vvEPA
United States
Environmental Protection
Agency
Office of Water
Washington, DC 20460
EPA-823-R-92-002
May 1990
Technical Guidance
Manual for Performing
Waste Load Allocations
Book
Estuaries
Parti
Estuaries and Waste Load
Allocation Models
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TECHNICAL GUIDANCE MANUAL
FOR PERFORMING WASTE LOAD ALLOCATIONS
BOOK III: ESTUARIES
PART 1: Estuaries and Waste Load Allocation Models
Project Officer
Hiranmay Biswas, Ph.D.
Edited by
Robert B. Ambrose, Jr. P.E.1
James L. Martin, Ph.D.,P.E.2
Sections written by
Robert B. Ambrose, Jr., P.E.1
James L. Martin, Ph.D., P.E.2
JohnF. Paul, Ph.D.3
1. Center for Exposure Assessment Modeling,
Environmental Research Laboratory, U.S. EPA, Athens, GA
2. AScI Corp., at the
Environmental Research Laboratory, U.S. EPA, Athens, GA
3. Environmental Research Laboratory,
U.S. EPA, Narragansett, Rl
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
401 M Street, S.W.
Washington, DC 20460
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Table of Contents
Glossary ix
Acknowledgments xv
Executive Summary xvii
PARTI: Estuaries and Waste Load Allocation Models xvii
Introduction xvii
Overview of Processes Affecting Estuarine Water Quality xvii
Model Identification and Selection xviii
PART II: Application of Estuarine Waste Load Allocation Models xix
Monitoring Protocols for Calibration and Validation of Estuarine WLA Models ... xix
Model Calibration, Validation, and Use xx
Simplified Illustrative Examples xxi
Preface xxiii
1. Introduction 1-1
1.1. Background 1-1
1.2. Introduction to Estuaries 1-2
1.3. Potential Problems to Address 1-3
1.4. Overview of the Waste Load Allocation 1-3
1.5. Steps in the Modeling Process 1-5
1.6. Organization and Scope 1-5
1.7. References 1-5
2. Overview of Processes Affecting Estuarine Water Quality 2-1
2.1. Organization Of This Section 2-1
2.2. Estuarine Morphology and Classification 2-1
2.3. Factors Affecting Circulation And Mixing 2-2
2.4. Sediment Transport and Sediment/Water Quality Interactions 2-4
2.5. Organic Wastes, Dissolved Oxygen And Nutrients 2-5
2.6. Synthetic Organic Chemicals 2-8
2.7. Metals 2-9
2.8. Model Structure 2-10
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SUPPLEMENT I: Factors Affecting Circulation and Mixing
Model Equations 2-10
SUPPLEMENT II: Sediment Transport and Sediment/Water Quality
Interactions 2-18
SUPPLEMENT III: Organic Wastes, Dissolved Oxygen and Nutrients .... 2-20
SUPPLEMENT IV: Synthetic Organics 2-26
SUPPLEMENT V: Metals 2-30
2.9. References 2-32
3. Model Identification and Selection 3-1
3.1. Introduction 3-1
3.2. Model Identification 3-1
3.3. Model Selection 3-11
3.4. References 3-22
IV
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List of Figures
Figure 2-1. Factors affecting changes in momentum 2-12
Figure 2-2. Relationship between water density, salinity, and temperature 2-13
Figure 2-3. Factors affecting change in constituent mass 2-15
Figure 2-4. Model dimensions 2-16
Figure 2-5. Sediment variables and processes 2-18
Figure 2-6. Basic variables and processes for dissolved oxygen 2-21
Figure 2-7. Standard variables for eutrophication and DO 2-21
Figure 2-8. Additional variables and processes for trophic interactions 2-23
Figure 2-9. Additional variables and processes for nutrient interaction 2-24
Figure 2-10. Benthic interactions for nutrients and DO 2-25
Figure 2-11. Basic variables and processes for reactive organic chemicals 2-27
Figure 3-1. Stratification circulation diagram and examples 3-4
Figure 3-2. Vertical velocity profiles 3-6
Figure 3-3. Vertical dye concentration profiles 3-6
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List of Tables
Table 1 -1. Organization of Guidance Manual for Performance of Wasteload
Allocations 1-1
Table 1-2. Major Constituents and Macronutrients in Seawater [Smith (1974)] .... 1-2
Table 2-1. Fundamental Model Equations 2-11
Table 3-1. General Scales of Interest 3-2
Table 3-2. Topographic Estuarine Classification 3-7
Table 3-3. Stratification Classification 3-7
Table 3-4. Summary of Methodology for Estuarine Water Quality Assessment ... 3-14
Table 3-5. Basic Model Features 3-22
Table 3-6. Water Quality Problems Addressed 3-22
Vll
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Glossary
Acute Toxicity - Any toxic effect that is produced
within a short period of time, usually 24-96 hours.
Although the effect most frequently considered is
mortality, the end result of acute toxicity is not neces-
sarily death. Any harmful biological effect may be the
result.
Aerobic - 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) - Simple plants, many microscopic,
containing chlorophyll. Algae form the base of the
food chain in aquatic environments. Some species
may create a nuisance when environmental condi-
tions are suitable for prolific growth.
Allochthonous - Pertaining to those substances, ma-
terials 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.
Autotrophic - Self nourishing; denoting those organ-
isms that do not require an external source of organic
material but can utilize light energy and manufacture
their own food from inorganic materials; e.g., green
plants, pigmented flagellates.
Bacteria - Microscopic, single-celled or noncellular
plants, usually saprophytic or parasitic.
Benthal Deposit2 - Accumulation on the bed of a
watercourse of deposits containing organic matter
arising from natural erosion or discharges of waste-
waters.
Benthic Region1 - The bottom of a waterway; the
substratum that supports the benthos.
Benthal Demand2 - The demand on dissolved oxygen
of water overlying benthal deposits that results from
the upward diffusion of decomposition products of the
deposits.
Benthos1 - Organisms growing on or associated prin-
cipally with the bottom of waterways. These include:
(1) sessile animals such as sponges, barnacles, mus-
sels, oysters, worms, and attached algae; (2) creep-
ing forms such as snails, worms, and insects; (3)
burrowing forms, which include clams, worms, and
some insects; and (4) fish whose habits are more
closely associated with the benthic region than other
zones; e.g., flounders.
Biochemical Oxygen Demand2 - A measure of the
quantity of oxygen utilized in the biochemical oxidation
of organic matter in a specified time and at a specific
temperature. It is not related to the oxygen require-
ments in chemical combustion, being determined en-
tirely 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 sub-
stances becomes greater each higher step in the food
chain.
Bloom - A readily visible concentrated growth or ag-
gregation 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.
Chlorophyll - 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 or-
ganisms to another.
Chronic Toxicity1 -Toxicity, marked by a long duration,
that produces an adverse effect on organisms. The end
result of chronic toxicity can be death although the
usual effects are sublethal; e.g., inhibits reproduction,
reduces growth, etc. These effects are reflected by
changes in the productivity and population structure of
the community.
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Coastal Waters1 - Those waters surrounding the con-
tinent which exert a measurable influence on uses of
the land and on its ecology. The Great Lakes and the
waters to the edge of the continental shelf.
Component Tide2 - Each of the simple tides into
which the tide of nature is resolved. There are five
principal components; principal lunar, principal solar,
N2, K, and O. There are between 20 and 30 compo-
nents which are used in accurate predictions of tides.
Coriolis Effect2- The deflection force of the earth's
rotation. Moving bodies are deflected to the right in
the northern hemisphere and to the left in the southern
hemisphere.
Datum2 - An agreed standard point or plane of state
elevation, noted by permanent bench marks on some
solid immovable structure, from which elevations are
measured or to which they are referred.
Density Current2 - A flow of water through a larger
body of water, retaining its unmixed identity because
of a difference in density.
Deoxygenation - The depletion of the dissolved oxy-
gen in a liquid either under natural conditions associ-
ated with the biochemical oxidation of organic matter
present or by addition of chemical reducing agents.
Diagenetic Reaction - Chemical and physical
changes that alter the characteristics of bottom sedi-
ments. Examples of chemical reactions include oxi-
dation of organic materials while compaction is an
example of a physical change.
Dispersion - (1) Scattering and mixing. (2) The mix-
ing of polluted fluids with a large volume of water in a
stream or other body of water.
Dissolved Oxygen2 - The oxygen dissolved in water,
wastewater, or other liquid, usually expressed in mil-
ligrams per liter, or percent of saturation. Abbreviated
DO.
Diurnal2 - (1) Occurring during a 24-hr period; diurnal
variation. (2) Occurring during the day time (as op-
posed to nighttime). (3) In tidal hydraulics, having a
period or cycle of approximately one tidal day.
Drought2 - In general, an extended period of dry
weather, or a period of deficient rainfall that may
extend over an indefinite number of days, without any
quantitative standard by which to determine the de-
gree of deficiency needed to constitute a drought.
Qualitatively, it may be defined by its effects as a dry
period sufficient in length and severity to cause at
least partial crop failure or impair the ability to meet a
normal water demand.
Ebb Tide1- That period of tide between a high water and
the succeeding low water; falling tide.
Enrichment - An increase in the quantity of nutrients
available to aquatic organisms for their growth.
Epilimnion - The water mass extending from the sur-
face to the thermocline in a stratified body of water; the
epilimnion is less dense that the lower waters and is
wind-circulated and essentially homothermous.
Estuary - That portion of a coastal stream influenced
by the tide of the body of water into which it flows; a
bay, at the mouth of a river, where the tide meets the
river current; an area where fresh and marine water
mix.
EuphoticZone1 -The lighted region of a body of water
that extends vertically from the water surface to the
depth at which photosynthesis fails to occur because
of insufficient light penetration.
Eutrophication - The natural process of the maturing
(aging) of a lake; the process of enrichment with nutri-
ents, especially nitrogen and phosphorus, leading to
increased production of organic matter.
Firth - A narrow arm of the sea; also the opening of a
river into the sea.
Fjord (Fiord)1 - A narrow arm of the sea between
highlands.
Food Chain - Dependence of a series of organisms,
one upon the other, for food. The chain begins with
plants and ends with the largest carnivores.
Flood Tide2 - A term indiscriminately used for rising tide
or landward current. Technically, flood refers to current.
The use of the terms "ebb" and "flood" to include the
vertical movement (tide) leads to uncertainty. The
terms should be applied only to the horizontal move-
ment (current).
Froude's Number - A numerical quantity used as an
index to characterize the type of flow in a hydraulic
structure that has the force of gravity (as the only force
producing motion) acting in conjunction with the resist-
ing force of inertia. It is equal to the square of charac-
teristic velocity (the mean, surface, or maximum
velocity) of the system, divided by the product of a
characteristic linear dimension, such as diameter or
expressed in consistent units so that the combinations
will be dimensionaless. The number is used in
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open-channel flow studies or in cases in which the free
surface plays an essential role in influencing motion.
Heavy Metals - Metals that can be precipitated by
hydrogen sulfide in acid solution, for example, lead,
silver, gold, mercury, bismuth, copper.
Heterotrophic1 - Pertaining to organisms that are
dependent on organic material for food.
Hydraulic Radius - 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.
Hydrodynamics - The study of the motion of, and the
forces acting on, fluids.
Hydrographic Survey2 - An instrumental survey
made to measure and record physical characteristics
of streams and other bodies of water within an area,
including such things as location, areal extent and
depth, positions and locations of high-water marks,
and locations and depths of wells.
Inlet - 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 Matter - Mineral-type compounds that are
generally non-volatile, not combustible, and not bio-
degradable. Most inorganic-type compounds, or reac-
tions, are ionic in nature, and therefore, rapid
reactions are characteristic.
Lagoon - 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 spe-
cies requirements or tolerance.
Manning Formula2 - A formula for open-channel flow,
published by Manning in 1890, which gives the value
of c in the Chezy formula.
Manning Roughness Coefficient - 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 Level - The mean plane about which the
tide oscillates; the average height of the sea for all
stages of the tide.
Michaelis-Menton Equation - A mathematical ex-
pression to describe an enzyme-catalyzed biological
reaction in which the products of a reaction are de-
scribed as a function of the reactants.
Mineralization - 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 miner-
alization of organic compounds occurs through com-
bustion and through metabolism by living animals.
Microorganisms are ubiquitous, possess extremely
high growth rates and have the ability to degrade all
naturally occurring organic compounds.
Modeling - 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 determine
efficiency of treatment or compliance with standards or
requirements.
Mouth2" The exit or point of discharge of a stream into
another stream or a lake, or the sea.
Nautical Mile - A unit of distance used in ocean
navigation. The United States nautical mile is defined
as equal to one-sixteenth of a degree of a great circle
on a sphere with a surface equal to the surface of the
earth. Its value, computed for the Clarke spheroid of
1866, is 1,853.248 m (6,080.20ft). The International
nautical mile is 1,852 m (6,070.10ft).
Nanoplankton2" Very minute plankton not retained in
a plankton net equipped with no. 25 silk bolting cloth
(mesh, 0.03 to 0.04 mm.).
Neap Tides -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.
Neuston - Organisms associated with, or dependent
upon, the surface film (air-water) interface of bodies of
water.
Nitrogenous Oxygen Demand (NOD)2 - A quantitative
measure of the amount of oxygen required for the
biological oxidation of nitrogenous material, such as
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ammonia nitrogen and organic nitrogen, in wastewa-
ter; usually measured after the carbonaceous oxygen
demand has been satisfied.
Nutrients1 - Elements, or compounds, essential as
raw materials for organism growth and development;
e.g., carbon, oxygen, nitrogen, phosphorus, etc.
Organic - Refers to volatile, combustible, and some-
times biodegradable chemical compounds containing
carbon atoms (carbonaceous) bonded together and
with other elements. The principal groups of organic
substances found in wastewater are proteins, carbo-
hydrates, and fats and oils.
Oxygen Deficit - The difference between observed
oxygen concentration and the amount that would
theoretically be present at 100% saturation for exist-
ing conditions of temperature and pressure.
Pathogen - An organism or virus that causes a dis-
ease.
Periphyton (Aufwuchs)1 - Attached microscopic or-
ganisms growing on the bottom, or other submersed
substrates, in a waterway.
Photosynthesis - The metabolic process by which
simple sugars are manufactured from carbon dioxide
and water by plant cells using light as an energy
source.
Phytoplankton - Plankton consisting of plant life.
Unattached microscopic plants subject to movement
by wave or current action.
Plankton1 - Suspended microorganisms that have
relatively low powers of locomotion, or that drift in the
water subject to the action of waves and currents.
Quality - A term to describe the composite chemical,
physical, and biological characteristics of a water with
respect to it's suitability for a particular use.
Reaeration - The absorption of oxygen into water
under conditions of oxygen deficiency.
Respiration - The complex series of chemical and
physical reactions in all living organisms by which the
energy and nutrients in foods is made available for
use. Oxygen is used and carbon dioxide released
during this process.
Roughness Coefficient2 - A factor, in the Chezy,
Darcy-Weisbach, Hazen-Williams, Kutter, Manning,
and other formulas for computing the average velocity
of flow of water in a conduit or channel, which repre-
sents the effect of roughness of the confining material
on the energy losses in the flowing water.
Seiche - Periodic oscillations in the water level of a lake
or other landlocked body of water due to unequal
atmospheric pressure, wind, or other cause, which sets
the surface in motion. These oscillations take place
when a temporary local depression or elevation of the
water level occurs.
Semidiurnal - Having a period or cycle of approxi-
mately one half of a tidal day. The predominating type
of tide throughout the world is semidiurnal, with two
high waters and two low waters each tidal day.
Slack Water-In tidal waters, the state of a tidal current
when its velocity is at a minimum, especially the mo-
ment when a reversing current changes direction and
its velocity is zero. Also, the entire period of low velocity
near the time of the turning of the current when it is too
weak to be of any practical importance in navigation.
The relation of the time of slack water to the tidal
phases varies in different localities. In some cases
slackwater occurs nearthe times of high and low water,
while in other localities the slack water may occur
midway between high and low water.
Spring Tide1 - Exceptionally high tide which occurs
twice per lunar month when there is a new or full moon,
and the earth, sun, and moon are in a straight line.
Stratification (Density Stratification) -Arrangement
of water masses into separate, distinct, horizontal lay-
ers as a result of differences in density; may be caused
by differences in temperature, dissolved or suspended
solids.
Tidal Flat1 - The sea bottom, usually wide, flat, muddy
and nonproductive, which is exposed at low tide. A
marshy or muddy area that is covered and uncovered
by the rise and fall of the tide.
Tidal Prism - (1) The volume of water contained in a
tidal basin between the elevations of high and low
water. (2) The total amount of water that flows into a
tidal basin or estuary and out again with movement of
the tide, excluding any fresh-water flows.
Tidal Range2 - The difference in elevation between high
and low tide at any point or locality.
Tidal Zone (Eulittoral Zone, Intertidal Zone) - The
area of shore between the limits of water level fluctua-
tion; the area between the levels of high and low tides.
Tide1 - The alternate rising and falling of water levels,
twice in each lunar day, due to gravitational attraction
XII
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of the moon and sun in conjunction with the earth's
rotational force.
Tide Gage - (1) A staff gage that indicates the height
of the tide. (2) An instrument that automatically regis-
ters the rise and fall of the tide. In some instruments,
the registration is accomplished by printing the heights
at regular intervals; in others by a continuous graph in
which the height of the tide is represented by ordinates
of the curve and the corresponding time by the abscis-
sae.
Toxicant - A substance that through its chemical or
physical action kills, injures, or impairs an organism;
any environmental factor which, when altered, pro-
duces a harmful biological effect.
Water Pollution1 - Alteration of the aquatic environ-
ment in such a way as to interfere with a designated
beneficial use.
Water Quality Criteria1 - A scientific requirement on
which a decision or judgement may be based concern-
ing the suitability of water quality to support a desig-
nated use.
Water Quality Standard1 - A plan that is established
by governmental authority as a program for water
pollution prevention and abatement.
Zooplankton - Plankton consisting of animal life.
Unattached microscopic animals having minimal capa-
bility for locomotion.
1 Rogers, B.C., Ingram, W.T., Pearl, E.H., Welter, L.W.
(Editors). 1981, Glossary, Water and Wastewater
Control Engineering, Third Edition, American Public
Health Association, American Society of Civil Engi-
neers, American Water Works Association, Water
Pollution Control Federation.
Matthews, J.E., 1972, Glossary of Aquatic Ecological
Terms, Manpower Development Branch, Air and
Water Programs Division, EPA, Oklahoma.
XIII
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Acknowledgements
The contents of this section have been removed to
comply with current EPA practice.
xv
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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 allo-
cations (WLAs) that are as technically sound as current
state of the art permits. The objective of such load
allocations is to ensure that water quality conditions
that protect designated beneficial uses are achieved.
This book provides technical guidance for performing
waste load allocations in estuaries.
PART I: ESTUARIES AND WASTE LOAD
ALLOCATION MODELS
Introduction
Estuaries are coastal bodies of water where fresh
water meets the sea. Most rivers and their associated
pollutant loads eventually flow into estuaries. The com-
plex loading, circulation, and sedimentation processes
make water quality assessment and waste load allo-
cation in estuaries difficult. Transport and circulation
processes in estuaries are driven primarily by river flow
and tidal action. As a consequence of its complex
transport processes, estuaries cannot be treated as
simple advective systems such as many rivers.
Wastewater discharges into estuaries can affect water
quality in several ways, both directly and indirectly. In
setting limits on wastewater quantity and quality, the
following potential problems should be assessed: sa-
linity, sediment, pathogenic bacteria, dissolved oxygen
depletion, nutrient enrichment and overproduction,
aquatic toxicity, toxic pollutants and bioaccumulation
and human exposure.
A WLA provides a quantitative relationship between
the waste load and the instream concentrations or
effects of concern as represented by water quality
standards. During the development of a WLA, the user
combines data and model first to describe present
conditions and then to extrapolate to possible future
conditions. The WLA process sequentially addresses
the topics of hydrodynamics, mass transport, water
quality kinetics, and for some problems, bioaccumula-
tion and toxicity.
For each of the topics addressed in a modeling study,
several steps are applied in an iterative process: prob-
lem identification, model identification, initial model
calibration, sensitivity analysis, model testing, refine-
ment, and validation.
After the WLAs have been put into effect, continued
monitoring, post-audit modeling and 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 proc-
esses in whatever type of model is applied (conceptual
or mathematical) in order to determine the appropriate
allocation of load. Insight into processes affecting water
quality may be obtained through examination of the
schemes available for their classification. Estuaries
have typically been classified based on their geomor-
phology and patterns of stratification and mixing. How-
ever, each estuary is to some degree unique and it is
often necessary to consider the fundamental proc-
esses impacting water quality.
To determine the fate and affects of water quality
constituents it is necessary first to determine processes
impacting their transport. That transport is affected by
tides, fresh water inflow, friction at the fluid boundaries
and its resulting turbulence, wind and atmospheric
pressure, and to a lesser degree (for some estuaries)
the effects of the earth's rotation (Coriolis force). The
resulting transportation patterns may be described (de-
termined from field studies) in waste load allocation
studies, or, as is becoming more frequently the case,
estimated using hydrodynamic models. Hydrodynamic
models are based on descriptions of the processes
affecting circulation and mixing using equations based
on laws of conservation of mass and momentum. The
fundamental equations generally include: (A) the con-
servation 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-
clude settling, resuspension, scour and erosion, co-
agulation and flocculation.
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The water quality parameters of interest vary with the
objectives of the waste load allocation study, from
"conventional pollutants" (e.g. organic waste, dis-
solved oxygen and nutrients) to toxic organics and
trace metals.
The focus of WLA models of conventional pollutants is
often DO and biochemical oxygen demand (BOD) as
a general measure of the health of the system, or the
focus can be primary productivity when eutrophication
is the major concern. Conventional WLA models usu-
ally include temperature, major nutrients, chemical
characteristics, detritus, bacteria, and primary produc-
ers. WLA models may include highertrophic levels (i.e.
zooplankton and fish) because of higher trophic level
effects on other more important variables, such as
phytoplankton, BOD and DO. Synthetic organic chemi-
cals include a wide variety of toxic materials whose
waste loads are allocated based upon threshold con-
centrations as well as tolerable durations and frequen-
cies of exposure. These pollutants may ionize and
different forms may have differing toxicological effects.
The transport of the materials also may be affected by
sorption and they can degrade through such proc-
esses as volatilization, biodegradation, hydrolysis, and
photolysis.
Trace metals may be of concern in many estuaries due
to theirtoxicological effects. The toxicity of trace metals
and their transport is affected by their form. Upon entry
to a surface water body, metal speciation may change
due to complexation, precipitation, sorption, and redox
reactions. Metals concentrations are diluted further by
additional stream flow and mixing. Physical loss can
be caused by settling and sedimentation, whereas a
physical gain may be caused by resuspension.
Model Identification and Selection
The first steps in the modeling process are model
identification and selection. The goals are to identify
the simplest conceptual model that includes all the
important estuarine phenomena affecting the water
quality problems, and to select the most useful analyti-
cal formula or computer model for calculating waste
load allocations. During model identification, available
information is gathered and organized to construct a
coherent picture of the water quality problem. There
are four basic steps in model identification: establish
study objectives and constraints, determine water
quality pollutant interactions, determine spatial extent
and resolution, and determine temporal extent and
resolution. Following model identification, another im-
portant step is advised: perform rapid, simple screen-
ing calculations to gain a better understanding of
expected pollutant levels and the spatial extent of
water quality problems.
The first step in identifying an appropriate WLA model
for a particular site is to review the applicable water
quality standards and the beneficial uses of the estuary
to be protected. Local, state, and federal regulations
may contribute to a set of objectives and constraints.
The final result of this step should be a clear under-
standing of the pollutants and water quality indicators,
the areas, and the time scales of interest.
After the pollutants and water quality indicators are
identified, the significant water quality reactions must
be determined. These reactions must directly or indi-
rectly link the pollutants to be controlled with the pri-
mary water quality indicators. All other interacting water
quality constituents thought to be significant should be
included at this point. This can best be done in a
diagram or flow chart representing the mass transport
and transformations of water quality constituents in a
defined segment of water. The final result of this step
should be the assimilation of all the available knowl-
edge of a system in a way that major water quality
processes and ecological relationships can be evalu-
ated for inclusion in the numerical model description.
The next step is to specify the spatial extent, dimen-
sionality, and scale (or computational resolution) of the
WLA model. This may be accomplished by determining
the effective dimensionality of the estuary as a whole,
defining the boundaries of the study area, then speci-
fying the required dimensionality and spatial resolution
within the study area. The effective dimensionality of
an estuary includes only those dimensions over which
hydrodynamic and water quality gradients significantly
affect the WLA analysis. Classification and analysis
techniques are available. Specific boundaries of the
study area must be established, in general, beyond the
influence of the discharge(s) being evaluated. Data
describing the spatial gradients of important water
quality constituents within the study area should be
examined. Dye studies can give important information
on the speed and extent of lateral and vertical mixing.
It is clear that choice of spatial scale and layout of the
model network requires considerable judgment.
The final step in model identification is to specify the
duration and temporal resolution of the WLA model.
The duration of WLA simulations can range from days
to years, depending upon the size and transport char-
acteristics of the study area, the reaction kinetics and
forcing functions of the water quality constituents, and
the strategy for relating simulation results to the regu-
latory requirements. One basic guideline applies in all
cases - the simulations should be long enough to
eliminate the effect of initial conditions on important
water quality constituents at critical locations.
XVIII
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The temporal resolution of WLA simulations falls into
one of three categories - dynamic, quasi-dynamic, and
steady state. Dynamic simulations predict hour to hour
variations caused by tidal transport. Quasidynamic
simulations predict variations on the order of days to
months. The effects of tidal transport are time-aver-
aged. Other forcing functions such as freshwater in-
flow, pollutant loading, temperature, and sunlight may
vary from daily to monthly. Steady state simulations
predict monthly to seasonal averages. All inputs are
time-averaged. Two schools of thought have persisted
regarding the utility of dynamic versus quasidynamic
and steady state simulations. For some problems the
choice is reasonably clear.
In general, if the regulatory need or kinetic response is
on the order of hours, then dynamic simulations are
required; if regulatory needs are long term averages
and the kinetic response is on the order of seasons to
years, then quasidynamic or steady simulations are
indicated.
The goal of model selection is to obtain a simulation
model that effectively implements the conceptual
model identified for the WLA. Models selected for
discussion here are general purpose, in the public
domain, and available from or supported by public
agencies. The selection of an estuarine WLA model
need not be limited to the models discussed in this
document. Other models that are available to a project
or organization should also be considered. The models
summarized in this report represent the typical range
of capabilities currently available. Estuarine WLA mod-
els can be classified as Level I to Level IV according
to the temporal and spatial complexity of the hydrody-
namic component of the model. Level I includes desk-
top screening methodologies that calculate seasonal
or annual mean pollutant concentrations based on
steady state conditions and simplified flushing time
estimates. These models are designed to examine an
estuary rapidly to isolate trouble spots for more de-
tailed analyses.
Level II includes computerized steady state or tidally
averaged quasidynamic simulation models, which
generally use a box or compartment-type network to
solve finite difference approximations to the basic par-
tial differential equations. Level II models can predict
slowly changing seasonal water quality with an effec-
tive time resolution of 2 weeks to 1 month. Level III
includes computerized one-dimensional (1-d) and
quasi two-dimensional (2-d), dynamic simulation mod-
els. These real time models simulate variations in tidal
heights and velocities throughout each tidal cycle.
Their effective time resolution is usually limited to
average variability over one week because tidal input
parameters generally consist of only average or slowly
varying values. The effective time resolution could be
reduced to under 1 day given good representation of
diurnal water quality kinetics and precise tidal input
parameters. The required data and modeling effort are
usually not mobilized in standard WLAs.
Level IV consists of computerized 2-d and 3-d dynamic
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 reso-
lution of the Level IV models can be less than 1 day
with a good representation of diurnal water quality and
intratidal variations.
The advantages of Level I and II models lie in their
comparatively low cost and ease of application. The
disadvantages lie in their steady state or tidally aver-
aged temporal scale. When hydrodynamics and pollut-
ant inputs are rapidly varying, steady state models are
difficult to properly calibrate.
The dynamic models (Levels III and IV) have advan-
tages over steady state and tidally averaged models in
representing mixing in partially mixed estuaries be-
cause advection is so much better represented. The
success with which these models can predict transient
violations depends upon both the accuracy and reso-
lution of the loading and environmental data, and the
model's treatment of short time scale kinetics such as
desorption or diurnal fluctuations in temperature, pH,
or sunlight. While dynamic models are capable of pre-
dicting diurnal and transient fluctuations in water quality
parameters, the input data requirements are much
greater.
PART II: APPLICATION OF ESTUARINE
WASTE LOAD ALLOCATION MODELS
Monitoring Protocols for Calibration and
Validation of Estuarine Waste Load
Allocation Models
The monitoring data collected in support of a modeling
study is used to: (1) determine the type of model
application required (e.g. dimensionality, state 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
XIX
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or navigation charts). Data are also required for trans-
port. Transport within the modeled system may either
be specified (measured, e.g. current meters) or com-
puted from hydrodynamic models. Flows into the sys-
tem must be measured, or in the case of the open
boundary, water surface elevations must be deter-
mined.
The water quality data required, beyond that needed
to quantify transport, will vary depending on how the
variables will be used and their anticipated impact on
the system. Data requirements will differ if the WLA
modeling study is intended for dissolved oxygen, eu-
trophication or toxics. Concentrations for all pertinent
water quality variables should be provided at the model
boundaries, providing the perturbation for model pre-
dictions, as well as at points within the waterbody to
provide a basis for estimating model parameters and
evaluating model predictions. Data should be available
to determine variations in water quality parameters
over space and time.
Planning monitoring studies should be a collaborative
effort of participants involved in budgeting, field collec-
tion, analysis and processing of data, quality assur-
ance, data management and modeling activities.
Collaboration insures that fundamental design ques-
tions are properly stated so that the available re-
sources are used in the most efficient manner possible
and that all critical data for modeling are collected. The
use of monitoring and modeling in an iterative fashion,
wherever possible, is often the most efficient means of
insuring that critical data are identified and collected.
A rigorous, well documented, quality assurance, qual-
ity control (QA/QC) plan should be an integral part of
any waste load allocation program.
Model Calibration, Validation, and Use
While models can be run with minimal data, their
predictions are subject to large uncertainty. Models are
best operated to interpolate between existing condi-
tions or to extrapolate from existing to future condi-
tions, such as in the projection of conditions under
anticipated waste loads. The confidence that can be
placed on those projections is dependent upon the
integrity of the model, and how well the model is
calibrated to that particular estuary, and how well the
model compares when evaluated against an inde-
pendent data set (to that used for calibration).
Model calibration is necessary because of the semi-
empirical nature of present day (1990) water quality
models. Although the waste load allocation models
used in estuary studies are formulated from the mass
balance and, in many cases, from conservation of
momentum principles, most of the kinetic descriptions
in the models that describe the change in water quality
are empirically derived. These empirical derivations
contain a number of coefficients and parameters that
are usually determined by calibration using data col-
lected in the estuary of interest.
Calibration alone is not adequate to determine the
predictive capability of a model fora particular estuary.
To map out the range of conditions over which the
model can be used to determine cause and effect
relationships, one or more additional independent sets
of data are required to determine whether the model is
predictively valid. This testing exercise, which also is
referred to as confirmation testing, defines the limits of
usefulness of the calibrated model. Without validation
testing, the calibrated model remains a description of
the conditions defined by the calibration data set. The
uncertainty of any projection or extrapolation of a cali-
brated model would be unknown unless this is esti-
mated during the validation procedure.
In addition, the final validation is limited to the range of
conditions defined by the calibration and validation
data sets. The uncertainty of any projection or extrapo-
lation outside this range also remains unknown. The
validation of a calibrated model, therefore, should not
be taken to infer that the model is predictively valid over
the full range of conditions that can occur in an estuary.
For example, a model validated over the range of
typical tides and low freshwater inflow may not describe
conditions that occur when large inflows and atypical
tides occur.
This is especially true when processes such as sedi-
ment transport and benthic exchange occur during
atypical events but not during the normal, river flow and
tidal events typically used to calibrate and validate the
model.
Following model calibration and validation, several
types of analyses of model performance are of impor-
tance. First, a sensitivity analysis provides a method to
determine which parameters and coefficients have the
greatest impact on model predictions. Second, there
are a number of statistical tests that are useful for
defining when adequate agreement has been obtained
between model simulations and measured conditions
in order to estimate the confidence that may be as-
signed to model predictions. Finally, a components
analysis indicates the relative contribution of processes
to variations in predicted concentrations. For example,
the cause of violations of a dissolved oxygen standard
can be determined from the relative contribution of
various loads and the effect of sediment oxygen de-
mand, BOD decay, nitrification, photosynthesis, and
reaeration.
xx
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Once the model is calibrated and validated, it is then
used to investigate causes of existing problems or to
simulate future conditions to determine effects of
changes in waste loads as part of the waste load
allocation procedure. Once critical water quality con-
ditions are defined for the estuary, harbor or coastal
area of concern, determining the waste assimilative
capacity is relatively straightforward. Models are avail-
able to relate critical water quality responses to the
loads for most problems. However, the definition of
critical conditions for estuaries is not straightforward.
For streams receiving organic loads, this is a straight-
forward matter of determining the low flow and high
temperature conditions. In estuaries, fresh water,
tides, wind, complex sediment transport, and other
factors can be important to determining the critical
conditions. As of yet, there are no clear methods of
establishing critical conditions, especially in terms of
the probability of occurrence. The analyst must use
considerable judgement in selecting critical conditions
for the particular system. Once loads and either critical
conditions or estimated future conditions are specified,
the calibrated model can be used to predict the water
quality response. The investigation may involve study
of extreme hydrological, meteorological, or hydro-
graphic events that affect mixing; waste loadings from
point and non-point sources; and changes in benthic
demands.
Simplified Illustrative 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 calcu-
lator or spreadsheet. While they may not be suitable as
the sole justification for a WLA, they can be valuable
for initial problem assessment. Three screening meth-
ods are presented for estimating estuarine water qual-
ity impacts: analytical equations for an idealized
estuary, the fraction of freshwater method, and the
modified tidal prism method. These example proce-
dures are only applicable to steady state, one-dimen-
sional estuary problems.
Deterministic water quality modeling of estuarine sys-
tems can be divided into two separate tasks: descrip-
tion of hydrodynamics, and description of water quality.
The WASP4 model was designed to simulate water
quality processes, but requires hydrodynamic informa-
tion as input. Hydrodynamic data may be directly speci-
fied 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 summa-
rized, selected model results are shown, and certain
WLA issues are briefly described.
XXI
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Preface
The document is the third of a series of manuals
providing information and guidance for the preparation
of waste load allocations. The first documents provided
general guidance for performing waste load allocation
(Book I), as well as guidance specifically directed
toward streams and rivers (Book II). This document
provides technical information and guidance for the
preparation of waste load allocations in estuaries. The
document is divided into four parts:
Part 1 of this document provides technical information
and policy guidance for the preparation of estuarine
waste load allocations. It summaries the important
water quality problems, estuarine characterisitics and
processes affecting those problems, and the simulation
models available for addressing these problems. Part
two 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 estu-
arine systems. The third part summarizes initial dilution
and mixing zone processes, available models, and
their application in waste load allocation.
This part, "Part 4: Critical Review of Estuarine Waste
Load Allocation Modeling," summarizes several histori-
cal case studies, with critical review by noted experts.
Organization: "Technical Guidance Manual for Performing Waste Load Allocations. Book
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
XXIII
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1. Introduction
Robert B. Ambrose, Jr., P.E.
Center for Exposure Assessment Modeling
Environmental Research Laboratory, U. S. EPA, Athens, GA
1.1. Background
This document is the third in a series of manuals
providing technical information and policy guidance for
the preparation of waste load allocations (WLAs) that
are as technically sound as current state of the art
permits. The objective of such load allocations is to
ensure that water quality conditions that protect desig-
nated beneficial uses are achieved. An additional
benefit of a technically sound WLA is that excessive
degrees of treatment, that do not produce correspond-
ing improvements in water quality, can be avoided.
This can result in more effective use of available funds.
This guidance document contains seven elements: 1)
an overview of water quality problems and estuarine
characteristics, 2) descriptions of estuarine simulation
models, 3) descriptions of the monitoring and data
collection necessary for model application, 4) guidance
on the model calibration and validation, 5) simplified
example case studies, 6) review and discussion of past
WLA studies, and 7) guidance on use of mixing zone
models.
Table 1-1 lists the various "books" and "chapters" that
make up the set of technical guidance manuals.
303(d)/TMDL program guidance is currently under de-
velopment. This guidance will address programs and
procedural issues related to total maximum daily loads,
wasteload allocations, and load allocations
(TMDLs/WLAs/LAs).
Users of this manual also should be aware that other
information may affect the wasteload allocation proc-
ess. For instance, criteria and standards for DO, am-
monia, and other parameters are in a continuous
process of change. Therefore, any standards used in
examples contained in this chapter should not be ap-
plied to real-life situations without first consulting the
latest applicable criteria and standards.
Table 1-1. Organization of Guidance Manuals for Performance of Wasteload Allocations
BOOK I
303 (d)/TMDL PROGRAM GUIDANCE
BOOK
BOOK III
BOOK IV
Under development
STREAMS AND RIVERS
Chapter 1 - BOD/Dissolved Oygen Impacts and Ammonia Toxicity
Chapter 2 - Nutrient/Eutrophication Impacts
Chapter 3 - Toxic Substance Impacts
ESTUARIES
LAKES, RESERVOIRS AND IMPOUNDMENTS
Chapter 1 - BOD/Dissolved Oxygen Impacts and Ammonia Toxicity
Chapter 2 - Nutrient/Eutrophication Impacts
Chapter 3 - Toxic Substance Impacts
1-1
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1.2. Introduction to Estuaries
Estuaries are coastal bodies of water where fresh
water meets the sea. They are traditionally defined as
semi-enclosed bodies of water having a free connec-
tion with the open sea and within which sea water is
measurably diluted with fresh water derived from land
drainage (Pritchard, 1967). These classical estuaries
are the lower reaches of rivers where saline and fresh
water mix due to tidal action. The term has been
extended to include coastal waters such as bays and
sounds that receive riverine discharge. The backwater
river reaches draining into the Great Lakes have also
been included as estuaries.
Estuaries are biologically productive bodies of water.
They are the spawning and nursury grounds for many
important coastal fish and invertebrates. Thus they
support commercial and recreational fishing and shell-
fishing. Many are valuable for recreational boating and
bathing, and prized for their aesthetics. At the same
time, many estuaries house important harbors, ports,
and navigation channels. Many have been used to
dilute and flush municipal and industrial wastewater.
These various uses of an estuary may cause conflict-
ing demands and burdens on its water quality.
1.2.1. Factors Affecting Estuarine Water Quality
Estuaries are the crossroads of river, sea, atmosphere,
and sediment. Most rivers and their associated pollut-
ant loads eventually flow into estuaries. Many major
cities and ports are located on estuaries, affecting their
quality through domestic and industrial wastewater
and dredging. Estuarine circulation can trap nutrients
and other pollutants from these waste discharges, the
upstream river drainage basin, subsurface waters of
the coastal ocean, and atmospheric deposition. Under-
lying sediments can store and transform these pollut-
ants, either releasing them to the water or burying
them. Sedimentation processes are filling or altering all
estuaries in response to sea level changes, sediment
influx, and intra-estuarine circulation patterns (Shubel,
1971). The complex loading, circulation, and sedimen-
tation processes make water quality assessment and
waste load allocation in estuaries difficult.
As estuaries mix fresh water with sea water, their
chemistry varies dramatically in space as well as with
time. Average values of the major constituents of
seawater, and average concentrations and ranges for
macronutrients are reported in Table 1 -2 . As a general
rule, in sea water nitrogen limits phytoplankton produc-
tivity, whereas in fresh water, phosphorus is the pri-
mary limiting nutrient. In estuaries, either nutrient may
limit growth.
The importance of atmospheric nitrogen deposition to
estuaries has recently received attention with esti-
mates that up to 39% of nitrogen reaching Chesapeake
Bay originated in atmospheric deposition (Fisher, et al,
1988). Nitrogen may deposit to watersheds or directly
to estuaries in rainfall and dryfall, which includes the
deposition of particles greater than 3 microns, aerosol
impaction, and gas absorption. A significant amount of
nitrogen input to a watershed is removed through de-
nitrification. Estimates range from 20 - 75% (Waddell,
1989). Annual nitrogen inputs of inorganic nitrogen in
bulk precipitation across the United States range from
0.1 g/m2/year in some western locations to as high as
0.8 g/m /year in the east. Organic nitrogen inputs range
from 0.1 to 0.4 g/m2/year (Waddell, 1989). Dry deposi-
tion may account for about the same input, doubling
the total nitrogen inputs.
1.2.2. Estuarine Transport
Transport and circulation processes in estuaries are
driven primarily by river flow and tidal action. In shallow
estuaries, wind stress can dominate transport. Longi-
tudinal salinity gradients lead to a net upstream drift of
heavier sea water. Strong river flow or weak tidal mixing
can lead to vertical stratification, where relatively fresh
water flows over saline bottom water. Entrainment of
bottom water may dilute pollutants in the surface, but
upstream transport of salt and pollutants can occur
along the bottom. Coriolis acceleration, deflecting cur-
rents to the right in the northern hemisphere, may be
significant in large estuaries.
As a consequence of these complex transport proc-
esses, estuaries cannot be treated as simple advective
systems such as many rivers. In rivers, flushing of
pollutants is driven primarily by advection. In estuaries,
however, both advection and dispersion must be con-
Table 1-2. Major Constituents and Macronutrients in
Seawater [Smith (1974)]
Constituent
chloride
sodium
magnesium
sulfate
calcium
potassium
bicarbonate
bromine
silicon
nitrogen
phosphorus
Average Cone.
(mg/L)
19350.0
10760.0
1300.0
2700.0
400.0
400.0
145.0
67.3
2.0
0.28
0.03
Cone. Range
(mg/L)
0.0-4.9
0.0-0.56
0.0-0.09
1-2
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sidered. Equations and models used for riverine waste
load allocation must be carefully considered before
application to estuaries.
1.3. Potential Problems to Address
Wastewater discharges into estuaries can affect water
quality in several ways, both directly and indirectly. In
setting limits on wastewater quantity and quality, all
potential problems should be assessed. Wastewater
limits should be set to assure attainment of water
quality standards.
13.1 Salinity
Salinity is important in determining available habitat for
estuarine organisms. Large wastewater discharges
into relatively small estuaries orembayments can alter
the local salinity regime through dilution. Large saline
discharges could introduce excess salinity into fresh-
water embayments of the Great Lakes. Even when the
salinity is not affected by the discharge, it is measured
and modeled in order to quantify advection and disper-
sion. These processes help determine how wastewa-
ter is assimilated into the estuary.
13.2. Sediment
Sediment enters estuaries from many sources, and
can alter the habitat of benthic organisms. Sediment is
also an important carrier of such pollutants as hydro-
phobic organic chemicals, metals, and nutrients. Sedi-
ment transport can move pollutants upstream, or
between the water column and the underlying bed.
Even when wastewater does not introduce excess
sediment into an estuary, it is often measured and
modeled in order to quantify the transport of sediment-
bound pollutants.
13.3. Bacteria and Viruses
Bacteria and viruses may enter estuaries in runoff from
farms and feedlots and in effluent from marinas as well
as from municipal or industrial wastewater discharges.
These pathogens may be transported to bathing
beaches and recreational areas, causing direct human
exposure and possibly disease. Pathogens also may
be transported to shellfish habitat; there they may
accumulate in oysters, clams, and mussels and, sub-
sequently, cause disease when eaten by humans.
134. Dissolved Oxygen Depletion
Adequate, sustained DO concentrations are a require-
ment for most aquatic organisms. Seasonal or diurnal
depletion of DO, then, disrupts or displaces estuarine
communities. Ambient DO levels are affected by many
natural processes, such as oxidation of organic mate-
rial, nitrification, diagenesis of benthic sediments, pho-
tosynthesis and respiration by phytoplankton and
submerged aquatic vegetation, and reaeration. The
natural balance can be disrupted by excessive waste-
water loads of organic material, ammonia, and nutri-
ents. Other sources of nutrients, such as runoff from
agricultural, residential, and urban lands and atmos-
pheric deposition, also can disrupt the DO balance.
Excessive heat input from power plants can aggravate
existing problems. Because of its intrinsic importance,
and because it is affected by so many natural and
man-influenced processes, DO is perhaps the best
conventional indicator of water quality problems.
135. Nutrient Enrichment and Overproduction
Adequate concentrations of nitrogen and phosphorus
are important in maintaining the natural productivity of
estuaries. Excessive nutrient loading, however, can
stimulate overproduction of some species of phyto-
plankton, disrupting the natural communities. Periodic
phytoplankton "blooms" can cause widely fluctuating
DO concentrations, and DO depletion in benthic and
downstream areas. Nutrient loads can be introduced in
wastewater and runoff and through atmospheric depo-
sition.
136. Aquatic Toxicity
Ammonia, many organic chemicals, and metals, at
often very low concentrations, can disable or kill
aquatic organisms. Acute toxicity is caused by high
exposure to pollutants for short periods of time (less
than 4 days). Chronic toxicity is caused by lower expo-
sures for long periods of time (greater than four days).
The toxicity of a chemical can be affected by such
environmental factors as pH, temperature, and sedi-
ment concentrations. Overall toxicity results from the
combined exposure to all chemicals in the effluent and
the ambient waters.
13 7. Bioaccumulation and Exposure to Humans
Lower concentrations of organic chemicals and metals
that do not cause aquatic toxicity can be taken up and
concentrated in the tissues of estuarine organisms. As
fish predators consume contaminated prey, bioaccu-
mulation of these chemicals can occur. This food chain
contamination can persist long after the original chemi-
cal source is eliminated. Humans that regularly con-
sume tainted fish and shellfish can receive harmful
doses of the chemical.
Human exposure to harmful levels of organic chemi-
cals and metals can also occur through drinking water
withdrawals from fresh water tidal rivers.
1.4. Overview of the Waste Load Allocation
Book I, 303 (d)/TMDL Guidance discusses the overall
TMDL process, procedures, and considerations. The
1-3
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reader is referred to this book for procedural guidance.
This book gives specialized modeling guidance.
A WLA provides a quantitative relationship between
the waste load and the instream concentrations or
effects of concern as represented by water quality
standards. The reliability of this relationship depends
upon the accuracy and completeness of the data,
certain characteristics of the model, and the skill and
judgment of the modeler. During the development of a
WLA, the user combines data and model first to de-
scribe present conditions and then to extrapolate to
possible future conditions. The process is iterative:
observed data are used to refine model input (or even
model equations) and modeling results are used to
guide monitoring efforts.
The WLA process sequentially addresses the topics of
hydrodynamics, mass transport, water quality kinetics,
and for some problems, bioaccumulation and toxicity.
141 Hydrodynamics
The topic of hydrodynamics addresses where the
water goes. Both primary and secondary water circu-
lation patterns can significantly affect water quality. In
some estuaries, monitoring programs can adequately
quantify the primary circulation patterns associated
with tidal excursions and tributary inflow. Hydrody-
namic models may be needed, however, to investigate
secondary currents associated with the net residual
tidal action, wind, density differences, or Coriolis accel-
eration. Hydrodynamic models also may be used to
interpolate data between monitoring stations or to ex-
trapolate data to future conditions. The final result of
the hydrodynamics study is a record of water flow and
volume (orvelocity and elevation) throughout the water
body over an appropriate period of time.
142. Mass Transport
Mass transport addresses the fate of dissolved, non-
reactive substances. These tracers are subject to ad-
vection with the water currents and to turbulent
diffusion. If only the primary circulation is resolved in
the hydrodynamics step, then secondary circulation,
such as density currents and lateral shear, are para-
meterized into dispersion coefficients. The values of
these coefficients are determined by calibrating the
model to salinity or dye tracer data. This calibration
process also can be used to refine the advective flows
estimated in the hydrodynamics step. Recalibration of
advective flows based on tracer data can be particu-
larly important in cases where net tributary inflow to the
estuary is uncertain. The final result of the mass trans-
port step is a record of advective and dispersive fluxes
(or the appropriate model coefficients) for dissolved,
nonreactive substances throughout the water body
over the period of study.
143. Water Quality Kinetics
Water quality kinetics describe what happens to a set
of physical, chemical, and biological constituents as
they are transported throughout the water body. The
set of constituents modeled depends upon the water
quality problem of concern. General models are avail-
able describing the primary constituents and reactions
for the water quality problems outlined in this manual.
For most WLA studies, the user must provide appropri-
ate site-specific values for the reaction coefficients and
the environmental conditions (such as temperature,
sunlight, and pH). In some complex studies, the user
may have to modify model equations describing the
reactions or add more simulated constituents. Although
literature values are available to guide initial model
parameterization, local monitoring data are required to
refine these values and construct a site-specific model.
The user arrives at appropriate parameter values
through an iterative model calibration and testing proc-
ess. The final result of the water quality kinetics step is
a record of constituent concentrations throughout the
water body for the period of study and for hypothetical
future periods under various waste load management
strategies.
144 Bioaccumulation and Toxicity
Often, water quality constituent concentrations (or tox-
icity units) are directly compared with appropriate
standards to infer potential risk to humans or the
aquatic community. Waste loads may be adjusted so
that concentrations do not exceed (or fall below) these
standards under design conditions. Alternatively,
waste loads may be adjusted so that concentrations
exceed standards for less than a specified frequency
and duration over a realistic range of future conditions.
Recent advances in environmental toxicology allow the
direct calculation or simulation of bioaccumulation and
toxicity for some classes of chemicals. To simulate
bioaccumulation by individual fish (or a local species of
fish), the user must specify an exposure scenario plus
a few physiological parameters. Although literature
values for the parameters are available, monitoring
data should be used for site-specific calibration. Direct
toxicity due to the narcotic effects of neutral hydropho-
bic organic chemicals can be predicted. To simulate
food chain bioaccumulation, the user must define the
main components of the local food web (who eats
whom), and calibrate the physiological parameters for
each. This task requires considerable judgment and a
good data base.
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1.5. Steps in the Modeling Process
For each of the topics addressed in a modeling study,
several steps are applied in an iterative process. The
first step is problem identification. The modeler reviews
existing data related to all potential problems, which
were discussed in Section 1.2. The second step is
model identification. Starting with knowledge of the site
and the water quality problems of concern, the modeler
reviews existing data and identifies an appropriate
simulation model or data base. Additional monitoring
is planned to gain further knowledge about existing
conditions and important processes.
The third step is initial calibration of the model to
existing data. Where site-specific data are lacking,
literature values and user judgment are employed.
Sensitivity analysis is used to estimate the uncertainty
in model predictions due to each uncertain input. This
information can be used to guide ongoing monitoring
efforts.
As more data sets become available, the calibrated
model is tested and refined. Recalibration should ad-
dress all previous data sets. Throughout this step, the
user should be guided by the principle of parsimony -
calibration and validation of the model should be ac-
complished with the fewest possible parameters. A
single longitudinal dispersion coefficient that ade-
quately represents an entire estuary is preferable to a
series of coefficients that allow a slightly better fit to
data. Model parameter values should be consistent
across the range of tested data. If values must vary,
they should follow some rational function. This func-
tional relationship becomes an external part of the
model that should be documented and tested.
After some effort at recalibration and testing, the
modeler decides either that the model is sufficiently
reliable to produce a sound waste load allocation, or
that available time and resources do not permit contin-
ued refinement. At this point, the degree of model
validation must be assessed. Traditional practice dic-
tates that an independent data set be used for a final
validation test of the model. Sometimes such a data
set is unavailable, or has already been used in the
recalibration process. In any case, a final uncertainty
analysis should document the model's expected reli-
ability over the range of conditions tested. Validation is
contingent upon the waste load options to be consid-
ered. A model may be considered valid to study some
options, but invalid to study others.
After the WLAs have been put into effect, some degree
of monitoring should be pursued to track the effective-
ness of the actual waste load reductions in meeting
water quality goals. When sufficient data are available,
a post-audit should test model predictions under the
new conditions. Refinements in the model at this point
may guide refinements in the waste load allocation and
contribute to more informed judgment in future studies
involving similar pollutants and estuaries.
1.6. Organization and Scope
The basic estuarine guidance document is comprised
of four parts. Part 1, "Estuaries and Waste Load Allo-
cation Models," summarizes the important water qual-
ity problems, estuarine characteristics and processes
affecting these problems, and the simulation models
that are available for addressing these problems. Part
2, "Application of Estuarine Waste Load Allocation
Models," provides a guide to monitoring and model
calibration and testing, and a case study tutorial on
simulation of waste load allocation problems in simpli-
fied estuarine systems.
Part 3, "Use of Mixing Zone Models in Estuarine Waste
Load Allocations," summarizes initial dilution and mix-
ing zone processes, available models, and their appli-
cation in waste load allocation. Part 4,"Critical Review
of Estuarine Waste Load Allocation Modeling," summa-
rizes several historical case studies, with critical re-
views by noted experts.
1.7. References
Fisher, D., Ceraso, J., Mathew, T., and Oppenheimer,
M. 1988. Polluted Coastal Waters: The Role of Acid
Rain. Environmental Defense Fund, New York.
Pritchard, D.W. 1967. What is an Estuary: Physical
Viewpoint. Estuaries, ed: Lauff, G.H., American Asso-
ciation for the Advancement of Science, Publication
No. 83, Washington, D.C.
Shubel, J.R. 1971. The Origin and Development of
Estuaries. The Estuarine Environment-Estuaries and
Estuarine Sedimentation. American Geological Insti-
tute.
Smith, F.G.W., ed. 1974. CRC Handbook of Marine
Science, Vol. I. CRC Press, Cleveland, OH.
Waddell, T.E. 1989. Draft Report: State of the Science
Assessment: Watershed and Estuarine Nitrogen
Transport and Effects. U.S. Environmental Protection
Agency, Athens, GA.
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2. Overview of Processes Affecting Estuarine Water Quality
James L. Martin, Ph.D., P.E.
AScI Corp., at the
Center for Exposure Assessment Modeling
Environmental Research Laboratory, U. S. EPA, Athens, GA
Robert B. Ambrose, Jr., P.E.
Center for Exposure Assessment Modeling
Environmental Research Laboratory, U. S. EPA, Athens, GA
John F. Paul, Ph.D., P.E.
Environmental Research Laboratory, U.S. EPA,
Narragansett, Rl
2.1. Organization Of This Section
This section is organized into six major parts. Section
2.2 contains an overview of estuarine morphology and
classification. A more detailed description of physical
processes impacting estuarine circulation and mixing
is provided in Section 2.3. Subsequent parts of Section
2 deal with major processes affecting water quality,
including sediment transport and sediment water qual-
ity interactions (Section 2.4), organic wastes, dissolved
oxygen (DO) and nutrients (Section 2.5), synthetic
organic chemicals (Section 2.6), and metals (Section
2.7). Sections 2.2 to 2.7 provide an overview of proc-
esses followed by supplemental text describing in
greater detail how each of these basic processes are
described in estuarine waste load allocation (WLA)
models.
2.2. Estuarine Morphology and Classification
The geomorphology of estuaries strongly affects the
transport of pollutants and ultimately their water quality
characteristics. Estuarine depth controls propagation
of the tidal wave. Shallow channels and sills increase
vertical mixing; deep channels are more likely to be
stratified and to have greater upstream salinity intru-
sion. Shallow sills near the mouth of an estuary may
limit circulation and flushing of bottom waters. The
length of the estuary and conditions at the upstream
boundary determine the type of tidal wave, the phase
between current velocities, and the tidal heights. The
width affects velocities (narrow constrictions increase
vertical mixing and narrow inlets restrict tidal action).
Wind-induced circulation is transient and interacts with
channel geometry to produce various circulation pat-
terns. Estuaries have typically been classified based
on their geomorphology and patterns of stratification
and mixing.
Based on their hydrodynamics, estuaries have been
classified as sharply stratified, partially stratified and
well mixed (Bowden 1967, Pritchard 1967). Sharply
stratified estuaries exhibit little mixing between the salt
wedge and fresh water flow. Examples include fjords
and salt-wedge estuaries, such as the Mississippi River
estuary. In sharply stratified estuaries tidal action is not
sufficient to mix the separate layers. Completely mixed
estuaries do not exhibit significant vertical density vari-
ations and tidal flow is normally greaterthan fresh water
inflow. Examples of this include the Delaware and
Raritan River estuaries which are normally well mixed.
Partially stratified estuaries are intermediate between
sharply stratified and completely mixed estuaries. Par-
tially stratified estuaries exhibit significant vertical den-
sity gradients but the gradients are less sharp than in
sharply stratified estuaries. Examples include the
James River Estuary (Mills et al. 1985).
Hannsen and Rattray (1966) proposed a classification
scheme based on vertical variations in salinity and the
strength of the internal density-driven circulation. A
stratification parameter is computed from the vertical
salinity gradient which is then compared to a circulation
parameter computed from net surface and fresh water
flow velocities. These parameters are calculated at
various points along the estuarine channel and may be
used to estimate degree of stratification of the system.
Further description of the method is provided by Mills
etal. (1985).
Based on their geomorphology, typical classifications
(Fischer et al. 1978) are: (1) drowned river valleys or
coastal plain estuaries (e.g., Chesapeake Bay, Dela-
ware Estuary), (2) bar-built estuaries (e.g., Galveston
Bay, Pamlico Sound), (3) fjords (e.g., Puget Sound),
and (4) other diverse formations (e.g., San Francisco
Bay).
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Coastal plain estuaries are generally broad and rela-
tively shallow (rarely over 30 m in depth) with gently
sloping bottoms and depths increasing uniformly to-
wards the mouth and with extensive areas of deposited
sediment. Such estuaries usually have been cut by
erosion and are drowned river valleys, often displaying
a dendritic pattern fed by several streams. Coastal
plain estuaries are usually moderately stratified and
can be highly influenced by wind. The majority of
estuaries in the contiguous United States are of the
drowned river or coastal plain type.
Bar-built estuaries are bodies enclosed by the deposi-
tion of a sand bar off the coast through which one or
more channels provide exchange with the open sea.
These are usually unstable estuaries, subject to grad-
ual seasonal and catastrophic variations in configura-
tion. Many estuaries along the Gulf Coast and Lower
Atlantic regions are of this type. They are generally
shallow (e.g. a few meters deep or less), often vertically
well mixed, and highly influenced by wind.
Fjords are generally long and narrow with steep sides
and relatively deep waters. They typically are strongly
stratified and have shallow sills at the estuarine mouth
that often limit mixing of deep waters. They usually are
formed by glaciation and are typically found in Alaska.
The fresh water streams that feed a fjord generally
pass through rocky terrain. Little sediment is carried to
the estuary and the bottom is likely to be a rocky
surface.
Estuaries not covered by the above classifications
usually are produced by tectonic activity, faulting, land-
slides or volcanic eruptions. An example is San Fran-
cisco Bay which was formed by movement of the San
Andreas Fault system (Mills et al. 1985).
2.3. Factors Affecting Circulation And Mixing
Estuaries and coastal seas have circulation patterns
that are highly variable in time and space. Awareness
of characteristic time and space scales of flows gener-
ated by the tides, winds, density gradients resulting
from the interaction of fresh and ocean water, and the
effects of the earth's rotation (the Coriolis force) will
help to define the mixing regime of the water body.
Estuaries generally are large water bodies that have
more vigorous circulations than occur in rivers and
most lakes. Like rivers and lakes, however, internal
factors such as friction and vertical mixing play similar
physical roles in the marine environment to those in
fresh water systems in the redistribution of pollutants.
The existence of stratification (vertical density gradi-
ents) in estuaries, as well as the more complex external
forcings (such as tidal fluctuations), modify the effects
of vertical mixing and friction to the extent that parame-
terizations used to evaluate mixing in fresh water must
be used with caution if at all. This section briefly
discusses the physical forces affecting estuaries. More
extensive discussions can be found in standard texts
on estuaries such as that by Fischer et al. (1978).
2.3.1 Tides
The ocean tides are produced principally by interaction
of the gravitational fields of the earth, moon, sun and,
to a lesser degree, other solar system bodies. The
principal effects are caused by the moon and occur on
a roughly 12.4-hour period. Solar effects occur at 1-day
periods. Because all the bodies in the solar system are
in motion relative to one another, the effects of their
gravitational fields vary in time. One result is the familiar
spring-neap cycle of tides. Astronomical tidal motion is
highly predictable. Such information is published annu-
ally in the National Ocean Service Tide Tables and
Tidal Current Tables. Tide tables provide predictions of
times and heights of high and low water. Tidal current
tables provide predicted times, magnitudes and direc-
tions of maximum ebb and flood and high and low water
slacks for principal coastal stations referenced to the
standard locations.
Tides are expressed in terms of amplitude (the vari-
ation of water level about some datum level) and tidal
current (the ebb and flood velocity fields). Tidal ampli-
tudes in North America vary from tenths of meters in
the Gulf of Mexico to more than 10 meters in parts of
Alaska and the Canadian Maritime Provinces. Tidal
current magnitudes are also highly variable, with the
highest values being recorded in topographically con-
strained straits. Tidal amplitude and tidal current are
usually out of phase so the time of high water is not the
same as the time of high water slack. Such differences
in phase and interaction between main and side chan-
nels can lead to tidal trapping of parcels of water in side
channels or embayments.
The effect of the tides is to cause: (1) time-variable
mixing through frictional interaction with the bottom and
(2) spatially asymmetric flow patterns on ebb and flood
through interaction with the bottom topography. The
interactions of the tides with other driving forces and
with topography also may result in residual circulation
patterns of small magnitude but great persistence,
which could play a significant role in the transport of
pollutants.
2.3.2. Earth's Rotation Effects -Coriolis Force
The effect of the earth's rotation on the motion of fluids
is to deflect the flow to the right (left) in the northern
(southern) hemisphere. In estuaries wide enough to be
affected by this force, the effect is to move less dense
water to the right (left) side, looking seaward, of the
estuary. A further effect is that the interface between
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waters of different densities tends to be sloped as the
pressure gradient forces and the Coriolis force balance
each other to achieve geostrophic balance. The effect
can be enhanced in estuaries by the action of the tides
and can result in regions of persistent inflow of sea
water on the left and outflow of fresher water on the
right. The Coriolis effect is considered important for low
Rossby numbers (NR<0.1, where NR is the Rossby
number, the ratio of the inertial force to the Coriolis
force).
The time scale for rotational effects is the local inertial
period, which increases north to south. Inertial periods
for the contiguous states range from about 15 hours in
Washington state to 30 hours in southern Florida. The
appropriate length scale in estuaries is the internal
Rossby radius, which is the ratio of the internal wave
speed to the local inertial frequency. This length scale
accounts for both local density structure (degree of
stratification) and water depth.
2.3.3. Fresh Water Inflow
Fresh water inflow volume to an estuary can vary from
short-term response to local storms or the passage of
hurricanes to seasonal wet and dry cycles. In some
estuaries, the volume of fresh water is sufficient to
maintain a density difference over large distances be-
fore being completely mixed into sea water. Such
density differences result in flow patterns that tend to
maintain the density differences. Areas with high gra-
dients, the pycnocline and fronts, tend to resist the
localized processes of mixing and may result in "pools"
of fresher water confined along one section of the
coast. Examples include the Chesapeake Bay Plume
and a band of fresher water confined within about 15
km of the shore along the South Atlantic Bight (Georgia
and the Carolinas). Pollutants introduced into these
waters may be confined there for relatively long peri-
ods.
Increased fresh water inflow can change the character
of an estuary from well-mixed to partially mixed or
possibly stratified. Decreased inflow could have the
opposite effect with concomitant increased upstream
intrusion of sea water. Such changes in the vicinity of
an outfall can change the degree of mixing of the
effluent. Fresh water inflow varies primarily on sea-
sonal scales but large amounts of fresh water can be
introduced to estuarine systems by severe storms,
especially tropical cyclones along the East and Gulf
Coasts during late summer and fall. The response of
estuarine circulation to changes in fresh water flow will
vary according to the type of estuary. The time scale
of the response is roughly the flushing time of the water
body, which can vary from a few days for an estuary
with large fresh water flows and strong tides (the
Columbia River estuary) or for numerous shallow es-
tuaries along the Gulf Coast (the Brazos River and
Colorado River Estuaries) to several months for an
estuary that is shallow and has weak tides such as
Pamlico Sound.
2.34. Friction and Vertical Mixing
Friction is the term in the equations of fluid motion that
accounts for the dissipation of energy by small scale
turbulent motions. Similarly, turbulence generated by
vertical shear in the fluid tends to mix dissolved con-
stituents and acts to reduce sharp vertical gradients.
Friction forces retard or change the direction of fluid
flow. The friction term is used here to parameterize the
turbulent transfer of momentum and mass within a fluid
or between the fluid and the boundaries, such as
between the atmosphere and the water (wind stress)
or between the water and the bottom. Frictional effects
are seen in the formation of turbulent boundary layers
in fluids and in the turbulent mixing of properties in
those layers. Frictional effects have rather short time
scales for small scale turbulence but several hours may
be required for the frictional spin-down of a fluid flow
after its driving force is removed. Bottom boundary
layers may have vertical scales up to 10 meters,
whereas horizontal boundary layers can be several
kilometers wide. In general, the effects of horizontal
boundary layers are ignored and efforts concentrate on
the vertical layers caused by wind stress and bottom
interactions. Because the scale of the vertical layers is
small, shallow water is more easily affected by friction
than deep ocean waters. Generally, the stronger the
flows, either due to tides or wind effects, the more
turbulent the water column with a tendency for rapid
vertical mixing.
2.35. Meteorological Effects
Meteorological effects considered here are the result
of both local and remote wind forcing and other atmos-
pheric pressure forcing separate from the wind. Rainfall
as an input of fresh water is considered separately.
Wind effects include generation of persistent circula-
tion patterns caused by seasonal weather changes in
a particular area, modification of circulation patterns by
localized weather, and generation of waves and storm
surges. Water responds to an applied wind stress
within a few hours and to the cessation of the wind in
about the same time frame. The winds vary on a variety
of time scales, such as diel variations (sea breeze), the
time scale of frontal passages and the seasonal
changes in prevailing winds. Variability of wind speed
and direction over periods shorter than the frontal
passage scale will be evidenced primarily in the pro-
duction of turbulent mixing within a few meters of the
surface.
Atmospheric pressure affects sea level through the
"inverse barometer" effect where low atmospheric
pressures cause the sea level to be higher than normal
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(about 1 cm per millibar) and high atmospheric pres-
sure lowers the sea level. This effect and those asso-
ciated with strong winds (wind setup and setdown)
modify the astronomical tides and are called meteoro-
logical tides.
In estuaries with relatively small input of fresh water
and small tide range, such as Mobile Bay, Alabama,
wind is the dominant force in driving the overall circu-
lation and in generating turbulent mixing. The wind
driven circulation has time scales of a few days at the
period of local frontal passages. On open coastlines
the winds are also the dominant forcing mechanism
through the generation of long-period waves(length
scales of order 100 to 1000 km, time scales 2 to 10
days). Sea level fluctuations due to strong storms (i.e.
winter or extratropical cyclones) are called storm
surges which can have devastating effects on low lying
coastal regions. In this way, both local and remote
winds can play a large role in the dynamics of an open
coast.
See Supplement I for greater detail on how
processes affecting circulation and mixing are
described in estuarine models. This Supple-
ment is found on page 2.10 at the end of this
chapter.
2.4. Sediment Transport and Sediment/Water
Quality Interactions
2.4.1 Concepts
Sediment typically is associated with agricultural and
urban runoff. Sediment not only affects water trans-
parency, but can carry chemicals such as nutrients and
toxic substances into receiving waters. Therefore, an
important aspect of water quality modeling is the capa-
bility to simulate sediment transport and sedi-
ment/water interactions.
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.
Sediments are also in a constant state of flux due to
the time varying currents in estuaries, and movement
of sediments along the bottom often does not occur in
a net downstream direction as in stream reaches.
Consequently estuaries tend to trap sediments (Mills
etal. 1985).
Estuarine sediment transport has two main compo-
nents — bed load and suspended load — both of which
may be important.
Even when no sediment is transported by the flow,
deposited sediments can have a strong influence on
water quality in the overlying water. Through adsorp-
tion, biofilm assimilation and other chemical/biochemi-
cal transformations, sediments can become sinks or
sources of materials such as oxygen, toxic chemicals,
or nutrients.
For water quality assessment purposes, the finer frac-
tions of materials (silts, clays, organic detritus and live
plankton materials) are often of most importance. Par-
ticles are characterized by size, shape, density, surface
area, and surface physical and chemical properties
including electric charge. A review of particle regime
composition, behavior and interaction with water den-
sity was given by Lai (1977).
2.4.2. Processes
2.4.2.1. Fall Velocities, Settling, Deposition
For water quality modeling, the fall velocity of particles
and their resistance to resuspension under shear
stress, once they are deposited, are most significant.
Fall velocities are functions of size, shape (drag coef-
ficient) and density (of both the water and particle) and
can be reasonably well predicted for larger mineral
particles (Dietrich 1982; Gibbs et al. 1971). For mi-
crometer-size particles and particularly for organic par-
ticles, the large diversity in sizes, shapes, and density
(Lai 1977; Ives 1973) often require indirect determina-
tions of fall velocities from settling traps or mass bal-
ances. Settling velocities are used to calculate the
movement of sorbed chemical downward through the
water column. The settling characteristics of particles
may vary as they respond to water quality conditions in
an estuary (See 2.4.2.4.).
2.4.2.2. Resuspension, Scouring, Erosion
The resuspension or entrainment of sediments is a
function of the sediment properties, and flow-induced
shear stress at the sediment-water interface. For non-
cohesive sediments, this relationship is "explosive" in
nature. Very low or no resuspension occurs until a
threshold shear stress is reached. Then resuspension
rates increase in proportion to some power of the
excess shear stress.
For cohesive sediments, which are of primary interest
in water quality studies, entrainment is affected by
salinity, sediment type, microfauna, organic content,
and the time-history of the bottom sediments (Sheng
1983). Bed compaction may result in there being a finite
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amount of sediment that can be entrained at a given
shear stress (Lick et al. 1987), where the amount
depends upon the time-history of the bottom sediment,
rather than entrainment depending solely on particle
density and shear velocity. The lack of well established
descriptions of entrainment for cohesive particles re-
quires site-specific calibration to refine initial esti-
mates.
2.4.2.3. Cohesion
Cohesion of particles in the deposited bed increases
the resistance to resuspension and is a function of
consolidation history (Stefan, Ambrose and Dortch
1988). Investigations of this behavior have been re-
viewed by Mehta (1986). In addition to bedshear,
stresses due to wind driven flows and perturbations by
boat movement or organisms (bioturbation) can greatly
increase rates of resuspension of cohesive sediments.
Resuspension effects of wind have been conceptual-
ized by Rodney and Stefan (1987).
2.4.2.4. Coagulation and Flocculation
Extremely fine particles often destabilize (coagulate) in
regions of significant salinity gradients and agglomer-
ate to form larger particles (flocculate). The resulting
floe may then settle at a much different rate, due to the
greater agglomerated mass, than the individual parti-
cles. Coagulation occurs when electrolytes, such as
sodium chloride, neutralize the repulsive forces be-
tween clay particles allowing them to adhere upon
collision (flocculate). Flocculation rates are dependent
upon the size distribution and relative composition of
the clays and electrolytes and upon local boundary
shear stresses (Mills et al. 1985; Stefan, Ambrose and
Dortch 1988).
2.4.2.5. Sorption
Suspended sediment, besides being a very important
water quality parameter in its own right, also can have
a very strong relationship with chemical species dis-
solved in the water through adsorption/desorption, for
example, of nutrients or synthetic organics (often toxic
materials). This is an area of very active research (e.g.
Golterman et al. 1983; Stumm and Morgan 1981;
Karickhoff 1984) and will be addressed in a later sec-
tion in more detail.
2.4.2.6. Bottom Boundary Layer
The interaction between particles and water chemistry
becomes particularly complex near the bed because
of: (a) strong vertical velocity gradients associated with
shear forces; (b) activities of organisms such as
biofilms, invertebrates, crustaceans andfish; and (c)
pore water movement, which leaches into and out of
the outlying waters.
Microcosm models or measurements of these systems
are necessary to provide the input or withdrawal rates
of dissolved substances. Examples include sedimen-
tary oxygen demand (Chen et al. 1984, Gantzer et al.
1988), phosphorus release and polychlorinated
biphenyl (PCB) resuspension.
See Supplement II for greater detail on sedi-
ment transport and sediment/ water quality
interactions. This Supplement is found on
page 2-18 at the end of this chapter.
2.5. Organic Wastes, Dissolved Oxygen And
Nutrients
2.5.1 Concepts
This section is a brief overview of the common proc-
esses used to model organic wastes, DO and nutrients
(referred to as conventional pollutants) and their inter-
actions. For more detailed information, the reader
should refer to other resources (Bowie et al. 1985;
Orlob 1983; Chapra and Reckhow 1983; Thomann and
Mueller 1987). The focus of WLA models of conven-
tional pollutants is often DO and biochemical oxygen
demand (BOD) as a general measure of the health of
the system, or the focus can be primary productivity
when eutrophication is the major concern. Conven-
tional WLA models usually include temperature, major
nutrients, chemical characteristics, detritus, bacteria,
and primary producers. WLA models may include
higher trophic levels (i.e. zooplankton and fish) be-
cause of their effects on other more important vari-
ables, such as phytoplankton, BOD and DO.
Zooplankton and fish also provide a means of control-
ling lower trophic levels, which can affect nutrients and
DO (bio-manipulation). Additional information on mod-
eling these processes is provided in Section 3.
2.5.2. Fate Processes
Upon entry to the estuary, settling of particulate organic
matter and particulate nutrients generally occurs. High
flow events may scour previously deposited material.
Organic matter is oxidized, drawing upon the DO sup-
ply, which is replenished by reaeration.
Organic nitrogen is mineralized to ammonia, which
reaches equilibrium with its ammonium form. Nitrifica-
tion further draws upon the DO supply converting am-
monia to nitrite and then nitrate. Nitrate may be
converted back to ammonia or to nitrogen gas through
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denitrification in low DO regions of the estuary. Ammo-
nia and nitrate may be taken up by phytoplankton and
aquatic plants and incorporated into the food chain,
eventually returning to the water as organic nitrogen.
Organic phosphorus is mineralized to orthophosphate,
which reaches sorptive equilibrium with suspended or
benthic sediment. Particulate sorbed phosphate set-
tles; dissolved phosphate is rapidly taken up by phyto-
plankton and aquatic plants and incorporated into the
food chain, eventually returning to the water as organic
phosphorus.
Organic material deposited to benthic sediment is oxi-
dized in the upper aerobic layer, and reduced in the
lower anaerobic layers. Upward fluxes of ammonia and
reduced organic species are produced, the latter con-
tributing to sediment oxygen demand.
The transfer, or flux of phosphorus, across the sedi-
ment water interface is enhanced by anaerobic condi-
tions as particulate phosphorus may be resolubilized
and reenterthe water. In some aquatic environments,
net sedimentation buries a substantial fraction of the
nutrients and organic matter deposited to the bed.
Although many of these interacting fate pathways are
well known and included in most recent conventional
water quality models, accurate simulations remain dif-
ficult. Extensive site-specific data collection is required
to characterize both the sources and the process rates
over the range of expected conditions. Many of the
rates are biologically mediated, with descriptive con-
stants and parameters that vary both with environ-
mental conditions and predominant species. The major
pathways and cycles will be briefly discussed in the
following sections and the supplement from the model
developer's perspective. Additional information is pro-
vided in Section 3.
2.5.2.1. Phytoplankton Kinetics
Phytoplankton kinetics assume a central role in eutro-
phication affecting both the nitrogen and phosphorus
cycles, the DO balance, and food chain response.
The reaction term for phytoplankton is expressed as
the difference between the growth rate and the death
and settling rates in each volume element. The growth
rate of phytoplankton is a complicated function of the
species present and their differing reactions to solar
radiation, temperature, and the balance between nutri-
ent availability and phytoplankton requirements. Phy-
toplankton "death" rates are conventionally expressed
as the sum of the endogenous respiration rate, the
death rate, and the grazing rate. Available information
does not allow simulation of individual species in a
natural environment. Hence, models either simulate
the phytoplankton community as a whole, or as classes
such as greens, diatoms, blue-greens, and dinoflagel-
lates.
Phytoplankton kinetics affect the oxygen, nitrogen,
phosphorus, and carbon cycles primarily through up-
take and secondarily through death. Proper specifica-
tion of average stoichiometry is necessary to
accurately model these interactions. The ratios of phy-
toplankton carbon to phytoplankton nitrogen, phospho-
rus, and chlorophyll-a vary among species and in time.
Few applied modeling frameworks account for the dy-
namics of stoichiometry. The user is forced to specify
average values or those characteristic of stressed sys-
tems.
2.5.2.2. The Phosphorus Cycle
Organic phosphorus in the water is present in various
particulate and dissolved forms that mineralize and
settle at different rates. Some models lump all organic
phosphorus into a single state variable; others divide
organic phosphorus into two, three, or four state vari-
ables that differ in settling and mineralization rates.
Mineralization or bacterial decomposition is generally
modeled as a first order temperature-corrected reac-
tion, although second order and saturating rates based
upon phytoplankton biomass have been employed.
Dissolved inorganic phosphorus sorbs to suspended
particulate matter in the water column. Subsequent
settling of the solids and sorbed phosphorus can pro-
vide a significant loss mechanism of phosphorus from
the water column to the benthos. Process based func-
tions that accurately calculate the phosphorus partition
coefficient would improve prediction of this important
variable significantly. Phosphorus may resolubilize un-
der anaerobic conditions and the flux of phosphorus to
the water column may be enhanced under anaerobic
conditions at the sediment-water interface as well as
by high pH conditions.
Dissolved inorganic phosphorus is taken up by phyto-
plankton at the stoichiometrically modified growth rate.
Although there is evidence for "luxury storage" of inor-
ganic phosphorus in phytoplankton, most models as-
sume the internal pool of phosphorus is biomass.
Grazing causes transfer of phytoplankton phosphorus
up the food chain. Upon respiration and death, biomass
phosphorus is recycled to the various forms of organic
and inorganic phosphorus at user-specified ratios.
2-6
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2.5.2.3. The Nitrogen Cycle
Nitrogen may be characterized as organic and inor-
ganic forms, where inorganic forms may include am-
monia-nitrogen, nitrate-nitrogen and nitrite-nitrogen.
As for organic phosphorus, some models lump all
organic nitrogen into a single state variable, whereas
others divide organic nitrogen into two, three, or four
state variables. Some modeling approaches use ni-
trogenous biochemical oxygen demand (NBOD) as a
state variable. Mineralization to ammonia can be rep-
resented as first-order, or second order or saturating
dependence on bacterial biomass.
Ammonia-nitrogen in the presence of nitrifying bacteria
and oxygen is converted to nitrite then nitrate-nitrogen.
The process of nitrification in natural water is complex,
depending upon DO, pH, total inorganic carbon, alka-
linity, Nitrosomonas and Nitrobacter bacteria, and flow
conditions.
Most models represent the reaction with a first-order,
temperature-corrected rate constant.
Some models treat nitrate and nitrite-nitrogen as a
single lumped variable. Some models allow spatial
variations calibrated by the user or empirical DO limi-
tation terms. Obviously, a process-based predictive
function for this rate would be quite valuable.
Denitrification is the reduction of nitrate to ammonia
and nitrogen gas. Primarily a benthic reaction, it is
included in some models as a loss rate of nitrate. It is
modeled as a first order reaction, sometimes multiplied
by a modified Michaelis-Menten term to suppress the
reaction in the presence of a small amount of oxygen.
Un-ionized ammonia may also be degassed and is of
additional importance due to its toxicity.
Both ammonia and nitrate are taken up by phytoplank-
ton at the stoichiometrically modified growth rate.
Some models include a preference function for ammo-
nia uptake when its concentration is high enough.
Grazing causes transfer of phytoplankton nitrogen up
the food chain. Upon respiration and death, biomass
nitrogen is recycled to the various forms of organic
nitrogen and ammonia at user-specified ratios.
2.5.2.4. The Carbon-Dissolved Oxygen Balance
Organic carbon is composed of a variety of materials
in estuaries, both dissolved and particulate. Some
models lump all organic carbon into a single state
variable expressed in units of oxygen—carbonaceous
biochemical oxygen demand (CBOD). Other models
represent various fractions of organic carbon, with their
separate oxidation and settling rates. Oxidation is gen-
erally modeled as a first order temperature-corrected
rate. Some models allow spatial variations calibrated
by the user.
Traditional models of organic waste do not compute
inorganic carbon and the associated variables of pH
and alkalinity. This carbonate system could be impor-
tant for simulating the effects of acidic wastes on un-
ionized ammonia concentrations or potential carbon
dioxide limitation in low alkalinity, high nutrient waters.
Models that include the carbonate system calculate
total inorganic carbon as the sum of bicarbonate, car-
bonate, and carbon dioxide. These species are in
equilibrium controlled by the equilibrium constants of
the dissociation reactions and the pH of the water.
Carbon dioxide (and thus total inorganic carbon) is
produced by respiration, consumed by algal growth,
and replenished by atmospheric exchange.
Carbonate alkalinity is the sum of bicarbonate concen-
tration plus twice the carbonate concentration plus the
hydroxide concentration minus the hydrogen ion con-
centration. Addition of acids and nitrification lowers the
pH and reduces alkalinity. Nitrate uptake by phyto-
plankton produces hydroxide and increases alkalinity.
DO is depleted by oxidation of organic carbon, nitrifica-
tion, and respiration. Benthic reactions depleting oxy-
gen are usually modeled as a spatially variable flux of
sediment oxygen demand. Respiration effects may be
combined for simplicity or separated into components
such as respiration by bacteria, plankton, macro-
phytes, fish, etc. The respiration of decomposers that
utilize organic matter is referred to as decomposition.
Oxygen is used during some chemical transformations,
such as nitrification and the oxidation of reduced sub-
stances (e.g. sulfide, methane, reduced iron, and re-
duced manganese).
Biochemical oxygen demand (BOD) is a measure of
the materials present in a sample which may be oxi-
dized by biochemical processes. The BOD exerted is
determined by the change in oxygen concentrations of
a sample overtime underspecific analytical conditions.
The modeling problem with BOD is that it combines the
effects of several oxygen consuming processes into
one variable; this approach may be too simple for
modeling some systems.
The more realistic approach is to separate oxygen
demands into various components, such as biodegrad-
able organic (carbonaceous) demands, nitrogenous
demands, and oxidation of other substances (e.g.,
reduced metals, sulfide, etc.). Biodegradable organic
demands may be due to dissolved and particulate
matter in the water column and bottom sediments.
2-7
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Some models separate water column organic matter
into participate and dissolved forms, referred to as
POM and DOM. Because some forms of organic mat-
ter decay at faster rates than others, organic matter
may be further divided into those that decay at a fast
rate (labile) and those that decay at a slower rate
(refractory). As labile organic matter decomposes, a
portion is transferred to the refractory state. A similar
approach can be used for organic sediments. Sources
of organic matter include external waste loads and
excretions and mortality of living substances.
DO is replenished by phytoplankton growth (photosyn-
thesis) and by reaeration. Many reaeration formulas
exist as well as in-situ measurement techniques.
Reaeration formulas based solely on velocity and
depth applicable to tidal rivers and estuaries include
O'Connor-Dobbins (1958, for slower, deeper rivers),
Churchill (1962, for moderately deep, faster streams)
and Owens et al. (1964, for shallow streams) (see
Thomann and Mueller 1987).
The Tsivoglou and Wallace method (1972) calculates
reaeration in rivers and streams from the slope and
travel time. Relationships that include the effects of bed
roughness, secondary flow and wind are under devel-
opment. Numerous relationships exist for wind-in-
duced reaeration. Wind induced reaeration may be
dominant in many estuaries due to the presence of
off-sea breezes and the large fetch near the ocean
outlet. However, a comprehensive approach to estu-
arine reaeration has not been developed. There re-
mains a need for critical review and assimilation of all
the formulas.
2.5.2.5. Benthic-Water Interactions
The decomposition of organic material in benthic sedi-
ment can significantly affect the concentrations of oxy-
gen and nutrients in the overlying waters. Areal fluxes
from the sediment due to diagenetic reactions can be
substantial nutrient sources or oxygen sinks. The oc-
currence of anoxia may dramatically increase nutrient
fluxes.
Most traditional models described these benthic fluxes
as spatially variable source and sink terms. Some
recent models have included benthic compartments in
which state variables are simulated. Particulate nitro-
gen, phosphorus, and carbon are added to the bed by
settling and lost by scour or sedimentation (burial).
Dissolved species of nitrogen, phosphorus, carbon,
and oxygen exchange with overlying water by pore
water diffusion. Benthic oxidation rates are generally
assumed first-order, with low rate constants producing
ammonia and consuming organic carbon and oxygen
equivalents (functionally, reduced organic species that
are oxidized at the water interface). Recently, efforts
have been made to simulate the diagenetic reactions
and resulting fluxes more realistically (DiToro 1986).
These efforts hold great promise for more accurate and
predictive modeling of organic and nutrient wastes.
Discussions of the processes impacting benthic fluxes
as well as modeling and measurement techniques may
be found in Hatcher (1986).
See Supplement III for greater detail on
organic wastes, dissolved oxygen and nu-
trients. This Supplement is found on page
2-20 at the end of this chapter.
2.6. Synthetic Organic Chemicals
2.6.1 Concepts
Synthetic organic chemicals include a wide variety of
toxic materials whose waste loads are allocated based
upon threshold concentrations as well as tolerable
durations and frequencies of exposure. These pollut-
ants may ionize and different forms may have differing
toxicological affects. The transport of the materials also
may be affected by sorption and they can degrade
through such processes as volatilization, biodegrada-
tion, hydrolysis, and photolysis.
2.6.2. Fate Processes
2.6.2.1. lonization
lonization is the dissociation of a chemical into multiple
charged species, lonization can be important because
of the different toxicological and chemical properties of
the unionized and ionized species.
2.6.2.2. Sorption
Sorption is the bonding of dissolved chemicals onto
solid phases such as benthic and suspended sediment,
biological material, and sometimes dissolved or colloi-
dal organic material. Sorption can be important in con-
trolling both the environmental fate and the toxicity of
chemicals. Sorption may cause the chemical to accu-
mulate in bed sediment or bioconcentrate in fish. Sorp-
tion may retard such processes as volatilization and
base hydrolysis, or enhance other reactions including
photolysis and acid-catalyzed hydrolysis.
A common assumption is that equilibrium sorption is
linear with dissolved chemical concentrations, and the
distribution is controlled by a partition coefficient and
the amount of solids present. For organic chemicals,
2-8
-------
lab studies have shown that the partition coefficient is
related to the hydrophobicity of the chemical and the
organic matter content of the sediment.
2.6.2.3. Settling, Deposition, and Scour
Suspended particles carrying sorbed chemicals can
settle through the water column and deposit on the
underlying bed.
Benthic particles carrying sorbed chemicals can scour
and become suspended in the water column. Mass
fluxes for settling, deposition, and resuspension are
controlled by the settling, deposition, and scour veloci-
ties, and the concentrations of suspended and benthic
sediment (See Section 2.4).
2.6.2.4. Loss Kinetics
Chemical concentrations and resulting observed toxic
effects often decline over time due to physical and
chemical processes. The loss processes considered
in most chemical fate models include volatilization,
hydrolysis, photolysis, and bacterial degradation.
Chemical oxidation and reduction are sometimes in-
cluded as well.
Volatilization is the flux of a chemical across the air-
water interface. The volatilization rate is proportional to
the gradient between the dissolved concentration in
the water and the concentration in the overlying atmos-
phere. For most chemicals, the partial pressure in the
atmosphere is negligible and the equation describing
volatilization reduces to a first-order form with the
removal rate coefficient.
The conductivity, or rate of transfer between the at-
mosphere and water column, is influenced by both
chemical properties (molecular weight, Henry's Law
constant) and environmental conditions at the air-
water interface (turbulence-controlled by wind speed,
current velocity, and water depth). Toxic chemical
models either require the user to input a value for the
transfer rate (kv) or internally compute a value using
the two-film theory first proposed by Lewis and Whit-
man (1924). This theory assumes that the rate of
transfer is controlled by diffusion through laminar lay-
ers in the air and water at the interface in which the
concentration gradients driving transfer are localized.
Hydrolysis is a reaction in which cleavage of a molecu-
lar bond occurs in the chemical and there is formation
of a new bond with either the hydrogen or the hydroxyl
component of a water molecule. Hydrolytic reactions
are usually catalyzed by acid and/or base and the
overriding factor affecting hydrolysis rates at a given
temperature is generally hydrogen or hydroxide con-
centration (Wolfe 1980).
Photodegradation (photolysis) is the transformation or
degradation of a compound that results directly from
the adsorption of light energy. Its rate is a function of
the quantity and wavelength distribution of incident
light, the light adsorption characteristics of the com-
pound, and the efficiency at which absorbed light pro-
duces a chemical reaction.
Photolysis is classified into two types that are defined
by the mechanism of energy absorption. Direct pho-
tolysis is the result of direct absorption of photons by
the toxic chemical molecule. Indirect or sensitized pho-
tolysis is the result of energy transfer to the toxic
chemical from some other molecule that has absorbed
the radiation.
Biodegradation encompasses the broad and complex
processes of enzymatic attack by organisms on or-
ganic chemicals. Bacteria, and to a lesser extent fungi,
are the mediators of biological degradation in surface
water systems. Dehalogenation, dealkylation, hydroly-
sis, oxidation, reduction, ring cleavage, and condensa-
tion reactions are all known to occur either
metabolically or via organisms that are not capable of
utilizing the chemical as a substrate for growth.
See Supplement IV for more detail on syn-
thetic organic chemicals. This Supplement is
found on page 2-27 at the end of this chapter.
2.7. Metals
2.7.1 Concepts
Metals are found naturally in the earth's crust. As a
result of irrigation in some regions, metals may be
solubilized and transported to surface waters. Metals
are also present in municipal treatment plants and
industrial effluents, in landfill leachates and in nonpoint
source runoff from urban areas.
27.2. Fate Processes
Upon entry to a surface water body, metal speciation
may change due to complexation, precipitation, sorp-
tion, and redox reactions. Metals concentrations are
diluted further by additional stream flow and mixing.
Physical loss can be caused by settling and sedimen-
tation, whereas a physical gain may be caused by
resuspension.
2.7.2.1. Metal Complexation, Precipitation
Heavy metals can form complexes with organic and
inorganic ligands and precipitate or dissolve. At equi-
2-9
-------
librium, the distribution of metals among the possible
complexes is controlled by the amount of metals and
ligands present, the reaction coefficients and solubility
products. In natural waters, sorption also affects the
distribution by reducing the amount of metal available
for complexation and precipitation.
Complexation reactions can affect transport by either
increasing or decreasing the soluble fraction. Some-
times one chemical species is known to be much more
toxic than another for a given heavy metal. This is
especially important because some states and EPA
have been moving towards "site-specific water quality
standards," in which chemical speciation will be con-
sidered on a site-by-site basis. For example, a site that
is known to have a great deal of naturally occurring
dissolved organics may not require as stringent a water
quality standard because the dissolved organic mate-
rial may complex the heavy metal and render it non-
toxic to biota.
2.7.2.2. Sorption
Heavy metals frequently adsorb or "bind" to solid sur-
faces. The mechanism of sorption or attachment is via:
1) physical adsorption to solid surfaces, 2) chemical
sorption or binding by ligands at the solid-water inter-
face, or 3) ion exchange with an ion at the solid water
interface. In addition, if the heavy metal is complexed
in solution by an organic ligand, it could sorb into the
organic solid phase much like an organic pollutant. The
mathematical formulation for describing the partition-
ing of a heavy metal between the solid phase and the
aqueous phase is the same as for organic chemicals
except the Kpi is usually called the "distribution coeffi-
cient" for heavy metal (although it may be referred to
as the partition coefficient or the binding constant in
some cases). In most measurements and simulation
models, all soluble complexes are lumped with the free
ion to give the dissolved metal concentration. Precipi-
tated metal is lumped with all sorbed species to give
the total particulate metal concentration. A spatially
variable, lumped distribution coefficient KD describes
the distribution between the two phases. There is no
general consistency in reported KD values for particular
methods in the natural environment, so site-specific
values should be used when possible.
2.7.2.3. Redox Reactions
Metals can change oxidation states through various
oxidation and reduction reactions. Under some condi-
tions, the kinetics of oxidation or reduction may be
important to simulate.
See Supplement V for greater detail on metals
as they relate to estuarine models. This Sup-
plement is found on page 2.31 at the end of
this chapter.
2.8. Model Structure
Mathematical models vary widely in their ability to
simulate the circulation and mixing processes as well
as the processes impacting DO variations, eutrophica-
tion, synthetic organic chemicals, and metals as de-
scribed in this Section. Some of the models that are
presently available for use in estuarine waste load
allocation studies and criteria for their selection are
discussed in the following section (Section 3.0).
SUPPLEMENT I:
FACTORS AFFECTING CIRCULATION AND MIXING MODEL
EQUATIONS
I. Model Equations
The processes affecting circulation and mixing dis-
cussed in Section 2.2 may be described using equa-
tions based on laws of conservation of mass and
momentum. The fundamental equations generally in-
clude: (A) the conservation of water mass (continuity),
(B) conservation of momentum, and (C) conservation
of constituent mass. The equations for the mean com-
ponents are provided in Table 2-1.
A. Continuity Equation
The continuity equation expresses the fundamental
principal that the sum of all volume transfers must
equal zero. For example, for a given control volume
the inflow minus outflow must equal the change in
storage over time. This expression alone, when used
in conjunction with measured data such as outflows,
surface elevation changes, and constituent concentra-
tions, has formed the basis for estimating flows used
to transport water quality constituents (using Equation
2.5) in many water quality studies. This type of solution
is of greatest utility for describing flows in very simple
systems and is often of limited use in estuarine studies
with the possible exception of one-dimensional tidally
averaged analyses. To predict flows, the continuity
equation is usually coupled with momentum equations
to form the basis of hydrodynamic models.
2-10
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Table 2-1. Fundamental Model Equations
A. Conservation of Water Mass (Continuity).
3x 3y 3z
(1) (2) (3)
B. Conservation of Momentum
x - direction:
du d(uu) d(uv) 3(uw) _ 1 3P 3 ["Ex3t/| 9 ["Ey3u1 a |"EZ
3f 3x ay 3z p ax y ax I ax I ay I ay I az I az ^ ' ;
(4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
y - direction:
=_
af ax ay az P ay y ax I ax I ay I ay I az I az I ^ '
(4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
z - direction:
3w 3(wt/> 3(wy) 3(ww) 1 ap , a |"EX awl a ["Ey3w1 a \EZ awl
3f 3x 3y 3z ~ p 3z 3x [ 3x J 3y [ 3y J 3z |_ 3z J
(4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
C. Conservation of Constituent Mass (Transport)
3C 3(uC) 3Q/C) 3(wC) 3 \KxdC] 3 \KydC] 3 \K2 3C] vc
"Ą+^T+^T+^^"^ |~a5T +9y 9y +^ l~^~ +
(14) (15) (16) (17) (18) (19) (20) (21)
where the numbered equation terms are:
(1 to 3) = the velocity gradients in the x ,y and z direction
(4) = local acceleration
(5 to 7) = are convective acceleration terms in the x,y and z direction
(8) = pressure gradient
(9) = the Coriolis force
(10) = gravitational acceleration
(11 to 13) = parameterization of the Reynold's stresses in the x, y and z direction
(14) = rate of change in concentration
(1 5 to 1 7) = advective terms
(1 8 to 20) = turbulent diffusion
(21) = constituent source/sink term (e.g. kinetics and transfers, boundary loadings)
Equation variables are defined as:
t = time
P = pressure
g = gravitational acceleration
p = density
f = Coriolis frequency
Ex, Ey, Ez = turbulent diffusion coefficient for momentum in the x, y and z direction
u, v, w = mean velocity components in the x, y and z direction
x, y, z = rectangular coordinates, where x and y are horizontal coordinates and z is vertical
Kx, Ky, Kz = turbulent diffusion coefficient for mass in the x, y and z direction
C = concentration of water quality constituent
S = Constituent source/sink term
2-11
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B. Conservation of Momentum
The conservation of momentum equation is derived
from Newtons's second law of motion, which states
that the sum of all forces acting on a system is equal
to the time rate of change of linear momentum of the
system, where momentum is mass times velocity. The
factors affecting changes in momentum are illustrated
by Figure 2-1 for a given control volume. The terms in
the conservation of momentum equation are expres-
sions of: (4) local acceleration, (5-7) convective accel-
eration, (8) pressure forces, (9) coriolis force, (10)
body force, and (11-13) turbulent stress terms. The
equations as written in Table 2-1 assume that the fluid
is incompressible, that the velocities are Reynold's
averages, that turbulent diffusion is much greater than
molecular diffusion, and that turbulent transfer of mass
and momentum is directly related to concentration and
velocity gradients (Boussinesq assumption). The
equations may be found in the literature in a number
of equivalent forms, differing due to mathematical ma-
nipulations or assumptions with regard to the system's
geometry or boundary conditions. Unknowns in the
equation include the velocities (u,v and w), the pres-
sure (P), and the eddy viscosity coefficients
(Ex,Ey,Ez).
INFLOW
The local acceleration (4) terms refer to the rate of
change of velocity with respect to time. They are also
referred to as the local inertia terms.
The convective acceleration (5-7) or convective inertia
terms express the effects on the momentum balance
of spatially varying velocities.
The pressure force (8) describes the effect of pressure
gradients on the velocity field. For a homogeneous
water body, i.e. one with no density differences, the
pressure gradients are proportional to the slope of the
water surface and the equal pressure surfaces are
parallel to the water surface throughout. Flows induced
by the water surface slope are referred to as barotro-
phic flow. Changes in density in nonhomogeneous
water bodies establish pressure gradients inducing
flows which are referred to as baroclinic.
An empirical relationship is generally used to establish
the relationship between water density, temperature,
and salinity and the relationship is generally referred
to as the "equation of state." The equation of state
provides a means of linking water quality and hydro-
dynamic models. The relationship is given by
WIND
GRAVITY
Figure 2-1. Factors affecting changes in momentum.
2-12
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p = pT + Aps + Apss (2.6)
where p is the water density (kg m"3), pr is the density
as a function of temperature, and Aps and Apss are
the changes in density due to dissolved and sus-
pended solids, respectively.
An empirical relationship between density and tem-
perature is given by (Gill 1982)
pT= 999.8452594 + 6.793952 x 10~2 T
- 9.095290 x 10~3 T2 + 1.001685 x 10~4 T3
- 1.120083 xW~6T4 + 6.536332 xW~9T5 (2.7)
where T is the temperature (°C) and the change in
density due to salinity is (Gill 1982)
ps = CSL (0.824493 - 4.0899 x 10 3 T
7.6438 x 10~5 T 2 - 8.2467 x 10~7 T 3
5.3875 x 10~9 T 4) + C SL L5 (- 5.72466
x 10~3 + 1.0227 x 10~4 T- 1.6546 x 10~6 T 2)
+ 4.8314 x\0~4CSL2
(2.8)
where CSL is salinity (kg m"3). The relative affect of
temperature and salinity on water density is illustrated
in Figure 2-2. The effect of suspended solids may also
be considered using (Gill 1982)
-,-3
(2.9)
where Apss is the change in density due to suspended
solids, Css the suspended solids concentration (g
m" ), and SG the specific gravity of the solid. Some
models include terms for the effects of spatial vari-
ations in the atmospheric pressure on the velocity
fields.
Some estuary models with vertical resolution, such as
the laterally averaged model CE-QUAL-W2 (Environ-
mental and Hydraulics Laboratory 1986) and
CELC3D, assume that the vertical acceleration is neg-
ligible compared to the vertical pressure gradient and
gravitational acceleration (the hydrostatic approxima-
tion; i.e. the magnitude of terms 4-7, 9 and 11-13 of the
vertical momentum equation, Equation 2.4, are negli-
gible compared to terms 8 and 10). The hydrostatic
assumption reduces the vertical momentum equation
to
p dz
(2.10)
Temperature
B T= 15 °C
-A- T- 20 °C
995 i i i . i i i i i i i • i i i . i i i . i .
0 3 B 9 12 15 18 21 24 27 30 33
SALINITY (Kg iff3)
Figure 2-2. Relationship between water density, salinity, and temperature.
2-13
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The formulation for the mean pressure, P, is performed
in one of two ways, either as a free surface calculation
or a rigid lid computation (i.e. the water surface eleva-
tion does not vary). For the more complex estuarine
application, the free surface formulation is required
due to the importance of tidal oscillations as a system
forcing function. Free surface versions of estuary mod-
els often exploit the hydrostatic pressure equation to
make an implicit relation between free surface eleva-
tion and the pressure field (Bedford 1985). Models
which solve for the free surface implicitly are attractive
due to less restrictive time step formulations (Paul and
Nocito, 1983).
The Coriolis force (6) describes the effect of the earth's
rotation which acts to deflect the motion of fluids to the
right (left) in the northern (southern) hemisphere. The
Coriolis force is an apparent force to allow a frame of
reference to be used that is relative to the rotating
earth. The force is usually described as a function of
the angular velocity of the earth (Q) and the latitude of
the estuary. The Coriolis frequency (f) is estimated
from
f= 2 Q sin ()
(2.11)
where Q is the angular velocity of the earth, O is the
latitude, and the time scale for rotational effects is
approximately of the order 1/f and ranges from about
15 hours in Washington State to 30 hours in southern
Florida.
The eddy viscosity terms (11 -13) arise from time-aver-
aging the turbulent fluctuations of velocity compo-
nents. The velocity components may be written as
U=u + u' ; V=v + v' ; W=w + w' (2.12)
where u,v,w are the mean velocity components and
u',v', and w' are the fluctuations relative to the mean
velocities. The time-averaging of the velocities gives
rise to turbulent correlation terms of the form:
wV UV ^V (2.13)
The Boussinesq analogy assumes that the turbulent
stresses are proportional to the mean velocity and the
turbulent stresses are often rewritten in the form shown
in Equations 2.2-2.4 (terms 11-13)
I I J-l C/W II J-T \JUl
uu = hx ~ ; uv = hy -^- ;
du
du_
dy
(2.14)
uw =hz -—
referred to as the eddy viscosity formulation. This
formulation is generally applicable where large scale
turbulence is of importance. These terms are unknown
quantities and represent what is referred to as the
closure problem in hydrodynamic modeling. Rewriting
the quantities in terms of eddy viscosity does not
eliminate the problem but has put the terms in a form
that has proved useful in practical calculations. A
variety of procedures have been developed for turbu-
lence closure, described as zero-equation, one-equa-
tion, two-equation, and higher order methods and have
been reviewed by Rodi (1980), Bedford (1985) and
others.
The horizontal eddy viscosity is often held constant in
models (Ex = Ey). Procedures for estimating the mag-
nitude of the eddy viscosity are described in Section 5
(Supplement III).
The vertical eddy viscosity at the interfaces of water
segments for models with vertical resolution is often
described as a constant or a function of the decay of
surface shear. The shear at the surface boundary is
generally described as a function of wind shear such
as
Ez (- , - )=pa Cda
dz dz
(u
(2.15)
in the x and y directions, respectively ,where p0 is the
surface water density, pa the air density, Cda the drag
coefficient, and uw and vw are the wind velocities in the
x and y directions at some height above the water
surface. This computation requires that representative
data be available for both wind speed and direction.
The vertical stress at the bottom boundary is usually
described as a function of bottom friction, such as in
the quadratic stress formulation
„ ,du dv 2
P Ez (— , — )=p Cd (u
dz dz
2-.0.5
v )
, vb)
(2.16)
where Cd is a drag coefficient and Ub and Vb are the
horizontal velocities at some point above the bottom.
A constant drag coefficient has been used in modeling
studies.
The drag coefficient has also been related to the Chezy
coefficient (CZ) as
(2.17)
or the Manning's roughness coefficient, n,
Cd = r (2.18)
RA
where R is the hydraulic radius (m). Guidance on the
selection of bottom roughness coefficients is provided
in Section 5 (Supplement I).
The vertical eddy viscosity is reduced significantly by
stable stratification. Some formulations to account for
2-14
-------
TIDAL EXCHANGE
REACTIONS
Figure 2-3. Factors affecting change in constituent mass.
this effect contain empirical relationships between ver-
tical eddy viscosity and the Richardson number (Ri),
an index of stratification stability given by
(2.19)
The most widespread of these formulations was devel-
oped by Munk and Anderson (1948) where
Ez = Ez,o (1 + 10 Ri)~°'5 (2.20)
where Ez,o is the value of Ez for neutral stratification
(i.e. the estuary is unstratified).
Boundary conditions, such as water surface elevations
and flows, provide the forcings which are propagated
through the model solutions as computed variations in
velocities and surface elevations.
C. Conservation of Constituent Mass
The conservation of constituent mass or transport
equation forms the basis for estimating variations in
water quality over space and time. The equation is a
statement that the time rate of change of concentra-
tions, or material accumulation, (14) is equal to the
material entering or leaving the system due to advec-
tive transport (15-17) orturbulentdiffusion (18-20) plus
the change due to physical, chemical, or biological
transformations (21) as illustrated by Figure 2-3. The
advection of constituents can be estimated from field
measurements, computations using tracers and conti-
nuity, or hydrodynamic models. The diffusion coeffi-
cients are related to turbulence. For three-dimensional
mass transport models using small time steps (on the
order of a few minutes) the governing equations con-
tain only turbulent diffusion terms. However, if the
equations are temporally or spatially averaged then
dispersion will result, and the magnitude of the disper-
sion term will depend upon how the averaging is done
(Harleman, R.F., in his review of this document).
The eddy viscosity and mass dispersion coefficient are
related by the turbulent Prandtl/Schmidt number (i.e.
the ratio of transfer of momentum and mass). A com-
plete review of dispersion relationships is found in
Fischer et al. (1978). Guidance on the selection of the
dispersion coefficient is provided in Section 5 (Supple-
ments III and V).
II. Model Complexity
The solution of the equations for circulation and mixing
(Equations 2.1-2.4) is generally based upon simplifica-
tions and assumptions regarding the spatial and tem-
poral complexity of the system and its boundary
conditions. These basic assumptions make it less
difficult to solve the governing equations. Generally,
simplifying assumptions may be made regarding the
2-15
-------
1-D Longitudinal
1-D Vertical
2-D Longitudinal-Lateral
2-D Longitudinal-Vertical
3-D
Figure 2-4. Model dimensions.
hydrodynamic complexity of the system, its dimension-
ality, temporal resolution, and kinetic resolution.
A. Spatial and Temporal Resolution
With regard to spatial resolution, models may be one,
two orthree dimensional. Most practical hydrodynamic
models are either one, two (vertically or laterally aver-
aged) or quasi-three dimensional, as illustrated by
Figure 2-4. This often prevents their application to
near-field problems where a high degree of turbulence
occurs. For example, a model which does not include
vertical momentum could not resolve momentum
transfer due to a submerged jet. Nihoul and Jamarf
(1987) describe available three-dimensional models.
Similarly, mass transport models may be one, two or
three dimensional. Tidally varying one-dimensional
models are useful for tidal flow in narrow, relatively
uniform channels, such as the long braided network of
sloughs sometimes found in deltas or tidal rivers (Fis-
cher et al. 1978). In wide and irregular channels, two
orthree dimensional models may be required.
With regard to temporal resolution, estuarine mass
transport problems are usually characterized as inter-
tidal or intra-tidal. Intra-tidal computations, which con-
sider variations within a tidal cycle, generally require
application of coupled hydrodynamic and water quality
models in order to obtain real time predictions.
For inter-tidal computations, a variety of simplified
methods are available to estimate circulation and mass
transport. Simplified modeling approaches are often
based on using either measured flows or flows esti-
mated using continuity (Equation 2.1) for use with
models based on constituent mass balance equations.
The most simple models solve only the transport equa-
tion (Equation 2.5), usually assuming steady-state
(3C/3f=0) to obtain average conditions. Models of
intermediate complexity estimate flows based on field
data or use simplified methods to describe circulation,
generally tidally averaged.
Mills et al. (1985) describes some simplified methods
for calculating estuarine circulation, including fraction
of freshwater methods, modified tidal prism method
and Pritchard's Box model for a two-dimensional estu-
ary.
2-16
-------
The freshwater and tidal prism method are described
further in Section 6 of Part 2 of this manual. Officer
(1976, 1977) described analytical solutions to decou-
pled hydrodynamic and mass transport equations.
Lung and O'Conner (1984) developed a tidally aver-
aged method for two-dimensional (longitudinal-verti-
cal) estuaries that allows analytical computation of
horizontal and vertical velocities and vertical eddy
viscosity terms.
Hydrodynamic models, based on the solution of the
equations for circulation and mixing (Equations 2.1-
2.4), are linked with water quality models, based on the
constituent mass balance equation (Equation 2.5),
when time varying predictions are required of both
flows and water quality, such as for intratidal variations.
Some models directly link solutions for the hydrody-
namic and constituent transport equations with equa-
tions of state allowing variations in water quality to be
considered in flow predictions. In other cases the
hydrodynamic predictions are separate from water
quality and may be averaged over space and time to
allow use of coarser time or space scales in water
quality modeling. This time and space averaging is
often difficult to accomplish since important advective
and diffusive information is lost in direct proportion to
the length of the spatial and temporal averaging period
and there are no quantitative guidelines for multidi-
mensional models to indicate the extent of the infor-
mation lost (Harleman, D., in review). Thus,
empiricisms are often introduced as a result of the
averaging. Studies on the interfacing problem have
been conducted by Ford and Thornton (1979), Walters
(1980), Imboden et al. (1983), Wang and Harleman
(1984), Shanahan and Harleman (1984) and others
which are applicable to estuarine conditions as well as
studies conducted on Chesapeake Bay.
B. Kinetics
Descriptions or predictions of estuarine circulation may
be coupled with detailed descriptions of constituent
transformations. Fora "conservative material" (one not
subject to transformations, i.e. salinity and some trac-
ers) the last term (S) in Equation 2.5 is equal to zero.
However, the constituents of interest in estuarine WLA
studies rarely behave conservatively. For most mate-
rials of interest, such as DO, nutrients, synthetic or-
ganics and metals, their physical, biological, and
chemical transformations must be estimated. The fac-
tors influencing those transformations is the subject of
the remainder of this section (Sections 2.3-2.6).
C. Additional Considerations
A tendency may be to select the resolution (spatial,
temporal and kinetic) for a particular waste load allo-
cation study on the scale of interest for the model
output rather than the physics, biology and chemistry
of the system. An additional tendency may be to base
model selection on those techniques which are per-
ceived to be the simplest to use. However, the relation-
ship between model simplicity and simplicity of
application is not straightforward.
For example, inappropriate spatial and temporal aver-
aging for hydrodynamic computations can result in a
model that is far removed from the physics of the
system. Inappropriate averaging may necessitate the
introduction of empiricisms which must then be cali-
brated to data, and may result in increased rather than
decreased data requirements to support the modeling
studies. For example, averaging may introduce disper-
sion terms whose magnitude depends on how the
averaging is done. Harleman (D.R.F., in his review)
suggests that the data required to support a two-di-
mensional laterally averaged model is often more than
that for a three-dimensional model, while the amount
of synoptic data required to support a one-dimensional
model (averages over a cross section) may be enor-
mous. Therefore, if the physics of the system is not
adequately considered, the data required to support a
modeling study may increase with increasing "simplic-
ity".
Similarly, the clumping of kinetics terms for "simpler"
models may, if not carefully done, introduce empiri-
cisms which have little relationship to the chemistry
and biology of the system. Thus, the empirical coeffi-
cients may often be determined only through calibra-
tion, often to inadequate data, and the coefficients
must often be varied over space and time to get the
"best" calibration. Alternatively, the uncertainty of
model predictions increases nonlinearly with the addi-
tion of uncertain parameters. Therefore, the Principle
of Parsimony should apply: that is that it should be
attempted to obtain a model calibration and validation
with the fewest possible parameters (R.V. Thomann,
in review of this document).
2-17
-------
SUPPLEMENT II:
SEDIMENT TRANSPORT AND SEDIMENT/WATER QUALITY
INTERACTIONS
I. Source and Sink Term Processes
The processes affecting sediments are illustrated in
Figure 2-5. Using the segmentation scheme illustrated,
constituent mass balance equations (Equation 2.5)
would be written for each vertical water segment. The
advective and diffusive transport terms were described
previously. The remainder of the processes would be
described in the source/sink term (S). The source/sink
term would typically be represented as
(2.21)
where A is area, V volume, C solids concentration and
P is a coefficient with units of velocity (e.g. settling or
resuspension velocity).
II. Settling
For settling the coefficient p is dependent upon
Brownian motion, turbulent diffusion, and fall veloci-
ties. Brownian motion is negligible for most particles of
interest in water quality modeling. The fall velocities
(ws) can be estimated from Stokes law, which is
(2.22)
where g is gravitational acceleration, d is particle di-
ameter, pp the particle density, pf the fluid density and
|i the dynamic viscosity of the fluid. Stokes settling or
fall velocities for a range of materials are tabulated in
Section 5 (Supplement VIM). The silts and clays carry-
ing pollutants typically range in diameter from 0.002 to
0.02 mm, with densities of 2 to 2.7 g/cm3.
PROCESSES
® ADVECTION
© VERTICAL DIFFUSION
© SETTLING
® AGGREGATION AND SETTLING
© DEPOSITION
© RESUSPENSION
G> BED LOAD TRANSPORT
(D CONSOLIDATION
® EROSION
© BURIAL
Figure 2-5. Sediment variables and processes.
2-18
-------
Stokes law is valid for Reynolds numbers
(Re = pf ws d/\i) less than about 0.1.
Collisions between small cohesive particles tend to
lead to coagulation and the formation offices. Floccu-
lation rates are dependent upon the size distribution
and relative composition of the clays and electrolytes
and upon local boundary shear stresses (Mills et al.
1985) as well as salinity. Turbulence increases the
collisions while salinity increases the cohesion be-
tween particles (Sheng 1983). The effective density of
the floe may vary considerably from that of the individ-
ual particles, making prediction of settling velocities
difficult and requiring site-specific model calibration
(Stefan, Ambrose and Dortch 1988).
III. Deposition
The deposition of sediments onto the surface sediment
layer is a process by which suspended sediments
leave the water column, either temporarily or perma-
nently, and become part of the bottom sediments
(Sheng 1983). In order to be deposited the particles
must overcome resistances due to turbulent transport
in the water column, resistances due to the thin viscous
layer at the interface, and resistances due to chemical
or biological activity after they reach the bottom. The
deposition velocity depends on the extent to which
settling is affected by turbulence. Sheng (1983) indi-
cated particles of diameters less than approximately
100 jim will completely follow the eddy motions. The
deposition velocity can be estimated as the product of
the settling velocity and the probability of deposition on
contact with the bed, which can vary from 0 for very
turbulent systems to 1 for stagnant pools, and deposi-
tion velocities will generally vary from 0 to 5 m/day
(Ambrose et al. 1988; Stefan, Ambrose and Dortch
1988).
IV. Entrainment
Entrainment or resuspension occurs when the flow
induced shear stress at the sediment-water interface
exceeds the cohesive forces of the surficial sediments
(Sheng 1983). For granular non-cohesive materials
the relationship between bed shear and entrainment is
"explosive" in nature. Very low or no resuspension
occurs until a threshold shear stress is reached. Then
resuspension rates increase in proportion to some
power of the excess shear stress. Powers of one have
been found in estuarine studies, but powers of four and
five have been found for granular river material accord-
ing to a review by Akiyama and Fukushima (Wang et
al. 1986). The rate of resuspension can be balanced
by the rate of deposition. At that point, vertical concen-
tration profiles above the bed show a balance of down-
ward fluxes of sediment by settling and upward fluxes
by turbulence as summarized by Vanoni (1975).
According to Rouse (see Vanoni 1975), the dimension-
less parameter Vs(Ku )" (where Vs = particle fall ve-
locity, K = 0.4 and u = bed shear velocity = Vi/j/p with
T/J = shear and p = water density) determines for flow
over flat bottoms the degree for which vertical sedi-
ment distribution will be uniform. It will be uniform
within + 10 percent when Vs(Ku )
0.02.
-1
is less than about
Rates of entrainment of non-cohesive materials have
been specified in numerous alternative forms by
Ariathurai (1982), Ariathurai and Krone (1976), and
others (see Wang et al. 1986; Mehta 1986). Akiyama
and Fukushima (in Wang et al. 1986) specified a
dimensionless resuspension rate parameter Es as:
s = 3xlO~UZW(l-5/z)
for 5 13.4
(2.23)
where
Rp=(g'D)/2D/v
g'=g(p,/p-l)
reduced acceleration of gravity of submerged parti-
cles; D = particle diameter; and v = kinematic viscosity.
The entrainment (or resuspension, scour or erosion)
rate depends not only upon the shear stress on the
benthic surface, and the sediment size but also on the
state of consolidation of the surficial benthic deposits.
Site-specific calibration is necessary to refine initial
estimates of scour (Stefan, Ambrose and Dortch
1998).
Entrainment of cohesive sediments is less well under-
stood. Unfortunately, cohesive sediments are of pri-
mary interest in water quality studies. For cohesive
sediments, the resuspension rate is affected by bottom
shear stress, salinity, sediment type, and the time
history of bottom sediments (Sheng 1983). Lick et al.
(1987) indicated that, as a result of cohesion and the
resulting compaction, only a finite amount of cohesive
sediment may be resuspended at a given shear stress
as opposed to non-cohesive sediments which have a
uniform rate of resuspension. Lick suggested that the
amount of cohesive sediment that can be entrained is
a function of the time after deposition, the shear stress,
and an effective critical stress which needs to be
determined experimentally for particular sediments.
2-19
-------
V. Burial
Burial refers to the net sedimentation velocity, or the
velocity by which deposited sediments are buried by
additional deposits. Burial, compaction, and the cohe-
sive forces between sediment particles result in vary-
ing sediment properties (e.g. density and porosity) with
depth below the upper mixed sediment zone.
SUPPLEMENT
ORGANIC WASTES, DISSOLVED OXYGEN AND NUTRIENTS
I. Important Processes and Variables
The basic variables and processes used in the predic-
tion of DO and nutrient concentrations are illustrated
in Figures 2-6 and 2-7, where separate constituent
mass balance equations are generally written for each
variable indicated by the boxes (constituents, C in
Equation 2.5). The processes affecting those variables
and the interactions between variables are indicated
by arrows, and comprise the source/sink terms in the
constituent mass balance equation (S, Equation 2.5).
These processes are often modeled as zeroth-order,
S = K0th (2.24)
where K is a constant with units of concentration/time;
first-order,
S=KistC (2.25)
where C is concentration and K is a rate term with units
of 1/time; or higher-order (nonlinear) processes where
the rate term is dependent upon variations of other
variables or constituents. The variables are also af-
fected by advective and dispersive transport, as de-
scribed by Equation 2.5. Transport and reaction rates
are affected by temperature as described below.
II. Temperature
Temperature affects transport through density terms
(as described by the equation of state, Equation 2.5)
as well as reaction kinetics. Temperature effects on
reaction processes are usually computed as the prod-
uct of a temperature adjustment factor and the rate
term measured at some reference temperature, where
the temperature adjustment factor (Xj) is estimated
from
-T-7>
(2.26)
where 9 is a coefficient, T is temperature, and Tr is a
reference temperature.
Temperature variations may either be modeled or
specified in water quality models (see Thomann and
Mueller 1987). The temperature (thermal energy)
equation can be obtained from the conservation of
mass equation (Equation 2.5) by replacing concentra-
tion (mass/volume) by the heat/volume (i.e. p Cp T).
Dividing through replaces C (concentration) with T
(temperature) and the source/sink term (S, Equation
2.5) may be given as
S = -
HA
VC
(2.27)
where A is area (m ), V volume, H the total heat flux
(Watts/m2), Cp is the specific heat of water
(Joule/Kg°C), and p0 the density of water at the given
temperature (Kg/m3).
The total heat flux includes fluxes due to conduction or
sensible heat transfer, evaporation, long wave back
radiation from the atmosphere, back radiation from the
water surface, and absorption of shortwave radiation.
All predictive approaches to temperature modeling are
based on one or more empirical functions that must be
specified, such as the wind speed function. Guidance
on the selection of the wind speed function is provided
in Section 5 (Supplement VI).
III. Indicator Bacteria
The bacteria of interest in WLA studies dealing with
organic wastes of human origin include total or fecal
coliforms, where the coliforms may be pathogenic in
some cases or are used as indicators of the presence
of pathogenic bacteria. Coliform bacteria generally can
not reproduce in aerobic natural waters and are mod-
eled using first-order kinetics, where the rate term
represents a die-off rate. However, coliforms can re-
produce in sediments and be resuspended in the water
column. Guidance on the selection of die-off rates and
their reference temperature (Tr) for temperature ad-
justments of the rate (Equation 2.26) is provided in
Section 5 (Supplement VII). Coliform die-off may also
vary with light and salinity as well as temperature.
Thomann and Mueller (1987) provide additional dis-
cussion of modeling considerations for indicator or
pathogenic bacteria.
2-20
-------
©
REAERATION
CARBONACEOUS DEOXYGENATION
NITROGENOUS DEOXYGENATION (NITRIFICATION)
PHOTOSYNTHESIS
RESPIRATION
SEDIMENT OXYGEN DEMAND
SETTLING AND DEPOSITION OF ORGANIC MATERIAL
Figure 2-6. Basic variables and processes for dissolved oxygen.
_ _ BENTHIC
0-0 GIVEN PREVIOUSLY ~ SEDIMENT
SORPTION. DEPOSITION OF INORGANIC MATERIAL
SETTLING AND DEPOSITION OF PHYTOPLANKTON
o) UPTAKE AND GROWTH
DEATH © MINERALIZATION (13) NUTRIENT REGENERATION
Figure 2-7. Standard variables for eutrophication and DO.
2-21
-------
IV. Organic Material and Dissolved Oxygen.
DO is depleted by oxidation of organic carbon, nitrifi-
cation, and respiration and is replenished by surface
exchange and primary production (Figure 2-6). More
complex interactions considering the effects of eutro-
phication have been considered (Figure 2-7).
Historically, deoxygenation by decomposition of or-
ganic material has been modeled using coupled equa-
tions for DO and Biochemical Oxygen Demand (BOD),
where BOD is a measure of the oxidizable matter due
to biochemical processes expressed in oxygen units.
BOD has typically been divided into two components,
Carbonaceous BOD (CBOD) and Nitrogenous BOD
(NBOD) due to the difficulty of predicting variations in
total BOD (CBOD + NBOD). CBOD removal proc-
esses usually included in model formulations include
decomposition or oxidation by organisms, and settling.
In addition, CBOD can be entrained or resuspended.
The source/sink term for CBOD can be written as
L + La (2.28)
where Kd is the water column deoxygenation rate
coefficient, Ks is the settling rate, Lthe ultimate CBOD
and La a zero order CBOD resuspension rate. For
DO, the loss rate due to deoxygenation is KdL. Further
information and guidance on the selection of rate terms
is provided in Section 5 (Supplement XI).
The utility of CBOD is limited since it lumps the effects
of a number of processes into one variable. Some
modeling approaches will separate oxygen consuming
reactions into various components. CBOD is essen-
tially the only variable presently written into most WLA
permits for the control of DO.
DO may also be depleted due to benthic demand.
Discussions of the processes impacting sediment oxy-
gen demand as well as modeling and measurement
techniques may be found in Hatcher (1986).
V. Phytoplankton
Primary productivity by phytoplankton produces oxy-
gen while respiration consumes oxygen. In addition,
phytoplankton are often of primary interest in assess-
ing eutrophication and in predicting nutrient interac-
tions.
For simplistic DO models, as illustrated by Figure 2-6,
it may be sufficient to describe the effects of phyto-
plankton using simple zeroth order terms for primary
productivity and community respiration. These terms
may often be estimated from field studies using meas-
urements of variations in carbon isotopes, oxygen or
carbon dioxide. This approach is often of limited utility
where changes in productivity are expected to occur
in response to waste loadings. Most estimates of pri-
mary productivity in common mathematical models
involve coupling algal growth equations with
stoichiometric equations for photosynthesis in order to
relate primary productivity to oxygen and nutrient pro-
duction/consumption.
Modeling of specific algal species is usually not at-
tempted. Instead major groups, such as diatoms,
greens, blue-greens and dino-flagellates are simu-
lated. Algal losses due to settling and grazing are also
often simulated. Some of the more complex models
include equations for zooplankton groups in order to
predict variations in grazing losses (Figure 2-8).
The growth rate of phytoplankton (G) is usually formu-
lated as the product of the maximum 20 ° C species or
group specific growth rate (under optimum light and
nutrient conditions) with a temperature adjustment
factor (Xj), a light adjustment factor (XL), and a nutrient
limitation factor (Xi\i).
G = G max XT XL XN
(2.29)
The temperature adjustment factor (Xj) is normally
computed using an expression similar to Equation
2.26. Light attenuation functions (XL) generally follow
the analysis by Steele (1962), accounting for the ef-
fects of supersaturating light intensities and light at-
tenuation through the water column, and lead to
XL = -
(2.30)
[exp (- -f- exp (- r| d)) - exp (- -f)
Is Is
where d is the depth (m), r| is the light extinction
coefficient including self shading (m), f is the photope-
riod correction, I0 is the incident light intensity just
below the surface (langley day"1', and ls is the algal
saturation light intensity at the maximum photosyn-
thetic rate. The above formulation is for a surface layer
and a more general formulation is given by Chapra and
Reckhow(1983).
Smith (1980) developed a framework for calculating ls
based upon the maximum growth rate, the quantum
yield of chlorophyll, the extinction coefficient per unit
of chlorophyll, and the ratio of carbon to chlorophyll in
the phytoplankton. This framework allows for adapta-
tion by changing the carbon to chlorophyll ratio. Recent
developments in phytoplankton kinetics models use
photosynthetically active radiation (PAR) (|j,Em~ day"
) instead of total energy ls (langley day"1). They also
apply Haldane kinetics in place of Steele's equation
(Megardetal. 1984).
2-22
-------
*~
__
DIATOMS
GREENS
BLUE
GREENS
DINO-.
FLAGELLATES
HERBIVOROUS
ZOOPLANKTON
FILTER-
rrrniMi^
-/onl
CARNIVOROUS
ZOOPLANKTON
J
k
ZOOPLANKTON
©--
T
SETTLING, DEPOSITION (lj) DEATH
UPTAKE AND GROWTH @ GRAZING
(19)
(20)
VOLUMETRIC GRAZING
PREDATION
Figure 2-8. Additional variables and processes for trophic interactions.
The nutrient limitation factor is based on the assump-
tion that phytoplankton follow Monod kinetics with
respect to the important nutrients. Generally, the mini-
mum function for inorganic nitrogen and phosphorus
is used:
CJN
CIP
KMN + CJN KMP + Cjp
(2.31)
where CIN is inorganic nitrogen (jig/l), CIP is inorganic
phosphorus (|ig/l), KMN is the Michaelis half-saturation
constant for nitrogen (|ig/l), and KMP is the Michaelis
half saturation constant for phosphorus (|ig/l). Occa-
sionally, XN is expressed as the product of the nitrogen
and phosphorus terms. Additional terms may include
separation of nitrogen into ammonia-nitrogen and ni-
trate-nitrogen. Dissolved available silica is included
where simulation of diatoms is required.
Phytoplankton "death" rates are conventionally ex-
pressed as the sum of the endogenous respiration
rate, the death rate, and the grazing rate. The first two
are generally modeled as the first order temperature
corrected rates. Grazing may be expressed as first
order, or second order if the herbivorous zooplankton
population is specified or simulated. To capture the
phytoplankton population dynamics properly,
zooplankton may have to be simulated. If average
phytoplankton levels are adequate, then the first order
approach is acceptable.
The relationship between phytoplankton kinetics and
variations in DO and nutrients is expressed using
stoichiometric relationships. Proper specification of av-
erage stoichiometry is necessary to accurately model
these interactions. The ratios of phytoplankton carbon
to phytoplankton nitrogen, phosphorus, and chloro-
phyll-a vary among species and in time. Few applied
modeling framework account for the dynamics of
stoichiometry. The user is forced to specify average
values or those characteristic of stressed systems.
Guidance on the selection of parameters and coeffi-
cients for modeling phytoplankton nutrients and set-
tling is provided in Section 5.
VI. Nutrients
Simulation of nutrients is critical to eutrophication mod-
els and to some DO models which include mechanistic
descriptions of phytoplankton kinetics. Simulation of
ammonia-nitrogen is also necessary in studies involv-
ing ammonia-toxicity. Sources of nutrients include bot-
tom sediments, point source load-
2-23
-------
SETTLING OF ORGANIC MATERIALS AT DIFFERENT RATES
SETTLING OF INORGANIC MATERIAL
UPTAKE AND GROWTH
DEATH AND NUTRIENT RECYCLING
MINERALIZATION OF ORGANIC NUTRIENTS AT DIFFERENT RATES
PARTITIONING OF NUTRIENTS WITH INORGANIC SEDIMENT
Figure 2-9. Additional variables and processes for nutrient interaction.
ings, non-point loadings from the watershed, and at-
mospheric deposition.
Atmospheric deposition has been implicated as a ma-
jor source of nutrients in some large estuaries.
For the simplified DO-BOD modeling, as illustrated by
Figure 2-6, it may be sufficient to consider only nitroge-
nous oxygen demand (NBOD). Similarly to CBOD,
NBOD is modeled as a first-order process, where
NBOD is expressed in oxygen units. Guidance on
first-order nitrification rate constants is provided in
Section 5 (Supplement X).
Models which include nutrient cycles vary in their
complexity, as illustrated by the nutrients considered
in the eutrophication model illustrated in Figure 2-7 as
compared to that illustrated in Figure 2-9. The primary
nutrients considered to impact eutrophication are ni-
trogen, phosphorus, and silica.
Nitrogen is present in particulate and dissolved, or-
ganic and inorganic forms (Figure 2-9). Nitrogen is
consumed by algae during growth, where the nitrogen
loss rate is stoichiometrically related to the algal growth
rate (Equation 2.29). During algal respiration and
death, some nitrogen is returned directly to the inor-
ganic nitrogen pool, while particulate organic nitrogen
may be lost due to settling. Organic nitrogen under-
goes bacterial decomposition whose end product is
ammonia-nitrogen. Nitrification may then result in the
oxidation of ammonia-nitrogen to nitrate-nitrogen and
finally to nitrate-nitrogen. Denitrification by bottom
sediments may be a major loss mechanism in some
systems. Guidance on selection of rate terms for the
various processes impacting nitrogen concentrations
is provided in Section 5 (Supplement XI).
Simulation of nitrogen is also of importance due to the
toxicity of unionized ammonia (NHs). Direct simulation
of ammonia speciation requires the simulation of pH.
However, if pH is not expected to vary it may often be
sufficient to simulate the nitrogen cycle in order to
predict total ammonia concentrations. Knowing the
equilibrium relationship between the two forms
2-24
-------
0000
(14) BEKTHK DECOMPOSITION
00 DEPOSmON OF ORGANIC MATERIAL
© oerosrnoH or ptiYTOPUAtwTON
§BENTHIC REMWERAUZATWN
DIFFUSION
SORPTKJN, DEPOSITION
Of INORGAMie MATERIAL
Figure 2-10.
Benthic interactions for nutrients and DO.
and that the total ammonia-nitrogen present or pre-
dicted (NHj) is the unionized ammonia plus the ionized
ammonia (NH4+), (NHj = NHa + NH4+ ) the portion
occurring as NHa can then be estimated from
1
1 +
NHT
(2.33)
Some caution needs to be exercised concerning the
reporting of units of nitrogen (i.e. as nitrogen or as
ammonia). Speciation is also effected by temperature
and the distribution of cations and anions. The aque-
ous ammonia calculations are discussed in detail by
Thurston et al. (1974) and Emerson et al. (1975), as
well as the effects of temperature and pH on calcula-
tions assuming zero salinity. These calculations are
also summarized by Bowie et al (1985). Whitfield
(1974) provided guidance on the effects of seawater
on ammonia speciation. The speciation of ammonia
may also be estimated using equilibrium speciation
models such as MINTEQA1 (Brown and Allison 1987).
Phosphorus may also occur in the water column in
organic or inorganic, particulate or dissolved forms
(Figure 2-9). Phosphorus is released during phyto-
plankton respiration and death in either organic or
inorganic form. Phosphorus is utilized in algal growth
as indicated in Equation 2.29. Dissolved inorganic
phosphorus sorbs to suspended particulate matter in
the water column, coming to an equilibrium expressed
either with a partition coefficient or as a calibrated
fraction dissolved:
foip=-
1
+KpipSS
(2.34)
where foip is the fraction inorganic phosphorus dis-
solved, SS is the suspended sediment concentration
(kg/L), and Kpip is the partition coefficient in (L/kg).
Subsequent settling of the solids and sorbed phos-
phorus can provide a significant loss mechanism of
phosphorus from the water column to the benthos.
Process based functions that accurately calculate
the phosphorus partition coefficient would improve
prediction of this important variable significantly.
Phosphorus loss mechanisms are generally de-
scribed using first-
2-25
-------
order kinetics, and guidance on rates is provided in
Section 5 (Supplement XII).
VII. Sediment Interactions
Sediment processes may have profound affects on DO
and nutrients in some systems. The decomposition of
deposited organic material releases nutrients and re-
sults in an oxygen demand. Denitrification by sedi-
ments is often a major loss mechanism for nitrogen
(Figure 2-10). Sediments may continue to have im-
pacts on water quality long after sources of organic
materials and nutrients have been eliminated.
Although often of critical importance, the predictive
capability of most presently available models of sedi-
ment interactions is limited. Description of these im-
pacts is often reduced to field measurements followed
by use of zeroth order rate terms based on those
measurements in models to describe their effects on
other variables and processes. Guidance on selection
of rate terms is provided in Section 5 (Supplement XV).
VIII. Surface Exchange
The surface exchange of dissolved oxygen, is typically
modeled based on Whitman's two-film model (Lewis
and Whitman 1924) assuming resistance in the liquid
controls. This reduces the source/sink (S, Equation
2.5) term for surface exchange to
S = K2(C-CS) (2.35)
where K2 is a reaeration rate, C is the water concen-
tration, and Csthe saturation concentration. The satu-
ration concentration for dissolved oxygen is typically
computed using empirical expressions including the
effects of temperature and dissolved solids. The
reaeration rate has been computed using a variety of
formulations. Guidance on the selection of reaeration
coefficients for dissolved oxygen is provided in Section
5 (Supplements XIII and XIV).
For other gases, such as unionized ammonia and
many toxic materials, the gas film rather than the liquid
film may control gas transfer, which must be reflected
in the formulation of the rate term.
Additionally, the method for computing saturation con-
centrations will vary (see Supplement IV, Volatiliza-
tion).
SUPPLEMENT IV: SYNTHETIC ORGANICS
I. Loss Rates
Synthetic organic concentrations are described using
the constituent mass balance equation (Equation 2.5)
similarly to other materials. The processes impacting
their physical, chemical and biological transformations
differ, as illustrated by Figure 2-11. Physical losses
occur through mechanisms such as volatilization, set-
tling, and sedimentation, while physical gains can oc-
cur through resuspension. Chemical transformations
may result from hydrolysis, photolysis, oxidation and
reduction and ionization. Biological transformation and
loss can result from bacterial degradation and accu-
mulation in biota. Additional differences result where
materials do not mix, or only partially mix, with the
mean flow, such as some oils. The mathematical treat-
ment of immiscible or only partially miscible oils often
requires specialized modeling techniques, such as
those used in oil-spill modeling.
For constant environmental conditions, the overall
chemical loss rate of synthetic organics is often ap-
proximated as a first-order reaction:
S=-KTC
(2.36)
where KT is the observed loss coefficient (day" ), C is
the total chemical concentration (g/m ) and, and S is
the source/sink term of the constituent mass balance
equation (Equation 2.5). The value KT represents a
single set of environmental conditions only.Changes
in temperature, velocity, depth, sunlight, wind, sedi-
ment concentrations, or pH can affect the total loss rate
in ways that can not be considered using this ap-
proach. Alternatively, each of the processes impacting
the transformations may be simulated.
An overview of methods used to describe these trans-
formation processes is provided below. Additional
information is provided by Chapra and Reckhow
(1983), Thomann and Mueller (1987) and elsewhere.
A method to complement field survey data is the
chemical process approach. This approach combines
laboratory-measured chemical constants with field-
measured environmental properties to estimate site-
specific rate coefficients, Ki (x,t), for several loss
processes "i";
Ki(x,t) = KiEi(x,t) (2.37)
where Ki is a laboratory measured second order rate
constant and Ei (x,t) is the intensity of the relevant
2-26
-------
©
PROCESSES
(e) HYDROPHOBIC SORPTION/DESORPTION
IONIC SORPTION/DESORPTION
IONIZATION
VOLATILIZATION
(J2 HYDROLYSIS
Bs
Lll^-
—&-
w
DISSOLVED
NEUTRAL
is.
\<
»t
SORBED
NEUTRAL
\ / ^^
&
DISSOLVED
IONIZED
I6
vi
}t
SOKBED
IONIZED
/-N
|
(
c
Y
r
pH
CEC
<3>—*~
Rr
Tw
(\3) OXIDATION
M4) REDUCTION
M5 BENTHIC BIODEGRADATION
WATER BIODEGRADATION
PHOTOLYSIS
PARAMETERS
Tair= air temperature
VwincF wind speed
Vwater= water velocity
Ddepth= water depth
Cair= atmospheric concentration
S=Solids concentration
foc= fraction organic carbon
Tw= water temperature
R0= concentration of oxidant
CEC= cation exchange capacity
Rr= concentration of reductant
Bs= bacterial concentration in sediment
Bw= bacterial concentration in water
1= incident light
Ke= extinction coefficient
Figure 2-11. Basic variables and processes for reactive organic chemicals.
2-27
-------
environmental parameter. If more than one loss proc-
ess is active for a chemical in an environment, the
overall loss coefficient can be estimated by summing
the individual rate constants. Combining the chemical
process approach with the field survey approach
should increase the reliability of modeling estimates,
allowing extrapolation to a much wider range of envi-
ronmental conditions.
II. Physical Loss Mechanisms
A. Volatilization
Volatilization in most models is treated similarly to
surface oxygen exchange (Equation 2.35) where the
loss due to volatilization (Sv) is equal to the difference
in chemical concentrations multiplied by a transfer
coefficient, as
Sv = kv(Cw-Co) (2.38)
where kv is the transfer rate, Cw the dissolved concen-
tration of the chemical in water, and Ca the saturation
dissolved concentration, dependent upon the atmos-
pheric partial pressure and Henry's Law constant for
the material.
A common assumption is that the atmospheric con-
centration is much less than the water concentration,
allowing simulation of the transfer as a pseudo-first
order rate. Where the toxicant mass balance expres-
sion (Equation 2.5) is written for the total concentration
(dissolved plus particulate), the concentration must
also be adjusted for the fraction dissolved (fd) as
Sv = kvfdCtw (2.39)
where Ctw is the total concentration in water.
The transfer rate is usually computed as the reciprocal
of the resistances in the two films (gas and liquid), as
kv=(RL+Ro)
-i
(2.40)
where RL is the liquid phase resistance and RG the gas
phase resistance.
The liquid and gas transfer coefficients are dependent
on turbulence at the interface, on temperature, and on
properties of the chemical such as diffusivity. Empirical
correlations have been developed relating transfer
coefficients either directly to physical parameters such
as wind velocity and the density and viscosity of the
water (MacKay et al. 1983; Southworth et al. 1979a),
plus the molecular weight and diffusivity of the chemi-
cal or to the field-measured transfer coefficients of
oxygen and water vapor (Liss and Slater 1974).
O'Connor (1983) has presented a theoretical develop-
ment for the liquid transfer coefficient applicable to a
wide range of hydrodynamic conditions, but applica-
tion requires estimates of several coefficients that are
not easily obtained.
B. Sorption
Many toxic materials sorb strongly onto particulates.
Estimates of sorption are required in modeling toxic
materials since processes impacting dissolved and
particulate fractions differ. Sorption is the bonding of
dissolved chemicals, C, onto solid phases, Si, such as
benthic and suspended sediment, biological material,
and sometimes dissolved or colloidal organic material
resulting in the formation of the chemical-sediment
bond, C-Sj.
= C- Si
(2.41)
Sorption reactions are usually fast relative to other
environmental processes, and equilibrium may be as-
sumed. For environmentally relevant concentrations
(less than 10~5 M or one-half water solubility), equilib-
rium sorption is linear with dissolved chemical concen-
tration (Karickhoff 1984) or:
C,=KP, Cd (2.42)
where Ci is chemical concentration in the solid phase
i (mg/kg), Cd is dissolved chemical concentration
(mg/L), and Kpi is the sorption partition coefficient
between the two phases (L/kg). At equilibrium, then,
the distribution among the phases is controlled by the
partition coefficient, Kpi. The total mass of chemical in
each phase is controlled by Kpi and the amount of solid
phase present.
Values for the partition coefficients can be obtained
from laboratory experiments. For organic chemicals,
lab studies have shown that the partition coefficient is
related to the hydrophobicity of the chemical and the
organic matter content of the sediment. Normalization
of the partition coefficient by the organic-carbon con-
tent of the sediment has been shown to yield a coeffi-
cient, Koc, that is relatively independent of other
sediment characteristics or geographic origin (Karick-
off 1981). Correlation of Koc with the water solubility
of the chemical or the octanol/water partition coeffi-
cient of the chemical has yielded successful predictive
tools for incorporating the hydrophobicity of the chemi-
cal in an estimate of its partitioning. These correlations
do poorly for chemicals with very low or very high
hydrophobicity, however, because of deviations from
hydrophobic adsorption.
Chemicals containing polar functional groups and low
octanol/water partition coefficients tend to exhibit hy-
drophilic contributions to adsorption. Large nonpolar
molecules with high octanol/water partition coefficients
generally require long time periods to reach
2-28
-------
equilibrium resulting in low estimates of Koc when
sorption is measured over short time frames (Karickoff
1984). The latter effect is particularly significant be-
cause it suggests that the assumption of instantane-
ous equilibrium used by the toxic chemical models may
not be valid for those chemicals for which adsorption
is the most important process (Ambrose et al. 1988).
In addition to the assumption of instantaneous equilib-
rium, implicit in the use of Equation 2.42 is the assump-
tion of reversibility. Laboratory data for very
hydrophobic chemicals suggest, however, that a hys-
teresis exists, with desorption being a much slower
process than adsorption. Karickhoff (1984) suggests
that this effect may be the result of intraparticle kinetics
in which the chemical is slowly incorporated into com-
ponents of the sorbant. This phenomenon is not well
understood and no quantitative modeling framework is
available to characterize it (Ambrose et al. 1988).
Empirical evidence has suggested that the partition
coefficient is inversely related to the particle concen-
tration. A particle interaction model has been proposed
by Di Toro (1985) which describes this relationship.
III. Chemical Loss Mechanisms
A. Hydrolysis
The overall hydrolysis rate constant in most toxic
chemical models is calculated by:
KH =
+ km, + kHB, • [OtT]) (2.43)
where kHAi is the acid hydrolysis rate constant for
phase i (L mole"1 sec"1', km\ii is the neutral hydrolysis
rate constant for phase i (sec" ), kHBi is the alkaline
hydrolysis rate constant for phase i (mole"1sec"1), [H+]
is the hydrogen ion concentration (moles L"1), and
[OH"] is the hydroxide ion concentration in (moles/L).
The models do not compute hydrogen or hydroxide ion
concentrations. Instead these are input to the models
assuming that their concentrations are unaffected by
the hydrolysis reaction because of the low concentra-
tion of the toxic chemical present and reacting.
B. Photolysis
A quantitative framework that permits the prediction of
direct photolysis from the incident light and the char-
acteristics of the chemical (Zepp and Cline 1978) has
been incorporated into several of the toxic chemical
modeling frameworks. Use of this framework in natural
water systems is complicated by the lack of a satisfac-
tory model of UV-light penetration that incorporates the
effects of both dissolved organics and particulate ma-
terial in the water column. A comprehensive frame-
work for photolysis also must include sensitized
photolysis. Unfortunately, the spectrum of com-
pounds, particularly dissolved organics, involved in
photochemical reactions is not known (Miller 1983). In
addition, valid frameworks to predict free radical reac-
tions have not been developed and the importance of
these reactions remain undetermined (Zepp 1980).
A less rigorous method for predicting the photolysis
rate coefficient Kp involves extrapolations of observed
rates from one environmental condition to another:
Kp = KPG [L] "LqPifi (2.44)
where KPG is the observed rate coefficient (s" ) for a
reference light intensity, [L] is the fraction of the refer-
ence light intensity averaged through the water col-
umn, cp Pi is the relative yield for the chemical in phase
i, and // is the fraction of the total chemical concentra-
tion in phase i. The reference light fraction [L] accounts
for depth, light extinction, cloud cover, latitude
changes, and surface light variability.
C. Oxidation/Reduction
Chemical oxidation of organic materials can be a con-
sequence of interactions between free radicals and the
pollutants. Free radicals can be formed as a result of
photochemical reactions. Free radicals that have re-
ceived some attention in the literature include alkylper-
oxy radicals, RO2; OH radicals, and singlet oxygen.
Oxidation is often modeled as a second order process
dependent upon concentration of the oxidant and
chemical.
D. Ionization
Consider a weak acid AHs or base BHs which may or
may not react with water modules to form charged
anions and cations (ionize):
Kai (2.45)
, Kbi (2.46)
where Ka and Kb are the equilibrium first ionization
constants for the reactions. These reactions are rapid.
At equilibrium, the distribution of chemicals between
the un-ionized and the ionized species is controlled by
the pH of the water and the ionization constants (Am-
brose et al. 1988). Stronger acids and bases may
undergo further ionization, controlled by ionization
constants Ka2, Kas, Kb2, Kb3, the second and third
ionization constants forthe acid and base respectively.
However, toxic organics are generally weak acids or
bases. Examples of weak acids are the phenols (chlo-
rophenol, dichlorophenol, trichlorophenol and pen-
tachlorophenol), and a base is benzidine (Mills et al.
1985).
2-29
-------
The ability to simulate ionization, the disassociation of
a chemical into charged species, may be critical for
chemicals that exhibit different chemical charac-
teristics in different ionic states. For some chemicals,
such as ammonia or hydrogen cyanide, it may be
necessary to predict ionization in order to predict vari-
ations in toxic effects. Increases in observed toxicity of
hydrogen cyanide (HCN) above pH 9 correlate well
with the fraction in the anionic form (CN), (Burns 1985).
Ionization was described previously for ammonia
(Supplement III, part V).
IV. Biological Loss Mechanisms
A. Biodegradation
Biodegradation is generally assumed to follow
Michaelis-Menten enzyme kinetics. Values for the half
saturation constant Km and the maximum rate of deg-
radation are not easily measured. Toxic chemical mod-
els generally assume the chemical concentration is
much less than the half saturation constant and sim-
plify the Michaelis-Menten equation to:
(2.47)
where KB is the second order rate coefficient (mL
11 1
cells" day" ). The bacterial activity, B (cells mL" ), is
equal to the reactant enzyme concentration (Ambrose
et al. 1988). However, enzyme concentration cannot
be measured in the field and the environmental and
ecological effects on enzyme activity are difficult to
estimate (Lewis et al. 1984). Consequently, other bio-
logical parameters are substituted, such as the con-
centration of bacterial cells.
The growth kinetics of the bacterial population degrad-
ing a toxic chemical are not well understood. The
presence of competing substrates and of other bacte-
ria, the toxicity of the chemical to the degrading bacte-
ria, and the possibilities of adaptation to the chemical
or co-metabolism make quantification of changes in
the population difficult as well as the extrapolation of
laboratory to field conditions questionable. As a result,
toxic chemical models generally assume a constant
biological activity rather than modeling the bacteria
directly. Often, measured first order biodegradation
rate constants obtained from experiments under field
conditions as used rather than second order rates
obtained from laboratory experiments that then require
the additional estimation of field bacterial concentra-
tions (Thomann and Mueller 1987).
SUPPLEMENT V: METALS
I. Modeling Techniques
The simulation of metals in aquatic systems has been
approached from several levels of complexity. Pres-
ently, only approximate methods are available for es-
timating the dynamic mass transport of metals in
complicated natural environments. The sorptive inter-
actions of metals with particulate matter is the major
process affecting the fate of toxic metals in the natural
environment (Medine and McCutcheon 1989).
Modeling studies have been conducted using field
derived or estimated, constant or varying, partition
coefficients to describe the association of metals with
solids, with associated transport due to settling and
resuspension. For example, the riverine model
MICHRIV (Large Lakes Research Station 1987) util-
izes this approach and was used to analyze metal
contamination in the Flint River, Michigan as described
by Delos et al. (1984) and Mills et al. (1985). Thomann
and Meuller (1987) described the simulation of sedi-
ment cadmium concentrations in the Sajo River, Hun-
gary, using a partition coefficient which varied with
suspended solids concentrations. Mills et al. (1985)
describes several screening level approaches consid-
ering sorption. These methods may also be appropri-
ate for some estuarine waste load allocations for met-
als. However, care should be exercised in using data
to estimate sorption that does not reflect similar water
chemistry and sediment characteristics to the system
being modeled (Medine and McCutcheon 1989).
An alternative approach to using descriptive methods
for partitioning may be required where sufficient field
data are not available for estimating partition relation-
ships, where chemical conditions are expected to
change or where it is necessary to identify the form of
the metal present in order to estimate its hazard.
Equilibrium speciation models, such as MINTEQA1
(Brown and Allison 1987) may provide estimates of
equilibrium aqueous speciation, adsorption, gas phase
partitioning, solid phase saturation states, and precipi-
tation-dissolution for multimetal, multiligand systems.
For waste load allocation purposes, equilibrium spe-
ciation models must then be run in conjunction with
transport and transformation models, such as WASP4
(Ambrose et al. 1988).
2-30
-------
II. Process Descriptions
The form of the metal will be determined by the net
result of interactions between complexation, chemical
precipitation, adsorption, and oxidation-reduction. The
combined effects of these interactions are computed
using computer programs such as MINEQL (Westhall
et al. 1986), MINTEQA1 (Brown and Allison 1987) and
others which compute equilibrium composition in a
multimetal, multiligand system, using mass balance
and mass action equations and considering the effects
of chemical precipitation, redox, and sorption.
A. Complexation.
Complexation refers to the reaction of a metal (e.g. Ag,
Cd, Cu, Pb, Zn, etc.) with organic and inorganic ligands
(e.g. OH", CC-32-, SC-42-, CI", F", NHs, S2", amino acids,
humates, fulvates, etc.) in water, to form a third species
(the metal-ligand complex).
To compute the form of a particular metal is likely to be
in, it is usually necessary to consider all of the dominant
sets of reacting ligands and competing metals. This
involves the simultaneous solution of a series of non-
linear equations. To develop these equations in a
general form, we may first represent the components
of a dissolved complex (metals and ligands) as X®,
where X® is the activity for the component j of the
complex (or molar concentration if ionic strength is
zero). For example, if "a" moles of component X(1)
reacts with "b" moles of component X(2) to form a
complex, the reaction may be written as
aX(l) + b X(2)=X(l)aX(2)b (2.48)
Assuming equilibrium, the reaction may be written as
X(lfX(2f
and then
C(i} = K(i} X(lfX(2)b (2.49)
where C(i) is the activity of the complex (X(1)aX(2)b)
and K is a stability constant. If we further let the
stoichiometric coefficients be represented as a(i,j) for
the complex i and component j (for example above a
= a(i,1) and b= a(i,2)) then the reaction may be written
in more general form as
(2.50)
7=1
where N is the total number of components (metals
and ligands) in complex i (2 in the above example), and
a(i,j) is the stoichiometric coefficient for the jth compo-
nent of the ith complex.
A mass balance may be written for any given compo-
nent distributed among all of the complexes. For ex-
ample the amount of a component X(j) in a complex
C(i) is a(i,j)C(i). The total amount of the component
among all complexes may be written as
XT(J ) = Ł a (ij) C (/)
(2.51)
where M is the total number of complexes. Substituting
from Equation 2.50, Equation 2.51 may be rewritten as
M
(2.52)
y=l
The solution procedure, used in such models as MIN-
EQL (Westall et al. 1986) and MINTEQA1 (Brown and
Allison 1987), is to make an initial guess as to the
activity (or concentration) of each of the j components.
The concentration of the individual species is then
computed, using Equation 2.50, and the total of each
component calculated (Equation 2.52, XT(J))- This total
is then compared to the known total (T(j)), as
for all components and if the difference (D(j)) is greater
than some criteria, a second guess estimate of the
activities is made. The solution procedure is iterated
until the known totals for each of the components and
computed totals converge to within some specified
difference. The procedure is accomplished numeri-
cally using techniques such as the Newton-Raphson
method for solving simultaneous non-linear equations.
B. Precipitation and Dissolution.
In some cases, the transport and fate of metals is
affected by chemical precipitation and dissolution,
either through direct precipitation of metal solids ( e.g.
CdS, CuSC-4) orthrough coprecipitation where a major
ion precipitate is formed which binds metals in the
process (Medine and McCutcheon 1989). The possi-
ble concentrations of metal ligand complexes are con-
strained by their solubility, as expressed by the
solubility product for the ith complex, KSp(i). However,
determination of the solubility requires consideration
of all possible reactions and equilibria (Stumm and
Morgan 1981). Chemical equilibrium models such as
MINTEQA1 can examine the process of precipitation
of pure metals forms in aqueous systems, assuming
equilibrium conditions.
C. Redox Reactions.
Metals can change oxidation states through various
oxidation and reduction reactions, expressed as
= M+,Kr
(2.53)
2-31
-------
where M++ is oxidized metal, M+ is reduced metal, e"
is an electron, and KM is the equilibrium coefficient for
reaction i. Oxidation-reduction reactions exert signifi-
cant controls on the chemistry of major ions and trace
metals and their mobility, particularly between sus-
pended and bed solids forms (Medine and McCutch-
eon 1989). Reduction reactions, such as in the
formation of sulfides in sediments, may strongly affect
the dissolved concentrations and ecotoxicity of trace
metals. Redox reactions are generally included in
chemical equilibrium models, such as MINTEQA1.
D. Sorptlon.
The modeling of metal adsorption to metals is receiving
considerable interest due to its importance in regulat-
ing metal movement in aquatic systems (Medine and
McCutcheon 1989). However, sorption is strongly af-
fected by the interactions between metals forms. Sorp-
tion is strongly affected by pH, often varying from 0 to
100 percent adsorption over a narrow range of pH
(often less than 2 units).
A standard relationship for metals sorption may be
written as
M+Sm=MSn
and
KAM =
(MSm)
[M](Sm)
(2.54)
(2.55)
where KAM is a standard adsorption constant and Sm
an adsorbing surface of type m and M is the free metal
ion concentration. Other models proposed to describe
adsorption and included in the MINTEQA1 code are
activity Langmuir sorption, activity Freundlich, ion ex-
change sorption, constant capacitance and triple-layer
surface complexation models (Medine and McCutch-
eon 1989, Brown and Allison 1987).
2.9. References
Akiyama, J. and Stefan, H.G. 1985. Turbidity Current
with Erosion and Deposition, ASCE, Jour, of Hydraulic
Engineering, 111(HY12).
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3. Model Identification and Selection
Robert B. Ambrose, Jr., P.E.
Center for Exposure Assessment Modeling
Environmental Research Laboratory, U.S. EPA, Athens, GA
3.1. Introduction
The first steps in the modeling process are model
identification and selection. Specific water quality prob-
lems are identified and study objectives are set. The
goals are to identify the simplest conceptual model that
includes all the important estuarine phenomena affect-
ing the water quality problems, and to select the most
useful analytical formula or computer model for calcu-
lating waste load allocations. Selection of too simple a
model can result in inaccurate predictions of future
water quality under hypothetical load reductions. This
can happen even if the model calibration "fits" existing
data. Inaccurate projection from present to future can
be caused by a changing balance among important
processes, such as carbonaceous, nitrogenous, and
sediment oxygen demand. The result is a waste load
allocation that is either too expensive or underprotec-
tive of water quality.
On the other hand, selection of too complex a model
will most likely result in misdirected study resources,
delays in the study, and increased cost. Predictive
uncertainty may increase because of extra "free"
model parameters that cannot be estimated with avail-
able data. Study costs will increase because of the
additional data requirements and the expanded com-
puter and manpower time needed for model runs,
analysis, and sensitivity studies.
This chapter provides general guidance and some
specific procedures for identifying an appropriate
model. The term "model" in Section 3.2 is used in a
general sense to identify the variables and equations
solved, the dimensionality, and the space and time
resolution. Specific analytical formulas and computer
models are discussed in Section 3.3.
3.2. Model Identification
During model identification, available information is
gathered and organized to construct a coherent picture
of the water quality problem. The goals are to develop
the most effective monitoring strategy and to select the
most appropriate computer model.
There are four basic steps in model identification:
— Establish study objectives and constraints
— Determine water quality pollutant interactions
— Determine spatial extent and resolution
— Determine temporal extent and resolution
These steps are generally considered sequentially.
They are related, however, and later steps may require
refinement of earlier decisions. Indeed, after the study
has been initiated, new data or model results may
suggest changes in the conceptual model initially iden-
tified.
Following model identification, another important step
is advised:
— Perform rapid, simple screening calculations
These calculations should help the modeler gain a
better understanding of expected pollutant levels and
the spatial extent of water quality problems. Analytical
solutions are often used along with available data
throughout the model identification stage. These tech-
niques are discussed in Section 3.3.2.
3.2.1. Study Objectives and Constraints
The first step in identifying an appropriate WLA model
for a particular site is to review the applicable water
quality standards and the beneficial uses of the estuary
to be protected. Local, state, and federal regulations
may contribute to a set of objectives and constraints.
Each may specify particular pollutants or classes of
pollutants, and imply time and space scales that must
be resolved by the model. For example, proscription of
"toxic pollutants in toxic amounts" implies simulation of
whole effluent toxicity dilution. Ammonia or metals
standards imply simulation of those specific chemicals.
Regulations may specify an "allowable mixing zone" in
the vicinity of the outfall. This requires that a model
have sufficient spatial resolution to resolve near-field
dilution and mixing processes. For example, the regu-
lation for a thermal outfall may require that waters
return to within 2 °C of the ambient temperature within
100 m of the outfall. This requires a model with an
analytical solution, or a numerical model segmented on
the order of 10 meters. By contrast, standards for
minimum daily average dissolved oxygen require an
3-1
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estuarine-wide, or far-field model that extends beyond
the range of influence of the discharge.
The next step in identifying an appropriate WLA model
for a site specific application is to review the existing
data on waste loads, stream flows, and ambient water
quality with respect to the beneficial uses of the estuary
and the applicable water quality standards. These data
should indicate whether standards violations or water
quality problems are associated with diurnal fluctua-
tions, storm events, flow variation, and/orseason of the
year. The modeler can use this information to deter-
mine the temporal resolution (steady-state, tidally av-
eraged, real time) and the important pollution sources
(point source, nonpoint source) that must be included
in the selected model. The ambient water quality data
should also indicate where violations or problems are
occurring and whether significant spatial gradients in
concentration exist. The combined information col-
lected on the water quality problems will help deter-
mine which driving forces (freshwater inflow, tides,
wind, etc.) must be represented in the model. In order
to further define required model capabilities, future
developments planned for the watershed should be
identified. Projected new point source discharges or
land use changes may require the WLA model to have
different capabilities than the existing situation merits.
The final result of this step should be a clear under-
standing of the pollutants and water quality indicators,
the areas, and the time scales of interest. The spatial
and temporal scales for a range of standard water
quality problems are suggested in Table 3-1. These are
for general guidance, and must be interpreted more
precisely for each specific waste load allocation.
3.22. Water Quality - Pollutant Interactions
After the pollutants and water quality indicators are
identified, the significant water quality reactions must
be determined. These reactions must directly or indi-
rectly link the pollutants to be controlled with the pri-
mary water quality indicators. All other interacting
water quality constituents thought to be significant
should be included at this point. This can best be done
in a diagram or flow chart representing the mass
transport and transformations of water quality constitu-
ents in a defined segment of water. Figures 2-4 through
2-10 (Section 2) illustrated variables and processes
important to the major water quality problems. Not all
of these have to be included in the actual WLA model
selected for use. Those excluded from a model, how-
ever, should be considered externally and parameter-
ized in the coefficients. Figure 2-4 covered sediment
transport. Figures 2-5 through 2-9 illustrated conven-
tional pollutant interactions affecting dissolved oxygen,
nutrient enrichment, and eutrophication. Figure 2-10
dealt with toxicants, such as organic chemicals.
Table 3-1. General Scales of Interest
Problem Context
Salinity
Sediment
Bacteria
Heat
D.O. Depletion
Nutrient Enrichment
Toxicity
Human Exposure
-metals
-volatile organics
-hydrophobic organics
Spatial Scale
Estuarine-wide
Estuarine-wide
Mid/Far-field
Near-field
Far-field
Far-field
Near-field
Far-field
Far-field
Far-field
Temporal Scale
Seasons
Days to Seasons
Hours/Days
Hours
Days to Seasons
Seasons to Year
Hours to Days
Weeks to Years
Days to Weeks
Seasons to Years
Each water quality constituent must be examined to
determine the important forcing functions and bounda-
ries, such as the air-water or water-benthic sediment
interfaces. For example, dissolved oxygen is influ-
enced strongly by reaeration across the air-water
boundary. The nature of the reaeration function, then,
should receive particular attention in the monitoring
and modeling process. Constant or spatially-variable
rate constants might be specified as calibration pa-
rameters. For estuaries dominated by flow or
wind,reaeration rates might better be specified as func-
tion of velocity, depth, and wind speed. At the benthic
boundary, sediment oxygen demand is usually speci-
fied as a spatially-variable flux, to be measured or
calibrated. This flux, however, can be expected to
change with future reductions in waste loads. There
have been recent attempts to include benthic organic
material as a model variable, with the flux computed
internally. While satisfying conceptually, the benthic
components of these models are difficult to calibrate
because of the long time frames controlling benthic
reactions. Good practice at present may be to include
these reactions in the conceptual model, but calculate
or estimate their effects external to the waste load
allocation model. An example calculational framework
was proposed by Di Toro (1986).
The final result of this step should be the assimilation
of all the available knowledge of a system in a way that
major water quality processes and ecological relation-
ships can be evaluated for inclusion in the numerical
model description. The conceptual model is the starting
point from which systematic reductions in complexity
can be identified that will provide an adequate repre-
sentation of the system, while meeting the objectives
of the study.
3-2
-------
3.2.3. Spatial Extent and Scale
The general area affected by the waste load allocation
and the significant water quality reactions were identi-
fied in steps 1 and 2. The purpose of this step is to
specify the spatial extent, dimensionality, and scale (or
computational resolution) of the WLA model. This may
be accomplished by determining the effective dimen-
sionality of the estuary as a whole, defining the
boundaries of the study area, then specifying the re-
quired dimensionality and spatial resolution within the
study area.
3.2.3.1. Effective Dimensionality
Real estuaries are, of course, three dimensional. There
are gradients in hydrodynamic and water quality con-
stituents over length, width, and depth. The effective
dimensionality of an estuary includes only those di-
mensions over which these gradients significantly af-
fect the WLA analysis. Justifiable reductions in
dimensionality result in savings in model development,
simulation, and analysis costs. Usually the vertical
and/or lateral dimension is neglected. Eliminating a
dimension from the WLA analysis implies acceptable
uniformity of water quality constituents in that spatial
dimension. For example, use of one dimensional lon-
gitudinal models implies acceptably small concentra-
tion deviations from the cross-sectional mean, both
vertically and laterally. This judgment requires under-
standing both the transport behavior of estuaries and
the specific goals of the WLA study.
For estuarine WLA modeling, the longitudinal (x) di-
mension can almost never be neglected. The analyst
must decide whether the lateral (y) or vertical (z)
dimensions must also be retained. The most frequent
cause of variation in the vertical direction is density
stratification. Lateral variations may be caused by large
widths and slow lateral mixing. Vertical and lateral
variations can be observed by plotting water quality
concentration variations with width and depth. If such
data are not available, vertical and lateral variations
can be predicted in one of several ways:
— density, salinity, or temperature gradients,
— tidal or residual velocity reversals over width or
depth,
— dye cloud splitting and differential advection,
— geomorphological classification.
A. Degree of Stratification.
Fisher et al. (1972) suggested a method to predict the
degree of stratification in an estuary as a whole. Fresh-
water is lighter than saltwater. This produces a buoy-
ancy of amount:
Buoyancy = A p g QR
where
(3-1)
A p= the difference in density between sea and river
water, (about 0.025 kg/m3),
g = acceleration of gravity, (about 9.81 m/sec ), and
QR = freshwater river flow, m /sec
The tide on the other hand is a source of kinetic energy,
equal to:
Kinetic energy = p W Ut (3-2)
where
p = the seawater density, about 1.025 kg/m ,
W = the estuary width, m, and
Ut = the square root of the averaged squared velocities,
m/sec.
Width and velocities should be taken at a repre-
sentative cross section of the estuary. The ratio of the
above two quantities, called the "Estuarine Richardson
Number," is an estuary characterization parameter
which is indicative of the vertical mixing potential of the
estuary:
R = ApgQR/pWUt3 (3-3)
If R is very large (above 0.8), the estuary is typically
considered to be strongly stratified and the flow domi-
nated by density currents. If R is very small, the estuary
is typically considered to be well-mixed and the vertical
density effects to be negligible.
Another desktop approach to characterizing the degree
of stratification in the estuary is to use a stratification-
circulation diagram (Hansen and Rattray, 1966). The
diagram (shown in Figure 3-1) is based on measure-
ments from a number of estuaries with known degrees
of stratification. Its use requires the calculation of the
Stratification Parameter = A S/S0
and the
Circulation Parameter = Us/Uf
where
(3-4)
(3-5)
AS = time averaged difference between salinity levels
at the surface and bottom of the estuary,
S0 = cross-sectional mean salinity,
3-3
-------
10-3
o
10
ID
'2
ID
'3
NM.
11S
10
IO2
U. /U,
IO
104
105
(Station code: M, Mississippi River; C, Columbia
River estuary; J, James River estuary; NM, Narrows of
the Mersey estuary; JF, Strait of Juan de Fuca; S,
Silver Bay. Subscripts h and I refer to high and low
river discharge; numbers indicate distance (In miles) from
mouth of the James River estuary.
Figure 3-1. Stratification circulation diagram and examples.
3-4
-------
Us = net non-tidal surface velocity, and
Uf = mean freshwater velocity through the section.
For best results, mean salinity and velocity should
represent averages over several tidal cycles. The
stratification parameter is much less sensitive to tidal
variations than the circulation parameter. To apply the
stratification-circulation diagram, calculate the pa-
rameters of Equations 3-4 and 3-5, and plot the result-
ing point on the diagram. Type 1 estuaries have
seaward flows at all depths, and the upestuary salt
intrusion is due to tidal diffusion. Type 1a represents
slight stratification as in a laterally homogeneous, well-
mixed estuary. In Type 1 b, there is strong stratification.
Type 2 is partially well-mixed and shows flow reversals
with depth. In Type 3a the transfer is primarily advec-
tive, and in Type 3b the lower layer is so deep, as in a
fjord, that circulation does not extend to the bottom.
Finally, Type 4 represents the salt-wedge type with
intense stratification (Dyer, 1973). The purpose of the
stratification-circulation analysis is to determine the
degree of vertical resolution needed for a modeling
study. If the estuary is well-mixed, the vertical dimen-
sion may be neglected, and all constituents in the
water column are assumed to be dispersed evenly
throughout. If the estuary is highly stratified, it is appro-
priate to model at least two layers. The approach for a
partially-mixed system is not so clear and judgment
must be exercised. For a recent toxics study (O'Con-
nor et al., 1983), the James River, which is partially
stratified, was treated as a 2-layer system.
A final desktop method for characterizing the degree
of stratification is the calculation of the estuary number
proposed by Thatcher and Harleman (1972):
(3-6)
where
Ed = estuary number,
Pt = tidal prism volume, m ,
Ud = densimetric velocity, m/sec,
= (gDAp/p)/2
A p= the density difference between river water and
3
sea water (about 0.025 kg/m ),
p = density of sea water (about 1.025 kg/m ),
U0 = maximum velocity at mouth of estuary, m/sec
D = depth, m,
g = acceleration due to gravity (9.81 m/sec ), and
T = tidal period, (about 44,700 sec).
Again, by comparing the calculated value with the
values from known systems, one can infer the degree
of stratification present.
The degree of stratification determined by one of the
above methods may be translated into the following
criteria for model selection:
— strongly stratified - include the vertical dimension in
at least a 2 layer model
— moderately stratified - may include the vertical
dimension in a multi-layered model, or
— vertically well-mixed - neglect vertical dimension,
unless water quality processes dictate vertical resolu-
tion
B. Tidal or Residual Velocity Reversals.
Beyond the use of a stratification diagram, the analysis
of vertical dimension reduction becomes more difficult
and intuitive. However, the following criteria seem
reasonable (Figure 3-2):
— tidal velocity reversals - should include vertical
dimension in at least a 2-layer model,
— residual velocity reversals - may include the vertical
dimension in a multi-layered model or may neglect
vertical dimension if vertical variability is small,
— no observable reversals - may neglect vertical
dimension.
C. Dye Studies.
Dye studies simply replace the Eulerean observations
of current meters with the Lagrangian movement of a
dye cloud study. Again, quantitative analyses are dif-
ficult, but the following criteria seem reasonable (Fig-
ure 3-3):
— Dye cloud separates and moves -cloud is respond-
ing to a vertical flow reversal and moves as 2 or more
distinct units, indicating the vertical dimension should
be included in at least a 2-layer model,
— Dye cloud spreads in non-Gaussian manner - some
differential shearing is present and the system may be
studied using a multi-layer model, or,
— Dye cloud moves downstream and diffuses in a
Gaussian manner - little differential shearing is present
and the system may be modeled neglecting the vertical
dimension.
3-5
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a) Tidal Velocity Reversal
b) Residual Velocity Reversal
c) No Observable Reversals
Figure 3-2. Vertical velocity profiles.
D. Geomorphological Classification.
Over the years, a systematic geomorphological clas-
sification of estuaries has evolved. If little or no data
are available, one can try to categorize the estuary
within the basic morphological definitions of Dyer
(1973). Dyer (1973) and Fischer et al. (1979) identify
four groups:
Drowned river valleys (coastal plain estuaries)
Fjords
Bar-built estuaries
Other estuaries that do not fit the first three classifica-
tions
Typical examples of North American estuaries are
presented in Tables 3-2 and 3-3. The characteristics
of each geomorphological classification were dis-
cussed in Section 2-1. Using these classifications, the
approach is to estimate the degree of stratification from
known conditions in a geomorphologically similar es-
tuary and use the criteria given below under "degree
of stratification".
3.2.3.2. Study Area Boundaries
After the effective dimensionality of the estuary has
been determined, specific boundaries of the study area
must be established. In general, the boundaries should
be located beyond the influence of the discharge(s)
being evaluated. Otherwise, proper specification of
boundary concentrations for model projections is very
difficult. Sometimes this guideline is not possible. One
rule strictly applies -boundaries influenced by a dis-
charge should be located far enough from the discharge
so that errors in the boundary concentrations do not
significantly affect predicted maxima or minima upon
which the WLA is being based.
Beyond these rules, several common sense guidelines
can help locate proper model boundaries. Boundaries
should be located where flow or stage and water quality
are well monitored. Upstream boundaries should be
located at a fall line, or at a gaging station in free-flowing,
riverine reaches. Downstream boundaries are best lo-
cated at the mouth of an estuary, or even nearby in
a) Cloud Separates
L
Injection Point
b) Non-Gaussian Spreading
Injection Point
L,
Injection Point
c) Gaussian Spreading with Downstream Movement
Figure 3-3. Vertical dye concentration profiles.
3-6
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Table 3-2. Topographic Estuarine Classification
Type / Domi- Vertical Degree Lateral
nant Long of Stratification Variability
Term Process
Coastal Plain / Moderate Moderate
River
Flow
Bar Built/ Wind Vertically Well High
Mixed
Fjords / Tide High Small
Other Various Various
Estuaries/
Various
Example
Chesapeake
Bay
James River
Potomac River
Delaware
Estuary
New York Bight
Little Sarasota
Bay
Apalachicola
Bay
Galveston Bay
Al be marie
Sound
Palmico Sound
Pugent Sound
Alberni Inlet
Silver Bay
San Francisco
Columbia
River
the ocean. For large estuaries with relatively unaf-
fected seaward reaches, the downstream boundary
can be located within the estuary near a tidal gage and
water quality monitoring station.
If these guidelines are not possible because of exces-
sive computational elements, consideration should be
given to nested grids. A crude grid could span the
estuary and predict tidal flows and concentrations.
Two or more internal elements in the coarse grid could
serve as boundaries to a fine grid. This strategy may
be particularly useful for assessing near-field effects in
a strongly tidal estuary.
3.2.3.3. Study Area Resolution
If the study area constitutes all or most of the estuary,
the model dimensionality should equal the effective
estuarine dimensionality. If, however, the study area is
a discrete segment of the estuary, then further simpli-
fications in dimensionality may be possible. Data de-
scribing the spatial gradients of important water quality
constituents within the study area should be examined.
Dye studies can give important information on the speed
and extent of lateral and vertical mixing. The rate of
mixing must be compared with water quality reaction
rates to determine if lateral or vertical gradients are to
be expected for particular constituents. For example, an
estuarine reach that mixes laterally in 1 day can be
laterally averaged for pollutants with characteristic reac-
tion times of days (such as BOD). This same reach,
however, should not be laterally averaged for pollutants
with reaction times of hours (such as coliform bacteria
or some organic chemicals).
Lateral mixing can be described by the convective
length, Lc, over which the discharge plume is mixed
laterally (Fischer et al., 1978, Holley and Jirka, 1986).
Complete mixing is defined when the concentration is
within 5 percent of its mean value everywhere in the
cross section. For centerline and side discharges, re-
spectively, the mixing length Lc is given by
= 0.luW2/Ey
= 0.4uW2/Ey
(3-7)
(3-8)
where
u = mean downstream velocity, m/day
W = channel width, m
2
Ey = lateral diffusion coefficient, m /day
These formulas strictly apply to steady, unidirectional
flow. Complete mixing is not achieved during ebb or
flood tide if the lateral mixing time Lc/u is greater than 6
hours. Steady discharges can become laterally well
mixed within the mixing length even if the lateral mixing
time exceeds 6 hours due to tidal reversals. Lateral
diffusion coefficients are best estimated by dye studies
or other site specific data. Several general formulas are
Table 3-3. Stratification Classification
Type
Highly Stratified
Partially Mixed
Vertically
Homogeneous
Lateral Type
Laterally
Homogeneous
Partially Mixed
Moderate to
High
Variability
River Discharge Example
Large Mississippi
River
Mobile River
Medium Chesapeake
Bay
James Estuary
Potomac River
Small Delaware River
Raritan River
Tampa Bay
San Francisco
Bay
San Diego Bay
3-7
-------
given in Bowie et al., (1985). The time required for
complete lateral mixing (Lc/u) can be usefully com-
pared to reaction half lives (A t V2) to predict the degree
of lateral mixing for various pollutants and water quality
constituents. Half lives can be estimated from the first
order reaction rate constant K:
At V2 = 0.693/K
(3-9)
The convective mixing length should be compared to
the study area dimensions to determine the relative
importance of lateral mixing on the study area as a
whole. If the effects are significant, or if regulations
enforce water quality standards at the edge of the
mixing zone, then a near-field model is required. Nu-
merical models should be composed of computational
elements with short length A x and width A y:
Ax<0.2Lc
Ay<0.2W
(3-10)
(3-11)
Smaller dimensions will give better precision, but at
greater computational cost.
If near field effects are judged unimportant, then spatial
resolution for the entire study area must be deter-
mined. Dye studies can give important information
about the advective velocities and flushing times
through the study area. The rate of downstream trans-
port must be compared with water quality reaction
rates to determine if longitudinal gradients are to be
expected for particular constituents. Steeper water
quality gradients require more detailed spatial resolu-
tion. The length of model computational elements
should be significantly less than that required for con-
centrations to halve:
Ax
-------
The size and transport characteristics of the study area
determine its flushing time. This is the time required to
remove a parcel of water (along with associated dis-
solved non-reactive pollutants) from an upstream lo-
cation in an estuary. Factors that control flushing
include tidal action, freshwater inflow, and wind stress.
All of these forcing functions are time variable. Flush-
ing time calculations are usually based on average
tidal range and average or low freshwater inflow, with
wind effects neglected. Because estuarine flushing is
inherently dispersive in nature, there is no unambigu-
ous point at which the original water and pollutants are
completely replaced. Flushing times can be defined for
90%, 95% or even 99% removal. Typical flushing times
range from days in small estuaries or those dominated
by tributary flow to months in large estuaries during low
tributary flow conditions.
Several formulas have been used to estimate flushing
times. The Fraction of Fresh Water Method, the Tidal
Prism Method, and the Modified Tidal Prism Method
are described in Mills, etal., (1985). These are screen-
ing calculations only and should not be considered
accurate. Better estimates can be obtained directly
from dye studies or simple box models calibrated to
salinity or dye data.
Flushing times give the minimum duration for simula-
tions of dissolved, non-reactive pollutants. Reaction
kinetics affect the required duration forthose pollutants
and water quality constituents controlled by various
physical, chemical, and biological transformations and
removal processes. Pollutants controlled by rapid loss
rates, such as fecal bacteria or some volatile organic
chemicals, can generally be characterized by simula-
tions that are shorter than the flushing time. For water
quality constituents affected by transformation rates,
the time required to complete the entire reaction chain
or cycle must be considered. Some chemicals that
interact extensively with benthic sediments may re-
quire simulations greatly exceeding flushing times be-
cause their removal is controlled by desorption and
benthic diffusion kinetics. Examples include nutrients
and hydrophobic organic chemicals. Sediment di-
agenesis models should be helpful in analyzing chemi-
cal dynamics and fate in such situations.
The dynamics of major loading and kinetic forcing
functions may dictate longer simulations than flushing
times and kinetic reactions suggest. Nonpoint sources
may provide significant "background" loads that must
be considered in a WLA study. These are highly inter-
mittent, but seasonal in nature and may extend sedi-
ment, dissolved oxygen, and nutrient enrichment
simulations from weeks to seasons. The annual sun-
light and temperature cycles almost require that eutro-
phication simulations range from seasons to years.
The final factor affecting the duration of simulations is
the strategy for relating simulation results to the regula-
tory requirements. Sometimes a set of "design condi-
tions" can be defined, allowing for shorter simulations.
Care must be taken to ensure that a particular combina-
tion of design conditions, such as flow, temperature, and
nonpoint source loads, does not reflect an unreasonably
low probability of occurrence and thus an overly restric-
tive WLA.
Another strategy is to extend a simulation for many
years, defining the variability of the major forcing func-
tions as realistically as possible. Often, historical records
of tide, flow, temperature, and rainfall are used to ensure
the proper interaction among processes. Predicted con-
centrations are expressed as a frequency or probability
of exceedance of water quality goals or standards.
Critical combinations of factors leading to violations may
be isolated and examined in more detail.
3.2.4.2. Temporal Resolution
The temporal resolution of WLA simulations falls into
one of three categories - dynamic, quasidynamic, and
steady state. Dynamic simulations predict hour to hour
variations caused by tidal transport. Diurnal forcing may
also be included, although not necessarily if output is to
be time-averaged. Quasidynamic simulations predict
variations on the order of days to months. The effects of
tidal transport are time-averaged, and net or residual
flows are used to drive advection. Other forcing func-
tions such as freshwater inflow, pollutant loading, tem-
perature, and sunlight may vary from daily to monthly.
Steady state simulations predict monthly to seasonal
averages. All inputs are time-averaged.
Two schools of thought have persisted regarding the
utility of dynamic versus quasidynamic and steady state
simulations. For some problems the choice is reason-
ably clear. Dynamic models are necessary for analysis
of control options for complex situations in estuaries.
Predicting the upstream migration of pollutants from an
outfall to a beach or water supply intake requires a
dynamic simulation. Predicting water quality effects
from batch discharges into ebbing tide requires a dy-
namic simulation.
On the other hand, quasidynamic and steady state
models are currently more practical for long term analy-
sis of water quality response. Predicting the year to year
eutrophication response or the accumulation of hydro-
phobic organic chemicals in the benthic sediments of
large estuaries is best accomplished by quasidynamic
simulations. In general, if the regulatory
3-9
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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.
Between these two extremes lie many WLA problems
that might be addressed by either dynamic or quasidy-
namic simulation. Some experts assert that even for
long term analyses where only average predictions are
needed, dynamic simulations are practical and more
desirable. Dynamic simulations can be expected to
more accurately account for interactions among the
important tidal and diurnal forcing functions controlling
average water quality conditions. Calculated maxima
and minima at a location can account forthe majortidal
and diurnal processes; calculated concentrations,
then, can be compared directly to water quality criteria
expressed in terms of daily or hourly maxima and
minima, or in terms of frequency or return intervals.
Quasidynamic and steady state simulations require
statistical calculations outside the model to relate pre-
dicted average concentrations with maxima or minima
criteria. Further, quasidynamic and steady simulations
require careful calibration to long term average salinity
data rather than shorter slack water data. It is argued
that data needs for calibrating dynamic models are
actually less because extensive averaging over cross
sections and time is not necessary.
Others prefer quasidynamic simulations when the
choice is ambiguous. Some experts assert that for
standard WLA analyses, dynamic models are often not
necessary and are too formidable for two and three
dimensional situations. Dynamic simulation requires
fully calibrated hydrodynamic models to drive the water
quality computations. It is argued that an extensive
data base is necessary to calibrate the dynamic calcu-
lations. Quasidynamic simulations cost less because
of their longertime steps and less use of hydrodynamic
simulation. The lower costs allow for longer simula-
tions than dynamic models, and thus greater ability to
explore seasonal and yearly trends. The lower costs
also allow for more water quality variables and proc-
esses to be simulated.
The computational time step used by the WLA model
will depend upon the temporal resolution chosen as
well as the spatial network, the transport charac-
teristics of the estuary, and the numerical solution
technique of the model. Most computer waste load
allocation models use explicit schemes—that is, vari-
ables at the new time step are calculated using known
values at previous time steps. This leads to several
common conditions that must be satisfied to ensure
model stability (i.e., solutions remain within bounds and
do not "blow up"). Furthermore, satisfying these condi-
tions will often result in smaller time steps that would
generally be needed from solution resolution conditions
alone.
The conditions, or criteria, for one-dimensional models
using explicit solution schemes are usually:
— a hydrodynamic criterion (Courant condition)
At
-------
governing equations. In these cases, the model may
be unconditionally stable, which means that the choice
of the time step is not limited by stability considera-
tions. Here, the time step should be chosen to provide
adequate resolution of temporal processes. Care
should still be taken because even implicit schemes
may have certain limiting time or space conditions.
3.3. Model Selection
The goal of model selection is to obtain a simulation
model that effectively implements the conceptual
model identified for the WLA. The available set of
general purpose models may not always fully imple-
ment a specific conceptual model. In this case, calcu-
lations or assumptions may be made outside the
model's computational framework, or model code may
be refined. Models that are known to the user and that
are easily modified provide valuable flexibility to the
WLA study. In the final analysis, how a model is used
is more important to the success of a WLA than exactly
which model is used. Nevertheless, while selection of
an appropriate model will not guarantee success, it will
help. Selection of an inappropriate model will not guar-
antee failure, but will render a successful outcome
more difficult.
Models may be classified in different and somewhat
arbitrary ways. Some models may not quite fit in any
category, or may fit well in several. In addition, models
tend to evolve with use. The exact capabilities of the
individual models described here may change. In par-
ticular, kinetic reactions may be modified and new
variables inserted. Dispersion functions may be up-
dated. Usually the computational framework and the
basic transport scheme remain stable over time. For
this reason, transport characteristics will provide the
basis for the model classification scheme used here.
Models selected for discussion here are general pur-
pose, 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 organi-
zation should also be considered. The models summa-
rized in this report represent the typical range of
capabilities currently available. Other available com-
puter programs can generally be grouped into one of
the following categories:
— Variants of the models discussed here;
— Proprietary models held by consulting firms;
— Models developed for research purposes.
It is recommended that where project staffs do not have
access to or familiarity with a wide range of computer
programs, effort should be focused on those discussed
in this document.
One important word of caution: it is highly likely that all
computerized models discussed here contain a few
undiscovered software and documentation errors. The
user must be careful to verify that the models are
implemented properly and are providing reasonable
calculations. With support from EPA's Office of Water,
the EPA Center for Exposure Assessment Modeling
(CEAM), Athens, Georgia, maintains some of these
models, providing their users with an information and
error clearinghouse. These models may be obtained
over the CEAM electronic bulletin board system, or by
mailing in the appropriate number of diskettes.
3.3.1. Classification of Models by Transport
Complexity
Estuarine WLA models consist of two components—hy-
drodynamic and water quality. In the simplest case,
hydrodynamics may be represented in a model by user-
supplied velocity and flow data. In a more complex
model, hydrodynamics may be represented by numeri-
cal solution of the equations of motion and continuity. In
either case, water quality conservation-of-mass equa-
tions are executed using the hydrodynamic output of
water volumes and flows. The water quality component
of the model calculates pollutant dispersion and trans-
formation or decay, giving resultant concentrations over
time. All the estuarine WLA models discussed in this
report include as a minimum the first order decay of BOD
and the prediction of DO concentrations. The more
comprehensive models include nutrient-algal relation-
ships and benthic source/sink terms. A few estuarine
models that include reaction rate coefficients and trans-
formation processes for toxic materials also are avail-
able.
Although the hydrodynamic submodel is independent of
the water quality submodel, water quality depends on
the advection, dilution, and dispersion controlled by
hydrodynamics. As a result, estuarine WLA models can
be classified as Level I to Level IV according to the
temporal and spatial complexity of the hydrodynamic
component of the model. The model classification
scheme followed in this report was recommended by
Ambrose et al. (1981).
Level I includes desktop screening methodologies that
calculate seasonal or annual mean pollutant concentra-
tions based on steady state conditions and simplified
flushing time estimates. These models are designed to
examine an estuary rapidly to isolate trouble spots for
more detailed analyses. They should
3-11
-------
be used to highlight major water quality issues and
important data gaps in the early, model identification
stage of a study.
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. Steady state models use an
unvarying flow condition that neglects the temporal
variability of tidal heights and currents. Tidally aver-
aged models simulate the net flow over a tidal cycle.
These models cannot predict the variability and range
of DO and pollutants throughout each tidal cycle, but
they are capable of simulating variations in tidally
averaged concentrations over time. Level II models
can predict slowly changing seasonal water quality
with an effective time resolution of 2 weeks to 1 month.
Level III includes computerized one-dimensional (1-d)
and quasi two-dimensional (2-d), dynamic simulation
models. These real time models simulate variations in
tidal heights and velocities throughout each tidal cycle.
One-dimensional models treat the estuary as well-
mixed vertically and laterally. Quasi 2-d models em-
ploy a link-node approach that describes water quality
in two dimensions (longitudinal and lateral) through a
network of 1-d nodes and channels. The 1-d equation
of motion is applied to the channels while the continuity
equation is applied at nodes between channels. Tidal
movement is simulated with a separate hydrodynamic
package in these models. Although the Level III mod-
els will calculate hour-to-hour changes in water quality
variables, their effective time resolution is usually lim-
ited to average variability over one week because tidal
input parameters generally consist of only average or
slowly varying values. In this case, model results
should be averaged to obtain mean diurnal variability
over a minimum of 1 week intervals within the simu-
lated time period (Ambrose and Roesch 1982). 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 re-
quired data and modeling effort are usually not mobi-
lized 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. While 2-d models
are beginning to find regular use for some engineering
applications, at the present time practical 3-d models
and modeling techniques are still developing. The only
3-d models currently reported in the literature are
hydrodynamic models that include simple first order
decay rates for uncoupled nonconservative pollutants
(Swanson and Spaulding 1983) and box type models
configured in three dimensions (HydroQual 1987). The
effective time resolution of the Level IV models can be
less than 1 day with a good representation of diurnal
water quality and intratidal variations. The required data
and modeling effort are usually not mobilized in standard
WLAs.
The advantages of Level I and II models lie in their
comparatively low cost and ease of application. The
disadvantages lie in their steady state or tidally aver-
aged temporal scale. When hydrodynamics and pollut-
ant inputs are rapidly varying, steady state models are
difficult to properly calibrate. Consequently, these mod-
els are less satisfactory in short estuaries or when waste
load, river inflow, or tidal range vary appreciably with a
period close to the flushing time of the water body.
Steady state and tidally averaged models require cali-
bration of a dispersion coefficient using field data. The
calibrated value is applicable to the condition monitored
and cannot be extrapolated to proposed modifications
in estuary shape, tidal volume, or river discharge.
As Hinwood and Wallis (1975) explain, dispersion is
caused by the combined action of turbulence and a
nonuniform velocity profile. Nonuniform velocities elon-
gate a wastewater slug, whereas turbulence, acting
normal to the mean velocity, mixes the waste. Velocities
at any section of the estuary vary due to shear at the
bed and sides of the channel. In addition, irregularities
in channel shape, salinity and temperature induced
density currents, and wind-induced currents, cause
nonuniform velocities. In a wide estuary, the Coriolis
force and streams entering on one side of the channel
also may produce nonuniform velocities.
Dispersion coefficients in the Level I through IV models
represent different transport phenomena. The flux of
matter through an estuary can be represented with the
following simplified notation:
Flux = Net advection from freshwater flow (1)
+ Tidal dispersion (2)
+ Net transverse gravitational circulation (3)
+ Net vertical gravitational circulation (4)
+ Transverse oscillatory shear (5)
+ Vertical oscillatory shear (6)
+ Turbulent or eddy diffusion (7)
One-dimensional, tidally averaged or steady state mod-
els calculate term 1 directly but represent terms 2
3-12
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through 7 with a tidal average or steady state longitu-
dinal dispersion coefficient. In contrast, the Level III
1-d, real time models calculate terms 1 and 2 directly
and use the cross-sectional averaged longitudinal dif-
fusion coefficient to represent terms 3 through 7. The
Level IV 2-d, depth-averaged models represent even
more terms directly. These models calculate terms
1,2,3 and 5 directly, using the depth-averaged longitu-
dinal and lateral diffusion coefficients only to represent
terms 4, 6 and 7.
As a model is simplified from Level IV to Level II, the
dispersion coefficients become larger and more
unique to each flow situation. The steady state or
tidally averaged Level II models require the dispersion
coefficient to include the effects of tidal mixing. As a
result, the coefficient must be calibrated using salinity
measurements, and it cannot be used to predict the
water quality effects of projected changes in estuarine
topography or river inflows. Due to shorter time scales,
the Level III and IV dispersion coefficients do not have
to include the effects of tidal mixing and can be more
closely based on the physical properties of the channel
(hydraulic radius and roughness coefficient). Changes
in these properties can then be made in the model to
predict the effect of proposed changes in channel
geometry or freshwater inflows.
The dynamic models (Levels III and IV) have advan-
tages over steady state and tidally averaged models
in representing mixing in partially mixed estuaries be-
cause advection is so much better represented. Al-
though shear effects and the effects of spatial
averaging must still be accounted for, the effects of
time averaging can be avoided.
The short time step of dynamic models allows them to
be more sensitive predictors of the duration of viola-
tions of water quality standards. Dynamic models can
provide a more accurate response to nonpoint source
loads and pollutant spills, short term events that can
produce water quality standard violations with a dura-
tion less than one tidal cycle in length. The success
with which these models can predict transient viola-
tions depends upon both the accuracy and resolution
of the loading and environmental data, and the model's
treatment of short time scale kinetics such as desorp-
tion or diurnal fluctuations in temperature, pH, or sun-
light. While dynamic models are capable of predicting
diurnal and transient fluctuations in water quality pa-
rameters, the input data requirements are much
greater. Lack of detailed data or process descriptions
often rendertheirreal predictive resolution significantly
longer than their computational time step.
The Level III, 1-d models can produce good estimates
of tide heights, mean velocities, and pollutant concen-
trations for estuaries with fairly regular channels that are
much longer than they are wide. Near points of waste
injection, however, model predictions can be signifi-
cantly in error due to lateral variations in concentrations.
The quasi 2-d approach can solve this problem, but the
difficulty in estimating effective dispersion coefficients
still remains. The Level IV longitudinal and lateral 2-d
models have the advantage of representing the lateral
variations in velocity and waste concentrations that arise
in all estuaries and bays because of the nonuniformity
of cross-sections, embayments, branching channels,
and bends (Hinwood and Wallis 1975). In addition, these
models can include the effects of Coriolis and wind
circulations. The remaining flaw is that the lateral-longi-
tudinal models assume an estuary is vertically well-
mixed. This assumption can lead to significant errors in
predictions for stratified estuaries.
3.3.2. Level I Models
The purpose of modeling at Level I is to screen trouble
spots for more detailed analysis. Level I desktop meth-
odologies may be done with a hand held calculator and
are based on steady state conditions, first order decay
coefficients, simplified estimates of flushing time, and
seasonal pollutant concentrations.
Level I screening of a given waterbody may entail se-
lected analyses to answer individual questions (e.g., is
the estuary stratified in a particular location; what is the
flushing time of the estuary; what is the annual phospho-
rus loading), or it may entail a comprehensive examina-
tion of the estuary. A comprehensive analysis may be
accomplished with models such as the Simplified Estu-
ary Model (SEM) or the Water Quality Assessment
Methodology (WQAM). SEM and WQAM both require
only hand calculations and are used chiefly for prelimi-
nary assessments of estuarine water quality. Documen-
tation on WQAM is available from CEAM.
3.3.2.1. Water Quality Assessment Methodology
WQAM is a steady state desktop model that includes
both one-dimensional and two-dimensional box model
calculations (Mills et al. 1985). Use of WQAM proce-
dures requires classification of an estuary into one of
three possible types: stratified, well-mixed, or partially
mixed. Two methods are presented to determine the
appropriate classification. The Hansen and Rattray
method utilizes vertical salinity gradients, freshwater
inflow velocities, and surface tidal current velocities
averaged over a tidal cycle to characterize the system.
The flow ratio calculation method classifies the estuary
using a comparison of freshwater flow volume and tidal
flood volumes (tidal prism) over a tidal cycle. Values
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calculated from these input data are compared to layer. The analysis is performed by solving a system of
ranges set for each estuarine classification. simultaneous linear equations for pollutant concentra-
tions in each layer. WQAM consists of a number of
WQAM includes calculations to estimate the transport individual analyses, listed in Table 3-4 (Mills et al. 1985).
of BOD, DO, pH, arbitrary conservative substances, The document is available from the Center for Exposure
thermal pollution, turbidity, sediment, and organic Assessment Modeling in Athens, Georgia.
chemicals in an estuary. Pollutant distribution can be
estimated using either a far field or a near field method 3.3.2.2. Simplified Estuarine Model
of analysis. The near field technique predicts initial
dilution of submerged discharges through the use of SEM is a one-dimensional steady state desktop model
tabulated data from MERGE, a computerized plume capable of simulating water quality in tidal rivers and
model. For well-mixed estuaries, far field pollutant non-stratified estuaries (Hydroscience 1971). Coupled
distributions can be predicted using the fraction of BOD-DO reactions, arbitrary conservative substances,
freshwater method, modified tidal prism method, or and uncoupled nonconservatives with first order decay
one-dimensional advection-dispersion equations. For (nutrients and coliforms) are represented in SEM. The
partially mixed and stratified estuaries, WQAM far field model is based on user-specified hydraulics that con-
analysis uses Pritchard's two-dimensional box model sider only longitudinal variations and handle only point
approach, which represents the estuary as a series of source inputs. Advection is represented in the form of
longitudinal segments with a surface and a bottom freshwater flow velocity and dispersion in the form of a
Table 3-4. Summary of Methodology for Estuarine Water Quality Assessment
Calculations
Estuarine Classification
Flushing Time
Pollutant Distribution
Thermal Pollution
Turbidity
Sedimentation
Methods
* Hansen & Rattray
* Flow ratio
* Fraction of freshwater
* Modified tidal prism
* Fraction of freshwater (conservative pollutants+)
* Modified tidal prism (conservative or first-order decay
pollutants)
* Dispersion-advection equations (conservative, first-order
decay pollutants+ and dissolved oxygen)
* Pritchard's Box Model (conservative pollutants+)
* Initial dilution
* Pollutant concentration at completion of initial dilution
(conservative pollutants+, pH, dissolved oxygen)
* Farfield distribution (conservative and first-order pollutants+,
and dissolved oxygen)
* A T of water passing through condenser
* Maximum discharge temperature
* Thermal block criterion
* Surface area criterion
* Surface temperature criterion
* Turbidity at completion of initial dilution
* Suspended solids at the completion of iniitial dilution
* Light attenuation and turbidity relationship
* Secchi disk and turbidity relationship
* Description of sediment movement
* Settling velocity determination
* Null zone calculations
Type of Estuary
1 D/2D
1 D/2D
1 D/2D
1 D
1 D
1 D
1 D
2 D
1 D/2D
1 D/2 D
2 D
N/A
N/A
1 D/2 D
1 D/2D
1 D/2D
1 D/2 D
1 D/2 D
1 D/2 D
1 D/2 D
1 D/2 D
1 D/2D
2 D
* One dimensional (1 D) means a vertically well-mixed system.
A two dimensional (2 D) estuary is vertically stratified.
+ These methods apply to
either conventional or toxic pollutants
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dispersion coefficient that accounts for the mixing and
translation of the tides.
SEM uses a synthetic parameter called the estuary
number (O'Connor, 1960) to determine the relative
magnitude of advection and dispersion at a given
location and to characterize the reach as either tidal
river or estuarine segment. The estuarine number (N)
is calculated from the values of the dispersion coeffi-
cient (E), the freshwater flow velocity (V) and the
deoxygenation coefficient (Kd). If the estuarine number
(N=KdE/V2) is less than 10, the reach is considered a
tidal river and initial dilution is calculated using fresh-
water inflow and the effects of tidal dispersion. Above
the breakpoint of 10, the reach is considered to behave
in a purely estuarine fashion, and the initial dilution
neglects freshwater inflow.
3.3.3. LevelII Models
Level II includes computerized steady state and tidally
averaged simulation models that generally use a box
or compartment-type network. Steady state models
are difficult to calibrate in situations where hydrody-
namics and pollutant releases are rapidly varying.
Consequently, these models are less appropriate
when waste load, river inflow, or tidal range vary
appreciably with a period close to the flushing time of
the waterbody.
Both tidally averaged and steady state models use a
dispersion coefficient calibrated from survey data. The
network and time step used by these models add
"numerical dispersion" to the calculations, which tends
to spread out concentration profiles in a similar manner
as dispersive mixing processes. Consequently, cali-
brated dispersion coefficients apply to the specific
network and situation monitored; they cannot be ex-
trapolated to major modifications in estuary shape,
tidal volume, or river discharge.
A recent modeling strategy is to drive a Level II com-
partment model that has been configured in two or
three dimensions with tidal-averaged or steady flows
and volumes from a 2-d or 3-d hydrodynamic model.
This strategy is briefly discussed under Level IV mod-
els. A variation of this strategy is to use compartment
models with net advective flows calculated from meas-
ured vertical and longitudinal salinity distributions. An
iterative calculation has been published by Lung and
O'Connor (1984) and Lung (1986) for two-dimensional
estuaries characterized by a horizontal seaward veloc-
ity in the upper layer and a net landward velocity in the
lower layer. This analysis gives analytical solutions to
the horizontal and vertical tidally-averaged velocities,
as well as values of vertical eddy viscosity. This analy-
sis has been applied to the Sacramento-San Joaquin
Delta, the James River Estuary, the Patuxent River
Estuary, and the Hudson River Estuary.
The Level II models supported by CEAM are QUAL2E
and the Water Quality Analysis Simulation Program
(WASP4), with its associated toxic chemical and eutro-
phication programs TOXI4 and EUTRO4. Other models
described here include HAR03, FEDBAK03, and AUTO-
QUAL.
3.3.3.1. QUAL2E
QUAL2E is a steady state one-dimensional model de-
signed for simulating conventional pollutants in streams
and well-mixed lakes. It has been applied to tidal rivers
with minor adaptations to the hydraulic geometry and
dispersion functions. Water quality variables simulated
include conservative substances, temperature, bacte-
ria, BOD, DO, ammonia, nitrite, nitrate, and organic
nitrogen, phosphate and organic phosphorus, and al-
gae. QUAL2E is widely used for stream waste load
allocations and discharge permit determinations in the
United States and other countries. It has a 15-year
history of application and is a proven, effective analysis
tool. QUAL2E Version 3 incorporates several uncer-
tainty analysis techniques useful in risk assessment.
This model can be obtained from the Center for Expo-
sure Assessment Modeling, Athens, Georgia (requires
4 diskettes).
3.3.3.2. WASP4
WASP4 is a general, multi-dimensional model that util-
izes compartment modeling techniques (DiToro et al.
1981; Ambrose et al. 1987). Operated in either the
quasidynamic or steady state mode, the user must
supply initial segment volumes, network flow fields, and
inflow time functions. The user also must calibrate dis-
persion coefficients between compartments. Depending
on the process model with which it is linked, WASP4 has
the capability of simulating a range of conventional and
toxic pollutants. Problems that have been studied using
WASP4 include BOD, DO dynamics, nutrients and eu-
trophication, bacterial contamination, and toxic chemical
movement (DiToro, 1981). WASP4, along with the as-
sociated programs TOXI4, EUTRO4, and DYNHYD4,
can be obtained from the Center for Exposure Assess-
ment Modeling, Athens, Georgia (requires 3 diskettes).
A. TOXI4
TOXI4 is a version of WASP4 that is designed to simu-
late organic chemicals and heavy metals (Ambrose et
al. 1987). TOXI4 was created by adapting the kinetic
structure of EXAMS-II to the transport framework of
WASP4 and adding sediment balance algorithms. It can
simulate up to three chemicals and three sediment
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classes. In addition to segment volumes, flows, and
dispersive exchanges, the user must supply sediment
deposition and scour rates, bed sediment velocity,
water column/sediment exchange coefficients, and
sediment/pore water exchange coefficients.
In TOXI4 the total transformation rate of an organic
chemical is based on the simple addition of the rate
constants for individual photolysis, hydrolysis, biolysis,
and oxidation reactions. These rate constants may
either be specified by the user or calculated internally
from second order rate constants and such environ-
mental conditions as light intensity, pH, bacteria, oxi-
dants, depth, velocity, and wind speed. Internal
transport and export of organic chemicals occur via
advective and dispersive movement of dissolved, sedi-
ment-sorbed, and biosorbed materials, and by volatili-
zation losses at the air-water interface. Internal
transport and export of heavy metals occur via advec-
tive and dispersive movement of dissolved, sediment-
sorbed, and biosorbed materials. Sorption of both
organic chemicals and heavy metals on sediments and
biomass is calculated assuming local equilibrium using
a constant partition coefficient and spatially varying
environmental organic carbon fractions. TOXI4 has
the capability of simulating up to two daughter products
of organic chemical transformations. Exchange be-
tween the water column and the bed can occur by
settling or resuspension of particulates, diffusion of
dissolved pollutants between the water column and
pore water, direct adsorption/desorption between the
water column and bed, and percolation or infiltration.
Within the bed, a pollutant can move vertically by
diffusion, turnover, percolation and burial, and horizon-
tally with bed load transport.
B. EUTR04
EUTRO4 is a version of WASP4 that is designed to
simulate conventional pollutants. EUTRO4 combines
a kinetic structure adapted from the Potomac Eutrophi-
cation Model with the WASP transport structure. EU-
TRO4 predicts DO, carbonaceous BOD,
phytoplankton carbon and chlorophyll a, ammonia,
nitrate, organic nitrogen, organic phosphorus, and or-
thophosphate in the water column and, if specified, the
underlying bed. In addition to segment volumes, flows,
and dispersive exchanges, the user must supply depo-
sition and resuspension velocities for organic solids,
inorganic solids, and phytoplankton. The fraction of
each water quality variable associated with these sol-
ids also must be given. Rate constants and half-satu-
ration coefficients for the various biochemical
transformation reactions must be specified by the user.
Finally, the time and/or space variable environmental
forcing functions, such as light intensity, light extinc-
tion, wind speed, cloud cover, temperature, and benthic
fluxes must be input.
3.3.3.3. HAR03
HAR03 is a steady state, multi-dimensional model that
utilizes compartment modeling techniques (Chapra and
Nossa 1974). An orthogonal system of segmentation is
used with each segment having up to six interfaces. The
model includes the effect of net advection and disper-
sive tidal exchange. HARO3 models the BOD-DO deficit
system as a coupled reaction with first order decay of
BOD. With minor modifications, the program may also
be used to model variables analogous to the BOD-DO
system such as ammonia-nitrate. Zero order net photo-
synthetic and benthic oxygen demands can be user-
supplied to the model and used in the DO balance.
3.3.3.4. FEDBAK03
FEDBAK03 is a steady state, multi-dimensional model
that utilizes compartment modeling techniques (Nossa
1978). Each estuarine segment may have up to six
interfaces. The model simulates net advection and dis-
persive tidal exchange. FEDBAK03 is written in general
form so that it is applicable for any substances that
undergo consecutive first order reactions with feedback.
The model is thus capable of simulating nitrification and
associated DO deficits as well as BOD-DO reactions.
The program can be modified to allow for the input of net
photosynthetic and benthic oxygen demands.
3.3.3.5. AUTOQUAL
AUTOQUAL and a later update AUTOQD are steady
state and quasidynamic models for simulating conven-
tional pollutants in streams and estuaries (Grim and
Lovelace 1973, Lovelace 1975). Transport is calculated
from user-specified flow and dispersion. Water quality
variables simulated include carbonaceous BOD, ni-
trogenous oxygen demand, DO, total phosphorus, and
total nitrogen.
3.3.4. Level III Models
Level III includes computerized 1-d and quasi 2-d mod-
els that simulate variations in tidal height and velocity
throughout each tidal cycle. Level III models are gener-
ally composed of separate but compatible hydrody-
namic and water quality models. These two models are
run sequentially, and the output of the hydrodynamic
model becomes part of the input to the water quality
model. Level III models enable the characterization of
phenomena rapidly varying within each tidal cycle, such
as pollutant spills, stormwater runoff, and batch dis-
charges. Level III models also are
3-16
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deemed appropriate for systems where the tidal
boundary impact, as a function of the hydrodynamics
and water quality, is important to the modeled system
within a tidal period.
The application of tidally varying (intratidal) models has
found most use in the analysis of short-term events, in
which the model simulates a period of time from one
tidal cycle to a month. Some seasonal simulations
have also been run. In most cases, the hydrodynamic
model must be run for several tidal cycles before an
actual event can be simulated. This will dampen out
any errors in the initial conditions and achieve stability
in the hydrodynamic simulation. Following this initial
period, the model will simulate a cyclical steady-state
in which the tidal characteristics are repeated for sub-
sequent tidal periods. This approach can be applied
when a particular design tide is used to simulate water
quality. In this case, the hydrodynamic model is run
and the cyclical steady state output saved as input to
the water quality model. By running the two models in
this fashion, multiple cases can be examined with the
water quality model without the need to rerun the
hydrodynamic model.
For simulating storm events where both loads and
flows are rapidly varying, the hydrodynamic model is
run for the entire simulation period. The first step is to
run the hydrodynamic model to steady-state for the
nonstorm period to obtain initial conditions for the
storm simulation. The storm flows are specified as
input to the hydrodynamic model, which must be run
for a sufficient number of tidal cycles after the storm
event to simulate the water quality response through-
out the estuary. The water quality model, using the
pollutant loads from an input file and the flows from the
hydrodynamic model, simulates the same period
(number of tidal cycles) as the hydrodynamic model.
Although the storm may only last a few hours, the
actual simulation time may be considerably longer
(days or weeks) in order to characterize the full re-
sponse of the system to the event.
In using Level III models, one must decide whether a
simple 1-d link-node longitudinal system is sufficient,
or whether a quasi 2-d model with branching networks
or triangular/rectangular configuration is required to
model the longitudinal and lateral variations in the
estuary. For estuaries with channels longer than their
width and which are reasonably well mixed across their
width, a 1-d model may be chosen. If large differences
exist in water quality from one side of an estuary to the
other, then a quasi 2-d model would be appropriate.
The length of model segments or links will depend on
the resolution required in the study, as discussed in
Section 2.3.3. The length and position of segments
depends on the physical properties of the estuary. Ho-
mogeneity of physical characteristics should be the
basis for defining segments. Where bends, constric-
tions, or other changes occur, smaller segments are
generally defined to improve resolution.
In their treatment of conventional pollutants, Level III
models deal mainly with biochemical processes. All
Level III models considered here can simulate simple
BOD-DO interactions. Most of these models also are
formulated to simulate the reactions and interactions of
organic phosphorus and orthophosphorus; organic ni-
trogen, ammonia, nitrite and nitrate; algal growth and
respiration; and DO. These models also include settling
rates and benthic flux rates for several different constitu-
ents such as phosphorus, nitrogen and sediment oxy-
gen demand. Only one model is designed to simulate
the physiochemical processes affecting organic chemi-
cals and metals.
The Level III model supported by CEAM is the Water
Quality Analysis Simulation Program (WASP4), with its
associated hydrodynamic program DYNHYD4 and its
toxic chemical and eutrophication programs TOXI4 and
EUTRO4. Other models described here include the
Dynamic Estuary Model, EXPLORE-1, and the MIT
Dynamic Network Model.
3.3.4.1. WASP4
The Water Quality Analysis Simulation program,
WASP4, is a general multi-dimensional model that uses
compartment modeling techniques (DiToro et al. 1981,
Ambrose et al. 1987). Version 4 may be operated in the
tidal dynamic mode through linkage with the associated
hydrodynamic model DYNHYD4. DYNHYD4 is a link-
node model that may be driven by either constantly
repetitive or variable tides. Unsteady inflows may be
specified, as well as wind that varies in speed and
direction. DYNHYD4 produces an output file of flows
and volumes that can be read by WASP4 during the
water quality simulation.
Two water quality programs accompany WASP4.
TOXI4 simulates organic chemicals, metals, and sedi-
ment in the water column and underlying bed. EUTRO4
simulates DO, carbonaceous BOD, phytoplankton carb-
on, chlorophyll a, ammonia, nitrate, organic nitrogen,
organic phosphorus, and orthophosphate in the water
column and, if specified, the underlying bed. These
programs are described more fully in Section 3.3.3.3.
WASP4, along with the associated programs TOXI4,
EUTRO4, and DYNHYD4 can be obtained from the
Center for Exposure Assessment Modeling, Athens,
Georgia (requires 3 diskettes).
3.3.4.2. Dynamic Estuary Model, DEM
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DEM is a quasi 2-d model that represents tidal flow in
the lateral and longitudinal directions with a branching
link-node network (Feigner and Harris 1970). Two
versions of the hydrodynamic component of DEM ex-
ist. One version is limited to steady inflows and con-
stantly repetitive tide. The steady inflow version cannot
explicitly handle short-term stochastic transients such
as wind stress or large storm flushing and has difficulty
in predicting long-term patterns such as the 2-week
spring-neap-tide cycle or the seasonal freshwater in-
flow pattern. Consequently, this version is most reli-
able when predicting high and low values for diurnal or
tidal cycles, or both, averaged over a relatively steady
2-week period (Ambrose and Roesch, 1982). Real
time simulations of water quality are possible with the
steady inflow version of DEM, but with some inaccura-
cies. Newer hydrodynamic versions of the model can
handle variable inflows and can thus generate a more
accurate real time prediction of water quality.
Several water quality submodels also have been used
with DEM. All versions include nutrient modeling and
algal growth, photosynthesis, and respiration. The fol-
lowing is a brief description of the versions of DEM
currently available:
— DEM, Chen-Orlob version, is the most comprehen-
sive version of the model currently available (Chen and
Orlob 1972). The model has the capability of repre-
senting 22 coupled biotic and abiotic constituents in-
cluding: temperature, pesticides, heavy metals,
CBOD, DO, phosphate, ammonia, nitrite, nitrate, total
dissolved solids, alkalinity, pH, carbon dioxide, phyto-
plankton, zooplankton, fish, benthic animals, sus-
pended detritus, and sediment detritus.
— DEM, Pearl Harbor version, is limited to steady
inflows and constantly repetitive tide (Genet et al.
1974). It incorporates the heat budget terms of the
Tidal Temperature Model and simulates temperature,
DO, CBOD, ammonia, nitrite, nitrate, total nitrogen,
phosphate, chlorophyll-a, and total dissolved solids.
— DEM, Potomac version, is documented as handling
only steady inflows and constantly repetitive tide, but
a newer version is available that is capable of handling
variable inflows (Roesch et al. 1979). The model simu-
lates CBOD, DO, ammonia, nitrate, phosphate, and
chlorophyll-a.
3.3.4.3. MIT Dynamic Network Model, MIT-DNM
MIT-DNM is a one-dimensional model that uses a finite
element, branching network to simulate the flow re-
gime of an estuary with unsteady tidal elevation and
upstream flow (Harleman et al. 1977). The model was
originally developed for aerobic, nitrogen limited sys-
tems and includes detailed simulation of the nitrogen
cycle as well as temperature, CBOD, DO, and fecal
coliforms. Two versions of the model are currently avail-
able, and are described below.
— MIT-DNM, Potomac version, includes nutrient mod-
eling and algal growth, photosynthesis, and respiration
and represents bacterially mediated reactions for am-
monia, nitrite, nitrate, phytoplankton-N, zooplankton-N,
particulate organic N, and dissolved organic N (Najarian
and Harleman 1975).
— MIT-DNM, St. Lawrence version, includes nutrient
modeling and algal growth, photosynthesis, and respi-
ration, and represents CBOD, DO, inorganic phospho-
rus, organic phosphorus, inorganic nitrogen, organic
nitrogen, phytoplankton, and zooplankton (Thatcher et
al. 1975).
3.3.4.4. EXPLORE-I
EXPLORE-I is a quasi 2-d model that represents tidal
flow in the lateral and longitudinal directions with a
branching link-node network (Chen and Orlob 1972).
The full 1-d hydrodynamic equations are solved, but the
water quality model excludes dispersive transport. EX-
PLORE-I has the capability of simulating DO, conserva-
tives, toxic pollutants, coliforms, sedimentary
phosphorus, soluble phosphorus, organic phosphorus,
organic nitrogen, ammonia, nitrite, nitrate, total organic
carbon, refractory organic carbon, phytoplankton,
zooplankton, CBOD, and benthic BOD. Sedimentation
and scour of organic matter is represented in the model
as well as algal growth, photosynthesis, and respiration.
3.3.5. LevelIVModels
Level IV includes a variety of computerized 2-d and 3-d
intratidal models. These may be divided into three broad
categories: 2-d vertically averaged (x-y), 2-d laterally
averaged (x-z), and 3-d. While they are not routinely
used in most WLAs, they are now finding use by experts
in special studies.
Although many 2-d vertically averaged, finite-difference
or finite-element hydrodynamic programs exist, rela-
tively few contain a water quality program that simulates
constituents other than salinity and/or temperature.
Likewise, a number of 2-d, laterally averaged models
(longitudinal and vertical transport simulations) treat
mass transport of salt and temperature but very few
include nonconservative constituents or water quality
routines. Models in this category simu-
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late vertical stratification but neglect lateral effects,
including Coriolis effects. Last is the category of 3-d,
finite-difference and finite-element models. These
models allow all physical processes to be included,
although many were developed for systems of con-
stant salinity (lakes or oceans). A summary of 3-d
marine and estuarine models is provided in Nihoul and
Jamarf(1987).
A Level IV model would be used when finer spatial
definition is required than is provided by a Level III
model and when finer temporal definition is required
than is provided by a Level II model that has been
configured in two or three dimensions and driven by
the averaged hydrodynamic output of a Level IV hy-
drodynamic model. In particular, these models will be
selected for investigations where diurnal and tidal fluc-
tuations are of prime importance to the study.
The quasi 2-d Level III model is applicable where there
is a need to project lateral differences in water quality
for wide estuaries. The quasi 2-d model, however,
which uses 1-d equations of motion applied to the
channels, cannot estimate longitudinal and lateral dis-
persion as effectively as the true 2-d model of Level
IV. Although the quasi 2-d and the true 2-d model both
assume that the estuary is vertically mixed, the true
2-d model can effectively represent lateral variation in
velocity and constituent concentration for estuaries
with nonuniform cross sections, branching channels,
and embayments. The 2-d model also can account for
the effect of Coriolis forces and wind circulation.
For a wide, stratified estuary the application of a 3-d
model would be appropriate for intratidal simulations.
There are no well documented intratidal 3-d models
with coupled constituent interactions applicable to ti-
dally driven estuaries. Fully 3-d models that can predict
longitudinal, lateral, and vertical transport are the most
complex and expensive to set up and run. Due to their
cost and complexity, these models have not been
widely used. For experts with access to supercomput-
ers, these models are feasible for special applications.
A recent modeling strategy is to drive a Level II com-
partment model that has been configured in two or
three dimensions with either averaged or tidally vary-
ing flows and volumes from a 2-d or 3-d hydrodynamic
model. This strategy attempts to combine the transport
rigor of Level IV models with the convenience, flexibil-
ity, and cost efficiency of compartment models. A
recent and currently ongoing example is a study of the
Chesapeake Bay. There, the averaged output of a
finite difference stretch coordinate hydrodynamic
model was linked to a specially adapted compartment
model, AESOP and run to steady state (HydroQual,
1987). When running the water quality model at differ-
ent time steps or on a coarser grid, the user must still
calibrate horizontal and vertical dispersion coefficients
to observed salinity or tracer data.
The criteria forthe specification of time and space scales
for Level IV models are similar to those discussed for
Level III with the additional need to consider a vertical
scale for a 3-d model application. For 2-d and 3-d
models, the time step would be calculated as a function
not only of the longitudinal space steps and longitudinal
dispersion coefficient (as described by Equations 3-14
and 3-15), but also as a function of the lateral and
vertical space steps and dispersion coefficients.
At present, no Level IV model is supported by CEAM. A
variety of these models currently being used is de-
scribed below.
3.3.5.1. H.S.Chen Model
The H.S. Chen model is a real time 2-d (x-y) model that
simulates conventional pollutants (Chen, 1978). The
hydrodynamic submodel considers inertial forces, con-
vective forces, hydrostatic pressure, wind forces, Cori-
olis forces, bottom friction, and internal water column
forces due to eddies. The parameters simulated by the
model include the following: conservatives, coliforms,
chlorophyll-a, organic nitrogen, ammonia, nitrite, nitrate,
organic phosphorus, inorganic phosphorus, CBOD, and
DO. Algal growth, photosynthesis, and respiration are
represented in the model as well as benthic oxygen
demand and bottom releases of ammonia and inorganic
phosphorus. Equations are solved by a finite element
technique.
3.3.5.2. FETRA
FETFxA is a real time, 2-d (x-y) water quality model that
utilizes a finite element solution technique to simulate
toxic pollutants (Onishi 1981). Hydrodynamic data must
be supplied by a separate model such as EXPLORE-I.
FETFxA consists of three submodels linked to simulate
the transport and transformation of sediments and con-
taminants by the processes of advection, diffusion/ dis-
persion, adsorption/ desorption, and degradation/
decay. The sediment transport submodel simulates ad-
vection and dispersion of sediments, fall velocity and
cohesiveness, and deposition or erosion for the bed.
Three sediment sizes are modeled, and calculations are
made of bed elevation changes and the distribution of
sediment sizes within the bed. The dissolved contami-
nant transport submodel predicts advection and diffu-
sion/dispersion of dissolved pollutants, adsorption by
both moving and stationary sediments, desorption from
sediments, and degradation or radionuclide decay. The
particulate contaminant
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transport submodel includes advection and dispersion
of sediment-attached contaminants, adsorp-
tion/desorption with sediment, degradation or radionu-
clide decay; and settling/resuspension.
3.3.5.3. TABS-2
TABS-2 is a generalized numerical modeling system
for open-channel flows, sedimentation, and constitu-
ent transport developed and supported by the U.S.
Army Engineers Waterways Experiment Station, Hy-
draulics Laboratory (Thomas and McAnally, 1985). It
consists of more than 40 computer programs to per-
form modeling and related tasks. The major modeling
components—RMA-2V, STUDH, and RMA-4—calcu-
late two-dimensional, depth-averaged (x-y) flows,
sedimentation, and dispersive transport, respectively.
The other programs in the system perform digitizing,
mesh generation, data management, graphical dis-
play, output analysis, and model interfacing tasks.
Utilities include file management and automatic gen-
eration of computer job control instructions.
TABS-2 has been applied to a variety of waterways,
including rivers, estuaries, bays, and marshes. It is
designed for use by engineers and scientists who may
not have a rigorous computer background.
3.3.5.4. WIFM-SAL
WIFM-SAL is a two dimensional depth-averaged (x-y)
finite difference model that generates time-varying
water surface evaluations, velocities, and constituent
fields over a space staggered grid (Schmalz, 1985).
This model was developed by the U.S. Army Engi-
neers, Waterways Experiment Station. Units of meas-
ure are expressed in the English system
(slug-ft-second). Results computed on a global grid
may be employed as boundary conditions on more
spatially limited refined grid concentrated around the
area of interest. In addition, the user may select either
of two distinct transport schemes. Scheme 1 is a
flux-corrected transport scheme capable of resolving
sharp front without oscillation. Scheme 2 is a full, three
time level scheme directly compatible with the three
time level hydrodynamics. The telescoping grid capa-
bility in conjunction with the user selectable constituent
transport scheme is a powerful concept in practical
transport problem solving.
3.3.5.5. FCSTM-H
FCSTM-H, by Earl Hayter at Clemson University, is a
finite element modeling system for simulating two-di-
mensional depth-averaged (x-y) surface water flow
and cohesive sediment transport consisting of three
separate computer programs (Hayter, 1987). FEGRD
is a two-dimensional finite element grid genera-
tion/modification program. FLWM-H is a hydrodynamic
model that solves the depth-averaged equations of mo-
tion and continuity for model horizontal velocity compo-
nents and flow depths. The effects of bottom, internal
and surface shear stresses and the Coriolis force are
represented in the equations of motion. CSTM-H is a
cohesive sediment transport model that solves the ad-
vection-dispersion equation for nodal depth-averaged
concentrations of suspended sediment and bed surface
elevations. The processes of erosion, dispersion, aggre-
gation, deposition and consolidation are simulated. A
layered bed model is used in simulating bed formation,
subsequent consolidation and erosion. An example
problem, including input and output data, is included.
FLWM-H and CSTM-H are semi-coupled in the following
manner. First, the flow field is calculated for the current
time step using FLWM-H. Second, the predicted flow
field is used in CSTM-H to calculate the transport of
cohesive sediments during the same time step. The flow
field may be updated due to erosion or deposition and/or
unsteady boundary conditions.
The following sediment related properties are calculated
for each element: sediment bed structure (bed density
and shear strength profiles, bed thickness and eleva-
tion), net change in bed elevation over a given interval
of time (e.g. over a certain number of tidal cycles), net
vertical mass flux of sediment over an interval of time,
average amount of time sediment particles are in sus-
pension, and the downward flux of sediment onto the
bed. These parameters are essential in estimating the
bed-water exchange of chemicals adsorbed onto cohe-
sive sediments.
The FCSTM-H modeling system may be used to predict
both short term (less than one year) and long term (one
year and longer) scour and/or sedimentation rates in
vertically well mixed bodies of water. Because of the
iterative routine used in the hydrodynamic model, long
term simulations will require large (order of magnitude
of one or more hours) CPU times, even on mainframe
computers. Limited computer resources and budgetary
constraints will often require extrapolation of short term
simulations.
3.3.5.6. CE-QUAL-W2
CE-QUAL-W2 is a dynamic 2-d (x-z) model developed
for stratified waterbodies (Env. and Hyd. Laboratories
1986). This is a Corps of Engineers modification of the
Laterally Averaged Reservoir Model (Edinger and
Buchak 1983, Buchak and Edinger, 1984a, 1984b).
CE-QUAL-W2 consists of directly coupled hydrody-
namic and water quality transport models. Hydrody-
namic computations are influenced by vari-
3-20
-------
able water density caused by temperature, salinity,
and dissolved and suspended solids. Developed for
reservoirs and narrow, stratified estuaries, CE-QUAL-
W2 can handle a branched and/or looped system with
flow and/or head boundary conditions. With two di-
mensions depicted, point and non-point loadings can
be spatially distributed. Relative to other 2-d models,
CE-QUAL-W2 is efficient and cost effective to use.
In addition to temperature, CE-QUAL-W2 simulates as
many as 20 other water quality variables. Primary
physical processes included are surface heat transfer,
shortwave and longwave radiation and penetration,
convective mixing, wind and flow induced mixing, en-
trainment of ambient water by pumped-storage in-
flows, inflow density current placement, selective
withdrawal, and density stratification as impacted by
temperature and dissolved and suspended solids. Ma-
jor chemical and biological processes in CE-QUAL-W2
include: the effects on DO of atmospheric exchange,
photosynthesis, respiration, organic matter decompo-
sition, nitrification, and chemical oxidation of reduced
substances; uptake, excretion, and regeneration of
phosphorus and nitrogen and nitrification-denitrifica-
tion under aerobic and anaerobic conditions; carbon
cycling and alkalinity-pH-CO2 interactions; trophic re-
lationships for total phytoplankton; accumulation and
decomposition of detritus and organic sediment; and
coliform bacteria mortality.
3.3.5.7. EHSM3D
The EHSM3D model was developed by Y. P. Sheng
at University of Florida calculates three-dimensional
unsteady currents and sediment dispersion in estuar-
ies and lakes (Sheng, et al., 1987, Sheng, 1989).
Given proper boundary and initial conditions, the code
can calculate the three-dimensional time-dependent
distributions of flow, velocity, temperature, salinity,
suspended sediment concentration, density, and dis-
solved species concentration. The status of the sedi-
ment dispersion model is preliminary since research is
continuing with the development and validation of this
portion of the model.
3.3.5.8. John Paul Hydrodynamic Model
This numerical model, developed by John Paul and
colleagues at the U.S. EPA, is capable of realistically
describing the hydrodynamics in lakes, embayments,
nearshore marine coastal areas, and river and thermal
outfall plumes (Paul and Nocito, 1989). The model is
time-dependent, three dimensional, and variable den-
sity. Both rigid-lid and free-surface flows can be deter-
mined. The main assumptions used in the
development of the model include hydrostatic pres-
sure variation, Boussinesq approximation, and eddy
coefficients to account for turbulence. A new solution
procedure, which is a modification of the simplified
marker and cell method, is used. The procedure permits
selected terms in the equations to be treated implicitly
in time. A compatible 3-D, time dependent numerical
physical transport model is available for use with this
model.
3.3.6. Summary of Model Capabilities
The important features of the models selected for dis-
cussion in this manual are summarized in Tables 3-5
and 3-6. The information provided in these tables is
primarily qualitative and sufficient to determine whether
a model may be suitable for a particular application. For
complete information, the potential user must consult
the appropriate user's manuals, the supporting agency,
and other experienced users.
Table 3-5 summarizes the basic features of the models.
The time scales are dynamic (D), quasidynamic (Q), and
steady (SS). Spatial dimensions are 1 (x), 2 (xy, xz, or
xx for link-node networks), or 3 (xyz or B, for box
models). Hydrodynamics are either input by the user (I)
or simulated (S). Solution techniques are analytical (A),
finite difference (FD) or finite element (FE). Finally,
models are implemented on mainframes (M) or personal
computers (PC).
Table 3-6 summarizes the water quality problems that
may be directly addressed by the models. All models
address salinity and bacteria either explicitly or by speci-
fying appropriate boundaries, loads, and first order de-
cay constants for another state variable. Sediment may
be modeled using calibrated deposition and scour ve-
locities (1), or by using functional relationships with
shear stress and shear strength to predict these veloci-
ties (2). Dissolved oxygen may be modeled along with
total BOD (1), with CBOD, NBOD, and prescribed sedi-
ment oxygen demand (SOD) and net photosynthetic
production (2), or with CBOD nitrification, SOD, and
simulated nutrients and phytoplankton (3). Nutrient en-
richment and eutrophication may be simulated using
total phytoplankton biomass (1), multiple phytoplankton
classes (2), or multiple phytoplankton and zooplankton
classes (3). Organic chemicals may be modeled with
calibrated decay rates and partition coefficients (1), with
predicted transformation rates and partition coefficients
(2), or with predicted rates and coefficients for the origi-
nal chemical plus reaction products (3). Metals may be
modeled as dissolved and particulate fractions with
calibrated partition coefficients (1), or as multiple spe-
cies predicted with a thermodynamic data base and
process models (2).
3-21
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Table 3-5. Basic Model Features
Model
SEM
WQAM
HARO3
FEDBAKO3
QUAL2
AUTOQUAL/QD
WASP4:
stand alone
with DYNHYD4
DEM
EXPLORE-I
MIT-DNM
Chen
FETRA
CE-QUAL-W2
TABS-2
WIFM-SAL
FCSTM-H
EHSM3D
J. PAUL
Time Scale
SS
SS
SS
SS
SS
Q
Q
D
D
D
D
D
D
D
D
D
D
D
D
Spatial Dimension
X
X
3
3
X
X
3
XX
XX
XX
X
xy
xy
xz
xy
xy
xy
xyz
xyz
Hydrodynamics
S
S
S
S
S
S
S
S
S
S
S
Solution Tern.
A
A
FD
FD
FD
FD
FD
FD
FD
FD
FD
FE
FE
FD
FE
FE
FE
FD
FD
Computer
—
-
vl
vl
vl, PC
vl, PC
vl, PC
vl, PC
vl
vl
vl
vl
vl
vl
vl
vl
vl
vl
vl
D-dynamic x-1 dimensional l-hydrodynamics input A-analytical solution M-mainframe computers
Q-quasidynamic (tidal-av- xy-2 dimensional, longitudinal- S-hydrodynamics FD-finite difference PC-personal computers
eraged) lateral simulated solution
SS-steady state xz-2 dimensional, longitudinal- B-compartment or bos 3D FE-finite element solution
vertical xx-link node branching 2D
xyz-3 dimensional
Table 3-6. Water Quality Problems Addressed
Model
SEM
WQAM
HARO3
FEDBAKO3
QUAL2
AUTOQUAL
WASP4:
EUTRO4
TOXI4
DEM
EXPLORE-I
MIT-DNM
Chen
FETRA
CE-QUAL-W2
TABS-2
WIFM-SAL
FCSTM-H
EHSM3D
J.PAUL
Salinity
Bacteria
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Sedimen
1
1
2
1
2
2
2
DO
2
2
2
2
3
2
3
3
3
3
3
3
Eutro-
shication
1
1
1
3
1
1
1
Org.
Chem.
1
1,2,3
Metals
1
1
3.4. References
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M.L. 1981. Models for Analyzing Eutrophication in
Chesapeake Bay Watersheds: A Selection Method-
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Chesapeake Bay Program, Annapolis, MD.
Ambrose, R.B. and Roesch, S.E. 1982. Dynamic
Estuary Model Performance. Journal of the Environ-
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Ambrose, R.B. Jr. et. al. 1987. WASP4, A General
Water Quality Model for Toxic and Conventional Pol-
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Blumberg, A.F. 1975. A Numerical Investigation into
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Bay Institute, Johns Hopkins University, Baltimore
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Bowie, G.L. et. al. 1985. Rates, Constants, and Kinet-
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(second ed.), U.S. Environmental Protection Agency,
Athens, Ga. EPA/600/3-85/040.
Buchak, E.M. and Edinger, J.E. 1984a. Generalized,
Longitudinal-vertical Hydrodynamics and Transport:
Development, Programming And Applications, Docu-
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WES, Vicksburg, Mississippi.
Buchak, E. M. and Edinger, J.E. 1984b. Simulation of
a Density Underflow into Wellington Reservoir using
Longitudinal-vertical Numerical Hydrodynamics,
Document No. 84-18-R, U.S. Army Corps of Engi-
neers, WES, Vicksburg, Miss., March.
Chapra, S. and Nossa, G.A. October, 1974. Documen-
tation for HARO3,2nd Edition. USEPA Region II, New
York, NY.
Chen, H.S., August 1978. A Mathematical Model for
Water Quality Analysis. Proceedings of ASCE Hydrau-
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Mathematical and Physical Models in Hydraulic Engi-
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Chen, C.W. and Orlob, G.T. December, 1972. Ecologi-
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Creek, California, for Office of Water Resources Re-
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D.C.
Grim, R. and Lovelace, N.L. 1973. AUTO_QUAL Mod-
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DiToro, D.M., 1986. A DiageneticOxygen Equivalents
Model of Sediment Oxygen Demand, in Sediment
Oxygen Demand; Processes, Modeling, and Measure-
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GA, pp 171-208.
Di Toro, D.M., Fitzpatrick, J.J., and Thomann, R.V.
1981. Water Quality Analysis Simulation Program
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Duluth, Ml.
Dyer, K.R. 1973. Estuaries: A Physical Introduction.
John Wiley and Sons, New York.
Edinger, J.E. and Buchak, E.M.1983. Developments
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Circulation in a Branching Tidal Estuary. Chesapeake
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Instruction Report E-86-5, USAGE Waterways Experi-
ment Station, Vicksburg, MS.
Feigner, K.D. and Harris, H.S. July, 1970. Documenta-
tion Report -FWQA Dynamic Estuary Model. Prepared
for USEPA, Water Quality Office, Washington, D.C.
NTIS No. PB 197 103.
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matical Simulation of Tidal Time-Averages of Salinity
and Velocity Profiles in Estuaries. Ralph M. Parsons
Laboratory, Massachusetts Institute of Technology,
Cambridge, MA, MITSG-772-11, NOAA-72110204.
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Waters. Academic Press, N.Y. 483 pp.
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T.O., Brocard, D.N., and Ferrara, R.A. January, 1977.
User's Manual for the M.I.T. Transient Water Quality
Network Model. EPA-600/3-77-010. USEPA Environ-
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Hayter, E.J. 1987. Finite Element Hydrodynamic and
Cohesive Sediment Transport Modeling System. Dept.
of Civil Engineering, Clemson University, Clemson, SC.
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Holley, E. and Jirka, G. 1986. Mixing in Rivers. U.S.
Army Corps of Engineers, Vicksburg, MS. COE TR-E-
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D.C.
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3-25
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TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
Book III: Estuaries-
Part 1: Estuaries and Wasteload Allocation Models
EPA DOCUMENT NUMBER: EPA 823/R-92-002 DATE: May 1990
ABSTRACT
As part of ongoing efforts to keep EPA's technical guidance readily accessible to
water quality practitioners, selected publications on Water Quality Modeling and
TMDL Guidance available at http://www.epa.gov/waterscience/pc/watqual.html
have been enhanced for easier access.
This document is part of a series of manuals that provides technical information
related to the preparation of technically sound wasteload allocations (WLAs) that
ensure that acceptable water quality conditions are achieved to support
designated beneficial uses. The document provides technical information and
policy guidance for performing WLAs in estuaries, which, because of their
complex transport processes, cannot be treated as simple advective systems like
many rivers.
Book III Part 1 contains an overview of estuary characteristics, water quality
problems, and the processes affecting those problems. It also provides
specialized modeling guidance for the WLA, discusses the steps involved in
modeling, and presents background information on 19 different models that are
classified according to the spatial and temporal complexity of the models'
hydrodynamic component. The companion volume "Part 2: Application of
Estuarine Waste Load Allocation Models" is a guide to monitoring, and to model
calibration and testing.
KEYWORDS: Wasteload Allocations, Estuaries, Modeling, Water Quality Criteria
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