-conservative toxic

—Fraction of freshwater method for conservative toxic

—Modified tidal prism method for non-conservative

toxic

Total Residual Chlorine

—Bacteria

—Simple DO depletion

Vertically Stratified Estuary:

—Nutrient enrichment

6-1
—Algal production/DO/sediment interaction

Laterally Variant Estuary:

—Ammonia toxicity

—Toxic chemical in water column and sediments

The chapter is divided into four parts discussing:

1. Screening Procedures

2. Screening Examples

3. WASP4 Modeling

4. WASP4 Examples

6.1. Screening Procedures

Often times, valuable information on estuarine water

quality impacts can be gained without application of a

sophisticated computer model. Simple screening procedures, which can be applied using only a hand

calculator or computer spreadsheet, have been developed to facilitate preliminary assessments of toxic and

conventional pollutants in estuaries . While these

screening procedures may not be suitable as the sole

justification for a waste load allocation, they do serve

a valuable purpose for initial problem assessment or

when available resources (staff, time, and/or field data)

are insufficient to allow for more rigorous modeling

analysis.

This section provides example descriptions of three

screening procedures used for estimating estuarine

water quality impacts: analytical equations for an idealized estuary, the fraction of freshwater method, and

the modified tidal prism method. These three example

procedures are only applicable to steady state, tidalaverage one- dimensional estuary problems. All three

procedures provide “far- field” calculations (well distanced from the outfall) in contrast to “near-field” predictions very close to the outfall. Far-field calculations

are unaffected by the buoyancy and momentum of the

wastewater as it is discharged.

These three screening procedures assume that the

wastewater is well mixed both vertically and laterally in

the estuarine model segment. The latter two screening

procedures are described in much greater detail in the

document “Water Quality Assessment: A Screening

Procedure for Toxic and Conventional Pollutants - Part

2" (Mills et al, 1985). Screening procedures for vertically- and laterally-variant estuaries are also described

in the manual but are too complex for example illustration herein. The reader is referred to that document for

a thorough discussion of several estuarine screening

procedures including explicit instruction on proper application and limitations of the various techniques.

6.1.1. Analytical Equations

Many estuarine analyses can be easily conducted by

making certain simplifying assumptions about the estuary and pollutant behavior. The simplifying assumptions common to all three screening techniques

presented herein are that the pollutant concentrations

do not vary significantly in the lateral or vertical directions (i.e. a one- dimensional system), and that tidalaveraged, steady state conditions are being

represented. By making a few additional simplifying

assumptions, pollutant behavior from point sources

can be described using relatively simple analytical

equations. These assumptions are that cross-sectional area, flow, and first-order reaction rates are

constant over the length of estuary of interest; and that

discharges are sufficiently distant from the upstream or

downstream boundary of the estuary.

Three separate equations are available to predict concentrations at any location in the estuary, depending

upon whether location of interest is: 1) at, 2) upstream

of, or 3) downstream of the point of discharge. Estuary

locations are specified as distance downstream of the

outfall. Locations upstream of the outfall are represented by negative distances, locations downstream

by positive distances. The predicted pollutant concentration, C, at any point in the estuary, x, for a point

source at location x=0 can be estimated from the

equations (Thomann and Mueller, 1987):

C = Co = W ⁄ (Qa) x = 0 (6-1)

C = Co ∗ exp ( j1 x ) x < 0 (6-2)

C = Co ∗ exp ( j2 x ) x > 0 (6-3)

where:

a = ( 1 + 4 K E ⁄ U

2

)

1

⁄2

j 1 = U ⁄ 2 E (1 + a )

j 2 = U ⁄ 2 E ( 1 − a )

C= pollutant concentration (M/L3)

W = point source pollutant load (M/T)

x = distance downstream of discharge (L)

K = first-order decay rate coefficient (1/T)

U = net non-tidal velocity

 = freshwater flow/cross-sectional area (L/T)

E = tidal dispersion coefficient (L2/T)

The net nontidal velocity can be directly determined

from freshwater flow data (e.g. USGS) and cross-sectional area (e.g. NOAA hydrographic charts), leaving

the tidal dispersion coefficient and first-order loss rate

coefficient as the only “calibration” parameters.

Several methods are available for estimating the tidal

dispersion coefficient (e.g. Thomann, 1972), the most

6-2
common of which is calibration to observed salinity or

chloride data. Since chloride and salinity behavior can

be assumed conservative (i.e. K=0), Equation 6-2 becomes:

C = Co ∗ exp (U x ⁄ E ) , x < 0 (6-4)

which can be restated in the form (Thomann and

Mueller, 1987):

ln C ⁄ Co = (U ⁄ E ) ∗ x (6-5)

Equation 6-5 states that the slope of the logarithms of

observed salinity versus distance (U/E) can be used to

determine E, given an estimate of net freshwater velocity. Specifically, by fitting a line through a plot of

salinity vs. distance on semi-log paper, E can be

determined as:

E =

U (x 2 − x 1)

ln (C 2 − C 1)

(6-6)

An application of this method is provided in the Screening Examples portion of this section (Subsection 6.2).

The analytical equations provided in Equations 6-1 to

6-3 can also be applied to multiple discharge situations

through the principal of superposition. Simply stated,

Equations 6-1 to 6-3 are applied to predict pollutant

concentrations for each discharger (independent of all

other discharges) throughout the estuary. The pollutant concentration distribution throughout the estuary

due to all discharges is determined by summation of

the predicted concentrations at any location for each

individual discharge. This procedure will also be demonstrated as part of the Screening Examples (Subsection 6.2).

6.1.2. Fraction of Freshwater Method

The fraction of freshwater method allows quick estimation of tidal average, steady-state pollutant concentrations resulting from point source or upstream discharge

without consideration of reaction losses or gains. The

method estimates estuarine flushing and dilution from

freshwater and tidal flow by comparing salinity in the

estuary to the salinity of local seawater, (i.e. the fraction

of freshwater). This method is useful for systems

where the assumption of constant cross- sectional

area and flow over distance is grossly violated.

The balance of freshwater to seawater is the basis of

this screening procedure. The fraction of freshwater in

any specified estuarine segment is calculated by examining the salinity ratio to seawater as follows:

fi =

Ss − Si

Ss

 (6-7)

where

f i = fraction of freshwater in segment i

S s = salinity of local seawater (ppt)

S i = salinity in estuary segment i (ppt)

From a different perspective, this ratio can be viewed

to define the degree of dilution of freshwater (and

pollutants) by seawater. With this in mind the total

dilution of a pollutant input can be calculated by multiplying the seawater dilution by the freshwater dilution.

This then provides a simple way to calculate concentrations of conservative pollutants. For a location x,

including or downstream of the discharge,

Cx = fx

W

Q

(6-8)

 where:

fx = fraction freshwater at location x

W = waste loading rate (M/T)

Q = freshwater inflow (L3/T)

The right hand side of Equation 6-8 can be divided into

two distinct terms. The term W/Q represents the classical approach to determining dilution in rivers caused

by upstream freshwater flow. The second term, fx,

accounts for the further dilution of the river concentration by seawater. Equation 6-8 also predicts concentrations at the point of discharge, Co, by using the

corresponding fraction of freshwater at that location, fo.

Concentrations upstream of the discharge are estimated from the concentration at the point of mix and

the relative salinity of the upstream location. Initial mix

concentrations are assumed to be diluted by freshwater in the upstream direction to the same degree that

salinity is diluted. The equation is:

Cx = fo

W

Q

Sx

So

(6-9)

 where:

fo = fraction of freshwater at discharge location

S x = salinity at location x

So = salinity at discharge location

Equations 6-8 and 6-9 can be used to predict conservative pollutant concentrations at all locations upstream and downstream of a discharge. The frac6-3
tion of freshwater method can also be applied to estimate pollutant concentrations in one-dimensional

branching estuaries. The calculations become more

tedious than those discussed here, but can still be

applied in most cases using only a hand calculator.

The reader is again referred to Mills et al. (1985) for a

thorough discussion of this topic.

6.1.3. Modified Tidal Prism Method

The modified tidal prism method estimates tidal dilution

from the total amount of water entering the estuary (or

estuarine segment) from tidal inflow, (i.e. the tidal

prism). It is more powerful than the fraction of freshwater method because it can consider not only tidal

dilution but also non-conservative reaction losses.

This method divides an estuary into segments whose

volumes (and lengths) are calculated considering low

tide volumes and tidal inflow. The tidal prism (or tidal

inflow) is compared for each segment to total segment

volume to estimate flushing potential in that segment

over a tidal cycle. The modified tidal prism method

assumes complete mixing of the incoming tidal flow

with the water resident in each segment.

The first step in the modified prism method divides the

estuary into segments. Each downstream segment

volume is equal to the upstream low tide volume plus

the tidal inflow over a tidal cycle. This results in increasing segment size as segments are defined seaward. Data on freshwater inflow and tidal flow (or

stage) are required for the calculation.

Estuarine segments are defined starting at the fall line

and proceeding seaward. An initial segment (referred

to as segment 0) is located above the fall line and has

a tidal prism volume (P0) supplied totally by freshwater

inflow over one tidal cycle:

P 0 = Q T (6-10)

where:

P0 = tidal prism of segment 0 (L3)

Q = freshwater inflow (L3/T)

T = length of tidal cycle (T)

The low tide volume (V0) in this section is defined as

the low tide volume of the segment minus inter-tidal

volume, P0.

Segment volumes starting from segment 1 are defined

proceeding seaward such that the low tide volume of

segment i (Vi) is defined as the low tide volume of the

previous segment plus the inter-tidal volume, expressed as:

V i = V i − 1 + P i − 1 (6-11)

This results in estuarine segments with volumes (and

lengths) established to match the local tidal excursion.

Once all segments are defined, an exchange ratio (ri)

can be calculated for each segment as:

r i =

P i

P i + V i

(6-12)

This exchange ratio represents the portion of water

associated with a segment that is exchanged with

adjacent segments during a tidal cycle. This is also

equivalent to the inverse of the segment flushing time

(in terms of tidal cycles, not actual time) and is important for calculations of reaction losses.

The tidal prism method can be applied in conjunction

with the fraction of freshwater method to estimate

non-conservative pollutant concentrations in cases

where decay and flushing play an approximately equal

role in reducing pollutant concentrations. The equations are (Dyer, 1973):

 segment at the outfall,

Cd = fd

W

Q

(6-13)

 segments downstream of the outfall,

Ci = Cd

fi

fd ∏

i = 1

n

(Bi) (6-14)

 segments upstream of the outfall:

Ci = Cd

Si

Sd ∏

i=1

n

(Bi) (6-15)

where:

Bi =

r i

1 − (1 − ri ) e

−Kt

 (6-16)

Ci = non-conservative constituent mean

 concentration in segment 3L ́ (M/L3)

Cd = conservative constituent mean concentration

 in segment of discharge (M/L3)

ri = the exchange ratio for segment 3L ́ as defined

 by the modified tidal prism method

 (dimensionless)

n = number of segments away from the outfall

 (i.e. n=1 for segments adjacent to the outfall;

 n=2 for segments next to these, etc.)

K = first-order decay rate (1/T)

t = segment flushing time

 = (1/ri) * Tidal Period (T)

6-4
An illustrative example demonstrating application of

this technique is provided in the following section of this

chapter.

6.2. Screening Examples

The screening procedures described herein can be

used to describe a wide range of water quality considerations. This section provides simple illustrative examples designed for three different situations. The

examples are simple by design, in order to best illustrate capabilities and use of the procedures. The range

documented herein provides a base which can be

expanded to consider many water quality concerns.

This section provides a description of screening procedure application to each of the examples, which can be

used as templates for future application. The format

describing each case study consists of a brief description of the water quality process(es) of concern, followed by a description of all model inputs, and ending

with a discussion of model output. Blank calculation

tables are provided for the latter two methods to assist

in future application of the procedures.

6.2.1. Example 1 - Analytical Solution for

Non-conservative Toxic

The first three illustrative examples involve a one-dimensional estuary whose pollutant concentrations are

simulated in response to point source discharge(s).

This type of estuary characterization simulates

changes in concentration longitudinally down the

length of the estuary.

Estuary widths are typically small enough that lateral

gradients in water quality can be considered insignificant. Further, depths and other estuarine features are

such that stratification caused either by salinity or

temperature is not important. This characterization is

usually relevant in the upper reaches of an estuary

(near the fall line) and in tidal tributaries. These

screening examples are also designed to represent

only steady state, tidally-averaged conditions. Temporal changes in water quality related to changes in

pollutant loads or upstream flows, or intra-tidal variations, are not represented. Application of the analytical equations requires the additional assumption that

flows, cross-sectional areas, and reaction rates are

relatively constant over the length of the estuary.

The first example consists of a wasteload allocation for

total residual chlorine (TRC) for a single discharger on

a tidal tributary (see Figure 6-1). The goal of the

wasteload allocation is to determine the maximum

amount of chlorine loading which will just meet the

water quality standard of 0.011 mg/l at critical environmental conditions.

One survey is available with data on salinity and TRC

throughout the estuary. The pertinent information for

this estuary/discharge situation is provided in Table

6-1.

The wasteload allocation will proceed by accomplishing three steps:

1. Determine dispersion coefficient

2. Determine decay rate

3. Determine maximum allowable load at critical conditions

Figure 6-1. Schematic of tidal tributary for analytical

equation example.

Upstream Flow: 4000 cfs

Discharge Flow: 300 cfs

Discharge Conc.: 2 mg/L

Estuary Cross-Sectional Area: 20,000 ft2

Observed DataRiver Mile Salinity(%) TRC(mg/L)

2 19 0.04

4 10 0.06

5 8 0.07

6 6 0.08

9 3 0.15

10 2 0.18

12 1 0.07

Table 6-1. Observed Conditions During Survey

6-5
The dispersion coefficient is determined by applying

Equation 6-6 to the observed salinity data. These data

are plotted in Figure 6-2 on semi-log paper as a function of distance from the mouth of the estuary. Note

that the analytical equations described herein require

that locations upstream of the pollutant source be

represented by negative distance units. A straight line

is fit through the observed salinity data (Figure 6-2),

and two points selected off this line to allow application

of Equation 6-6.

For the distances of -10 and -2, the corresponding

salinities are 1.8 and 18.1, respectively. The net freshwater velocity is calculated by dividing net freshwater

flow (4000 cfs) by cross-sectional area (20,000 ft2) as

0.20 ft/sec. This velocity is translated into units of

miles/day (0.20 ft/sec = 3.28 mi/day), to allow the

predicted dispersion coefficient to result in the most

commonly used units of mi2/day. Applying the observed salinity and velocity data to Equation 6-6 results

in:

E =

3.28 (−10 − (−2))

ln (1.8 ⁄ 18.1)

 (6-17)

= 11.4 mi 2⁄ day

The second step in the wasteload allocation process

for this example is calibration of the first-order rate

coefficient describing TRC decay. This is accomplished by determining the expected range of values

from the scientific literature, and applying different

values from within this range to Equations 6-1 to 6-3.

The decay rate coefficient which best describes the

observed data, and is consistent with the scientific

literature, is selected as the calibration value. For this

example, acceptable decay rate coefficients were

found to range from 0.5 to 5.0/day. Figure 6-3 shows

plots of model predictions versus observed data for

rate coefficients of 0.5, 1.0, and 5.0/day. The value of

1.0/day best describes the observed data, and is therefore selected as the calibration value. The required

calculations for predicting these concentrations

throughout the estuary are demonstrated in Table

6-2.

The final step in the wasteload allocation process is to

determine the maximum allowable load under critical

environmental conditions. Equation 6-1 predicted the

concentration at the point of mix as a function of

pollutant load; this equation can be rearranged to determine the loading required to obtain a specific concentration under given environmental conditions.

Wd = C ∗ Q ∗ a (6-18)

where:

 Wd = allowable pollutant load [M/T]

 Q = net freshwater inflow [L3/T]

 C = desired concentration [M/L3]

 a = ( 1 + 4KE/U2 )1/2 [dimensionless]

For wasteload allocation purposes, model parameters

should be representative of critical environmental conditions. Some parameters (e.g. upstream flow) will be

dictated during specification of critical conditions. Engineering judgement is usually required for many parameters to determine how (if at all) they are expected

to change from observed to critical environmental conditions. For this example, the critical

Inputs

Q = 4000 cfs K = 1/day E = 11.4 mi2/day U = 3.28 mi/day

 River Mile Distance Below

Discharge (x)

Equation Predicted

Concentration

(mg/L)

0 10 6-3 0.004

1 9 6-3 0.005

2 8 6-3 0.007

3 7 6-3 0.010

4 6 6-3 0.013

5 5 6-3 0.017

6 4 6-3 0.023

7 3 6-3 0.031

8 2 6-3 0.041

9 1 6-3 0.055

10 0 6-1 0.073

11 -1 6-2 0.054

12 -2 6-2 0.040

13 -3 6-2 0.029

14 -4 6-2 0.022

15 -5 6-2 0.016

Table 6-2. Predicted Concentrations Throughout Estuary

Under Observed Conditions

Figure 6-2. Determination of tidal dispersion from salinity

data.

6-6
environmental condition is the drought freshwater flow

of 2000 cfs. Since net velocity is directly related to flow

(U=Q/A), the velocity under critical conditions is recalculated as 1.64 mi/day. Environmental conditions not

expected to change under critical conditions for this

example are the tidal dispersion coefficient, pollutant

decay rate coefficient, and cross-sectional area. The

tidal dispersion coefficient and cross- sectional area

are often relatively insensitive to upstream flow in

estuarine systems.

The pollutant decay rate may change significantly between observed and critical conditions. Caution should

be used in projecting future conditions that the same

process(es) that comprised the observed loss rate will

be applicable under future projection conditions. For

example, a loss rate that includes settling which was

calibrated to high freshwater flow conditions may not

be directly applicable to future drought flow simulations. The best procedure is to perform sampling

surveys during periods as close to critical environmental conditions, to minimize the degree of extrapolation required.

For this example, Equation 6-16 is used to calculate the

allowable loading of chlorine to meet the water quality

standard as

Wd = 0.01 mg/l * 2000 cfs * 4.24 * 5.39

 = 457 pounds/day.

Note that 5.39 is a lumped units conversion factor

representing (lbs/day)/(cfs*mg/l). Given that the treatment plant flow is assumed to remain constant at 80

cfs, this translates into an allowable effluent concentration of:

 Cd = 457 pounds/day / 80 cfs / 5.39 = 1.06 mg/l

To demonstrate a multiple discharge situation, the

effect of a proposed second discharge on estuarine

TRC concentrations at critical environmental conditions will be evaluated. The specifics of this discharge

are:

 Location: River mile 5

 Flow: 40 cfs

 Concentration: 2 mg/l

Table 6-3 demonstrates the steps involved in evaluating multiple discharges. Column (4) is based upon

information in Columns (2) and (3) and represents the

incremental impact caused by the original discharge.

Figure 6-3. Calibration of TRC decay rate.

Discharge 1 Discharge 2 Sum

River Mile Distance Below

Discharge (x)

Equation Concentration Distance Below

Discharge (x)

Equation Concentration Total concentration

(1) (2) (3) (4) (5) (6) (7) (8)

0 10 6-3 0.007 5 6-3 0.007 0.014

1 9 6-3 0.009 4 6-3 0.009 0.018

2 8 6-3 0.011 3 6-3 0.012 0.023

3 7 6-3 0.014 2 6-3 0.015 0.029

4 6 6-3 0.018 1 6-3 0.019 0.037

5 5 6-3 0.022 0 6-1 0.024 0.046

6 4 6-3 0.028 -1 6-2 0.016 0.044

7 3 6-3 0.035 -2 6-2 0.011 0.046

8 2 6-3 0.044 -3 6-2 0.008 0.052

9 1 6-3 0.056 -4 6-2 0.005 0.061

10 0 6-1 0.071 -5 6-2 0.004 0.075

11 -1 6-2 0.049 -6 6-2 0.002 0.051

12 -2 6-2 0.033 -7 6-2 0.002 0.035

13 -3 6-2 0.023 -8 6-2 0.001 0.024

14 -4 6-2 0.016 -9 6-2 0.001 0.017

15 -5 6-2 0.011 -10 6-2 0.001 0.012

Table 6-3. Predicted Concentrations Throughout Estuary for Multiple Discharge Situation

6-7
Column (7) is based upon information in Columns (5)

and (6) and represents the incremental impact caused

by the proposed discharge. Column (8) represents

the expected concentration distribution throughout the

estuary, and consists of the sum of incremental concentrations from columns (4) and (7). The results of

this analysis are shown graphically in Figure 6-4.

6.2.2. Example 2 - Fraction of Freshwater

Method for Conservative Toxic

The next two examples also involve one dimensional

estuaries, but do not require the assumption of constant flows and cross-sectional areas throughout the

estuary. Instead, the estuary is divided into a sequence of segments used to simulate longitudinal

water quality differences. For analysis purposes each

segment

s considered of uniform quality. A single segment

describes water quality across the entire width of the

estuary, consistent with the assumption of lateral homogeneity. Similarly, a single segment is also used to

describe water quality from surface to bottom consistent with the lack of vertical stratification.

The example discussed in this section involves consideration of conservative pollutant behavior, and is amenable to analysis using the fraction of freshwater

method. Figure 6-5 shows a schematic of the estuary

and how it is compartmentalized into 15 segments.

Table 6-4 serves as a worksheet for calculating conservative pollutant concentrations using this method.

Four inputs are required for the worksheet (Table 6-4):

Freshwater inflow to the estuary, Q

Salinity of seawater at the downstream boundary, Ss

Pollutant loading rate, Wd

Salinity of each segment, Si

The location of these inputs are denoted in Table 6-4

by the underscore (__) character. Table 6-5 contains

input values obtained for the first example. Freshwater

inflow is 2,000 cmd, the salinity of local seawater is 30

ppt, and the loading rate of pollutant is 10,000 g/day.

These inputs, in conjunction with Equations 6-7 to 6-9,

allow completion of the calculation table.

The first calculation in determining the pollutant distribution is to determine the fraction of freshwater, fi, for

each segment. This is obtained from Equation 6-7, and

applied to each model segment. These results are

entered into the third column of the worksheet in Table

6-4. The second calculation required is to divide the

fraction freshwater in each segment by the fraction of

freshwater in the segment receiving discharge. These

values are entered into the fourth column of Table 6-4.

Figure 6-4. Estuary TRC concentration in response to two discharges.

6-8
Figure 6-5. Schematic for illustrative vertically stratified estuary.

Seg # Salinity, Si

 (ppt)

Fraction

of

Freshwater

, fi

fi / fd Si /Sd Pollutant

Concentrat

ion (mg/L)

0 ____

1 ____

2 ____

3 ____

4 ____

5 ____

6 ____

7 ____

8 ____

9 ____

10 ____

11 ____

12 ____

13 ____

14 ____

 Freshwater Inflow Local Seawater Salinity Load

 Q=___cmd Ss = ___ppt Wd =___g/day

Table 6-4. Calculation Table for Conservative Pollutant by

Fraction of Freshwater Method [Mills et al.(1985)]

Seg # Salinity, Si

 (ppt)

Fraction

of

Freshwater

, fi

fi ⁄ fd Si ⁄ Sd Pollutant

Concentrat

ion (mg/L)

0 1 0.97 1.26 0.14 0.54

1 3 0.90 1.17 0.43 1.66

2 5 0.83 1.09 0.71 2.73

 3 ← Wd 7 0.77 1.00 1.00 3.85

4 10 0.67 0.87 1.43 3.35

5 12 0.60 0.78 1.71 3.00

6 14 0.53 0.70 2.00 2.65

7 16 0.47 0.61 2.29 2.35

8 18 0.40 0.52 2.57 2.00

9 19 0.37 0.48 2.71 1.85

10 21 0.30 0.39 3.00 1.50

11 23 0.23 0.30 3.29 1.15

12 25 0.17 0.22 3.57 0.85

13 27 0.10 0.13 3.86 0.50

14 29 0.03 0.04 4.14 0.15

Freshwater Inflow Local Seawater Salinity Load

Q = 2000 cmd Ss = 30 ppt Wd = 10,000 g/day

Table 6-5. Completed Calculation Table for Fraction of

Freshwater Method

6-9
The third set of calculations is to divide the salinity in

each segment by the salinity in the segment receiving

discharge. Finally, pollutant concentrations for each

segment are obtained using Equation 6-8 (for segments including and downstream of the one receiving

discharge) or Equation 6-9 (for segments upstream of

the discharge).

Table 6-5 contains a completed calculation table for

the first example, including the expected pollutant distribution. Concentrations are at a maximum of 3.8 mg/l

in Segment 12 (the segment receiving discharge),

decreasing rapidly in the upstream direction and more

gradually proceeding seaward. The assumption of

conservative behavior is commonly used in screening

level analysis of toxics. The conservative assumption

will provide an upper bound of expected pollutant

concentrations; if water quality standard violations are

indicated for conservative pollutant behavior then application of a fate and transport model may be warranted. Caution should be exercised when

considering these results as upper bounds to ensure

that the assumption of complete mixing is valid. Incomplete mixing could result in actual concentrations

greater than those predicted using this approach.

6.2.3. Example 3 - Modified Tidal Prism Method

for Non-Conservative Toxic

This third illustrative example is for the same estuary

as described in the previous example (Figure 6-5), but

considers non-conservative pollutant behavior. Firstorder kinetics are used to describe pollutant loss. This

situation lends itself to application of the Modified Tidal

Prism Method. Table 6-6 serves as a worksheet for

calculating non-conservative pollutant concentrations.

The first four inputs are identical to those required for

the fraction of freshwater method and are used to

calculate the conservative constituent concentration in

the segment receiving discharge (Equation 6- 13). The

fifth and sixth inputs, low tide and inter-tidal water

volumes, are used to calculate the exchange ratio for

each segment. The final input is the first-order decay

rate constant, k. Required model inputs are noted by

an underscore (_) in Table 6-6.

Seg # Subtidal

Water

Volume, Vi

106 m

3

Intertidal

Water Volume,

Pi 106 m3

Salinity, Si

ppt

Fraction

Fresh, fi

fi /fd Si/Sd Segment

Exchange

Ratio, ri

n ∏ BiPollutant

Concentration

mg/L

0 __ __ __

1 __ __ __

2 __ __ __

3 __ __ __

4 __ __ __

5 __ __ __

6 __ __ __

7 __ __ __

8 __ __ __

9 __ __ __

10 __ __ __

11 __ __ __

12 __ __ __

13 __ __ __

14 __ __ __

Seven inputs are required for this worksheet:

• Freshwater inflow to the estuary, Q

• Salinity of seawater at the downstream boundary, Ss

• Pollutant loading rate, Wd

• Salinity of each segment, Si

• Low tide volume for each segment, Pi

• Inter-tidal volume for each segment, Pi

Freshwater Inflow Local Seawater Salinity Load Decay Tidal Cycle

Q = ____cmd Ss =___ppt Wd = ___g/day K = ___/day T = ___ days

Table 6-6. Calculation Table for Non-Conservative Pollutant by Modified Tidal Prism Method [Mills et al., (1985)]

6-10
For this example, identical conditions (salinity, freshwater inflow, and loading) are used as the first example, with the primary difference being the addition of a

first-order decay rate of 0.5 day-1. The first step in

performing the modified tidal prism method is to define

the estuarine segmentation using the procedures described previously. That is, segment sizes must be

selected such that low tide volume in each segment is

equal to the high tide volume for the segment immediately upstream. The required information on tidal

prism volumes can be obtained from tidal stage information (tidal gaging stations or NOAA predictions) in

conjunction with channel geometry information (from

hydrographic maps). Calculation of segment volumes

is the most time consuming step of the modified tidal

prism method. The information on the sub-tidal and

inter-tidal volume of each segment of the example

estuary is entered in columns 2 and 3 of Table 6-6. The

fraction freshwater is calculated from local salinity values; they are identical to those used for the first example. The segment exchange ratios are calculated from

the segment volumes using Equation 6-12. Finally,

pollutant concentrations are calculated using: Equation 6-13 for the segment receiving discharge; Equation 6-14 for segments downstream of the discharge;

and Equation 6-15 for segments upstream of the discharge.

A completed calculation table is provided for this example in Table 6-7. Pollutant concentrations follow a

similar trend as for the first example, but decrease

significantly faster in both the upstream and downstream directions. The difference in pollutant concentrations is caused solely by pollutant decay. The

greater the distance from the outfall, the greater the

difference in predicted concentrations, as longer travel

time provides greater opportunity for decay.

A single first-order loss term is used to describe the

behavior of many pollutants, even though multiple fate

processes may be occurring simultaneously. Rate coefficients for first-order processes are additive, therefore, these multiple processes can be combined into a

single “lumped” parameter. Application of this model

may include “calibration” of the first-order loss rate to

available in-stream pollutant data. As discussed for the

analytical equation example, caution should be used in

projecting future conditions to insure that the same

process(es) that comprised the observed loss rate will

be in place under future projection conditions.

6.3. WASP4 MODELING

Deterministic water quality modeling of estuarine systems can often be divided into two separate tasks:

1. Description of hydrodynamics (current, tides, circulation, mixing, etc.).

2. Description of water quality processes.

The WASP4 model was designed to simulate water

quality processes, but requires hydrodynamic information as input. This information can be entered into

WASP4 by reading the output results from a separate

 Freshwater Inflow Local Seawater Salinity Load Decay Tidal Cycle

 Q = 2000 cmd Ss =30 ppt Wd = 10,000 g/day K = 0.01/day T = 0.48 days

Table 6-7. Completed Calculation Table for Non-Conservative Pollutant by Modified Tidal Prism Method

 Seg # Subtidal

Water

Volume, Vi

106 m

3

Intertidal

Water Volume,

Pi 106 m3

Salinity, Si

ppt

Fraction

Fresh, fi

fi /fd Si/Sd Segment

Exchange

Ratio, ri

n ∏ BiPollutant

Concentration

mg/L

0 5.0 0.5 1 — — 0.14 0.09 3 0.40 0.22

1 5.5 0.7 3 — — 0.43 0.11 2 0.62 1.02

2 6.2 1.0 5 — — 0.71 0.14 1 0.83 2.26

3← Wd 7.2 1.2 7 0.77 1.00 1.00 0.14 — 1.00 3.85

4 8.4 1.4 10 0.67 0.87 — 0.14 1 0.83 2.77

5 9.6 1.8 12 0.60 0.78 — 0.16 2 0.72 2.15

6 11.4 2.0 14 0.53 0.69 — 0.15 3 0.61 1.62

7 13.4 2.4 16 0.47 0.61 — 0.15 4 0.52 1.21

8 15.8 3.3 18 0.40 0.52 — 0.17 5 0.45 0.91

9 19.1 3.6 19 0.37 0.48 — 0.16 6 0.39 0.73

10 22.7 3.8 21 0.30 0.39 — 0.14 7 0.33 0.49

11 26.5 4.2 23 0.23 0.30 — 0.14 8 0.27 0.31

12 30.7 4.4 25 0.17 0.22 — 0.13 9 0.22 0.18

13 35.1 4.6 27 0.10 0.13 — 0.12 10 0.17 0.08

14 39.7 4.8 29 0.03 0.04 — 0.11 11 0.13 0.02

6-11
hydrodynamic model of the system or through direct

specification of hydrodynamic data in the WASP4 input

file. Mixing is simulated through use of dispersion

coefficients. Both hydrodynamic and water quality

aspects of the WASP model are summarized below.

The reader is referred to the WASP4 User’s Manual

(Ambrose et al., 1988) for a complete description of

model theory and use.

6.3.1. WASP Transport

The description of water movement and mixing in

estuarine systems using WASP4 always includes advective flows and dispersive mixing. However, the

distinction between the real-time description of tidal

hydrodynamics compared to the description of tidal-averaged conditions must be made both for flow and

dispersion, as values for these processes will differ

dramatically depending on the assumption.

In simulating estuaries with WASP4, the modeler must

decide between the tidal averaged approach and real

time approach. For the tidal averaged approach, hydrodynamic conditions (and water quality) are averaged over a tidal cycle. In the real time approach,

calculations are performed on (figuratively) a minute

by minute basis simulating intratidal changes.

All of the illustrative modeling examples provided in this

manual assume tidally averaged conditions. Under

this assumption, tidal flow is characterized as a mixing

process, not advective flow. Advective flows represent

net freshwater inflow or known advective circulation

patterns. In contrast, real time intratidal calculations

can also be conducted with WASP4 to simulate tidal

variations. Under this condition, variations in freshwater flow, circulation and tidal flow must be specified.

For this type of application the use of DYNHYD4, a

component of the WASP4 modeling system, is recommended to define the complex hydrodynamics. These

are not illustrated explicitly in this manual. All further

discussions in this manual focus on tidal averaged

conditions.

Turbulent mixing and tidal mixing between water column segments in WASP4 are characterized by dispersion coefficients. These dispersion coefficients, when

coupled with a concentration gradient between segments, account for mixing. The dispersion coefficient

can be derived from literature estimates but are usually

obtained by direct calibration to dye or salinity data.

Structurally the WASP4 program includes six mechanisms for describing transport, all of which are addressed together in one section of the input file. These

“transport fields” consist of: advection and dispersion

in the water column; advection and dispersion in the

pore water; settling, resuspension, and sedimentation

of up to three classes of solids; and evaporation or

precipitation. Of these processes, advection and dispersion in the water column are usually the dominant

processes controlling estuarine water movement and

mixing. The other processes, however, also can play

a role in pollutant transport depending on specific conditions. These are not elaborated on herein, because

they represent complex physio- chemical processes

beyond the intent of these simplified examples.

The description of advective flows within WASP4 is

fairly simple. Each inflow or circulation pattern requires

specification of the routing through relevant water column segments and the time history of the corresponding flow. The flow routing specification is simply the

fraction of the advective flow moving from one segment

to another. Dispersion requires only specification of

cross- sectional areas between model segments, characteristic lengths, and their respective dispersion coefficients. Specific examples of advection and mixing

inputs are provided in the illustrative case studies at the

end of this chapter.

6.3.2. WASP4 Description of Water Quality

WASP4 is a general purpose water quality model in that

it can be used to simulate a wide range of water quality

processes. WASP4 contains two separate kinetic submodels, EUTRO4 and TOXI4, each of which serves a

distinct purpose. This section briefly describes the

capabilities of each kinetic submodel for simulating

water quality. It will serve as background information

for the illustrative examples, where the specifics of

water quality simulation will be provided.

The first kinetic subroutine in WASP4 is EUTRO4.

EUTRO4 is a simplified version of the Potomac Eutrophication Model, PEM (Thomann and Fitzpatrick

1982), and is designed to simulate most conventional

pollutant problems (i.e. DO, eutrophication). EUTRO4

can simulate concentrations of up to eight state variables (termed systems by WASP4) in the water column

and sediment bed. These systems correspond to:

EUTRO4

System Number State Variable

1 Ammonia nitrogen

2 Nitrate nitrogen

3 Inorganic phosphorus

4 Phytoplankton carbon

5 Carbonaceous BOD

6 Dissolved oxygen

7 Organic nitrogen

8 Organic phosphorus

6-12
EUTRO4 can be used to simulate any or all of these

parameters and the interactions between them. The

WASP4 users manual discusses in detail all of the

possible interaction between state variables.

Three of the illustrative examples provided at the end

of this chapter will focus upon the more common

applications of EUTRO4: simple DO, algal nutrients,

and eutrophication. The first EUTRO4 example considers a simple model simulating CBOD, ammonia

nitrogen (NH3-N), and DO. This type of model complexity is most often used when algal impacts are

considered unimportant. This corresponds to the

“modified Streeter-Phelps” model described in the

WASP4 users manual. The second EUTRO4 example

considers algal nutrients and simulates total nitrogen

and phosphorus concentrations only. This type of

simulation is often used when eutrophication is of

concern, but resources or data are insufficient to allow

application of a complex eutrophication model. The

final EUTRO4 example simulates all aspects of the

eutrophication process, and includes all eight state

variables simulated by WASP4.

The TOXI4 submodel is a general purpose kinetics

subroutine for the simulation of organic chemicals and

metals. Unlike EUTRO4, TOXI4 does not have a

specific set of state variables. Instead, TOXI4 simulates up to three different chemicals and three different

types of particulate matter of the users choosing.

TOXI4 identifies these state variables in terms of

WASP4 systems as:

System Number TOXI4 State Variable

1 Chemical 1

2 Solids type 1

3 Solids type 2

4 Solids type 3

5 Chemical 2

6 Chemical 3

The chemicals can be related (e.g., parent compounddaughter product) or totally independent (e.g., chemical and dye tracer). Reactions specific to a chemical

or between chemicals and/or solids are totally at the

control of the user, using the flexible kinetic parameters

made available by the model. TOXI4 can provide simulation of ionization, sorption, hydrolysis, photolysis,

oxidation, bacterial degradation, as well as extra reactions specified by the user. TOXI4 simulates concentrations both in the water column and bottom

sediments.

This chapter will provide three illustrative examples

using TOXI4: bacterial degradation and dye tracer;

ammonia toxicity; and toxic pollutant in water column

and sediments. These simulations will provide a broad

spectrum of potential TOXI4 applications and demonstrate the use of ionization, equilibrium sorption, volatilization, biodegradation, and general first-order

decay.

6.4. WASP4 Examples

The remaining six examples demonstrate the use of

WASP4 for estuarine WLA modeling. The purpose of

these examples is to provide a set of templates to

facilitate future WASP4 modeling for a wide range of

estuarine situations. The most useful portion of these

examples (for potential WASP4 users) is the line by line

description of the WASP4 input files and diskette copies of the files themselves. These descriptions are too

detailed for inclusion in the body of the text; they are

instead supplied in an Appendix to this manual which

is available on diskette from the U.S.E.P.A. Center for

Exposure Assessment Modeling. This portion of the

chapter will provide background information on each

example, describe the types of inputs required, show

selected WASP4 model results, and briefly describe

WLA issues.

6.4.1. Example 1- Bacteria in a

One-Dimensional Estuary

The first illustrative example using WASP4 involves a

simple non-branching estuary. The analysis is designed to provide an example which is reasonably

realistic. Although not a wasteload allocation in the

traditional sense, this example illustrates the use of a

modeling study in an analysis of bacterial loads. Since

the example is intended only for illustration of the

application and potential use of a model, such as

WASP4, emphasis is not placed on providing details

on data requirements and calibration-validation procedures.

6.4.1.1. Problem Setting

In this example, a single discharger has been identified

to the Trinity estuary. The estuary has popular sport

and commercial fisheries, including shellfish. A dye

study was conducted during March of 1980 and used

to identify a 2 km buffer zone within which shellfishing

was closed. The buffer zone was identified by computing a one day travel time from the sewage outfall of the

city of Harris. The criteria on which the closing of the

shellfishery within the buffer zone was based is not

dependent upon the bacterial wasteload concentrations, but rather the presence of a discharger. This is

often the practice for bacterial loadings. Therefore, the

purpose of this study is not to determine whether a

reduction in load is necessary but whether the buffer

zone is adequately protective of human health and

6-13
whether continuing high coliform counts may be attributed to the discharger.

High coliform counts have been detected in the Trinity

estuary outside of the buffer zone, leading to periodic

closing of the estuary. The area has a large waterfowl

population. However, comparisons of fecal coliform

and fecal streptococci counts suggests that the problem is of human origin. The pertinent water quality

criterion pertains to shellfishing and the applicable

standard is 70 counts/100 ml. The criterion for fishing

is 1000 counts/100 ml. A summary of the problem

setting and treatment plant data is presented in Figure

6-6 and Table 6-8.

6.4.1.2. System Characteristics

The Trinity estuary is approximately 30 km long and

receives flow from the Trinity river. The estuary is

relatively regular in shape and has no other major

tributaries. The city of Trinity is located at the upestuary extremity and the city of Harris is located approximately midway along the estuary. The upstream

section of the Trinity river above the fall line is gauged

by the USGS. The gauge is located near the crossing

of Highway 64. The average monthly flows and temperatures taken at the USGS gauge are provided in

Figures 6-7 and 6-8. An analysis of the morphometry

of the system indicated that the mean tidal widths and

depths could be adequately represented by

W =300 e

0.0625X

(6-19)

and

D = 2.43 e

0.033X

(6-20)

where W is the width and D the depth of the estuary, in

meters, and X is the distance from the village of Trinity,

in kilometers (see Figure 6-6). The village of Trinity

does not discharge wastes to the estuary. A water

surface elevation gauge is located near the mouth of

the estuary, and an analysis of the tidal components

was conducted, with the results provided in Table 6-9

and Figure 6-9a. The water surface elevation for the

period of interest was then computed from

Y = ∑

i=1

7

hi cos [2 π t ⁄ Ti − Pi ] (6-21)

where Y is the water surface elevation deviation (m) at

time t (hrs), hi is the amplitude (m), Ti the period (hrs),

and Pi the phase (in radians) of the seven principal

Figure 6-6. The Trinity Estuary.

Harris City WTP

Present

Flow MGD 17

BOD5 mg/l 65

CBODu (1) mg/l 130

Total Coliforms counts/100 ml 1E + 7

DO mg/l 5

(1) Based on long term BOD estimates of CBODu/CBOD5 = 2.0

Table 6-8. Treatment Plant Effluent Characteristics

Figure 6-7. Average monthly river flow at the Highway 64

USGS gauge.

6-14
semidiurnal and diurnal tidal components (see Table

6-9).

6.4.1.3. Supporting Studies

Historical data within the study area are limited. Data

are available for temperature at the USGS gauge.

Data were available for salinity within the system which

was used in model calibration. For this level of study

it was determined that no supporting field studies

would be conducted.

Symbol Name Period

(hours)

Phase

(degrees)

Amplitude

(cm)

Semi-Diurnal

Components

M2 Principal Lunar 12.42 330 23.0

S2 Principal Solar 12.00 334 5.2

N2 Larger Lunar Elliptic 12.66 303 4.9

K2 Luni-solar

semi-diurnal

11.97 328 1.6

Diurnal Components

K1 Luni-solar diurnal 23.93 106 15.8

O1 Principal lunar diurnal 25.82 89 9.8

P1 Principal solar diurnal 24.07 104 4.9

Table 6-9. Tidal Periods, Amplitudes and Phases for the

Trinity Estuary during March, 1989

Figure 6-8. Mean monthly temperatures at the Highway 64

USGS gauge.

Figure 6-9a. Variations in water surface elevations at the

mouth of the Trinity Estuary during March, 1989.

6.4.1.4. Model Application

For this analysis, model application consisted of: first

determining the model network (including morphometry of model segments), then determining appropriate flows and exchange coefficients, and finally

simulating bacterial concentrations. The flows for this

application were estimated using a one-dimensional

hydrodynamic model which was supplied flow data at

the riverine boundary and water surface elevations at

the mouth of the estuary. A one-dimensional hydrodynamic model, DYNHYD5, is part of the WASP4 modeling system. The WASP4 model may also be coupled

with other available hydrodynamic models. The hydrodynamic model was first calibrated and then used to

supply flow and volume information to the WASP4

model. Flows were computed over a period of one

month in order to examine the effects of successive

neap and spring tides. The WASP4 model was then

applied to estimate bacterial concentrations.

Several types of information were required to apply

WASP. These are described in the Appendix available

on disk from the U.S.EPA Center for Exposure Assessment Modeling. The determination of these types of

data and their use in this illustrative example is described below.

6-15
— General model information: The TOXI4 submodel

was selected for these simulations. TOXI4 was selected rather than EUTRO4 as a result of its convenience in simulating conservative materials. However,

the basic structure and information required in the data

input are the same. Five systems were simulated,

where system 1 was the bacteria, system 2 was salinity, 3 and 4 were solids (not pertinent to this analysis),

and 5 was the dye tracer, treated as a conservative

material. This combination of systems is not unique;

other combinations could have worked equally as well.

The general model information required included the

number of model segments, computational time step,

length of simulation, and variables (systems) to be

modeled.

— Network: The model network refers to how the

system is subdivided for analysis. For this application

an analysis of the historical data indicated significant

longitudinal gradients, with small lateral and vertical

variations, allowing application of a one-dimensional

model. A network consisting of 15 segments was

established. The variations in bottom morphometry

and water quality were reasonably regular, and for

simplicity segments were delineated every two kilometers. The depths of the segments were determined as

well as segment volumes and interfacial areas from

available morphometry data. An analysis of the system’s morphometry indicated that variations in width

and depth were reasonably described by Equations

6-19 and 6-20. The resulting network is illustrated in

Figure 6-9b.

— Dispersion coefficients: Since a hydrodynamic

model was used to estimate the effects of tidal mixing,

no dispersion was specified. However, where other

structures or nonuniformities cause additional dispersion, it may be necessary to specify dispersion rates in

other applications. Initial estimates can be derived

from the literature and refined through calibration to dye

or salinity data.

— Segment volumes: The initial volume of each segment is required, as well as a description of how the

volume changes with flow. Volumes are determined

from segment width and depth (taken from hydrographic maps) and segment length (user specified).

For this application, the segment widths and depths

were determined from Equations 6-19 and 6-20, obtained through analysis of the system. Changes in

volume in this example were computed by the hydrodynamic model and supplied to the water quality model.

Predicted variations in volumes are illustrated in Figure

6-10.

— Flows: Advective flow patterns must be described

for segment interfaces, and inflows where they occur.

Freshwater inflow data are often available from USGS

gaging stations. Tidal data are often available from

NOAA. For this application internal flows were estimated using a one-dimensional hydrodynamic model.

The internal flows are computed by the hydrodynamic

model given the model network and morphometry, the

boundary conditions, and factors affecting water movement, such as the bottom roughness. For this application a constant flow of 50 cms was assumed for the

Trinity river and a time-varying water surface elevation

specified at the ocean boundary (see Figure 6-9b).

— Boundary concentrations: The concentration of

bacteria, dye, and salinity must be specified at each

system boundary (segments 1 and 15). This information is typically collected during the same water quality

surveys used to collect calibration and validation data.

For this application it was assumed that the bacterial

and dye

Figure 6-9b. Model network for the Trinity Estuary.

6-16
boundary conditions were zero. The salinity at the

ocean boundary was specified as 32 ppt.

— Pollutant loads: Pollutant loading rates are required

for bacteria and dye for each point source. Loadings

can be measured during water quality surveys or taken

from discharge monitoring reports. The bacterial

loads for this study were computed assuming no chlorination or other disinfection, resulting in the high effluent concentrations given in Table 6-8. The loadings

were then computed from the discharge rate and bacterial concentration. The equivalent load for organisms was determined by multiplying the effluent

concentration (counts/100 ml) by the flow rate which,

after unit conversions, yielded counts per day which

was then converted to kilocounts per day for input. To

convert this back to counts/100 ml, from the output of

TOXI4 in units of μg/l, the values were multiplied by

10-7 ( 1 μg ( μ count here) = 10-6 g (counts), and 100

ml = 0.1 liter).

— Model constants: A first-order rate coefficient is

required to describe bacterial decay. Initial estimates

can be derived from the literature and refined through

calibration to observed bacteria data. For this study,

simulations were conducted with no die-off and then

with rates of 1.0 day-1. Guidance on selection of bacterial die-off rates is provided in Section 5. Salinity and

the dye tracer were treated as conservative materials

(no decay was specified).

— Initial concentrations: Concentrations of dye and

bacteria in each model segment are required for the

beginning of the simulation. For these simulations,

since initial conditions were not available, bacterial and

salinity simulations were conducted over a 30 day

period. The concentrations at the end of that period

were then used for the initial conditions in subsequent

simulations. The initial conditions of the dye tracer

were assumed to be zero, neglecting any background

concentrations.

Figure 6-10. Predicted variations in volumes near the mouth, near the midpoint, and at the upper extremity of the Trinity Estuary.

6-17
6.4.1.5. Model Simulations

Simulations were first conducted for salinity to insure

that model predictions adequately corresponded with

field observations. Simulations were conducted over

a period of one month. A comparison of the monthly

averaged salinities in the Trinity estuary, along with

maximum and minimum values, is provided in Figure

6-11. Figures 6-12 and 6-13 illustrate variations of

salinity with time at two locations in the estuary: near

mouth (Figure 6-12) and near the midpoint of the estuary (15 km up estuary; Figure 6-13).

Following evaluation of simulations of salinity, simulations of dye injections were conducted. In this illustrative example, it was assumed that data were not readily

available and no attempt was made to compare simulations with results of the dye study used as the basis

for establishing the buffer zone. This comparison

would be highly desirable in a practical application. Dye

simulations were conducted simulating the release of

Figure 6-11. Monthly averaged salinities in the Trinity Estuary versus distance upstream from its mouth.

Figure 6-12. Predicted variations in salinity during March,

1989, near the mouth of the Trinity Estuary.

Figure 6-13. Predicted variations in salinity during March,

1989, near the mid-point of the Trinity Estuary.

6-18
Figure 6-15. Spring tide dye simulations for the Trinity Estuary.

Figure 6-14. Neap tide dye simulations for the Trinity Estuary.

6-19
Figure 6-16. Predicted average, minimum and maximum bacterial concentrations for March versus distance from the mouth of

the Trinity Estuary assuming no die-off.

Figure 6-17. Predicted average bacterial concentrations during March, with standard deviations, versus distance from the

mouth of the Trinity Estuary assuming no die-off.

6-20
Figure 6-18. Predicted average, maximum and minimum bacterial concentrations during March versus distance from the mouth

of the Trinity Estuary assuming a bacterial die-off rate of 1.0 day -1.

Figure 6-19. Predicted average bacterial concentrations, with their standard deviations, for March versus distance from the

mouth of the Trinity Estuary, assuming a bacterial die-off rate of 1.0 day-1.

6-21
a slug of dye from the Harris WTP discharge. Simulations included a dye injection near the spring tide and

again near the neap tide. The results of these simulations are compared in Figures 6-14 and 6-15. The

neap tide simulations indicated little movement of the

dye centroid (Figure 6-14), while greater movement

occurs during the spring tide (Figure 6-15). However,

the centroid of the dye slug was predicted to move less

than 2 km after two days in either simulation.

Following salinity and dye simulations, simulations

were made of bacterial concentrations. For these

simulations, an extreme case was selected assuming

raw sewage with no disinfection was discharged continuously over the 30 day period of simulation. Simulations were first conducted assuming that there was

no die-off (treating bacteria as a conservative constituent) and then using representative die-off rates. The

results of these simulations are provided in Figures

6-16 to 6-20 as averages over the period of simulation.

The averages are compared to the minimum and

maximum over the period of simulation at each model

segment as well as to the standard deviations of the

bacterial concentrations. Figures 6-16 and 6-17 illustrate results assuming that bacteria act conservatively,

while Figures 6-18 and 6-19 illustrate projections assuming a die-off rate of 1.0 day-1. A comparison of the

monthly averaged concentrations for several die-off

rates is provided in Figure 6-20.

The results of these simulations indicate that a moderate die-off rate would probably reduce bacterial concentrations below the criteria of 70 counts/100 ml

outside of the buffer zone, extending 2 km both above

and below the sewage outfall. However, if die-off was

occurring at low rate, acceptable concentrations could

easily be exceeded, as demonstrated where the bacteria were assumed not to die-off (act conservatively).

More probably, the additional contamination observed

is due to non-point sources. This analysis did not

consider near-field effects or the possibility of bacterial

resuspension from sediments, which should be considered before determining the appropriate enforcement and/or allocation action. Additionally, this

application considered a flow regime over a single

month. Additional simulations, with collection of supporting field data, may be required for critical environmental conditions to evaluate model performance and

estimate variations in bacterial populations.

6.4.2. Example 2 - DO in a One-Dimensional

Estuary

This second WASP4 example is for a simple branching

estuary considering DO depletion. Given the nature of

Figure 6-20. Comparison of predicted bacterial concentrations for different die-off rates versus distance from the mouth of the

Trinity Estuary.

6-22
the pollution problem, the eutrophication kinetic subroutine (EUTRO4) is required. The water quality variables of concern consist of DO, CBOD, and

nitrogenous BOD. Water quality processes simulated

include reaeration, sediment oxygen demand, nitrification and deoxygenation of CBOD.

This level of kinetic complexity has been extremely

popular for simulating DO and the impact of oxygen

demanding substances. Model calibration will consist

of specification of the nitrification rate, CBOD deoxygenation rate, and reaeration rate. WASP4 provides

the option of internally calculating the reaeration rate

as a function of water depth and velocity. The reaeration rate will be manually specified for these simulations as model hydrodynamics are based upon tidal

averaged conditions.

6.4.2.1. Problem Setting

In this example, three dischargers have been identified

to the Rhode Estuary, including the city of Rhode, the

town Holcombville, and Port Holcomb. The Holcombville WWTP discharges to Holcomb Creek, a

tributary of the Rhode Estuary, while the Rhode and

Port Holcomb WWTP discharge to the mainstem estuary. The city of Rhode is presently considering

upgrading their WWTP to provide additional capacity.

The city of Rhode is presently out of compliance for

oxygen and proposes a modification of the existing

plant to provide additional capacity and to come into

compliance. The purpose of this example is to evaluate the proposed modifications. A summary of the

problems setting and treatment plant data is presented

in Figures 6-21 to 6-29 and Table 6-10.

Figure 6-21. Morphometry of the Rhode Estuary.

Figure 6-22. Mean salinity profile for the Rhode Estuary.

6-23
Figure 6-23. Results of the Rhode Estuary tracer study.

Figure 6-24. Average monthy flow at the Highway 64 USGS

gauge.

Figure 6-25. Mean monthly temperatures at the Highway 64

gauge.

6-24
Figure 6-26. Mean depths for the Rhode Estuary versus distance upestuary from its mouth.

Figure 6-27. Mean widths of the Rhode Estuary versus distance upestuary from its mouth.

6-25
Figure 6-28. Mean depths of Holcomb Creek versus distance upstream from its mouth.

Figure 6-29. Mean widths for Holcomb Creek versus distance upstream from its mouth.

6-26
6.4.2.2. System Characteristics

The upstream section above the fall line is gauged by

the USGS. The gauge is located near the crossing of

Highway 64. The estuary has popular sport and

commercial fisheries, including shellfish. The average

monthly flows and temperatures taken at the USGS

gauge are provided in Figures 6-24 and 6-25. The

measured depths and widths at mean tide are provided

in Figures 6-26 to 6-29. Mean tidal amplitude is 0.28

m. The pertinent water quality criterion is a minimum

DO of 5.0 mg/l. From historical data, critical DO conditions occur in mid-August when the flow for the

Rhode River at the USGS gauge is approximately 20

cms, and the Holcomb Creek (ungauged) flow is estimated to be 10 cms. Average August water temperatures is 27 oC.

6.4.2.3. Supporting Studies

Historical data within the study area were limited. Data

were available for temperature at the USGS gauge.

For this level of study, it was decided that an initial

water quality survey would be conducted during the

week of August 1. High and low slack measurements

of DO, NH3-N, BOD5, and salinity were taken along

the estuary and creek. The slack tide data were translated to mid-tide for comparison with the tidally averaged model. Flows during the study period for the

Rhode River at the USGS gauge were approximately

20 cms, and the Holcomb Creek (ungauged) flows

were estimated to be 10 cms, with averaged water

temperatures of 27 oC at the USGS gauge. A single

measurement near the USGS gauge indicated a BOD5

of 0.7 mg/l in the Rhode River from that study. Two

measurements of SOD were available, determined

using an in-situ respirometer, from previous studies. A

value of 1 g m-2 day-1 was measured in the lower

estuary approximately 2 km above Port Holcomb and

2 g m-2 day-1 was measured approximately 1 km

down-estuary of the Rhode WWTP discharge. A dye

study was conducted with Rhodamine WT injected as

a slug near the Rhode City WWTP discharge. The

results of the dye study were used to evaluate model

performance.

6.4.2.4. Model Application

This example requires similar information as the previous WASP4 example, with the exception of pollutant

kinetics. However, it was elected not to use a hydrodynamic model for this application. Instead, simulations of tidally averaged conditions were conducted.

Model inputs are described in detail in the Appendix

available from the Center for Exposure Assessment

Modeling, and are summarized below:

-- General model information: Given the nature of the

pollution problem, the eutrophication kinetic subroutine (EUTRO4) is required for this example. The water

quality variables of concern consist of DO, CBOD, and

nitrogenous BOD. Water quality processes simulated

include reaeration, sediment oxygen demand, nitrification and deoxygenation of CBOD.

-- Model Network: Analysis of the monitoring data

indicated significant longitudinal gradients, with small

lateral and vertical variations, allowing application of a

one-dimensional model. A network was established

consisting of 15 segments in the Rhode Estuary and 5

segments in Holcomb Creek. The variations in bottom

morphometry and water quality were reasonably regular, and for simplicity segments were delineated every

two kilometers. The depths of the segments were

determined as well as segment volumes and interfacial

areas from available morphometry data. The resulting

network is illustrated in Figure 6-30.

-- Dispersion coefficients: These coefficients are required to describe tidal mixing between all model segments. Initial estimates can be

Rhode City WTP

Present: Trickling filter plant presently at capacity.

Proposed: Activated sludge plant.

Present Proposed

Flow MGD 17 24

BOD5 mg/L 60 30

CBODu (1) mg/L 120 60

NH3-N mg/L 30 20

DO mg/L 5 5

(1) Based on long term BOD estimates of CBODu ⁄ CBOD5 = 2.0

Holcombville

Present

Flow MGD 1.2

BOD5 mg/L 65

CBODu (1) mg/L 130

NH3-N mg/L 40

DO mg/L 5

Port Holcomb

Present

Flow MGD 0.48

BOD5 mg/L 80

CBODu (1) mg/L 160

NH3-N mg/L 42

DO mg/L 5

Table 6-10. Treatment Plant Effluent Characteristics

6-27
derived from the literature and refined through calibration to dye or salinity data. Their determination is

described below.

-- Segment volumes: The initial volume of each segment is required, as well as a description of how the

volume changes with flow. Volumes were determined

from segment width and depth (taken from hydrographic maps) and segment length (user specified).

-- Flows: Net river flows during the survey period were

20 cms for the Rhode River and 10 cms for Holcomb

Creek.

-- Boundary concentrations: Boundary concentrations

are required for CBOD, NBOD, and DO at segments

1, 15 and 20 (ocean and tidal river boundaries).

-- Pollutant loads: Loading rates are required for

CBOD, NBOD, and DO for each point source (WWTP

and tidal rivers).

-- Model parameters: Specification of salinity, temperature and sediment oxygen demand distribution

both spatially and temporally.

-- Model constants: Nitrification rate, CBOD deoxygenation rate, and reaeration rate.

-- Initial concentration: Concentrations of CBOD,

NBOD, and DO in each model segment are required

for the beginning of the simulation. However, where

simulations are conducted until steady-state is

achieved, initial conditions are irrelevant.

6.4.2.5. Model Simulations

Simulations were first conducted for salinity and the

dye tracer in order to evaluate predicted transport. To

simulate steady-state salinity distribution using EUTRO4, the CBOD system was used with no decay

specified (treated as a conservative material). Boundary conditions were established for salinity and initial

conditions were set to zero. Simulations were then

conducted until a steady-state salinity distribution was

achieved.

The exchange coefficients in this example were estimated first from the salinity profile, indicating a dispersion rate of approximately 30 m2

 sec-1. Boundary

flows and concentrations were input, with 30 ppt as the

ocean boundary, and simulations were conducted for

a period of 50 days using constant boundary conditions. The 50-day period was selected as sufficient for

the predicted concentrations to reach steady-state for

comparison with field data. Simulations indicated that

a constant exchange coefficient of 22 m2 sec-1 allowed

reasonable representation of the salinity distribution. A

comparison of model predictions and field data for

different exchange coefficients is provided in Figure

6-31.

Figure 6-30. Model segmentation for the Rhode Estuary.

Figure 6-31. Comparison of predicted and observed salinities

for different values of the dispersion coefficient. (m2/s).

6-28
Beginning August 1, in conjunction with other water

quality surveys, a dye study was conducted. Rhodamine WT was injected in the effluent of the Rhode

City WTP. The dye density was adjusted with alcohol

to avoid sinking, and a steady concentration of 8 mg/l

was maintained in the effluent over one complete tidal

cycle. This 8 mg/l concentration in the effluent was

calculated to provide a completely mixed concentration of approximately 100 ppb in the Rhode Estuary

near the point of discharge. Monitoring continued for

8 days following the discharge. High and low slack

data were obtained and processed to provide tidally

averaged concentrations. As with salinity, the dye was

simulated using the CBOD system and treating it as a

conservative material. Boundary concentrations were

set to zero and loadings of dye were specified with a

duration of 12.5 hours. Since the model had been

previously calibrated using salinity data, the dye data

were used to evaluate model performance. The predicted and observed concentrations are compared in

Figure 6-32, and as illustrated, the simulations were

considered acceptable.

Following evaluation of the simulations of salinity and

the dye tracer, simulations were conducted for NBOD,

CBOD, and then DO. This sequence results from

NBOD and CBOD being unaffected by DO (if DO does

not approach zero), while DO is affected by these

parameters as well as SOD and reaeration. Therefore, simulations proceed from the simple to the complex.

Simulations were conducted first using literature values for the nitrification rate and CBOD deoxygenation

rate. It was elected to specify a reaeration rate rather

than use model formulations to calculate a rate, because reaeration rates had been measured in the

vicinity under similar conditions. The salinity, SOD and

temperature were specified in the model parameter

list. The SOD was assumed to be 2.0 g m-2 day-1 in

the vicinity of the Rhode WWTP and 1.0 elsewhere.

Simulations were conducted with varying nitrification

and deoxygenation rates. Field data and model predictions are compared in Figures 6-33 to 6-36. While

no statistical analyses were performed, visual inspection indicated that model predictions were adequate for

this study.

6.4.2.6. Model Predictions

Once reasonable predictions were obtained, simulations were conducted projecting DO, NBOD and

CBOD concentrations in the estuary following implementation of the proposed modifications at the Rhode

WWTP (Table 6-10, see Figure 6-37). These simulations suggested that little change would be expected

in the DO concentrations as a result of the proposed

modifications.

Figure 6-32. Comparison of measured and observed dye concentrations.

6-29
Figure 6-33. Measured and predicted DO concentrations in the Rhode Estuary versus distance upestuary from its mouth.

Figure 6-34. Predicted and observed NBOD and CBOD concentrations in the Rhode Estuary versus distance upestuary from its

mouth.

6-30
Figure 6-35. Predicted and observed NBOD and CBOD concentrations in the Rhode Estuary versus distance upestuary from its

mouth.

Figure 6-36. Measured and predicted DO concentrations in Holcomb Creek versus distance upstream from its mouth.

6-31
The final waste load allocation should not result from

a single model projection. The model should be evaluated using independent data, if possible. A component analysis should be performed to determine the

relative contributions of SOD, reaeration, CBOD and

NBOD to the DO concentrations. The component

analysis may provide information which would be useful in project design. Sensitivity analyses should also

be performed to determine the effects of assumptions

concerning the selection of model parameters. Consideration should also be given to the applicability of

calibrated rates to future conditions. Examples include

CBOD deoxygenation and nitrification rates and sediment oxygen demand, which can decrease under future conditions where improved wastewater treatment

occurs. The tested model can be used to estimate the

reduction in waste load required to meet water quality

objectives.

Port Holcomb was clearly in violation of its permit,

discharging essentially raw wastewater into the estuary. However, as a result of its advantageous location,

its discharges seemed to have little impact on DO

concentrations, when averaged over the estuarine

cross-section. Additional field and modeling work is

required to identify the extent of the problem. However, as a result of the bacteriological problem that has

resulted, permit/enforcement action is pending which

would impact its BOD release as well.

Figure 6-37. Comparison of DO predictions under existing and proposed conditions for the Rhode City WWTP.

6.4.3. Example 3 - Nutrient Enrichment in a

Vertically Stratified Estuary

The third and fourth examples apply to a vertically

stratified estuary. This type of estuary has significant

differences in water quality both longitudinally and with

depth. Estuary widths are still narrow enough that

lateral variations in water quality are not important;

vertical stratification is such, however, that the water

column must be divided into discrete vertical layers.

This type of characterization typically occurs in deeper

estuaries or in areas characterized by a salinity intrusion wedge.

6.4.3.1 Problem Setting

The city of Athens, population 180,000, is located on

the upper reaches of Deep Bay (Figure 6-38). This

relatively deep estuary is driven by moderate 1 meter

tides and a large but seasonably variable inflow from

Deep River, which is gauged above the fall line. The

seaward reaches of Deep Bay are used for both commercial fishing and shellfishing, and the upper reach is

spawning habitat. Boating and recreational fishing are

popular, as are several bathing beaches. Pertinent

6-32
criteria and water quality goals are 5.0 mg/L for DO

and 25 μg/L chlorophyll a.

Athens is maintaining a poorly operated secondary

wastewater treatment plant that discharges from a

surface pipe near shore 15 km from the mouth of Deep

Bay. Periodic episodes of low benthic DO near the

discharge and moderate phytoplankton blooms downstream have been occurring. Renovation of the plant

to high performance secondary or possibly tertiary

treatment is being considered, as are point and nonpoint source controls in the watershed.

Bathymetric surve6.4.3.2 Deep Bay Network

Analysis of the monitoring data show significant differences between surface and bottom mean velocity and

salinity, indicating a partially mixed estuary. Because

of these vertical variations and because bottom water

DO was reported to be low, a 2 dimensional x-z network was chosen. For convenience, segments were

delineated every 2 kilometers, giving 20 water column

segments with 2 vertical layers of 10 segments each.

Surface water segments are a uniform 2 meters in

depth, while underlying water segments range from 10

meters near the mouth to 0.5 meters upstream. The

resulting network is illustrated in Figure 6-40.

6.4.3.3 Deep Bay Salinity

Simulation of salinity allows calibration of dispersion

Figure 6-38. Deep Bay location map.

Rms

Velocity2

Net

Velocity2

Station Date Tidal

Range1

Surface Bottom Surface Bottom

S1 4/19-23 0.9 340 260 +2.1 +0.2

(km 3) 6/13-17 1.0 350 260 +0.6 +0.0

8/14-18 0.9 330 260 +0.2 -0.0

S2 4/19-23 1.1 370 270 +5.3 +0.7

(km11) 6/13-17 1.2 350 260 +1.4 +0.2

8/14-18 1.1 350 250 +0.4 +0.0

S3 4/19-23 0.8 320 310 +10.4 +8.9

(km 17) 6/13-17 0.9 300 300 +2.8 +2.3

8/14-18 0.8 290 280 +0.7 +0.6

1

meters 2

cm/sec

Table 6-11. Summary of Deep Bay Tidal Monitoring Data

6-33
Salinity

(kg/L)

Temperatu

re (oC)

Secchi

Depth (m)

Station Date Surface Bottom Surface Bottom

S1 4/19-23 14.0 21.1 14 15 3.3

6/13-17 22.5 24.5 23 22 2.7

8/14-18 27.2 28.0 22 21 3.0

S2 4/19-23 15.7 15.5 15 17 1.7

6/13-17 8.5 12.3 25 22 1.3

8/14-18 19.5 21.8 23 22 1.5

S3 4/19-23 0.1 0.3 16 18 0.7

6/13-17 1.0 3.1 26 23 0.5

8/14-18 9.1 10.7 24 22 1.0

Table 6-12. Summary of Deep Bay Estuarine Data

Water Quality (mg/l)

 Present

Constituent Minimum Maximum Watershed Controls

TKN 0.1 0.4 0.02

ORG-N 0.0 0.3 0.01

Nitrate-N 0.3 0.6 0.10

Ortho-P 0.04 0.12 0.01

Organic-P 0.01 0.05 0.005

BOD5 0.5 1.0 0.2

DO 5 14 7-14

SS 10 1000 10-250

Monthly

Flow

(m3/sec)

Month Average Survey

Year

Month Average Survey

Year

January 90 85 July 60 40

February 80 75 August 50 20

March 120 150 Sept 50 40

April 210 300 October 110 150

May 175 200 Nov 140 140

June 120 100 Dec 130 150

Table 6-13. Deep River Data

Figure 6-39. Deep Bay navigation chart.

Design Capacity - 60 MGD

Secondary Treatment, with problems

Nitrogen Phosphorus

Alternative DO BOD5 ORG NH3 NO3 Org PO4

Present 4 40 15 15 0 3 7

Good Secondary5 20 0 15 15 3 7

Tertiary 6 10 0 2 10 0 0.5

Table 6-14. Summary of Athens POTW Effluent Data

6-34
coefficients and density currents. Information needs

are as follows:

—General model information: One system is simulated

-system 1 is interpreted as salinity, and systems 2-8

are bypassed. The simulation begins on day 21, representing the April 21 survey, and ends on day 147, a

week following the August 11 survey.

—Dispersion coefficients: This estuary requires two

types of dispersion coefficients - longitudinal dispersion (representing tidal mixing) and vertical eddy diffusion.

—Segment volumes: Mean tide volumes are specified

for all surface and subsurface segments.

—Flows: Tributary flow is partitioned to surface and

bottom segments and routed through the estuary.

Monthly river flows are specified. A density flow from

the ocean is routed upstream

along the bottom with vertical entrainment and downstream flow along the surface.

—Boundary concentrations: A constant downstream

concentration of 30 mg/L was assumed. Upstream

salinity concentrations are set to 0.

—Pollutant loads: No loads are input.

—Environmental parameters: No parameters are input.

—Kinetic constants: No constants are needed.

—Environmental time functions: No time functions are

needed.

Figure 6-40. Deep Bay model segmentation.

6-35
—Initial concentrations: Initial salinity concentrations

are assigned each segment based upon an April survey. Dissolved fractions are set to 1.0.

Analysis of the depth-averaged salinity data during the

three monitoring periods indicates estuarine-wide dispersion from 20 to 50 m2

/sec. A constant value of

30 m2/sec was assigned. The tributary inflow was

partitioned 70% to surface and 30% to bottom layers.

Analysis of bottom current data indicates that a net flow

of approximately 10 m3/sec enters the estuary along

the bottom at the mouth. This bottom inflow was attenuated upstream, entraining a fraction to the surface

to satisfy continuity and match surface and bottom

salinity data. The salinity simulation began on the first

day of the April survey, using survey results as initial

conditions. The simulation continued through August,

with water column concentrations printed out corresponding to the July and August surveys. Results are

illustrated in Figure 6-41.

6.4.3.4 Deep Bay Dye Study

To better evaluate vertical and horizontal dispersion

near the Athens outfall, a dye study was carried out.

Information needs for the model are similar to those for

salinity:

—General model information: One system is simulated

-system 1 is interpreted as dye, and systems 2-8 are

bypassed. The simulation begins on day 75, the day

preceding the June 14 dye study, and terminates on

day 110.

—Dispersion coefficients: The same longitudinal and

vertical dispersion coefficients calibrated in the salinity

simulation are used. The upstream portion of the network is divided into lateral segments, and lateral dispersion coefficients are required.

Figure 6-41. Deep Bay salinity Apr-Aug mean response.

6-36
—Segment volumes: The same mean tide volumes

from the salinity simulation are used, except the upstream segments are divided into three for lateral

resolution.

—Flows: The same flows from the salinity simulation

are used, except the flow is partitioned laterally in the

upper network.

—Boundary concentrations: Upstream and seaward

boundary concentrations of 0 are specified.

—Pollutant loads: A one day load of dye is specified

for the near shore surface segment adjoining the Athens POTW.

—Environmental parameters: No parameters are

needed.

—Kinetic constants: One constant is specified - a low

nitrification rate is entered, representing net loss of

dye.

—Time functions: No time functions are needed.

—Initial concentrations: Initial concentrations of 0 are

entered.

Beginning on June 14 (day 75), Rhodamine WT was

metered into the 3 m3/sec waste stream. A steady 10

mg/L concentration in the effluent was maintained for

one day. High and low slack samples were taken daily

for one week along the near shore, center channel, and

far shore at both surface and bottom. The slack tide

data were translated to mid-tide for comparison with

the tidal-averaged model. The salinity network was

modified for the dye study to calculate lateral mixing

near the outfall (Figure 6-40). Vertical and lateral dispersion coefficients in the upper network were adjusted to best fit the dye profiles. Lateral and

longitudinal variations in the surface layer after one day

are shown in Figure 6-42. The lateral variations had

virtually disappeared by the second day. Vertical and

longitudinal variations in mid-channel after one and

two days are shown in Figure 6-43. Mid-channel profiles for the first 2 weeks are shown in Figure 6-44. The

model was judged sufficiently calibrated for estuarinewide transport.

6.4.3.5 Deep Bay Total Nutrients

To evaluate eutrophication potential throughout Deep

Bay, simulations of total nitrogen and phosphorus

were conducted. Information needs are as follows:

—General model information: Two systems are simulated - system 1 is interpreted as total nitrogen and

system 3 as total phosphorus. Systems 2 and 4-8 are

bypassed. The simulation begins on day 1 (April 1) and

terminates on day

Figure 6-42. Deep Bay dye study June 15, surface.

6-37
Figure 6-43. Deep Bay dye study center channel, surface and bottom.

Figure 6-44. Deep Bay dye study center channel, surface.

6-38
210 (early November). An extra benthic segment is

specified to receive depositing nutrients.

—Dispersion coefficients: Same as salinity simulation.

—Segment volumes: Same as salinity simulation.

—Flows: The same water column flows used in the

salinity simulation are used. In addition, settling and

deposition velocities for particulate phosphorus are

specified.

—Boundary concentrations: Upstream and ocean

concentrations of total nitrogen and phosphorus must

be specified.

—Pollutant loads: Constant loads of nitrogen and

phosphorus in the effluent are specified for the segment adjoining Athens POTW.

—Environmental parameters: No parameters are

needed.

—Kinetic constants: No constants are needed.

—Time functions: No time functions are needed.

—Initial conditions: Initial concentrations of total nitrogen and total phosphorus are specified for each segment, along with the dissolved fractions.

Total nitrogen loading from Deep River and Athens

POTW were entered and representative settling and

deposition velocities of 5 and 2.5 meters/day for particulate phosphorus were input. It was assumed that

80% of the phosphorus and 100% of the nitrogen in

the water was dissolved and not subject to settling.

Total nitrogen and phosphorus profiles for surface

waters during August are shown in Figure 6-45. These

profiles indicate nitrogen limitation, as the N:P ratio is

less than 25. If all the nitrogen is converted to biomass,

then phytoplankton levels of 500 μg/L chlorophyll a are

possible near the outfall. Of course light and nutrient

limitations to growth along with respiration and death

should keep biomass levels to a fraction of this.

Several useful sensitivity studies could suggest possible waste management strategies. First, a component

analysis could reveal the relative contributions of Deep

River, Athens POTW, and the ocean to total nitrogen

and phosphorus throughout Deep Bay. Second, simulations with the effluent at improved secondary and

tertiary treatment levels could suggest the expected

impact of point source controls. Third, simulations with

the river concentrations at various levels could suggest

the expected impact of watershed controls.

Figure 6-45. Deep Bay total N and P - August 11, surface and bottom.

6-39
Figure 6-46. Deep Bay dissolved oxygen - June-Sept, surface and bottom.

Figure 6-47. Deep Bay phytoplankton - June-Sept, surface.

6-40
There are significant advantages and disadvantages

in simulating nutrients without phytoplankton to estimate eutrophication potential. The advantages lie in

the lessened requirements for field data and modeling

resources. Several sites could be evaluated for nutrients only, as compared to the resources required to

apply a complex eutrophication model to a single

estuary. Further, some states have standards (or

goals) for nutrient concentrations and do not require

projections of algal density.

The disadvantages of simulating only nutrients relate

to several simplifying assumptions required for this

type of application. For example, the rate of conversion of dissolved phosphorus into particulate form is

dependent upon algal concentration and growth rate.

Because algal dynamics are not simulated, these values must be estimated. Further, because algal growth

is directly related to nutrient concentrations, calibration

parameters may not apply well to future conditions of

different nutrient levels. Finally, for situations where

algal density is of ultimate concern, nutrient projections

alone will only provide an indirect estimate of expected

phytoplankton concentrations.

6.4.4 Example 4 - Eutrophication in a Vertically

Stratified Estuary

This case study considers simulation of seasonal eutrophication in Deep Bay. The problem setting and

model network are as described in the preceding section. Here, the entire eutrophication process is simulated, including nutrients, phytoplankton,

carbonaceous BOD, and DO. This is typically the

highest level of complexity used for conventional pollution problems. It requires significant amounts of field

data and careful calibration to apply with confidence.

For this example, it is assumed that two intensive

surveys in June and August along with biweekly slack

tide surveys allowed calibration of a seasonal simulation. Model information needs are as follows:

—General model information: All 8 systems are used

here. Extra benthic segments are specified to simulate

long term benthic-water column exchanges of nutrients and DO. The simulation begins on day 1 (April 1),

and terminates on day 210 (early November).

—Dispersion coefficients: The same water column

dispersion coefficients from the salinity simulation are

used. Extra pore water dispersion coefficients for benthic-water column exchange of dissolved chemicals

must be specified.

—Segment volumes: The same water column volumes from the salinity simulation are used. A benthic

volume underlies each bottom water segment.

—Flows: The same flows from the salinity simulation

are used.

—Boundary concentrations: Tributary and ocean concentrations of all 8 systems must be specified.

—Pollutant loads: Constant loads for all 8 systems in

the effluent must be specified for the segment adjoining Athens POTW.

—Environmental parameters: Values for average salinity and background sediment oxygen demand for

each segment are given. The time variable temperature and light attenuation functions used by each segment must be specified.

—Kinetic constants: Rate constants, temperature coefficients, half saturation constants and other kinetic

information must be specified. Processes include nitrification, denitrification, phytoplankton growth (light and

nutrient limitation), phytoplankton death, carbonaceous deoxygenation, reaeration, mineralization, and

benthic decomposition. If a constant is not specified,

then the relevant reaction or process is bypassed.

—Environmental time functions: Time variability in

temperature, light extinction, incident light, and length

of daylight must be specified.

—Initial conditions: Initial concentrations of each state

variable and the fraction dissolved in each model

segment are required. The solids settling field affecting

each variable must also be specified.

The simulation proceeded from April 1 to November 1,

with seasonal light, temperature, and flow data provided. Figures 6-46 and 6-47 show predicted upper

layer chlorophyll a and lower level DO during mid July,

August and September. Chlorophyll concentrations

increase dramatically over the course of the summer,

and lower layer DO decreases to a minimum of about

4 mg/L. Diurnal swings about this minimum are predicted to be minimal. The impact of phytoplankton

growth is significant on upper layer DO, with levels

maintained near saturation and diurnal swings of about

one and a half mg/L. Phytoplankton die-off depresses

both upper and lower layer DO somewhat. Phytoplankton growth is limited somewhat by nitrogen, but more

by light. Sensitivity studies show the relative importance of the variable light attenuation coefficients, the

phytoplankton saturating light intensity, and

6-41
the calibrated Michaelis-Menton nitrogen half saturation coefficient.

Calibration of a model of this complexity is a significant

task and cannot be reduced to a neat formula to be

summarized here. Some issues of note are the long

seasonal or multiyear time scale and the complex

interaction among variables, environmental conditions, and kinetic constants. While some water quality

models can be calibrated to surveys conducted over a

few days, a calibration data set for a eutrophication

model typically requires a full season of data. The

implications of this are apparent, as data collection

programs for model calibration and validation will require years.

Regulations related to eutrophication can differ significantly from state to state. Water quality standards,

criteria, or goals can relate to chlorophyll, transparency, nutrients, and/or DO. Selection of critical conditions is very difficult because of the need to

characterize a season or even an entire year, not a

single day or event. This is complicated by the kinetic

interactions. For example, light attenuation is often

critical, but choice of reasonable design extinction

coefficients is not often given sufficient study. Actual

data for a representative or drought year are often

used instead of statistical characterizations of design

conditions. As another approach, constant steady conditions of statistical significance are also used.

For performing a waste load allocation on Deep Bay,

the calibration year combining high spring flows with

very low summer flows and warm temperatures was

judged to provide reasonable worst case conditions. A

series of simulations with various combinations of

POTW treatment levels and watershed controls were

performed. It was concluded that tertiary treatment

without watershed controls could still result in phytoplankton levels of 30 μg/L and lower DO levels of 4.5

mg/L. A combination of watershed controls and advanced secondary treatment was judged most reasonable.

6.4.5. Example 5 - Ammonia Toxicity in a TwoDimensional Estuary

The fifth and sixth examples consider toxic pollutants

in a laterally variant two-dimensional estuary. This

type of estuary characterization differs from the previous two in that lateral variations in water quality are

significant enough that the estuary cannot be assumed

to be laterally well mixed. The need for describing

lateral variation in water quality sometimes is dictated

by the pollutant of concern as well as the nature of the

system. For example, point sources of pollutants that

act in an indirect manner (e.g. oxygen demanding

substances, algal nutrients) often can be treated as

laterally homogeneous even when significant lateral

gradients exist near the outfall. These pollutants typically exert their maximum influence a significant distance away from the outfall, where conditions are more

likely to be laterally well mixed. Direct-acting pollutants

such as those causing acute toxicity will often require

lateral variation to be described, as concentrations near

the outfall (where lateral gradients will be highest) are

of primary concern.

For model application to a two-dimensional estuary,

multiple segments extend across the width of the estuary, allowing for the description of lateral changes in

water quality. Depending upon the degree of vertical

stratification, the system can be treated as two-dimensional (no vertical stratification) or three-dimensional

(with vertical stratification). Again, vertical layer(s) to

describe sediment quality can be added to either framework (using WASP4) when necessary to describe sediment/water interactions.

The fifth case study concerns ammonia toxicity and is

simulated using the kinetic submodel TOXI4. Ammonia

toxicity is often a concern near discharges of municipal

waste, as the unionized form of ammonia is toxic to fish

and other aquatic life. Two processes are simulated -

the dissociation of ammonia to ionized and aqueous

forms and the first-order loss of total ammonia through

nitrification. Model kinetic inputs for this simulation are

quite straightforward. All that is required is a description

of the ionization constant for ammonia and the ammonia loss rate.

6.4.5.1. Problem Setting

The City of Boatwona, population 285,000, is located

on the shore of the Boatwona Bay (Figure 6-48). This

relatively shallow estuary is driven by moderate 0.50

meter tides and a medium but seasonably variable

inflow from the Boatwona River, which is gauged above

the fall line. The Boatwona estuary provides for a rich

commercial fishing and shellfishing industry. Boating

and recreational fishing are popular, as are several

bathing beaches.

Just outside the City of Boatwona is a large fertilizer

plant which discharges into the estuary. Because this

discharge is high in ammonia there have been instances of ammonia toxicity in the bay. Unionized

ammonia is toxic to fish at fairly low concentrations.

The water quality criterion is 0.08 mg/L for a 30 day

average.

Bathymetric surveys have produced a chart of soundings at low tide, used for navigation (Figure 6-49).

Three surveys were conducted (May, August and November) to characterize tide, temperature, and pH.

Continuous velocity data, temperature data and pH

6-42
data were obtained from moorings at sampling stations

S1, S2, and S3 over these three five-day periods

(Table 6-15).

The Boatwona River flow, Ammonia and pH data are

summarized as monthly averages (Table 6-16).

6.4.5.2. Boatwona Estuary Network

Analysis of the monitoring data illustrates a definite

lateral flow pattern. Because of these lateral flows, the

bay was segmented to demonstrate the fate and transport of the ammonia discharge (Figure 6-50). Segments were defined every 5 kilometers, giving 6 water

column segments.

6.4.5.3. Boatwona Estuary Nitrogen Simulation

The WASP4 model was given flow information averaged from the continuous flow meters that were installed during the sampling surveys.

—General model information: One system is simulated

-system 1 is interpreted as total ammonia-nitrogen.

The organic toxic chemical model TOXI4 was used for

this study because of its capabilities of simulating both

unionized and ionized forms of chemicals. The remaining sys- Figure 6-49. Boatwona Estuary depth chart.

S1 S2 S3

Sample

Time

Temp pH Temp pH Temp pH

May 17.0 6.8 16.5 7.1 15.3 6.9

August 19.2 6.9 18.2 6.9 17.0 7.0

Nov 17.4 6.8 16.7 6.8 16.9 6.8

Table 6-15. Boatwona Estuary Survey Data

Month Average Flow (cm) pH N

January 12 6.2 2.3

February 15 6.4 0.8

March 18 6.1 2.1

April 22 6.2 4.2

May 15 6.6 6.6

June 11 6.8 2.3

July 8 6.9 9.4

August 10 7.1 7.3

September 15 6.8 3.7

October 13 6.8 0.9

November 14 6.6 1.3

December 13 6.7 4.2

Table 6-16. Boatwona River Survey Data

Figure 6-48. City of Boatwona waste water treatment plant

location.

6-43
Boundary concentrations: Monthly averaged ammonia

concentrations are assumed for the Boatwona River.

The seaward boundaries are assumed zero.

Pollutant loads: Based upon continuous monitoring

studies conducted at the fertilizer plant.

Model parameters: Specification of temperature and

pH distribution both spatially and temporally.

Kinetic constants: Ionization constants and nitrification rate for ammonia.

Environmental time functions: Temporal temperature

functions.

Initial concentrations: Initial ammonia concentrations

within the estuary are assumed zero. Dissolved fractions are set to 1.0.

Figure 6-51 shows selected output from this simulation

of ionized/un-ionized ammonia concentrations over

time in the segment receiving the loading. Model

calibration would consist of conducting a dye study as

previously mentioned. A dye study would then be

followed by calibration of the ammonia loss rate to total

ammonia data. Ammonia dissociation parameters are

chemical constants and do not require adjustment

during the calibration process.

It is important to note that the ammonia loss rate is a

lumped parameter, combining (potentially) several different processes. The dominant loss process will typically be nitrification, but also will include phytoplankton

uptake. Hydrolysis of organic nitrogen and sediment

ammonia release can also affect the net loss rate.

Algal uptake/recycle of ammonia can be especially

important in eutrophic systems.

Waste load allocation for ammonia toxicity consists of

determining the maximum allowable loading to comply

with water quality standards at critical environmental

conditions. pH must be included with temperature and

flow as an important environmental condition, as pH

and temperature determine the percentage of total

ammonia in un-ionized form. It should be noted that

there is uncertainty in the appropriateness of current

ammonia criteria, due to the limited range of data

available in describing toxicity. Current research indicates that the toxicity of the un-ionized ammonia may

vary with changes in temperature and pH. This information is not reflected in present criteria.

6.4.6. Example 6: Alachlor in a Laterally Variant

Estuary

The sixth example study considers the fate of a hydrophilic, reactive chemical in a two- dimensional estuary.

This example represents simulation of any hydrophilic,

reactive chemical. These chemicals typically have

relatively high solubility and low affinity for solids, and

are subject to transformation (and possible degradation) in the environment. Possible transformation

processes include hydrolysis, photolysis, oxidation,

reduction, and biodegradation. In addition, volatilization can lead to loss of chemical from the water.

The same estuary is used as for example 5; however,

benthic sediments also are being considered. Two

layers of benthic sediments are simulated - upper

surficial sediment and deep sediments. This simulation uses Systems 1 through 3 in TOXI4. Two types

of solids are represented, corresponding to inorganic

and organic materials, respectively. System 1 represents the pollutant. System 2 represents inorganic

solids, and System 3 represents organic solids. Environmental fate parameters for this simulation are those

for the pesticide Alachlor, and were taken from

Schnoor et al. (1987). Volatilization and hydrolysis

were found to be insignificant for this pollutant, with

biodegradation serving as the main route of degradation. Biodegradation will be treated as a first-order loss

process for this simulation, with separate values used

for the water column and the sediment.

Figure 6-50. Boatwona Estuary flow pattern.

6-44
Readers viewing the input file will find that it varies only

slightly from the one for the previous example. Ionization coefficients have been removed. The first-order

biodegradation rate constants are lower, and the partition coefficient is higher than values in the previous

example. Figure 6-52 displays selected results for the

input values, indicating the response of the water

column and benthic sediments to changes in pollutant

loading. No discussion of the WLA significance of this

example is given. This example is provided primarily

to serve as a template for general application.

6.5 References

Ambrose, R.B., Wool, T.A., Connolly, J.P., Schanz,

R.W. 1988. WASP4, A Hydrodynamic and Water

Quality Model - Model Theory, User’s Manual and

Programmer’s Guide. EPA/600/3-87/039, U.S. Environmental Protection Agency, Athens, Georgia.

Dyer, K.R., 1973. Estuaries: A Physical Introduction.

John Wiley & Sons, New York.

Mills, W.B., Porcella, D.B., Ungs, M.J., Gherine, S.A.,

Summers, K.V., Mok, L., Rupp, G.L. and Bowie, G.L.,

1985. Water Quality Assessment: A Screening Procedure for Toxic and Conventional Pollutants in Surface and Ground Water Part 1, EPA/600/6-85/002b,

U.S. Environmental Protection Agency, Athens, Georgia.

Schnoor et. al. 1987. Processes, Coefficients and

Models for Simulating Toxic Organics and Heavy Metals in Surface Waters. U.S. Environmental Protection

Agency, Athens, Georgia, EPA/600/3-87/015.

Figure 6-51. Ammonia simulation results.

6-45
Figure 6-52. Hydrophobic (Alachlor) chemical simulation for example 6.

6-46
6.5 References

Ambrose, R.B., Wool, T.A., Connolly, J.P., Schanz,

R.W. 1988. WASP4, A Hydrodynamic and Water

Quality Model - Model Theory, User’s Manual and

Programmer’s Guide. EPA/600/3-87/039, U.S. Environmental Protection Agency, Athens, Georgia.

Dyer, K.R., 1973. Estuaries: A Physical Introduction.

John Wiley & Sons, New York.

Mills, W.B., Porcella, D.B., Ungs, M.J., Gherine, S.A.,

Summers, K.V., Mok, L., Rupp, G.L. and Bowie, G.L.,

1985. Water Quality Assessment: A Screening Procedure for Toxic and Conventional Pollutants in Surface and Ground Water Part 1, EPA/600/6-85/002b,

U.S. Environmental Protection Agency, Athens, Georgia.

Schnoor et. al. 1987. Processes, Coefficients and Models for Simulating Toxic Organics and Heavy Metals in

Surface Waters. U.S. Environmental Protection

Agency, Athens, Georgia, EPA/600/3-87/015.

Thomann, R.V. 1972. Systems Analysis and Water

Quality Management. McGraw-Hill, New York.

Thomann, R.V. and Fitzpatrick, J.J. 1982. Calibration

and Verification of a Mathematical Model of the Eutrophication of the Potomac Estuary. Prepared for Department of Environmental Services, Government of the

District of Columbia, Washington, D.C.

6-47

DISCLAIMER 

We have made efforts to ensure that this electronic document is an accurate 

reproduction of the original paper document. However, this document does not 

substitute for EPA regulations; nor is it a regulation itself. Thus, it does not and 

cannot impose legally binding requirements on EPA, the states, tribes or the 

regulated community, and may not apply to a particular situation based on the 

circumstances. If there are any differences between this web document and the 

statute or regulations related to this document, or the original (paper) document, 

the statute, regulations, and original document govern. We may change this 

guidance in the future. 

Supplemental material such as this disclaimer, a document abstract and glossary 

entries may have been added to the electronic document.