&EPA
          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
          Estuaries

          Part 2
          Application of Estuarine
          Waste Load Allocation Models

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TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
       Book III: Estuaries-
       Part 2: Application of Estuarine Waste Load Allocation Models

EPA DOCUMENT NUMBER:  EPA 823/R-92-003  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

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        FOR




Part    Application of                            Allocation
                                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, Rl

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

                  U.S. ENVIRONMENTAL PROTECTION AGENCY
                               401 M Street, S.W.
                             Washington, DC 20460

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                              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

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    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 N BOD 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

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                                List of
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

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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 etal. (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 etal. (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

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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

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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
                                       VIM

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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
                                        [X

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                                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
           [Amboroseand 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

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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 etal. (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 etal. (1985)]	  5-50
                                        XII

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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 etal.  (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 etal.  (1985), and Velz (1984)]	  5-56

Table 5-37.  Settling Velocities in m/day at 20 °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 etal. (1985)]	  5-61

Table 5-40.  Rate Coefficients for Nitrogen Transformations [Bowie etal. (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 etal. (1985)]	  5-64

Table 5-43.  Formulas to Estimate Reaeration Coefficients for Deeper, Bottom
            Boundary Generated Shear Flows [Bowie et al. (1985), Rathbun
            (1977), Gromiecetal. (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 etal. (1985)]	  5-68

Table 5-45.  Empirical Wind Speed Relationships for Mass  Transfer and Reaeration
            Coefficients [Bowie etal. (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
                                        X!!!

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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 [Milllsetal. (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 etal. (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

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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 neces-
 sarily 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 condi-
 tions are suitable for prolific growth.

AHochthonous1- Pertaining to those substances, ma-
 terials or organisms in a waterway which originate
 outside and are brought into the waterway.

Anaerobic - Refers to life or processes occurring in
 the absence of free oxygen; refers to conditions char-
 acterized 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 organ-
 isms 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 waste-
 waters.

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 prin-
 cipally with the bottom of waterways. These include:
 (1) sessile animals such as sponges, barnacles, mus-
 sels, oysters, worms, and attached algae; (2) creep-
 ing  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 oxida-
 tion of organic matter in a specified time and at  a
 specific temperature. It is not related to the oxygen
 requirements in chemical combustion,  being deter-
 mined 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 or-
 ganisms 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 coeffi-
 cient 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 dura-
 tion, that produces an  adverse effect on organisms.
 The end result of chronic toxicity  can be death al-
 though the  usual effects  are sublethal; e.g., inhibits
 reproduction, reduces growth, etc. These effects are
 reflected by changes in the productivity and popula-
 tion structure of the community.
                                                 xv

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Coastal Waters1 - Those waters surrounding the con-
 tinent 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 compo-
 nents 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 oxy-
 gen in a liquid either under natural conditions associ-
 ated 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 sedi-
 ments.  Examples of chemical reactions include oxi-
 dation of organic materials while compaction is an
 example of a physical change.

Dispersion2 -  (1) Scattering and mixing.  (2) The mix-
 ing of polluted fluids with a large volume of water in a
 stream or other body of water.

Dissolved Oxygen  - The oxygen dissolved  in water,
 wastewater, or other liquid, usually expressed in mil-
 ligrams 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 op-
 posed 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 de-
 gree 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, lead-
 ing 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 uncer-
 tainty. The terms should  be applied only to the hori-
 zontal 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 re-
 sisting force of inertia. It is  equal to the square of
 characteristic  velocity (the mean, surface, or maxi-
 mum velocity) of the system, divided by the product
 of a characteristic linear dimension, such as diameter
 or expressed in consistent units so that the combina-
 tions will be dimensionaless. The number is used in
                                                 xvi

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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 bio-
 degradable. Most inorganic-type compounds, or reac-
 tions, 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 Factor  - A factor whose absence, or exces-
 sive concentration, exerts some restraining influence
 upon a population through incompatibility with spe-
 cies 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     Level  - 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 ex-
 pression to describe an enzyme-catalyzed biological
 reaction in which the products of a reaction are de-
 scribed 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 ani-
 mals. Microorganisms  are ubiquitous, possess ex-
 tremely  high growth rates and have the ability to
 degrade all naturally occurring organic compounds.

Modeling2 - The simulation of some physical or ab-
 stract 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 test-
 ing of designated locations or parameters to deter-
 mine 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 (6,070.10ft).

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)  - A quantita-
 tive measure of the amount of oxygen required for the
 biological oxidation of nitrogenous material, such as
                                                xvi i

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 ammonia nitrogen and organic nitrogen, in wastewa-
 ter; 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 some-
 times biodegradable chemical compounds containing
 carbon atoms (carbonaceous) bonded together and
 with other elements. The principal groups of organic
 substances found in wastewater are proteins, carbo-
 hydrates, and fats and oils.

Oxygen Deficit1 - The difference between observed
 oxygen concentration and the amount that would
 theoretically be present at 100% saturation for exist-
 ing conditions of temperature and pressure.

Pathogen1 - An organism or virus that causes a dis-
 ease.

Periphyton (Aufwuchs)1 - Attached microscopic or-
 ganisms 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 repre-
 sents 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 approxi-
 mately 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 direc-
 tion 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  -Arrange-
 ment of water masses into separate, distinct, horizon-
 tal 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 fluctua-
 tion; 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
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 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 regis-
ters 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 abscis-
sae.

Toxicant1 - A substance that through its chemical or
physical action kills, injures, or impairs an organism;
any environmental factor which, when altered, pro-
duces a harmful biological effect.

Water Pollution1  - Alteration of the aquatic environ-
ment  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 concern-
ing the suitability of water quality to support a desig-
nated 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 capa-
bility for locomotion.
1 Rogers, 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 Engi-
 neers, American Water Works Association, Water
 Pollution Control Federation.

2Matthews, J.E., 1972, Glossary of Aquatic Ecological
 Terms, Manpower Development Branch,  Air and
 Water Programs Division,  EPA, Oklahoma.
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The contents of this section have been removed to
comply with current EPA practice.
                                                xxi

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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 allo-
cations (WLAs) that are as technically sound as cur-
rent 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.

       I:              AND          LOAD
ALLOCATION

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 com-
plex loading, circulation, and sedimentation processes
make water  quality assessment and waste load allo-
cation 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: sa-
linity, 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, bioaccumula-
tion and toxicity.

For each of the topics addressed in a modeling study,
several steps are applied in an iterative process:  prob-
lem identification,  model  identification, initial model
calibration, sensitivity analysis, model testing, refine-
ment, and validation.
After the WLAs have been put into effect, continued
monitoring, post-audit modeling and refinementshould
lead to more informed future WLAs.

Overview of            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  proc-
esses 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 geomor-
phology and patterns of stratification and mixing.  How-
ever, each estuary is to some degree unique and it is
often necessary to consider  the fundamental  proc-
esses impacting water quality.

To determine the  fate  and affects of water quality
constituents it is necessary  first to determine  proc-
esses impacting their transport. That transport  is af-
fected by tides, fresh water inflow, friction at the fluid
boundaries and its resulting turbulence, wind and at-
mospheric 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. Hy-
drodynamic models are based on descriptions of the
processes affecting circulation and mixing using equa-
tions based on  laws of conservation  of mass and
momentum.  The fundamental equations generally in-
clude: (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 ag-
glomerate and settle in areas of significant salinity
gradients. Processes impacting  sediment transport
include settling,  resuspension, scour and erosion, co-
agulation and flocculation.
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The water quality parameters of interest vary with the
objectives of the waste load allocation study,  from
"conventional  pollutants"  (e.g. organic waste, dis-
solved 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 usu-
ally include temperature,  major nutrients,  chemical
characteristics, detritus, bacteria, and primary produc-
ers. 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 chemi-
cals  include a wide variety of toxic  materials whose
waste loads are allocated based upon threshold con-
centrations as well as tolerable durations and frequen-
cies  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 proc-
esses 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 tocomplexation, 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 analyti-
cal 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 im-
portant step is advised: perform rapid, simple screen-
ing  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 under-
standing 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 indi-
rectly link  the pollutants to be controlled with  the pri-
mary 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 constitu-
ents 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 descrip-
tion.

The next step is to specify the spatial extent,  dimen-
sionality, and scale (or computational resolution) of the
WLA model. This may be accomplished by determin-
ing  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  dimen-
sionality 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) be-
ing evaluated. Data describing the spatial gradients of
important  water quality constituents within the study
area should be examined. Dye studies can give impor-
tant 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 char-
acteristics of the study area, the reaction kinetics  and
forcing functions of the water quality constituents,  and
the strategy for relating simulation results to the regu-
latory 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.
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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-aver-
aged. Other forcing functions such as freshwater in-
flow, 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 mod-
els can  be classified as Level I  to Level IV according
to the temporal and spatial complexity of the hydrody-
namic component of the model. Level I includes desk-
top 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 de-
tailed 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 par-
tial differential equations.  Level II models can predict
slowly changing seasonal water quality with an effec-
tive time resolution of 2 weeks to 1 month. Level III
includes computerized one-dimensional  (1-d)   and
quasi two-dimensional (2-d), dynamic simulation mod-
els. 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 simula-
tion 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 aver-
aged temporal scale. When hydrodynamics and pol-
lutant inputs are rapidly varying, steady state models
are difficult to properly calibrate.

The dynamic models  (Levels III and IV)  have advan-
tages over steady state and tidally averaged models
in representing mixing in partially mixed estuaries be-
cause advection is so much better represented. The
success with which these models can predict transient
violations depends upon both the accuracy and reso-
lution 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.

       II: APPLICATION OF
         LOAD ALLOCATION

Monitoring Protocols for Calibration and
Validation of Estuarine        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  vari-
ables); (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 sys-
tem (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
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or navigation charts). Data are also required for trans-
port. Transport within the modeled system may either
be specified (measured, e.g. current meters) or com-
puted from hydrodynamic models. Flows into the sys-
tem  must be measured, or in  the case of the open
boundary, water surface elevations must be deter-
mined.

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, eu-
trophication or toxics. Concentrations for all pertinent
water quality variables should be provided at the model
boundaries, providing the perturbation for  model pre-
dictions, 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 collec-
tion, analysis and processing of  data, quality assur-
ance, data management and modeling activities.

Collaboration insures that fundamental design ques-
tions are  properly stated so that the available re-
sources 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, qual-
ity 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 condi-
tions or to extrapolate from existing to future condi-
tions, 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 inde-
pendent data set (to that used for calibration).

Model calibration is  necessary because of the semi-
empirical 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 col-
lected 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 extrapo-
lation 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  de-
scribe conditions that occur when large inflows and
atypical tides occur.

This is especially true when processes such as sedi-
ment 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 impor-
tance. 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  ob-
tained between model simulations and measured con-
ditions in  order to estimate the confidence that may be
assigned to model  predictions. Finally, a components
analysis  indicates  the relative contribution of proc-
esses to variations in  predicted  concentrations.  For
example, the cause of violations of a dissolved oxygen
standard  can be determined from the relative contribu-
tion of various loads and the  effect of sediment oxygen
demand,  BOD decay, nitrification, photosynthesis, and
reaeration.
                                                 XXVI

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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 con-
ditions  are defined for the estuary,  harbor or coastal
area of concern, determining the waste assimilative
capacity is relatively straightforward. Models are avail-
able 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 straight-
forward 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  hydro-
graphic events that affect mixing; waste loadings from
point and non-point sources; and changes in benthic
demands.

Simplified illustrative
This section presents illustrative examples of estuarine
modeling using both simple screening procedures and
the water quality model WASP4. The screening  proce-
dures 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 meth-
ods for conservative and nonconservative toxicants
and chlorine residual. Bacteria and DO depletion are
simulated. Nutrient enrichment, phytoplankton produc-
tion, 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 calcu-
lator 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 meth-
ods are presented for estimating  estuarine water qual-
ity impacts: analytical  equations for an  idealized
estuary, the fraction  of freshwater method, and the
modified tidal prism method. These example proce-
dures are only applicable to steady state, one-dimen-
sional estuary problems.

Deterministic water quality modeling of estuarine sys-
tems can be divided into two separate tasks: descrip-
tion 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 di-
rectly 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  eutrophica-
tion and toxicant programs are described and used.

For the six examples using WASP4, background infor-
mation is provided, the required input data are sum-
marized,  selected model results are shown,  and
certain WLA issues are briefly described.
                                                xxvi i

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The  document is the third of a series of manuals
providing information and guidance for the preparation
of waste load allocations. The first documents pro-
vided 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 guid-
ance 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 simula-
tion 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 summa-
rizes initial dilution and mixing zone processes, avail-
able  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
        Estuaries"
Part
1
2
3
4
Title

Estuaries and Waste Loac
Application of Estuarine Waste
Use of Mixing
Critical
Zone Models in Estuarine
Allocation Models
Load Allocation Models
Waste Load Allocation


Modeling
Review of Estuarine Waste Load Allocation Modeling
                                                 XXIX

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      4.                                    for                   and                  of


                                     James L Martin, Ph.D., P.E.
                                          AScl Corp., at the
                               Center for Exposure Assessment Modeling
                       Environmental Research Laboratory, U.S. EPA, Athens, GA
4.1.          Considerations
This section addresses data needs for the calibration
and validation of estuarine waste load allocation mod-
els. The type and amount of data will depend on: (1)
the study objectives, (2) system characteristics, (3)
data presently available, (4) modeling approach se-
lected, (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 pos-
sible,  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 exam-
ple, 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 objec-
tives  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 collec-
tion, analysis and processing of data, quality assur-
ance, data management and  modeling  activities.
Collaboration insures that fundamental design ques-
tions  are  properly  stated so that the available re-
sources 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 objec-
tives 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.  How-
ever,  the effort expended and the acceptable uncer-
tainty  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  charac-
teristics of that particular system. The kind  of data
required  is determined  by the characteristics of the
system, the dominant processes controlling the con-
stituent, and the time and space scales of interest. The
same factors that control  selection of modeled proc-
esses 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 advan-
tages 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 alterna-
tive or surrogate parameters for these  initial judgments.
For example, suspended solids may be used  in some
situations as a surrogate for strongly sorbed constitu-
ents.  Reconnaissance or preliminary surveys may be
required to provide a sufficient data base for planning
where only limited data are available.
                                                 4-1

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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 pre-
dictions. Uncertainties in the determination or estima-
tion of driving forces for the model (e.g. loadings, wind)
will be propagated  in model predictions.  The greater
the uncertainty (spatial, temporal or analytical) associ-
ated with data used in model forcing functions, estima-
tion of model parameters, or evaluation of  model
predictions, the greater the resulting uncertainty asso-
ciated with  those predictions.  One fundamental issue
that may impact  monitoring studies is the acceptable
degree of uncertainty in both data and model projec-
tions.

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 re-
quire 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 suc-
cessful completion of data collection efforts. An objec-
tive 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 valida-
tion 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 analy-
sis procedures have not changed which might make the
historical data unsuitable  for comparative purposes.
Where historical data are not available it may be neces-
sary to perform reconnaissance studies to obtain suffi-
cient data for  planning.  A reconnaissance study as
defined here is a survey of the site to obtain sufficient
data to make preliminary judgments. Additional recon-
naissance studies may be required particularly in areas
where the greatest uncertainties exist. The reconnais-
sance  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 Condions
Boundary condition data are external to the model do-
main 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 proc-
esses  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 up-
stream 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 constitu-
ents 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 simula-
tions 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

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are small, the initial conditions may dominant projec-
tions making it difficult to determine sources of error,
such as in modeling approaches.

4.2.4.  Calibration
Most estuarine hydrodynamic and water quality mod-
els 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 adjust-
ing 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 concen-
trations for the parameters of interest but on processes
affecting those concentrations, such as sediment oxy-
gen demand, settling and resuspension velocities, etc.
While resources often limit the extent of the calibration
data, more than one set describing a range of condi-
tions 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.  Vali-
dation  conditions should be sufficiently different from
calibration conditions to test model assumptions with-
out violating them (where the assumptions are consid-
ered 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 obvi-
ously would not predict well under situations where the
sediment oxygen demand was drastically different due
to some event.  A second example is that an applica-
tion assuming constant morphometry could not be
expected to perform well after flood events,  dredging,
or construction resulted  in  variations in  that  mor-
phometry. 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 condi-
tions, such as the  effects of waste loads. The projec-
tions 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 appropri-
ate.  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 con-
ducted.

Wherever possible, all stations and depths should be
sampled synoptically.  For estuaries that are stationary
wave systems (high water slack occurs nearly simulta-
neously everywhere),  this goal may be  difficult to
achieve due to the logistics  and manpower required.
Synoptic sampling schemes are constrained  by dis-
tance between  stations,  resources in terms of  man-
power 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 move-
ment 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 condi-
tions 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 dis-
charging facilities  prior to  the survey so that all waste
discharged can be characterized.   Estimates of non-
point loads are also required.

Where project resources  limit the number of samples,
an alternative may be to temporally integrate the  sam-
ples during collection  or  prior to analysis.  This will,
however, not provide information on the variability as-
sociated with those measurements.
                                                4-3

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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 repre-
sentative conditions and not during unusual climatic
events in order to allow comparison between sampling
times.  Some stations may be selected for more de-
tailed 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
Ecker1978).

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 parame-
ters. 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 esti-
mated using  ratio and regression  methods to deter-
mine the uncertainty associated with loading estimates
for various sampling designs (see for example Co-
chran 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 ex-
tend 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, includ-
ing  all major  embayments.   The spatial  coverage re-
quired 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 cross-
channel transects are generally required are the upper
and lower boundaries of the  system. Additional sam-
pling 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 evalu-
ation, sufficient samples should be collected to estimate
missing data by interpolation.
                                                4-4

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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      Requirements

4.5.1.  Estuary Bathymetry
Data are always required  to determine  model mor-
phometry.  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 verti-
cal 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 mix-
ing and narrow inlets restrict tidal action).  Wind-in-
duced circulation  is transient and interacts with
channel geometry to produce various circulation pat-
terns and affects vertical mixing and sediment trans-
port.

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 tran-
sects can measure depth profiles with a high frequency
fathometer connected to a continuous strip-chart re-
corder.  Depths must be corrected to mean tide level
at the time of measurement (Kuo etal. 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 wave-
lengths 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 dra-
matically effect estuarine circulation and water quality.
These are generally some of the more difficult systems
to model.  An initial decision may be whether to meas-
ure flows and quality and  provide information to the
model as boundary conditions or to attempt to model
them.  Where modeling is required then the corre-
sponding bathymetry data must be collected.
 Table 4-1.  Estuarine Transport Data
Morphometry Data:
Hydrodynamie Data:
Meteorological Data:
Water Quality Data:
Channel Geometry, "roughness" or
bottom type
Water surface elevations
Velocity and direction
Incoming flow
Point and distributed flows
Solar radiation
Air temperature
Precipitation
Wind speed and direction
Wave height, period and direction
Relative humidity
Cloud cover
Salinity
Water temperatures
Suspended sediments
Dye studies
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 bal-
ance principles, and both concentrations and flows are
required to compute mass rates of change. For exam-
ple,  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 in-
volving fraction of freshwater, modified tidal prism meth-
ods,  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 disper-
sion  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
                                                 4-5

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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 net-
work 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 inte-
grated 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 prop-
erly 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 chang-
ing. Generally, hourly and often daily data are suffi-
cient.   Flows  must  be  estimated for ungauged
tributaries, and where the influence of ungauged tribu-
taries is appreciable, a flow monitoring program initi-
ated.  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 coeffi-
cients, computing transport or for calibration and con-
firmation 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 freshwa-
ter 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 prin-
cipal developed  by the U.S. Geological  Survey (Yot-
sakura 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 move-
ment 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 quan-
tities are geometry and time varying dye concentrations
and  the unknowns  are advection and dispersion.
Diachishin (1963) provides guidance on estimating lon-
gitudinal, 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. Car-
ter and Okubo (1972) described a technique to estimate
a longitudinal dispersion coefficient from peak dye con-
centrations and describe the slug release method used
in Chesapeake Bay. Thomann and Meuller (1987) pro-
vided an example of computing tidal dispersion coeffi-
cients 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-dimen-
sional (longitudinal) model it may be preferable to dis-
tribute 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 con-
tinuous 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  back-
ground florescence
                                                4-6

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should be determined to aid in determining quantities
of dye to be released and subtracted from field meas-
urements. Care should also be exercised to schedule
dye studies to avoid non-representative meteorologi-
cal conditions. Some of the considerations for plan-
ning 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 proc-
esses 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 ge-
ometry 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 mod-
els  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 constitu-
ents such as salinity,  temperature, and other tracers
which can be used to evaluate hydrodynamic predic-
tions. An intensive data sampling program which in-
cludes concurrent  water surface elevation,  velocity
and dye/dispersion studies or salinity profiles provides
the best assessment of the hydrodynamic model ap-
plication.

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 pre-
dictions. 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 re-
sults of steady-state simulations as the  initial condi-
tions 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 pro-
vided for tributary and point sources and water surface
elevations provided for the open (ocean) boundary(ies).
Salinity, and often temperature, conditions may be re-
quired 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 an-
nually 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 re-
quired 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 evalu-
ation or for water quality modeling purposes, then data
on air temperature, cloud cover, humidity and precipita-
tion 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 constitu-
ents used to calibrate and validate transport predictions,
such as salinity and temperature.  The
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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 deter-
mined with careful consideration of the model applica-
tion.

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 in-
cluded 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 con-
tinuous monitor placed at the edge of a channel would
provide little usable information fora 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 exam-
ple, the effects of an overestimation of vertical veloci-
ties,  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 re-
quire an iterative effort in conjunction with the applica-
tion of the water quality models for the constituents of
interest (i.e. dissolved oxygen).  However, initial  cali-
bration 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 ve-
locity 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 consid-
ered 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 analy-
sis. 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 tox-
ics. 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 deter-
mine 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 con-
texts, 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 pre-
dictions, 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 measure-
ments. For example, strongly sorbed contaminants are
strongly affected by sediment  interactions, including
resuspension, settling, and sedimentation.  Some inde-
pendent measurement of these  processes may be re-
quired 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).
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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 de-
scriptions  of sampling collection, preservation,  han-
dling, 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 moni-
toring activities and a quality assurance coordinator
assigned to implement and coordinate QA activities.
There are a variety of  documents which describe pro-
cedures for quality assurance, and a complete descrip-
             tion of a quality assurance plan is beyond the scope of
             this report. Additional information is provided in:

             Guidelines and Specifications for Preparing Quality As-
             surance 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 As-
             sociation.  1980.

             Methods  for  the  Chemical  Analysis of  Water and
             Wastes.   EPA-600/4-79-020. USEPA Environmental
             Support Laboratory. 1979.
Table 4-2.  Water Quality Variables
  Constituent
  Problem Context
  Effects
 Salinity or Conductivity
 Temperature

 Suspended Solids
 UV Light
 Light Extinction
 Dissolved Oxygen
 BOD-5
 Long Term CBOD
 Carbon Dioxide
 NBOD
 Bottom Demand
 Total phosphorus
 Soluble reactive phosphorus
 Total kjeldahl nitrogen
 Ammonia-nitrogen
 Nitrate-nitrogen
 Nitrite-nitrogen
 Dissolved available silica
 Chlorophyll-a and Phaeophyton
 Phytoplankton (major groups)
 Alkalinity
 Total inorganic carbon
 pH
 Contaminant (dissolved particulate, total)
 Dissolved organic carbon
 Total organic carbon
 Porosity
 Grain size
 Percent solids
 Eh
 Biomass
 Meteorologic Data
 wind, temperature, etc.
 Toxicity (cereodaphnia toxic units, etc.)
 Coliform Bacteria (Fecal, Total, Streptococci)
All
All

All
Eutrophication, Toxics
Eutrophication, Toxics
All
DO
DO
Toxics, Eutrophication
DO
Eutrophication DO
Eutrophication DO
Eutrophication DO
Eutrophication DO
Eutrophication DO, Toxicity
Eutrophication DO
Eutrophication DO
Eutrophication DO
Eutrophication DO
Eutrophication DO
Toxics
Toxics
Toxics
Toxics
Toxics
Toxics
Sediments
Sediments
Sediments
Toxics, DO
Toxics
All

Toxicity
Human Health
Transport, dissolved oxygen
Transport, kinetics, dissolved
oxygen, toxicity
Transport, light extinction, sorption
Heat, algal growth, photolysis
Heat, algal growth, photolysis
Indicator, toxicity, sediment release
Dissolved Oxygen
Dissolved Oxygen

Dissolved Oxygen
Dissolved Oxygen, nutrient release
Algae
Algae
Dissolved oxygen, algae
Dissolved oxygen, toxicity, algae
Dissolved oxygen, algae
Dissolved oxygen, algae
Algae
Algal indicator
Dissolved oxygen, nutrient cycles, pH
pH, carbonate species, metals
pH, carbonate species, metals
Speciation, ionization, toxicity
Allocation
Sorption, activity
Sorption, activity
Pore water movement, toxicity
Settling, sorption, sediments
Sorption, sediments
Indicator, speciation
Biouptake
Gas transfer, reaction rates

Toxicity
Human Health
                                                    4-9

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    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 ele-
ments 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 rees-
tablished during subsequent  sampling periods. Sta-
tions 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 immedi-
ately downstream of a bridge or piling no matter how
convenient it may be. Stations can be  relocated using
electronic positioning equipment such as range instru-
ments, radar or Loran if they are sufficiently accurate
to allow  relocation  within an  acceptable distance.
Methods should be established for maintaining posi-
tions 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 s/fudetermination 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 measure-
ments  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 pres-
ervation requirements. The QA plan should contain a
detailed description of techniques for samples  requir-
ing special handling, such as toxics  and anaerobic
samples.

An established sequence of collection should be de-
veloped 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 labora-
tory personnel, and the laboratory personnel should log
samples into  the laboratory, noting the time and date
received, sample identities and other pertinent informa-
tion from the field logs. The samples should be checked
for proper preservation and transferred to proper stor-
age 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 re-
sults. 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 tech-
niques 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 applica-
ble, 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 interfer-
ences or conditions which could effect  the analysis.
Strip chart or electronically produced information on the
analysis should  be ar-
                                                4-10

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  5    Value
       Median
       5%
       Value
                5%         50 %    84% 95%
                    Percent Less Than Value Shown


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

chived. Generally, the results of each analysis should
be recorded on prepared forms  for each sample con-
taining information on the  results of all analysis per-
formed.

After completion of the analysis, the analytical results
should be reviewed by the laboratory's quality assur-
ance  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 indi-
cated by analysis of split samples, recovery of spikes,
periodic laboratory audits and other methods. Wher-
ever 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 distrib-
uted,  the median and log standard deviation can  be
estimated  from the plots and can then be  used to
estimate the mean using standard statistical transfor-
mations.  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 distri-
bution 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 ana-
lytical 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 priori-
ties, and  inform data users of the status of the informa-
tion 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 informa-
tion 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 pro-
cedures,  and status as perhaps indicated by analytical
codes. Checks should be established to insure that all
data are recorded and that accurate transfer of informa-
tion 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 his-
tory 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 rea-
sonable ranges as reported  in the literature. Analyses
should be conducted of the confidence associated with
the predicted results.
                                                 4-11

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Wherever available, model testing should not be lim-
ited to comparisons with concentrations but  model
components should be compared to available data to
insure that they are reasonable.  For example, produc-
tivity data for a system could be computed for eutro-
phication models and compared to field data.   A
component, or mass balance, analysis will also provide
information  on the dominant factors affecting predic-
tions (see Thomann and Meuller 1987).

A model application should be most accurate in esti-
mating conditions that occur between those measured
for calibration and validation, analogous to interpola-
tion. However, model applications often require projec-
tion 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 func-
tions. 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 post-
audit 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 cop-
ies of the computer codes and their  users manuals
used for prediction and manipulation are archived for
later use. The archived files should contain a descrip-
tion of all of the files necessary to do the analysis and
sufficient information to allow duplication of the  re-
ported results.

4.7.
Ambrose, R.B.  1983. Introduction to Estuary Studies,
Prepared for the  Federal Department of Housing and
Environment, Nigeria, Environmental Research Labo-
ratory, 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, Environ-
mental Research Laboratory, Athens, GA.

Ambrose, R.B., Connoly, J.P., Southerland, E., Barn-
well, T.O., and  Schnoor, J.L.  1988b. Waste Load
Allocation Models, J. Water Poll. Cntrl. Fed. 60(9). pp.
1646-1656.

Brown, LC. 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 Labora-
tory, Athens, GA.
Brown, S.M. and  Ecker, R.M.  1978.  Water Quality
Monitoring Programs for Selected Subestuaries of the
Chesapeake Bay,  Batelle Pacific Northwest Laborato-
ries. Prepared for the USEPA Environmental Research
Laboratory, Athens, GA.

Carter, H.H. and Okubo, A.  1972.  Longitudinal Disper-
sion 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.  Evalu-
ation of River Load Estimation Methods for Total Phos-
phorus, J. Great Lakes Res. 7(3), pp. 207-214.

Elliot, J.M.   1977.  Some Methods for the Statistical
Analysis of Samples of Benthic Invertebrates. Freshwa-
ter 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 Pa-
per 582-A.

Gilbert, R.O.  1987. Statistical Methods for Environ-
mental 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 Wil-
son, 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. Oxygen-
Sag in a Tidal River, ASCE J. Environ. Engr. Div., 103
(EE3).

Mills, W.B. etal. 1985. Water Quality Assessment: A
Screening Procedure for Toxic and Conventional Pol-
lutants 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.,andGaines, 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 Estimat-
ing 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, Wash-
ington, D.C.

Yotsukura, N. and Kilpatrick, F.A.  1973. Tracer Simi-
lation of Soluble Waste Concentration, ASCE J. Envi-
ronmental Engr. Div. Vol. 99, EE4, pp. 499-515.
                                              4-13

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                  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 condi-
tions.  Third, model testing procedures needed to cali-
brate 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 in-
creasing loads into the estuary, is provided.

Section  5.2 reviews a general procedure for calibrating
models  of the dissolved oxygen balance, of the nutri-
ents 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 alloca-
tion.  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 calibra-
tion 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. Meth-
ods to determine causes of existing conditions and to
project  effects of changes  in waste loads are  dis-
cussed.  Presently, methods to  modify model coeffi-
cients such as sediment oxygen demand rates  and
deoxygenation rate coefficients are not well developed.
Model calibration is necessary because of the semi-
empirical 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 col-
lected in the estuary of interest.  Occasionally, all im-
portant 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 rela-
tionships.  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 formula-
tions 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 butthisshould 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 prin-
ciples 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 constitu-
ents that are unimportant during the calibration phase.
The benthic flux of nutrients may become more impor-
tant when point sources are cleaned up and may need
to be included in any long term projection. Also, model-
ers  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 pur-
pose  models) and unless rigorous validation  proce-
dures 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, reason-
ably 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, chemi-
cal, or biological characteristics.   When parameters
are  allowed to vary from one segment to the next to
cause an exact match between predictions and meas-
urements, the selected coefficients are contaminated
with an accumulation of measurement errors from the
field data and approximation error for the model formu-
lations 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 fre-
quency.  For example, dissolved solids and other con-
servative constituents should be simulated, especially
those natural tracers occurring  in point and non-point
sources.   Where undocumented sources are sus-
pected, curtains of stations  or upstream  and down-
stream 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 sec-
tions 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  in-
volve 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 proce-
dures are followed,  it should be possible to detect
unreliable results in most cases.  Nevertheless, a pau-
city 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 measure-
ments to aid calibration,  there are calibration proce-
dures 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 formula-
tion of model data sets.  To avoid these  calibration
errors, there are two methods that should  be em-
ployed.  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 avail-
able.  Section 6 provides some simple formulations
that may be useful and Thomann and Mueller (1987)
provide  a wealth of additional information.  When sim-
ple calculations are not possible, selective hand calcu-
lations 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 sug-
gested.

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 cali-
brated 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 extrapo-
lation 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 oc-
cur 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 speak-
ing, 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 in-
itially testing a computer model  on different computer
systems using a benchmark set of input data as verifi-
cation.  In this latter case, the term verification is more
appropriate because  model simulations on a different
computer are being compared with an exact bench-
mark condition derived by the developer on his original
computer.  For engineering purposes, these calcula-
tions 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 valida-
tion. 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 alloca-
tion 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 Francis-
co Bay, it is necessary to continually update assess-
ments and waste load allocation studies.  It is possible,
however, to adequately validate a model and set  rea-
sonable waste loads in a short period of study (i.e., 6
                                                 5-3

-------
MODEL
CALIBRATION


FIRST INDEPENDENT
DATA SET
        MODEL
      VALIDATION
SECOND INDEPENDENT
     DATA SET
     USE MODEL TO
      DETERMINE
         WLA
Figure 5-1. Model calibration and verification procedure.

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 in-
volves 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). Ide-
ally, agreement should be evaluated in terms of

prespecified criteria. Very little guidance is available,
however, to make this fully feasible.
            COMPILE HISTORIC DATA
          FROM MONITORING & OTHER
              SYNOPTIC STUDIES
           PRELIMINARY CALIBRATION
                    I
           DETERMINE IF ADDITIONAL
           CALIBRATION IS NECESSARY
                 NO
                                     YES
                USE PRELIM, CAUB. TO DESIGN
                SYNOPTIC DATA COLLECTION
                     FOR CALIBRATION
                         COLLECT DATA ACCORDING
                             TO STUDY DESIGN
             USE CAUB. TO DESIGN
             SYNOPTIC STUDY TO
           COLLECT VALIDATION DATA
                    I
                                                        CALIBRATE
                                                          MODEL
     SUCCESSFUL
               VALIDATE MODEL
                  PROJECT & DETERMINE
                  WASTELOAD ALLOCATION
                              IMPLEMENT LOAD
                               RESTRICTIONS
                       UNSUCCESSFUL
             REFORMULATE MODEL
           OR REVISE CAUB. CRITERIA
                                                I     PERFORM POST-AUDIT   .
                                                i	!
Figure 5-2. Relationship between data collection, model calibration, validation, and waste load allocation procedures.


                                                  5-4

-------
                 CALIBRATION OR VALIDATION
                   DATA SET CONSISTS OF:
                                     Table 5-1.   Guidance Manuals for Rates, Constants, and
                                                Kinetics Formulations for Conventional and
                                                Toxic Pollutants
  BOUNDARY CONDITIONS
   (FLOWS AND LOADS)
   INITIAL DATA
(FOR DYNAMIC MODELS)
INITIAL WATER QUALITY
DATA DEFINING WATER
 QUALITY WITHIN THE
  MODEL DOMAIN
                                  COMPARE TO DETERMINE
                                     IF REASONABLE
                                   EQUIVALENCE EXISTS
                          SIMULATION  SIMULATED RECIEVING
Figure 5-3. Relationship between data set components,
water quality model, and set of model coefficients for model
calibration.
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 coef-
ficient.

A number of methods (e.g., least squares and maxi-
mum 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 calibra-
tion 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 correla-
tions between parameters that influence the  selection
of an optimum set.  As a result, calibration by optimi-
zation is not frequently used unless extremely complex
models are employed  where significant time savings
may be achieved.

The most useful compilations of these model formula-
tions 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, McCutch-
eon 1989, 1990, and Rich 1973).

In general, models are calibrated in phases beginning
with the selection of the model  parameters and coeffi-
cients that are independent (or assumed to be inde-
pendent 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 Fig-
ure  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.
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 Formula-
   tions  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., Proc-
   esses, Coefficients, and Models for Simulating Toxic Or-
   ganics and Heavy  Metals  in  Surface  Waters,
   EPA/600/3-87/015, U.S.  Environmental Protection Agency,
   Athens, Georgia, 1987
                                       Table 5-2. Outline of a General Calibration Procedure for
                                       Water Quality Models for Conventional Pollutants when
                                       BaroclinicCirculationEffectsareUnimportant[McCutch-
                                       eon.(1989)]
                                      Step
                                             Procedure
                                           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.
                                           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.
                                           Calibrate any process models such as water
                                           temperature that are not affected by any other water
                                           quality constituent.
                                           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.
                                           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.
                                     5.2.1. Phase I of Calibration
                                     Phase I concentrates on the calibration of the hydrody-
                                     namic and mass transport models.  In general, there is
                                     a complex interaction between circulation and density
                                     differences caused  by gradients of salinity and tem-
                                     perature that must be taken into account in stratified
                                     estuaries. In vertically mixed estuaries, the
                                                     5-5

-------
Table 5-3.  Guidance on the Selection of Model Coefficients and Parameters - Phase I
Calibration Parameters for
Complex Model
Bottom roughness coefficient
Eddy Viscosity:
Vertical!
Lateral 1
Horizontal
Dispersion Coefficient'
Vertical
Lateral!
Horizontall
Wind speed function
Surface drag coefficient
Simple Model


Dispersion Coefficient:
Vertical
Lateral!
Horizontal!


Range of Values
0.010to0.120
10-2 to 10° cms"1
102 to 106cms~1
1 02 to 1 06 cm s"1

10~2 to 10° cms"'
102to 106cms"1
102to106cms~1
See Supplement VI
0.001 to 0.0025
Guidance Documents and References
Hydrodynamic model documentation
/i.e. Ambrose et al. (1988)], Chow
C\959\ Frecnh (1985), Barnes (1972)
Hydrodynamic model documentation.
Assumed to be the same order as the
dispersion coefficient. Bowie et al.
(1985), MAS (1977), Officer (1979), and
Dyer (1973)
Bowie etal. (1985), Fisher et al. (1979),
Thomann and Mueller (1987), MAS
(1977), and Officer (1976)
Bowie et al. (1985), Ryan and
Harleman (1973), Brutsaert (1982), and
VlcCutcheon (1989)
O'Connor (1983)
  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.
interaction among salinity, temperature and circulation
is usually not significant. When vertical salinity gradi-
ents are not present, vertically mixed one-and two-di-
mensional  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 hydrody-
namic model can first be calibrated and then the salin-
ity and temperature  models calibrated  afterwards.
Model calibration for stratified estuaries involves deter-
mining  bottom  and surface friction coefficients  (see
Supplements I and II) and vertical, lateral, and horizon-
tal 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 calibra-
 Phase I
      TEMPERATURE
              HYDRODYNAMICS (CIRCULATION)

                             ^
                           SALINITY (MASS TRANSPORT)
 Phase II
BIOCHEMICAL
OXYGEN
DEMAND



Phase III \
NITROGEN PHOSPHORUS j (J^S^L
nvoi c r^vr-i c UULIrUnM
x^ % \ BACTERIA
^V y* |
ALGAE & BIOMASS i
	 . . .j
T • •
/
DISSOLVED


OXYGEN
BALANCE
SUSP!
SEDI



i
ENDED
UIENT




TOXIC
CHEMICALS
AND METALS
Figure 5-4. Phased calibration procedure.
tion  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 his-
toric 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-di-
mensional 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 cir-
culation 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
                                                  5-6

-------
Complex Model
Simple Model
Range of Values
                                                                                                    Guidance Documents and  References
                    CBOD:

              Deoxygenation rate
                  coefficient
             Decay rate coefficient

              Settling coefficient
         CBOD:

    Deoxygenation rate
        coefficient
   Decay rate coefficient

    Settling coefficient

     NBOD decay rate
        coefficient
                                           Bowie etal. (1985)
0.05 to 0.4 d"1 (20°C)

0.05 to 0.4 d"1 (20°C)

approximately 0.0

0.1 to 0.5 d"1 (20°C)
                                                                                                     Bowie et al. (1985), Thomann and Mueller (1987)
           Nitrogen transformations:

              ON hydrolysis rate
                  coefficient
              Ammonification rate
                  coefficient
                Nitrification rate
                  coefficient
                                                                    Bowie etal. (1985)
                         0.001 to 0.14 in d"1 (20°C)

                         0.02 to 1.3 in d"1 (20°C)

                         0.1 to 20 in d"1 (20°C)
          Phosphorus transformations
                                                                    Bowie etal. (1985)
                                                                       0.001 to 0.2 d"1 (20°C)
             Biomass coefficients:

          Ammonia preference factor

              N half sat. constant

              P half sat. constant

             Light half sat. constant

              Light ext. coefficient

             Max growth rate coeff.

             Respiration rate coeff.

                 Settling rate

          Non-predatory mortality rate

           Zooplankton grazing rate
                                                                    Bowie etal. (1985)
                         0 to 1.0
                         0.001 to 0.4 mg L
                                        -1
                                           -1
                         0.0005 to 0.08 mg L

                         0.1 x10"5to20.5x10"5Wm"2
                         2.3 to 6.9 in m"

                         0.2 to 5 d"1 (20°C)

                         0.05 to 0.15 d"1  (20°C)

                         0.05 to 0.6 md"1

                         0.003 to 0.17 d"1

                         0.35 to 0.8 d"1
                                       Thomann (1972) - Delaware
                                                Estuary
          Phytoplankton stochiometry:

                    Carbon

                   Nitrogen

                  Phosphorus

                     Silica
                                                Net photsynthesis rate

                                                  Net respiration rate
                         (% dry weight biomass)

                         10 to 70

                         0.6 to 16

                         0.16to5

                         20 to 50

                         0.5 to 5 g O2 m"2 d"1

                         same order of magnitude as
                         photosynthesis rate
                              Bowie et al. (1985) - see their table of values for
                                            various species.
                                    Thomann (1972), Mills et al. (1985)

                                            Mills etal. (1985)
              Coliform die-off rate
                  coefficient
   Coliform die-off rate
        coefficient
0 to 84 d
                             Bowie et al. (1985), Thomann and Mueller (1987)
                Settling velocity
                         1 to 100 md"
                                                                                                                  Thomann in review
             Resuspension velocity
                                                                       0.1 to 50 m yr
                                                                                                                  Thomann in review
              Net settling velocity
                                                                       0.1 to 50 cm yr
                                                                                                                  Thomann in review
Definition of symbols and explanation of terms:
ON  =    organic nitrogen
Ammonification = oxidation of ammonia to nitrate
       ON hydrolysis = degradation of organic nitrogen to ammonia
       Nitrification = oxidation of nitrite to nitrate
                                                                         5-7

-------
Table 5-5.   Guidance on the Selection of Model Coefficients and Parameters - Phase III
Calibration Parameters for
Complex Model

Sediment oxygen demand rate
Rearation rate coefficient

Toxicant Fate Processes:

Volatilization rate coeffiient
Biodegradation rate coefficient
Photolysis rate coefficient
Hydrolysis rate coefficient
Acid
Neutral
Base
Partitioning coefficient

Metals Fate Processes:
Solubility constants
Chemical equilibrium constants
Simple Model

Sediment oxygen
demand rate
Rearation rate
coefficient
Toxics 1st order decay
coefficient








Conservative heavy
metals with settling


Range of Values

0.0 to 11 ing O2m"2d"1
order of 0.001 to 0.1 d" or
K2 = (depth)"1 d"1, depth in m
Mot well defined
See range for each individual
chemical









Guidance Documents and
References
Bowie et al. (1985), Krenkel and
Novotny (1980)
Bowie etal. (1985), Kim and Holley
(1988), Thomann and Mueller (1987)

Schnoor et al. (1 987), Mills et al. (1 985)






Thomann and Mueller (1987)
Thomann in review
See data bases in MINTEQA2 model
[Brown and Allison (1987)] and other
geochemical speciation models, and
Stumm and Morgan (1981), Schnoor et
al. (1987)
Definition: K2 = reaeration coefficient.
 combination of freshwater inflow, wind conditions, tidal
 conditions, and storm effects represent a critical circu-
 lation  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 coef-
 ficients and literature estimates of eddy viscosity val-
 ues 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 con-
 ditions lead to a reasonable worst case design stand-
 ard. 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  appro-
 priate  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-dimen-
sional models are occasionally calibrated with current
velocity and water surface  elevation data but more
                                                  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.

5.22  Phase II of Calibration
Phase II involves the selection of coliform die-off coef-
ficients, settling and  re-suspension velocities for sus-
pended sediment, BOD coefficients, and  the set of
coefficients describing the nutrient cycles and photo-
synthesis. The selection of die-off coefficients is rela-
tively 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 read-
ily available for the collection of calibration data.  Sus-
pended 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 pre-
sent 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 VIM.

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 dis-
solved BOD like that observed in streams because of
the limited surface area available. Also, brackish wa-
ters 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 nitrifica-
tion 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.  Supple-
ment 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 phytoplank-
ton 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 valida-
tion 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 qual-
ity system without at least one process rate measure-
ment.

5.2 3. Phase III of Calibration
The final phase of calibration can be either difficult or
extremely easy depending on how well other compo-
nents have  been  calibrated and whether  process
measurements such as the reaeration rate and sedi-
ment 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 cali-
bration.  Infact.it is more useful to attempt a quick step
through the calibration procedure to obtain a
                                                5-9

-------

-^ —

^

12.2 _
12.1
21
9.9 _
2.0


A
133.0
130.7
i
.5

22U4
55.2

23.8

/32.0
^ 14.3


B
235.2
213-6
!
1S
89.7
93.9

_ 27.2
21.4
.0
7.6
8.2


— ^— -

^

                                                                        (C)

-.44 —



12.2 _
12.1
9.9 i
2.0


A
133.0
130.7
i
9.8

7.4 /
/4.2
D
22.4
55?

28.3

B
235.2
213.6
1
33
i
C
89.7
93.9

_ 27.2
21.4
.0
^ 7'6
8.2


— ^_



                         (B)                                             (D)
    EXAMPLE OF TWO MODELS BEING CALIBRATED ON  EXAMPLE OF TWO MODELS BEING VALIDATED ON
        SAME SYSTEM: A) MODEL 1; (B) MODEL 2          SAME SYSTEM: (C) MODEL 1; (D) MODEL 2
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)].
preliminary indication of which parameters and coeffi-
cients 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 coeffi-
cients 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 guid-
ance 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 bio-
concentration 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 specia-
tion 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 dis-
solved concentrations. Estimates of the distribution
coefficient can be obtained from Schnoor et al. (1987)
or Thomann and Mueller (1987). Geochemical spe-
ciation models such as MINTEQA2 (Brown and Allison
1987) can be used to estimate distribution coefficients
(when dissolved solids are not very high — i.e., appli-
cable for fresh or brackish waters but not sea waters)
in addition to being used to determine potential mobility
as indicated above.
                                                5-10

-------
5.3. Model Validation
Validation testing is designed to confirm that the cali-
brated 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 con-
ditions 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 vali-
dation 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 whetherthe 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 condi-
tions).

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 coeffi-
cients is quite low using split data sets.

Too many times, limited studies only attempt calibra-
tion.  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 recali-
brated 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 avail-
able 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 sensitiv-
ity test provides a method to determine which parame-
ters and coefficients are the most important. Second,
there are a number of statistical tests that are useful
for defining when adequate agreement has been ob-
tained between model simulations and measured con-
ditions.

The sensitivity analysis  is simply  an investigation of
how  much influence changes in  model coefficients
have on simulated results. Typically, important coeffi-
cients, 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 pa-
rameters 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 esti-
mate 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 indi-
cate that a visual fit of model predictions to measured
data can quite accurately be used  to obtain accurate
calibrations, especially if performed by experts. How-
ever,  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 model-
ers.

5.4.1. Root Mean Square Error
The most widely used criterion to evaluate the agree-
ment between model predictions and  measurements
is perhaps the  root mean square (rms) error or stand-
ard error of the estimate (Ambrose and Roesh 1982)
defined as
              - Cs)2
              N
                                            (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 com-
puted for a series of measurements at multiple points
overtime as
   rmsg =

where
                     0.5
(5.2)
   N; = 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 con-
sidered to be equally valid.  For example, this statistic
would be useful for obtaining an overall calibration for
         o
         o
               DISCREPANCY BETWEEN
          SIMULATIONS AND MEASUREMENTS

Figure 5-6. Cumulative frequency diagram.
two or more sets of data containing different numbers
of measurements that are all equally accurate. Differ-
ent weighting schemes could be applied if measure-
ments 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 ex-
presses 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 com-
parable  between two or more separate sets of data.
For example, one data set may contain more meas-
urements 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 dis-
crepancies between model predictions and measure-
ments 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 es-
                                                5-12

-------
tuary or with time, the relative error may be a more
appropriate statistic fortesting calibration or validation.
The relative error is defined as (Thomann 1982)
                                             (5.3)
where the overbars denote the average measured or
simulated valued. Averages are performed over mul-
tiple sites or over time and cumulative frequency of
error can be computed (Thomann 1982).  The cumu-
lative frequency (see for example Figure 5.6) can be
used to estimate the median error and various percen-
tiles such as the 10th  and 90th exceedance frequen-
cies.  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  under-
stood 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 dis-
crepancies are not constant as may occur when cali-
bration 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  gen-
eral, 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
                                             (5.4)
Table 5-6.  Relative Error in a Number of Estuarine Model
          Calibrations for Dissolved Oxygen. [Thomann
          (1982) and Ambrose and Roesch (1982)]

Estuary
New York Harbor
Manhasset Bay, NY
Wicomico Estuary, MY
Relative Error
ICm-Cil
Cm
5% to 35 %
5%
58%
Um-Us
Cm



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 vari-
ous types of bias in predictions of dynamic state vari-
ables.  The regression equation is written as
                                             (5.5)
where
   a = intercept value
   b = slope of the regression line
   s = 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
   10
  Q o
  e
  5 6
  HI
  DC
  Q- 4
              MEASURED  . ,
              PREDICTED  la'
                                      I	I
         2   4   6  8  10
           MEASURED
24  6   8  10
   MEASURED
                                                       10
                                                      Q o
                                                      LU o

                                                      la
                                                      W
                                                      £ 4

                                                        2

                                                        0
                                                                              10
                                         TIME,daya
                                                             2  4  6  8  10
                                                               MEASURED
                               2  4  6   8  10
                                  MEASURED
                                                    Figure 5-7. Types of bias and systematic error determined
                                                    by regression analysis [(O'Connor (1979), Thomann (1982),
                                                    and NCASI (1982)].
                                                5-13

-------
Table 5-7.  Hydrodynamic Model Error Statistics for the Delaware Estuary [Ambrose and Roesch (1982)]
Tidal Response Variables
Tidal range (m)
High water arrival (min)

N
15
15
Calculated Errors
E
-0.012
18.4
RE
-0.00
-0.09
SE
0.093
19.9
cv
0.02
0.10
Regression Statistics
a
1.03
0.94
b
-0.06
-6.69
r
0.98
1.00
Table 5-8.  Hydrodynamic Model Error Statistics for the Potomac Estuary [Ambrose and Roesch (1982)]
Tidal Response Variables
Tidal range (m)
High water arrival (min)

N
82
82
Calculated Errors
E
-0.001
0.076
RE
-0.00
0.02
SE
0.036
0.27
CV
0.06
0.07
Regression Statistics
a
0.92
0.97
b
0.046
0.03
r
0.98
0.99
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 de-
grees of freedom. See standard texts such as Ken-
nedy  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 em-
ploying 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)
                                             (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=(2sx')A                              (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 re-
quires 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
                                                 5-14

-------
Table 5-9.   Transport Model Error Statistics for the Delaware Estuary [Ambrose and Roesch (1982)]
Tidal Response Variables
Chloride concentration (mg/L)
Movement of 500 mg/L Isochlor (km)
Peak dye concentration (ug/L) '
All data:
Period 1:
Period 2:
Movement of dye peak (km)
All data:
Period 1:
Period 2:
Width of 0.1 ug/L dye isocline (km)
All data:
Period 1:
Period 2:

N
35
5
14
7
7
14
7
7
14
7
7
Calculated Errors
E
-140
-1 9
0.03
0.06
001
3.4
1.6
50
1.3
1.0
1.6
RE
-0 10
-022
0.09
0.14
005
0.26
0.54
021
0.05
0.04
0.06
SE
440
28
0.10
0.14
003
6.0
5.1
66
3.2
2.3
4.0
CV
031
033
0.30
0.32
0.14
0.45
1.73
028
0.13
0.10
0.14
Regression Statistics
a
097
078
0.82
0.52
076
1.12
0.15
1 26
0.83
0.84
0.38
D
-980
-005
0.09
0.27
0.07
1.8
4.2
-1 1
5.5
4.5
20.0
•
097
099
0.82
0.62
092
0.96
0.44
098
0.90
0.96
0.47
Table 5-10.  Transport Model Error Statistics for the Potomac Estuary [Ambrose and Roesch (1982)]

Tidal Response Variables

Chloride concentration (mg/L)
Dye concentration (ug/L)
All data:
Period 1:
Period 2:
Peak dye concentration (ug/L)
Movement of dye peak (km)
Width of 0.1 ug/L dye isocline (km)


N
37

189
50
139
14
14
10
Calculated Errors

E
-85.

0.00
0.11
-0.03
-0.01
-0.9
1.9
RE
-0.02

0.00
0.27
-0.14
-0.01
-0.14
0.10
SE
200.

0.12
0.18
0.08
0.15
1.4
1.3
CV
0.05

0.44
0.44
0.37
0.22
0.22
0.07
Regression Statistics

a
0.95

0.69
0.68
0.85
0.96
0.98
0.66
b
300.

0.08
0.05
0.06
0.02
1.0
4.5
r
1.00

0.84
0.81
0.85
0.91
0.97
0.96
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 meth-
ods  require  some knowledge of the distribution  of
discrepancies  between  measurements  and predic-
tions  or involve  tests to determine the distribution.
Methods requiring a priori knowledge of the distribu-
tions 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 distri-
bution.  If the distribution is normal, the F-test (Ken-
nedy 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.
54.6. 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 Estuar-
ies by Ambrose and Roesch (1982).

The work of Ambrose and Roesch (1982) is important
because it presents benchmarks to which other cali-
brations 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 er-
rors, coefficient of variation, regression intercept, re-
gression slope, and correlation coefficients but only for
two estuaries.  Nevertheless, the Potomac and  Dela-
ware Estuaries are among the most important East
                                                5-15

-------
Table 5-11. Water Quality Model Error Statistics for the Delaware Estuary [Ambrose and Roesch (1982)]
Quality Response Variables

N
Calculated Errors
E
RE
SE
CV
Regression Statistics
a
b
r
 (a) Median Concentrations (mg/L)
Dissolved Oxygen
BOD
Ammonia-N
Nitrate-N
Organic-N
36
8
36
36
36
-0.15
-0.70
0.05
-0.11
-0.11
-0.04
-0.11
-0.10
-0.08
-0.19
0.69
0.97
0.16
0.24
0.21
0.18
0.15
0.33
0.17
0.37
0.84
0.84
0.90
0.90
0.14
0.44
0.37
0.10
0.04
0.39
0.93
0.93
0.91
0.91
0.27
 (b) DO categories
Zone 2 (mg/L)
Zone 3 (mg/L)
Zone 4 (mg/L)
Zone 5 (mg/L)
Calibration (mg/L)
Verification (mg/L)
DO Minimum'3
2 mg/L Reach Length (km)c
9
9
9
9
16
20
9
9
-0.21
0.13
-0.10
-0.41
-0.06
-0.22
-0.07
-2.7
-0.04
0.06
-0.04
-0.08
-0.02
-0.06
-0.05
-0.13
0.50
0.66
0.82
0.73
0.53
0.79
0.55
6.0
0.10
0.28
0.32
0.15
0.14
0.21
0.41
0.28
0.78
1.21
0.82
0.74
0.88
0.81
1.54
0.90
0.90
-0.38
0.35
0.87
0.39
0.47
-0.79
-0.64
0.91
0.78
0.86
0.92
0.95
0.92
0.78
0.89
Table 5-12. Water Quality Model Error Statistics for the Potomac Estuary, 1965-1975 [Amborose and Roesch (1982)]
Quality Response Variables

N
Calculated Errors
E
RE
SE
CV
Regression Statistics
a
b
r
 (a) Median Concentrations
DO (mg/L)
NHs (mg/L)
NOs (mg/L)
TPO (mg/L) (as PO4)
CHL (ug/L)
32
41
39
40
31
-0.04
0.02
0.05
0.01
2.7
-0.01
0.02
0.07
0.01
0.04
1.02
0.27
0.18
0.20
19.3
0.17
0.31
0.26
0.16
0.27
0.80
1.01
0.79
1.03
0.92
1.12
0.01
0.21
-0.03
8.70
0.86
0.95
0.90
0.98
0.87
 (b) Extreme Concentration
DO Min. (mg/L)
NHs Max. (mg/L)
NOs Max. (mg/L)
TPO Max. (mg/L, as PO4)
CHL Max. (ug/L)
9
15
12
14
8
-0.02
-0.02
-0.11
-0.15
-4.1
-0.01
-0.01
-0.09
-0.05
0.03
0.35
0.20
0.25
0.30
6.1
0.23
0.11
0.20
0.10
0.05
1.08
0.91
0.85
1.00
1.02
-0.15
0.15
0.08
-0.16
-7.1
0.93
0.96
0.93
0.97
0.99
 (c) Reach Length
DO < 5 mg/L
DO < 3 mg/L
NHs > 1 mg/L
NOs > 1 mg/L
TPO > 1 mg/L (as PO4)
9
9
15
12
14
-2.1
-1.1
1.7
-0.3
0.0
-0.10
-0.11
0.08
-0.02
0.0
4.3
3.2
6.8
6.6
8.6
0.20
0.33
0.32
0.46
0.23
0.81
0.66
0.93
0.91
0.80
2.1
2.2
3.2
1.0
7.6
0.78
0.70
0.94
0.95
0.79
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
                                                  5-16

-------
Table 5-13. Chlorophyll-a Model Error Statistics for the Potomac Estuary, 1977-78 [Ambrose and Roesch (1982)]
Quality Response Variables
Median concentration (ug/L)a
Peak concentration (ug/L)
Peak Location (km)b
100 ug/L reach length (km)c

N
32
8
8
8
Calculated Errors
E
12.2
11.3
-4.8
2.8
RE
0.16
0.07
-0.15
0.11
SE
53.2
35.1
17.7
10.9
CV
0.69
0.23
0.55
0.42
Regression Statistics
a
0.82
1.16
0.14
0.86
b
26.2
-14.2
22.9
6.5
r
0.69
0.94
0.09
0.89
  Concentrations are median values by river segment (16-26 km) and survey period.
Table 5-14. Water Quality Model Error Statistics for the Potomac Estuary, 1977-1978 [Ambrose and Roesch (1982)]
Quality Response Variables

N
Calculated Errors
E
RE
SE
CV
Regression Statistics
a
b
r
 (a) Median Concentrations (mg/L)
DO
CBOD
NH3
NO3
32
29
29
40
-0.20
-1.00
-0.11
-0.02
-0.03
-0.31
-0.45
-0.03
1.15
1.57
0.26
0.15
0.16
0.48
1.07
0.24
0.54
0.25
0.38
0.85
3.00
1.47
0.04
0.08
0.77
0.33
0.59
0.97
 (b) Extreme Concentration  (mg/L)
DO Min
CBOD Max
NH3 Max
N03 Max
8
8
10
10
-0.03
-0.26
0.04
-0.08
-0.01
-0.04
0.04
-0.05
0.86
1.92
0.14
0.18
0.25
0.32
0.13
0.11
0.70
1.30
0.89
0.90
0.99
-2.09
0.15
0.10
0.62
0.66
0.95
0.85
 (c) Extreme Location  (km)
DO Min
CBOD Max
NH3 Max
NO3 Max
8
8
10
10
-1.2
-6.0
-1.4
-2.4
-0.10
-0.82
-0.54
-0.31
3.7
10.5
6.9
5.5
0.31
1.45
2.67
0.70
1.02
0.01
-0.03
0.71
-1.4
1.1
1.2
-0.2
0.99
0.04
-0.11
0.89
 (d) Reach Length (km)
DO < 5 mg/L
8
-3.2
-0.22
5.4
0.37
0.66
1.7
0.97
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 observa-
tions 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 coef-
ficient of variation should be 5 to 10 percent for hydrody-
namic variables, less than 45 percent for transport vari-
ables,  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 guid-
ance is summarized  in Table 5.1 S.for water quality vari-
ables.   The general guidance  is summarized in Table
5.15.
                                                  5-17

-------
Table 5-15. Preliminary Guidance on Error Statistic Criteria for Calibrating Estuarine Water Quality Models
Error Statistics
Relative Error3
Relative Error"
Cofficient of Variation
Correlation Coefficient
Criteria for Model Variables
Hydrodynamic

±30%
10%
0.94
Transport

+25%
45%
0.84
Water Quality

+45%
90%
0.60
DO
15%
±3%
17%
0.80
Chlorophyll-a

±16%
70%
0.70
 See Equation (5.3)
 See Equation (5.4)
Example 5.1.
Calibration of Hydrodynamics, Mass Transport, and Toxic
Chemical  Model for the Delaware Estuary
Ambrose (1987) calibrated a tidal transport and vola-
tile chemical model of the Upper Delaware Estuary
(see Figure 5.8) to determine if seven volatile chemi-
cals discharged  by the Northeast Philadelphia
Wastewater Pollution Control Plant (NEWPCP) mi-
grate 6 miles (9.7 km) upstream to the Baxter Drink-
ing Water Plant intake. Earlier versions of the WASP
and  DYNHYD models (Ambrose et al.  1988) were
calibrated using data collected for conventional pol-
lution studies from the  summer of 1968  until July
                          1976, and from volatile chemical data collected in Octo-
                          ber 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).
                                                    Sampling station
                                                 •(•  River miles Irom NEWPCP
                                                '•	 Model segment boundaries
                                                i—v Bridge
                                                 S  Sewage  disposal
                                                 W  Water supply
Figure 5-8. Upper Delaware Estuary [Ambrose (1987)].
                                               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 ob-
tained with the selected Manning n values by com-
paring 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 cali-
brated 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
              Wilmington  Philadelphia
                                    Trenton
 a>
 D)
 c
 o
 a;
 "o
 -a
     7-
6-
                1    I    1
                                             an approximate manner using average  long term set-
                                             tling, scour and sedimentation data.

                                             Chemical rate constants were determined from the lit-
                                             erature and by various predictive methods. Volatilization
                                             rate constants were determined from the Whitman two
                                             layer resistance model using relationships between oxy-
                                             gen, 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

                                            Table 5-16.  Environmental Properties Affecting Interphase Transport and
                                                      Transformation Processes [Ambrose (1987)]
            I    I    I     I    I    I     I    I
       50   60  70   80   90  100 110 120  130  140

        Location, in river miles above Delaware Bay
O
X
^-fr1""
Observed Mean Tide
Predicted Mean Tide
Observed Average Spring Tide
Predicted Average Spring Tide
Environmental
Property
Sediment cone.
Suspended (mg/L)
Benthic (kg/L)
Organic carbon fraction
Suspended sediment
Benthic sediment
Sediment settling velocity
(m/day)
Bed sediment resuspen-
sion velocity (cm/yr)
Pore water diffusion
(cm2/s)
Benthos mixing factor (0-
1)
Surficial sediment depth
(cm)
Water column depth (m)
Water column temp (°C)
Average water velocity
(mis)
Wind speed at 10 cm (mis)
pH and pOH
(standard units)
Concentration of oxi-
dants (moles/L)
Surface light intensity
(Langleys/day)
Cloud cover (fraction)
Light extinction
coefficient (m"1)
Active bacterial
populations
suspended (cells/ml)
benthic (cells/1 OOg)
Input
Value
20-50
1.35
0.015
0.065
5.0
5.0
1.0x 10"
0.5
6.1
3-10
25
0.65
2.0
7.0
1.0x 10"
—
0.3
3.0
1.0x 10
2.0x 10
Environmental Process
Kpa
X
X
X
X






X








Ks°
X
X
X
X
X
X

X
X
X
X
X
X






Kvc




X


X
X








KHa








X


X





Ko"








X



X




KPH







X
X




X
X
X

Ksy








X







X
                                                  Sorption
                                                 3 Benthos-water column exchange
                                                 ' Volatilization
                                                  Hydrolysis
                                                                          ' Oxidation
                                                                          f Photolysis
                                                                          3 Bacterial degradation
Figure 5-9. Observed and predicted tidal ranges in the
Delaware Estuary [Ambrose (1987)].
                                                5-19

-------
Table 5-17.  Chemical Properties Affecting Interphase Transport and Transformation Processes [Ambrose (1987)]
Chemical Properties3
General molerular weight (g/mole)
Solubility (mg7L)
Sorption
Octanol-water partition, Kow
(mg/L octanol per mg/L water)
Organic carbon partition, Kre (L/kg)
Volatilization
Henry's Law constant (m -atm/mole)
Vapor pressure (torr)
Volatilization ratio to oxygen
Hydrolysis
Acid-catalysis rate constant (per molar per
hour)
Base-catalysis rate constant (per molar
per hour)
Neutral rate constant (per hour)
Photolysis near surface rate constant
(per day)
Oxidation constant (per molar per
hour)
Bacterial degradation second order
rate constant (ml per cell per hour)
Compund Simulated
DCP
113
2.7x10°
15
1
2.31 x 10"
2
0.53
0
0
7.2x1 0"4
0
100
1.0x10'9
DMM
76 1
3.35x10°°
1C
0.4
1.7x 10"4d
325e
0.12f
0
0
	
	
	
DCE
99.0
8.69x10
30
14
9.4 x 10~3
61
0
0
2.0x1 0"9
0
100
1.0x10"9
PCE
1658
200
759
364
1.53x10"2
14
0.51
0
0
0
0
100
1.0x10"9
TCE
13139
1.1 x 10
263
126
9.1 x 10~3
57.9
0.55
0
0
0
0
500
1x10-'°
MC
8494
2.0 x 10
18.2
88
2.03 x 10~3
362.4
0.65
0
0
1.1 5x1 0~7
0
100
	
CF
11938
8.2x10
91
44
2.88 x10"3
150.5
0.58
0.23
0
2.5x1 0"9
0
100
	
 a Values from Mabey et al. (1982) unless otherwise noted
 t> Valvani et at. (1981)
                        c Leo etal. (1971)
                   d Mine and Mookerjee (1975)
     Boublik etal. (1984)
Shubert and Brownawell (1982)
                                             Distance from NEWPCP,  in  miles
Observed
transect — -
 median
                                                       Predicted slack tide concentrations
                                                       Observed slack tide concentrations
                                                        95%
                                                        Confidence
                                                        Interval
 Figure 5-10.       Observed and predicted dye concentrations [Ambrose (1987)].

                                                           5-20

-------
         Delaware River near Philadelphia
           Baxter [Ambrose (1987)]
[Ambrose (1987)]
Compound
Simulated
DCP
DMM
DCE
PCE
TCE
MC
CF
Predicted Rate Constants (day" )
KVd
0.11
0.10
0.12
0.11
0.12
0.14
0.12
KHU
0.02
10'B
10'5
0
0
10"B
10"B
KR°
10'4
0
10'4
10-"
10'5
—
—
KOU
10"b
—
10'°
10'°
10'°
10'B
10'B
KPH
0
—
0
0
0
0
0
K'
0.13
0.10
0.12
0.11
0.12
0.14
0.12
a Volatilization c Biodegradation e Photolysis
b Hydrolysis d Oxidation f Total
equation of Liss (1973) which ignores the vapor
pressure deficit in the atmosphere
E = 4.46 + 272.7 l/l/(5.9)
The Evaporation rate is in m day"1 and W is wind
speed in m sec" at a 1 0 cm (0.33 ft) height estimated
from 2 m (6.6 ft) measurements in the area and
converted to the 1 0 cm (0.33 ft) height assuming that
the logarithmic prof le is valid and that the roughness
height of the water surface is typically 1 mm (0.0033
ft).
-

Compound
Simulated
DCP
Median
95% Interval
DMM
Median
95% Interval
DCE
Median
95% Interval
PCE
Median
95% Interval
TCE
Median
95% Interval
CF
Median
95% Interval
MC
Median
95% Interval
5-
Concentrations (g/L)
NEWPCP
Effluent
6,050
1,360-16,800
591
25-2,820
213
67-2,380
54
30-85
9.3
2.0-33
4.4
3.2-7.5
2.5
1.7-11
Baxter
Observed
66
56-84
9.4
7.7-13.6
2.0
1.2-3.0
2.1
0.2-2.6
0.4
0-2.5
0.4
0.3-0.9
0.04
0-0.9
Predicted
57
12-138
6.2
0.3-30
2.1
0.7-24
0.5
0.3-0.8
0.09
0-0.3
0.04
0.03-0.07
0.03
0-0.15
Error
Factor
1.2-1
1.5-1
1.0
4.Z1
4.4-1
10.0'1
1.3-1

Data  defining the environmental  properties and
chemical properties are reproduced in Tables 5.16
and 5.17.  Table 5.18 gives the computed rate con-
stants 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 speci-
fied 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 avail-
able)  to be  governed by mean and  spring tides
(noted to occur during the study) and a steady fresh-
water 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 chemi-
cals 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 concentra-
tions were compared to the  median and range of
concentrations obtained  from grab samples col-
      lO4-;

       5-
       5-
   a
   o

      io3-
    o
    a
    o
   u
      101-
       5-
           detection limit
            DCF
                   T
T
T
                  DMM   DCE   PCE
           TCE
            MC
                                I 85%
                                • Confidence
                                I Interval
                                                CF
 Figure 5-11.      Northeast Water Pollution Control Plant Effluent
 Concentrations, October 2-3, 1983
 [Ambrose (1987)].
  lected 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 |jg/L)  at  the water
  intake (see Table 5.19).

5-21

-------
       200
        100-
    c   200
        100-
    OL
    o
    o
         10-
          c _
                                                 Logan
                                                  Point
               Low     Flood     High         Ebb
                             Tidal Stage
                    Observed Data
                                        Model Predictions
Confidence   median
Interval
                                                95%
                                                Confidence
                                                Interval
_]
O)
c
c
o
1
"c
. ^
Low Flood High Ebb
Tidal Stage
Observed Data Model Predictions
Bj> 95% ''^-C~~- ) 95%
^ Confidence median /^x^ C Confidence
) Interval ,' — - ) Interval
Figure 5-12. Observed and predicted DCP concentrations
[Ambrose (1987)].
                                        Figure 5-14. Observed and predicted DCE concentrations
                                        [Ambrose (1987)].
        100-
         50-
                                              Tacony—
                                               Palmyra
    .£   lOO-
    a
         50-
                                                 Baxter
                                                 Logan
                                                  Point
               Low
                       Flood     High
                              Tidal Stage
                                              Ebb
                    Observed Data
                                        Model Predictions
                                         S^- )
                         Confidence    median /^\ C Confidenc
                         Interval           *'"'*-. > Interval
                                                                               Low
                                                               Flood     High
                                                                      Tidal Stage
Ebb
Observed Data
median L_
•
j> 95%
S Confidence
,) Interval
Model Predictions
'>O" •> 95%
median /^x^ C Confidence
+'"*"+ ) Interval
Figure 5-13. Observed and predicted DMM concentrations
[Ambrose (1987)].
                                        Figure 5-15. Observed and predicted PCE concentrations
                                        [Ambrose (1987)].
                                                            5-22

-------
At this  point, the  model is  sufficiently calibrated to
establish a link between the high concentrations meas-
ured 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 underpre-
dict because of the coefficients chosen from the litera-
ture and only predicts averaged values) to determine
where water quality standards are violated. If stand-
ards 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.
  Desirable
 Water Uses
                   W,
   V   §
   Water  1> a
   Quality  | £
  Standards »



^-1


_^


  Effluent
 BOD Loads
  Resulting i
   Water  £ .§.
   Quality  »
        0
  Allocated
 BOD Loads
  Projected
   Water
   Quality
Figure 5-16. Componennts of the waste load allocation
procedure.
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  cali-
brated 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  allo-
cation  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 5-17. General waste load allocation procedure. Note
WQ = water quality, NPDES = National Pollution Discharge
Eliminiation System, and TMDL = total maximum daily load.
                                                 5-23

-------
Table 5-20. Main Sources of Criteria to Protect Designated
          Water Uses
  Primary
 Documents
 Secondary
 Documents
  Historical ^
 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.
Any information available in the open literature.
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. ill of the Red Book for pre-1950 work in
this area.
  Useful for tracing the development of criteria and citation of
  additional information
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, Driscolletal. 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 cool-
ing, 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 docu-
ments.

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 re-
sponse of the estuary.  The modeling alternative in-
volves 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 judge-
ment (typically from experts). The complexity of es-
tuary  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 assimi-
lative 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 capac-
ity 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 individ-
ual dischargers  waste load allocations (see  EPA 1985
for definitions).  This includes simulation with existing
and projected loads, and incorporation of reserve ca-
pacity 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
                                                   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. Forthe total maximum daily loads selected, evaluate
the cost-benefit of the standards chosen.  This step
may be somewhat controversial and applied in differ-
ent 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 Sys-
tem) 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, deter-
mining  the waste assimilative capacity  is relatively
straightforward.  Models are available to relate critical
water quality responses to the loads for most prob-
lems.  See Chapter 3 for guidance.

However, the definition of critical conditions for estuar-
ies  is not  straightforward.  For streams  receiving or-
ganic loads, this is  a straightforward matter of
determining the low flow and high temperature condi-
tions.  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 un-
derstanding the  exact  effects of the processes de-
scribed 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 de-
mands. If the physical, chemical, and biological char-
acteristics  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 sen-
sitivity 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 deoxy-
genation  coefficient, and other parameters  are rou-
tinely 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 conser-
vatively extrapolate to future conditions. In addition, it
is  possible  to consult  the  existing data and  make
reasonable estimates.  See Supplement XV for guid-
ance.  Crude estimates of deoxygenation rate coeffi-
cients can also be made in  a similar manner but with
less certainty.  Tabulations of deoxygenation coeffi-
cients 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 dis-
solved oxygen problems are conceptually simplified in

many cases by noting that a linear relationship usually
exists between loads and deficits.  Only when phyto-
plankton and second order toxic chemical modeling is
                                                5-25

-------
required, does a nonlinear relationship between defi-
cits or chemical concentrations and load exist.  It is
also possible to investigate which components of a
waste load (unoxidized carbon or nitrogen versus nu-
trients that result in eutrophication), cause a dissolved
oxygen deficit. The linear relationship between waste
load components and deficit or other chemical concen-
trations (e.g., BOD or ammonia) is also very useful to
investigate the effect of multiple sources. A compo-
nent 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 exam-
ple, the cause of violations  of a  dissolved oxygen
standard can be determined from the relative contribu-
tion 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 maxi-
mum  deficit  are computed  by keeping  up with the
deficit calculated in each time step for each process:
                            reaeration, deoxygenation, nitrification, sediment oxy-
                            gen demand, net photosynthesis, and by dilution with
                            other loads and tributaries.

                            Multiple sources that do not significantly increase es-
                            tuary 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 con-
                            tribute 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 be-
yond secondary levels at the Salisbury, Maryland Sew-
age 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 dis-
                            charge 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

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

-------
t
O *-»
E J

^E
q ~
d
          \
                                                               TOTAL DEFICIT
      -2
                                   14
                                                 10
 .
S

r    9

    7600
  «•»»
  >»
9 5 sooo
3 5
  «-> 2800
                  NITROGENOUS



                  CARBONACEOUS
                                                              POINT SOURCES
                     18
                                   14
                                                 10
J-
O

HI
D

q
d
    0»
                   • DEFICIT BOUNDARY CONDITION
                                                               BACKGROUND


                                                        BENTHIC DEMAND
                     18
                                   14
                                          12
                                                  10
 s -7  o
 6L ^
 pf U)
      -4
      -6

      22
                                                PHOTOSYNTHESIS LESS RESPIRATION
                    18     18     14     12     10      8      84

                            MILES ABOVE MOUTH OF WiCOMICO RIVER
       DAM  SALISBURY
              STP
Figure 5-19.     Component deficits for July 1971 dissolved oxygen verification [Robert Thomann in Review].
                                          5-28

-------
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 hydrody-
namic 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 relation-
ships between  n, the drag coefficient (Cd), and turbu-
lent mixing. The quadratic stress formulation relates
the eddy  viscosity approximation of the  vertical
Reynolds stress to a  drag  coefficient  and  average
velocities as follows
                               2°'5
     Ez (du/dz ) = p0Cd (ub  + vb  )' (ub)      (5.10)
and
                               2°'5
     Ez (dv/dz ) = p0Cd (ub  + vb  )'  (vb)      (5.11)
where
   Po = density of water,
   du/dz , dv/dz = 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
                                             (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 momen-
tum equations given in Table 2.1 of the second section
in  Part I of this guidance manual. The two- and three-
dimensional models based on these formulas are cali-
brated  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 Man-
ning 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
Table 5-21. Relationship between Various Friction Factors used to Quantify Friction Loss in Estuaries

Manning n
Chezy Cz
Drag
Coefficient Cd
Darcy-
Weisbach f
Fanning ft
Manning n

= n
=£*,-
gn2
C?R1/3
8gn2
C?R1/3
2 2
Chezy Cz
Ci RHW
Cz

= CZ
9
Cz2
8g
cz2
= ~c^
Drag
Coefficient
2 2
Cd = u* /U
Cd/2CiR1/e
g1/2
g1/2
cii2
= Cd
= 8Cd
= 2Cd
Darcy-
Weisbach
f
CiRH1/8f1/2
(8g)1/2
(8g)V2
(01/2
f
~8
= f
f
~ 4
Fanning
ff
CiRH1/V/2
(2g)1/2
(2g)1/2
(fr)V2
ff
2
= 4ff
= 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)] asio = (1/2) p Cd U2 or Cd = 2u» 2/U2 where bed shear velocity, t, divided by
        water density, p, is the shear velocity, ut = (g RwS)1/2. S is the energy gradient of the flow. U is the average flow velocity.
                                                 5-29

-------
and gravel beds using an approximate form of Sticklers
equation (Henderson 1966, Garde and Ranga  Raju
1977)
= 0.031
                                           (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 /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, how-
ever, flow resistance  is a function of the  Reynolds
number of the flow
   Re =
        4UR
                                      (5.15)
where U is the average flow velocity, R is the hydraulic
radius (cross sectional area divided by wetted perime-
ter), and v   is the kinematic viscosity of estuarine
waters.  Figure 5.20, modified from a Moody diagram
for flow resistance, gives the general relationship be-
tween the  ratio  of the Manning n to depth to the
one-sixth power (hydraulic radius  is approximately
          O.O25
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 signifi-
cant 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 (Am-
brose, personal communication, Ambrose 1987, Am-
brose 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 val-
ues 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 de-
creases the apparent roughness coefficient (McCutch-
eon  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 verti-
cally averaged models or  models having gross repre-
     cc
     c
           0.006
                                                REYNOLDS NUMBER
Figure 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

-------
Table 5-22.  Values of the Manning n for Different Types of
          Vegetation in Wetland Areas
          [Chow (1959) and Jarrett (1985)]

Type of Vegetation
Grass:
Short
Tall
Brush:
Scattered with Dense
Weeds
Sparse Trees and Brush
in Winter
Sparse Trees and Brush
in Summer
Medium to Dense Brush
in Winter
Medium to Dense Brush
in Summer
Trees:
Dense, Straight Willows
Stumps or Cyprus Knees
Stumps with Dense
Sprouts, Grass and
Weeds
Dense Stand of Trees,
Few Fallen Trees, and no
Branches hanging in
water
Dense Stand of Trees,
Some Fallen Trees, or
Branches Hanging in
Water
Value of n
Minimum

0.025
0.030

0.035
0.035
0.040
0.045
0.070

0.110
0.030
0.050
0.080
0.100
Typical

0.030
0.035

0.050
0.050
0.060
0.070
0.100

0.150
0.040
0.060
0.100
0.120
Maximum

0.035
0.050

0.070
0.060
0.080
0.110
0.160

0.200
0.050
0.080
0.120
0.160
sentation of the vertical structure. When this occurs, it
is important to conduct a sensitivity analysis to deter-
mine if the overall calibrated model shows any sensi-
tivity 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 contin-
ues. First, sea grass and other vegetation influence
shallow open water flows. Second, emergent vegeta-
tion such as  Cyprus trees, mangroves, bushes, and
marsh grasses may control flow through wetland ar-
eas. 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 Regu-
lation,  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 Man-
ning 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.  How-
ever, 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 forthis 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 = «fe + «/+ «1 + «2 + «3             (5.16)
where typical values are on the order of 0.020,

   nb = Manning n associated with bottom  rough-
   ness conditions,
   nf = correction related to form roughness or bed
   irregularity due to ripples and dunes,
   n-| = correction related to the nonuniform depth
   of the flow, and
                                                5-31

-------
Table 5-23. Manning n Corrections for Ripples and Dunes
Bed Topography
Smooth Bed
nf
0.00
Table 5-24. Manning n Corrections for the Relative Effect of
          Obstructions
Relative Effect of Obstructions
Negligible
Minor
ni
0.00
0.010to0.015
Table 5-25. Manning n Corrections for Changes in Channel
          Depth and Width
Variation of Channel Cross Section
Gradual
Alternating occasionally
n2
0.00
0.005
   112 = correction for the nonuniform width of the
   flow.
   113 = correction for effects of vegetation
Alternatively, Chow (1959) notes that  a multiplicative
version of Equation (5.16) can be used as well. How-
ever, that form is better adopted to meandering chan-
nels 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 m 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 correc-
tions 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)
                 RHP
                             cos a
(5.17)
and
         Table 5-26.  Adjustments for the Manning n due to Vegetation
                   [Jarret (1985)]
Amount
of Vegeta-
tion
Small
Medium
Range of ns
0.002 to 0.01
0.010 to 0.025
Description of Conditions
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.
Grass from 1 12 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.
            bdh_+dQ_
              dt + dx

         where
                                                                                                 (5.18)
            dt
               = local inertia term,
            d ^—- = force due to advection or momentum
               dx

            change due to mass transport of water,

               dh
            gA — = force due to potential energy of the fluid
               dx
            or gravitational body force,

              sn 2<9 \O\
            ——^   4 = force due to bottom shear or fric-

            tional resistance (quadratic stress law),

             Adc
               p dx
                    = force due to longitudinal pressure dif-
            ference caused by density differences along the
            axis of the estuary,
            A r^
            - s-^2- W 10 2 cos a = Force due to wind shear
             RHP
            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,
                                                 5-32

-------
   g = Gravitational constant,
   A = Cross sectional area,

   — = Slope of the energy gradient or approxi-
   ox
   mately the water surface slope, where h is the
   depth of flow to water surface from an arbitary da-
   tum,
   n = Manning roughness coefficient,
   Ci = Units conversion factor (1.0 when RH is ex-
   pressed in m and 1.49 when RH is expressed in
   feet),
   RH = Hydraulic radius (cross-sectional area di-
   vided by wetted perimeter of the cross section
   that is approximately equal the depth in wide es-
   tuaries),
   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),

   pa= The density of air,

   p = Density of water,

   a = Angle of wind direction from the axis of the
   estuary,
   Wio = 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 approxima-
tions when lateral and vertical differences are unimpor-
tant, 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 be-
tween 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 gra-
dients are small enough to neglect.  The best exam-
ples 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 ap-
proximate equations are written as
dt
              __    _
            dx ~8 dx
                           •u \u
                                                     Cda Pa „,  2
                                                   + —	W 10  cos a
                                                     RH p
                                                and
                                                   dt   dx
                                           (5.19)
                                                                                           (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 rough-
ness 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 align-
ment and sediment size distributions do not vary sig-
nificantly.   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 nec-
essary, 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 vari-
ations in cross section, bottom topography, and ob-
structions. 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 val-
ues 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 turbu-
lence 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 ex cess 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 associ-
ated 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 con-
tained in the flow (generally expected to cover or
occupy approximately one percent or more of the cross
sectional area).  These include submerged rock out-
crops, 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 obstruc-
tion. 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 ac-
count, 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 modi-
fied unless some large discrepancy is  noted.
                                                5-34

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EXAMPLE 5.3.
Initial Selection of the Manning n for a Hypothetical Estuary
Table 5.27 illustrates the Manning n selection proce-
dure.  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 forthis. Obstruc-
tions (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.
Table 5-27.  Reach Characteristics for a Hypothetical Estuary and Calculation of the Manning n Value
Segment
Number

1




2




3



4


5


6





Description

Wetland with dense
stand of straight trees,
few fallen trees, very little
brush and no weeds

Wetland with marsh
grass



Shallow area with sea
grass over 70% of the
bottom, extending over
about 50% of the depth
Deep well defined
channel

Wide deep channel in the
vicinity of the turbidity
maximum
Wide deep channel down
estuary of the turbidity
maximum with significant
sediment transport into
the estuary
Bed
Material

Fine
grain



na




Sandy



Sandy


Fine
grain

Fine
grain



Bed
Topo-
graphy
Irregular
surface



na




Flat



Dunes


Ripples


Fluid mud
layer over
much of
the
channel
Channel
Change

Meandering.
irregular,
braided and
indistinct
channel in areas
Meandering,
irregular,
braided and
indistinct
channel in areas
No significant
change


Some narrowing
of channel and
bends
Straight


Straight




Obstruc-
tions

A few fallen
trees



None




None



Submerg
ed

None


A few small
islands



Vegeta-
tion

See de-
scription



See de-
scription



See de-
scription


None


None


Minor
vegetal
ion on
the
shores

nf

0.01




0.035




0.025



0.025


0.02


0.015





ni

0




0




0



0.01


.005


0





n2

0




0




0



0


0


0





nz

0




0




0.01



0


0


0





n

0.01




0.035




0.035



0.035


0.025


0.015




                                               5-35

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EXAMPLE 5.4.
Selection of the Manning n for the Delaware Estuary
Figure 1 from Ambrose and Roesch (1982) and Am-
brose (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 estu-
ary 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 calibra-
tion 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 con-
sistent 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  be-
tween  measured and  predicted tidal range for mean
tide and average spring tide events.  Table 5.7 indi-
cates that discrepancies (as  measured by the coeffi-
cient of variation) are less than 10 percent throughout
the estuary. Thatcher  and Harleman (1981) also cali-
brated 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
    0.04
  ID
  Z  0.02
                                                 NOS data points
                                              A  USGS data points
                                             	 Calculated
                                            40    60     BO    100

                                            DISTANCE FROM CAPES IN MILES
                                                                   120
                                                                        140
                              CO
                              UJ
                              z

                                                Mean Sea Level (MSL)
                                       20     40    60    80    100

                                             DISTANCE FROM CAPES IN MILES
                                                                   120
                                                                        140
                 40     60    80    100

                 DISTANCE FROM CAPES IN MILES
                            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)].

                            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 neglect-
                            ing  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 meas-
                            ured 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)].
                                                5-36

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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 sur-
face elevations on a temporary basis. Shallower es-
tuaries   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.
          0.0025
     u]   0.0020
     O
     UJ
     O
     O

     <   0.0015
     cc
     O
          0.0010
                                               T
........  D»acon & W«bb
	  Wu
_.._.._.._..  Smith
_._._._.  Garratt
^— ^ — ^_  Amorocho
—^^^—^  O'Connor
                                                I
                                   I
                                               10           15

                                           WINDSPEED^  (m/s)
                                               20
25
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
SELECTION OF EDDY VISCOSITY VALUES
Mixing coefficients required in a typical hydrodynamic
model cannot be precisely estimated. Mixing is con-
trolled 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 selec-
tion 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 com-
monly 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 tur-
bulence 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 read-
ily 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 hydro-
dynamics models, is not available. To fully understand
the basic limitations of the eddy viscosity model and to
fully understand when difficulties in selecting calibra-
tion 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  per-
                            formed.   Second,  validation of the  hydrodynamic
                            model should be accomplished by comparing simula-
                            tions  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 calibra-
                            tion and validation data.

                            Typically, a constant eddy viscosity value is only appli-
                            cable 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 aver-
                            aged  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 estu-
ary 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 neces-
sary, especially when water quality  results are sensi-
tive 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  in-
creases for elements containing separation zones and
wakes of flow around islands, headlands,  and penin-
sulas.

Second-order Approximation  for Stratified  Flow
Models - For laterally averaged two dimensional mod-
els 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 vis-
cosity varies with depth and degree of  stratification.
This works well for cases where the estuary  is rela-
tively 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 Com-
mittee 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 formu-
lations are only  approximately  useful for estuarine
flows when  the  flows are approximately  boundary-
layer 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 mod-
els are obtained when lateral and horizontal values are
modified to account for roughness, excessive turbu-
lence 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 predic-
tive 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 strati-
fied flows of estuaries and in many cases, more elabo-
rate methods that simulate the generation, transport,
and dissipation  (under different conditions) of turbu-
lence 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 predic-
tively valid simulations of critical hydrodynamic condi-
tions  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 Fran-
cisco 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 Man-
ning's n, Supplement I

B. Depth Averaged Two Dimensional Models:

  1. Estimate a  uniform lateral and longitudinal eddy
viscosity coefficient for all computation elements (seg-
ments 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 eddv diffusivitv:
      = 0.0051
(5.21)
    where EH is the horizontal eddy viscosity (lat-
     eral, 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 eddv 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 gradi-
ents.

 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 loca-
tion 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 se-
lected. 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 formu-
lations 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 occasion-
ally been applied. Unfortunately, these model applica-
tions 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 atmos-
pheric 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 equa-
tions are only valid for slight stratification. Knight et al.
(1980) shows that the Holzman  form is quite inaccu-
rate, 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 conclu-
sions are most important when  the RAND two- and
three-dimensional hydrodynamic model is  being ap-
plied. The Mamajev formula was  used primarily to
provide quick simulated mixing when stratification be-
comes 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 func-
tions  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 pa-
rameters  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 gen-
eral trend of vertical eddy viscosity with changes  in
stratification as measured by the gradient Richardson
number. There are typically  large discrepancies  in
values of p 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 stratified-
flows. In addition, Odd and Rodger (1978) show that
highly stratified
                                                5-40

-------
Table 5-28. Vertical Eddy Viscosity Formulations for Flow in Estuaries
Investigator
Munk and An-
derson (1948)
Rossby and
Montgomery
(1935)
Sverdrup
(1936)
Holzman
(1943))
Pasquill
(1949)
Kent and
Prit chard
(1957)
Prit chard
(1960)
Vreugdenhil
(1966)
Nelson (1972)

Odd and
Rodger
(1978)




Knight et al.
(1980)
Uedaetal.
(1981)
French and
McCutcheon
(1983)
Formulation for Ez
E_ EZO
' [1+p(n)R/]n
E_ Ezo
"' [1+P(/7)R/]"
E Ez°
[1+p(n)R/]n
Ez = Ezo[1+P(/7)R/]
t- Ezo
[1+p(n)R/]n
p EZO
[1+p(n)R/f
E_ Ezo
" [1+p(n)R/f
E £zo
[1+p(n)R/f
P EZO
[1+p(n)R/f
1)
E_ Ezo
"' [1+p(/7)R/f
2) For Ri continually increasing to over
75% of depth:
E ° for Pi ^ 1
' [i+p(/7)R/r
F fnr Pi - 1
[1+P(/7)]"
For the occurrence of a peak Ri in the
lower 75% of the flow at z0:
£° fnr Pif-nl ^ 1
[1+p(n)R/(zo)]n
£ fnr Pi/VM *- 1
[1+P(/7)]"
Except where Ez > Ezo, then
EZ=EZO
E_ Ezo
' [i+p(/7)R/r
p p 0-y 6 R '
tz = tzo e
Ez = Ezo[1+P(-1)R/]
E Ezo
[1+p(n)R/]n
E Ezo
[1+p(n)R/]n
Comments
n = 1 and p(n) = 10, based on oceanic thermocline Anderson measurements
from Jacobsen (1913) for Render's Fjord and Schultz's Grund recognized that a
general empirical equation could be written.
n = 1 and p(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.
n = 1 and p(n) = 1 0 to 1 3, based on wind profiles over Spitzbergen snow field.

Empirical equation proposed to explain evaporative flux in the atmosphere.
Incorrectly presupposes that a critical Ri of 1/p(n) exists which is quite
inconsistent with the observations of Jacobsen (1913) and others.
For n = 1 , p(n) = 1 2, and for n = -1 and p(n) = -12. From wind profiles in 2-meter
layer over grass.
For n = 1 , p(n) = 2.4; for n = 2, p(n) = 0.24; and for n = -1 , p(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.
For n = 2, p(n) = 0.28, based on a re-evaluation of the James River Estuary
data.
For n = 1 , p(n) = 30, data source unknown.

For n = 1 , p(n) = 1 0; for n = 2, p(n) = 2.5 or 5; and for n = -1 , p(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).
For n = 1 , p(n) = 1 40 to 1 80 and for n = 2, p(n) = 1 0 to 1 5; 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.
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 p(1) = 160 or
p(2) = 13. n =1 remaining somewhat better than n = 2. Improves Reynold
stress prediction to ± 60 for 60% of the data.


Collected additional data in Great Ouse Estuary with less stratification and
found that p(1 ) = 1 1 0 to 1 60 and p(2) = 1 3 to 20 consistent with Odd and
Rodger (1978).
Formula in poor agreement with Great Ouse Estuary data.
Formula in poorest agreement with Great Ouse Estuary data. p(-1)=3.4.
For n = 2, p(n) = 2.5, in the atmospheric boundary layer.

For n=1 , p(n) = 30 and for n = 2, p(n) = 10 from Great Ouse Estuary analyzed
by Odd and Rodger (1 978) but the root mean square error was minimized
instead of the relative error.
                                                        5-41

-------
Table 5-28.  Vertical Eddy Viscosity Formulations for Flow in Estuaries (continued)
Investigator
French and
McCutcheon
(1 983)
(continued)
Mamajev
(1 958)
French (1979)
Henderson-
Sellers (1982)
McCutcheon
(1 983)
Formulation for Ez
Ez = Ezo(1+a/(2Ro')
L Ezo
C\+ak2Ro')
Ez = Ezoe-°ARi
r EZO f
C/-[l+RoJ
Ezo
^' 1 40.74 R;
y- EZO
z~1+a(z/L)
Comments
Derived from Monin-Obukhov stability function for atmospheric boundary layer.
ak2 are empirical coefficients determined from unstratified flows (k = 0.41) and
from the atmospheric boundary layer (a = 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'
= ck2z2(3u/3z) where c = ratio of momentum mixing length to mass mixing
length and assumed constant for small z/L; and minimum Ap is small (i.e., less
than 3 to 5%). This form is generally inaccurate like the Holzman (1 943) eq.
because Ro'<(aK2) except for small values of Ro'. Does not fit strongest
stratification data from the Great Ouse Estuary at all.
Derived from eq. above by noting these eqs. are approximately equal as ak2Ro'
-> 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 ak2 is known
without data fitting from unstratified flows (k = 0.4) and the atmospheric
boundary layer (a = 5) and Ro' is less error prone than Ri.
Based on data of Jacobsen (1913) and reported by author to better fit than
other forms. Knight et al. (1 980), Nelson (1 972), and Delft (1 974) show this is
inaccurate.
Derived from dimensional analysis and calibrated with Great Ouse Estuary
calibrated for each estuary of interest and it lacks some vertical resolution
because of the definition of Ro.
Derived from Ueda et al. (1981) atmospheric boundary layer data.
a = 5 to 7 (wider range reported is 0.6 to 1 2 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,
1/9
u« = shear velocity = (gSD) 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.
3(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.
Ro'  =


Ro«  =
        Ri
                              gradient Richardson number =
Richardson number based on shear velocity = -rr-j —^
       gross Richardson number based on shear velocity
                                   put 8z
                                       gPAp
p   =  average density.
g   =  gravitational constant.
8P/8z=   density gradient
du/dz=   velocity gradient.
a   =  Monin-Obukhov constant = 5.
Ap  =  density difference over the depth
       of flow.
  conditions are difficult to reproduce as others would
  expect (Munk and Anderson 1948, Henderson-Sell-
ers 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 min-
utes (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 con-
ditions 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 (3.
                                             Of the two forms of the Munk-Anderson formula, the
                                             Rossby-Montgomery form seems superior to the Kent-
                                             Pritchard. This is clearly demonstrated from the stud-
                                             ies  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 formula-
                                             tion 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 tur-
                                             bulence  and the upper  layer conditions  where some
                                                 5-42

-------
Table 5-29.  Observed Values of the Constants in Various Forms of the Munk-Anderson Stability Function
Source
Rossby and Montgomery
(1935)
Sverdrup (1936)
Munk and Anderson (1948)
Pasquill (1949)
Kent and Pritchard (1957)
Pritchard (1960)
Pasquill (1962)
Vreugdenhil (1966)
Nelson (1972)
Odd and Rodger (1978)
Knight etal. (1980)
Uedaetal. (1981)
Henderson-Sellers (1982)
French and McCutcheon
(1985)
P(1)
40
10-13
10
12
2.4
—

30
10
160
1 1 0-1 60
2.5
0.74
30
P(2)
—
—
—
—
0.24
0.28

—
2.5,5.0
13
13-20
—
—
10
P(-1)
—
—
—
12
0.06
—
2.5
6
—
3.3
—
3.4
—
—
—
Flow condition
Heywood's wind profiles at Leafield
Wind profiles over Spitzbergen snow field. From Munk and
Anderson (1948)
Oceanic thermocline from Jacobsen (1 91 3) for Randers Fjord
and Schultz's Grund
Wind profiles in 2 meter layer over grass. From Nelson
(1972).
James River Estuary
James River Estuary
Rider's (1954) wind profiles.
Taylor's (1 960) analysis of Rider's (1 954) and eddy flux data
of Swinbank(1955)
Data source unknown. From Nelson (1972)
Wind profiles Rider (1955) and questionable pipe flow data
from Elision and Turner (1960). (1954) and Deacon
Great Ouse Estuary. Fit by minimizing the relative error.
Great Ouse Estuary. Visual fit.
Atmospheric boundary layer. From Henderson-Sellers (1982).
Rederived from data of Ueda et al (1 981 )
Great Ouse Estuary. Fit by minimizing the root mean square
error.
turbulence is dissipated. When the exact stratification
structure must be known to determine a waste load
allocation or a cause and effect, more elaborate turbu-
lence closure schemes may be required (see Rodi
1980, Sheng (1983), and Blumberg 1977).  If vertical
structure is  repeated during critical conditions, how-
ever, 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 devel-
oped by  Odd and Rodger (1978) can be developed.
Odd and Rodger noted that the Munk-Anderson for-
mula 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 analy-
sis 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, McCutch-
eon (1983) notes that  the most direct application of the
atmospheric boundary layer work involves the Monin-
Obukhov stability  parameter (see Table 5.28). How-
ever,  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 ad-
dition, 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-Sell-
ers 1982).  The result is that only limited direct appli-
cation 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 con-
                                                5-43

-------
stant determined in unstatified flows as 0.4 and a de-
termined 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 con-
stants should retain the same value determined from
other conditions (i.e., k = 0.4 and a = 5).  The second
two equations under French and McCutcheon (1983)
in Table 5.28 must be equivalent  in  the limit
k  a 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 formu-
lations do  as well as any  others in describing the
vertical mixing in the Great Ouse Estuary and this was
accomplished  without the  extensive calibration  re-
quired for all other formulations (French and McCutch-
eon 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 du/dz.

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 Ross by-Montgomery equation if the
estuary  is not strongly stratified.  The  McCutcheon
formulation can be used without calibration in some
cases. The value of (3(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 a
or (3 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 nec-
Table 5-30a. Various Means of Representing the Stability of Stratification and the Relationship between Various Parameters
Parameter



Gradient
Richardson
number, Ri
Shear Richard-
son Number,
Ro'
Shear Gross
Richardson
number, Ro-
Gross Richard-
son number, Ro
Densimetric
Froude number,
Fr
Monin-Obukho
Stability parar-
meter. z/L
Flux Richard-
son nymber, Rf
Brunt-Viasala
frequency, N2
Ri
<3P
®dz
r -?
-Tsui
\K\
=Ri

= R/(/C2)cp21

—
—
= Ri for
small z/L
=R/cpm
=4rf
\dz\
Ro'
gz2dP
pu*dz

Ro'
k2m=Monin-Obukhov stability function
                                                5-44

-------
essary 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 in-
 volved but these  have not been thoroughly checked
 and tested.
SUPPLEMENT IV:   BRIEF REVIEW OF TURBULENCE CLOSURE MODELS
In recent years, 2 and 3 dimensional turbulence clo-
sure models have been employed in environmental
problems (e.g., HYDROQUAL 1987).  ASCE Task
Committee  (1988) gives a good review and assess-
ment 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 aver-
aged mean quantities. Turbulent quantities are aver-
aged 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 tur-
bulence modeling is to relate  these turbulent coeffi-
cients to average variables (i.e.,  velocity, pressure,
and concentration),  empirical constants,  and func-
tions, 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  signifi-
cant velocity gradient (Rodi 1980). Table 5.28 lists
some empirical formulations developed for this theory.
As ASCE Task Committee(1988)  points out, the mix-
ing length theory assumes that the transport and his-
tory 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 forthe transport and history of eddy affects,
one-equation models have been developed which re-
late 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,  one-
equation 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 (Laun-
der 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 (s-equation) which is used to deter-
mine 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 turbu-
lent 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 criti-
cized 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. There-
fore,  more complex stress/flux  -equation models have
been developed which abandoned the k-equation used
by the above two methods. These models  are promis-
ing 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 en-
vironmental applications (e.g., HYDROQUAL 1987), it
should be noted that turbulence models can be reason-
ably applied only when the model assumptions are not
violated, and the extensive require-
                                               5-45

-------
ments for expertise, data, and computation facilities
are met. Presently, cost compared with the benefits
might make it unfeasible to employ a turbulence clo-
sure 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 Sup-
                                             plement 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.
SUPPLEMENT V.  SELECTION OF DISPERSION COEFFICIENTS
Dispersion coefficients are empirical analogs of the
molecular diffusion coefficient defined in the advective-
diffusive equation:
   dC
                                            (5.22)
                                             where C  is concentration of the constituent being
                                             modeled; U, V, and Ware 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. SS 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.
  105  10*
        10'
10'
                                 10
                                    -2
                                           DIFFUSION COEFFICIENT In mtt*i2 d«y"1
10
                                         10
10'
10
10"12    ID"14    10"
   10
10'
                 10
          10
                                            DIFFUSION COEFFICIENT In f..? t ~1
                                           io3      ho1      ho"1
                                                            10
                  10'
                    -T
                   10
                                                                                                10
           OCEANS, COASTAL AND DIFFUSERS - HORIZONTAL
                     OCEANS, - HORIZONTAL (OKUBO
                            E&J
                            >EPTH-
                            AVE.
                        ESTUARINE-
                          LONG.
                        LAT. AVERG.
                          LON6ITUDNAL
                         TABLES(5-17)
                   ESTUAR1NE - LONG.,
                   TIDALLY AVERAGED
                                         1971)
                                   ESTUARINE
                                    LATERAL
                                 HORIZONTAL
                                                      ULENT DIFFUSION
                                         VERTICAL
                                      (KOHANDFAN 1170)
                                                                  THERMAL AND
                                                                MOLECULAR DIFFUSIO
                                                                V
                                                                   !7
                                                     RETARDED DIFFUSION OF
                                                   4YDROPHOBIC AND IONIC SOLUTE:
                                                     IN SOILS AND SEDIMENTS
                                                                 SALTS AND
                                                                 GASES IN
                                                                  WATER
                                                        THERMAL DIFFU3.
                                                        SALTS IN WATER
10°
  10'
   10'
                                    10"
                                   10       10
                                   DIFFUSION COEFFICIENT In m
   10"
   2 --1
   10
                                     10
            10
                              10
10
   12
1010     10"      10'      10*     10'     10 "
                                   DIFFUSION COEFFICIENT In em
  10 *
   2 .-1
                                                                       10"
                                                                       10
                                                               10
                              10"
Figure 5-24. Diffusion Coefficients.
                                                 5-46

-------
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~~ G "1 / / ~
R / /
M • Gunnerson, 1960 /f /
- c // /
D J '/ /
	 /V- y _
2>y=Q.QQ\L*ll//- / y
//T/ Limits of data
//"/"/Olson and Ichiye
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NRDL » //// ' R /G ^
experiment, 1968 \*/ / '/ , R Rpdioactivity in
V j& >fc Bikini Lagoon
A y jtrn M
— w *X yoCv \ 1 Mile outfall field —
V *s\' ^^
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4/3 ^r j f S
y~ ' ~~^7 &£ /
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— *'•*/./ —
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/ °/^rS* x Gunnerson
"7*?" / / +Hidaka J -
y« / / f Parker, 1961
1 1 1 1 1 1 1 1
0.1 1 10 102 103 104 105 106 10
                                  Horizontal scale of diffusion phenomenon (L = ft)
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 gradi-
ents (SU/dx, SV/dy, and SW/dz) to correlations of turbu-
lent fluctuations of concentration, c',  and velocity (u1,
v', and z') written as: u'c', v'c', and w'c' (McCutcheon
1989). As such, the coefficients of proportionality rep-
resent 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 overtime
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 val-
ues 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 Equa-
tion 5.22 is solved. Therefore, at least minor differ-
ences are expected to be found if different numerical
schemes, with differing degrees of numerical disper-
sion are employed, or if different length and time scales
are used in solving the equations.  As a result, any
observational experience obtained from similar estu-
aries or from predictive equations based on past expe-
rience, 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 differ-
ence  may occur between the  final calibrated values
and the previous estimates. In addition, the use of case
studies from other estuaries must be carefully  consid-
ered 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 cali-
bration 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 meth-
ods include:

   a. Estimation of shear flow dispersion.  Fischer
     et al. (1979) notes that dispersion can be rea-
     sonably 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). Fis-
     cher et  al. (1979) note that the maximum lon-
     gitudinal dispersion due to shear is
     approximately
     Kx = 0.1(0.2 U2)T(0.8)                  (5.23)
     Where  Kx is expressed in m s"  , (0.2U) is as-
     sumed to approximate the deviation of the ve-
     locity in a  cross section from the cross
     sectional average, T is the tidal period in sec-
     onds, and the constant 0.8 is derived by Fis-
     cher et  al. (1979, see their Figure 7.4). U is
     the mean tidal velocity. Fischer et al. (1979), il-
     lustrates this method of estimation.

   b. Fraction of freshwater method.  Officer (1976)
     describes how freshwater and  observed longi-
     tudinal salinity gradients can be used to esti-
     mate longitudinal dispersion.

   c. 4/3's law.  It has been widely observed that
     lateral dispersion can be estimated from the
     empirical formula:
                             4,
     Ky = constant (length scale)                (5.24)
    See Bowie et al. (1985), Officer (1976), and Fig-
     ure 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-di-
mensional 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

-------
Table 5-30b. Tidally Averaged Longitudinal Dispersion Coefficients Observed in Selected One Dimensional Estuaries
           [Hydroscience (1971), Officer (1976) and Bowie et al. (1985)]
Estuary
Freshwater Inflow
(mV)
(ftV)
Low Flow Net
Non-tidal Velocity
(ms-1)
(fts1)
Longitudinal Dispersion
Coefficient
(mV1)
(ftV1)
Comments
                                                    North America
Hudson River
Mouth
Potomac
San Francisco Bay
Suison Bay
Sacramento and
San Joaquin
Rivers
Northern Arm
Southern Arm
Yaquina
106 to 637 3,750to
22,500
56 2000
— —
17 _
low flow 	
—

— —
— —
450 to 1 ,500 4,840 to
16,133
6 to 59 65 to 635
600 to 1,400 600to15,000
9 to 90 1 00 to 1 ,000
30 to 1,770 320to19,000
1 0 to 1 00 1 90 to 1 ,900
60 to 853 650 to 9, 180
14to99 140 to 1,066
From O'Conner (1962). Found
correlation between flow and Kx
Estimated from the fraction
freshwater method and dye
studies by Hetling and O'Connell
(1 965, 1 966). A very consistent
relationship between Kx and
distance downstream of Chain
Bridge observed
Determined by Bailey (1966) from
dye studies of one to a few days
in duration.
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.
Burt and Marriage (1957)
determined these values by
fraction of freshwater method.
High flow Kx significantly higher
than low flow Kx.
                                                   United Kingdom
Narrows of Mersey
Severn
Southampton
Thames
Tay
25.7 907.6
103 3,637


low flow 	
high flow 	
50 1 ,766
100 3,531
200 7,063
300 10,600
— —




161 1,733
359 3,864
54 to 1 74 581 to 1 ,873
158 1700
53 570
84 904
338 3,638
50 to 135 540 to 1,453
70 to 210 750 to 2,260
30 to 470 320 to 5,060
70 to 700 750 to 7,530
Estimates based on the fraction
freshwater method measured at
various locations along with
salinity concentrations averaged
over tidal cycles.
Kx values recomputed by Bowden
(1 963) 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.
Kx computed by fraction
freshwater method by Dyer
(1973).
At 1 6 Km (1 0 miles) and 40 Km
(25 miles) downestuary of London
Bridge.
At 48 Km (30 miles) downestuary
of London Bridge.
Estimates by the fraction
freshwater method. Estimated by
the fraction freshwater method.
Kx varies at each location as a
function of freshwater discharge.
                                                       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.
                                                       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)]
Estuary
Freshwater Inflow
(mV)
(ftV)
Low Flow Net
Non-tidal Velocity
(ms'1)
(fts1)
Longitudinal Dispersion
Coefficient
(mV)
(ftV)
Comments
                                                    United Kingdom
Irish Sea







North Sea


Firth of Fal


Blackwater



















0.0035 0.0115
















500 to 900 5,380 to
9,690






21 .7 to 9.6 234 to 103


0.4 to 3.6 4.3 to 38.9


13 to 27 140 to 291


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.
Estimated from dye spreading experiments
with instanteous point injections tracked for
up to 60 hr. Kx = ax/2f.
Estimated from dye spreading experiments
with instanteous point injections tracked for
up to 7 hr. Kx = ox/2f.
Estimated from dye spreading experiments
with instanteous point injections tracked for
up to 12 hrs.Kx = ox/2f.
Japan
Osaka Bay and
Mizushima Bay

Ariake Bay














0.5 5.4


0.25 to 5 2.7 to 53.8


Determined by calibration of a heat balance
model for thermal plume injected into the
bay from a power plant.
Determined by Higuchi (1967) from
diffusion of small dye patches in the bay.
The data follows the 4/3's law.
                     Discharge, IcPftV1
                         468
                 1	1	1	1	1	1	1	1	1	1	r—r
       0    40    80   120  160   200  240  280

                      Discharge, rrfs1

Figure 5-26. Relationship between longitudinal dispersion
coefficient and discharge in a Scottish estuary
[West and Williams (1972)].
                                                               HI
                                                               Q
                                                               LI-
                                                               fc
                                                               o
                                                               o
 2.8

 2.6
 2.4
 2.2
 2.0
 1.8
' 1.6
 1.4
 1.2

 1.0
 0.8
 0.6


 0.2
  0
                                                                              KILOMETERS FROM CHAIN BRIDGE
                                                                            10     20     30     40    50
                                                    O
                                                    E

                                                  0.6 S

                                                    z
                                                    O

                                                  0.4
                                                                                                                  5 °
                                                                           4    8    12   16   20   24   28   32  36
                                                                                 MILES FROM CHAIN BRIDGE
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

-------
Table 5-32. Lateral Dispersion Coefficients in Estuaries and Coastal Waters [Officer (1976)]
Estuary
Lateral Dispersion Coefficient
(mV)
(ftV)
Comments
                                               United Kingdom
Severn Estuary
Fal Estuary
Blackwater Estuary
North Sea (between
U.K. and Europe)
Irish Sea (between
U.K. and Ireland)
2 22
1.5 16
3 to 9 32 to 97
1.4 to 6.0 15 to 65
110 to 1,480 1,184to15,930
25 270
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.
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 = ov/21.
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 = c,y/2t.
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 = oy/2t.
Based on a simple heat balance by Bowden (1948).
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
(0.01 6 ft s'1).
                                                   Japan
 Osaka Bay and
 Mizushima Bay
0.5
             5.4
Determined by calibration of a heat balance model fora thermal plume injected
into the bay from a power plant.	
 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  dis-
   charge. If the waste load allocation covers more
   than a single freshwater discharge condition, longi-
   tudinal dispersion coefficients are typically related
   to changing freshwater discharge as illustrated  in
   Figure 5.26.
                                 5. Relate dispersion coefficient to location. The lon-
                                   gitudinal 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.  McCutch-
                                   eon (1983) lists various formulas that are useful.
                                   Typically a formula is selected and modified if nec-
                                   essary  during calibration. See  guidance  on the
                                   selection of vertical eddy viscosity.
                                                   5-51

-------
Table 5-33. Evaporation Formula for Lakes and Reservoirs [Ryan and Harleman (1973)]
Investigator
Marcians
and Har-
beck(1954)
Kohler
(1 954)
Zaykov
(1949)
Meyer
(1942)
Morton
(1976)
Rohwer
(1931)
Evaporation Rate
Expression
in Original Form
E=6.25x10-4u8(e0-e8)
E=0.00304u4(e0-e2)
E=[.15+.108u2](e0-e2)
E=1 0(1+0.1 U8)(e0-e8)
E=(300+50u8)(e0-ea)/p
E=0.771[1.465-.0186B]x
[0.44+0. 118u](e0-ea)
where B = atmos. press
Units* for
E, u, and
E*
cm(3 hr)"1
knots
mb
in. (day)'1
miles(day)"1
in. Hg
mm(day)"1
ms"1, mb
in. (month)"1
25 ft-wind
mph
in. Hg
in. (month)"1
mph
in. Hg
in. (day)"1
mph
in. Hg
Observation
Levels
8m-wind
8m-ea
4m-wind
2m-ea
2m-wind
2m-ea
25 ft - wind
25 ft-ea
8m-wind
2m-ea
0.5-1 ft-wind
1 inch-ea
Time
Scale
Incremen
ts
3 hrs
Day
Day

Monthly
Monthly
Daily
Water
Body
Lake
Hefner,
Oklahoma
2587 acres
Lake
Hefner,
Oklahoma
2587 acres
Ponds and
small
reservoirs
Small
lakes and
reservoirs
Class A
pan
Pans
85ft
diamter
tank
1 300 acre
reservoir
Formula at
Sea Level**
12.4u8(e0-es)
17.2u2(eo-e2)
15.9u4(e0-e2)
17.5u2(e0-e2)
(43+14u2)(eo-e2)
(73+7.3u3)(e0-e8)
(80+10u2)(e0-e2)
(73.5+1 2.2u8)(e0-e2)
(73.5+1 4.7u2)(eo-e2)
(67+10u2)(eo-e2)
Remarks
Good agreement with
Lake Mead, Lake
Eucumbene and
Russian Lake data.
Essentially the same as
the Lake Hefner
Formula.
Based on Russian
experience.
Recommended by
Shulyakovskiy.
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
Data from
meteorological stations.
Measurement heights
assumed.
Extensive pan
measurements using
several types of pans
Correlated with tank and
reservoir data.
  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 e0) 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)(e0-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 e0 - ea  is the difference
between the saturation vapor pressure of the atmos-
phere at the ambient temperature (e0) and the meas-
ured 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 reac-
tions. 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 coeffi-
cients a and b (McCutcheon 1989) by disproportionate
amounts unless the physical meaning of the two coef-
ficients is well understood (e.g., see Wunderlich 1972,
Ryan and Harleman 1973).
Table 5-34.  Evaporation Formulas [Wunderlich (1972) and McCutcheon (1989)]

Investigator
Penman (1956)


Meyer (1942)


Harbeck et al.
(1958)

Turner (1966)


Fry

Easterbrook
(1969)


Jobson (1980)

Fayeetal. (1979)

McCutcheon
(1982)

Evaporation Rate Expression
E=f(u, eo, e, etc.)
0.35(0.5+0.01 U2)(eo-e2)


0.36(1 +0.1 U7.6)(eo-e7.6)


0.078u2(eo-e2)

0.00030u2(eo-e2)


0.0001 291 U2(eo-e2)

0.000302 U2(C0-C2)
0.000001 942 U2(C0-C2)
C is relative humidity, unitless
(3.01 + 1.13u2)(eo-e2)

0.70(3.01 +1.13u2)(eo-e2)

0.45(3.01 + 1.13u2)(eo-e2)

Units for E, u, & e

mm day
mi/day @ 2m
mm Hg
in. month
mph @ 7.6m
in. Hg
in. day"
mph @ 2m
in. Hg
ft. day"1
mph @ 2m
in.Hg
cm. day "
km. day" @ 2m
mb
-2 -1
g cm s
ft. s"1


mm day "
ms" @ 2m
kilopa seals
mm day
ms @ 2m
kilopa seals
mm day "
ms @ 2m
kilopa seals
Time
Scale
—


Daily


Daily

—


—

—


—

—

15 min

Type of Water Body

Lake, meteorological data collected on land


Small lakes, reservoirs, and pan evaporation


Lake Mead, NV

Lake Michie, NC


—

Lake Hefner, mid-lake
Lake Hefner combined data

San Diego Aqueduct, CA. Energy balance.

Chattahoochee River, GA.

West Fork Trinity River, TX.

                                                5-53

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SUPPLEMENT VII:   SELECTION OF BACTERIA DIE-OFF COEFFICIENTS
Traditionally, the bacteria die-off process is considered
as a simple first-order decay, such that
   dt
      = -KBN
                                           (5.26)
where N  = bacteria concentration {num/L }
      KB = die-off or decay rate {1/T}

The resulting distribution downstream is
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
   dt
where
                —
                                           (5.27)
   Vu = resuspension velocity {L/T}
   H = water column depth {!_}
   Ms = solids concentration in the sediment {Ms/L3}
   RN = bacteria concentrations based on solids
   {num/Ms}
The solution of equation 5.21 is
     = N0ext(-KB t)
                     VUMSRN
                      HKB
[l-e~KBt]
(5.28)
For bacteria analysis and modeling, the order of mag-
nitude 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, respec-
tively. 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 forthe 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-or-
         der. Under these situations, the decaying process is
         divided into different stages.  Each stage can be de-
         scribed reasonably well by first-order  decay and a
         different decay rate (Thomann and Mueller 1987).

         An alternative way of selecting the initial bacteria de-
         cay rate is described in Thomann and Mueller (1987).
         They  recommend an  empirical equation which in-
         cludes the effects of salinity, temperature, sunlight and
         settling of bacteria.
                                                      KB = [0.8 + 0.006(%seawater)] 1.07
                                                                                    T-20
                                                                                               (5.29)
                                                    where
   % sea water = percent of salinity compared to
   sea water
   1.07 = temperature correction coefficient
   T = temperature in oC
   a = constant coefficient in light correction function
   lo = 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 resus-
   pension, which is already accounted for with a re-
   suspension term in Eq.  5-22.  But, lumping
   resuspension into Vs is also feasible; then Vs be-
   comes net settling rate.
    H = water column depth, m.
Following is a simple  example to calculate  bacteria
transport.

 T = 25°C
   Q = 200 m3/sec
   u = 0.01 m/sec
   E = 50 m /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 as-
                                                5-54

-------
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)]
Organism

Total coliform
Total or fecal coli-
form
Fecal coliform
E. coli
Fecal streptococci

Coxsackie
Echo 6
Polio type I
Enteric (polio,
Echo, and cox-
sackie)
Dieoff Rate^
Coefficient
(d~1 base e)

1.4
(0.7 to 3.0)
48.
(8. to 84)
0.0 to 2.4
2.5 to 6.1
0.48
0.48 to 8.00
1.0
[summer)
0.60
(summer)
37 to 1 1 0
0.08 to 2.0
18 to 55

0.12
0.03
0.08
0.03
0.16
0.05
1.1 to 2.3
Temperature
(°C)

20
—
—
—
20
20
—
—
—
—
—

25
4
25
4
25
4
24
Reference
Coliforms:
Mancini (1978)
Mitchell and
Chamberlain (1978)
Hydroscience (1977b)
Hydroscience (1976b)
Chen (1970)
Tetra Tech (1 976)
Velz(1984)
Velz(1984)
Fujiokaetal. (1981)
Anderson etal. (1979)
Fujiokaetal. (1981)
Viruses:
Colwell and Hetrick
(1975)
Colwell and Hetrick
(1975)
Colwell and Hetrick
(1975)
Fujiokaetal.' (1980)
Comments

Seawater
Collected from 14 ocean outfalls, variable temp.
New York Harbor Salinity: 2 to 1 8 o/oo. Sample kept in
darkness
New York Harbor Salinity: 1 5 o/oo. Sample kept in
sunlight
Derived from the calibration of a model for San
Francisco Bay
Derived from model calibration for Long Island, New
York Estuaries
Observed in New York Harbor
Vloracaibo Strait, Venezula; from observations by Parra
Pardi.
Seawater kept in sunlight
Seawater, 10 to 30 o/oo
Seawater kept in sunlight

Vlarine waters
Marine waters
Vlarine waters
Seawater collected off Hawaii
*Ranqe of values or time of year in parenthesis.
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 m/E = le 0-°K-5000 )/50 = 26 ppr[

 b) the average salinity between the outlet and bathing
   area

   S =(2.6 + 7.0)72 = 4.8 PPT
 c)Take 35 PPT as 100% sea water salinity, then

   % seawater = 4.8/35 = 14 %
 d) Decay rate estimation
   Kb (25°C) = [0.8 + (0.006 • 14)] 1.4 = 1.24  day
                                               -1
  This decay rate will be used without the calibra-
  tion or adjustment that is needed in a real prob-
  lem.
e) Concentration and Bathing Area with  no disinfec-
  tion:
       0e
    2(50)
                                                  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)]
Organism
Dieoff
RateCoefficient
(d~1 base e)
Temperature
(°C)
Reference
Comments
Coliforms:
Total coliforms
Total or fecal
coliforms
0.8
.2 (summer)
1.1 (winter)
2.0 (Jn/Sept)
2.5 (Oct/May)
0.58 (Dec/Mar
1 .0 (Apr/Nov)
2.0 (Jn/Sept)
0.9 (Oct/May)
0.62 (Dec/Mar
0.7 (Apr/Nov)
15.1
0.48 (winter)
1 .03 (summer]
0.12 (summer;
1 .73 (summer]
5.5 (summer)
2.2 (summer)
1 .1 (winter)
1 .84 (summer;
1 .84 (summer]
26.4
0.5
0.41
1 .51 (summer;
0.2 to 0.7
2.0
1.7
20
20
5
—
—
—
—
—
—
—
—
—
—
—
—
10
—
—
7.9 to 25.5
19
Mancini (1978)
Frost and Streeter
(1 924)
Hoskinsetal. (1927)
Hoskinsetal. (1927)
Kittrell and Kochtitzky
(1947)
Kittrell and Furfari
(1963)
Kittrell and Furfari
(1963)
Kittrell and Furfari
(1963)
Kittrell and Furfari
(1963)
Kittrell and Furfari
(1963)
Velz (1970)
Velz (1984)
Velz (1984)
Wasseretal. (1934)
Wuhrmann(1972)
Mahlock(1974)
Velz (1984)
Klock(1971)
Marais(1974)
Average freshwater
From observed disappearance rates in the Ohio River.
From observed disappearance rates in the Upper Illinois
River.
From observed disappearance rates in the lower Illinois
River
From observed disappearance rates in a shallow turbulent
stream
From observed disappearance rates in the Miissouri River
downstream of Kansas City, Missouri
From observed disappearance rates in the Tennessee River
at Knoxville.
From observed disappearance rates in the Tennessee River
at Chattanooga.
From observed disappearance rates in the Sacramento
River downstream of Sacramento, California
From observed disappearance rates in the Cumberland
River in Tennessee.
From observed disappearance rates in the Scoito River,
Ohio. Original data from Kehr et al.
From observed disappearance rates in the Upper Miami
River, Ohio. Original data from Velz et al.
From observed disappearance rates in the Hudson
River.downstream of Albany, New York. Original data from
Halletal
From observed disappearance rates in the Glatt River
From observed disappearance rates in a groundwater fed
stream
From observed disappearance rates in the Leaf River,
Mississippi
From observed disappearance rate in Yaracuy River,
Venezula by Parra Pardi.
From observed disappearance rates in a wastewater lagoon.
From observed disappearance rates in maturation ponds
                                                       5-56

-------
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)]
Organism

Fecal streptococe
S.faecalis
S. bovis
Dieoff
RateCoefficient
(d~1 base e)
2.6(1. 19)T'20
8.64
9.6 (August)
1.25
2.62 to 0.384
3.3 to 2. 7
1.0
0.01 to 3.5
0.48 to 2.0
0.48
1.0 to 3.0
0.48
Temperature
(°C)
—
10to 17
—
15
10
20
20
20
20
20
20
20
Reference
Marais(1974)
Zanonietal. (1978)
Gannon etal. (1983)
Thornton et al. (1980)
Chen etal.
Baca and Arnett (1 976)
U.S. Army Corps of
Fngineers (1974)
Chen and Orlob(1975)
Hydroscience (1971)
Chen and Wells (1975)
Comments
-rom observed disappearance rates in oxidation ponds
From observed disappearance rates in Lake Michigan
From observed disappearance rates in FordLake, Ypsilanti,
Michigan
October 1976, March 1977, June 1977. From observed
disappearance rates in DeGray Reservoir, Arkansas.
Derived from model calibration(1976)
Derived from model calibration for various streams.
Derived from model calibration for Lake Ontario.
Derived from model calibration for Lake Washington.
Derived from model calibration for various streams.
Derived from model calibration for Boise River, Idaho.
pi:
0.4 to 0.9
0.1 to 0.4
0 to 0.8
0.3
0.1
1.0 to 3.0
0.05 to 0.1
1.5
20
4
20
20
20
18
20
USEPA(1974)
Kenner(1978)
Geldrich and Kenner
(1969)
Dutka and Kwan (1 980)
Geldrich and Kenner
(1969)
Freshwater
Kanawha River
Stormwater, observed from 0 to 3rd day
Observed from 3rd to the 14th day.
Hamilton Bay, Lake Ontario observed from 0 to 10th day.
Observed from 10th to 28th day.
Stormwater
Pathogens:
Salmonella ty-
ohinurium
Salmonella
:hompson
1.1
0.1
0.5 to 3
0.1
20
20
18
18
Geldrich and Kenner
(1969)
Dutka and Kwan (1 980)
Stormwater, observed from 0 to 3rd day.
Observed from 3rd to 14th day
Hamilton Bay, Lake Ontario observed from 0 to 10th days
Observed from 1 0th to 28th day
Viruses'
Coxsackie
0.77
21 to 23
Herrmann etal. (1974)
Lake Wingra
Fecal  Coliform Bacteria  Reduction  percent with a
growth factor of 2
   2(400)-200
              = 75%
      2(400)
If there is no background concentration of fecal coli-
form  bacteria in the bathing area, reducing the 75%
concentration in  the fecal coliform bacteria load will
result in 200/100 ml fecal coliform bacteria concentra-
tion in the bathing area.
                                                   5-57

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SUPPLEMENT VIM:  CALIBRATING SIMPLE SEDIMENT MODELS
Section 2.4 and Supplement I of Section 2 introduced
the important processes concerning sediment trans-
port in  estuaries. Settling is always an important po-
tential factor to water quality problems and a careful
analysis and calibration of settling coefficients is al-
ways 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.
  velocity can not be used in describing the pollutant
  transport.  For example, the concentrations of pollut-
  ant 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

Table 5-38. Settling Velocities for Phytoplankton
tion.
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 estuar-
ies. During every tidal cycle, particle settling attains a
maximum during the slack tides. Later, the sediments
on the bottom can be resuspended and carried up-
stream 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 estu-
ary, this upstream transport is balanced by the down-
stream 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 mi-
nus resuspension. This net settling can be arrived at
by calibrating the model against the suspended solid
balance. But, in some situations, this net settling
Table 5-37. Settling Velocities in m/day at 20 °C for Inorganic
Particles [Ambrose et al. (1987)]
Particle Diameter,
mm
Fine Sand
0.3
0.05
Silt
0.05
0.02
0.01
0.005
0.002
Clay
0.002
Particle Density, g cm
1.8
300
94
94
15
3.8
0.94
0.15
0.15
2.0
400
120
120
19
4.7
1.2
0.19
0.19
2.5
710
180
180
28
7.1
1.8
0.28
0.28
2.7
800
200
200
32
8.0
2.0
0.32
0.32
Algal Type
Total Phytoplank-
ton
Diatoms
Green Algae
Blue-green Algae
Flagellates
Dinoflagellates
Chrysophytes
Coccolithophores
Settling
Velocity
(m/day)
0.05-0.5
0.05-0.2
0.02-0.05
0.4
0.03-0.05
0.05
0.2-0.25
0.04-0.6
0.05-0.4
0.1 -0.2
0.1 -0.25
0.03-0.05
0.3-0.5
2.5
0.05-0.19
0.05-0.4
0.02
0.8
0.1 -0.25
0.3
0.05-0.15
0.
0.2
0.1
0.08-0.2
0.5
0.05
0.09-0.2
8.0
0.5
0.25- 13.6
References
Chen & Orlob (1975), Tetra Tech (1976), Chen
(1970), Chen SWells (1975, 1976)
O'Connor et al. (1975, 1981) Thomann et al.
(1974,1975,1979), Di Toro & Matystik (1980), Di
Foro & Connolly (1980), Thomann & Fitzpatrick
(1982)
Canaleetal. (1976)
.ombardo (1972)
Scavia (1980)
Bierman etal. (1980)
Youngberg (1977)
Jorgensen (1976)
Bierman (1976), Bierman et al. (1980)
rhomann et al. (1979), Di Toro & Connolly (1980)
Fetra Tech (1980), Porcella et al. (1983)
Canaleetal. (1976)
SmaydaS Boleyn (1965)
.ehmanetal. (1975)
Jorgensen et al. (1978)
Bierman (1976), Bierman et al. (1980)
Canaleetal. (1976)
-ehmanetal. (1975)
Fetra Tech (1980), Porcella et al. (1983)
DePinto et al. (1976)
Bierman (1976), Bierman et al. (1980)
Canaleetal. (1976)
-ehmanetal. (1975)
DePinto etal. (1976)
Fetra Tech (1980), Porcella et al. (1983)
-ehmanetal. (1975)
Bierman etal. (1980)
Fetra Tech (1980), Porcella et al. (1983)
O'Connor etal. (1981)
-ehmanetal. (1975)
Collins SWIosinski (1983)

                                               5-58

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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 unox-
idized nitrogen in the form of ammonia and  organic
nitrogen that must be taken into account.  To improve
the chances for describing the oxygen balance, how-
ever, 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

           POINT AND NON-POINT
              SOURCE INPUTS
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

          AUTOCHTHONOUS SOURCES
 Dud Invertebrates      F»cal     Algal Exudates
alga*, ll»h, mlcrobM      Ptll»t»
                               CARBONACEOUS BOD
                                      DISSOLVED AND
                                       SUSPENDED
                                                                        SCOURING AND LEACHING
                                                                        FROM BENTHIC DEPOSITS
          MICROBIAL
         DEGRADATION
                                      SETTLING FROM
                                      WATER COLUMN
                ADSORPTION/ABSORPTION BY
                      BENTHIC BIOTA
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 rela-
tive 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 alloca-
tion.

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 imme-
diately 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 im-
mediate  oxidation.  These bacteria also  can settle,
especially as part of any floe generated  as  a result of
the stabilization  of freshwater  particles.  Third, dis-
solved CBOD can be adsorbed by benthic biota, es-
pecially  by  filamentous growth  on  surfaces, and
benthic plants can filter particulate material. However,
there  is usually limited contact between benthic bacte-
ria and plants, and the water column with  the result that
only oxidation and, occasionally, settling are the impor-
tant processes to  describe  in calibrating a model.
Exceptions to the general expectations occur when
significant interactions occur with tidal flats and adjoin-
ing wetlands. Also in brackish and saline waters, me-
tabolism 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 freshwa-
ter where settling is more likely.  In general, the CBOD
mass  balance is expressed as:
   _
   dt
= -Kr L+La
                                           (5.30)
where L is ultimate CBOD in mg L  , 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:
                                           (5.31)

where  Kd is  the  water column deoxygenation  rate
coefficient (i.e., oxidation rate) in d" , Ks is the settling
rate  coefficient in  d"1,  and  Ku is the sorption  rate
coefficient in d"1.  Unexplainable discrepancies occa-
sionally are  observed (see  Krenkel and  Novotny
1980),  but in  general, Kd can be estimated from the
bottle deoxygenation rate coefficient, Ki, 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 proce-
dures).  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
                                                     YJL
                                                     D
                                           (5.32)
Vs is the settling velocity measured in m d   and D is
depth of flow in m.  Unfortunately, Equation (5.32) is
only useful in describing the settling of discrete parti-
cles.  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 pa-
rameter,  Ks = Ks + Ku, is defined and selected by trial
and error. Generally, it is possible to locate large areas
where Ks = 0 so that Kd can be selected.  If Kd is not
approximately equal to the bottle coefficient, Ki, addi-
tional 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,
Ks can be determined in other parts of the estuary
where settling and sorption are occurring by selecting
Kd + Ks so that model predictions agree with measure-
ments. 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 veloci-
ties 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).  There-
fore, 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 trans-
formation of oxidizable nitrogen.  One is to consider
the actual process of transformation:  from organic
nitrogen, through nitrite to nitrate, where oxygen con-
sumption is involved in the process.  This will be dis-
cussed in SupplementXI. The other approach that will
be discussed here simply lumps the organic and am-
monia 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

        dN
   dt = -

Where
(5.33)
   N = NBOD concentrations, mg/L.

   NBOD = 4.57(N0+Ni)+l. 14N2 can be used as the up-
   per limit of NBOD (see Bowie et al. 1985)

   No = organic nitrogen concentrations, mg/L

   N; = ammonia nitrogen concentration, mg/L

   N2 = nitrite-nitrogen concentration, mg/L

   KN = overall NBOD reaction rate, I/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 20°c; 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
                             iT-io
                                                                                               (5-34)
                                                       for  10
-------
Table 5-40.  Rate Coefficients for Nitrogen Transformations [Bowie et al. (1985)]
PONa-»DON
K
e
DON^NHS
K
e
PON^NHS
K
q
NH3^NO2
K
e
NH3^NO3
K
e
NO2^NO3
K
e
SEDN^NHS
K
e
References
Calibration values derived from field data








0.020
0.020
0.02
0.02














linear
linear
1.020
linear














0.020
0.020
0.02
0.024














linear
linear
1.020
linear






0.035
0.03b
0.03C
0.03C
0.075

0.14
0.001




0.003
0.1
0.01 b
.005b
0.1b
0.2b
linear
1.08
1.08
1.08
1.08

linear
1.02




1.020
1.047
Nl
1.08
1.02
1.072







0.003-
0.03




0.02
0.02











1.02




1.047
1.047




0.04

0.1 2b
0.20
0.09-
0.13C
0.025C


0.060
0.1
0.1
0.16






linear

1.08
1.08
1.08
1.08


linear
linear
1.020
linear













0.09




0.25
0.25











1.02




1.047
1.047






0.0025

0.004


0.001




.0015
.0015
0.95-
1.8C





1.08

1.08


1.02




1.047
1.047
1.14



Thomann et al. (1976)
Thomann et al. (1979)
DiToro and Conolly (1980)
DiToro and Matystik (1 980)
Thomann & Fitzpatrick (1982)
O'Connor et al. (1981)
Salas and Thomann (1973)
ChenS Orlob(1972, 1975)
Scaviaetal. (1976)
Scavia (1980)
Bowie etal. (1980)
Canaleetal. (1976)
TetraTech (1980)
Porcella etal. (1983)
Nyholm (1978)
Bierman et al. (1980)
Jorgensen (1976)
Jorgensen et al. (1978)
Recommendations from Model Documentation
































.1-.4
0.02-
0.04


.005-
.05
.001-
.02


Nl
1.02-
1.09


1.02-
1.04
1.045


.1-.5
.1-.5
.1-.5
.1-.5
.05-.2
.05-.2


Nl
1.02-
1.09
1.047
1.047
1.02-
1.03
1.02








0.04-
3.0
0.001-
1.3d






logistic
Nl
5.-10.
3.-10.
0.5-
2.0
0.5-
2.0
0.2-
0.5
0.2-
0.5


Nl
1.02-
1.09
1.047
1.047
1.02-
1.03
1.02



.01-.1


.001-
.01
.001-
.02



1.02-
1.09


1.02-
1.04
1.040


Bacaetal. (1973)
Baca and Arnett (1 976)
Duke and Marsh (1973)
Roesneret al. (1978)
Smith (1979)
Brandes(1976)
Granney and Krassenski
(1981)
Collins and Wlosinski (1 983)
  Abbreviations are defined as follows:
     Nl - 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.
  Unavailable nitrogen decaying to algal-available nitrogen.
  DiToro & Connolly (1980) & Di Toro & Matystik (1980) multiply the PON-NHs rate by a chlorophyll limitation factor, Chi a/K-i+Chl a,
  where Ki is a half-saturation constant = 5.0 mg Chi a/L.
  DiToro & Connoly (1980) and Thomann & Fitzpatrick (1982) multiply the NHs-NOs rate by an oxygen limitation factor, O2/K2+O2, where
  K2 is a half-saturation constant = 2.0 mg O2/L.
  O'Connor etal. (1981)  multiply the  NHs-NOs rate by an oxygen limitation factor, O2/Ks+O2, where Ks 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.
  Literature value.
                                                           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 avail-
able 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 consum-
ing dissolved oxygen at the same time.

Table 5.41  lists the coefficients for the denitrification
process which reduce the nitrate of N2 under anaero-
bic conditions.

Values in the  above  two  tables can  be  used as  a
guidance for selecting initial values of these coeffi-
cients.  Models should be calibrated for the specific
problem later on.
Table 5-41.  Rate Coefficients for Denitrification
          [Bowie etal. (1985)]
Nitrate -> Nitrogen Gas
K
0.1*
0.1"
0.09*
0.1*
0.002
0.02-0.03
0.0-1.0***
e
1.045
1.045
1.045
1.045
No information
No information
1 .02-1 .09***
References
Di Toro and Connolly (1980)
Di Toro and Connolly (1980)
Thomann and Fitzpatrick (1982)
O'Connor etal. (1981)
Jorgensen (1976)
Jorgensen et al. (1978)
Baca and Arnett (1976)
 *This rate is multiplied by an oxygen limitation factor, Ki/[Ki+O2],
        where Ki is a half-saturation constant = 0.1 mg O2/L.
 ** The same rate applies to sediment NOs denitirfication
 *** Model documentation values
Another important phenomenon that needs to be men-
tioned is the toxity of un-ionized ammonia to aquatic
life. The ionization equibrum is
   NH3-nH20
Equibrum is reached rapidly, and is largely controlled
by pH and temperature. Figure 5.29 gives the percent-
age of un-ionized  ammonia under different pH and
temperature conditions. Usually, water quality models
predict ammonium concentration, which  can be re-
lated to the total concentration in Fig. 5.29. Additional
guidance  on processes  affecting  ammonia toxicity
may be found in U.S. EPA (1 985b and 1 989).
   100
    so E
    60 -

    40 -
                                                        20 -
                                                         2-
                                                        1.0 •
                                                        0.8 :
                                                        0.6'
                                                      LU
                                                      O 0.2'
                                                      DC
                                                      HI
                                                      Q.

                                                        0.1 •
                                                       0.08;
                                                       0.06 •
                                                       0.04-
   0.01 -
                                                                          pH9.0
                  10    15    20    25
                   TEMPERATURE ((?)
30
      35
                                                    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.
Table 5-42.  Rate Coefficients for Phosphorus Transformations [Bowie et al. (1985)]
           (K = 1st order rate coefficient in d"1 and  6 = temperature correction factor)
POP^DOP
K



0.22b



0.22b











e



1.08



linear











POP^P04
K
0.14
0.03
0.03b

0.14
0.001
0.02

0.003
0.02
0.1
0.1
0.005
0.1
0.5-0.6
0.1-0.7C
0.1-0.7C
0.005-0.05C
0.001 -0.02C
e
linear
1.08
1.08

linear
1.02
linear

1.020
1.020
1.047
1.14
1.08
1.02
1.072
1 .02-1 .09C
1 .02-1 .09C
1 .02-1 .04C
1.040
DOP^P04
K



0.22b















q



1.08















SEDP^DOP
K



0.0004















e



1.08















SEDP^P04
K



0.0004

0.001


0.0015
0.001
0.0015
1.04147

0.0018

0.1-0.7C

0.004-0.04C

e



1.08

1.02


1.047
1.020
1.047
1.14b

1.02

1 .02-1 .09C

1 .02-1 .04C

References
Thomann et al. (1975)
Thomann et al. (1975)
DiToro and Conolly (1980)
DiToro and Matysik (1980)
Salsbury et al. (1983)
Thomann & Fitzpatrick
(1 982)
Salas and Thomann
(1 978)
Chen SOrlob (1972,
1976)
Scaviaetal. (1976)
Scavia (1980)
Connie etal. (1976)
Tetra Tech (1 980)
Bowie etal. (1980)
Porcalia et al. (1983)
Nyholm (1978)
Bierman et al. (1980)
Jorgensen (1976)
Jorgensen et al. (1978)
Bacaetal. (1973)
Baca and Arnett (1 976)
Smith (1976)
Brandes(1976)
Sediment
DOP^P04
K
0.0004
e
1.08
SA^DOP
K
0.02
e
1.08
SA^P04
K
0.02
e
1.08
References
Thomann & Fitzpatrick (1982)
  Abbreviations are defined as follows:
    POP - Participate Organic Phosphorus
    OOP - Dissolved Organic Phosphorus
    SEDP - Sediment Organic Phosphorus
    PO4 - Phosphate
    SA - Settled Algae
    Linear - linear temperature correction assumed.
  DiToro &  Connolly (1980), DiToro & Matystik(1980) and Salsibury et al. (1980) multiply this rate by a chlorophyll limitation factor, Chi
  a/Ki+Chl  a, where Ki is a half-saturation constant = 5.0 mg Chi a/L. Thomann & Fitzpatrick (1982) multiply this rate by an algal carbon
  limitation  factor, Algal-C/K2+Algal-C, where Ks is a half-saturation constant = 1.0 mg C/L.  Nyholm (1978) uses a sediment release con-
  stant which is multiplied by the total sedimentation of algae and detrirus.
  Model documentation values.
                                                     5-64

-------
SUPPLEMENT XIII:  SELECTION OF REAERATION COEFFICIENTS
Three methods are used to select reaeration coeffi-
cients:

 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 coeffi-
cient, 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
     .3
                  .3  .4.5.6 .81      2     3456

                    VELOCITY, ft./sec.
Figure 5-30. Reaeration Coefficient (day  versus depth and
velocity using the suggested method of Covar (1976) [Bowie
et al. (1985)].
to those used in streams are the most useful. When
the flow is vertically stratified and wind shear dominates
waterturbulence at the surface, KL is typically specified.
The values of K2 and KL are related according to:
 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"  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 equa-
tion,  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 veloc-
ity. Alternatively, expert practitioners (personal  com-
munication, Thomas Barnwell, Jr., U.S. EPA Center for
Exposure Assessment Modeling) use a minimum esti-
mate on the order of 0.6/D where  depth  is in  me-
ters. 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
                                               5-65

-------
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)]
Citation
K2 (base e, 20°C, day'1)
Units
Applicability
Derived from Conceptual Models
O'Connor and
Dobbins (1958)
Dobbins (1964)
12.8uv2
D1.5
Ci[1 +F 2(US )° 375] J~4.1 0(US )° 125]
(0.9+F)15D [ (0.9+F)05 J
coth [ ] is the hyperbolic contangent
U: ft/s
D: ft
U:m/s
D:m
forCi=117
U:ft/s
D:ft
S:ft/ft
for Ci=62.4
U:m/s
D:m
S:m/m
Conceptual model based on the film penetration
theory for moderately deep to deep rivers;1
ft
-------
Table 5-43.  Formulas to Estimate Reaeration Coefficients for Deeper, Bottom Boundary Generated Shear Flows
            [Bowie et al. (1985), Rathbun (1977), Gromiec elal. (1983), and McCutcheon (1989)] (concluded)
Citation
K2 (base e, 20°C, day'1)
Units
Applicability
Semi-Empricial Models (continued)
McCutcheon
and Jennings
(1 982)
Churchill et al.
(1962)
/nn -f Dm/24 T'l
[ n(30.48D )2 J
/
Dm=1.42(1.1)T-20
[/ = 0.001 6+0.0005 D ] D < 2.26 ft
[1 = 0.0097 ln(D ) - 0.0052] D >2.26 ft
0.035U2695
Q 3.085o 0.823
0.746U2695
Q 3.085
-------
Table 5-44. Constant Values of Surface Mass Transfer Coefficients Applied in the Modeling of Estuaries, Coastal Waters, and
          Lakes [Bowie et al. (1985)]
KL
(md-1)
1
0.6
2
Location or type of
water body
New York Bught
Estuaries
Lake Erie
Reference
O'Connor et al. (1981)
O'Connor (personal communication)
Di Toro and Connolly (1980)
Comment



Table 5-45.  Empirical Wind Speed Relationships for Mass Transfer and Reaeration Coefficients [Bowie et al. (1985)]
Reference
Formulation
Comment
Estuaries
Thomann and Fitzpa-
trick (1 982)
K2 = 1 3 U°-5- + 3.281 (0.728(jo.5 - 0.371 u + 0.0372(j2
D1.5 D
K2 in d-1 , D in ft, U In t s-1 , u In m s-1
Applied in the Potomac Estuary. Combines
O'Connor-Dobbins and wind speed
formulations.
Lakes
Chen etal. (1975)
Banks (1975)
K|_ = 86,400Dm Dm in m2s-1 , u in m s-1
(200-60uo.5) x 10-6
KL = 0.362uo.s for 0 < u < 5.5 m s-1
KL = 0.0277U2 for u > 5.5 m s-1


Notation:
K.2  =    reaeration coefficient ("M),
KL  =   surface mass transfer coefficient (LI'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.
included because its rational derivation indicates that
it may be occasionally useful. The Krenkel and Orlob
(1962) and Thackston and Krenkel (1969) energy dis-
sipation  equations are included for similar reasons,
although these equations are more applicable to shal-
lower depths than the Dobbins equation. The equation
by Ozturk (1979) is included for completeness but little
is known about the limitations of applicability and use-
fulness.  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) equa-
tion 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 h\2 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 equa-
                                                        tion).

                                                      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, com-
                                                        pute 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, com-
                                                        pute KL values from the O'Connor (1983) formula-
                                                        tions.

                                                     When estuarine reaeration is dominated by wind-gen-
                                                     erated water turbulence, or the flow is deep and strati-
                                                     fied, 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 relat-
                                                 5-68

-------
ing «2 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, deter-
                                                    mine whether any of the other wind speed relation-
                                                    ships in Table 5.33 are useful.   The  crude
                                                    screening approach of Kim and Holley (1988) may
                                                    be the next most useful approach
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. reaera-
tion 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 O/KL) described by
   — = -L  -
   KL  Kz  Kx
                                        (5.37)
where  KT is the transfer coefficient through the diffu-
sional 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
J_
KL
                1
1
         D
                     Pw
                          Du*  Pa Vg

                         K ZQ M* Pw Vw
    (5.38)

    where

   D  = molecular diffusivity
   va = kinematic viscosity of air
   K
      = kinematic viscosity of water
      = the Von Karmen constant
                                                     pa  = density of air
                                                     pw  = density of water

                                                     u*  = shear velocity
                                                     z0u* = is given as
                                                     ZQ
                                                      and
                                                            T-  U*
                                                         *} = r0 —exp
                                                               U*c
    u*c  = critical shear stress
    u*t  = transition shear stress

    u* = (Cn) 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)


    -^=
    A/CD  K


  The quantities A,i, u*t, Y0,  u*c, and ze are dependent on
  the size of the water body and values for these parame-
  ters are given  in Table 5.46  from O'Connor, 1983);

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

Small scale
Intermediate
Xi
10
3
u*t
9
10
To
10
6.5
U.c
22
11
Ze
0.25
0.25
                                               5-69

-------
small scale values are for laboratory studies, interme-
diate scale values are  for small scale field sites and
large scales are for large lake or ocean scales.

A Fortran implementation which calculates drag coef-
ficients and reaeration  coefficients using O'Connor's
method is available for the U.S. EPA Center for Expo-
sure 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 (°C), and
watertemperature (°C). Values forthe drag coefficient
and reaeration coefficient  are calculated by the pro-
gram.  The program is available through the CEAM
bulletin  board.  A more detailed description of the
equation development may be  found  in O'Connor
(1983).
SUPPLEMENT XV:  SELECTION OF SOD RATES
Guidance on the Selection of Sediment Oxygen De-
mand Rates is given in Table 5.47.
Table 5-47. Measured Values of Sediment Oxygen Demand in Estuaries and Marine Systems [Bowie et al. (1985)]
SOD
(g O2/m2 day)
0.10±0.03(12°C)
0.20±0.05 (20°C)
0.22±0.09 (28°C)
0.37±0.15(36°C)
2.32±0.16
1.88±0.018
0.1 4-0.68 (5°C)
0.20-0.76 (10°C)
0.30-1. 52 (15°C)
0.05-0.10
1 .25-3.9
0.02-0.49
0.9-3.0
0.4-0.71
0-10.7
0.3-3.0
Environment
A North Carolina estuary
Buzzards Bay near raw sewage outfall
Buzzards Bay control
Puget Sound sediment cores
San Diego Trough
(deep marine sediments)
Yaquina River Estuary, Oregon
Eastern tropical Pacific
Baltic Sea
Baltic Sea
Delaware Estuary (22 stations)
Fresh and brackish waters, Sweden
Experimental Conditions
45 day incubation of 0.6 liters
sediment in 3.85 liters BOD dilution
water, light
In situ dark respirometers stirred, 1 -3
days; temperature unknown
Laboratory incubations
In situ respirometry for 5-1 3 hours,
4°C, light
Dark laboratory incubators, stirred,
20°C
Shipboard incubations, 15°C, stirred,
dark
In situ light respirometer stirred, 10°C
Laboratory incubations, stirred, dark,
10°C
In situ dark respirometry, 1 3-1 4°C
In situ respirometry, 0-1 8°C
Laboratory cores, 5-1 3°C
References
NCASI(1981)
Smith etal. (1973)
Pamatmat et al. (1973)
Smith (1974)
MartinS Bella (1971)
Pamatmat (1971)
EdbergS Hofsten (1973)
EdbergS Hofsten (1973)
Albert (1983)
EdbergS Hofsten (1973)
                                               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 Engi-
neers, 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 Protec-
tion Agency Report EPA/600/3-87/039, Athens, Ga.

American Public Health Association, Water Pollution
Control Federation, and American Water Works Asso-
ciation..  1985.  Standard Methods for the Examination
of Water and Wastewaters,  16th  ed., Washington,
D.C.

Amorochio, J., and DeVries, J.J. 1980.  A new Evalu-
ation of wind stress coefficient over water surfaces,
Journal of Geophysical Research, 85(C1).

ASCE Task Committee on Turbulence  Models in Hy-
draulics  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-TS-
84-204,  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, Wash-
ington, D.C., Contract 68-01-0056.

Bailey, T.E.  1966. Fluorescent  tracer studies of an
estuary, Journal of the Water Pollution Control Federa-
tion, 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 Re-
view of  the Development and application of Mathe-
matical  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 Re-
search, 23(8), 1393-1442.

Bedford, K.W. 1985. Selection of Turbulence and Mix-
ing Parameterizations for Estuary Water Quality Mod-
els,  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, Ameri-
can 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 Sci-
entific Publications, Amsterdam.

Bowden,  K.F. 1963. The mixing processes in a tidal
estuary, International Journal of Air and Water Pollu-
tion,  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,  Con-
stants, and Kinetics  Formulations in  Surface Water
Quality Modeling, 2nd  Edition, EPA/600/3-85/040,
U.S. Environmental Protection Agency, Athens, Geor-
gia.

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 QUAL2E-
UNCAS:  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 Simula-
tion of Aquatic Environments, in Systems Analysis and
Simulation in Ecology, Vol. 3B, Pattern, C., ed., Aca-
demic 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 Environ-
mental and Community Services.

Chen C.W., Smith,  D.J., and  Lee, S.S. 1976. Docu-
mentation  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, McGraw-
Hill, New York, chap. 5.

Covar, A.P. 1976.  Selecting the Proper Reaeration
Coefficient for use in Water Quality Models, Proceed-
ing  of the U.S.  EPA Conference on Environmental
Simulation and Modeling, Cincinnati, Ohio.

Deacon, E.L. 1955. The Turbulent Transfer of Momen-
tum in The Lowest Layers of the Atmosphere, Division
of Meterological Physics, Technical Paper  No. 4.,
Commonwealth Scientific and Industrial Research Or-
ganization, 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 Conven-
tional 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 Pro-
tection 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 So-
ciety 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 Chatta-
hoochee 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 Admini-
stration.

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  Environ-
ments, 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 Engineer-
ing, 110(1), 1-9.

Garde, R.J. and Ranga Raju, K.G. 1977. Mechanics
of Sediment Transportation and Alluvial Stream Prob-
lems, 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 estu-
arine 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 Stud-
ies, U.S. Geological  Survey  Professional  Paper 298,
U.S. Government Printing Office, Washington, D.C.

Henderson, F.M. 1966. Open Channel Flow, Macmil-
lan, New York, 98.

Henderson-Sellers, B. 1982. A simple formula for ver-
tical 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 Associa-
tion for  Hydraulic Research,  Proceedings of the
Twelfth Congress, 4, 79-88.

Hine, J., and Mookerjee, P.K. 1975.  The intrinsic hy-
drophilic character or organic compounds; correlations
in terms of structural contributions, J. Organic Chem.,
40, 292-298.

Hinze, J.0.1959. Turbulence, McGraw-Hill, New York.

Holzman, B. 1943. The influence of stability on evapo-
ration, 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 Hy-
drodynamic/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 Mod-
eling 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 Coef-
ficients for Streams in Colorado,  Water-Resources
Investigations Report 85-4004,  U.S. Geological Sur-
vey, 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 Pa-
per 1122, U.S. Governement Printing Office, Washing-
ton, 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 Engi-
neering, 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. Gov-
ernment 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: Meth-
odology 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.,  Mines, W.G.,  Rickert, D.A.,  and
Rinella,  F.A.  1971. Steady-State Dissolved Oxygen
Model of the Willamette River, Oregon, U.S. Geologi-
cal 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, Nash-
ville, 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 In-
vestigations 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 prob-
lems, Reviews of  Geophysics and Space  Physics,
20(4), 851-875.

Meyer, A.F. 1942. Evaporation from Lakes and Res-
ervoirs, 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 Proce-
dure for Toxic and Conventional Pollutants in Surface
and Ground Water Part 1, (Revised 1985), EPA/600/6-
85/002a, U.S. Environmental Protection Agency, Ath-
ens, Georgia.

Monin, A., and Yaglom, A. 1971. Statistical Fluid Me-
chanics, 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,  Uni-
versity of California, Davis, California,  Research and
Development Technical Report ECOM 68-G10-2.

Mortimer, C.H. 1981. The Oxygen Content of Air-Satu-
rated Fresh Waters Over Ranges of Temperature and
Atmospheric Pressure  of Limnological Interest,  Inter-
national Association of Theor. and Appl.  Limnolo,
Communication Number 22, Stuttgart, Germany.

Morton, F.I.  1976. Climatological estimates of eva-
potranspiration, Journal  of the Hydraulics  Division,
American Society of Civil Engineers, 102(HY3), 275-
291.

Munk, W.H. and Anderson, E.R. 1948. J. Marine Re-
search, 7(3), 276-295.

National Academy of Sciences. 1977. Studies in Estu-
aries, Geophysics, and the Environment, Washington,
D.C.

National Council for Air and Stream Improvement.
1982. A Study of the Selection, Calibration and Verifi-
cation 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, Univer-
sity 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,  EPA-
600/3-79-094.

O'Connor, D.J. 1983. Wind effects on gas-liquid trans-
fer 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, Ameri-
can 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 Estuar-
ies (And Associated Coastal Waters), John Wiley and
Sons, New York, New York.

Okubo, A, and R.V. Osmidov. 1970. Empirical depend-
ence of coefficient of horizontal turbulent diffusion in
the  ocean  on the scale of the phenomenom in ques-
tion, 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 Nos-
trand, 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.,  Gottin-
gen, 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.I: Data Analy-
sis  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 Trans-
actions, Royal Society of London, 246(918).

Rodi, W. 1980. Turbulence Models and Their Applica-
tion in Hydraulics, International Assoc. for Hydraulic
Research, Delft, The Netherlands.

Rodi, W. 1984. Examples of turbulence-model appli-
cations, 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 Sur-
faces, 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,
lll(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 Uni-
versity, 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 expe-
rienced 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 Sur-
face Waters, Report EPA/600/3-87/015, U.S. Environ-
mental Protection Agency, Athens, Ga.

Schubert, W.M. and Brownawell, D.W. 1982. Methylal
hydrolsis: reversal reactions under dilatometric condi-
tions and invalidity of the dilatometric method,  Journal
of American Chemical Society, 104(12), 3487-3490.

Sheng, Y.P.  1983. Mathematical Modeling  of Three-
Dimensional Coastal Currents and Sediment Disper-
sion: 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 Allo-
cations, Book III: Estuaries, Draft Rept., U.S. Environ-
mental 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. Geo-
logical  Survey, Water Supply Paper 2059, U.S. Gov-
ernment Printing Office, Washington, DC.

Stommel, H. 1953. Computation of pollution in a verti-
cally 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-lnterscience, 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 Vari-
ation on Performance of Recirculating Cooling Ponds,
U.S. Environmental Protection Agency, Report EPA-
660/2-74-085, Corvallis, Oregon.

Thatcher, M.L., and Harleman,  D.R.F. 1981. Long-
term salinity calculation in Delaware Estuary, Journal
of the Hydraulics Division, American Society of Civil
Engineers, 107(EE1), 11-27.

Thibodeaux, L.J.  1979.  Chemodynamics:  Environ-
mental 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 mod-
els, 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. Buoy-
ancy effects on the turbulent transport processes in the
lower atmosphere, Quart.  J. Roy.  Meteor. Soc., 107,
561-578.

U.S. Environmental Protection Agency. 1985. Techni-
cal Support Document for Water Quality-based Toxics
Control, Office of Water, Washington, DC.

U.S. Environmental Protection Agency.  1985b. Am-
bient 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.  Ambi-
ent 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 Investiga-
tions: 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  Re-
search,  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 Engineer-
ing, American Society of Civil Engineers, 111 (3), 272.
                                               5-76

-------
Whittmore, R.,etal. 1989. National Council for Air and
Stream Improvement, Tufts University, Medford, Mas-
sachusetts.

Wunderlich, W.O. 1972. Heat and Mass Transfer Be-
tween A Water Surface and the Atmosphere, Water
Resources Research, Laboratory Report Number 14,
Report no. 0-6803, Tennessee Valley Authority, Nor-
ris, Tennessee.
Zaykov, B.D. 1949. Evaporation from the water sur-
face 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, Ath-
ens, Ga.
                                              5-77

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               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 model-
based estuarine WLA application.  WASP4 is a gen-
eral multi-dimensional model supported and available
through the U.S. EPA  Center for Exposure Assess-
ment 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 rep-
resentative 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 ex-
amples 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 pro-
vided 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 estu-
arine 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 char-
acterizations:

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 pro-
cedures, which  can  be  applied using only a  hand
calculator or computer spreadsheet, have been devel-
oped 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 ide-
alized estuary, the  fraction of freshwater method, and
the modified tidal prism method.  These three example
procedures are only  applicable to steady  state, tidal-
average one- dimensional estuary problems. All three
procedures provide "far- field" calculations (well dis-
tanced from the outfall) in contrast to "near-field" pre-
dictions 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 verti-
cally- and laterally-variant estuaries are also described
in the manual but are too complex for example illustra-
tion herein. The reader is referred to that document for
a thorough discussion of several estuarine screening
procedures including explicit instruction on proper ap-
plication 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 es-
tuary and pollutant behavior. The simplifying assump-
tions  common to all  three screening techniques
presented herein are that the pollutant concentrations
do not vary significantly in the lateral or vertical direc-
tions (i.e. a one- dimensional system), and that tidal-
averaged,  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-sec-
tional  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 con-
centrations 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 repre-
sented by negative distances, locations downstream
by positive distances. The predicted pollutant concen-
tration, 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 = C0=W/(Qo)  x = 0                    (6-1)

   C = Co * exp (j\x)   x< 0                   (6-2)

   C = Co * exp (J2x)   x>0                    (6-3)

where:

   a = (l+4KE/U2)/2

   jl = U/2E  (1 +a)

   j 2 = U/2 E  ( 1 - a )
   C= pollutant concentration (M/L )
   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 (L /T)
The net nontidal velocity can be directly determined
from freshwater flow data (e.g. USGS) and cross-sec-
tional  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 be-
comes:

   C = C0*exp(Ux/E),  x<0                (6-4)

which  can be  restated in  the  form (Thomann and
Mueller, 1987):
           = (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 ve-
locity.  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 i)
In (C 2 - C i)
(6-6)
An application of this method is provided in the Screen-
ing 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 pollut-
ant 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 dem-
onstrated as part of the Screening Examples (Subsec-
tion 6.2).

6.12.  Fraction of Freshwater Method
The fraction of freshwater method allows quick estima-
tion of tidal average, steady-state pollutant concentra-
tions 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 ex-
amining the salinity ratio to  seawater as follows:
   fi =
where
Ss-Sj
  ss
(6-7)
          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 multi-
        plying the seawater dilution by the freshwater dilution.
        This then provides a simple way to calculate concen-
        trations of conservative pollutants.  For a location x,
        including  or downstream of the discharge,
                                                          -
                                                        Q
                                                                                           (6-8)
                                              where:
   fx = fraction freshwater at location x
   W = waste loading rate (M/T)
   Q = freshwater inflow  (L /T)
The  right hand side of Equation 6-8 can be divided into
two distinct terms.  The term W/Q represents the clas-
sical approach to determining dilution in rivers caused
by upstream freshwater flow.  The second term,  fx,
accounts for the further  dilution of the river concentra-
tion  by seawater. Equation 6-8 also predicts concen-
trations at the  point of discharge, C0, by using the
corresponding fraction of freshwater at that location, f0.

Concentrations upstream  of the discharge are esti-
mated 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 freshwa-
ter in the upstream direction to the same degree that
salinity is diluted. The equation is:
                                                           sx
                                                                                           (6-9)
                                              where:
                                                 fo = fraction of freshwater at discharge location

                                                 S x = salinity at location x
                                                 S0 = salinity at discharge location

                                              Equations 6-8 and 6-9 can be used to predict conser-
                                              vative  pollutant concentrations at all locations  up-
                                              stream and downstream of a discharge.  The frac-
   //• = fraction of freshwater in segment i
                                                  6-3

-------
tion of freshwater method can also be applied to esti-
mate 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.

6.13. 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 fresh-
water 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 in-
creasing segment size as segments are defined sea-
ward.  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 (Po)  supplied totally by freshwater
inflow over one tidal cycle:
                                           (6-10)
where:
   Po = tidal prism of segment 0 (L )
   Q = freshwater inflow (L /T)
   T = length of tidal cycle  (T)
The low tide volume (Vo)  in this section is defined as
the low tide volume of the segment minus inter-tidal
volume, Po.

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, ex-
pressed as:

   Vi = Vi-l+Pi-l                        (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 (n)
can be calculated for each segment as:
          Pi
       P, + V,
                                            5-12)
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 impor-
tant 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 equa-
tions are (Dyer, 1973):
 segment at the outfall,
    Cd=fd
w_
o
 segments downstream of the outfall,
(6-13)
                                           (6-14)
              i= 1
 segments upstream of the outfall:
                                           (6-15)
where:
             r i
                                                                     -Kt
                                                                                              (6-16)
   C; = non-conservative constituent mean

        concentration in segment "i"  (M/L )

   Cd = conservative constituent mean concentration

         in segment of discharge (M/L )

   r; = the exchange ratio for segment "i" as defined

       by the modified tidal prism method

       (dimensionless)

   n = number of segments away from the outfall

       (i.e. n=l 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/n)  * 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 consid-
erations. This section provides simple illustrative ex-
amples designed for three different situations. The
examples are simple by design, in order to best illus-
trate 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 proce-
dure 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 descrip-
tion of the  water quality process(es) of concern, fol-
lowed 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-di-
mensional 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 insignifi-
cant. 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. Tempo-
ral  changes in water quality related to changes in
pollutant loads or upstream flows,  or intra-tidal vari-
ations, are not represented.  Application of the analyti-
cal  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 environ-
mental conditions.
               Freshwater  Flow
           Proposed
             WWTP      WWTP

                 5           10

                  River  Mile
15
Figure 6-1. Schematic of tidal tributary for analytical
equation example.

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 accomplish-
ing three steps:

 1. Determine dispersion coefficient

 2. Determine decay rate

 3. Determine maximum allowable load at critical con-
   ditions
Table 6-1.  Observed Conditions During Survey
Upstream Flow:
Discharge Flow:
Discharge Cone.:
Estuary Cross-Sectional Area:
Observed Data-
River Mile
2
4
5
6
9
10
12
4000 cfs
300 cfs
2 ma/
20.000 fP
Salinity(%)
19
10
8
6
3
2
1
-
TRC(mg/L)
0.04
0.06
0.07
0.08
0.15
0.18
0.07
                                                 6-5

-------
                                                      Table 6-2.  Predicted Concentrations Throughout Estuary
                                                                Under Observed Conditions
                    Miles below Mouth
Figure 6-2. Determination of tidal dispersion from salinity
data.
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 func-
tion 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 fresh-
water 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 mi  /day.  Applying the ob-
served salinity and velocity data to Equation 6-6 results
in:
   E =
3.28 (-10-(-2))
  In (1.8/18.1)
(6-17)
     = 11.4 mi /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 accom-
plished 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 there-
fore selected  as the calibration value.  The required
nputs
Q = 4000 cfs
River Mile
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
K = 1/day
Distance Below
Discharge (x)
10
9
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
E = 1 1 .4 mi2/day
Equation
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-1
6-2
6-2
6-2
6-2
6-2
U = 3.28 mi/day
Predicted
Concentration
(mg/L)
0.004
0.005
0.007
0.010
0.013
0.017
0.023
0.031
0.041
0.055
0.073
0.054
0.040
0.029
0.022
0.016
         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 de-
         termine the loading required to obtain a specific con-
         centration under given environmental conditions.
                                                     = C*Q*a
                                                                                                  (6-18)
                                                     where:
                                                   Wd = allowable pollutant load  [M/T]
                                                   Q = net freshwater inflow [L /T]
                                                   C = desired concentration [M/L ]
                                                   a = ( 1 + 4KE/U2 )1/2 [dimensionless]
                                               For wasteload allocation purposes, model parameters
                                               should be representative of critical environmental con-
                                               ditions. Some parameters  (e.g. upstream flow) will be
                                               dictated during specification of critical conditions.  En-
                                               gineering judgement  is usually required  for many pa-
                                               rameters to determine how (if at all) they are expected
                                               to change from observed to critical environmental con-
                                               ditions. For this example, the critical
                                                  6-6

-------
     0.1

   • 0.09 -

    O.OS -

    0.07 -

 o  0.06 -
 \

 E,  0.05 -
 o
 E  0.04 -

    0.03 -

    0.02 -

    O.O1 -

      0
Observed TRC Dot

Predicted TRC
Figure 6-3. Calibration of TRC decay rate.
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 recal-
culated 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 be-
tween 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  simula-
tions.   The  best  procedure  is to  perform sampling
surveys during periods  as close  to critical  environ-
              mental conditions, to minimize the degree of extrapo-
              lation required.

              Forthis example, Equation 6-16 is used to calculate the
              allowable loading of chlorine to meet the water quality
              standard as

                 Wd = 0.01 mg/1 * 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 treat-
              ment plant flow is assumed to remain constant at 80
              cfs, this translates into an allowable effluent concentra-
              tion  of:

                   Cd = 457 pounds/day / 80 cfs / 5.39 = 1.06 mg/1
              To demonstrate a multiple discharge situation, the
              effect of a proposed second  discharge on  estuarine
              TRC concentrations  at critical environmental condi-
              tions will be evaluated. The specifics of this discharge
              are:

                Location:    River mile 5

                Flow:       40 cfs

                Concentration: 2 mg/1

              Table 6-3 demonstrates the steps involved in evaluat-
              ing multiple discharges.  Column (4)  is based upon
              information in Columns (2) and (3) and represents the
              incremental impact caused by the original discharge.
Table 6-3.  Predicted Concentrations Throughout Estuary for Multiple Discharge Situation

River Mile
(1)
0
1
2
3
4
5
6
7
8
g
10
11
12
13
14
15
Discharge 1
Distance Below
Discharge (x)
(2)
10
9
8
7
3
5
4
3
2
1
0
-1
•2
•3
•4
•5
Equation
(3)
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-3
6-1
6-2
6-2
6-2
6-2
6-2
Concentration
(4)
0.007
0.009
0.011
0.014
0.018
0.022
0.028
0.035
0.044
0.056
0.071
0.049
0.033
0.023
0.016
0.011
Discharge 2
Distance Below
Discharge (x)
(5)
5
4
3
2
1
0
•1
•2
•3
•4
•5
•6
•7
•8
•9
•10
Equation
(6)
6-3
6-3
6-3
6-3
6-3
6-1
6-2
6-2
6-2
6-2
6-2
6-2
6-2
6-2
6-2
6-2
Concentration
(7)
0.007
0.009
0.012
0.015
0.019
0.024
0.016
0.011
0.008
0.005
0.004
0.002
0.002
0.001
0.001
0.001
Sum
Total concentration
(8)
0.014
0.018
0.023
0.029
0.037
0.046
0.044
0.046
0.052
0.061
0.075
0.051
0.035
0.024
0.017
0.012
                                                  6-7

-------
              0.1

            0.09  -

            o.oa  -
            0.07 -
        O   0.06 -
        en
        >§   0.05 -\
        O
        o:
            0.04 -
            O.03 -
            O.O2 -
            0.01  -
                                         Estuary Concentration
                                                                  10
                                      15
                                               River Mile
Figure 6-4. Estuary TRC concentration in response to two discharges.
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 con-
centrations 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 con-
stant flows and cross-sectional areas throughout the
estuary.   Instead, the estuary is  divided into  a se-
quence 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 ho-
mogeneity. Similarly, a single segment is also used to
describe water  quality  from surface to bottom con-
sistent with the  lack of vertical stratification.

The example discussed in this section involves consid-
eration of conservative pollutant behavior, and is ame-
nable 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 con-
servative 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 distri-
bution 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.
                                                 6-8

-------
Table 6-4.  Calculation Table for Conservative Pollutant by
           Fraction of Freshwater Method [Mills et al.(1985)]
Table 6-5.  Completed Calculation Table for Fraction of
           Freshwater Method
Freshwater Inflow Local Seawater Salinity Load
Q= 	 cmd Ss = 	 ppt Wd = 	 g/day
Seg#
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Salinity, Si
(PPt)




	
	
	


	
	

	
	
	
Fraction
of
-reshwatei
fi














fi/fd














Si/Sd














Pollutant
Concentral
on (mg/L)














                                                                Freshwater Inflow   Local Seawater Salinity  Load

                                                                Q = 2000 cmd      Ss = 30 ppt       Wd  = 10,000 g/day
                                                  TOP  VIEW
                                   Village  WPCP
                                                  SIDE  VIEW
                            Village WPCP
                             Jo3T""T"T_8  !7J6;5!4;3|2

. 	 . 	 L-.
10
20
9 1
19 ;
8
18
; 7
! l7
; s
! 16
»>>^_—
i 5
1 15
4 '
14 i
3
13
2 i
12 •
r i
1 j
ii <
Seg#
0
1
2
3<- Wa
4
5
6
7
8
9
10
11
12
13
14
Salinity, Si
(PPt)
1
3
5
7
10
12
14
16
18
19
21
23
25
27
29
Fraction
of
-reshwater
, fi
0.97
0.90
0.83
0.77
0.67
0.60
0.53
0.47
0.40
0.37
0.30
0.23
0.17
0.10
0.03
fi/fd
1.26
1.17
1.09
1.00
0.87
0.78
0.70
0.61
0.52
0.48
0.39
0.30
0.22
0.13
0.04
S//Sd
0.14
0.43
0.71
1.00
1.43
1.71
2.00
2.29
2.57
2.71
3.00
3.29
3.57
3.86
4.14
Pollutant
Concentrat
on (mg/L)
0.54
1.66
2.73
3.85
3.35
3.00
2.65
2.35
2.00
1.85
1.50
1.15
0.85
0.50
0.15
                            Depth Scale W-s
                                         MO
      Horizontal Scale
                          2000  4000
Figure 6-5. Schematic for illustrative vertically stratified estuary.
                                                         6-9

-------
Table 6-6.  Calculation Table for Non-Conservative Pollutant by Modified Tidal Prism Method [Mills et al., (1985)]
-reshwater Inflow Local Seawater Salinity Load Decay Tidal Cycle
2 = cmc

Seg#
0
1
3
4
5
6
8
9
10
11
12
13
14
Ss = ppt

Subtidal
Water
Volume, Vi
106m3
—

	
	
—

_
_



—

Intertidal
Water Volume,
—

	
	
—

_
_



—

Salinity, Si
3Pt
—

	
	
—

_
_



—
Wd= c

Fraction
Fresh, fi












3/day H
fi/fd












Si/Sd












C = /day T =

Segment
Exchange
Ratio, n












n












days
n e<












Pollutant
Concentrator
mg/L












 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
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 seg-
ments 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 dis-
tribution. 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 ap-
plication of a fate  and transport model may be war-
ranted.   Caution should be  exercised  when
considering  these  results as upper bounds  to ensure
that the assumption of complete mixing is  valid.  In-
complete 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.  First-
order 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.
                                                 6-10

-------
Table 6-7.   Completed Calculation Table for Non-Conservative Pollutant by Modified Tidal Prism Method
Freshwater Inflow Local Seawater Salinity Load Decay Tidal Cycle
Q = 2000cmd Ss=30ppt Wd = 10,000 g/day K= 0.01 /day T = 0.48 days

Seg#
0
1
2
3<- Wd
4
5
6
7
8
9
10
11
12
13
14
Subtidal
Water
Volume, Vi
106m3
5.0
5.5
6.2
7.2
8.4
9.6
11.4
13.4
15.8
19.1
22.7
26.5
30.7
35.1
39.7
Intertidal
Water Volume,
Pi 1 0e m3
0.5
0.7
1.0
1.2
1.4
1.8
2.0
2.4
3.3
3.6
3.8
4.2
4.4
4.6
4.8
Salinity, Si
ppt
1
3
5
7
10
12
14
16
18
19
21
23
25
27
29
Fraction
Fresh, fi
—
—
—
0.77
0.67
0.60
0.53
0.47
0.40
0.37
0.30
0.23
0.17
0.10
0.03
:i/fd
—
-
-
1.00
D.87
D.78
D.69
D.61
D.52
D.48
D.39
D.30
D.22
D.13
D.04
Si/Sd
D.14
D.43
D.71
1.00
-
-
—
-
-
-
—
-
-
—
-
Segment
Exchange
Ratio, n
D.09
D.11
D.14
D.14
D.14
D.16
D.15
D.15
D.17
D.16
D.14
D.14
D.13
D.12
D.11
n
3
2
1
—
1
2
3
4
5
6
7
8
9
10
11
n e<
D.40
D.62
D.83
1.00
D.83
D.72
D.61
D.52
D.45
D.39
D.33
D.27
D.22
D.17
D.13
Pollutant
Concentration
ng/L
D.22
1.02
2.26
3.85
2.77
2.15
1.62
1.21
D.91
D.73
D.49
D.31
D.18
D.08
D.02
For this example, identical conditions (salinity, fresh-
water inflow, and loading) are used as the first exam-
ple, with the primary difference being the addition of a
first-order decay rate of 0.5 day" .  The first step in
performing the modified tidal prism method is to define
the estuarine segmentation using the procedures de-
scribed 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 immedi-
ately  upstream.  The  required  information  on tidal
prism volumes can be obtained from tidal stage infor-
mation (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 val-
ues; they are identical to those used for the first exam-
ple. The segment exchange ratios are calculated from
the segment volumes using Equation 6-12.   Finally,
pollutant concentrations are calculated  using: Equa-
tion 6-13 for the segment receiving discharge; Equa-
tion 6-14 for segments downstream of the discharge;
and Equation 6-15 for segments upstream of the dis-
charge.

A completed calculation table is  provided for this ex-
ample in Table 6-7.  Pollutant concentrations follow a
similar trend as for the first example,  but decrease
significantly faster in both the upstream and down-
stream directions. The difference in pollutant concen-
trations 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 co-
efficients for first-order processes are additive, there-
fore, 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 sys-
tems can often be divided into two separate tasks:

 1.  Description of hydrodynamics (current, tides, cir-
   culation, mixing, etc.).

 2. Description of water quality processes.

The WASP4  model was designed  to simulate water
quality processes, but requires hydrodynamic informa-
tion as input.  This information can be  entered into
WASP4 by reading the output results from a separate
                                                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 ad-
vective flows and dispersive  mixing.  However,  the
distinction between the real-time description of tidal
hydrodynamics compared to the description of tidal-av-
eraged  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, hy-
drodynamic conditions (and water quality) are aver-
aged 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 freshwa-
ter 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 recom-
mended 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 col-
umn segments in WASP4 are characterized by disper-
sion coefficients.  These dispersion coefficients, when
coupled with a concentration gradient between seg-
ments, 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 mecha-
nisms for describing  transport, all of which are  ad-
dressed 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 dis-
persion 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 con-
ditions. 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 col-
umn segments and the time history of the correspond-
ing 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, char-
acteristic lengths, and their respective dispersion coef-
ficients.   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 sub-
models, 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 Eutro-
phication 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 vari-
ables (termed systems by WASP4) in the water column
and sediment bed.  These systems correspond to:

System Number
1
2
3
4
5
6
7
8
EUTRO4
State Variable
Ammonia nitrogen
Nitrate nitrogen
Inorganic phosphorus
Phytoplankton carbon
Carbonaceous BOD
Dissolved oxygen
Organic nitrogen
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 con-
siders a simple  model simulating CBOD, ammonia
nitrogen (NHs-N), and DO.  This type of model com-
plexity 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 simu-
lates 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
1
2
3
4
5
6
TOXI4 State Variable
Chemical 1
Solids type 1
Solids type 2
Solids type 3
Chemical 2
Chemical 3
The chemicals can be related (e.g., parent compound-
daughter product) or totally independent (e.g., chemi-
cal 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 simu-
lation of ionization,  sorption,  hydrolysis, photolysis,
oxidation, bacterial degradation, as well as extra reac-
tions specified by the user. TOXI4 simulates concen-
trations  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 demon-
strate the use of ionization, equilibrium sorption, vola-
tilization,  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 cop-
ies 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 de-
signed 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 proce-
dures.

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 comput-
ing 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  concentra-
tions, 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

-------
              TRINITY RIVER
                                Highway 64
Table 6-8.  Treatment Plant Effluent Characteristics
Harris Citv WTP	
Figure 6-6. The Trinity Estuary.
whether continuing high coliform counts may be attrib-
uted 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  prob-
lem 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 upestu-
ary extremity and the city of Harris is located approxi-
mately 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 tem-
peratures taken  at the USGS  gauge are provided in
Figures 6-7 and 6-8.  An analysis of the morphometry
Present
Flow
BOD5
CBODU(1)
Total Coliforms
DO
MGD
mg/l
mg/l
counts/100 ml
mg/l
17
65
130
1E + 7
5
                                                     (1) Based on long term BOD estimates of CBODu/CBODs =2.0

                                                     of the system indicated that the mean tidal widths and
                                                     depths could be adequately represented by
                                                        W=300e
                                                                0.0625X
                                            (6-19)
                                                     and
                                                           = 2.43e
                                                                  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
            cos [2 7i t/Ti - Pi ]
5-21)
where Y is the water surface elevation deviation (m) at
time t (hrs), hi is the amplitude (m), Tj the period (hrs),
and  Pi the phase  (in  radians) of the seven principal
           48
           36
            IJSS
                                                    Figure 6-7. Average monthly river flow at the Highway 64
                                                    USGS gauge.
                                                 6-14

-------
Table 6-9.   Tidal Periods, Amplitudes and Phases for the
          Trinity Estuary during March, 1989
Symbol

M2
S2
N2
K2
Ki
Oi
Pi
Name
Semi-Diurnal
Components
Principal Lunar
Principal Solar
Larger Lunar Elliptic
Luni-solar
semi-diurnal
Diurnal Components
Luni-solar diurnal
Principal lunar diurnal
Principal solar diurnal
Period
(hours)

12.42
12.00
12.66
11.97
23.93
25.82
24.07
Phase
(degrees)

330
334
303
328
106
89
104
Amplitude
(cm)

23.0
5.2
4.9
1.6
15.8
9.8
4.9
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.
6.4.1.4. Model Application

For this analysis, model application consisted of: first
determining  the model network (including  mor-
phometry of model segments), then determining ap-
propriate 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 hydrody-
namic model, DYNHYD5, is part of the WASP4 mod-
eling system.  The WASP4 model may also be coupled
with other available hydrodynamic models. The hydro-
dynamic 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 Centerfor Exposure Assess-
ment Modeling. The determination of these types of
data and their use in this illustrative example is de-
scribed below.

                                                                74
                                                                                     500
                                                                                                	I
                                                                                                 8QO
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.
                                                6-15

-------
— General model information: The TOXI4 submodel
was  selected for these simulations. TOXI4 was se-
lected rather than EUTRO4 as a result of its conven-
ience 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 salin-
ity, 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 kilome-
ters.  The depths of the segments were determined as
well  as segment volumes and interfacial areas from
available morphometry data.  An analysis of the sys-
tem's morphometry  indicated that variations in width
and depth were reasonably described by Equations
                             Longitudinal Scat®
                               018
                               KHonwlws
                                    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 disper-
                                    sion, 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 seg-
                                    ment is  required, as well as a description of how the
                                    volume  changes with flow.  Volumes are determined
                                    from  segment width and  depth  (taken from hydro-
                                    graphic  maps) and  segment length (user specified).
                                    For this application, the segment widths and depths
                                    were determined from Equations 6-19  and  6-20, ob-
                                    tained through analysis of the system.  Changes in
                                    volume  in this example were computed by the hydro-
                                    dynamic 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 esti-
                                    mated 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 move-
                                    ment, such as the bottom roughness. For this applica-
                                    tion 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 informa-
                                    tion 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
                               (Wid
-------
  O

  "  '
  "I
i£J
CO

LJ

LJ
JZ

o

CD
—i
O

LJ
  O °
  > co
                                         LEGEND
                                         30  KM
                                         20  KM
                                        "TO "KM"
                                        	f'KM"
       0.0    70.0    140.0    210.0    280.0    350.0    420.0   490.0    560.0   630.0   700.0    770.0
                                           TIME  (HOURS)
Figure 6-10. Predicted variations in volumes near the mouth, near the midpoint, and at the upper extremity of the Trinity Estuary.
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 forthis study were computed assuming nochlori-
nation or other disinfection, resulting in the high efflu-
ent concentrations given in Table 6-8. The loadings
were then computed from the discharge rate and bac-
terial  concentration.  The equivalent load for organ-
isms  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 |jg/l,  the values were multiplied by
10~7 ( 1 ng ( n count here) = 10~6 g (counts), and 100
ml = 0.1 liter).
                                                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 bac-
                                                terial 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.
— Model  constants:  A first-order rate coefficient is
required to describe bacterial decay.  Initial estimates
                                                 6-17

-------
      Q_
      CL
      <
      (f)
                                          10       15

                                               DISTANCE
       20
25
30
Figure 6-11. Monthly averaged salinities in the Trinity Estuary versus distance upstream from its mouth.
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
           22	
           20
Figure 6-12. Predicted variations in salinity during March,
1989, near the mouth of the Trinity Estuary.
mouth (Figure 6-12) and near the midpoint of the estu-
ary (15 km up estuary; Figure 6-13).

Following evaluation of simulations of salinity, simula-
tions of dye injections were conducted. In this illustra-
tive example, it was assumed that data were not readily
available and no attempt was made to compare simu-
lations 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
            3.5


             3


            2.5


             2


            1.5


             1


            0.5
                                                                             10
                                                                                  15   20

                                                                                  TIME (DAYS)
                                                                                             25
                                                                                                  30
                                                                                                       35
 Figure 6-13. Predicted variations in salinity during March,
 1989, near the mid-point of the Trinity Estuary.
                                                  6-18

-------
                  0.045
    Q
    OL
    Ld
    o

    o
    u
 0.015	
                   0.01
                  0.005	
                        0
                                                            25
30
                                                  DISTANCE (KM)
Figure 6-14.
        Q
        h-

        cr
        i—

        u
        o

        o
        o
Neap tide dye simulations for the Trinity Estuary.


    0.035
                     0.005
                                                                           25
                                                                    30
                                                  DISTANCE
Figure 6-15. Spring tide dye simulations for the Trinity Estuary.
                                                      6-19

-------
      GO
      o
      Q
      \—
      <
      ct:
      LJ
      O

      o
      o
      Ld
      i—
      o
      <
      CD
                                             10        15        20


                                                  DISTANCE (KM)
25
30
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.
       LO
       O
       o
       Q
       i—
       <
       UJ
       O

       o
       o
       LJ


       O
       <
       CO
                                                                             25
                                                   DISTANCE (KM)
          30
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

-------
        CO
        o
        o
  Q
  i—
  <

  i—
  z
  LJ
  O

  O
  o

  _J

  E
  UJ
  i—
  o

  m
                        20
                        10-
                           0         5        10        15        20


                                                   DISTANCE (KM)



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.
CO
(—
z:

o
CJ,


o
      O

      O
      O
       .
      Ld

      O
      <
      CQ
                       50
                       40
                       30
                       20
                 10
                      -10
                                    I

                                    5
10        15


     DISTANCE (KM)
                                                              \

                                                            20
25
30
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

-------
      CO
      o
      Q
      K.
      UJ
      O
      O
      o
       LJ
       h-
       O
       <
       m
                                         10       15

                                             DISTANCE
Figure 6-20.
Trinity Estuary.
Comparison of predicted bacterial concentrations for different die-off rates versus distance from the mouth of the
a slug of dye from the Harris WTP discharge.  Simula-
tions included a dye injection near the spring tide and
again nearthe neap tide.  The results of these simula-
tions 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 con-
tinuously over the 30 day period of simulation. Simu-
lations were first conducted assuming that there was
no die-off (treating bacteria as a conservative constitu-
ent) 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 illus-
trate results assuming that bacteria act conservatively,
while Figures 6-18 and 6-19 illustrate projections as-
suming 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 moder-
                                     ate die-off rate would probably reduce bacterial con-
                                     centrations  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 bac-
                                     teria 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 con-
                                     sidered before determining the appropriate enforce-
                                     ment and/or allocation action.  Additionally, this
                                     application considered a  flow regime over a single
                                     month. Additional simulations, with collection of sup-
                                     porting field  data, may be required for critical environ-
                                     mental 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
                                                6-22

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                                       RHODE  ESTUARY
                                      Port Holcomb
                                                                             USGS GAUGE
          Open Boundary
                                                                            Highway 64
                                                                Rhode City
               1          I         I
               0       5000    10000
                  Distance (m)
Figure 6-21.
Morphometry of the Rhode Estuary.
the pollution problem, the eutrophication kinetic sub-
routine (EUTRO4) is required. The water quality vari-
ables  of concern  consist of DO, CBOD, and
nitrogenous BOD. Water quality processes simulated
include reaeration, sediment oxygen demand, nitrifica-
tion 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 deoxy-
genation rate, and reaeration rate.  WASP4 provides
the option of internally calculating  the reaeration rate
as a function of water depth and velocity.  The reaera-
tion rate will be manually specified for these  simula-
tions 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 Hol-
combville  WWTP discharges to Holcomb Creek, a
tributary of the Rhode Estuary, while the Rhode and
Port Holcomb WWTP discharge to the mainstem es-
tuary.  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 evalu-
                                    ate 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.
                                      i-
                                      0.
                                      Q.
                                              30
                                              25
                                              20
                                              15
                                              10
                                                 \
                                                       	1	1	1	T~~
                                                          10    15    20    25

                                                        DISTANCE (m) (Thousands)
                                    Figure 6-22. Mean salinity profile for the Rhode Estuary.
30
                                               6-23

-------
        D)
        3
        
D x x " *
~ x x g
B H H a - n *
i i i i i
) 5 10 15 20 25 3
+
DAY 1
a
DAY 5
X
DAY 9
0
                                      DISTANCE (M) (Thousands)
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

-------
    5
    «•••
    i
    i-
    QL
    UJ
    O
16



14



12



10



 8



 6



 4



 2



 0
                       i    i   i   i   f   r   i   r i    i   i   i   i   i    i   i
                       0     4000  6000   12000   16000  20000  24000 26000
                         2000  6000   10000  14000  18000  22000  26000  30000
                                                                                LOW TIDE

                                                                                     A


                                                                                HIGH TIDE
                                         DISTANCE (M)
Figure 6-26. Mean depths for the Rhode Estuary versus distance upestuary from its mouth.
                 12
                 10
                   8
                   6
                                                                LOW TIDE

                                                                      A


                                                                HIGH TIDE
                        \   i    r  r   (   i   i   i   i   i    i   i   i    i   i   i
                        0     4000   6000   12000  16000 20000  24000  28000
                          2000   6000  10000  14000  18000  22000  26000  30000
                                          DISTANCE (M)
Figure 6-27. Mean widths of the Rhode Estuary versus distance upestuary from its mouth.
                                              6-25

-------
  Q.
  Ul
  Q
                       I       I       I       I       I      1
                       0    2000  4000  6000  8000  10000


                                  DISTANCE (M)
                                                                     LOW TIDE

                                                                         A

                                                                     HIGH TIDE
Figure 6-28. Mean depths of Holcomb Creek versus distance upstream from its mouth.
   X
   I-
   Q
           3000
            2500
            2000
1500
            1000
             500
                              I       I       I      I       I
                            2000 4000  6000  8000 10000

                                  DISTANCE (M)
                                                        LOW TIDE

                                                            A

                                                        HIGH TIDE
Figure 6-29. Mean widths for Holcomb Creek versus distance upstream from its mouth.
                                      6-26

-------
Table 6 10.  Treatment Plant Effluent Charactoriotico
Rhode City WTP

Present: Trickling filter plant presently at capacity.
Proposed:  Activated sludge plant.

Flow
BODs
CBODU(1)
NH3-N
DO

MGD
mg/L
mg/L
mg/L
mg/L
Present
17
60
120
30
5
Proposed
24
30
60
20
5
(1) Based on long term BOD estimates of CBODU/CBOD5 = 2.0

Holcombville

Flow
BODs
CBODU(1)
NH3-N
DO

MGD
mg/L
mg/L
mg/L
mg/L
Present
1.2
65
130
40
5
Port Holcomb

Flow
BODs
CBODU(1)
NH3-N
DO

MGD
mg/L
mg/L
mg/L
mg/L
Present
0.48
80
160
42
5
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 con-
ditions  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 esti-
mated to be 10 cms.  Average August water tempera-
tures is 27 °C.

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, NHs-N, BODs, and salinity were taken along
the estuary and creek.  The slack tide data were trans-
lated to mid-tide for comparison with the tidally aver-
aged 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 °C at the USGS gauge.  A single
measurement nearthe USGS gauge indicated a BODs
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" day"  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 pre-
vious WASP4 example, with the exception of pollutant
kinetics. However, it was elected not to use a hydro-
dynamic model for this application.  Instead, simula-
tions 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 subrou-
tine (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, nitrifica-
tion 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 regu-
lar, 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 re-
quired to describe  tidal mixing between all model seg-
ments. Initial estimates can be
                                               6-27

-------
      12 O City  STP
                 T
              Town WWTP
        <>  Village WPCP
                                      SCALE

                                       Mltert
                                       2000  1000
Figure 6-30. Model segmentation for the Rhode Estuary.

derived from the literature and refined through calibra-
tion to dye or salinity data.   Their  determination is
described below.

- Segment volumes: The initial volume of each seg-
ment  is required, as well as a description of how the
volume changes with flow. Volumes were determined
from segment width and  depth  (taken from  hydro-
graphic 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, tem-
perature and sediment oxygen demand  distribution
both spatially and temporally.

-  Model constants:  Nitrification rate,  CBOD deoxy-
genation 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 EU-
TRO4, the CBOD system was used with no decay
specified (treated as a conservative material). Bound-
ary 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 esti-
mated first from the salinity profile, indicating a disper-
sion  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 condi-
tions.  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.
              5    10   15   20    25

                 DISTANCE (m) (Thousands)
Figure 6-31. Comparison of predicted and observed salinities
for different values of the dispersion coefficient. (m2/s).
                                                6-28

-------
   X
    O)
    3
   <^s
   z
   o
   z
   111
   o
   z
   o
   o
20
SIMUL-1


SIMUL-5


SIMUL-9
    +
 DAY 1
    a
 DAY 5
    X
 DAY 9
                                       10       15

                                   DISTANCE (M) (Thousands)
Figure 6-32. Comparison of measured and observed dye concentrations.
Beginning August 1, in conjunction with other water
quality surveys, a dye study was conducted.  Rho-
damine 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 concentra-
tion 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 pre-
dicted 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.  There-
                                  fore, simulations proceed from the simple to the com-
                                  plex.

                                  Simulations were conducted first using literature val-
                                  ues 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, be-
                                  cause  reaeration  rates had  been measured in the
                                  vicinity undersimilar 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  pre-
                                  dictions are compared in Figures 6-33 to 6-36. While
                                  no statistical analyses were performed, visual inspec-
                                  tion indicated that model predictions were adequate for
                                  this study.

                                  6.4.2.6. Model Predictions

                                  Once reasonable predictions were obtained, simula-
                                  tions were conducted projecting DO,  NBOD  and
                                  CBOD concentrations  in the estuary following imple-
                                  mentation of the proposed modifications at the Rhode
                                  WWTP (Table 6-10, see Figure 6-37).  These simula-
                                  tions suggested that little change would  be expected
                                  in the DO concentrations as a result of the proposed
                                  modifications.
                                               6-29

-------
     o
     5
     ^-*
     z
     o
      Z
      UJ
      o
      z
      o
      o
      V
                                        I

                                       10
 I

15
 I

20
 I
25
                                                                                      D.O.
                                                                                   PRED. D.O.
30
                                    DISTANCE (M) (Thousands)
Figure 6-33. Measured and predicted DO concentrations in the Rhode Estuary versus distance upestuary from its mouth.

     Q
     QL
     U

     O
     O
                                   PRED. NBOD

                                   	^	
                                       7^


                                   PRED. CBOD

                                       +-


                                     N-BOD

                                       +


                                      CBOD
                                        10        15


                                       DISTANCE (M)  (Thousands)
                     I

                    25
                    30
Figure 6-34. Predicted and observed NBOD and CBOD concentrations in the Rhode Estuary versus distance upestuary from its

mouth.
                                                6-30

-------
3 I!
o ca
c c
CONCENTRATION (MG/L) ^£ ,
£ CONCENTRATION (MG/L)
en
/
6
5
4
3
2
1
0
Predicted and o
OR i-
.0
07
. /
Oc
.O
Oe
.9
04
.**
0«5
.O
0.2
0.1
0
^,
	 • — " — ~*C






D.O.
PRED. D.O.
i i i i
0 2E+03 4E+03 6E+03 8E+03 1E+04
DISTANCE (M)
bserved NBOD and CBOD concentrations in the Rhode Estuary versus distance upestuary from its
A

/
/
2
^^
A^-^__ 	 _
• 	 *~— m m


I I I I
N-BOD
CBOD
PRED. CBOD
PRED. NBOD
                   0       2E+03    4E+03    6E+03    8E+03    1E+04




                                        DISTANCE (M)




Figure 6-36. Measured and predicted DO concentrations in Holcomb Creek versus distance upstream from its mouth.




                                            6-31

-------
   O
   5
   «^»
   z
   o
   I-
    Z
    UJ
    o
    z
    o
    u
                                                 I
                                                15
        I
       20
5        10

     DISTANCE (M) (Thousands)
 I
25
                                                                                    EXISTING
                                                                                   PROPOSED
30
Figure 6-37. Comparison of DO predictions under existing and proposed conditions for the Rhode City WWTP.
The final waste load allocation should not result from
a single model projection. The model should be evalu-
ated using independent data, if possible.  A compo-
nent 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 use-
ful in project design.  Sensitivity analyses should also
be performed to determine the effects of assumptions
concerning the selection  of model parameters.  Con-
sideration should also be given to the applicability of
calibrated rates to future conditions. Examples include
CBOD deoxygenation and nitrification rates and sedi-
ment oxygen demand, which can decrease under fu-
ture 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 estu-
ary. 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.  How-
ever, as a result of the bacteriological problem that has
resulted, permit/enforcement action is pending which
would impact its BOD release as well.

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 intru-
sion 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 com-
mercial fishing  and shellfishing, and the upper reach is
spawning habitat. Boating and recreational fishing are
popular, as are several bathing  beaches.  Pertinent
                                               6-32

-------
                                                                     DEEP BAY
                                                                      Location Map
                                        Athens

    Gage
                    20
                                                  SCALE
                                                I   I   I    i  =1
                                                61234
                                                  kilometers
Figure 6-38.     Deep Bay location map.
criteria and water quality goals are 5.0 mg/L for DO
and 25 |jg/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 down-
stream have been occurring. Renovation of the plant
to high performance secondary  or possibly tertiary
treatment is being considered, as are point and non-
point source controls in the watershed.

Bathymetric surve6.4.3.2  Deep Bay Network

Analysis of the monitoring data show significant differ-
ences 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 net-
work 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

Table 6-11.  Summary of Deep Bay Tidal Monitoring Data
Rms Net
2 • 2
Station Date Tidal Surface Bottom Surface Bottom
Range1
S1
(km 3)

S2
(km11)

S3
(km 1 7)

4/19-23
6/13-17
8/14-18
4/19-23
6/13-17
8/14-18
4/19-23
6/13-17
8/14-18
0.9
1.0
0.9
1.1
1.2
1.1
0.8
0.9
0.8
340 260
350 260
330 260
370 270
350 260
350 250
320 31 0
300 300
290 280
+2.1 +0.2
+0.6 +0.0
+0.2 -0.0
+5.3 +0.7
+1.4 +0.2
+0.4 +0.0
+10.4 +8.9
+2.8 +2.3
+0.7 +0.6
-meters
cm/sec
                                              6-33

-------
                                                                  DEEP BAY
                                                                  Navigation Chart *
                                      Athens
                   20
                                          * soundings in meters


                                                SCALE
Figure 6-39. Deep Bay navigation chart.

Table 6-12. Summary of Deep Bay Estuarine Data
Table 6-14. Summary of Athens POTW Effluent Data
Design Capacity - 60 MGD
Secondary Treatment, with problems
                     Nitrogen	Phosphorus
Alternative
Present
Good Sec-
ondary
Tertiary
DO
4
5

6
BOD5
40
20

10
ORG NH3 N03
15 15 0
0 15 15

0 2 10
Org PO4
3 7
3 7

0 0.5
                                      ^
Station
S1


S2


S3


Salinity Temperatu Secchi
(kg/L) re (°C) Depth (m)
Date Surface Bottom Surface Bottom
4/19-23 14.0 21.1
6/13-17 22.5 24.5
8/14-18 27.2 28.0
4/19-23 15.7 15.5
6/13-17 8.5 12.3
8/14-18 19.5 21.8
4/19-23 0.1 0.3
6/13-17 1.0 3.1
8/14-18 9.1 10.7
14 15
23 22
22 21
15 17
25 22
23 22
16 18
26 23
24 22
3.3
2.7
3.0
1.7
1.3
1.5
0.7
0.5
1.0
                                              01234
                                                kilometers
Table 6-13. Deep River Data

Month
January
February
March
April
May
June

Average
90
80
120
210
175
120
Monthly (mj/sec)
Flow
Survey Month
Year
85
75
150
300
200
100
July
August
Sept
October
Nov
Dec

Average
60
50
50
110
140
130

Survey
Year
40
20
40
150
140
150
Water Quality
Present
constituent Minimum
FKN
ORG-N
\litrate-N
Ortho-P
Organic-P
30D5
DO
SS
0.1
0.0
0.3
0.04
0.01
0.5
5
10
(mg/l)
Maximum Watershed Controls
0.4
0.3
0.6
0.12
0.05
1.0
14
1000
0.02
0.01
0.10
0.01
0.005
0.2
7-14
10-250
                                             6-34

-------
                                                                            DEEP BAY
                                                                            Model Segmentation
SCALE
meters
• u
• 1
•2
•3
•4
10
20

9
19

8
18

7
17
Side View


6
16
5
15

4
14

3
13

2
12

1
11
                                 Dye Study
                                  Network
                                                            I    I   I    I   I
                                                            01234
                                                              kilometers
Figure 6-40.
Deep Bay model segmentation.
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, rep-
resenting 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 disper-
sion (representing tidal mixing) and vertical eddy diffu-
sion.

—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 down-
                                    stream 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 in-
                                    put.

                                    —Kinetic constants: No constants are needed.

                                    —Environmental time functions: No time functions are
                                    needed.
                                               6-35

-------

   c
  "o
                                                                                      Apr 21 Sur
                                                                                      	1	
                                                                                      Apr 21 Bot
                                                                       June 15 Su
                                                                       - 1 -

                                                                       June 15 Bo
                                                                       - B -

                                                                       Aug 11  Sur
                                                                                      Aug 11  Bot
                    0
                          1          5          9         13         17
                                3         7         11          15        19
                                        Distance above Mouth, km
Figure 6-41.
Deep Bay salinity Apr-Aug mean response.
—Initial concentrations: Initial salinity  concentrations
are assigned each segment based upon an April sur-
vey. Dissolved fractions are set to 1.0.

Analysis of the depth-averaged salinity data during the
three monitoring periods indicates estuarine-wide dis-
persion from 20 to 50 m /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 at-
tenuated 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 corre-
sponding 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 net-
                                      work is divided into lateral segments, and lateral dis-
                                      persion coefficients are required.
                                                 6-36

-------
  o
  5
  o
                 0.2
                 0.1
                                                                                    Center Cha
                                                                                    Near Shore
                                                                                    Far Shore
                                                        13         17
                                         7         11         15         19
                                      Distance from Mouth, km
Figure 6-42.
Deep Bay dye study June 15, surface.
—Segment volumes: The same mean tide volumes
from the salinity simulation are used, except the up-
stream  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 Ath-
ens 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
                                     foroneweekalongthe nearshore, 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 dis-
                                     persion coefficients  in the upper network were  ad-
                                     justed  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 pro-
                                     files for the first 2 weeks are shown in Figure 6-44. The
                                     model was judged sufficiently calibrated for estuarine-
                                     wide 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 simu-
                                     lated - 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
                                                6-37

-------
                0.25
   en
   o"
   8
  o
  0
                 0.05
                          1           5          9          13         17
                                3          7          11         15         19
                                         Distance from Mouth, km
                                                                                        June 15 Su
                                                                                        	1	
                                                                                        June 15 Bo
June 16 Su
                                                                                        June 16  Bo
Figure 6-43. Deep Bay dye study center channel, surface and bottom.
   O

   &
   Q
                 0.08
                 0.06
                 0.04
                 0.02
                                                                       T
                                                                       17
                                           7          11          15         19
                                         Distance  from Mouth, km
 June 16
	1	
  June 17
  June 19
 	1	
  June 21
 	B	
  June 23
 	X	
  June 30
Figure 6-44. Deep Bay dye study center channel, surface.
                                                  6-38

-------
  s
  u
  6
  o
                                 Surface TN
                                 	1	
                                 Bottom TN
                                 	>•	

                                 Surface TP
                                 	f-	

                                 Bottom TP
                                    59         13        17
                                         7          11         15
                                       Distance  from Mouth, km
                     19
Figure 6-45. Deep Bay total N and P - August 11, surface and bottom.
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 seg-
ment 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 nitro-
gen and total phosphorus are specified for each seg-
ment, 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 par-
ticulate 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 |jg/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 possi-
ble 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, simu-
lations 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.
                                                6-39

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   o>

   
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There are significant advantages and disadvantages
in simulating nutrients without phytoplankton to esti-
mate eutrophication potential. The advantages lie in
the lessened requirements for field data and modeling
resources.  Several sites could be evaluated for nutri-
ents 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 conver-
sion of dissolved phosphorus into particulate form is
dependent  upon algal concentration and growth rate.
Because algal dynamics are not simulated, these val-
ues 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 eu-
trophication in  Deep Bay. The  problem  setting  and
model network are as described in the preceding sec-
tion. Here, the  entire eutrophication process is simu-
lated,  including  nutrients,   phytoplankton,
carbonaceous  BOD, and DO. This is  typically the
highest level of complexity used for conventional pol-
lution 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 simula-
tion. 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 nutri-
ents 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 ben-
thic-water column exchange of dissolved chemicals
must be specified.

—Segment volumes: The same water column  vol-
umes 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 con-
centrations of all 8 systems must be specified.

—Pollutant loads: Constant loads for all 8 systems in
the effluent must be specified for the segment adjoin-
ing Athens POTW.

—Environmental parameters: Values for average sa-
linity and  background sediment oxygen demand  for
each segment are given. The time variable tempera-
ture and light attenuation functions used by each seg-
ment must be specified.

—Kinetic constants: Rate constants, temperature co-
efficients,  half saturation constants  and other kinetic
information must be specified. Processes include nitri-
fication, denitrification, phytoplankton growth (light and
nutrient limitation), phytoplankton  death,  carbona-
ceous 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 pro-
vided.  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 pre-
dicted  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. Phytoplank-
ton growth is limited somewhat by nitrogen, but more
by  light. Sensitivity studies  show the relative impor-
tance of the variable light attenuation coefficients, the
phytoplankton saturating light intensity, and
                                                6-41

-------
the calibrated Michaelis-Menton nitrogen half satura-
tion 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 condi-
tions, 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 re-
quire years.

Regulations related to eutrophication can differ signifi-
cantly  from  state to state. Water quality standards,
criteria, or goals  can relate  to chlorophyll, transpar-
ency, nutrients, and/or DO. Selection of critical condi-
tions  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 con-
ditions 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 phyto-
plankton levels of 30 |jg/L and lower DO levels of 4.5
mg/L. A  combination of watershed controls  and ad-
vanced secondary treatment was judged most reason-
able.

6.4.5.  Example 5 - Ammonia Toxicity in a Two-
Dimensional Estuary
The fifth and sixth examples consider toxic pollutants
in a laterally variant two-dimensional estuary.  This
type of estuary characterization differs from the pre-
vious 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 typi-
cally exert their maximum influence a significant dis-
tance 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 estu-
ary, allowing for the description of lateral changes in
water quality.  Depending  upon the degree  of vertical
stratification, the system can be treated as two-dimen-
sional  (no vertical stratification) or three-dimensional
(with vertical stratification). Again, vertical layer(s) to
describe sediment quality can  be added to either frame-
work (using WASP4) when necessary to describe sedi-
ment/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 ammo-
nia 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  in-
stances 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 sound-
ings at low tide, used  for navigation (Figure 6-49).
Three surveys were conducted (May, August and No-
vember)  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 trans-
port of the  ammonia discharge (Figure 6-50).  Seg-
ments 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 aver-
aged  from the continuous flow meters that were in-
stalled 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  re-
maining sys-
                       Waste Water Treatment Plant
 3.2 mg/l Ammonia
                            50 kg/day Ammonia
                                 Scale
                                  5000
                                 meters
10,000
                                       Scale
                                                  =l
                              0         5000

                                       meters


         Figure 6-49. Boatwona Estuary depth chart.

         Table 6-15. Boatwona Estuary Survey Data
10,000
S1 S2 S3
Sample
Time
May
August
Nov
Temp pH
17.0 6.8
19.2 6.9
17.4 6.8
Temp pH
16.5 7.1
18.2 6.9
16.7 6.8
Temp pH
15.3 6.9
17.0 7.0
16.9 6.8
                                                    Table 6-16. Boatwona River Survey Data
Figure 6-48. City of Boatwona waste water treatment plant
location.
Month
January
February
March
April
May
June
July
August
September
October
November
December
Average Flow (cm)
12
15
18
22
15
11
8
10
15
13
14
13
PH
6.2
6.4
6.1
6.2
6.6
6.8
6.9
7.1
6.8
6.8
6.6
6.7
N
2.3
0.8
2.1
4.2
6.6
2.3
9.4
7.3
3.7
0.9
1.3
4.2
                                                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:  lonization constants and nitrifica-
tion rate for ammonia.

Environmental time functions: Temporal temperature
functions.

Initial concentrations: Initial ammonia concentrations
within the estuary are assumed zero.  Dissolved frac-
tions 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 dif-
ferent processes. The dominant loss process will typi-
cally 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 indi-
cates that the toxicity of the un-ionized ammonia may
vary with changes in temperature and pH. This infor-
mation is not reflected in present criteria.

6.4.6.  Example 6: Alachlorin a Laterally Variant
Estuary
The sixth example study considers the fate of a hydro-
philic, reactive chemical in a two- dimensional estuary.
                              Scale
                                I
                              5000
                              meters
                          10,000
Figure 6-50.
Boatwona Estuary flow pattern.
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 degrada-
tion) in the environment.  Possible transformation
processes  include hydrolysis,  photolysis, oxidation,
reduction, and biodegradation.  In addition, volatiliza-
tion 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 simula-
tion uses Systems 1 through 3 in TOXI4.  Two types
of solids are represented, corresponding to inorganic
and organic materials, respectively.  System 1 repre-
sents the pollutant.  System 2  represents  inorganic
solids,  and System 3 represents organic solids.  Envi-
ronmental 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 degrada-
tion. Biodegradation will be treated as a first-order loss
process for this simulation, with separate values used
for the  water column and the sediment.
                                                6-44

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         0      10      20      30


                         •  Ionized Ammonia
                         40      50      60      70     80      90      100    110
                               Time (days)

                                    _A_ Unionized Ammonia
Figure 6-51.
Ammonia simulation results.
Readers viewing the input file will find that it varies only
slightly from the one for the previous example, loniza-
tion coefficients have been removed.  The first-order
biodegradation rate constants are lower, and the par-
tition 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
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. Envi-
                                     ronmental 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 Pro-
                                     cedure for Toxic and Conventional Pollutants in Sur-
                                     face and Ground Water Part 1, EPA/600/6-85/002b,
                                     U.S. Environmental Protection Agency, Athens, Geor-
                                     gia.

                                     Schnoor et. al. 1987.  Processes, Coefficients and
                                     Models for Simulating Toxic Organics and Heavy Met-
                                     als in Surface Waters.  U.S. Environmental Protection
                                     Agency, Athens, Georgia, EPA/600/3-87/015.
                                               6-45

-------
  a*
  3
   U
   o



  "5
  •w
   o
      s.o




      7.0 -




      S.O •




      3.0 •




      4.O




      3.O




      2.O




      t ,O -
         O.O
                       4O       so       120      iso

                                           Tim®  (days)
                                                           2OO
       24O
                                                                               23O
                                                                                           32Q
        •4O.O
   o»
   J*
   u
        35.0 -
        30.0 -
        2S.Q H
   5    20. o -
        15.0 -i
"5    1 O.O -

"o


       S.O -
         O.O
                                 Upp«r S«d!nr»«nt Loyar


                                        Ssgrnsnt j^B
                       —,—


                        4O
                                SO        ISO      1 SO


                                         Tim®   (doya)
	I	'	f—!	T

 2OO
                                                                                    2.BQ
Figure 6-52.      Hydrophobic (Alaehlor) chemical simulation for example 6.
                                               6-46

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6.5 References                                  U.S. Environmental Protection Agency, Athens, Geor-
Ambrose, R.B., Wool, T.A., Connolly, J.P., Schanz,   9'a'
R.W.  1988.  WASP4,  A Hydrodynamic  and Water   Schnooret.al. 1987. Processes, Coefficients and Mod-
Quality Model - Model Theory, User's Manual and   eb for Simu|atjng Toxic Qrganics and Heavy Metals in
Programmer's Guide.  EPA/600/3-87/039, U.S. Envi-   surface Waters.  U.S.  Environmental Protection
ronmental Protection Agency, Athens, Georgia.        Agency, Athens, Georgia, EPA/600/3-87/015.

Dyer,  K.R., 1973.  Estuaries: A Physical Introduction.   Thomanni R.v. 1972. Systems Analysis and Water
John Wiley & Sons, New York.                       Qua|ity Management. McGraw-Hill, New York.

Mills, W.B., Porcella, D.B., Ungs, M.J., Gherine, S.A.,   Thomanni RA/.  and Fitzpatrick, J.J. 1982. Calibration
Summers, K.V., Mok, L, Rupp, G.L. and Bowie, G.L.,   and verification of a Mathematical Model of the Eutro-
1985. Water Quality Assessment: A Screening Pro-   phication of the Potomac Estuary. Prepared for Depart-
cedure for Toxic and Conventional Pollutants in Sur-   ment of Envjr0nmental Services, Government of the
face and Ground  Water Part 1, EPA/600/6-85/002b,   District of Co|umbiai Washington, D.C.
                                              6-47

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