United States Office of Water
Environmental Protection March 1990
Agency Washington DC 20460
Technical Guidance
Manual for Performing
Waste Load Allocations
Book
Estuaries
Part 2
Application of Estuarine
Waste Load Allocation Models
-------
United State* Office of Water
Environmental Protection March 1990
Agency Washington DC 20460
Technical Guidance
Manual for Performing
Waste Load Allocations
Book III
Estuaries
Part 2
Application of Estuarine
Waste Load Allocation Models
-------
TECHNICAL GUIDANCE MANUAL
FOR PERFORMING WASTE LOAD ALLOCATIONS
BOOK III: ESTUARIES
Part 2: Application of Estuarine Waste Load Allocation Models
Project Officer
Hiranmay Biswas. Ph.D.
Edited by
James L Martin. Ph.D.,P.E.2
Robert B. Ambrose, Jr. P.E.1
Steve C. McCutcheon. Ph.D., P.E.1
Sections written by
Robert B. Ambrose. Jr., P.E1
James L Martin. Pn.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. American Scientific International, Inc., at the
Environmental Research Laboratory, U.S. EPA, Athens, GA
3. Environmental Research Laboratory,
U.S. EPA, Narragansett, Rl
4. Limno-Tech, Inc. (LTI), Ann Arbor, Michigan
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
401 M Street, S.W.
Washington, DC 20460
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Glossary
Acute Toxicity1 - Any toxic effect that is produced
within a short period of time, usually 24-96 hours.
Although the effect most frequently considered is mor-
tality, the end result of acute toxicity is not necessarily
death. Any harmful biological effect may be the result
Aerobic1 - Refers to life or processes occurring only in
the presence of free oxygen; refers to a condition
characterized by an excess of free oxygen in the
aquatic environment.
Algae (Alga)1 - Simple plants, many microscopic, con-
taining chlorophyll. Algae form the base of the food
chain in aquatic environments. Some species may
create a nuisance when environmental conditions are
suitable for prolific growth.
Allochthonous1- Pertaining to those substances.
materials or organisms in a waterway which originate
outside and are brought into the waterway.
Anaerobic2 - Refers to life or processes occurring in
the absence of free oxygen; refers to conditions 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 or-
ganisms 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 was-
tewaters.
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) creeping
forms such as snails, worms, and insects; (3) burrow-
ing 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 coefficient
in the velocity formulas.
Chlorophyll1 - Green photosynthetic pigment present
in many plant and some bacterial cells. There are
seven known types of chlorophyll; their presence and
abundance vary from one group of photosynthetic
organisms to another.
Chronic Toxicity1 - Toxicity, marked by a long 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.
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Heterotrophic1 - Pertaining to organisms that are de-
pendent 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.
Hydrographlc 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, area! extent and
depth, positions and locations of high-water marks,
and locations and depths of wells.
Inlet1 - A short, narrow waterway connecting a bay,
lagoon, or similar body of water with a large parent
body of water an arm of the sea, or other body of
water, that is long compared to its width, and that may
extend a considerable distance inland.
Inorganic Matter2 - Mineral-type compounds that are
generally non-volatile, not combustible, and not
biodegradable. Most inorganic-type compounds, or
reactions, are Ionic in nature, and therefore, rapid
reactions are characteristic.
Lagoon1 - A shallow sound, pond, or channel near or
communicating with a larger body of water.
Limiting Factor1 - A factor whose absence, or exces-
sive concentration, exerts some restraining influence
upon a population through incompatibility with
species requirements or tolerance.
Manning Formula2 - A formula for open-channel flow,
published by Manning in 1890. which gives the value
of c in the Chezy formula.
Manning Roughness Coefficient2 - The roughness
coefficient in the Manning formula for determination
of the discharge coefficient in the Chezy formula.
Marsh1 - Periodically wet or continually flooded area
with the surface not deeply submerged. Covered
dominantly with emersed aquatic plants; e.g., sedges,
cattails, rushes.
Mean Sea Level2 - The mean plane about which the
tide oscillates; the average height of the sea for all
stages of the tide.
Michaelis-Menton Equation2 - A mathematical ex-
pression to describe an enzyme-catalyzed biological
reaction In which the products of a reaction are
described as a function of the reactants.
Mineralization2-The process by which elements com-
bined in organic form In living or dead organisms are
eventually reconverted into inorganic forms to be
made available for a fresh cycle of plant growth. The
mineralization of organic compounds occurs through
combustion and through metabolism by living
animals. Microorganisms are ubiquitous, possess ex-
tremely high growth rates and have the ability to
degrade all naturally occurring organic compounds.
Modeling2 - The simulation of some physical or
abstract phenomenon or system with another system
believed to obey the same physical laws or abstract
rules of logic. In order to predict the behavior of the
former (main system) by experimenting with latter
(analogous system).
Monitoring2 - Routine observation, sampling and 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
1666, is 1,853.248 m (6,080.20ft). The International
nautical mile is 1,852 m (6,070.10 ft).
Nanoplankton2 * Very minute plankton not retained in
a plankton net equipped with no. 25 stlk bolting cloth
(mesh, 0.03 to 0.04 mm.).
Neap Tides1 - Exceptionally low tides which occur
twice each month when the earth, sun and moon are
at right angles to each other these usually occur
during the moon's first and third quarters.
Neuston2 - Organisms associated with, or dependent
upon, the surface film (air-water) interface of bodies
of water.
Nitrogenous Oxygen Demand (NOD)2 - A quantita-
tive measure of the amount 6f oxygen required for the
biological oxidation of nitrogenous material, such as
ammonia nitrogen and organic nitrogen, in was-
tewater; usually measured after the carbonaceous
oxygen demand has been satisfied.
vii
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ments, the registration is accomplished by printing the
heights at regular intervals; in others by a continuous
graph in which the height of the tide is represented by
ordinates of the curve and the corresponding time by
the abscissae.
Toxicant1 - A substance that through its chemical or
physical action kills, injures, or impairs an organism;
any environmental factor which, when altered,
produces a harmful biological effect
Water Pollution1 Alteration of the aquatic 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. Un-
attached microscopic animals having minimal
capability for locomotion.
1 Rogers. B.G.. Ingram, W.T., Pearl. E.H.. Welter. LW.
(Editors). 1981, Glossary, Water and Wastewater Con-
trol Engineering, Third Edition. American Public
Health Association, American Society of Civil En-
gineers, 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.
DC
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Acknowledgments
Although we authors bear ultimate responsibility for the
content of our respective sections, a guidance manual
such as this is truly a collaborative effort within our
professional community. The role of project manager
is important in setting goals, direction, and boundaries
to these projects. Hiranmay Biswas provided such
project direction.management of peer review process
and the resources necessary to complete the manual.
We were able to draw upon working documents
produced by JRB Associates and Camp, Dresser, and
McKee, Inc. We acknowledge the authors of this
material: Richard Wagner, Jane Metcalf, and Elizabeth
Southerland of JRB. and Chris Qarkson of COM.
Peer review of early draft material is particularly helpful
to authors still trying to focus their efforts and bring an
appropriate balance to the material. Sandra Bird, AScI
Corporation, provided extensive and helpful reviews of
Sections 2. 4, and 5. and located material for Chapter
3. Robert R. Swank reviewed all of Parts 1 and 2,
providing technical comments and alertly catching er-
rors and inconsistencies through to the end. Robert
Ryans provided editorial comments for Parts 1 and 2,
and helpful suggestions on style. Keith Little, Research
Triangle Institute, made helpful general comments.
Peer review of the draft manual was provided by a
prestigious group of professionals. Thorough com-
mentary was received from Robert V. Thomann, Man-
hattan College, Donald R.F. Harleman, Massachusetts
Institute of Technology, Steven C. Chapra, University
of Colorado at Boulder, and Wu-Seng Lung, University
of Virginia These academic leaders represent the dif-
ferent approaches to water quality modeling in an
effective manner. We have sought to represent their
points faithfully, and, where conflicting advice was
given, to balance their viewpoints fairly.
In addition, helpful review comments were provided by
a group of government engineers and managers from
the Office of Municipal Pollution Control, the Office of
Marine and Estuarlne Protection, and the Permits
Division of the Office of Water Enforcement and Per-
mits. Specifically, we acknowledge Steve Glomb,
Permits Division. Office of Water, USEPA; Robert El-
liott, Chief, Water Quality Management Branch. USEPA
Region VI; Mark Dortch, Chief. Water Quality Modeling
Group, USAGE Waterways Experiment Station; Ernest
E. Watkins, Municipal Facilities Division, Office of
Water, USEPA; Robert Vaughn, Chief. Water Stand-
ards and Planning Branch. USEPA Region II; Edwin H.
Liu, Monitoring Coordinator. USEPA Region IX; and
Jerad Bales, Hydrologist, Water Quality Division,
USGS, Raleigh, NC.
Judy Webb, Donna Hinson, Stephanie Hopkins and
Tawnya Robinson, AScI Corporation, collected, refor-
matted, and produced the final draft document. Andy
Simms drafted the figures. The final layout was for-
matted by Tad Slawecki and Cathy Whiting of LJmno-
Tech, Inc.
We are grateful for their efforts.
XI
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Executive Summary
The Technical Guidance Manual for Performing Waste
Load Allocations, Book III: Estuaries is the third in a
series of manuals providing technical information and
policy guidance for the preparation of waste load al-
locations (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.
PART I: ESTUARIES AND WASTE LOAD
ALLOCATION MODELS
Introduction
Estuaries are coastal bodies of water where fresh water
meets the sea. Most rivers and their associated pol-
lutant loads eventually flow into estuaries. The complex
loading, circulation, and sedimentation processes
make water quality assessment and waste load alloca-
tion 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 advectlve systems such as many rivers.
Wastewater discharges into estuaries can affect water
quality in several ways, both directly and Indirectly. In
setting limits on wastewater quantity and quality, the
following potential problems should be assessed:
salinity, sediment, pathogenic bacteria, dissolved
oxygen depletion, nutrient enrichment and over-
production, aquatic toxicity. toxic pollutants and bioac-
cumulation and human exposure.
A WLA provides a quantitative relationship between the
waste load and the instream concentrations or effects
of concern as represented by water quality standards.
During the development of a WLA, the user combines
data and model first to describe present conditions and
then to extrapolate to possible future conditions. The
WLA process sequentially addresses the topics of
hydrodynamics, mass transport, water quality kinetics,
and for some problems, bioaccumulation and toxicity.
For each of the topics addressed in a modeling study,
several steps are applied in an iterative process: 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 refinement
should lead to more informed future WLAs.
Overview of Processes Affecting Estuarine
Water Quality
The estuarine waste load allocation process requires a
fundamental understanding of the factors affecting
water quality and the representation of those proces-
ses 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 proces-
ses impacting water quality.
To determine the fate and affects of water quality
constituents it is necessary first to determine proces-
ses impacting their transport. That transport is affected
by tides, fresh water inflow, friction at the fluid boun-
daries and its resulting turbulence, wind and atmos-
pheric pressure, and to a lesser degree (for some
estuaries) the effects of the earth's rotation (Coriolis
force). The resulting transportation patterns may be
described (determined from field studies) in waste load
allocation studies, or, as is becoming more frequently
the case, estimated using hydrodynamic models.
Hydrodynamic models are based on descriptions of
the processes affecting circulation and mixing using
equations based on laws of conservation of mass and
momentum. The fundamental equations generally 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 in-
elude settling, resuspension, scour and erosion,
coagulation and flocculation.
xiii
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The temporal resolution of WLA simulations falls Into
one of three categories - dynamic, quasi-dynamic, and
steady state. Dynamic simulations predict hour to hour
variations caused by tidal transport. Quasidynamic
simulations predict variations on the order of days to
months. The effects of tidal transport are time-
averaged. Other forcing functions such as freshwater
inflow, pollutant loading, temperature, and sunlight
may vary from daily to monthly. Steady state simula-
tions predict monthly to seasonal averages. All inputs
are time-averaged. Two schools of thought have per-
sisted regarding the utility of dynamic versus
quasidynamic and steady state simulations. For some
problems the choice is reasonably dear.
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 dis-
cussion here are general purpose, In the public
domain, and available from or supported by public
agencies. The selection of an estuarine WLA model
need not be limited to the models discussed in this
document. Other models that are available to a project
or organization should also be considered. The models
summarized in this report represent the typical range
of capabilities currently available. Estuarine WLA
models can be classified as Level I to Level IV accord-
ing to the temporal and spatial complexity of the
hydrodynamic component of the model. Level I in-
cludes desktop screening methodologies that calcu-
late seasonal or annual mean pollutant concentrations
based on steady state conditions and simplified flush-
ing time estimates. These models are designed to
examine an estuary rapidly to isolate trouble spots for
more detailed analyses.
Level II includes computerized steady state or tidally
averaged quasidynamic simulation models, which
generally use a box or compartment-type network to
solve finite difference approximations to the basic 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
models. These real time models simulate variations in
tidal heights and velocities throughout each tidal cycle.
Their effective time resolution is usually limited to
average variability over one week because tidal input
parameters generally consist of only average or slowly
varying values. The effective time resolution could be
reduced to under 1 day given good representation of
diurnal water quality kinetics and precise tidal input
parameters. The required data and modeling effort are
usually not mobilized in standard WLAs.
Level IV consists of computerized 2-d and 3-d dynamic
simulation models. Dispersive mixing and seaward
boundary exchanges are treated more realistically than
in the Level III 1-d models. These models are almost
never used for routine WLAs. The effective time resolu-
tion of the Level IV models can be less than 1 day with
a good representation of diurnal water quality and
Intratldal variations.
The advantages of Level I and II models lie in their
comparatively low cost and ease of application. The
disadvantages lie in their steady state or tidally
averaged temporal scale. When hydrodynamics and
pollutant inputs are rapidly varying, steady state
models are difficult to properly calibrate.
The dynamic models (Levels III and IV) have ad-
vantages over steady state and tidally averaged
models in representing mixing in partially mixed es-
tuaries because advection is so much better repre-
sented. The success with which these models can
predict transient violations depends upon both the
accuracy and resolution of the loading and environ-
mental data, and the model's treatment of short time
scale kinetics such as desorption or diurnal fluctua-
tions in temperature, pH, or sunlight. While dynamic
models are capable of predicting diurnal and transient
fluctuations in water quality parameters, the input data
requirements are much greater.
PART II: APPLICATION OF ESTUARINE
WASTE LOAD ALLOCATION MODELS
Monitoring Protocols tor Calibration and
Validation of Estuarine Waste Load
Allocation Models
The monitoring data collected in support of a modeling
study is used to: (1) determine the type of model
application required (e.g. dimensionality, state 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
xv
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Once the model is calibrated and validated, it is then
used to investigate causes of existing problems or to
simulate future conditions to determine effects of chan-
ges in waste loads as part of the waste load allocation
procedure. Once critical water quality conditions are
defined for the estuary, harbor or coastal area of con-
cern, determining the waste assimPath/e capacity is
relatively straightforward. Models are available to relate
critical water quality responses to the loads for most
problems. However, the definition of critical conditions
for estuaries is not straightforward. For streams receiv-
ing organic 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 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 inves-
tigation may involve study of extreme hydrological,
meteorological, or hydrographic events that affect
mixing; waste loadings from point and non-point sour-
ces; and changes in benthic demands.
Simplified Illustrative Examples
This section presents illustrative examples of estuarine
modeling using both simple screening procedures and
the water quality model WASP4. The screening 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 methods
for conservative and nonconservative toxicants and
chlorine residual. Bacteria and DO depletion are simu-
lated. Nutrient enrichment, phytoplankton production,
and DO depletion In a vertically stratified estuary are
simulated. Finally, ammonia toxicity and a toxicant in
a .wide, laterally variant estuary are simulated.
The screening procedures can be applied using cal-
culator or spreadsheet. While they may not be suitable
as the sole justification for a WLA they can be valuable
for Initial problem assessment. Three screening
methods are presented for estimating estuarine water
quality impacts: analytical equations for an idealized
estuary, the fraction of freshwater method, and the
modified tidal prism method. These example 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
directly specified in an input dataset, or may be read
from the output of a separate hydrodynamic model.
The examples here illustrate tidal-averaged modeling
with user-specified hydrodynamics. Both the
eutrophication and toxicant programs are described
and used.
For the six examples using WASP4, background infor-
mation is provided, the required input data are sum-
marized, selected model results are shown, and certain
WLA issues are briefly described.
xvii
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Preface
The document is the third of a series of manuals provid-
ing information and guidance for the preparation of
waste load allocations. The first documents provided
general guidance for performing waste load allocation
(Book I), as well as guidance specifically directed
toward streams and rivers (Book II). This document
provides technical information and guidance for the
preparation of waste load allocations in estuaries. The
document is divided into four parts:
This part. "Part 1: Estuaries and Waste Load Allocation
Models," 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 af-
fecting those problems, and the simulation models
available for addressing these problems. The second
part provides a guide to monitoring and model calibra-
tion and testing, and a case study tutorial on simulation
of waste load allocation problems in simplified es-
tuarine systems. The third part summarizes initial dilu-
tion and mixing zone processes, available models, and
their application in waste load allocation. Finally, the
fourth part summarizes several historical case studies,
with critical reviews by noted experts.
Organization: 'Technical Guidance Manual for Performing Waste Load Allocations. Book III:
Estuaries"
Part
1
2
3
4
Title
Estuaries and Waste Load Allocation Models
Application of Estuarine Waste Load Allocation Models
Use of Mixing Zone Models in Estuarine Waste Load Allocation Modeling
Critical Review of Estuarine Waste Load Allocation Modeling
xix
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4. Monitoring Protocols for Calibration and Validation of
Estuarine Waste Load Allocation Models
James L Martin, Ph.D., P.E.
AScl. Corporation at the
Center for Exposure Assessment Modeling
Environmental Research Laboratory, U.S. EPA, Athens, GA
4.1. General Considerations
This section addresses data needs for the calibration
and validation of estuarine waste load allocation
models. The type and amount of data will depend on:
(1) the study objectives, (2) system characteristics, (3)
data presently available, (4) modeling approach
selected, (5) the degree of confidence required for the
modeling results, and (6) project resources. Each of
these factors should be considered in the planning
stage of the monitoring effort in order to formulate
fundamental questions that can be used in sample
design.
Quantitative estimates should be made, wherever 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 ex-
ample, 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 resour-
ces 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 as-
surance, data management and modeling activities.
Collaboration insures that fundamental design ques-
tions are properly stated so that the available resources
are used in the most efficient manner possible and that
all critical data for modeling are collected. The use of
monitoring and modeling in an iterative fashion,
wherever possible, is often the most efficient means of
insuring that critical data are identified and collected.
4.1.1. Study Objectives
The study objectives will often determine the degree of
effort required for the monitoring study. The objectives
should be clearly stated and well known prior to the
planning of any monitoring study. Obviously, the pur-
pose 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 pro-
gram 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.
4.12. System Characteristics
Each estuary is unique, and the scope of the monitor-
ing study should be related to the problems and char-
acteristics 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 proces-
ses and resolution will be integral in determination of
the monitoring required. A model can only describe
the system, and that description can be no better than
the data which determines how it is applied, drives it.
and is used to evaluate its predictions. The particular
advantages of models are that they can be used to
interpolate between known events and extrapolate or
project to conditions for which, for whatever reason.
data are not available.
4.1.3. Data Asa/lability
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 con-
stituents. Reconnaissance or preliminary surveys may
be required to provide a sufficient data base for plan-
ning where only limited data are available.
4-1
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4.2.4. Calibration
Most estuarine hydrodynamic and water quality
models are general In that they can be applied to a
variety of sites and situations. However, the values of
model parameters may be selected on a site specific
basis, within some acceptable range. The process of
adjusting model parameters to fit site specific informa-
tion is known as model calibration, and requires that
sufficient data be available for parameter estimation.
The data base should include not only information on
concentrations for the parameters of Interest but on
processes affecting those concentrations, such as
sediment oxygen demand, settling and resuspension
velocities, etc. While resources often limit the extent of
the calibration data, more than one set describing a
range of conditions is desirable.
4.2.5. Validation/Evaluation
It is always wise to test the calibration with one or more
independent data sets in order to insure (or validate)
that the model accurately describes the system.
Validation conditions should be sufficiently different
from calibration conditions to test model assumptions
without violating them (where the assumptions are
considered reasonable). For example, if the rate of
sediment oxygen demand is assumed not to change
(i.e. is specified as a zero order rate), then the model
obviously would not predict well under situations
where the sediment oxygen demand was drastically
different due to some event A second example is that
an application assuming constant morphometry could
not be expected to perform well after flood events,
dredging, or construction resulted in variations in that
morphometry. Discussions of the procedures for
model validation/evaluation are provided in Chapra
and Reckhow (1983) and Thomann and Mueller (1987).
4.2.6. Post Audit Data
One type of data that is often ignored is post-audit data.
Generally, models will be calibrated and validated and
then applied to make some projection about 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 projec-
tions were accurate and management decisions ap-
propriate. 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 par-
ticular event in order to make short-term forecasts.
Intensive surveys should encompass at least two full
tidal cycles of approximately 25 hours duration (Brown
and Ecker 1978). Intensive surveys should usually be
conducted regardless of the type of modeling study
being conducted.
Wherever possible, all stations and depths should be
sampled synoptically. For estuaries that are stationary
wave systems (high water slack occurs nearly simul-
taneously 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
movement of the tidal wave is progressive up the
channel, sampling the estuary at the same stage of the
tide may be possible by moving upstream with the tide
to obtain a synoptic picture of the water quality varia-
tions at a fixed tide stage, that is a lagrangian type of
sampling scheme (Thomann and Mueller 1987). Sam-
pling should not be conducted during unusual climatic
conditions in order to insure that the data is repre-
sentative of normal low flow, tidal cycle and ambient
conditions.
Boundary conditions must be measured concurrently
with monitoring of the estuary. In addition, a record of
waste loads during the week prior to the survey may
be critical. It is necessary to identify all of the waste
discharging facilities prior to the survey so that all waste
discharged can be characterized. Estimates of non-
point loads are also required.
Where project resources limit the number of samples.
an alternative may be to temporally integrate the
samples during collection or prior to analysis. This will.
however, not provide information on the variability
associated with those measurements.
432. Trend Monitoring
Trend monitoring is conducted to establish seasonal
and long term trends in water quality. Intensive data is
4-3
-------
require some a priori knowledge of the fraction of the
total flows associated with all sampling stations.
4.5. Model Data Requirements
4.5.1. Estuary Bathymetry
Data are always required to determine model 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 vertical
mixing while deep channels are more likely to be
stratified with greater upstream Intrusion. Deep fjords
with shallow sills usually have little circulation and
flushing in bottom waters. The length of the estuary
determines the type of tidal wave, phase between
current velocities and tidal heights. The width effects
velocities (narrow constrictions increase vertical
mixing and narrow inlets restrict tidal action). Wind-in-
duced circulation is transient and interacts with chan-
nel geometry to produce various circulation patterns
and affects vertical mixing and sediment transport.
Bathymetric data are available for most estuaries from
U.S. Coastal and Geodetic Navigation Charts and Boat
Sheets or from sounding studies conducted by the U.S.
Army Corps of Engineers. The National
Oceanographic Survey can provide data on computer
tapes. The charts tend to slightly underestimate
depths in navigation channels to allow for siltation.
Alternatively, a vessel traveling along established 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 et al. 1979). Slopes
of the water surface should also be considered in data
reduction. Fathometer frequencies used in measuring
bottom depths should be between 15 and 210 KHz
(wavelengths between 85 and 6 mm). Short
wavelengths are most useful for measuring soft.
muddy bottoms, while long wavelengths are used with
a hard, firm bottom (Ambrose 1983).
For certain estuaries, such as many of those along the
Gulf of Mexico, the affects of tidal marshes can dramati-
cally effect estuarine circulation and water quality.
These are generally some of the more difficult systems
to model. An initial decision may be whether to
measure flows and quality and provide information to
the model as boundary conditions or to attempt to
model them. Where modeling is required then the
corresponding bathymetry data must be collected.
4.5.2. Transport
Either description or prediction of transport is essential
to all waste load allocation studies. All mechanistic
Table 4-1. Estuarine Transport Data
Hydrodynamic Data:
Meteorological Data:
Water Quality Data:
Channel Geometry, 'roughness' or bot-
tom 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
waste load allocation models are based on mass
balance principles, and both concentrations and flows
are required to compute mass rates of change. For
example, a loading to the system is expressed in units
of massAime, 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 condi-
tions being analyzed) may be sufficient for applications
involving fraction of freshwater, modified tidal prism
methods, or Pritchard's methods (as described in Mills
et al. 1985J. Models such as QUAL2E (Brown and
Bamwell 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 dis-
persion 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
flow measurement and hydrodynamic modeling are
discussed below.
4.5.2.1. Flow Measurement
Row measurements can be used directly in waste load
allocation models or be used to aid in the calibration
4-5
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4.5.2.3. Hydrodynamic Models
Hydrodynamic models may be used to generate flow
fields for waste load allocation models. Major proces-
ses impacting transport In estuaries incorporated in
hydrodynamic models include river flow, tidal action,
fresh and salt water mixing, salinity gradients and
stratification, wind stress, coriolis force, channel
geometry and bottom friction. Data required to drive
the hydrodynamic models includes initial and bound-
ary conditions as well as calibration and validation
data.
Generally, unknowns solved for In hydrodynamic
models include velocities and water surface elevations.
However, most hydrodynamic models applicable to
estuaries include forces due to changes in density and,
as such, include transport of salinity and possibly
temperature to be coupled with the hydrodynamic
equations at the intra-tidal time scale. The accurate
prediction of water surface elevations or velocities is
not sufficient to test the model application for waste
load allocation purposes, but the models must also
accurately transport materials as well. Therefore, data
requirements as discussed below will include con-
stituents such as salinity, temperature, and other
tracers which can be used to evaluate hydrodynamic
predictions. An intensive data sampling program
which includes concurrent water surface elevation,
velocity and dye/dispersion studies or salinity profiles
provides the best assessment of the hydrodynamic
model application.
A. Initial conditions
Initial conditions are generally not required for flows in
hydrodynamic models. Generally, velocity fields are
set up within relatively few model time steps. Initial
conditions are required for materials such as tracers,
salinity or temperature used to validate transport
predictions. An exception is where the initial condi-
tions are rapidly flushed, or the flushing period is short
in comparison to the simulation period. For rapid
flushing it is often reasonable to run the model to a
steady-state using the initial boundary conditions and
use the results of steady-state simulations as the initial
conditions for subsequent simulations. Where initial
conditions are required, data will generally not be avail-
able for all model segments, due to the fine spatial
resolution required in hydrodynamic models. Where
data are not available it may be possible to estimate
missing data by interpolation.
B. Boundary conditions
Hydrodynamic boundary conditions consist of flows or
heads. Head refers to the elevation of the water surface
above some datum. Generally, flow information is
provided for tributary and point sources and water
surface elevations provided for the open (ocean)
boundary(ies). Salinity, and often temperature, condi-
tions may be required at the boundaries in order to
estimate density effects on circulation (baroclinic ef-
fects).
Water surface elevation Information is often available
for major estuaries from tide gauge records such as
the Coast and Geodetic Survey Tide Tables published
annually by NOAA. These records may be processed
into tidal constituents. Records are often available for
time periods of 15 minutes which is usually sufficient
for model application. These tide tables do not include
the day-to-day variations In sea level caused by chan-
ges 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 Na-
tional Weather Service stations from the National
Climatic Center in Asheville. North Carolina. However.
the class of the stations should be identified to deter-
mine if all the required data are available. If the estuary
is large or nearby stations are unavailable then either
the use of several stations or field monitoring of
meteorological conditions may be required. If
temperature is to be simulated, as part of the
hydrodynamic model evaluation or for water quality
modeling purposes, then data on air temperature,
cloud cover, humidity and precipitation must be avail-
able. 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 con-
stituents used to calibrate and validate transport
predictions, such as salinity and temperature. The
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
4-7
-------
dinator assigned to implement and coordinate QA
activities. There are a variety of documents which
describe procedures for quality assurance, and a com-
plete description of a quality assurance plan is beyond
the scope of this report. Additional information Is
provided in-.
Guidelines and Specifications for Preparing
Quality Assurance Project Plans. USEPA Office
of Research and Development Municipal En-
vironmental Research Laboratory. 1980.
Standard Methods for the Examination of Water
and Wastewater, 15th Edition. American Public
Health Association. 1980.
Methods for the Chemical Analysis of Water and
Wastes. EPA-600/4-79-020. USEPA Environ-
mental Support Laboratory. 1979.
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-
Table 4-2. Water Quality Variables
Constituent
Problem Context
Effect*
Salinity or Conductivity
Temperature
Suspended Solids
UVUght
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 paniculate, total)
Dissolved organic carbon
Total organic carbon
Porosity
Grain size
Percent solids
Eh
Biomass
Meteorologic Data
wind, temperature, etc.
Toxicity (cereodaphnia toxic units, etc.)
Coliterm Bacteria (Fecal. Total. Streptococci)
All
All
All
Eutrophieation, Toxics
Eutrophication, Toxics
All
DO
DO
Toxics, Eutrophication
DO
Eutrophication DO
Eutrophication DO
Eutrophication DO
Eutrophieation DO
Eutrophication DO, Toxicity
Eutrophieation DO
Eutrophication DO
Eutrophication DO
Eutrophieation 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
-------
16%
V«hi«
Mtdlin
u
-I
8% 10% 84% |8%
P»re«nt L«M TTiin Vilu* SMwn
Figure 4-1. Illustration of us* of log probability plot to
estimate statistics for data Including
non-d elects.
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.
Wherever possible, questionable samples should be
rerun. In some cases additional analysis may be in-
cluded beyond the requirements of the modeling ac-
tivities to insure the quality of the analytical results,
such as to perform a dissolved solids or anion-cation
balances where applicable.
Analytical results have tittle 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. comrn.) 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 dis-
tributed, 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 dis-
tribution of samples, it may be necessary to explore
alternative analytical methods. Where more than one
technique is used for a particular analysis care should
be exercised to insure each sample is identified as to
the type of analysis performed and its associated
analytical variability.
The laboratory supervisors should maintain tracking
records indicating the samples received, source, time
of collection and their stage in the analytical process.
This tracking record canoe used to insure that samples
are analyzed within preset time frames, aid in setting
priorities, and inform data users of the status of the
information they require. A common conflict occurs
between laboratories wanting to prevent release of
information until all possible checks are completed for
all samples collected and data users who want any data
they can obtain as quickly as possible. If preliminary
or partial results are released, they should be properly
identified Indicating their status and updated when new
information becomes available.
4.63. Data Management
QA plans should also extend to data management,
Insuring that data storage and retrieval mechanisms
are established and that information on the identity and
quality of the analytical results is maintained for each
record. Care should be exercised to insure that the
identity of the sample is preserved. Data should include
time and location of collection, value, units, variability
and information on significant figures and rounding
procedures, and status as perhaps indicated by
analytical codes. Checks should be established to
insure that all data are recorded and that accurate
transfer of information occurs between different media
(such as between laboratory forms and data bases).
Modeling activities should be performed in a stepwtse
manner with testing at all stages in the application to
insure that predictions are accurate and reasonable.
The degree of model testing will be determined to some
degree by the model's complexity and its previous
history of testing and applications. However, a healthy
skepticism is often the best method of avoiding errors
and improper applications. All assumptions should be
clearly stated and supported for independent review.
The QA for modeling activities should include, but not
be limited to validation against independent data sets
to insure that concentrations are accurately predicted.
The QA activities should include calculations to insure
that mass Is properly conserved, numerical stability is
maintained, and that model parameters are within
reasonable ranges as reported in the literature.
Analyses should be conducted of the confidence as-
sociated with the predicted results.
Wherever available, model testing should not be limited
to comparisons with concentrations but model com-
ponents should be compared to available data to in-
sure that they are reasonable. For example,
productivity data for a system could be computed for
eutrophication models and compared to field data. A
component, or mass balance, analysis will also provide
information on the dominant factors affecting predic-
tions (see Thomann and Meuller 1987).
4-11
-------
Som. R.J. 1973. A Manual of Sampling Techniques.
Crane, Russak and Co., New York, New York.
Story, A.H., McPhearson, R.L, and Gaines, J.L 1974.
Use of Fluorescent Dye Tracers in Mobile Bay,: J. Water
Poll. Cntr. Fed., 46(4). pp. 657-665.
Thomann, R.V. and Mueller, J.A. 1987. Principles of
Surface Water Quality Modeling and Control. Harper &
Row, New York, N.Y.pp. 91-172.
Whitfield, P.M. 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.
Washington, D.C.
Yotsukura, N. and Kilpatrick, F.A. 1973. Tracer Simila-
tion of Soluble Waste Concentration, ASCE J. Environ-
mental Engr. Div. Vol. 99, EE4, pp. 499-515.
4-13
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5. Model Calibration, Validation, and Use
Steve C. McCutcheon, Ph.D., P.E.
Center for Exposure Assessment Modeling
Environmental Research Laboratory, U.S. EPA, Athens, GA
Zhu Dongwei
Research Fellow from Nan/ing 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
calibrate and validate models are reviewed and as-
sessed. Finally, guidance on how the calibrated model
can be utilized in a waste load allocation to describe
existing conditions and project the effects of reducing
or increasing loads into the estuary. Is provided.
Section 5.2 reviews a general procedure for calibrating
models of the dissolved oxygen balance, of the
nutrients that cause eutrophication problems, and of
toxic chemicals and sediment. A comprehensive list-
ing in a series of Supplements assists in defining the
set of potential model coefficients and parameters that
may be required to calibrate a model for waste load
allocation. The Supplements are provided for each of
the important coefficients and give specific guidance
on how these parameters can be selected.
Section 5.3 briefly describes the validation procedure
that is intended to estimate the uncertainty of the
calibrated model and help establish that the model
formulation chosen is at least useful over the limited
range of conditions defined by the calibration and
validation data sets. Section 5.4 reviews important
statistical methods for testing the calibrated model.
These methods are useful to aid in the various 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.
Methods to determine causes of existing conditions
and to project effects of changes in waste loads are
discussed. Presently, methods to modify model coef-
ficients 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
relationships. More often than not, it is not possible to
directly measure all the necessary coefficients and
parameters.
In general, coefficients must be chosen by what is in
essence a trial and error procedure to calibrate a
model. There is guidance on the appropriate range for
coefficients but because each estuary is unique, there
Is always a chance that coefficients will be different
from any other observed condition and fall outside the
range. Because unique coefficients outside the normal
ranges can also result if inappropriate model 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 ade-
quacy of calibration and validation. Also very impor-
tant is the experience required to be able to determine
5-1
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to imply a localized mass balance In the riverine sec-
tions of the estuary.)
Other types of concentration measurements can be
performed to better calibrate water quality kinetics.
These measurements should be focused In areas some
distance from suspected loads but where large water
quality gradients are suspected. This may involve
measurements away from shorelines and areas with
contaminated sediments.
Unfortunately, these selective types of measurements
can not be made in all cases and the calibration can be
error prone. However, if proper validation procedures
are followed, it should be possible to detect unreliable
results in most cases. Nevertheless, a paucity of post-
audit studies makes it impossible to ensure that unreli-
able 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
employed. First, conservation of mass should always
be checked. This is done by simulating a conservative
constituent such as dissolved solids or by using a
hypothetical unit loading of 1,10, or 100 concentration
units to be sure that dilution, transport, and mixing are
properly quantified. Second, the calibration should be
compared to any analytical or simpler solution avail-
able. Section 6 provides some simple formulations
that may be useful and Thomann and Mueller (1987)
provide a wealth of additional information. When
simple calculations are not possible, selective hand
calculations using the more elaborate equations in
critical areas are recommended to be sure that the
modeler understands the data sets that have been
formulated. A sensitivity analysis to indicate critical
locations and important processes that should be
checked, is suggested.
Calibration alone is not adequate to determine the
predictive capability of a model for a particular estuary.
To map out the range of conditions over which the
model can be used to determine cause and effect
relationships, one or more additional independent sets
of data are required to determine whether the model is
predicth/ely valid. This testing exercise, which also is
referred to as confirmation testing (Reckhow and
Chapra 1983). defines the limits of usefulness of the
calibrated model. Without validation testing, the
calibrated model remains a description of the condi-
tions defined by the calibration data set. The uncer-
tainty 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 ex-
trapolation outside this range also remains unknown.
The validation of a calibrated model, therefore, should
not be taken to infer that the model is predictively valid
over the full range of conditions that can occur in an
estuary. For example, a model validated over the
range of typical tides and low freshwater inflow may not
describe conditions that occur when large inflows and
atypical tides occur. This is especially true when
processes such as sediment transport and benthic
exchange occur during atypical events but not during
the normal, river flow and tidal events typically used to
calibrate and validate the model.
To stress the limited nature of a calibrated model.
validation testing is used here in place of the frequently
used terminology "model verification." Strictly 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
initially testing a computer model on different computer
systems using a benchmark set of input data as
verification. In this latter case, the term verification is
more appropriate because model simulations on a
different computer are being compared with an exact
benchmark condition derived by the developer on his
original computer. For engineering purposes, these
calculations are "precise enough" to serve as exact
definitions.
In the past, the adequacy of model calibration and
validation generally has been evaluated by visually
comparing model predictions and measured data.
There are statistical criteria, as well, that should be used
in testing the adequacy of a calibration or validation.
These will be critically reviewed in the final part of this
section.
Figures 5.1 and 5.2 describe, in general terms, the
calibration and validation procedure. As noted in the
introductory section of this manual, waste load 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-
5-3
-------
CALBNATON CM VAUMTOM
OATA6ET
(FLOWS AND LOADS)
MW.DATA
(FCROVNM ~ ~
MTKLWATEH
DATA OEFMNd WATER
OUAUrrwrMHTHE
> REASONABLE
EOLMALENCE
MATER QUALITY
WATER QUMJTV
Figure 5-3.
Relationship between data set components,
water quality model, and set of model
coefficient* for model calibration.
prespecifled criteria. Very little guidance is available,
however, to make this fully feasible.
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 coeffi-
cient.
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 optimiza-
tion 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 pol-
lutants given in Table 5.1. In addition, guidance is
available from a number of reference books (e.g.,
Thomann and Mueller 1987, Krenkel and Novotny
1980, McCutcheon 1989.1990, and Rich 1973).
In general, models are calibrated in phases beginning
with the selection of the model parameters and 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 barodinic
circulation is not important. The final phases focus on
Table 5-1. Guidance Manuals for Rates, Constants, and
Kinetics Formulations for Conventional and
Toxic Pollutants
Bowie. G.L. Mills, W.B.. Porcella, O.B.. Campbell. C.L.
Pagenkopf, J.R, Rupp. G.L. Johnson. K.M.. Chan. P.W.H..
and Ghennl, 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.. McKeehnie, 0.. and Sahoo, D..
Processes, Coefficients, and Models for Simulating Toxic
Organic* and Heavy MataJs In Surface Waters, EPA/600/3-
87/015. U.S. Environmental Protection Agency. Athens. Geor-
gia, 1987
Table 5-2. Outline of a General Calibration Procedure lor
Water Quality Models for Conventional
Pollutants when Barocllnlc Circulation Effects
are Unimportant [McCutcheon, (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 coeffi-
cient, eddy viscosity coefficients, or empirical flow ver-
sus stage coefficients to predict the proper residence
time through the reach of interest Dye studies to deter-
mine time of travel or average velocity may be used in
place of hydraulic measurements tor some simpler
models.
Select dispersion or mixing coefficients (or eddy dif-
tusivities) 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 tempera-
ture that are not affected by any other water quality con-
stituent.
Calibrate any process model affected by the processes
first calibrated. In conventional models, this may in-
clude biochemical oxygen demand (BOD), fecal
eoliform bacteria, and nitrification.
Finally, calibrate all constituents or material cycles af-
fected 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.
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.
52.1. Phase I of Calibration
Phase I concentrates on the calibration of the
hydrodynamic and mass transport models. In general.
there is a complex interaction between circulation and
density differences caused by gradients of salinity and
temperature that must be taken into account in
stratified estuaries. In vertically mixed estuaries, the
5-5
-------
Table 5-4. Guidance on the Selection of Model Coefficients and Parameters - Phase II
Calibration Parameters for
Complex Model
CBOD:
Deoxygenation rate
coefficient
Decay rate coefficient
Settling coefficient
Nitrogen transformations:
ON hydrolysis rate
coefficient
Ammonification rate
coefficient
Nitrification rate
coefficient
Phosphorus transformations
OP-PO4
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
Phytoplankton stochiometry:
Carbon
Nitrogen
Phosphorus
Silica
Coliform die-off rate
coefficient
Settling velocity
Resuspension velocity
Net settling velocity
Simple Model
CBOD:
Deoxygenation rate
coefficient
Decay rate coefficient
Settling coefficient
NBOD decay rate
coefficient
Net photsynthesis rate
Net respiration rate
Coliform die-off rate
coefficient
Range of Values
0.05 to 0.4 d'1 (20°C)
0.05to0.4d'1(20°C)
approximately 0.0
0.1to0.5d'1 (20°C)
0.001 to 0.14 in d'1 (20°Q
0.02 to 1.3 in d-1 (20°C)
0.1 to 20 in d'1 (20°C)
0.001 to 0.2 d'1 (20°C)
Oto 1.0
0.001 to 0.4 mg L'1
0.0005 to 0.08 mgL'1
0.1 x 10* to 20.5 x 10* W m*
2.3 to 6.9 in m'1
0.2to«d'' (20°C)
0.05 to 0.15 d'1 (20°C)
0.05 to 0.6 m d'1
0.003 to 0.17 d'1
0.35 to 0.8 d'1
(% dry weight biomass)
10 to 70
0.6 to 16
0.16 to 5
20 to 50
O-StoSgOznvV1
same order of magnitude as
photosynthesis rate
0 to 84 d'1
1 to 100 m d'1
0.1 to 50m yr'1
0.1 to 50 cm yr'1
Guidance Documents and References
Bowie et al. (1985)
Bowie et al. (1985). Thomann and
Mueller (1987)
Bowie et al. (1985)
Bowie et al. (1985)
Bowie et al. (1985)
Thomann (1972) - Delaware
Estuary
Bowie et al. (1985) - see their table of
values for various species.
Thomann (1972), Mills et al. (1985)
Mills et al. (1985)
Bowie et al. (1985). Thomann and
Mueller (1987)
Thomann in review
Thomann in review
Thomann in review
Definition of symbols and explanation of terms:
ON organic nitrogen
ON hydrolysis = degradation of organic nitrogen to ammonia
Ammonification » oxidation of ammonia to nitrate
Nitrification = oxidation of nitrite to nitrate
5-7
-------
often are calibrated by indirect means. The dominant
calibration parameter for a one-dimensional model is
the roughness coefficient (the Manning n orChezy 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.
523. Phase II of Calibration
Phase II involves the selection of coliform die-off coef-
ficients, settling and re-suspension velocities for
suspended sediment, BOD coefficients, and the set of
coefficients describing the nutrient cycles and
photosynthesis. The selection of die-off coefficients is
relatively straightforward compared with other phases
of the calibration (see Supplement VII, and Thomann
and Mueller 1987, and Bowie et al. 1985). Derivation
of parameters describing sediment transport and BOD
is somewhat more Involved. The calibration of nutrient
and phytoplankton models requires some skill and
expertise because of the complexity of the potential
interactions between a number of the components of
the cycles involved.
Suspended sediment and BOD models are somewhat
more difficult to calibrate because the processes can
not be fully defined by measurement techniques readily
available for the collection of calibration data.
Suspended sediment is continually exchanged with
bottom deposits and this exchange can be relatively
important in tracing the fate of nutrients and sorbed
contaminants. Unfortunately, it is only feasible at
present to measure changes In suspended sediment
at various locations overtime and to measure long term
net deposition or erosion of sediments. The limited
guidance available for calibrating simple sediment
transport models is presented in Supplement VIII.
The calibration of a model for BOD is complicated if
settling and sorption to organic material is occurring
along with biodegradation. If only water column BOD
measurements are available, it is difficult to determine
the relative importance of deoxygenation. settling, and
adsorption of dissolved BOD on the dissolved oxygen
balance. Settling is usually not important, however.
because of recent advances (since the late 1960s) in
regulating organic solids in waste effluents. This is
especially true away from a localized mixing zone at
the point of discharge where some flocculation and
settling may occur. In addition, the relatively large
depths of estuaries preclude rapid adsorption of dis-
solved BOD like that observed in streams because of
the limited surface area available. Also, brackish
waters tend to slow biotic reactions and growth which
should slow the uptake of dissolved organic carbon.
Therefore, calibration of BOD models frequently can
be a simple matter of accounting for the decay of BOD
measured in the water column. Recommendations for
calibration of a BOD model are given in Supplement IX.
The effect of nitrification can be modeled in two ways.
First, simple nitrogenous BOD (NBOD) models have
been utilized. Second, and most useful, are nitrification
models of organic nitrogen, ammonia, nitrite, and
nitrate. NBOD models are typically only useful when
nitrification is relatively unimportant in the dissolved
oxygen balance. Supplement X gives useful guidance
for the Implementation of an NBOD model. 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
phytoplankton models typically involve several
separate major components and a number of minor
components that are frequently Ignored or lumped in
with the major components. The most difficult problem
faced in the calibration process is that a unique set of
coefficients is difficult to derive. The limited guidance
available on the calibration of nitrogen and phosphorus
models is given in Supplements XI and XII.
Wlosinski (1984) illustrates this problem with a simple
example involving an interactive four component
model shown in Figure 5.5. This example is somewhat
abstract but it shows that exactly the same values of
the state variables can be computed in two cases with
significantly different process rates controlling the
magnitude of mass transfer between environmental
components. In addition, Wlosinski shows that 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
quality system without at least one process rate meas-
urement
52.3. Phase III of Calibration
The final phase of calibration can be either difficult or
extremely easy depending on how well other com-
ponents 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
calibration. In fact, it is more useful to attempt a quick
step through the calibration procedure to obtain a
5-9
-------
in addition to being used to determine potential
mobility as indicated above.
5.3. Model Validation
Validation testing is designed to confirm that the
calibrated model is useful at least over the limited range
of conditions defined by the calibration and validation
data sets. As indicated earlier In this section, the pro-
cedure 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 predicth/ely 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
validation ensures that the calibration parameters are
fully independent of the validation data. To extend the
range of conditions over which the calibrated model
is valid, however, it may be useful to save the initial
study for validation testing if it is expected that data
collected at a later date will provide a less severe test
of the calibrated model.
At present, it is very difficult to assemble the necessary
resources to conduct the desired number of surveys.
Therefore, it is important that surveys be scheduled in
an innovative manner and the choice of calibration and
validation data sets remain flexible in order to make the
test of the calibrated model as severe as possible.
Many studies are faced with severely limited resources
for sampling and laboratory analysis that preclude
collection of more than one set of data. If this highly
undesirable circumstance occurs, the historic data
should be investigated to determine whether the model
can be calibrated a priori and validated with one set of
data or wee 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
recalibrated to obtain the overall optimum calibration.
This should improve the overall predictions but it
should not be used as a shortcut to avoid rigorous
validation testing. Overall optimum calibration can be
achieved by minimizing the least squares error for all
data available in multiple sets or by obtaining the best
overall fit between predictions and measurements from
visual inspection.
5.4. Model Testing
During and after the calibration and validation of a
model, at least two types of testing are important. First,
throughout the calibration procedure, a sensitivity test
provides a method to determine which parameters and
coefficients are the most important. Second, there are
a number of statistical tests that are useful for defining
when adequate agreement has been obtained be-
tween model simulations and measured conditions.
The sensitivity analysis is simply an investigation of
how much influence changes in model coefficients
have on simulated results. Typically, important 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 per-
cent have been used frequently. The coefficients and
parameters are changed one at a time and the effects
are typically ranked to show which parameters have
the most influence and which have the least influence.
A sensitivity analysis also is useful when applied to a
preliminary calibration of a model using historic or
estimated conditions. In this case, the ranking can be
used to determine which coefficients and parameters
should be measured and which can be estimated. For
example, if a model is sensitive to SOD rates, these
should be measured rather than estimated. If other
parameters like the wind speed function have little
influence, very little effort should be expended to es-
timate its exact form.
5-11
-------
tuary or with time, the relative error may be a more
appropriate statistic for testing calibration or validation.
The relative error is defined as (Thomann 1982)
(53)
where the overbars denote the average measured or
simulated valued. Averages are performed over multi-
ple sites or over time and cumulative frequency of error
can be computed (Thomann 1982). The cumulative
frequency (see for example Figure 5.6) can be used to
estimate the median error and various percentiles such
as the 10th and 90th exceedance frequencies.
Southeriand et al. (1984) notes that the 50th percentile
of median error is usually reported In waste load alloca-
tions since this is the most easily understood value.
The relative error behaves poorly for small values of
measurements if discrepancies are not proportional to
the magnitude of the measurement (i.e., small values
of Cm magnify discrepancies) and if Cm > Cs, (since the
maximum relative error is usually taken to be 100
percent). Therefore, the relative error is best for com-
puting composite statistics when discrepancies are not
constant as may occur when calibration over an exten-
sive range is attempted.
Thomann (1982) and Ambrose and Roesch (1982)
seem to offer the best available guidance on what
relative errors may be appropriate to achieve adequate
estuarine dissolved oxygen model calibration. In
general, median relative errors should be 15 percent or
less. Values of the relative error obtained for a number
of estuaries by Thomann (1982) and Ambrose and
Roesch (1982) are given in Table 5.6. Note that
Ambrose and Roesch define the relative error without
the absolute brackets as
(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
Savannah Estuary, GA
San Joaquin Delta, CA
Potomac Estuary, MY
Delaware Estuary. PA
Relative Error
JC^
5% to 35%
5%
58%
15%
10%
^?
-3% to -1%
1%
so that on average, values of this statistic are smaller
than or equal to the values obtained from Equation
(5.3).
5.43. Regression Analysis
A regression analysis is very useful in identifying
various types of bias in predictions of dynamic state
variables. The regression equation is written as
« (5.5)
where
a = intercept value
b a slope of the regression line
e a 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,
Southeriand eta!. 1984). These include:
1. The square of the correlation coefficient, r*
(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
(b)
2 4 6 8 10
MEASURED
2 4 6 B 10
MEASURED
2 4 8 8 10
MEASURED
24 a 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 5-9. Transport Model Error Statistics for the Delaware Estuary [Ambrose and Roeseh (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 l:
Period 2:
Width ol 0.1 ug/L dye isodine (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
0.01
3.4
1.6
5.0
1.3
1.0
1.6
RE
-0.10
-0.22
0.09
0.14
0.05
0.26
0.54
0.21
0.05
0.04
0.06
SE
440.
2.8
0.10
0.14
0.03
6.0
5.1
6.6
3.2
2.3
4.0
CV
0.31
0.33
0.30
0.32
0.14
0.45
1.73
0.28
0.13
0.10
0.14
Regression Statistics
a
Q.97
0.76
0.82
0.52
0.76
1.12
0.15
1.26
0.83
0.84
0.38
b
48.0
-0.05
0.09
0.27
0.07
1.8
4.2
1.1
5.5
4.5
20.0
r
0.97
0.99
0.82
0.62
0.92
0.96
0.44
0.98
0.90
0.96
047
Table 5-10. Transport Model Error Statistics for the Potomac Estuary [Ambrose and Roeseh (1982)]
Tidal Response Variables
Chloride concentration (mg/L)
Dye concentration (ug/L)
All data:
Period 1:
Period Z
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
Q.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. OtherTechniques
Beck (1987) and Southerland et al. (1984) describe
other techniques that can be used to aid in parameter
estimation to calibrate models. Generally, these
methods require some knowledge of the distribution of
discrepancies between measurements and 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 be-
tween an observed distribution and a normal distribu-
tion. If the distribution is normal, the F-test (Kennedy
and Neville 1976) of the variances of measurements
and predictions is a measure of the goodness of fit. In
addition, the Kolmogorov-Smirnov two sided test can
be used to evaluate goodness of fit
5,4.6. Guidance on Statistical Criteria tor
Calibration and Validation
Few studies have included calculations of statistical
criteria to guide model calibration and validation and
what work that is available in engineering reports has
not been adequately compiled. An exception of note
are the studies of the Potomac and Delaware Estuaries
by Ambrose and Roeseh (1982).
The work of Ambrose and Roeseh (1982) is important
because it presents benchmarks to which other
calibrations can be compared and evaluated. In this
regard, these data are very similar to the compilation
of error statistics compiled by Thomann (1982) to
define how well a calibrated model should simulate
dissolved oxygen. Thomann's guidance only covers
relative error statistics. Ambrose and Roeseh define
average errors, relative errors, root mean square er-
rors, coefficient of variation, regression intercept,
regression slope, and correlation coefficients but only
for two estuaries. Nevertheless, the Potomac and
Delaware Estuaries are among the most important East
5-15
-------
Table 5-13. Chlorophyll-* Modal Error Statistic*forth* Potomac Estuary, 1977-78 [Ambroseand Roeach (1982)]
Quality Response Variable*
Median concentration (ug/L)*
Peak concentration (ug/L)
Peak Location (km)6
100 ug/L reach length (km)c
N
32
8
8
8
Calculated Error*
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 Statistic*
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.
b Distance of peak concentration below Blue Plains Sewage Treatment Plant (river kilometer 16).
c River kilometers in which concentration exceeds 100 ug/L
Table) 5-14. Water Quality Model Error Statistics for the Potomac Estuary, 1977-1978 [Ambrose and Roesch (1982)1
Quality Response Variables
N
Calculated Errors
E 1 RE 1 SE 1 CV
Regression Statistics
a 1 b
r
(a) Median Concentrations (mq/L)
00
CBOO
NH3
NOa
32
29
29
40
020
-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 Concentration6 (mg/L)
DO Mm
CBODMax
NHaMax
NOa Max
8
8
10
10
0.03
0.26
0.04
0.08
-0.01
0.04
0.04
0.05
(c) Extreme Location' (km
DOMin
CBODMax
NH3Max
NOa Max
DO < 5 mg/L
DO < 3 mg/L
CBOD > 4 mg/L
NH3 > 1 mg/L
NH3 > .5 mg/L
NOa > 1 mo/L
8
8
10
10
(d
8
8
8
10
10
10
1.2
-6.0
-1.4
-24
0.10
0.82
0.54
0.31
0.86
1.92
0.14
0.18
3.7
10.5
6.9
5.5
0.25
0.32
0.13
0.11
0.31
1.45
2.67
0.70
0.70
1.30
0.89
0.90
1.02
0.01
-0.03
0.71
0.99
-2.09
0.15
0.10
-14
1.1
1.2
-0.2
0.62
0.66
0.95
085
0.99
0.04
0.11
089
Reach Length" (km)
-3.2
-0.4
12.7
0.2
0.0
2.7
0.22
0.25
0.65
0.07
0.0
O.11
5.4
2.7
17.7
1.1
2.4
6.3
0.37
1.66
0.90
0.39
0.30
0.26
0.66
0.70
0.21
0.84
0.83
-003
1.7
0.8
3.0
0.3
. 1.4
21 9
0.97
0.53
0.64
0.95
092
-003
Concentrations are median values by river segment (16-26 km) and survey period.
6 Median concentrations during survey at minimum or maximum location.
e Distance of extreme concentration below Blue Plains Sewage Treatment Plant (river kilometer 16)
d River kilometers in which concentration exceeds or falls below indicated value.
Estuaries, respectively. Tables 5.11, 5.12, 5.13, and
5.14 provide error statistics from the calibration of
water quality models in the two estuaries. Example 5.1
gives a visual illustration of how well observations and
simulations should agree to help put these statistics
into perspective.
From this work by Ambrose and Roesch (1982) and
Thomann (1982) it is possible to develop preliminary
guidance on how well simulations should agree with
measurements to achieve adequate calibration.
Ambrose and Roesch (1982) indicate that the coeffi-
cient of variation should be 5 to 10 percent for
hydrodynamic variables, less than 45 percent for
transport variables, and generally less than 90 percent
for water quality variables. The correlation coefficient
should be greater than 0.94 for hydrodynamic vari-
ables, greater than 0.84 for transport variables, and
generally greater than 0.60 for water quality variables.
The general guidance is summarized in Table 5.15.
5-17
-------
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, leav-
ing 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 D-
lustrates the agreement obtained with the selected
Manning n values by comparing measured and simu-
lated average spring tide and mean tide (Ambrose
1987). Also see Table 5.7 for a statistical charac-
terization of how well the model was calibrated.
Mass transport components of the model were
calibrated using Rhodamine WT dye data collected in
July 1974 from a four day steady release from
NEWPCP and slack-water salinity measurements. The
agreement between simulated and measured slack-
water dye concentrations is shown in Figure 5.10.
Calibration involved changing the longitudinal disper-
sion coefficient until the best agreement was obtained.
See Table 5.9 for the statistical evaluation of the agree-
ment between measured and simulated charac-
teristics.
The seven problem chemicals were checked and it was
found that more that 99% of the total chemical was
dissolved In the water column. As a result, suspended
sediment parameters were calibrated in an ap-
3 7-
o
I
Wllmlnglon Philadelphia
Trenton
50 60 70 BO 90 100 110 120 130 140
Location. In river miles above Delaware Bay
Obiirrad U«an Tld*
Pr»dlcM y*en TW«
ObMnwd Awrag*. Spring Tide
Awog« Spring TUU
proximate manner using average long term settling,
scour and sedimentation data
Chemical rate constants were determined from the
literature and by various predictive methods.
Volatilization rate constants were determined from the
Whitman two layer resistance model using relation-
ships between oxygen, water vapor, and the chemicals
of concern. Reaeration was predicted with the O'-
Connor-Dobbins (1958) equation (see Supplement
XIII). Evaporation was predicted with the regression
Table 5-16. Environmental Properties Affecting Interphase
Transport and Transformation Processes
[Ambrose (1937)]
Environmental
Property
Sediment cone.
Suspended (mg/L)
Benthie flcg/L)
Organic carbon traction
Suspended sediment
Benthie sediment
Sediment settling
velocity (m/dav)
Bed sediment resuspen-
sion velocity (cm/vr)
Pore water diffusion
(cma/sl
Benthos mixing factor
(0-1)
Surficial sediment
deoth (em)
Water column depth
(ml
Water column temp
<°C>
Average water velocity
(m/s)
Wind speed at 10 em
(m/s)
pH and pOH
(standard units)
Concentration of
oxidants
-------
Table 5-18. Predicted Chemical Lots Rale Constants In the
Delaware River near Philadelphia
[Ambrose (1987)]
Compound
Simulated
DCP
DMM
DCE
PCE
TCE
MC
CF
Predicted Rate Constants (day'1
Kv-
0.11
0.10
0.12
0.11
0.12
0.14
0.12
KH"
0.02
10*
10*
0
0
10*
to-8
"Pi"
10-
0
10-
10-
10*
_
-
>V
10"
_
10*
10*
10*
to-8
10*
Km'
0
_
0
0
0
0
0
K1
0.13
0.10
0.12
0.11
0.12
0.14
0.12
* Volatilization e Biodegradation * Photolysis
"Hydrolysis "Oxidation 'Total
equation of Uss (1973) which ignores the vapor pres-
sure deficit in the atmosphere
E = 4.46 + 2717 W
(5.9)
,-V
The Evaporation rate is in m day and W is wind speed
in m sec"1 at a 10 cm (0.33 ft) height estimated from 2
m (6.6 ft) measurements in the area and converted to
the 10 cm (0.33 ft) height assuming that the logarithmic
profile is valid and that the roughness height of the
water surface is typically 1 mm (0.0033 ft).
Data defining the environmental properties and chemi-
cal properties are reproduced in Tables 5.16 and 5.17.
Table 5.18 gives the computed rate constants for
volatilization, hydrolysis, biodegradation. oxidation,
and photolysis plus the total loss rate constant.
The calibration of the chemical kinetics model is more
of a one step validation process of confirming that the
literature values are correctly applied for the model and
physical conditions at the site. To check the validity of
the model, the loads of chemicals and the uncertainty
associated with the loads were specified as presented
in Figure 5.11. Hydrodynamics and mass transport for
the October 1983 period when the volatile chemical
samples were collected, were assumed (there were no
measurements available) to be governed by mean and
spring tides (noted to occur during the study) and a
steady freshwater inflow of 3010 ft3 sec"1 (85.2 m3
sec'1). The model was used to simulate 30 days with
mean tide, steady freshwater flow, and constant loads
of chemicals from NEWPCP so that a dynamic steady
state (i.e.. tidal conditions simulated by the model
closely matched the simulations of the preceding tidal
cycle) was achieved. The simulation was continued
one more day to represent the spring tide observed
when the volatile chemical samples were collected.
These simulations of width and depth average con-
centrations were compared to the median and range
of concentrations obtained from grab samples col-
lected at three locations upstream of the waste inflow.
These results are given in Figures 5.12,5.13,5.14, and
Table 5-19. Observed and Predicted High Slack
Concentrations at Baxter [Ambrose (1987)]
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
Concentrations (g/U
NEWPCP
Effluent
6.050
1,360-16,800
591
25-2,820
213
67-2.380
54
3045
9.3
2.0-33
4.4
3.2-7.6
2.5
1.7-11
Baxter
Observed
66
56-84
9.4
7.7-13.6
2.0
1.2-3.0
£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
(W.3
0.04
0.03-0:07
0.03
0-0.15
Error
Factor
1.2-1
1.5'1
1.0
4.2'1
4.4-'
10.0-1
1.3-1
B-a
8-j
d s^
JO
I 10*,
5-
l» «
detection limit
DCP
DMM DCE PCE TCE MC CF
U!
Figure 5-11. Northeast Water Pollution Control Plant Effluent
Concentrations, October 2-3,1983
[Ambrose (1987)].
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, respective-
ly. Predicted and simulated concentrations of TCE,
CF, and MC were below detection limits (1 /*g/L) at the
water intake (see Table 5.19).
5-21
-------
At this point, the model is sufficiently calibrated to
establish a link between the high concentrations
measured at the water intake and the waste load and
establishes that any other loads are insignificant. Next
the concentrations measured at, and predicted at and
between monitoring locations can be compared to
water quality standards (keeping in mind that this par-
ticular model has a tendency to slightly underpredict
because of the coefficients chosen from the literature
and only predicts averaged values) to determine where
water quality standards are violated. If standards do
not exist or are not adequate, a human and ecological
risk assessment can be performed. If it is determined
that the loads should be reduced, the model can be
used to make a preliminary estimate of the total load
reduction required or after the calibration is refined
somewhat to better predict concentrations at the water
intake or other critical locations, the model can be used
to set loads. To set the final loads, the calibrated model
could be used to investigate the effect of extremely low
flow and extremely high tides as well as typical condi-
tions.
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.
SEA
BOOLMCtt
n
B.
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 chan-
ges in waste loads as part of the waste load allocation
procedure. To understand how the calibrated model
is used, it is first necessary to review the general waste
load allocation procedure.
5.6.1 Waste Load Allocation Procedure
There are several components of the waste load alloca-
tion 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
Rgure 5-16. Componennts of the wast* toad allocation
procedure.
Figure 5-17. General waste load allocation procedure. Note
WO = water quality, NPDES = National
Pollution Discharge Elimination System, and
TMDL = total maximum dally load.
5-23
-------
N
Figure 5-18 Model segmentation - Wlcomlco River, Maryland.
5-27
-------
SUPPLEMENT!: SELECTION OF MANNING n VALUES
The effect of bottom friction on the flow in estuaries is
represented in a variety of ways in flow or
hydrodynamic models. The most common method
used in the United States and in many other countries,
employs the Manning roughness coefficient to quantify
friction and turbulent hydraulic losses in the flow. How-
ever, 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 tur-
bulent mixing. The quadratic stress formulation relates
the eddy viscosity approximation of the vertical
Reynolds stress to a drag coefficient and average
velocities as follows
(du/dz )
2)0'5 (ub) (5.10)
and
Po £« (dv/dz ) = p0 Cd («b 2 + vb 2)" to) (5.11)
where
po = density of water,
du/dz, dv/dz = the vertical velocity gradient in the
xand y directions, respectively,
Ub, vb = horizontal velocities at a point above the
bottom in the x and y directions, respectively, and
EE 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
calibrated by varying the Manning n until any measure-
ments of average velocity and tidal amplitude at a
number of sites plus any observations of salinity in-
trusion 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 Factor* used to Quantify Friction Loss In Estuarlee
Manning n
Chezy Cz
Drag
Coefficient Cd
Darcy-
Weisbach f
Fanning ft
Manning n
n
-SlRM"'
n
gn2
"cl?7*
8gn2
"clR175
2gn2
"eta'7'
Chezy Cz
-£"«"
-Ci
-*
-JS_
Ct2
2fl
c,2
DraB
Coefficient
Cd - u^/U2
Ci/2C,RI/8
B1/a
_
-------
Table 5-22. Value* of the Manning n for Different Type* of
Vegetation In Wetland Areas
[Chow (1959) and Jarretl (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 sen-
sitivity in the important decision variables (I.e.,
dissolved oxygen, chlorophyll a, or sedimentary con-
taminant 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 con-
tinues. 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
areas. At present, there do not seem to be many
studies of the effect of sea grass on friction loss (per-
sonal communication, Florida Dept. of Environmental
Regulation, 1989). There are, however, investigations
of friction losses In grassed open channels that show
that losses are a complex function of the Reynolds
number. As flow Increases, grasses are pushed flatter
along the bottom and less area of grass is in direct
contact with the flow. In effect, the relative roughness
decreases as a function of flow velocity or Reynolds
number. Perhaps the best study of this effect is by
Chen and the US Geological Survey.
In the absence of solid guidance on this topic, it should
be noted that Chow (1959), Jarrett (1985) and others
give guidance on the effect of grass on channel and
overbank flow. Values on the order of 0.025 to 0.050
are reasonable.
In wetlands and other areas of emergent vegetation,
relative roughness Is less likely to vary and the Manning
n is expected to be constant The scale of the rough-
ness 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. Arce-
ment and Schneider (1984) report more recent infor-
mation for more tranquil flows in floodplains. However.
it is not expected that n can be precisely defined in any
published study. Row in wetlands occurs in ill defined
channels where the uncertainty in average velocity.
area, depth, and slope make it very difficult to deter-
mine n.
As larger and larger model scales are employed, more
and more large scale turbulent friction losses due to
flow non-uniformity must be included in estimates of
the Manning n to adequately represent losses due to
energy dissipation. Empirical relationships have not
been derived for this purpose but similar corrections of
this nature have been derived for river flows that can
be used as guidance. Guidance for riverine reaches
works well in the upper sections of estuaries where the
transition from riverine conditions occur. The
guidance is less useful downestuary where the scales
of flow may increase by an order of magnitude in some
cases.
Conceptually, the riverine estimation procedure can be
formulated as a process of modifying a base value of
the Manning n such that
"composite = «b + «f + 11 + "2 + "3 (5.16)
where typical values are on the order of 0.020,
nb = Manning n associated with bottom roughness
conditions,
nr = correction related to form roughness or bed ir-
regularity due to ripples and dunes,
m = correction related to the nonuniform depth of
the flow, and
5-31
-------
x = Longitudinal direction along the axis of the
estuary,
g = Gravitational constant,
A = Cross sectional area,
= Slope of the energy gradient or approximately
the water surface slope, where h is the depth of
flow to water surface from an arbitary datum,
n = Manning roughness coefficient,
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
divided 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,
WIQ = 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
gradients are small enough to neglect. The best ex-
amples of link-node models are the EXPLORE I (Baca
etal. 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
u \u
and
M _ -dQ
dt = dr
(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 roughness
coefficient used to calibrate the model. Normally.
these effects are minor and relatively reliable guidance
can be formulated.
Guidance on the selection of Manning n values is as
follows:
1. Select Initial values based on bed material and
correct for bed variations - Values should be
uniform for areas where bottom topography,
channel alignment and sediment size distributions
do not vary significantly. Smaller values should be
selected for bottoms covered with fluid mud or
other fine-grain material. Typically a value of 0.02
is appropriate for reaches with fine grain sedi-
ments and 0.025 to 0.030 is appropriate for
reaches with sand bottoms. If necessary, a
precise initial estimate can be made by computing
the Reynolds number and the relative roughness
(i.e., 2R/ks. where ks is the sand grain diameter or
the height of the ripples and dunes) and consulting
Rgure 5.18. If the bed is covered with vegetation
(I.e., none of the sediments are in contact with the
flow) then Table 5.22 should be used to select
an n value and correct for variations in cross
section, bottom topography, and obstructions. If
the bed is partially covered with vegetation, the
initial selection should be based on the bed
materials present and corrections should be made
for vegetation, and variations in cross section,
bottom topography, and obstructions. Where it is
not clear whether exposed bed materials are im-
portant in causing friction losses, both procedures
should be followed to see if any significant dis-
crepancies 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.
5-33
-------
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 for this. Obstructions
(there were very few fallen trees) and vegetation were
taken into account in the initial selection. The selection
for segment 2 was governed by the same procedure.
Segment 3 Involved selection of a value representative
of flat sandy bottoms and correcting for the seagrass.
The final value should be compared with Table 5.22
where the value Is exactly the same as the value for
flows over tall grass. Segments 4 and 5 Involve straight
forward selections for sandy and fine grain materials
and minor corrections for changes in cross section and
obstructions. Segment 6 Involves selection of a
smaller value to reflect the influence of fluid mud. The
few Islands and vegetation on the shores of a wide
channel is probably negligible.
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 tress,
lew fallen trees, very lit-
tle 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 chan-
nel
Wide deep channel in
the vicinity of the tur-
bidity maximum
Wide deep channel
down estuary of the tur-
bidity maximum with
significant sediment
transport into the es-
tuary
Bed
Material
Rne
grain
na
Sandy
Sandy
Fine
grain
Fine
grain
Bed
Topo-
graphy
Irregular
surface
na
Flat
Dunes
Ripples
Ruid mud
layer over
much of
thecnan-
nsl
Channel
Change
Meandering.
Irregular,
braided and In-
distinct channel
in areas
Meandering,
irregular,
braided and in-
distinct channel
In areas
No significant
change
Some narrow-
Ing of channel
and bends
Straight
Straight
Obstruc- i
tone
A few fal-
len trees
Nons
None
Sub-
merged
Nons
A few
small
islands
Vegeta-
tion
See de-
| _ m\ i
scnpuon
See de-
scription
Seede-
scription
None
None
Minor
vegeta-
tion on
the
shores
nt
0.01
0.035
0025
0025
0.02
0.015
ni
0
0
0
0.01
.005
0
na
0
0
0
0
0
0
na
0
0
0.01
0
0
0
n
0.01
0.035
0.035
0.035
0.025
0.015
5-35
-------
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 Parnlico-Albermarte
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
0.0020
8
u
< 0.0015
cc
O
0.0010
I
I
I
I
S'/J/./
10
15
20
25
W1NDSPEEqQ (m/s)
Rgure 5-23. Water surface drag coefficient ae a function of wind speed measured at a 10-m height [O'Connor (1983)]
5-37
-------
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 es-
tuary 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 nor-
mally necessary, especially when water quality results
are sensitive to hydrodynamic variables.
Uniform values of the horizontal and lateral mixing
coefficients are applied to elements of similar depth
and roughness. Values should be increased where
turbulence of the flow increases. This Includes 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
models and three-dimensional models, it is usually
possible to obtain a reasonable calibration with a con-
stant lateral and vertical eddy viscosity and by relating
the vertical eddy viscosity toa measure of stability such
as the Richardson or Froude numbers so that eddy
viscosity varies with depth and degree of stratification.
This works well for cases where the estuary is relatively
deep. Vertical mixing coefficients are typically two or
more orders of magnitude smaller than lateral and
horizontal coefficients and can be even smaller
depending on the degree of vertical stratification (Mc-
Dowell 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 for-
mulations 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 Rod! 1980 and ASCE Task
Committee 1988).
Third-order Approximation for Three Dimensional
Models - The best results for three-dimensional
models are obtained when lateral and horizontal values
are modified to account for roughness, excessive tur-
bulence 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
stratified flows of estuaries and in many cases, more
elaborate methods that simulate the generation,
transport, and dissipation (under different conditions)
of turbulence are required.
Fourth-order Approximation - In a significant number
of cases, it is expected that an eddy-viscosity based
approach will not be adequate to make predictively
valid simulations of critical hydrodynamic conditions
nor can eddy viscosity approaches simulate some
complex unsteady flows. This is especially true, in
some of the larger and very important estuaries in the
U.S. These include Cheaspeake Bay and its larger
tribuatary estuaries, Long Island Sound and New York
Harbor areas, Boston Harbor, Tampa Bay, San 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
Manning's n, Supplement I
B. Depth Averaged Two Dimensional Models:
1. Estimate a uniform lateral and longitudinal eddy
viscosity coefficient for all computation elements
(segments or nodes). At least two approaches
have proven useful.
5-39
-------
Table 5-28, Vertical Eddy Viscosity Formulations for Row In Estuaries
Investigator
Munk and
Anderson
(1948)
Rossbyand
Montgomery
(1935)
Sverdrup
(1936)
Holzman
(1943))
Pasquill
(1949)
Kent and
Pntchard
(1957)
Pntchard
(1960)
Vreugdenhil
(1966)
Nelson (1972)
Odd and
Rodger
(1978)
Knight et al.
(1980)
Ueda et al.
(1981)
French and
McCutcheon
(1983)
Formulation for Ez
E.- E»
[1+/»(n)RI]n
E nr E»
- (1+«n)RI]B
E E»
~* [It-lOON]"
E, - £ [1+«n) Ri]
E _ E.
" [H-/JOORI1"
E T, E»
" |i+«n)RIJ"
E - E»
"" [1+AnlRil"
E r E»
* [H-«n)Riln
E.- El°
- [1+«n)Hir
D
E _ E»
[l+fln)Rir
2) For Ri continually increasing to over
75% of depth:
F *° fnr Bi «- 1
t1+0(n)Ri]n
f n *° for Ri ^ 1
[1+«n>r
For the occurrence of a peak Ri In the
lower 75% of the flow at z»
F n *° fnr BifTnt «- 1
[l+«n)Ri(2o)]n
F. *° for Rffral ^ 1
[i*«n)]n
Except where Ei > En. then
£,-£*,
E _ E»
' [1i-/»(n)RI]n
El-E».-^R'
£,-£ [!+/»(- 1)Ri]
E - E~
~* II+ftnlRI]"
E r, E~
- l1+«n)Rir
Continents
n m 1 and ^(n) - 10. based on oceanic thermodine Anderson measurements
from Jocubsan (iy i J) lor pUtnaer a rjora ana aCnuiB ijiuiiu ivuuunizau uuu
a general empirical equation could be written.
n - 1 and 0(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 ft(n) - 10 to 13. based on wind profiles over Spitzbergen snow
field.
Empirical equation proposed to explain evaporative flux In the atmosphere. In-
correctly presupposes that a critical Ri of 1//I(n) exists which is quite inconsis-
tent with the observations of Jacobsen (1913) and others.
For n - l.0(n) - 12, and for n - -1 and ft(n) - -12. From wind profiles in 2-
meter layer over grass.
For n - 1,l(n) - 2.4; for n - 2,ft(n) 0.24; and for n - -1. ft(n) = 0.06
from tidally averaged data collected in James River Estuary. The semi- empiri-
cal formulation for n 2 was derived from an energy dissapation per unit
length (vs. volume) basis with the flawed assumption that stratified and un-
stratified velocity gradients are equivalent.
For n 2. 0(n) - 0.28. based on a re-evaluation of the James River Estuary
data.
Forn » l,£(n) 30, data source unknown.
For n - 1. ft(n) - 10; for n - 2.£(n) » 2.5 or 5; and for n - -l.0(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 - 1.0(n) » 140 to 180 and torn = 2,ft(n) » 10 to 15; determined by
minimization of relative error from an excellent data base collected in the
Great Ouse Estuary. Relative error puts more weight on fit to highly stratified
data. Best fit obtained from n - 1 but still the average percentage error in
shear stress exceeded 100% for 35% of the measurements.
Better fit to data obtained with a hybrid formula that compensates for the ef-
fect of a strong thermoclme 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 0(1) = 160
or 0(2) » 13. n =1 remaining somewhat better than n = 2. Improves
Collected additional data in Great Ouse Estuary with less stratification and
found that£(1) - 110 to 160 and 0(2) = 13 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. 0(-l)»3.4.
For n » 2, ft(n) - 2.5, in the atmospheric boundary layer.
For n - 1, ft(n) - 30 and for n - 2, £(n) - 10 from Great Ouse Estuary
analyzed by Odd and Rodger (1978) but the root mean square error was mini-
mized instead of the relative error.
5-41
-------
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)
Pntchard (1960)
Pasquill (1962)
Vreugdenhil (1966)
Nelson (1972)
Odd and Rodger (1978)
Knight et al. (1980)
Uedaetal. (1981)
Henderson-Sellers (1982)
French and McCutcheon
(1985)
0(V
40
10-13
10
12
2.4
_
"
30
10
160
110-160
2.5
0.74
30
1(2)
-
-
-
-
0.24
0.28
_
2.5.5.0
13
13-20
-
_
10
«-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 thermodine from Jacobsen (1913) for Randers
Rord 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 (1960) analysis of Rider's (1954) and eddy flux data
of Swmbank (1955)
Data source unknown. From Nelson (1972)
Wind profiles Rider (1955) and questionable pipe flow data
from Elision and Turner (i960). (1954) and Deacon
Great Ouse Estuary. Fit by minimizing the relative error.
Great Ouse Estuary, visual fit.
Atmospheric boundary layer. From Henderson-Sellers
(1982).
Redenved from data of Ueda et al (1981)
Great Ouse Estuary. Fit by minimizing the root mean
square error.
bulence and the upper layer conditions where some
turbulence is dissipated. When the exact stratification
structure must be known to determine a waste load
allocation or a cause and effect, more elaborate tur-
bulence 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
developed by Odd and Rodger (1978) can be
developed. Odd and Rodger noted that the Munk-
Anderson formula shoud be modified if RI>1 and a
significant peak in Ri occurred in the lower 75 percent
of the depth of flow. Second, French and McCutcheon
(1983) show that less precise, more empirical ap-
proaches may yield better results. French (1979)
shows that a simpler stability function can be derived
by dimensional analysis that uses a gross Richardson
number based on shear velocity. French and Mc-
Cutcheon (1983) found that this simpler equation (see
Table 5.28) predicted eddy Viscosity better than the
complex four equation hybrid model proposed by Odd
and Rodgers (1978) that is also given in Table 5.28.
Unfortunately, the simplification by French must be
calibrated for any use whereas the Odd and Rodger
hybrid equation is a direct extension of the Munk-
Anderson formulation that may be considered for use
without calibration in screening calculations (or at least
the Odd-Rodger formulation should be considered
before the French equation when calibration is not
possible).
The final type of formulation is a class of equations
adapted from work in the atmospheric boundary layer
using different stability parameters. First, McCutcheon
(1983) notes that the most direct application of the
atmospheric boundary layer work involves the 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-Sellers
1982). The result is that only limited direct application
of the other data for stratified flows is fully feasible. Any
application of this sort is limited to small values of Ri.
Second, McCutcheon (French and McCutcheon 1983)
shows that the Monin-Obukhov stability function can
be converted to a Richardson number (based on shear
5-43
-------
or £ for each individual estuary Is presently required if
the waste load is sensitive to vertical mixing. Where
Ri>l, higher order turbulence closure modeling is
necessary 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 S.SOa. 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 closure
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 averaged mean
quantities. Turbulent quantities are averaged over a
time step that is large compared with the time scale of
turbulent motion. The equations In Table 2.1 are the
result Averaging and relating the resulting turbulent
fluxes to mean flow properties introduces eddy vis-
cosity and eddy diffusrvity 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 functions, so
that this set of equations become a closed set having
one more equation than unknown. Turbulence closure
models are classified according to how the equations
are closed.
Prandtl (1925) suggests that eddy viscosity can be
related to the local gradient of mean velocity and a so
called mixing length. This theory has been applied and
modified by many researchers (e.g.. Munk-Anderson
1948, Patanker and Scalding 1970) but mainly In two-
dimensional thin-layer flows with only one significant
velocity gradient (Rod! 1980). Table 5.28 lists some
empirical formulations developed for this theory. As
ASCE Task Committee(l98B) points out, the mixing
length theory assumes that the transport and history of
eddy effects can be neglected. It is therefore, not very
suitable when these effects are important, as in many
estuaries. In some cases, .however, mixing length
models give reasonably good results when applied to
estuaries.
To account for the transport and history of eddy affects.
one-equation models have been developed which 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
(Launder and Spalding 1972). Two-equation models
have also been develolped and have become more
popular based on their greater utility.
Two-equation turbulence closure models introduce
one more equation (e-equation) which is used to deter-
mine the length scale. Together with the k-equation
(Rod), 1980), they can account for the transport of
turbulent energy and also the length scale of the tur-
bulent motion. They can be used in the situations
where the length scale can not be prescribed by em-
pirical equations, and have been applied successfully
in many situations where simpler models failed (Rodi.
1980,1984). But. the length scale equation has been
criticized as not universal enough (e.g., Mellor and
Yamada. 1982). Also, the k-equation assumes a direct
relation between eddy viscosity and eddy diflusivity,
and turbulent kinetic energy (which is a velocity scale).
In some situations, eddy fluctuations, stress, and the
scale used to describe them develop differently.
Therefore, more complex stress/flux -equation models
have been developed which abandoned the k-equation
used by the above two methods. These models are
promising in the sense of universality, but are still in the
stage of research and have not yet been tested enough
(see Rodi 1980, Launder 1984. Mellor and Yamada
1982, Gibson and Launder 1978). So far, turbulence
closure models have been employed mainly in the
research programs. Though there have been some
notable environmental applications (e.g.. HYDRO-
QUAL 1987). it should be noted that turbulence models
can be reasonably applied only when the model as-
sumptions are not violated, and the extensive require-
5-45
-------
10'
106
10s
O»
io
'§ 10
"5
o
01
10"
10
10'
-3
1
~~ G 1
R
M
_ C
D x
1 1 1 1 1
Gunnerson. 1960
I I /
/ '-
/ /
/j
* __
.'// /
/y A
//r"/ Limits of data
///^Toison and Ichiye
/t ,/Q.G>]
_ NRDL 1 /// ' -G f Drift cards
Deep-layer / /s ft *
experiment. 1968 vV./y.v/ /'.?. 'Radioactivity in
f >*^ ../ R~~ Bikini Lagoon
A */-"^"« NU
| "^ /oC^£ ^ 1 Mile-outfall field -
&' /? %° Current-gross pair
~" A ,
-------
Table i
-30b. Tldally Averaged Longitudinal Dispersion Coefficients Observed In Selected One Dimensional Estuaries
[Hydroselence (1971), Officer (1976) and Bowie et al. (1985)]
Estuarv
Hudson River
Mouth
Potomac
San Francisco Bay
Suison Bay
Sacramento and
San Joaquin
Rivers
Northern Arm
Southern Arm
Yaquma
Freshwa er Inflow
fmVM (trVM
10610637 3.750 to
22.500
56 2000
17 _
low flow _
Low Flow Net
Non-tidal Velocity
(ms''l I fits'1)
North A
Longitudinal Dispersion
Coefficient
(mVM 1 WrV'l
menca
450 to 1.500 4.840 to
16.133
6 to 59 6510635
600 to 1.400 600 to 15.000
9 to 90 100 to 1.000
30 to 1.770 320 to 19,000
10 to 100 190 to 1.900
6010853 650 to 9.180
14 to 99 140 to 1.066
CoftifTionlfl
From O'Connor (1962). Found
correlation between flow and Kx
Estimated trom the fraction fresh-
water method and dye studies by
Hetling and O'Connell (1965.
1966). A very consistent relation-
ship between Kx and distance
downstream of Chain Bridge ob-
served
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 measure-
ments 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.
Bun and Marriage (1957) deter-
mined these values by fraction of
freshwater method. High flow Kx
significantly higher than low flow
Kx.
United Kmadom
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 174 581101.873
158 1700
53 570
84 904
338 3.638
.50 to 135 540 to 1.453
70 to 210 750 to 2.260
3010470 320105.060
70 to 700 750 to 7.530
670 7.212
Estimates based on the fraction
freshwater method measured at
various locations along with
salinity concentrations averaged
over tidal cycles.
Kx values recomputed by Bow-
den (1963) from estimates of
Stommel (1953). Bowden in-
cluded the freshwater inflow from
tributaries in the fraction of fresh-
water method and derived sig-
nificantly larger values. The
higher values are representative
Kx computed by fraction fresh-
At 16 Km (10 miles) and 40 Km
(25 miles) downestuary of Lon-
don Bridge.
At 48 Km (30 miles) downestuary
of London Bridge.
Estimates by the fraction fresh-
water method. Estimated by the
fraction freshwater method Kx
varies at each location as a func-
tion of freshwater discharge.
Derived by Higuchi (1967) from
an observed longitudal salinity
profile caused by freshwater in-
flow of the Chikugo River. Dif-
fusion of small dye patches were
5-49
-------
Table 5-32. Lateral Dispersion Coefficients In Estuaries and Coastal Waters [Officer (1976)]
Estuarv
Lateral Dispersion Coefficient
(rnVMI jftVl
Comments
United Kingdom
Severn Estuary
Fal Estuary
Blackwatar Estuary
North Sea (between
U.K. and Europe)
Irish Sea (between
U.K. and Ireland)
2 22
1.5 16
3to9 32 to 97
1.4 to 6.0 15 to 65
110 to 1.480 1.184 to 15.930
25 270
Estimated by de Turvilla and Jarman (1965) from the mixing of the thermal
plume entering the estuary with the River Usk into the Bristol Channel using ob-
served 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 spread-
ing of an instanteous point injection. Spreading occurred over periods of up to
7 hrs. Kv - ov/2l.
Estimated from dye spreading perpendicular to the axis of longitudinal spread-
ing of an instantaneous point injection. Spreading occurred over periods of up
to 12 hrs. Kv - ov/2t.
Estimated from dye spreading perpendicular to the axis of longitudinal spread-
ing of an instanteous point injection. Spreading occurred over periods of up to
12 hrs. Ky = ov/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"'
to 016 ft s'M.
Japan
Osaka Bay and
Mizushima Bav
0.5
5.4
Determined by calibration of a heat balance model for a thermal plume in-
iected into the bav from a oower 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, lon-
gitudinal dispersion coefficients are typically re-
lated 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. Mc-
Cutcheon (1983) lists various formulas that are
useful. Typically a formula is selected and modified
if necessary during calibration. See guidance on the
selection of vertical eddy viscosity.
5-51
-------
the evaporative heat flux is a significant part of the
estuary heat balance.
Typically, a wind speed function is selected from the
compilations of available functions given In Tables 5.33
and 5.34. The best choice from the compiled values is
one that has been developed for a water body of similar
size at approximately the same latitude. Shore line
conditions that influence aerodynamic roughness and
the atmospheric boundary layer over the estuary
should be similar if possible. When the wind speed
function is modified during calibration, it is usually best
to change the function by a constant multiplier rather
than arbitrarily changing the coefficients a and b (Mc-
Cutcheon 1989) by disproportionate amounts unless
the physical meaning of the two coefficients is welt
understood (e.g., see Wunderlich 1972. Ryan and Har-
leman 1973).
TaWe 5-34. Evaporation Formula* [Wundwtlch (1972) and McCutcheon (1989)]
Investigator
Penman (1956)
Meyer (1942)
Harbeck et al.
(1956)
Turner (1966)
Fry
Easterbrook
(1969)
Jobson (1980)
Faye et al. (1979)
MeCuteheon
(1982)
Fulford and
Strumm (1984)
Evaporation Rate Expression
E-f(u. e0. e, etc.)
0.35(0.5+0.01U2)(e
-------
Table 5-35. Reported Decay Rate Coefficients far Bacteria end Viruses In Seawater and BrecUsh Water
[Thomann and Mueller (1987). Bowie et aL (1985), and Velz (1984)]
Organism
OleoffRate
Coefficient'
Id'1 base e)
Temperature
pa
Reference
Comments
Conforms:
Total coliform
Total or fecal
eollform
Fecal coliform
E.coli
Fecal streptococci
1.4
(0.7 to 3.0)
46.
(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)
37tP!10
0.08 to 2.0
18 to 55
20
20
20
Mancini (1978)
Mitchell and Cham-
berlain (1978)
Hydrosctanee
(1977b)
. t . .
(19760)
Chen (1970)
Tetra Tech (1976)
Velz (1984)
Velz (1984)
Fujioka et al. (1981)
Anderson et al.
(1979)
Fujioka etal. (1981)
Seawater
Collected from 14 ocean outfalls, variable temp.
New York Harbor Salinity: 2 to 18 o/oo. Sample kept
in darkness
New York Harbor Salinity: 15 o/oo. Sample kept in
sunlight
Derived from the calibration of a model for San Fran-
cisco Bay
Derived from model calibration for Long Island. New
York Estuaries
Observed in New York Harbor
Moracaibo Strait, Venezula; from observations by
Parra Pardl.
Seawater kept in sunlight
Seawater, 10 to 30 o/oo
Seawater kept in sunlight
Viruses:
Coxsaekie
Echo 6
Polio type 1
Enteric (polio.
Echo, and cox-
sackie)
0.12
0.03
0.08
0.03
0.16
0.05
1.1 to 2.3
25
4
25
4
25
4
24
Colwell and Hetrlck
(1975)
Colwell and Hetrtek
(1975)
Colyvell and Hetrick
(1975)
Fujioka et al. (1980)
Manna waters
Marine waters
Marine waters
Seawater collected off Hawaii
Range of values or time of year in parenthesis.
sunned 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
5 = S0e UX/E = 7
-------
Table 5-36. Reported Decay Rale Coefficients for Bacteria and Viruses In Freshwater and Stormwater
[Thomann and Mueller (1987), Bowie et aL (1985), and Velz (1984)]
Organism
Fecal streptococc
S.faecaJis
S. bovis
Pathogens:
Salmonella
typhmunum
Salmonella
thompson
Viruses:
Coxsackie
Polio type 1
Enteric polio.
Echo, and cox-
sackie)
DleoffRate
Coefficient
Id'1 base el
1:
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
1.1
0.1
0.5 to 3
0.1
0.77
0.26
0.15
Temperature
(°C1
20-
4
20
20
20
18
20
20
20
18
18
21 to 23
21 to 23
0
Reference
USEPA (1974)
Kenner (1978)
Geldrlch and Kenner
(1969)
Outka and Kwan
(1980)
Geldrlch and Kenner
(1969)
commema
^ ^
Kanawha River
Stormwater. observed from 0 to 3rd day
Observed from 3rd to the 1 4th day.
Hamilton Bay, Lake Ontario observed from 0 to 10th day.
Observed from 10th to 28th dav.
Stormwater
Geldrich and Kenner
(1969)
Dutka and Kwan
(1980)
Herrmann etal (1974)
Herrmann et al (1974)
Dahling and Sarfer-
man (1979)
Stormwatar. observed from 0 to 3rd day.
Observed from 3rd to 14th dav
Hamilton Bay. Lake Ontario observed Irom Oto 10th days
Observed from 10th to 28th day
Lake Winara
Lake Winara
Tanana River, Alaska under ice cover
Fecal Colfform Bacteria Reduction percent with a
growth factor of 2
75%
2(400)-200
2(400)
If there is no background concentration of fecal
conform 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 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 un-
oxidized 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
POINT AND NON-POINT
SOURCE INPUTS
not recommended for waste load allocations because
of the difficulty in forecasting total BOD. Occasionally,
total BOD is used in screening-level models where
adequate data are not available, but these types of
studies should not be confused with a more precise
waste load allocation model study. Rgure 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 sour-
ces, autochthonous sources due to the recycling of
organic carbon in dead organisms and excreted
materials, the benthic release of reduced minerals and
AUTOCHTHONOUS SOURCES
DM* InmtsbrrtM Ftcal Algal ExudttM
IBM, (Uh, mlerobM Pttteta
CARBONACEOUS BOD
DISSOLVED AND
SUSPENDED
SCOURING AND LEACH1NO
PROM BENTHIC DEPOSITS
MICROBIAL
DEGRADATION
SETTLING PROM
WATER COLUMN
ADSORPTION/ABSORPTION BY
BENTHIC BIOTA
Figure 5-28. Sources and sinks of carbonaceous BOD In the aquatic environment [Bowie el al. (1985}].
5-59
-------
SUPPLEMENT X: SELECTION OF NBOD COEFICIENTS
There are two usual approaches to describe the trans-
formation of oxkJIzable 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 Supplement XI. The other approach that will
be discussed here simply lumps the organic and am-
monia nitrogen together (called total kjetdahl nitrogen.
TKN). This total kjeldahl nitrogen will be oxidized
through a first-order decay. The oxidation of TKN Is
NBOD.
Decay of NBOD is written as
dt =
Where
(533)
N - NBOD concentrations, mg/L.
NBOD = 4.57(N0 + N.) -t- 1.14N2 can be used as the
upper limit of NBOD (see Bowie et al. 1985)
No = organic nitrogen concentrations, mg/L
Nj = 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 dose 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
(5-34)
for 10
-------
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 Nz under anaerobic
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.
Tabl« 5-41. Rale Coefficients for Denltrmcatlon
[Bowie el al. (1985)]
Nitrate - Nitrogen Gas
K
0.1-
0.1"
0.09-
0.1
0.002
0.02-0.03
0.0-1.0""
8
1.045
1.045
1.045
1.045
No information
No information
1.02-1.09*"
References
Di Tore and Connolly (1980)
Oi Toro and Connolly (1980)
Thomann and Fitzpatriek (1982)
O'Connor et al. (1981)
Jorgensen (1976)
Jorgensen et al. (1978)
Baca and ArneK (1976)
This rate is multiplied by an oxygen limitation factor,
Ki/[Kt +Oa], where Ki is a half-saturation constant -
0.1 mg Oz/L
" The same rate applies to sediment NOs denitlrfication
*** Model documentation values
Another important phenomenon that needs to be men-
tioned Is the toxity of un-ionized ammonia to aquatic
life. The lonization equibrum Is
NH3-nffiO 5 NH*++OH+(n-l)'faO (535)
Equibrum is reached rapidly, and is largely controlled
by pH and temperature. Rgure 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.
100
40-
5 10 15 20 25 30
TEMPERATURE (ff)
Figure 5-29. Effect of pH and temperature on un-lonlzed
ammonia [Wlllingham (1976)].
35
5-63
-------
SUPPLEMENT XIII: SELECTION OF REAERATION COEFFICIENTS
Three methods are used to select reaeratlon coeffi-
cients:
1. Reaeration coefficients are computed by various
empirical and semi-empirical equations that relate
«2 to water velocity, depth, wind speed and other
characteristics of the estuary.
2. Reaeration occasionally is determined by calibra-
tion of the model Involved.
3. Reaeration is measured using tracer techniques on
rare occasions.
In most cases, Kz Is computed by a formula that is
included in the model being applied. Only a very few
models (see Bowie et al. 1935 for example) force the
user to specify values of Kz, 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
«2 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 Ka, similar
.1 a 4 A .5.6.81 2 3456
Figure 5-30. Reaeration Coefficient (day'1 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
water turbulence at the surface, KL'IS typically
specified. The values of Ka and KL are related accord-
ing to:
*2 = ^ (536)
where H Is the average depth with the units of meters
when KL is expressed in units of m d"1. In effect, «2 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 Ka. The
reason for this is that the equation Is derived from the
film penetration theory, which seems to be applicable
for most of the conditions found in estuaries except
those related to wind-generated turbulence (i.e. flows
are deep to moderately deep and rarely very shallow,
and velocities range from zero to moderately fast but
never extremely fast). Covar (1976) defines, in more
precise terms, what are thought to be the limitations of
the O'Connor-Dobbins equation. Generally, flows
should be deeper than approximately 0.6 m (2 ft) and
velocities should not exceed 0.5 m s"1 (1.5 ft s"1) at
depths of 0.6 m (2 ft) or exceed 1.5 m s"1 (5 ft s"1) at
depths of 15 m (50 ft) as illustrated in Figure 5.30.
Estimation errors are expected to be small, however, if
velocities only occasionally exceed 0.5 m s"1 to 1.5 m
s'1 (1.5 ft s"1 to 5 ft s'1) as noted in Figure 5.30.
If alternative formulations seem necessary, it may be
useful to examine those in Table 5.43. Following the
O'Connor-Dobbins equation, the Hirsh equation (Mc-
Cutcheon and Jennings 1981), the Dobbins equation,
and the Churchill et al. equations may be most useful.
The Hirsh equation is derived from the Velz iterative
method using the surface renewal theory that has been
used extensively In estuaries and deeper streams. Ex-
perience 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 Ka not related to velocity. Alter-
natively, expert practitioners (personal communica-
tion, Thomas Barnwell, Jr., U.S. EPA Center for
Exposure Assessment Modeling) use a minimum es-
timate on the order of 0.6/D where depth is in meters.
The equations by Churchill et al. (1962) are included
because of the applicability at higher velocities in
deeper flows. The complex equation by Dobbins is
5-65
-------
Table 5-43. Formulae to Estimate Reparation Coefficients for Deeper, Bottom Boundary Generated Shear Row*
[Bowie el al. (1985). Rathbun (1977), Gromlee el al. (1983), and MeCuteheon (1989)] (concluded)
Citation
K2 (base e. 20°C. day'1)
Unite
Seml-Emprlclal Modele (continued
McCutcheon
and Jennings
(1982)
Churchill et al.
(1962)
Churchill et al.
(1962)
Owens et al.
(1964)
Owens et al.
(1964)
Harleman et al.
(1977)
Ozturk
r J Dml24 Y'*,
"T 2U30.480^I J
1
Dm-L^LI)7'20
[1 - 0.001 6+0.0005 0 ] D S 2.26 ft
[1 - 0.0097 InfO ) - 0.0052] 0 >2.26 ft
0.035U iB99
D3-OBSSM33
0.746U ""
034US 0.033
D:ft
T:°C
U.-ft/s
ttft
U:m/s
D:m
Empirical Formulae
11.6U0989
o 1-673
5.0HJO.BB9 691U
D t B73 °r Q 1.67
217UO.G7
D1-"
5.32U °-87
D1-"
23.3U °-n
Ql.TS
6.92U °-n
D1-78
&
U4/3
U:ft/s
D:fl
U:m/s
D:m
U:ft/9
ttft
U:m/s
D:m
U:ft/s
D:rt
U-m/s
D:m
U:tt/s
D:ft
W:ft
Aift2
U:m/s
0:m
ApplleabHhv
Originally derived by Hirsch (1972) to replace
the Velz (1984) interative method. Expressions
for the mix interval, I are derived from the exten-
sive experience in applying the interative
method. The underlying concept is similar to
the surface-renewal theory.
Based on dimensional analysis. Derived from
data collected In rivers below Tennessee Valley
Authority (U.S.) dams.
See Churchill et al. above. This form almost as
good and is recommended by Churchill et al. 2
ft(0.61 m)sDs11 ft (3.35m) and 1.8fl/ssUs5
ft/s (0.55 m/ssUs1.5 m/s)
Developed (rom oxygen recovery data collected
on six English streams following deoxygenation
with sodium sulfide by Gameson et al. (1955)
and Owens et at. (1964) and collected below
TVA dams by Churchhill et al. (1962): 0.1 ft/ssll
S5ft/s (0.03 m/ssUsl.5 m/s).
This second formula was developed for 0.1 ft/s
sUs 1.8 ft/s (0.03 m/ssUsO.55 m/s); 0.4 fts
Dsl.Sft (0.12 msOsO.46 m) from a restricted
data set at the Water Pollution Research
Laboratory.
Equation of unknown original developed for the
MIT Transient Water Quality Model.
Equation developed exclusively for estuaries.
See Bowie etal. (1985)
Notation
U
D
= averaged velocity or tidal velocity [Hartei
= average depth of flow.
- U/(gD)1/2 a Froude number.
man (1977)]
gravitational constant.
S = slope of water surface.
D. - longitudinal dispersion coefficient.
Dy averaged vertical eddy diffusivity.
u> {gOSf *» shear velocity.
O stream discharge.
h change in water surface elevation In a reach (between two points).
t time of travel in the reach over which change in elevation is measured.
Dm molecular diffusion coefficient for oxygen in water.
T water temperature
I mix interval.
W top width of estuary.
A cross sectional area.
5-67
-------
ing K2 or KL to wind speed measurements. These are
listed in Table 5.45.
The selection of KL values seem to be best made
according to the following procedure:
1) Select a constant KL, especially if surface dissolved
oxygen is near saturation (Bowie et al. 1985. DiToro
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 fe IN WIND
DOMINATED ESTUARIES
D.J. O'Connor, (1983) developed a relation between
the transfer coefficient of slightly soluble gases (le.
reaeration coefficient, Kufor 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 dif-
fusion. In fully established rough flow, turbulence ex-
tends to the surface and turbulent transfer processes
dominant. In the transition region between smooth
and rough flow where both transfer mechanisms con-
tribute, O'Connor envisions the exchange as a transfer
in series and the overall coefficient (1/Ki_) described by
]fe = ~k * J5 (5-37)
where Kr is the transfer coefficient through the dif-
fusional sublayer and Kz is the surface renewal transfer
at the boundary of the d'rffusional sublayer.
Based on the physical behavior in the smooth and
rough layers KL is then developed by O'Connor as
[*]'
Du.
T(U.)
(538)
where
D = molecular diffusivity
va = kinematic viscosity of air
vw = kinematic viscosity of water
K = the Von Karmcn constant
pa
pv
density of air
density of water
shear velocity
is given as
U.
u-c
u-t
where
Co
Ua
= critical shear stress
= transition shear stress
drag coefficient
wind speed
The drag coefficient is a non-linear function of wind
speed derived from formulation described in O'Connor
(1983)
1000 (--
(539)
The quantities Ai. u.\, r0, u.c. and Ze are dependent on
the size of the water body and values for these
parameters are given in Table 5.46 from O'Connor,
Table 5-46. Transfer-Wind Correlations [O'Connor (1983)]
Small scale
Intermediate
Large scale
i,
10
3
3
2
u.t
9
10
10
9
To
10
6.5
5
2.5
u.c
22
11
11
6.2
z.
0.25
0.25
0.35
0.15
5-69
-------
5.5. References
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the Delaware Estuary, Journal of Environmental En-
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703-721.
Ambrose, R.B., Jr., and Roesch, S.R. 1982. Dynamic
estuary model performance, Journal of Environmental
Engineering Division, American Society of CMI En-
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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-
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American Public Health Association, Water Pollution
Control Federation, and American Water Works As-
sociation.. 1985. Standard Methods for the Examina-
tion of Water and Wastewaters, 16th ed., Washington,
D.C.
Amorochio, J., and DeVries. J.J. 1980. A new Evalua-
tion of wind stress coefficient over water surfaces,
Journal of Geophysical Research, 85(C1).
ASCE Task Committee on Turbulence Models In
Hydraulics Computations. 1988. Turbulence model-
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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 Ceariock, D.B. 1973. EXPLORE-): A River Basin
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Battelle Memorial Institute, Richland, Washington, for
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estuary. Journal of the Water Pollution Control Federa-
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Barnes, H.H., Jr. 1967. Roughness Characteristics of
Natural Channels, U.S. Geological Survey, Water
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Beck, M.B. 1985. Water Quality Management: A
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of the analysis of uncertainty, Water Resources Re-
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Bedford, K.W. 1985. Selection of Turbulence and
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Models, U.S. Army Engineer Waterways Experiment
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Benson, B.B., and Krause, D. 1984. The concentration
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Bowden, K.F. 1963. The mixing processes in a tidal
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Brown, D.S. and Allison, J.D. 1987. MINTEQA1, An
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5-75
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5-77
-------
6. SIMPLIFIED ILLUSTRATIVE EXAMPLES
David W. Dilks, Ph.D.
Scott C. Him,
Paul L. Freedman, P.E.
LTI, U'mno-Tech, Inc.
Ann Arbor, Michigan
Robert B. Ambrose, Jr, P.E.
Center lor Exposure Assessment Modeling
Environmental Research Laboratory, Athens, GA
James L Martin, Ph.D.,P.E.
Timothy A. Wool, AScI
AScI Corporation 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 general
multi-dimensional model supported and available
through the U.S. EPA Center for Exposure Assessment
Modeling. Athens, Georgia (requests require 3 double
sided double density diskettes). WASP4, a general-
complexity water quality model, can be used to simu-
late a wide range of water quality processes in different
types of estuaries. Depending upon the type of es-
tuary/water quality processes simulated, the repre-
sentative 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 selec-
tion, model development, calibration, waste load al-
location, or all-indusive instructions on WASP4 use.
Model input files for each WASP4 example are
provided in an Appendix to this manual which is avail-
able from the Center for Exposure Assessment Model-
ing on diskette. These input files can be used as
templates in simulation of water quality. The templates
allow estuarine modelers to modify an existing input file
to meet site-specific modeling needs instead of the
more time consuming and difficult task of developing
the entire input file from scratch.
The examples provided herein consider eight water
quality concerns in three basic types of estuarine char-
acterizations:
One-Dimensional Estuary:
Analytical equation for non-conservative toxic
Fraction of freshwater method for conservative
toxic
Modified tidal prism method for non-conserva-
tive toxic
Total Residual Chlorine
Bacteria
Simple DO depletion
Vertically Stratified Estuary:
Nutrient enrichment
6-1
-------
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
common of which is calibration to observed salinity or
chloride data. Since chloride and salinity behavior can
be assumed conservative (i.e. K=0), Equation 6-2
becomes:
C=C0«exp(r/jc/E), x<0 (6-4)
which can be restated in the form (Thomann and
Mueller, 1987):
In C/Co = (U/E ) x (6-5)
Equation 6-5 states that the slope of the logarithms of
observed salinity versus distance (U/E) can be used to
determine E, given an estimate of net freshwater
velocity. Specifically, by fitting a line through a plot of
salinity vs. distance on semi-log paper, E can be deter-
mined as:
'h(c.-co
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 pol-
lutant concentration distribution throughout the es-
tuary due to all discharges is determined by summation
of the predicted concentrations at any location for each
individual discharge. This procedure will also be
demonstrated as part of the Screening Examples (Sub-
section 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 vio-
lated.
The balance of freshwater to seawater is the basts 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:
(6-7)
/I = fraction of freshwater in segment i
5 = 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
dDutlon 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 concentra-
tions of conservative pollutants. For a location x, in-
cluding or downstream of the discharge,
C« =/* |f (6-8)
where:
fx = fraction freshwater at location x
W = waste loading rate (M/T)
Q = freshwater inflow (L3/T)
The right hand side of Equation 6-8 can be divided into
two distinct terms. The term W/Q represents the 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 con-
centrations at the point of discharge. Co. by using the
corresponding fraction of freshwater at that location.
fo.
Concentrations upstream, of the discharge are es-
timated 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 fresh-
water in the upstream direction to the same degree that
salinity is diluted. The equation is:
c -r w ?i
\~X-JO -^ T~
(6-9)
where:
fo o fraction of freshwater at discharge location
S x = salinity at location x
So = salinity at discharge location
Equations 6-8 and 6-9 can be used to predict conser-
vative pollutant concentrations at all locations
upstream and downstream of a discharge. The frac-
6-3
-------
= (1/r.) Tidal Period (T)
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 con-
siderations. This section provides simple Illustrative
examples designed for three different situations. The
examples are simple by design, in order to best il-
lustrate 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 pro-
cedure 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 -AnalyticalSolution tor
Non-conservative Toxic
The first three Illustrative examples involve a one-
dimensional estuary whose pollutant concentrations
are simulated in response to point sourcedischarge(s).
This type of estuary characterization simulates chan-
ges in concentration longitudinally down the length of
the estuary.
Estuary widths are typically small enough that lateral
gradients in water quality can be considered Insig-
nificant. 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 screen-
ing examples are also designed to represent only
steady state, tidally-averaged conditions. Temporal
changes in water quality related to changes In pollutant
loads or upstream flows, or intra-tldal variations, are
not represented. Application of the analytical equa-
tions 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
Freshwater Flow
Proposed
WWTP WVTP
0
5 10
Rlvgr Mile
15
Figure 6-1. Schematic of tidal tributary for analytical
aquation example.
water quality standard of 0.011 mg/l at critical environ-
mental conditions.
One survey is available with data on salinity and TRC
throughout the estuary. The pertinent information for
this estuary/discharge situation is provided in Table
6-1.
The wasteload allocation will proceed by 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 Row:
Discharge Row:
Discharge Cone.:
Estuary Cross-Sectional Araa:
Observed Data-
River Mile
2
4
5
6
9
10
12
4000 Cfs
300 cfs
2mg/L
20,000ft2
Salinity (X)
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
-------
Figure 6-3. Calibration of THC decay rat*.
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 es-
tuarine 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 environmen-
tal conditions, to minimize the degree of extrapolation
required.
For this example. Equation 6*16 is used to calculate the
allowable loading of chlorine to meet the water quality
standard as
Wd - 0.01 mg/1 2000 cfs 424 539
= 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 - 457pounds/day/80 cfs/539 = 1.06 mg/1
To demonstrate a multiple discharge situation, the
effect of a proposed second discharge on estuanne
TRC concentrations at critical environmental condi-
tions will be evaluated. The specifics of this discharge
are:
Location: River mile 5
Row: 40 cfs
Concentration: 2mg/l
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
9
10
11
12
13
14
15
Discharge 1
Distance Below Equation Concentration
Discharge (x)
(2) (31 (41
10 6-3 0.007
9 6-3 0.009
8 6-3 0.011
7 6-3 0.014
6 6-3 0.018
5 6-3 0.022
4 6-3 0.028
3 6-3 0.035
2 6-3 0.044
1 6-3 0.056
0 6-1 0.071
1 6-2 0.049
-2 6-2 0.033
-3 6-2 0.023
-4 6-2 0.016
5 6-2 0.011
Discharge 2
Distance Below Equation Concentration
Discharge (x)
(5) (6) (7)
5 6-3 0.007
4 6-3 0.009
3 6-3 0.012
2 6-3 0.015
1 6-3 0.019
0 6-1 0.024
1 6-2 0.016
2 6-2 0.01 1
3 6-2 0008
4 6-2 0.005
5 6-2 0.004
-6 6-2 0.002
-7 6-2 0.002
-8 6-2 0.001
-9 6-2 0.001
-10 6-2 0.001
Sum
Total concentration
(8)
0.014
0.018
0.023
0.029
0.037
0046
0.044
0046
0052
0061
0075
0051
0035
0024
0.017
0012
6-7
-------
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 St - ppt Wd - g/day
Seg*
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Salinity.
& (ppt)
Fraction
of Fresh-
water, f i
fi/fd
S,/Sd
Pollutant
Con-
centra-
tlon
(mg/L)
Freshwater Inflow Local Seawater Salinity Load
O-2000cmd 5. -30 ppt Wd -
10,000 g/day
Seg*
0
1
2
3- Wd
4
S
6
7
8
9
10
11
12
13
14
Salinity,
Si (ppt)
1
3
S
7
10
12
14
16
18
19
21
23
25
27
29
Fraction
of Fresh-
water, 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
t
ttw
Rgure 6-5. Schematic for Illustrative vertically stratified estuary.
Horizontal Scole
0 2OOO *000
mt't't,
6-9
-------
Table 6-7. Completed Calculation Table for Non-Conservative Pollutant by Modified Tidal Prism Method
Freshwater Inflow Local Seawater Salinity
O- 2000 and S. -30 pot
Seg*
0
1
2
3- Wd
4
5
6
7
S
9
10
11
12
13
14
Subtidal
Water
Volume.Vi
10* ms
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
Int6ftid&J
Water
Volume.Pi
10" m'
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
48
Salinity, SI
ppt
1
3
5
7
10
12
14
16
18
19
21
23
25
27
29
Load
W« - 10.000 g/day
Fraction
Fresh, fi
_
_
_
0.77
0.67
0.60
0.53
047
0.40
0.37
0.30
0.23
0.17
0.10
0.03
fl/fd
v
_
_
1.00
0.87
0.78
0.69
0.61
0.52
0.48
0.39
0.30
0.22
0.13
0.04
Decay
K - 0.01/day
St/Sd
0.14
0.43
0.71
1.00
_
_
_
_
_
M
_
_
_
_
-
Segment En-
change Ratio.
n
0.09
0.11
0.14
0.14
0.14
0.16
0.15
0.15
0.17
0.16
0.14
0.14
0.13
0.12
0.11
Tidal Cycle
T -0.48 days
n
3
2
1
_
1
2
3
4
5
6
7
8
9
10
11
n*
0.40
0.62
0.83
1.00
0.83
0.72
0.61
0.52
0.45
0.39
0.33
0.27
0.22
0.17
0.13
Pollutant
Concentra-
tion mg/L
0.22
1.02
2.26
3.85
2.77
2.15
1 62
1.21
0.91
073
0.49
0.31
0.18
0.08
0.02
For this example, Identical conditions (salinity, fresh-
water inflow, and loading) are used as the first example,
with the primary difference being the addition of a
first-order decay rate of 0.5 day . The first step in
performing the modified tidal prism method is to define
the estuarlne segmentation using the procedures
described previously. That Is, segment sizes must be
selected such that low tide volume in each segment is
equal to the high tide volume for the segment 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
values; they are identical to those used for the first
example. The segment exchange ratios are calculated
from the segment volumes using Equation 6-12. Final-
ly, pollutant concentrations are calculated using:
Equation 6-13 for the segment receiving discharge;
Equation 6-14 for segments downstream of the dis-
charge; and Equation 6-15 for segments upstream of
the discharge.
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
downstream directions. The difference in pollutant
concentrations Is caused solely by pollutant decay.
The greater the distance from the outfall, the greater
the difference In predicted concentrations, as longer
travel time provides greater opportunity for decay.
A single first-order loss term Is used to describe the
behavior of many pollutants, even though multiple fate
processes may be occurring simultaneously. Rate
coefficients for first-order processes are additive.
therefore, these multiple processes can be combined
Into a single lumped" parameter. Application of this
model may include "calibration" of the first-order loss
rate to available in-stream pollutant data. As discussed
for the analytical equation example, caution should be
used in projecting future conditions to insure that the
same process(es) that comprised the observed loss
rate will be in place under future projection conditions.
6.3. WASP4 MODELING
Deterministic water quality modeling of estuarine 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
-------
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 (NHa-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-Pheips" model described In the
WASP4 users manual. The second EUTR04 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 paniculate matter of the users choosing.
TOXI4 identifies these state variables in terms of
WASP4 systems as:
System Number TOXI4 State Variable
i
2
3
4
5
6
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 mode!. TOXI4 can provide
simulation of ionization, sorption, hydrolysis,
photolysis, oxidation, bacterial degradation, as well as
extra reactions specified by the user. TOXI4 simulates
concentrations both in the water column and bottom
sediments.
This chapter will provide three illustrative examples
using TOXI4: bacterial degradation and dye tracer;
ammonia toxicity; and toxic pollutant in water column
and sediments. These simulations will provide a broad
spectrum of potential TOXI4 applications and
demonstrate the use of ionization, equilibrium sorption,
volatilization, blodegradation, and general first-order
decay.
6.4. WASP4 Examples
The remaining six examples demonstrate the use of
WASP4 for estuarine WLA modeling. The purpose of
these examples is to provide a set of templates to
facilitate future WASP4 modeling for a wide range of
estuarine situations. The most useful portion of these
examples (for potential WASP4 users) is the line by line
description of the WASP4 input files and diskette
copies of the files themselves. These descriptions are
too detailed for inclusion in the body of the text; they
are instead supplied in an Appendix to this manual
which is available on diskette from the U.S.E.P.A. Cen-
ter for Exposure Assessment Modeling. This portion
of the chapter will provide background information on
each example, describe the types of inputs required,
show selected WASP4 model results, and briefly
describe WLA issues.
6.4.1. Example 1- Bacteria in a One-Dimensional
Estuary
The first illustrative example using WASP4 involves a
simple non-branching estuary. The analysis is
designed to provide an example which is reasonably
realistic. Although not a wasteload allocation in the
traditional sense, this example illustrates the use of a
modeling study in an analysis of bacterial loads. Since
the example is intended only for illustration of the
application and potential use of a model, such as
WASP4, emphasis is not placed on providing details
on data requirements and calibration-validation 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 shellfishmg
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
-------
Table 6-9. Tidal Periods, Amplitude* and Phase* lor the
Trinity Estuary during March, 1989
Symbol Name
Mj
Sa
Na
Ka
K,
Oi
P]
S«ml-Dlurn»l
Components
Principal Lunar
Principal Solar
Larger Lunar Elliptic
Luni-tolar
semi-diurnal
Diurnal Components
Luni-soiar diurnal
Principal lunar diurnal
Principal solar diurnal
Period
(hours)
12.42
12.00
12.66
11.97
23.93
25.82
24.07
Phase Amplitude
(degrees) (em)
330
334
303
328
106
89
104
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
hydrodynamic model, DYNHYD5, is part of the WASP4
modeling system. The WASP4 model may also be
coupled with other available hydrodynamic models.
The hydrodynamic model was first calibrated and then
used to supply flow and volume information to the
WASP4 model. Flows were computed over a period of
one month in order to examine the effects of succes-
sive neap and spring tides. The WASP4 model was
then applied to estimate bacterial concentrations.
Several types of Information were required to apply
WASP. These are described in the Appendix available
on disk from the U.S.EPA Center for Exposure Assess-
ment Modeling. The determination of these types of
data and their use in this illustrative example is
described below.
Figure 6-8. Mean monthly temperatures at the Highway 64
USGS gauge.
Figure 6-9«. Variations In water surface elevations at the
mouth of the Trinity Estuary during March, 1989.
6-15
-------
7R1
o:
U
t o
'
U
_
-2
LJ
do
> o
LEGEND
30 KM
20 KM
"TOFT
.._...
.< r" i
0.0
70.0
MO.O 210.0
280.0 350.0 420.0
TIME (HOURS)
490.0 SEO.O 630.0 700.0
770.0
Figure 6-10. Predicted variation* In volumee n«ar tha mouth, near the midpoint, and at tha 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 re-
quired for bacteria and dye for each point
source. Loadings can be measured during
water quality surveys or taken from discharge
monitoring reports. The bacterial loads for this
study were computed assuming no chlorination
or other disinfection, resulting in the high ef-
fluent concentrations given in Table 6-8. The
loadings were then computed from the dis-
charge rate and bacterial concentration. The
equivalent load for organisms was determined
by multiplying the effluent concentration
(counts/100 ml) by the flow rate which, after unit
conversions, yielded counts per day which was
then converted to kilocounts per day for input.
To convert this back to counts/100 ml, from the
output of TOXI4 in units ol/igfl, the values were
multiplied by 10~7 (1 ^g (p count here) = 10"6
g (counts), and 100 ml - 0.1 liter).
Modei constants: A first-order rate coefficient is
required to describe bacterial decay, initial es-
timates can be derived from the literature and
refined through calibration to observed bacteria
data. For this study, simulations were con-
ducted with no die-off and then with rates of 1.0
day"1. Guidance on selection of bacterial die-off
rates is provided in Section 5. Salinity and the
dye tracer were treated as conservative
materials (no decay was specified).
Initial concentrations: Concentrations of dye
and bacteria in each model segment are re-
quired 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 con-
centrations 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.
6-17
-------
0.005
DISTANCE (KM)
Figure 6-14. Neap tide dye simulation* for the Trinity Estuary.
<
cr
DISTANCE (KW)
Rgure 6-15. Spring tide dye simulations for the Trinity Estuary.
OAYO
DAY 1
DAY 2
DAY 1
Mt
DAY 2
DAYO
6-19
-------
8
en
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 *'.
8
in
,
s
i
AVERAGE
AVG + 1STD
AVG - 1STD
-10
DSTANCE (KM)
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
-------
RHODE ESTUARY
Port Holeomb
WTP
USGS GAUGE
Open Boundary
WTP
HolcombvllU
WTP
0 5000 10000
Distance (m)
Figure 6-21. Morphometry of the Rhode Estuary.
Highway 64
Rhode City
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
deoxygenation rate, and reaeration rate. WASP4
provides the option of internally calculating the reaera-
tion rate as a function of water depth and velocity. The
reaeration rate will be manually specified for these
simulations as model hydrodynamics are based upon
tidal averaged conditions.
6.4.2.1. Problem Setting
In this example, three dischargers have been identified
to the Rhode Estuary, including the city of Rhode, the
town Holcombville, and Port Holeomb. The Hol-
combville WWTP discharges to Holeomb Creek, a
tributary of the Rhode Estuary, while the Rhode and
Port Holeomb 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
evaluate the proposed modifications. A summary of the
problems setting and treatment plant data is presented
in Pigures 6-21 to 6-29 and Table 6-10.
30
28
20
16
10
6
\
\
0 6 10 IS 20 25
DISTANCE (m) (Thoucindi)
Rgure 6-22. Mean Mllnlty profile for the Rhode Estuary.
30
6-23
-------
X
Q.
UJ
o
16
14
12
10
8
6
4
MS)
i i i i i i I I I I I I I I i r
0 4000 8000 12000 16000 20000 24000 28000
2000 BOOO 10000 UOOO 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.
i-S
12
10
8
6
4
2
i I i I i i i i i i i i i I i i
0 4000 8000 12000 16000 20000 24000 28000
2000 6000 10000 14000 18000 22000 26000 30000
LOW TIDE
A
HIGH TIDE
DISTANCE (M)
Figure 6-27. Mean widths of the Rhode Estuary versus distance upesluary from Its mouth.
6-25
-------
Table 6-10. Treatment Plant Effluent Characteristics
Rhode City WTP
Present Trickling filter plant presently at capacity.
Proposed: Activated sludge plant
Present Proposed
Row
BODs
CBODu (1)
NHs-N
DO
MOD
mg/L
mgA.
mg/L
mg/L
17
60
120
30
5
24
30
60
20
5
(1) Based on long term BOD estimates of CBODu/CBODg - 2.0
Holeombvllle
Present
Flow
BODs
CBODu (1)
DO
MOD
mgA.
mgA.
mgA.
mgA.
65
130
40
5
Port Holeomb
Present
Flow
BODs
CBODu (1)
NHs-N
DO
MOD
mgA.
mgA.
mgA.
mgA.
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 com-
mercial fisheries, including shellfish. The average
monthly flows and temperatures taken at the USGS
gauge are provided in Rgures 6-24 and 6-25. The
measured depths and widths at mean tide are provided
in Figures 6-26 to 6-29. Mean tidal amplitude Is 0.28 m.
The pertinent water quality criterion Is a minimum DO
of 5.0 mg/l. From historical data, critical DO conditions
occur in mid-August when the flow for the Rhode River
at the USGS gauge is approximately 20 cms. and the
Holeomb Creek (ungauged) flow is estimated to be 10
cms. Average August water temperatures 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.
NHa-N, BODs, and salinity were taken along the es-
tuary and creek. The slack tide data were translated to
mid-tide for comparison with the tidally averaged
model. Rows during tbe study period for the Rhode
River at the USGS gauge were approximately 20 cms.
and the Holeomb Creek (ungauged) flows were es-
timated to be 10 cms. with averaged water tempera-
tures of 27 °C at the USGS gauge. A single
measurement near the 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 Holeomb and
2 g m"zday"1 was measured approximately 1 km down-
estuary of the Rhode WWTP discharge. A dye study
was conducted with Rhodamine WT injected as a slug
near the Rhode City WWTP discharge. The results of
the dye study were used to evaluate model perfor-
mance.
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
hydrodynamic model for this application. Instead.
simulations of tidally averaged conditions were con-
ducted. Model inputs are described in detail in the
Appendix available from the Center for Exposure As-
sessment Modeling, and are summarized below:
General model information: Given the nature of
the pollution problem, the eutrophication kinetic
subroutine (EUTRO4) is required for this ex-
ample. 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 ap-
plication of a one-dimensional model. A net-
work was established consisting of 15
segments in the Rhode Estuary and 5 segments
in Holeomb Creek. The variations in bottom
morphometry and water quality were reasonab-
ly regular, and for simplicity segments were
delineated every two kilometers. The depths of
the segments were determined as well as seg-
ment volumes and interfacial areas from avail-
able morphometry data. The resulting network
is illustrated In Figure 6-30.
Dispersion coefficients: These coefficients are
required to describe tidal mixing between all
model segments. Initial estimates can be
6-27
-------
UJ
o
o
o
20
10
SIMUL-1
SIMUL-5
SIMUL-9
DAY 1
a
DAY 5
X
DAY 9
10 15 20 25
DISTANCE CM) (Thousands)
30
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.
Rhodamine WT was injected in the effluent of the
Rhode City WTP. The dye density was adjusted with
alcohol to avoid sinking, and a steady concentration of
8 mg/l was maintained in the effluent over one complete
tidal cycle. This 8 mg/l concentration in the effluent
was calculated to provide a completely mixed con-
centration of approximately 100 ppb in the Rhode
Estuary near the point of discharge. Monitoring con-
tinued 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 treat-
ing it as a conservative material. Boundary concentra-
tions 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 perfor-
mance. The predicted and observed concentrations
are compared in Figure 6-32. and as illustrated, the
simulations were considered acceptable.
Following evaluation of the simulations of salinity and
the dye tracer, simulations were conducted for NBOD,
CBOD, and then DO. This sequence results from
NBOD and CBOD being unaffected by DO (if DO does
not approach zero), while DO is affected by these
parameters as welt as SOD and reaeration. Therefore,
simulations proceed from the simple to the complex.
Simulations were conducted first using literature
values for the nitrification rate and CBOD deoxygena-
tion rate. It was elected to specify a reaeration rate
rather than use model formulations to calculate a rate,
because reaeration rates had been measured in the
vicinity under similar conditions. The salinity, SOD and
temperature were specified in the model parameter list
The SOD was assumed to be 2.0 g m"2 day'1 in the
vicinity of the Rhode WWTP and 1.0 elsewhere.
Simulations were conducted with varying nitrification
and deoxygenation rates. Field data and model
predictions are compared in Figures 6-33 to 6-36. While
no statistical analyses were performed, visual 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 im-
plementation of the proposed modifications at the
Rhode WWTP (Table 6-10, see Figure 6-37). These
simulations suggested that little change would be ex-
pected in the DO concentrations as a result of the
proposed modifications.
6-29
-------
o
5
lit
o
o
o
7
6
5
4
3
2
1
D.O.
PRED. D.O.
0 2E*03 4E+03 6E+03 BE*03 1E*04
DISTANCE (M)
Figure 6-35. Predicted and observed NBOD and CBOD concentrations In the Rhode Estuary versus distance upestuary from Its
mouth.
O
z
o
p
<
DC
H
Ul
O
o
o
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
N-BOD
CBOD
PRED. CBOD
\
PRED. NBOD
i i i I
0 2E+03 4E+03 6E«03 BE«03 1E*04
DISTANCE CM)
Figure 6-36. Measured and predicted DO concentrations In Holcomb Creek versus distance upstream from Its mouth.
6-31
-------
DEEP BAY
Location Map
Athens
20
SCALE
i i i i^
61234
kilometers
Figure 6-38. Deep Bay location map.
criteria and water quality goals are 5.0 mg/L for DO and
25 f*g/L chlorophyll a.
Athens is maintaining a poorly operated secondary
wastewater treatment plant that discharges from a
surface pipe near shore 15 km from the mouth of Deep
Bay. Periodic episodes of low benthic DO near the
discharge and moderate phytoplankton blooms
downstream have been occurring. Renovation of the
plant to high performance secondary or possibly ter-
tiary treatment is being considered, as are point and
nonpoint source controls in the watershed.
Bathymetric surveys have produced a chart of sound-
ings at low tide, used for navigation (Figure 6-39).
Surveys were conducted in April, June, and August to
characterize tide, salinity, temperature, and light trans-
mittance. Continuous velocity and salinity data were
obtained from moorings at S1. S2. and S3 over these
three five-day periods (Tables 6-11 and 6-12). Deep
River flow data are summarized as monthly averages.
and the observed range of water quality constituents is
tabulated in Table 6-13. A study on the upper water-
shed has produced estimates of these water quality
constituents under a program of nonpoint source
watershed controls. A study of the Athens POTW has
produced average quality for the present effluent, and
estimates were made of effluent quality expected fol-
lowing possible plant upgrading (Table 6-14).
Table 6-11. Summary of Deep Bay Tidal Monitoring Data
Rms Net
Velocity2 Velocity2
Station Date Tidal Surface Bottom Surface Bottom
RanoV
S1
(Icm3)
S2
(km 11)
S3
(km 17)
4/1943
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
320 310
300 300
290 280
+ 2.1 +0.2
+0.6 +0.0
+0.2 -00
+ 5.3 +0.7
+ 1.4 +0.2
+04 +0.0
+ 10.4 +8.9
+ 2.8 +2.3
+0.7 +0.6
1iMt*n
2cm/Me
6-33
-------
DEEP BAY
Model Segmentation
SCALE
meters
10
zo
9
8
18
7
17
Side View
8
.
5
15
4
14
3
13
2
12
1
11
20
Dye Study
Network
01234
kilometers
Figure 6-40. Deep Bay model segmentation.
6.4.3.2 Deep Bay Network
Analysis of the monitoring data show significant dif-
ferences between surface and bottom mean velocity
and salinity, indicating a partially mixed estuary. Be-
cause of these vertical variations and because bottom
water DO was reported to be low. a 2 dimensional x-z
network was chosen. For convenience, segments
were delineated every 2 kilometers, giving 20 water
column segments with 2 vertical layers of 10 segments
each. Surface water segments are a uniform 2 meters
in depth, while underlying water segments range from
10 meters near the mouth to 0.5 meters upstream. The
resulting network is illustrated in Figure 6-40.
6.4.3.3 Deep Bay Salinity
Simulation of salinity allows calibration of dispersion
coefficients and density currents. Information needs
are as follows:
General model information: One system is simu-
lated - system 1 is interpreted as salinity, and
systems 2-8 are bypassed. The simulation
begins on day 21, representing the April 21 sur-
vey, and ends on day 147, a week following the
August 11 survey.
Dispersion coefficients: This estuary requires
two types of dispersion coefficients - lon-
gitudinal dispersion (representing tidal mixing)
and vertical eddy diffusion.
Segment volumes: Mean tide volumes are
specified for all surface and subsurface seg-
ments.
Rows: Tributary flow is partitioned to surface
and bottom segments and routed through the
estuary. Monthly river flows are specified. A den-
sity flow from the ocean is routed upstream
6-35
-------
Center Cho
Near Shore
Far Shore
0.2
ai
1 5
3 7 11
Distance from Mouth, km
Figure 6-42. Deep Bay dye study June 15, surface.
19
Segment volumes: The same mean tide
volumes from the salinity simulation are used,
except the upstream segments are divided into
three for lateral resolution.
Rows: The same flows from the salinity simula-
tion 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 ad-
joining the Athens POTW.
Environmental parameters: No parameters are
needed.
Kinetic constants: One constant is specified - a
low nitrification rate is entered, representing net
loss of dye.
Time functions: No time functions are needed.
Initial concentrations: Initial concentrations of 0
are entered.
Beginning on June 14 (day 75), Rhodamine WT was
metered into the 3 m3/sec waste stream. A steady 10
mg/L concentration in the effluent was maintained for
one day. High and low slack samples were taken daily
for one week along the near shore, center channel, and
far shore at both surface and bottom. The slack tide
data were translated to mid-tide for comparison with
the tidal-averaged model. The salinity network was
modified for the dye study to calculate lateral mixing
near the outfall (Figure 6-40). Vertical and lateral 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 Rgure 6-42. The lateral variations had
virtually disappeared by the second day. Vertical and
longitudinal variations in mid-channel after one and two
days are shown in Figure 6-43. Mid-channel profiles for
the first 2 weeks are shown in Figure 6-44. The model
was judged sufficiently calibrated for 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
simulated - system 1 is interpreted as total
nitrogen and system 3 as total phosphorus. Sys-
tems 2 and 4-8 are bypassed. The simulation
begins on day 1 (April 1) and terminates on day
6-37
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Surface TN
-i
Bottom TN
Surface TP
Boltom TP
-,
7 11
Distance from Mouth, Icn
19
Figure 6-45. Deep Bay total N and P - August 11, surface and bottom.
210 (early November). An extra benthic seg-
ment is specified to receive depositing nutrients.
Dispersion coefficients: Same as salinity simula-
tion.
Segment volumes: Same as salinity simulation.
Flows: The same water column flows used in
the salinity simulation are used, in addition, set-
tling and deposition velocities for paniculate
phosphorus are specified.
Boundary concentrations: Upstream and ocean
concentrations of total nitrogen and phos-
phorus must be specified.
Pollutant loads: Constant loads of nitrogen and
phosphorus in the effluent are specified for the
segment adjoining Athens POTW.
Environmental parameters: No parameters are
needed.
Kinetic constants: No constants are needed.
Time functions: No time functions are needed.
Initial conditions: Initial concentrations of total
nitrogen and total phosphorus are specified for
each segment, along with the dissolved frac-
tions.
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 Rgure 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 ^g/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 pos-
sible waste management strategies. First, a com-
ponent analysis could reveal the relative contributions
of Deep River. Athens POTW, and the ocean to total
nitrogen and phosphorus throughout Deep Bay
Second, simulations with the effluent at improved
secondary and tertiary treatment levels could suggest
the expected impact of point source controls. Third.
simulations with the river concentrations at various
levels could suggest the expected impact of watershed
controls.
6-39
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There are significant advantages and disadvantages in
simulating nutrients without phytoplankton to estimate
eutrophication potential. The advantages lie in the
lessened requirements for field data and modeling
resources. Several sites could be evaluated for
nutrients only, as compared to the resources required
to apply a complex eutrophication model to a single
estuary. Further, some states have standards (or
goals) for nutrient concentrations and do not require
projections of algal density.
The disadvantages of simulating only nutrients relate
to several simplifying assumptions required for this
type of application. For example, the rate of conver-
sion of dissolved phosphorus into paniculate form is
dependent upon algal concentration and growth rate.
Because algal dynamics are not simulated, these
values must be estimated. Further, because algal
growth is directly related to nutrient concentrations.
calibration parameters may not apply well to future
conditions of different nutrient levels. Finally, for situa-
tions where algal density is of ultimate concern,
nutrient projections alone will only provide an indirect
estimate of expected phytoplankton concentrations.
6.4.4 Example 4 - Eutrophication in a Vertically
Stratified Estuary
This case study considers simulation of seasonal
eutrophication in Deep Bay. The problem setting and
model network are as described in the preceding 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 nutrients and DO. The
simulation begins on day 1 (April 1), and ter-
minates on day 210 (early November).
Dispersion coefficients: The same water column
dispersion coefficients from the salinity simula-
tion are used. Extra pore water dispersion coeffi-
cients for benthic-water column exchange of
dissolved chemicals must be specified.
Segment volumes: The same water column
volumes from the salinity simulation are used. A
benthic volume underlies each bottom water
segment
Rows: The same flows from the salinity simula-
tion are used.
Boundary concentrations: Tributary and ocean
concentrations of all 8 systems must be
specified.
Pollutant loads: Constant loads for all 8 systems
in the effluent must be specified for the segment
adjoining Athens POTW.
Environmental parameters: Values for average
salinity and background sediment oxygen
demand for each segment are given. The time
variable temperature and light attenuation func-
tions used by each segment must be specified.
Kinetic constants: Rate constants, temperature
coefficients, half saturation constants and other
kinetic Information must be specified. Proces-
ses include nitrification, denitrification.
phytoplankton growth (light and nutrient limita-
tion), phytoplankton death, carbonaceous
deoxygenation, reaeration, mineralization, and
benthic decomposition. If a constant is not
specified, then the relevant reaction or process
is bypassed.
Environmental time functions: Time variability in
temperature, light extinction, incident light, and
length of daylight must be specified.
Initial conditions: Initial concentrations of each
state variable and the fraction dissolved in each
model segment are required. The solids settling
field affecting each variable must also be
specified.
The simulation proceeded from April 1 to November 1,
with seasonal light, temperature, and flow data
provided. Rgures 6-46 and 6-47 show predicted upper
layer chlorophyll a and lower level DO during mid July.
August and September. Chlorophyll concentrations
Increase dramatically over the course of the summer.
and lower layer DO decreases to a minimum of about
4 mg/L Diurnal swings about this minimum are
predicted to be minimal. The impact of phytoplankton
growth is significant on upper layer DO. with levels
maintained near saturation and diurnal swings of about
one and a half mg/L Phytoplankton die-off depresses
both upper and lower layer DO somewhat.
Phytoplankton growth Is limited somewhat by nitrogen.
but more by light. Sensitivity studies show the relative
importance of the variable light attenuation coeffi-
cients, the phytoplankton saturating light intensity, and
6-41
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data were obtained from moorings at sampling stations
S1. S2, and S3 over these three five-day periods (Table
6-15).
The Boatwona River flow, Ammonia and pH data are
summarized as monthly averages (Table 6-16).
6.4.5.2. Boatwona Estuary Network
Analysis of the monitoring data illustrates a definite
lateral flow pattern. Because of these lateral flows, the
bay was segmented to demonstrate the fate and
transport of the ammonia discharge (Figure 6-50).
Segments were defined every 5 kilometers, giving 6
water column segments.
6.4.5.3. Boatwona Estuary Nitrogen Simulation
The WASP4 model was given flow Information
averaged from the continuous flow meters that were
installed during the sampling surveys.
General model Information: One system is simu-
lated - system 1 is interpreted as total ammonia-
nitrogen. The organic toxic chemical model
TOXI4 was used for this study because of its
capabilities of simulating both unionized and
ionized forms of chemicals. The remaining sys-
Scale
=f=
0 5000
meters
Figure 6-49. Boatwona Estuary depth chart.
10.000
3.2 mo/1 Ammonia
Waste Water Treatment Plant
II
90 kg/dty Anvnonta
Scale
5000
meters
10.000
Figure 6-48. City of Boatwona waste water treatment plant
location.
Table 6-15. Boatwona Estuary Survey Data
SI S2 S3
Sample
Time
May
August
Ncv
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 68
Temp pH
15.3 6.9
17.0 7.0
16.9 6.8
Table 6-16. Boatwona River Survey Data
Month
January
February
March
April
May
June
July
August
September
October
November
December
Average Row (cms)
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
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10
20 30
_»_ Ionized Ammonia
40 SO 60 70
Time (days)
80
90
100 110
. Unionized Ammonia
Figure 6-51'. Ammonia simulation results.
tion. reduction, and biodegradation. In addition,
volatilization can lead to loss of chemical from the
water.
The same estuary is used as for example 5; however,
benthic sediments also are being considered. Two
layers of benthic sediments are simulated - upper sur-
ficial sediment and deep sediments. This simulation
uses Systems 1 through 3 in TOXI4. Two types of
solids are represented, corresponding to inorganic
and organic materials, respectively. System 1 repre-
sents the pollutant. System 2 represents inorganic
solids, and System 3 represents organic solids. En-
vironmental 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 wilt be treated as a first-order toss
process for this simulation, with separate values used
for the water column and the sediment.
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.
6-45
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6.5 References
Ambrose. R.B.. Wool. TA. 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. En-
vironmental 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, SA,
Summers, K.V., Mok, L, Rupp, G.L and Bowie, G.L,
1985. Water Quality Assessment: A Screening Proce-
dure (or Toxic and Conventional Pollutants in Surface
and Ground Water Part 1, EPA/600/6-85/002b, U.S.
Environmental Protection Agency, Athens, Georgia.
Schnoor et. al. 1987. Processes, Coefficients and
Models for Simulating Toxic Organics and Heavy Me-
tals in Surface Waters. U.S. Environmental Protection
Agency, Athens, Georgia, EPA/600/3-87/015.
Thomann, R.V. 1972. Systems Analysis and Water
Quality Management McGraw-Hill, New York.
Thomann. R.V. and Rtzpatrick, J.J. 1982. Calibration
and Verification of a Mathematical Model of the
Eutrophlcation of the Potomac Estuary. Prepared for
Department of Environmental Services. Government of
the District of Columbia, Washington, D.C.
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