&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
-------
Click here for
DISCLAIMER
Document starts on next page
TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
Book III: Estuaries-
Part 2: Application of Estuarine Waste Load Allocation Models
EPA DOCUMENT NUMBER: 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
-------
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
-------
Table of Contents
Glossary v
Acknowledgments xxi
Executive Summary xxiii
PART I: Estuaries and Waste Load Allocation Models xxiii
Introduction xxiii
Overview of Processes Affecting Estuarine Water Quality xxiii
Model Identification and Selection xxiv
PART II: Application of Estuarine Waste Load Allocation Models xxv
Monitoring Protocols for Calibration and Validation of Estuarine WLA Models . . xxv
Model Calibration, Validation, and Use xxvi
Simplified Illustrative Examples xxvii
Preface xxix
4. Monitoring Protocols for Calibration and Validation of Estuarine WLA Models .... 4-1
4.1. General Considerations 4-1
4.2. Types of Data 4-2
4.3. Frequency of Collection 4-3
4.4. Spatial Coverage 4-4
4.5. Model Data Requirements 4-5
4.6. Quality Assurance 4-8
4.7. References 4-12
5. Model Calibration, Validation, and Use 5-1
5.1. Introduction And Terminology 5-1
5.2. Model Calibration 5-4
5.3. Model Validation 5-11
5.4. Model Testing 5-11
Example 5.1. Calibration of Hydrodynamics, Mass Transport, and Toxic
Chemical Model for the Delaware Estuary 5-18
5.6 Application of The Calibrated Model In Waste Load Allocations 5-23
Example 5.2. Component Analysis of Dissolved Oxygen Balance in the
Wicomico Estuary, Maryland 5-26
-------
SUPPLEMENT I: Selection of Manning n Values 5-29
EXAMPLE 5.3. Initial Selection of the Manning n for a Hypothetical Estuary . . 5-35
EXAMPLE 5.4. Selection of the Manning n for the Delaware Estuary 5-36
SUPPLEMENT II: Selection of Surface Drag Coefficients 5-37
SUPPLEMENT III: Selection of Eddy Viscosity Values 5-38
SUPPLEMENT IV: Brief Review of Turbulence Closure Models 5-45
SUPPLEMENT V: Selection of Dispersion Coefficients 5-46
SUPPLEMENT VI: Selection of Wind Speed Functions: 5-52
SUPPLEMENT VII: Selection of Bacteria Die-off Coefficients 5-54
SUPPLEMENT VIII: Calibrating Simple Sediment Models 5-58
SUPPLEMENT IX: Selection of CBOD Coefficients 5-59
SUPPLEMENT X: Selection of 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
-------
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
-------
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
-------
Figure 6-8. Mean monthly temperatures at the Highway 64 USGS gauge 6-15
Figure 6-9a. Variations in water surface elevations at the mouth of the Trinity
Estuary during March, 1989 6-15
Figure 6-9b. Model network for the Trinity Estuary 6-16
Figure 6-10. Predicted variations in volumes near the mouth, near the midpoint, and
at the upper extremity of the Trinity Estuary 6-17
Figure 6-11. Monthly averaged salinities in the Trinity Estuary versus distance
upstream from its mouth 6-18
Figure 6-12. Predicted variations in salinity during March, 1989, near the mouth of
the Trinity Estuary 6-18
Figure 6-13. Predicted variations in salinity during March, 1989, near the mid-point of
the Trinity Estuary 6-18
Figure 6-14. Neap tide dye simulations for the Trinity Estuary 6-19
Figure 6-15. Spring Tide dye simulations for the Trinity Estuary 6-19
Figure 6-16. Predicted average, minimum and maximum bacterial concentrations for
March versus distance from the mouth of the Trinity Estuary assuming
no die-off 6-20
Figure 6-17. Predicted average bacterial concentrations during March, with standard
deviations, versus distance from the mouth of the Trinity Estuary
assuming no die-off 6-20
Figure 6-18. Predicted average, maximum and minimum bacterial concentrations
during March versus distance from the mouth of the Trinity Estuary
assuming a bacterial die-off rate of 1.0 day ~1 6-21
Figure 6-19. Predicted average bacterial concentrations, with their standard
deviations, for March versus distance from the mouth of the Trinity
Estuary, assuming a bacterial die-off rate of 1.0 day"1' 6-21
Figure 6-20. Comparison of predicted bacterial concentrations for different die-off
rates versus distance from the mouth of the Trinity Estuary 6-22
Figure 6-21. Morphometry of the Rhode Estuary 6-23
Figure 6-22. Mean salinity profile for the Rhode Estuary 6-23
Figure 6-23. Results of the Rhode Estuary tracer study 6-24
Figure 6-24. Average monthy flow at the Highway 64 USGS gauge 6-24
VII
-------
Figure 6-25. Mean monthly temperatures at the Highway 64 Gauge 6-24
Figure 6-26. Mean depths for the Rhode Estuary versus distance upestuary from its
mouth 6-25
Figure 6-27. Mean widths of the Rhode Estuary versus distance upestuary from its
mouth 6-25
Figure 6-28. Mean depths of Holcomb Creek versus distance upstream from its
mouth 6-26
Figure 6-29. Mean widths for Holcomb Creek versus distance upstream from its
mouth 6-26
Figure 6-30. Model segmentation for the Rhode Estuary 6-28
Figure 6-31. Comparison of predicted and observed salinities for different values of
the dispersion coefficient (m2/s) 6-28
Figure 6-32. Comparison of measured and observed dye concentrations 6-29
Figure 6-33. Measured and predicted DO concentrations in the Rhode Estuary
versus distance upestuary from its mouth 6-30
Figure 6-34. Predicted and observed NBOD and CBOD concentrations in the Rhode
Estuary versus distance upestuary from its mouth 6-30
Figure 6-35. Predicted and observed NBOD and CBOD concentrations in the Rhode
Estuary versus distance upestuary from its mouth 6-31
Figure 6-36. Measured and predicted DO concentrations in Holcomb Creek versus
distance upstream from its mouth 6-31
Figure 6-37. Comparison of DO predictions under existing and proposed conditions
for the Rhode City WWTP 6-32
Figure 6-38. Deep Bay location map 6-33
Figure 6-39. Deep Bay navigation chart 6-34
Figure 6-40. Deep Bay model segmentation 6-35
Figure 6-41. Deep Bay salinity Apr-Aug mean response 6-36
Figure 6-42. Deep Bay dye study June 15, surface 6-37
Figure 6-43. Deep Bay dye study center channel, surface and bottom 6-38
Figure 6-44. Deep Bay dye study center channel, surface 6-38
VIM
-------
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
-------
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
-------
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
-------
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!!!
-------
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
-------
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
-------
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
-------
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
-------
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
XVIII
-------
of the moon and sun in conjunction with the earth's
rotational force.
Tide Gage2 - (1) A staff gage that indicates the height
of the tide. (2) An instrument that automatically 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.
xix
-------
The contents of this section have been removed to
comply with current EPA practice.
xxi
-------
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.
XXIII
-------
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.
xxiv
-------
The temporal resolution of WLA simulations falls into
one of three categories - dynamic, quasi-dynamic, and
steady state. Dynamic simulations predict hour to hour
variations caused by tidal transport. Quasidynamic
simulations predict variations on the order of days to
months. The effects of tidal transport are time-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
xxv
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
4-7
-------
frequency of data collection for tributaries and point
sources was discussed previously (see section 4.3).
The sampling stations for tributaries should generally
be above the fall line, or region of tidal influence. The
open, or ocean boundary, is generally specified as
either constant or time-varying conditions which are
not impacted by interactions with the estuary. In some
cases this may require that the model and its boundary
be extended into the ocean to a point where this
assumption is valid or to where data are available. The
station(s) used for open boundary should be 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).
4-8
-------
4.6. Quality Assurance
A rigorous, well documented, quality assurance (QA)
plan should be an integral part of any waste load
allocation program. The QA plan should include 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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
IU
106
105
10<
*vi
CN
*-"
v '°3
«J
C
0)
• — n
£ 102
*^«
O)
O
C
o
g 10
'•5
"5
*-<
c
o
N
O
X
01
io-2
10~3
1Q— 4
I I I I I I I I
1 1 1 1 1 1 1 1 *
~~ 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
* >6 • G' I
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\' ^^
//' // i^° Current-gross pair
4/3 ^r j f S
y~ ' ~~^7 &£ /
/ • f 7& '
— *'•*/./ —
Ji /Co**. / o Orlob, S = 0.00327, 1 in. mesh
/ °/^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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
o>
-------
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
-------
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
-------
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
-------
DISCLAIMER
We have made efforts to ensure that this electronic document is an accurate
reproduction of the original paper document. However, this document does not
substitute for EPA regulations; nor is it a regulation itself. Thus, it does not and
cannot impose legally binding requirements on EPA, the states, tribes or the
regulated community, and may not apply to a particular situation based on the
circumstances. If there are any differences between this web document and the
statute or regulations related to this document, or the original (paper) document,
the statute, regulations, and original document govern. We may change this
guidance in the future.
Supplemental material such as this disclaimer, a document abstract and glossary
entries may have been added to the electronic document.
------- |