United State*      OfBoeofWeJer         	
Environment* Protection              March 1990
Agency        Washington DC 20460
Technical Guidance
Manual for Performing
Waste Load Allocations

Book III
Estuaries

Parti
Estuaries and Waste Load
Allocation Models

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United States       Office of Water
Environmental Protection               March 1990
Agency        Washington DC 20460
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
                      John F. Paul, Ph.D.3
            1. Center for Exposure Assessment Modeling,
        Environmental Research Laboratory, U.S. EPA, Athens, GA

            2. American Scientific International, Inc., at the
        Environmental Research Laboratory, U.S. EPA, Athens, GA

               3. Environmental Research Laboratory,
                   U.S. EPA, Narragansett, Rl
                        Prepared for

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

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                              Table of Contents

Glossary     	v

Acknowledgments	xi

Executive Summary	xiii

     PART I: Estuaries and Waste Load Allocation Models   	xiii

     Introduction  	xiii
     Overview of Processes Affecting Estuarine Water Quality	xiii
     Model Identification and Selection	xiv

     PART II: Application of Estuarine Waste Load Allocation Models	  xv

     Monitoring  Protocols for Calibration and Validation of Estuarine WLA Models   .  .  xv
     Model Calibration, Validation, and Use   	xvi
     Simplified Illustrative Examples   	xvii

Preface      	xix

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
                                         Hi

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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
     SUPPLEMENTS    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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                                          Glossary
Acute Toxicity1  - Any toxic effect that is produced
 within a short period of time, usually 24-96 hours.
 Although the effect most frequently considered is mor-
 tality, the end result of acute toxicity is not necessarily
 death. Any harmful biological effect may be the result

Aerobic1 - Refers to life or processes occurring only in
 the  presence of free oxygen; refers to a condition
 characterized by an excess of free oxygen in  the
 aquatic environment.

Algae (Alga)1 - Simple plants, many microscopic, con-
 taining chlorophyll.  Algae form the base of the food
 chain  in aquatic environments. Some species may
 create a nuisance when environmental conditions are
 suitable for prolific growth.

Allochthonous1- Pertaining to those  substances,
 materials or organisms in a waterway which originate
 outside and are  brought into the waterway.

Anaerobic2 - Refers to  life or processes occurring in
 the absence of free oxygen; refers to conditions char-
 acterized by the absence of free oxygen.

Autochthonous1   Pertaining  to those substances,
 materials, or organisms originating within a particular
 waterway and remaining in that waterway.

Autotrophic1 - Self nourishing; denoting those  or-
 ganisms that do not require an external source of
 organic material but  can  utilize light energy and
 manufacture their own food from inorganic materials;
 e.g., green plants, pigmented flagellates.

Bacteria1-  Microscopic, single-celled or noncellular
 plants, usually saprophytic or parasitic.

Benthal Deposit2 - Accumulation  on  the bed of a
 watercourse of  deposits containing organic matter
 arising from natural erosion or discharges of was-
 tewaters.

Benthic Region1 -  The bottom of a waterway; the
 substratum that supports the benthos.

Benthal Demand2  The demand on dissolved oxygen
 of water overlying benthal deposits that results from
 the upward diffusion of decomposition products of the
 deposits.

Benthos1 - Organisms growing on or associated prin-
 cipally with the bottom of waterways. These include:
 (1) sessile animals such as sponges, barnacles, mus-
 sels, oysters, worms, and attached algae; (2) creeping
 forms such as snails, worms, and insects; (3) burrow-
 ing forms, which include dams, worms, and some
 insects: and (4)  fish whose habits are more closely
 associated with the benthic region than other zones;
 e.g., flounders.

Biochemical Oxygen  Demand2 - A measure of the
 quantity of oxygen utilized In the biochemical oxida-
 tion of organic matter in a specified time and at a
 specific temperature.  It is not related to the oxygen
 requirements in  chemical combustion, being deter-
 mined entirely by the  availability of the material as a
 biological food and by the amount of oxygen utilized
 by the microorganisms during oxidation. Abbreviated
 BOD.

Biological Magnification1 - The ability of certain or-
 ganisms to remove from the environment and store in
 their tissues substances present at nontoxic levels in
 the surrounding water. The concentration of these
 substances becomes  greater each higher step in the
 food chain.

Bloom1   A readily visible  concentrated  growth or
 aggregation of minute organisms, usually algae, in
 bodies of water.

Brackish  Waters1 - Those areas where  there  is a
 mixture of fresh and salt water;  or, the salt content is
 greater than fresh water but less than sea water; or,
 the salt content is greater than in sea water.

Channel Roughness2 - That roughness of a channel,
 including the extra roughness due to local expansion
 or contraction and obstagles, 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 chan nel in contact
 with the water. It is expressed as roughness coefficient
 in the velocity formulas.

Chlorophyll1 - Green photosynthetic pigment present
 in many  plant and some bacterial cells. There  are
 seven known types of chlorophyll; their presence and
 abundance vary from one group of photosynthetic
 organisms to another.

Chronic Toxicity1 - Toxicity, marked by a long dura-
 tion, that produces an adverse effect on organisms.
 The end  result of chronic toxicity can be death al-
 though the usual effects are  subiethal; e.g., inhibits
 reproduction, reduces growth, etc. These effects are
 reflected  by changes  in the productivity and popula-
 tion structure of the community.

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

Coriolis  Effect2-  The deflection force of the earth's
 rotation. Moving  bodies are deflected to the right in
 the northern hemisphere and to the left in the southern
 hemisphere.

Datum2 - An agreed standard point or plane of state
 elevation, noted by permanent bench marks on some
 solid immovable structure, from which elevations are
 measured or to which they are referred.

Density Current2 - A flow of water through a larger
 body of water, retaining its unmixed identity because
 of a difference in density.

Deoxygenation2  - The depletion of  the dissolved
 oxygen  in  a liquid  either under natural conditions
 associated with the biochemical oxidation of organic
 matter present or by addition of chemical reducing
 agents.

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

Dissolved Oxygen2 - The oxygen dissolved in water,
 wastewater, or other liquid, usually expressed in mil-
 ligrams per liter, or percent of saturation. Abbreviated
 DO.

Diurnal2 - (1) Occurring during a 24-hr period; diurnal
 variation. (2) Occurring during the day time (as op-
 posed to night time). (3) In tidal hydraulics, having a
 period or cycle of approximately one tidal day.

Drought2 - In  general, an extended  period of dry
 weather, or a period of deficient  rainfall  that may
 extend over an indefinite number of days, without any
 quantitative standard by which to determine the de-
 gree of  deficiency needed to constitute a drought.
 Qualitatively, it may be defined by its effects as a dry
 period sufficient in length and severity to cause at least
 partial crop failure or  impair the ability to meet a
 normal water demand.

Ebb Tide1- That period of tide between a high water
 and the succeeding low water; falling tide.
Enrichment1 - An increase in the quantity of nutrients
 available to aquatic organisms for their growth.

Epilimnion1 - The water mass  extending from the
 surface to the thermocline in a stratified body of water.
 the epQimnion is less dense that the lower waters and
 is wind-circulated and essentially homothermous.

Estuary1 - That portion of a coastal stream influenced
 by the tide of the body of water into which it flows; a
 bay, at the mouth of a river,  where the tide meets the
 river current; an area where fresh and marine water
 mix.

Euphotic Zone1 - The lighted region of a body of water
 that extends vertically from the water surface to the
 depth at which photosynthesis fails to occur because
 of insufficient light penetration.

Eutrophication1 -The natural process of the maturing
 (aging) of  a lake; the process of  enrichment  with
 nutrients, especially nitrogen and phosphorus, lead-
 ing to Increased production of organic matter.

Firth1 - A narrow arm of the sea; also the opening of a
 river into the sea

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

Food Chain1 - Dependence of a series of organisms,
 one upon the other, for food. The chain begins with
 plants and ends with the largest carnivores.

Flood Tide2 - A term indiscriminately used for rising
 tide or landward current. Technically, flood refers to
 current The use of the terms "ebb"  and "flood" to
 include the vertical movement (tide) leads to uncer-
 tainty. The terms should  be  applied only  to the
 horizontal movement (current).

Froude's Number2 - A numerical quantity used as an
 index to characterize the type of flow in a hydraulic
 structure that has the force of gravity (as the only force
 producing motion)  acting  in conjunction with the
 resisting force of inertia. It is equal to the square of
 characteristic velocity (the  mean, surface, or maxi-
 mum velocity) of the system, divided by the product
 of a characteristic linear dimension, such as diameter
 or expressed in consistent units so that the combina-
 tions will be dimensionaless. The number is  used in
 open-channel flow studies or in cases in which the free
 surface plays an essential role in influencing motion.

Heavy Metals2 - Metals that can be precipitated by
hydrogen sulfide in acid solution, for example, lead,
silver, gold, mercury, bismuth, copper.
                                                  VI

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Heterotrophic1 - Pertaining to organisms that are de-
pendent on organic material for food.

Hydraulic Radius2 - The right cross-sectional area of
 a stream of water divided by the length of that part of
 its periphery in contact with its containing conduit; the
 ratio of area to wetted perimeter. Also called hydraulic
 mean depth.

Hydrodynamics2 - The study of the motion of. and the
 forces acting on. fluids.

Hydrographic Survey2 - An instrumental survey made
 to  measure and record physical characteristics of
 streams and other  bodies of water within an area.
 including such things as location, areal extent and
 depth, positions and locations of high-water marks.
 and locations and depths of wells.

Inlet1 - A short, narrow waterway connecting a bay,
 lagoon, or similar body of water with a  large parent
 body of water; an arm of the sea, or other body of
 water, that is long compared to its width, and that may
 extend a considerable distance inland.

inorganic Matter2 - Mineral-type compounds that are
 generally  non-volatile, not  combustible, and not
 biodegradable. Most inorganic-type compounds, or
 reactions,  are ionic in nature, and therefore, rapid
 reactions are characteristic.

Lagoon1 - A shallow sound, pond, or channel near or
 communicating with a larger body of water.

Limiting Factor1 - A factor whose absence, or exces-
 sive concentration, exerts some restraining influence
 upon a population through incompatibility  with
 species requirements or tolerance.

Manning Formula2 - A formula for open-channel flow,
 published by Manning in 1890. which gives the value
 of c in the Chezy formula.

Manning Roughness  Coefficient2 - The roughness
 coefficient in the Manning formula for determination
 of the discharge coefficient in the Chezy formula.

Marsh1 - Periodically wet or continually flooded area
 with the  surface not deeply submerged. Covered
 dominantly with emersed aquatic plants; e.g.. sedges,
 cattails, rushes.

Mean Sea Level2 - The mean plane about which the
 tide oscillates; the average height of the sea for all
 stages of the tide.

Michaelis-Menton Equation2 - A mathematical ex-
 pression to describe an enzyme-catalyzed biological
 reaction in which the products of a reaction are
 described as a function of the reactants.

Mineralization2 -The process by which elements com-
 bined in organic form in living or dead organisms are
 eventually reconverted into inorganic forms to be
 made available for a fresrTcyde of plant growth. The
 mineralization of organic compounds occurs through
 combustion and through metabolism by living
 animals. Microorganisms are ubiquitous, possess ex-
 tremely high growth rates and have  the ability  to
 degrade all naturally occurring  organic compounds.

Modeling2 - The simulation of some physical  or
 abstract phenomenon or system with another system
 believed to obey the same physical laws or abstract
 rules of logic,  in order to predict the behavior of the
 former  (main  system)  by experimenting with latter
 (analogous system).

Monitoring2 - Routine observation, sampling and test-
 ing of designated  locations or parameters to deter-
 mine efficiency of treatment  or compliance with
 standards or requirements.

Mouth2" The exit or point of discharge of a stream into
 another stream or a lake, or the sea.

Nautical Mile2 - A unit of distance used in ocean
 navigation. The United States nautical mile is defined
 as equal to one-sixteenth of a degree of a great circle
 on a sphere with a surface equal to the surface of the
 earth. Its value, computed for the Clarke spheroid of
 1866, is 1.853.248 m (6,080.20ft). The International
 nautical mile is 1,852 m (6,070.10 ft).

Nanoplankton2 * Very minute plankton not retained in
 a plankton net equipped with no. 25 silk bolting cloth
 (mesh,  0.03 to 0.04 mm.).

Neap Tides1 - Exceptionally low tides which  occur
 twice each month when the earth, sun and moon are
 at right angles to each other; these  usually  occur
 during the moon's first and third quarters.

Neuston2 - Organisms associated with, or dependent
 upon, the surface film (air-water) interface of bodies
 of water.

Nitrogenous Oxygen Demand (NOD)2 - A quantita-
 tive measure of the amount of oxygen required for the
 biological oxidation of nitrogenous material, such as
 ammonia nitrogen and  organic  nitrogen,  in  was-
 tewaten usually measured after the carbonaceous
 oxygen demand has been satisfied.
                                                vii

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Nutrients1 - Elements, or compounds, essential as raw
 materials for organism growth and development; e.g.,
 carbon, oxygen, nitrogen, phosphorus, etc.

Organic1  Refers to volatile, combustible, and some-
 times biodegradable chemical compounds contain-
 ing carbon atoms (carbonaceous) bonded together
 and with other elements. The principal groups of or-
 ganic substances found In wastewater are proteins,
 carbohydrates, and fats and oOs.

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

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

Periphyton (Aufwuchs)1 - Attached  microscopic or-
 ganisms growing on the bottom, or other submersed
 substrates, in a waterway.

Photosynthesis1  - The metabolic process by which
 simple sugars are manufactured from carbon dioxide
 and  water  by plant cells  using light as an  energy
 source.

Phytoplankton1 - Plankton consisting  of plant life.
 Unattached microscopic plants subject to movement
 by wave or current action.

Plankton1  - Suspended microorganisms that have
 relatively low powers of locomotion, or that drift in the
 water subject to the action of waves and currents.

Quality2  A term to describe the composite chemical,
 physical, and  biological characteristics of a water with
 respect to it's suitability for a particular use.

Reaeration2 - The absorption of oxygen into water
 under conditions of oxygen deficiency.

Respiration1 - The complex series of chemical and
 physical reactions in all living organisms by which the
 energy and nutrients in foods is made available for
 use. Oxygen is used  and carbon dioxide released
 during this process.

Roughness Coefficient2 - A factor, in the  Chezy,
 Darcy-Weisbach,  Hazen-Williams. Kutter.  Manning.
 and other formulas for computing the average velocity
 of flow of water in a  conduit or channel, which repre-
 sents the effect of roughness of the confining material
 on the energy losses in the flowing water.

Seiche1 - Periodic oscillations in the water level of a
 lake or other landlocked body of water due to unequal
 atmospheric pressure, wind, or other cause, which
 sets the surface in  motion. These oscillations take
 place when a temporary local depression or elevation
 of the water level occurs.

Semidiurnal2 - Having a period or cycle of ap-
 proximately one half of a tidal day. The predominating
 type of tide throughout the world is semidiurnal, with
 two high waters and two low waters each tidal day.

Slack Water2 - In tidal waters, the state of a tidal current
 when Its velocity is at a minimum, especially the 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 slack water occurs near the times of high and
 low water, while in other localities the slack water may
 occur midway between high and low water.

Spring Tide1 - Exceptionally high tide which occurs
 twice per lunar month when there is a new or full moon,
 and the earth,  sun, and moon  are in a straight line.

Stratification (DensityStratification)1 -Arrangement
 of water masses into separate, distinct, horizontal
 layers as a result of differences in density; may be
 caused by differences in temperature, dissolved or
 suspended solids.

Tidal Flat1 - The sea  bottom, usually wide, flat, muddy
 and nonproductive, which is exposed at low tide. A
 marshy or muddy area that is covered and uncovered
 by the rise and fall of the tide.

Tidal Prism2 -  (1) The volume of water contained in a
 tidal basin between the elevations of high and low
 water. (2) The total amount of water that flows into a
 tidal basin or estuary and out again with movement of
 the tide, excluding any fresh-water flows.

Tidal  Range2  - The difference in elevation  between
 high and low tide at any point  or locality.

Tidal Zone (Eulittoral Zone, Intertidal Zone)1  - The
 area of shore between the limits of water level 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
 of the moon and sun in conjunction with the earth's
 rotational force.

Tide Gage2 - (1) A staff gage that indicates the height
of the tide. (2) An instrument that automatically
registers the rise and fall  of the tide.  In some instru-
                                                 VIII

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merits, the registration is accomplished by printing the
heights at regular intervals; in others by a continuous
graph in which the height of the tide is represented by
ordinates of the curve and the corresponding time by
the abscissae.

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

Water Pollution1 - Alteration of the aquatic environ-
ment in  such a way as to interfere with a designated
beneficial use.

Water Quality Criteria1 - A scientific requirement on
which a decision or judgement may be based concern-
ing the suitability of water quality to support a desig-
nated use.

Water Quality Standard1 - A plan that is established
by governmental authority as a  program for water
pollution prevention and abatement.

Zooplankton2 - Plankton consisting of animal life. Un-
attached microscopic animals having  minimal
capability for locomotion.
1 Rogers. B.G.. Ingram. W.T.. Pearl. E.H.. Welter. LW.
 (Editors). 1981. Glossary. Water and Wastewater Con-
 trol Engineering. Third Edition, American Public
 Health Association, American Society of Civil  En-
 gineers, American Water Works Association, Water
 Pollution Control Federation.

2Matthews, J.E., 1972, Glossary of Aquatic Ecological
 Terms,  Manpower Development Branch,  Air and
 Water Programs Division, EPA. Oklahoma.
                                                 be

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                                  Acknowledgments
Although we authors bear ultimate responsibility for the
content of our respective sections, a guidance manual
such as this is truly  a collaborative effort within our
professional community. The role of project manager
is important in setting goals, direction, and boundaries
to these projects. Hiranmay  Biswas  provided such
project direction,management of peer review process
and the resources necessary to complete the manual.

We were able to draw  upon working documents
produced by JRB Associates and Camp, Dresser, and
McKee.  Inc. We acknowledge the authors of this
material. Richard Wagner, Jane Metcalf, and Elizabeth
Southerland of JRB, and Chris Clarkson of COM.

Peer review of early draft material is particularly helpful
to authors still trying to focus their efforts and bring an
appropriate balance to the material. Sandra Bird, AScI
Corporation, provided extensive and helpful reviews of
Sections 2. 4, and 5, and located material for Chapter
3.  Robert R. Swank reviewed all  of  Parts 1 and  2.
providing technical comments and alertly catching er-
rors and inconsistencies through to the end. Robert
Ryans provided editorial comments for Parts 1 and 2.
and helpful suggestions on style. Keith Little, Research
Triangle Institute, made helpful general comments.

Peer review of the draft manual was provided  by a
prestigious  group of professionals. Thorough com-
mentary was received from Robert V. Thomann, Man-
hattan College, Donald R.F. Harieman, Massachusetts
Institute of Technology, Steven C.  Chapra, University
of Colorado at Boulder, and Wu-Seng Lung, University
of Virginia. These academic leaders represent the dif-
ferent approaches to water quality modeling in  an
effective manner. We nave sought to represent their
points faithfully, and, where conflicting advice was
given, to balance their viewpoints fairly.

In addition, helpful review comments were provided by
a group of government engineers and managers from
the Office of Municipal Pollution Control, the Office of
Marine and Estuarine Protection, and the Permits
Division of the Office of Water Enforcement  and Per-
mits. Specifically, we acknowledge Steve Glomb, Per-
mits Division. Office  of Water. USEPA; Robert Elliott,
Chief, Water  Quality Management Branch, USEPA
Region VI; Mark Dortch, Chief. Water Quality Modeling
Group. USACE Waterways Experiment Station; Ernest
E. Watkins, Municipal Facilities  Division. Office of
Water. USEPA; Robert Vaughn. Chief,  Water  Stand-
ards and Planning Branch. USEPA Region II;  Edwin H.
Liu, Monitoring Coordinator. USEPA  Region IX; and
Jerad Bales. Hydrologist, Water Quality  Division,
USGS, Raleigh. NC.

Judy Webb. Donna  Hinson, Stephanie Hopkins and
Tawnya Robinson, AScI Corporation, collected, refor-
matted, and produced the final draft document. Andy
Simms drafted the figures. The final  layout was for-
matted by Tad Slawecki and Cathy Whiting of LJmno-
Tech, Inc.

We are grateful for their efforts.
                                                xi

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                                  Executive Summary
The Technical Guidance Manual for Performing Waste
Load Allocations, Book III: Estuaries is the third in a
series of manuals providing technical information and
policy guidance for the preparation of waste load al-
locations (WLAs) that are as technically sound as cur-
rent state of the art permits. The objective of such load
allocations is to ensure that water quality conditions
that protect designated beneficial uses are achieved.
This book provides technical guidance for performing
waste load allocations in estuaries.

PART I:  ESTUARIES AND WASTE LOAD
ALLOCATION MODELS

Introduction
Estuaries are coastal bodies of water where fresh water
meets the sea. Most rivers and their associated pol-
lutant loads eventually flow into estuaries. The complex
loading,  circulation, and sedimentation processes
make water quality assessment and waste load alloca-
tion in estuaries difficult. Transport and circulation
processes in estuaries are driven primarily by river flow
and tidal action. As a consequence of its complex
transport processes, estuaries cannot be treated as
simple advective systems such as many rivers.

Wastewater discharges into estuaries can affect water
quality in several ways, both directly and indirectly. In
setting limits on wastewater quantity and quality, the
following  potential  problems should be assessed:
salinity, sediment,  pathogenic bacteria,  dissolved
oxygen depletion,  nutrient enrichment and over-
production, aquatic toxicity, toxic pollutants and bioac-
cumulation and human exposure.

A WLA provides a quantitative relationship between the
waste load and the instream concentrations or effects
of concern as represented by water quality standards.
During the development of a WLA, the user combines
data and model first to describe present conditions and
then to extrapolate to possible future conditions. The
WLA process  sequentially addresses the topics  of
hydrodynamics, mass transport, water quality kinetics,
and for some problems, bioaccumulation and toxicity.

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

Overview of Processes Affecting Estuarine
Water Quality
The estuarine waste load allocation process requires a
fundamental understanding of the factors affecting
water quality and the representation of those proces-
ses in whatever type of model is applied (conceptual
or mathematical) in order to determine the appropriate
allocation  of load. Insight into  processes affecting
water quality may be obtained through examination of
the schemes available for their classification. Estuaries
have typically been classified based on their geomor-
phology and patterns of stratification and mixing. How-
ever, each estuary is to some degree unique and it is
often necessary to consider the fundamental proces-
ses impacting water quality.

To determine the  fate and affects of water quality
constituents it is necessary first to determine proces-
ses impacting their transport. That transport is affected
by tides, fresh water inflow, friction at the fluid boun-
daries and its resulting turbulence, wind and atmos-
pheric pressure,  and to a lesser  degree (for some
estuaries)  the effects of the earth's rotation (Coriolis
force). The resulting transportation patterns may be
described (determined  from field studies) in waste load
allocation studies, or, as is becoming more frequently
the case, estimated using  hydrodynamic models.
Hydrodynamic models are based  on descriptions of
the processes affecting circulation and mixing using
equations based on laws of conservation of mass and
momentum. The fundamental equations generally in-
clude: (A) the conservation of water mass (continuity),
(B) conservation of momentum, and (C) conservation
of constituent mass.

An important aspect of estuarine WLA modeling often
is the capability to simulate  sediment transport and
sediment/water interactions. Sediments not only affect
water transparency, but can carry  chemicals such as
nutrients and toxic substances into receiving waters.
Unlike rivers, which have reasonably constant water
quality conditions, the large changes in salinity and pH
in an  estuary directly affect the transport behavior of
many suspended  solids. Many colloidal particles ag-
glomerate and settle in  areas of  significant salinity
gradients. Processes impacting sediment transport in-
clude  settling,  resuspension, scour and erosion,
coagulation and flocculation.
                                                xiii

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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 usual-
ly include temperature, major nutrients, chemical char-
acteristics, detritus, bacteria, and primary producers.
WLA models may include higher trophic levels (I.e.
zooplankton and fish) because of higher trophic level
effects on other more Important variables, such  as
phytbplankton. 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 lexicological affects.
The transport of the materials also may be affected by
sorption and they can degrade through such proces-
ses as volatilization, biodegradation, hydrolysis, and
photolysis.

Trace metals may be of concern in many estuaries due
to their lexicological effects. The toxicity of trace me-
tals 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 resuspen-
sion.

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 mode! 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 in-
directly link the pollutants to be  controlled  with the
primary water quality indicators. All other  interacting
water quality constituents thought  to be  significant
should be included at this point. This can best be done
In a diagram  or flow chart representing the mass
transport and  transformations  of water quality con-
stituents in a defined segment of water. The final result
of this step should be the assimilation of all the available
knowledge of a system in a way that major water quality
processes and  ecological relationships can be
evaluated for inclusion in the numerical model descrip-
tion.

The next step is to specify the  spatial extent, dimen-
sionality, and scale (or computational resolution) of the
WLA model. This may be accomplished by determining
the effective dimensionality of the estuary as a whole,
defining the boundaries of the study area, then specify-
ing 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 genera), 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 dear 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
regulatory requirements. One basic guideline applies
in all cases - the simulations should be long enough to
eliminate the  effect of initial conditions on important
water quality constituents at critical locations.
                                                  xiv

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The temporal resolution of WLA simulations falls into
one of three categories - dynamic, quasi-dynamic, and
steady state. Dynamic simulations predict hour to hour
variations  caused by tidal  transport Quasidynamic
simulations predict variations on the order of days to
months.  The effects of tidal transport are  time-
averaged. Other forcing functions such as freshwater
inflow,  pollutant  loading, temperature,  and sunlight
may vary from daily to monthly. Steady state simula-
tions predict monthly to seasonal averages. All inputs
are time-averaged. Two schools of thought have per-
sisted regarding the utility of dynamic versus
quasidynamic and steady state simulations. For some
problems the choice is reasonably dear.

In general, if the regulatory need or kinetic response is
on the order of hours, then dynamic simulations are
required; if regulatory needs are long term averages
and the kinetic response is on the order of seasons to
years, then quasidynamic or steady simulations are
indicated.

The  goal of model selection is to obtain a simulation
model  that  effectively  implements the conceptual
model identified for the WLA Models selected for dis-
cussion here are general purpose, in the  public
domain, and available from or supported  by public
agencies.  The selection of an estuarine WLA model
need not be limited to the models discussed in this
document. Other models that are available to a project
or organization should also be considered. The models
summarized in this report represent  the typical  range
of capabilities currently available.  Estuarine WLA
models can be classified as Level I to Level IV accord-
ing to  the temporal  and  spatial complexity  of the
hydrodynamic component  of the model.  Level I in-
cludes desktop screening methodologies that calcu-
late seasonal or annual mean pollutant concentrations
based on steady  state conditions and simplified flush-
ing time  estimates. These models  are designed to
examine an estuary rapidly to isolate trouble spots for
more detailed analyses.

Level II includes  computerized steady state or tidally
averaged  quasidynamic simulation models, which
generally use a box or compartment-type  network to
solve finite difference approximations to the basic par-
tial differential equations. Level II models can predict
slowly changing seasonal water quality with an effec-
tive time resolution of 2 weeks to 1 month. Level III
includes computerized one-dimensional  (1-d) and
quasi two-dimensional (2-d), dynamic  simulation
models. These real time models simulate variations in
tidal heights and velocities-throughout each tidal cycle.
Their effective time resolution is usually  limited to
average variability over one week because tidal input
parameters generally consist of only average or slowly
varying values. The effective time resolution could be
reduced to under 1 day given good representation of
diurnal water quality kinetics and precise tidal input
parameters. The required data and modeling effort are
usually not mobilized in standard WLAs. Level IV con-
sists of computerized 2-d and 3-d dynamic simulation
models. Dispersive mixing and seaward boundary ex-
changes are treated more realistically than in the Level
III 1 -d models. These models are almost never used for
routine WLAs.

The effective time resolution of the Level IV models can
be less than 1 day with a good representation of diurnal
water quality and intratidal variations.

The advantages of Level I and II models lie in their
comparatively low cost and ease of application. The
disadvantages lie in  their steady state or tidally
averaged^temporal scale. When hydrodynamics and
pollutant'inputs are  rapidly  varying, steady state
models are difficult to property calibrate.

The dynamic models (Levels III and IV)  have ad-
vantages  over steady state  and tidally averaged
models  in representing mixing in partially mixed es-
tuaries because advection is  so much better repre-
sented.  The success with which these models can
predict transient violations depends upon  both the
accuracy and resolution of the loading and environ-
mental data, and the model's treatment of short time
scale kinetics such as desorption or diurnal fluctua-
tions in  temperature. pH, or sunlight. While dynamic
models are capable of predicting diurnal and transient
fluctuations in water quality parameters, the input data
requirements are much greater.

PART II: APPLICATION OF ESTUARINE
WASTE LOAD ALLOCATION MODELS

Monitoring Protocols 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
                                                xv

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or navigation charts). Data are also required  for
transport Transport within the modeled system may
either be specified (measured, e.g. current meters) or
computed from hydrodynamic models. Rows into the
system 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,
eutrophication or toxics.  Concentrations for all  per-
tinent water quality variables should be provided at the
model boundaries, providing  the perturbation  for
model predictions, as well as at points within the water-
body 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  as-
surance, data management and modeling activities.

Collaboration insures that fundamental design ques-
tions are properly stated so that the available resources
are used in the most efficient manner possible and that
all critical data for modeling are collected. The use of
monitoring and  modeling in  an iterative  fashion,
wherever possible, is often the most efficient means of
insuring that critical data are  identified  and collected.
A rigorous, well  documented,  quality assurance,
quality control (QA/QC) plan should be an integral part
of any waste load allocation program.

Model Calibration, Validation, and Use
While  models  can be run with  minimal data, their
predictions are subject to large uncertainty. Models are
best operated to interpolate between existing  condi-
tions or to extrapolate from existing to future  condi-
tions, such as  in the projection of conditions under
anticipated waste loads. The confidence that can be
placed on those  projections is dependent upon  the
integrity  of the model, and  how well the model is
calibrated to that particular estuary, and how well the
model compares  when evaluated against  an inde-
pendent data set (to that used for calibration).

Model calibration is necessary because of the semi-
empirical  nature of present day (1989) water quality
models. Although the waste load allocation models
used in estuary studies are formulated  from the mass
balance  and,  in many cases,  from conservation of
momentum principles, most of the kinetic descriptions
in the models that describe the change in water quality
are empirically derived. These empirical  derivations
contain a number of coefficients and parameters that
are usually determined by calibration using data col-
lected in the estuary of interest

Calibration alone is not adequate to determine the
predictive capability of a model for a particular estuary.
To map out the range of conditions over which the
model  can be used to determine cause and effect
relationships, one or more additional independent sets
of data are required to determine whether the model is
predictively valid. This testing exercise,  which also is
referred to as confirmation testing, defines the limits of
usefulness of the calibrated model. Without validation
testing, the calibrated model remains a description of
the conditions defined by the calibration data set. The
uncertainty of  any projection or extrapolation of a
calibrated model would be unknown unless this is
estimated during the validation procedure.

In addition, the final validation is limited to the range of
conditions defined  by the calibration and validation
data sets. The uncertainty of any projection or  ex-
trapolation outside  this range also remains unknown.
The validation of a calibrated model, therefore, should
not be taken to infer that the model is predictively valid
over the full range of conditions that can occur in an
estuary. For example, a model validated over the range
of typical tides and low freshwater  inflow may  not
describe conditions that occur when large inflows and
atypical tides occur.

This is especially true when processes such as 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 proces-
ses to variations  in predicted concentrations. For ex-
ample, the cause of violations of a dissolved oxygen
standard can be determined from the relative contribu-
tion of various loads and the effect of sediment oxygen
demand, BOD decay, nitrification, photosynthesis, and
reaeration.
                                                  xvi

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Once the model is calibrated and validated, it is then
used to investigate causes of existing problems or to
simulate future conditions to determine effects of chan-
ges in waste loads as part of the waste load allocation
procedure. Once critical water quality conditions are
defined for the estuary, harbor or coastal area of con-
cern,  determining the waste assimilative capacity is
relatively straightforward. Models are available to relate
critical water quality responses to the loads for most
problems. However, the definition of critical conditions
for estuaries is not straightforward. For streams receiv-
ing organic loads, this is a straightforward matter of
determining the low flow and high temperature condi-
tions. In estuaries, fresh  water, tides, wind, complex
sediment transport, and other factors can be important
to determining the critical conditions. As of yet, there
are no clear methods of establishing critical conditions.
especially in terms of the probability of occurrence. The
analyst must use considerable judgement in selecting
critical conditions for the particular system.  Once
loads and either critical conditions or estimated future
conditions are specified,  the calibrated model can be
used to predict the water quality response. The inves-
tigation may involve  study of extreme hydrological,
meteorological, or hydrographic events that affect
mixing; waste loadings from point and non-point sour-
ces; and changes in benthic demands.

Simplified Illustrative Examples
This section presents illustrative examples of estuarine
modeling using both simple screening procedures and
the water quality model WASP4. The screening proce-
dures are based upon simple analytical equations and
the more detailed guidance provided in "Water Quality
Assessment: A Screening Procedure for Toxic and
Conventional Pollutants - Part 2." WASP4 examples
demonstrate model based estuarine WLA application.

WASP4 is a general multi-dimensional compartment
model supported and available through the U.S. EPA
Center for Exposure Assessment Modeling.
The examples provided consider eight water quality
concerns  in three basic  types of  estuaries. A  one
dimensional estuary is analyzed by screening methods
for conservative and nonconservative toxicants  and
chlorine residual. Bacteria and DO depletion are simu-
lated. Nutrient enrichment, phytoplankton production,
and DO depletion In a vertically stratified estuary are
simulated. Finally, ammonia toxicity and a toxicant in
a wide, laterally variant estuary are simulated.

The screening procedures can be applied using cal-
culator or spreadsheet While they may not be suitable
as the sole justification for a WLA, they can be valuable
for  initial  problem assessment. Three  screening
methods are presented for estimating estuarine water
quality impacts: analytical equations for an idealized
estuary, the fraction of freshwater  method, and the
modified tidal prism method.  These example proce-
dures are only applicable  to steady state, one-dimen-
sional estuary problems.

Deterministic water quality modeling of estuarine  sys-
tems can be divided into two separate tasks: descrip-
tion  of  hydrodynamics,  and  description of water
quality. The WASP4 model was designed to simulate
water quality processes,  but requires hydrodynamic
information as input. Hydrodynamic data may be
directly specified in an input dataset, or may be read
from the output of a separate hydrodynamic model.
The examples here illustrate tidal-averaged modeling
with  user-specified hydrodynamics.  Both  the
eutrophication and toxicant programs are described
and used.

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

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                                            Preface
The document is the third of a series of manuals provid-
ing information and guidance for the preparation of
waste load allocations. The first documents provided
general guidance for performing waste load allocation
(Book  I),  as  well as guidance  specifically directed
toward streams and rivers (Book II). This document
provides technical information and  guidance for the
preparation of waste load allocations in estuaries. The
document is divided into four parts:

Part 1 of this document provides technical information
and policy guidance for the preparation of estuarine
waste load allocations. It summarizes the important
water quality problems, estuarine characteristics and
processes affecting those problems, and the simula-
tion models available for addressing these problems.
This part. "Part 2: Application of Estuarine Waste Load
Allocation Models." provides a guide to monitoring and
model calibration and testing, and a case study tutorial
on simulation of waste load allocation problems  in
simplified estuarine  systems. The third  part  sum-
marizes initial dilution and  mixing zone processes,
available models, and their  application in waste load
allocation. Finally, the fourth part summarizes several
historical case studies, with critical reviews by noted
experts.
       'Organization: 'Technical Guidance Manual for Performing Waste Load Allocations. Book
        Estuaries"
Part
1
2
3
4
Title
Estuaries and Waste Load Allocation Models
Application of Estuarine Waste Load Allocation Models
Use of Mixing Zone Models in Estuarine Waste Load Allocation Modeling
Critical Review of Estuarine Waste Load Allocation Modeling
                                                xix

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                                     1. Introduction

                                    RobertB. 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 discus-
sion 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
development. 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
process. For instance, criteria and standards for DO.
ammonia, 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 Manual* for Performance of Wasteload Allocations
    BOOK I    303 (d)/TMDL PROGRAM GUIDANCE

              Under development

    BOOK II   STREAMS AND RIVERS

              Chapter 1 - BOD/Dissolved Oygen Impacts and Ammonia Toxlcity

              Chapter 2 - Nutrient/Eutrophication Impacts

              Chapter 3 - Toxic Substance Impacts

    BOOK III   ESTUARIES

    BOOK IV   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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12.. 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 connection with
the open sea and within which sea water is measurably
diluted with fresh water derived from land drainage
(Prrtchard. 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
shellfishing. 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 conflicting
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 pol-
lutant 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 pol-
lutants, 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
primary limiting nutrient. In estuaries, either nutrient
may limit growth.
The importance of atmospheric nitrogen deposition to
estuaries has recently received attention with  es-
timates that up to 39%  of  nitrogen  reaching
Chesapeake Bay originated in atmospheric deposition
(Fisher, et al. 1988). Nitrogen may deposit to water-
sheds  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 denitrification. 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/m2/year in  the
east. Organic nitrogen inputs range from  0.1 to  0.4
g/m2/year (Waddell. 1989).  Dry deposition may  ac-
count for about the same input, doubling the total
nitrogen Inputs.

7.22. 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. Lon-
gitudinal 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 relative-
ly fresh water flows over saline bottom water. Entrain-
ment of bottom water may dilute pollutants in  the
surface, but upstream transport of salt and pollutants
can  occur  along the bottom. Coriolis acceleration,
deflecting currents to the right in the northern hemi-
sphere, may be significant in large estuaries.

As a consequence of these complex transport proces-
ses, estuaries cannot be treated as simple advectlve
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 Maeronutrlent* In
            Seawater [Smith (1974)]
Constituent
chloride
sodium
magnesium
sulfata
calcium
pot&ssiuffl
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.

1.3.1. Salinity
Salinity Is important In determining available habitat for
estuarine organisms. Large wastewater discharges
into relatively small estuaries or embayments 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 wastewater
is assimilated Into the estuary.

1.3.2. 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 hydrophobic
organic chemicals, metals, and  nutrients.  Sediment
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.

7.3.3. 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.

13.4. 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
material, nitrification, diagenesis of benthic sediments,
photosynthesis and respiration by phytoplankton and
submerged aquatic vegetation, and  reaeration.  The
natural balance can be disrupted by excessive was-
tewater loads of organic  material,  ammonia,  and
nutrients. Other sources  of nutrients, such as runoff
from agricultural, residential, and urban lands and at-
mospheric 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.

7.3.5. 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
phytoplankton,  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 at-
mospheric deposition.

7.3.6. Aquatic Toxicity
High  concentrations  of ammonia, many organic
chemicals, and metals can disable or kill aquatic or-
ganisms. Acute toxicity is caused by high exposure to
pollutants for short periods of time (less than 4 days).
Chronic toxicity is caused by lower exposures 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 sediment concentra-
tions. Overall toxicity results from the combined ex-
posure to all chemicals in the effluent and the ambient
waters.

7.3.7. 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, bioac-
cumulatlon of these chemicals can occur. This  food
chain contamination can  persist long after the original
chemical source Is eliminated. Humans that regularly
consume 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 1,303 (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 char-
acteristics 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 describe 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.

1.4.1. Hydrodynamics
The topic  of hydrodynamics addresses where the
water goes. Both primary and secondary water circula-
tion 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.
Hydrodynamlc models may be needed, however, to
investigate secondary currents associated with the net
residual tidal action, wind, density differences, or
Coriolls acceleration. Hydrodynamtc models also may
be used to interpolate data between monitoring sta-
tions or to extrapolate data to future conditions.  The
final result of the hydrodynamics study is a record of
water  flow and  volume (or velocity and elevation)
throughout the water body over an appropriate period
of time.

1.4.2. 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
parameterized 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 particular-
ly  Important in cases where net tributary inflow to the
estuary is uncertain. The final result of the mass
transport step is a record of advective and dispersive
fluxes  (or the appropriate model coefficients) for dis-
solved, nonreactlve substances throughout the water
body over the period of study.

1.4.3. 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 ap-
propriate site-specific values for the reaction coeffi-
cients 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 con-
stituents. 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 calibra-
tion and testing process. The final result of the water
quality kinetics step is a record  of constituent con-
centrations  throughout the water body for the period
of study and for hypothetical future periods  under
various waste load management strategies.

1.4.4. Bioaccumulation and Toxicity
Often, water  quality constituent concentrations  (or
toxicity 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 litera-
ture values for the parameters are available, monitoring
data should be used for site-specific calibration. Direct
toxicity  due to the narcotic  effects of neutral
hydrophobic 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 con-
tinued 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
relia bility over the range of conditions tested. Validation
is contingent upon the waste load options to be con-
sidered. 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 Alloca-
tion Models," summarizes the  important water quality
problems, estuarine characteristics and processes af-
fecting 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
simplified estuarine systems.

Part 3, "Use of Mixing Zone Models In Estuarine Waste
Load  Allocations," summarizes initial dilution and
mixing zone processes, available models,  and their
application in waste load allocation. Part  4,"Critical
Review of Estuarine Waste Load Allocation Modeling,"
summarizes several historical case studies, with critical
reviews by noted experts.

1.7. References
Fisher, D., Ceraso, J., Mathew, T., and Oppenhetmer,
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  As-
sociation 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 In-
stitute.

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.
                                                1-5

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    2. Overview of Processes Affecting Estuarine Water Quality


                                     James L Martin, Ph.D., P.E.
                                      ASct, Corporation at the
                              Center for Exposure Assessment Modeling
                        Environmental Research Laboratory, U.S. SPA, 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
quality interactions (Section 2.4), organic wastes, dis-
solved 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 processes followed by supplemental text describing
in greater detail how each of these basic processes are
described  in  estuarine waste load allocation (WLA)
models.

2J2. 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 In-
trusion. 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
variations and tidal flow is normally greater than fresh
water Inflow.  Examples of this include the  Delaware
and Rarrtan River estuaries which are normally  well
mixed. Partially stratified  estuaries are intermediate
between  sharply stratified and completely mixed es-
tuaries. Partially stratified  estuaries exhibit significant
vertical density 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 circula-
tion 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
(Rscher et al. 1978) are: (1) drowned river valleys or
coastal plain estuaries (e.g.. Chesapeake Bay.
Delaware Estuary), (2} bar-built estuaries (e.g.. Galves-
ton 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
towards 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
gradual seasonal and catastrophic variations in con-
figuration. 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,
landslides or volcanic eruptions. An example is San
Francisco 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
generated by the tides, winds, density gradients result-
ing 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
gradients) 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
parameterizations used to evaluate mixing in fresh
water must be used with caution if at all. This section
briefly discusses the physical forces affecting es-
tuaries. More extensive discussions can be found in
standard texts on estuaries such as that by Fischer et
al. (1978).

23.1. 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 cyde of tides. Astronomical tidal motion
is highly predictable. Such Information is published
annually 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 variation
of water level about some datum level) and tidal current
(the ebb and flood velocity fields). Tidal amplitudes 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 mag-
nitudes are also highly variable, with the highest values
being recorded in topographically constrained 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 channels 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 circula-
tion patterns of small magnitude but great persistence.
which could play a significant role in the transport of
pollutants.

2.32. 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
before being completely mixed into sea water. Such
density differences result in flow patterns that tend  to
maintain the density differences.  Areas with high
gradients, 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
periods.

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. Freshwater inflow varies primarily on seasonal
scales but large amounts of fresh water can  be intro-
duced to estuarine systems by severe storms, espe-
cially tropical cyclones along the East and Gulf Coasts
during late summer and fad. 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 estuaries along the
Gulf Coast (the Brazos River and Colorado River Es-
tuaries) to several months for an estuary that is shallow
and has weak tides such as Pamlico Sound.

23.4. 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.

2.3.5. 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 chan-
ges in prevailing winds. Variability of wind speed and
direction over periods shorter than the frontal passage
scale will be evidenced primarily in the production 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 as-
 sociated with strong winds (wind setup and setdown)
 modify  the astronomical tides  and are  called
 meteorological tides.

 I n 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  circulation
 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 (l.e. winter or ex-
 tratropical 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 Supplement 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
transparency,  but can  carry chemicals  such as
nutrients and toxic substances into receiving waters.
Therefore, an important aspect of water quality model-
ing is the capability to simulate sediment transport and
sediment/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. Con-
sequently estuaries tend to trap sediments (Mills et al.
1985).
Estuarine sediment transport has  two main com-
ponents - 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, days, 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).

2.42. 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 coeffi-
cient) 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
micrometer-size particles and particularly for organic
particles, the large diversity in sizes, shapes, and den-
sity (Lai 1977; Ives 1973) often require indirect deter-
minations of fall velocities from settling traps or mass
balances. 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 "explosive11 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
                                                2-4

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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 entrapment depending solely on particle
density and shear velocity. The lack of well established
descriptions of entrapment for cohesive particles re-
quires site-specific calibration to refine Initial estimates.

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, stres-
ses due to wind driven flows and perturbations by boat
movement or  organisms (bloturbatlon) can greatly In-
crease 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 agglo-
merate to form larger  particles (flocculate). The re-
sulting floe may then settle at a much different rate, due
to the greater agglomerated mass, than the individual
particles. Coagulation occurs when electrolytes, such
as sodium chloride, neutralize the  repulsive forces
between clay  particles allowing them to adhere upon
collision (flocculate). Rocculation 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 organlcs (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 section
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
biphenyi (PCS) resuspension.
  See Supplement II for greater detail on
  sediment transport and sediment/
  water quality Interactions.  This Sup-
  plement 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 pro-
cesses used to model organic wastes,  DO and
nutrients (referred to as conventional pollutants) and
their interactions. For more detailed information, the
reader should refer to other resources (Bowie et al.
1985;  Oriob 1983; Chapra and Reckhow 1983; Tho-
mann and Mueller 1987). The focus of WLA models of
conventional pollutants  is often DO  and biochemical
oxygen demand (BOO)  as a general measure of the
health of the system, or the focus can  be primary
productivity when eutrophication is the major concern.
Conventional WLA models  usually include  temper-
ature, major nutrients, chemical  characteristics,
detritus, bacteria, and primary producers. WLA models
may include higher trophic levels (i.e. zooplankton and
fish) because of their effects on other more important
variables, 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
modeling these processes Is provided in Section 3.

2.52. Fate Processes
Upon  entry to the estuary, settling of paniculate or-
ganic  matter and paniculate nutrients generally oc-
curs. High flow events may scour previously deposited
material. Organic matter is oxidized, drawing upon the
DO supply, 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
ammonia to nitrite and  then nitrate. Nitrate  may be
converted back to ammonia or to nitrogen gas through
                                               2-5

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denftrification in low DO regions of the estuary. Am-
monia 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 toorthophosphate,
which reaches sorptive equilibrium with suspended or
bent hie sediment.  Participate sorbed phosphate set-
tles; dissolved phosphate  is rapidly taken up by
phytoplankton and aquatic plants and incorporated
into the food chain, eventually returning to the water as
organic phosphorus.

Organic  material  deposited to benthic sediment Is
oxidized 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 reenter the 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  en-
vironmental 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 provided 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
nutrient availability and phytoplankton requirements.
Phytoplankton "death" rates are conventionally ex-
pressed as the sum of the endogenous respiration rate,
the death rate, and the grazing rate. Available informa-
tion 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 stolchlometry is necessary to
accurately model these interactions. The ratios of
phytoplankton carbon to phytoplankton nitrogen,
phosphorus, and chlorophyil-a vary among species
and in time. Few applied modeling frameworks ac-
count for the dynamics of stoichiometry. The user is
forced to specify average values or those characteristic
of stressed systems.

2.5.2.2. The Phosphorus Cycle

Organic phosphorus in the water is present in various
paniculate 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
paniculate 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
under 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-
piankton 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 ail
organic nitrogen into a single state variable, whereas
others divide organic nitrogen into two. three, or four
state variables.  Some modeling approaches use
nitrogenous biochemical oxygen demand (NBOD) as
a state variable.  Mineralization to ammonia can  be
represented as first-order, or second order or saturat-
ing 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,
alkalinity, 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 limita-
tion  terms. Obviously,  a process-based  predictive
function for this rate would be quite valuable.

Denftrification 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
phytoplankton at  the  stoichiometrlcally modified
growth rate. Some models include a preference func-
tion for ammonia 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 paniculate.  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
generally modeled as a first order temperature-cor-
rected 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
unionized ammonia concentrations or potential carb-
on dioxide limitation in low alkalinity, high nutrient
waters. Models that Include the carbonate system cal-
culate total Inorganic carbon as the sum of bicar-
bonate, carbonate, and carbon dioxide. These species
are in equilibrium controlled by the equilibrium  con-
stants of the dissociation reactions and the pH of the
water. Carbon dioxide (and thus total inorganic carb-
on) Is produced by respiration, consumed by algal
growth, and replenished by atmospheric exchange.

Carbonate alkalinity is the  sum of bicarbonate  con-
centration plus twice the carbonate concentration plus
the hydroxide concentration minus the hydrogen ion
concentration. Addition of acids and nitrification lowers
the pH  and  reduces alkalinity.  Nitrate uptake by
phytoplankton  produces hydroxide  and increases
alkalinity.

DO is depleted by oxidation of organic carbon, nitrifica-
tion,  and respiration. Benthic reactions depleting
oxygen are usually modeled as a spatially variable flux
of sediment oxygen demand. Respiration  effects may
be combined for simplicity or separated into com-
ponents such as respiration by  bacteria,  plankton,
macrophytes, fish, etc. The respiration  of decom-
posers that utilize organic  matter is  referred to as
decomposition. Oxygen is used  during some chemical
transformations, such as nitrification and the oxidation
of reduced substances (e.g. sulfide, methane, reduced
iron, and reduced manganese).

Biochemical oxygen demand (BOD) is a  measure of
the materials present in a sample which may be
oxidized by biochemical processes. The BOD exerted
is determined by the change in oxygen concentrations
of a sample over time under specific analytical condi-
tions. The modeling problem with BOD is  that it com-
bines 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
biodegradable  organic  (carbonaceous)  demands,
nitrogenous demands, and oxidation of other substan-
ces (e.g., reduced metals, sulfide, etc.). Biodegradable
organic demands may be due to dissolved and panicu-
late matter in the water column and bottom sediments.
                                                2-7

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Some models separate water column organic matter
into paniculate and dissolved forms, referred to as
POM and DOM. Because some forms of organic matter
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 (refrac-
tory). 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
development. Numerous relationships exist for wind-
induced 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 es-
tuarine  reaeration has  not been developed. There
remains 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 sed-
iment can  significantly affect  the concentrations of
oxygen and nutrients in the overlying waters.  Area!
fluxes from the sediment due to digenetic reactions can
be substantial nutrient sources or oxygen sinks. The
occurrence  of anoxia may dramatically increase nu-
trient 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. Paniculate
nitrogen, 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 gener-
allyassumed  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
digenetic reactions and resulting fluxes more realisti-
cally (DfToro 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 111 for greater detail on
 organic wastes, dissolved oxygen and
 nutrients. 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 pol-
lutants may ionize and different forms may have differ-
ing lexicological 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.

2.62. Fats 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 lexicological 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 sedi-
ment, biological material, and sometimes dissolved or
colloidal organic material. Sorption can be important
in controlling both the environmental  fate  and  the
toxicrty of chemicals. Sorption may cause the chemical
to accumulate in bed sediment or bioconcentrate in
fish. Sorption may retard such processes as volatiliza-
tion 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

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lab studies have shown that the partition coefficient is
related to the hydrophobiclty 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
velocities, 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 atmos-
phere and water column, is influenced by both chemi-
cal  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-flm theory first proposed by Lewis and Whit-
man (1924). This theory assumes that the rate of trans-
fer is controlled  by diffusion  through laminar layers in
the  air and water at the interface in which  the  con-
centration gradients driving transfer are localized.

Hydrolysis is a reaction in which cleavage  of a
molecular 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 concentration (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
produces a chemical reaction.

Photolysis Is classified into two types that are defined
by the  mechanism of energy absorption. Direct
photolysis Is the result of direct absorption of photons
by the toxic chemical molecule. Indirect or sensitized
photolysis 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,
hydrolysis, oxidation, reduction, ring cleavage, and
condensation 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
  synthetic organic chemicals. This Sup-
  plement is found on page 2-27  at the
  end of this chapter.
2.7. Metals

2.7.7. 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 nonpomt
source runoff from urban areas.

2.72. 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.

32.7.2.1. Metal Complexation, Precipitation

Heavy metals can form complexes with organic and
Inorganic ligands and precipitate or dissolve. At equi-
                                                2-9

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 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
 material 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 Kp, 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.
                         Precipitated metal is lumped with all sorbed species to
                         give the total paniculate metal concentration. A spatial-
                         ly variable, lumped distribution coefficient KD
                         describes the distribution between the two phases.
                         There is no general consistency in reported Ko 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 Supplement 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
                         described 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 concentrations, 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)



  (D   (2)   (3)

  B.  Conservation of Momentum

  x - direction:
  to   aj^   %u   9&^_i.aP   fa        rfxjul   j_ [^/]   j_ [Ezja]
  at     ax      ay      az       p  ax        ^axlaarjayldyjazlazj       v/
  f*\   i^\      JMI       ^vt        tf*i     f**i  t** **\     * ^ \ "       *  t* \"       V^ *  *
  (4)   (5)      (6)       (7)        (8)      (9)  (10)     w(11)

  y - direction:
  (4)    (5)     (6)      (7)         (8)   (9)  (10)      '(11)-       "(12)-       "(13)

  z  direction:
   at     ax      ay       dz  ~   P ar
  (4)     (5)       (6)      (7)         (8)   (9)  (10)

  C.  Conservation of Constituent Mass (Transport)
  (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)          B local acceleration
         (5 to 7)     a are convective acceleration terms in the x.y and z direction
         (8)          = pressure gradient
         (9)          = the  Coriolis force
         (10)        - gravitational acceleration
         (1 1 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
         (18 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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S. 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) corrective ac-
celeration, (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
manipulations or assumptions with  regard to  the
system's geometry or boundary conditions. Unknowns
in the equation include the velocities (u,v and w), the
pressure (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, l.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. Rows induced
by the water surface slope are  referred to as
barotrophic flow. Changes In  density In non-
homogeneous water  bodies establish pressure
gradients Inducing flows which are referred to as
barodinic.

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
hydrodynamic models. The relationship is given by
                  WIND
                        GRAVITY


Figure 2-1.   Factor* affecting change* In momentum.
                                               2-12

-------
    p = pT + Aps + AOSS                    (2.6)
where p is the water density (kg m"3), p^  Is the density
as a function of temperature, and Aps and Apss are
the changes in  density due to  dissolved and
suspended solids, respectively.

An empirical  relationship  between  density and
temperature is given by (Gill 1982)
        9993452594 + 6.793952*
- 9.095290 * 10~3 T2
                        1.001685 x 10~ 7
                                   ~4 
   - 1.120083* 10"6 74 + 6.536332* 10"9 TS   (2.7)
where T is the temperature (C) and the change in
density due to salinity is (Gill 1982)
A/?s
              .824493 - 4.0899* 10~3 T
   + 7.6438* 10~5 T 2 - 8.2467* 10~7 T 3

   + 5.3875* 10~9 7 4) + CSL " (- 5.72466

   * 10~3 -f- 1.0227* 10~4 7 - 1.6546* 10~6 T 2)
     4.8314 *10~4CSL2
                                        (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)
          Css (1 - 1/K? ) x 10"3             (19)
where Vss is the change in density due to suspended
solids,  Css the suspended solids concentration (g
m"3), and SG the specific gravity of the solid.  Some
models Include terms for the effects of spatial varia-
tions 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 negligible com-
pared to the vertical pressure gradient and gravitational
acceleration  (the hydrostatic approximation; i.e. the
magnitude of terms 4-7, 9 and 11-13 of the vertical
momentum equation, Equation 2.4, are negligible com-
pared to terms 8 and 10). The hydrostatic assumption
reduces the vertical momentum equation to
        _
   P  dz ~8
(2-10)
                                                                        Temperature
      D)
      V)
      z.
      UJ
      o
                  0   3   6    9   12   15  18  21   24 27  30  33

                                  SALINITY (Kg rff3)

 Figure 2-2.   Relationship between water density, salinity, and temperature.
                                               2-13

-------
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
models 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 Corioiis frequency (f) is estimated from

   f=2sin( 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
Rorida.

The eddy  viscosity  terms (11-13)  arise from time-
averaging the turbulent fluctuations of velocity com-
ponents. The velocity components may be written as

    I/  HTH   5 r  V T V  t  W  W T IV     \*L.)
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:

   Wu1   iT7   ITw1                          (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)
r = ,~  uV

 iTw1 = EZ 4-f
                            du
                                            (2.14)
referred to as the eddy viscosity formulation. This for-
mulation is generally applicable where large scale tur-
bulence 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 tur-
                                                     bulence closure, described as zero-equation, one-
                                                     equation, two-equation, and higher order methods and
                                                     have been reviewed by Rod! (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
                                                                                               (2.15)
                                                     in the x and y directions, respectively.where po is the
                                                     surface water density, pa the air density, C
-------
                                                                            TIDAL EXCHANGE
                                              REACTIONS

Figure 2-3.   Factor* affecting chang* In constituent mat*.
this effect contain empirical relationships between ver-
tical eddy viscosity and the Richardson number (Ri),
an index of stratification stability given by
Ri = -'
                                           (119)
The  most  widespread  of these  formulations was
developed by Munk and Anderson (1948) where

   i - w> (1 + 10 /li) ~0-5                   (120)
where Ez,0 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) or turbulent diffusion (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 con-
tinuity, 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
(Harteman,  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 dif-
ficult to  solve the governing  equations. Generally,
simplifying assumptions  may be made regarding the
                                                2-15

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                       1-D Longitudinal
     1-D Vertical
                 2-D Longitudinal-Lateral
    2-D Longitudinal-Vertical
                                                                3-D
Figure 2-4.   Model dlmnlonr

hydrodynamic complexity of the system,  its dimen-
sionality, temporal resolution, and kinetic resolution.

A Spatial and Temporal Resolution
With regard to spatial resolution, models may be one,
two or  three  dimensional.  Most  practical
hydrodynamic models are either one, two (vertically or
laterally averaged)  or quasi-three dimensional, as il-
lustrated by Figure 2-4. This often prevents their ap-
plication 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-dimen-
sional 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 (Fischer et al. 1978). In wide and irregular chan-
nels, two or three dimensional models may be re-
quired.
With regard to temporal resolution,  estuarine mass
transport problems are usually characterized as inter-
tidal or intra-tidal. Intra-tidai 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 es-
timated 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
(dC/Bt = 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 es-
tuary.
                                                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
decoupled hydrodynamic and mass transport equa-
tions. Lung and 0'Conner (1984) developed a tidally
averaged method for two-dimensional (longitudinal-
vertical) estuaries that allows analytical computation of
horizontal and vertical velocities and vertical eddy vis-
cosity 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
hydrodynamic and  constituent  transport equations
with  equations  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 advec-
tive 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
multidimensional models to indicate the extent of the
information lost (Harleman, D., in review). Thus, em-
piricisms are often introduced as a result of the averag-
ing.   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 con-
stituent transformations. For a "conservative material"
(one not subject to  transformations, i.e. salinity and
some tracers) the last term (S) In Equation 2.5 is equal
to zero. However, the constituents of interest in es-
tuarine WLA studies rarely behave conservatively. For
most materials of interest, such as DO, nutrients, syn-
thetic organics and metals, their physical, biological,
and chemical transformations must be estimated. The
factors 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 alloca-
tion 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 perceived to
be the simplest to use. However, the relationship be-
tween model simplicity and simplicity of application is
not straightforward.

For example, inappropriate spatial and  temporal
averaging 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
calibrated to data, and may result in increased rather
than decreased data requirements to support the
modeling studies. For example, averaging may intro-
duce dispersion 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-dimensional 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 enormous.  Therefore, if the  physics of the
system is not adequately considered, the data required
to support a modeling study may increase with increas-
ing "simplicity".

Similarly, the clumping of kinetics terms for "simpler1
models may, if not carefully done,  introduce  em-
piricisms 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

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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
5o9:
                                          (Z2i)
where A Is area, V volume. C solids concentration and
fi \sa coefficient with units of velocity (e.g. settling or
resuspension velocity).
                        IL Settling
                        For settling the coefficient ft is dependent upon
                        Brownian motion, turbulent diffusion,  and fall
                        velocities. Brownian motion is negligible for most par-
                        ticles  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
                        diameter, pp the particle density, pi  the fluid density
                        and AC the dynamic viscosity of the fluid. Stokes settling
                        or fall velocities for a range of materials are tabulated
                        in Section 5 (Supplement VIII). The silts and clays
                        carrying pollutants typically range in diameter from
                        0.002 to 0.02  mm. with densities of 2 to 2.7 g/cm3.

i


i

*.

SAND
  BED LOAD TRANSPORT
                                 CONSOLIDATION
                               CD  EROSION
                               0  BURIAL
 Rgure 2-5.  Sediment variables and processes.
                                               2-18

-------
Stokes  law is  valid  for Reynolds numbers
(Re = p\  ws d/ff) less than about 0.1.

Collisions between small  cohesive particles tend to
lead to coagulation and the formation of floes. Floc-
culation rates are dependent upon the size distribution
and relative composition of the days 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 in-
dividual  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 permanently,
and  become part of the bottom sediments (Sheng
1983).  In order to be deposfted the particles  must
overcome resistances due to turbulent transport in the
water column, resistances due to the thfn 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 fim will completely follow the eddy motions. The
deposition velocity can be estimated as the product ol
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
Entrapment or  resuspenslon 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 entrapment 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 ol 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 concentra-
tion profiles above the  bed  show a balance of
downward fluxes  of sediment by settling and upward
fluxes by turbulence as summarized by Vanonl (1975).
According to Rouse (see Vanoni 1975), the dimension-
less parameter V>(Ki>Y\ (where V8 =  particle fall
velocity, K  =  0.4 and u  =  bed shear velocity =
Vtb/p with Tt = shear and p  = water density) deter-
mines for flow over flat bottoms the decjree for which
vertical sediment distribution will be uniform. It will be
uniform within  10 percent when Vs^u")"1 is less than
about 0.02.

Rates of entrapment of non-cohesive materials have
been specified In numerous alternative forms by
Ariathural  (1982), Ariathural and Krone  (1976), and
others (see Wang et al. 1986; Menta 1986). Akiyama
and Fukushima fin Wang et al. 1986) specified a dimen-
sionless resuspension rate parameter Es as:
   Ei
   for

   


where
        5  13.4
(2.23)
reduced acceleration of gravity  of submerged  par-
tides: D = partide diameter; and v - kinematic vis-
cosity. 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
primary Interest In water quality studies. For cohesive
sediments, the resuspension rate is affected by bottom
shear stress, salinity, sediment type, and the time his-
tory 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 deter-
mined 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
cohesive forces between sediment particles result in
varying sediment properties (e.g. density and porosity)
with depth below the upper mixed sediment zone.
SUPPLEMENT 111:     ORGANIC WASTES, DISSOLVED OXYGEN AND NUTRIENTS
1.  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 = *oth                                (2-24)
where K is a constant with units of concentration/time;
first-order,
where C Is concentration and K is a rate term with units
of lAime; 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
described by Equation  2.5.  Transport  and reaction
rates are affected by temperature as described below.

H. 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
product of a temperature adjustment factor and the
rate term measured at some reference temperature,
where the temperature adjustment factor (XT) Is es-
timated from

   *T=s0r-Tr                             (126)

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) equa-
tion can be obtained from the conservation of mass
equation  (Equation 2.5) by replacing concentration
(mass/volume) by the heat/volume ( l.e.p Cp T). Divid-
ing through  replaces C (concentration) with T
(temperature)  and the source/sink term  (S, Equation
2.5) may be given as
where A is area (m2), V volume, H the total heat flux
(Watts/m2),  Cp Is the  specific  heat  of  water
(Joule/KgC), and />o the density of water at the given
temperature fKo/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 short wave 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
modeled using first-order kinetics, where the rate term
represents a die-off rate.  However, coliforms can
reproduce in sediments and be resuspended in the
water column.  Guidance on the selection of die-off
rates and their reference temperature (Tr) for tempera-
ture adjustments 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

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                                     BENTHIC SEDIMENT
                          REAERAT10N
                          CARBONACEOUS DEOXYGENAT10N
                          NITROGENOUS DEOXYGENATION (NITRIFICATION)
                          PHOTOSYNTHESIS
                          RESPIRATION
                          SEDIMENT OXYGEN DEMAND
                          SETTLING AND DEPOSITION OF ORGANIC MATERIAL
Figure 2-6.   Basle variable* and proce*sm for dlaaotved oxygen.
                                                                  [13)  WATER
                                                                      COLUMN
                                                                          BENTHIC
                                                                         SEDIMENT
GIVEN PREVIOUSLY                              ~
SORPTJON. DEPOSITION OF INORGANIC MATERIAL
SETTLING AND DEPOSITION OF PHYTOPLANKTON
UPTAKE AND GROWTH
DEATH      3)  MINERALIZATION       3) NUTRIENT REGENERATION
Rgure 2-7.   Standard variables for eulrophleation and DO.
                                             2-21

-------
FV. Organic Material and Dissolved Oxygen.
DO is depleted by oxidation of organic carbon, nitrifica-
tion, and respiration and is replenished by surface
exchange and primary production (Rgure 2-6). More
complex interactions  considering the effects of
eutrophication have been considered (Rgure 2-7).

Historically, deoxygenation by decomposition of or-
ganic material has been modeled using coupled equa-
tions for DO and Biochemical Oxygen Demand (BOO),
where BOD is a measure of the oxidizabfe 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 proces-
ses  usually Included  in model  formulations include
decomposition or oxidation  by organisms,  and set-
tling. In addition. CBOD  can be  entrained or
resuspended. The source/sink term for CBOD can be
written as

   5 = CK
-------
 f

-








DIATOMS

GREENS

BLUE
CRFFNS

DINO-
FLAGELLATES
	 JT\ 	
                                                   HERBIVOROUS
                                                   ZOOPLANKTON
                                        CARNIVOROUS
                                        ZOOPLANKTON
                                                   FILTER-
                                                   FEEDING
                                                   ZOOPLANKTON
                                                                      r
        SETTLING, DEPOSITION
        UPTAKE AND GROWTH
Qj)  DEATH
  GRAZING
                         VOLUMETRIC GRAZING
                         PREDAT10N
Figure 2-8.   Additional variable* and proees**s 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 min-
imum function for inorganic nitrogen and phosphorus
is used:
        Min [
                            CIP
                         KM? + CIP
1
where CIN Is inorganic nitrogen fcg/l), CIP Is Inorganic
phosphorus (g/l), KMN is the Michaelis half-saturation
constant for nitrogen (ug/l). and KMP Is the Michaelis
half saturation constant for phosphorus  (tig/I).  Oc-
casionally, XN is expressed as  the product of the
nitrogen and phosphorus terms. Additional terms may
include separation of nitrogen Into ammonia-nitrogen
and nitrate-nitrogen. Dissolved available silica is in-
cluded 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 cor-
rected 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
              average  stolchlometry Is  necessary to  accurately
              model these interactions. The ratios of phytoplankton
              carbon to phytoplankton nitrogen, phosphorus, and
              chlorophyll-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 eulrophication
              models and to some DO models which  include
              mechanistic descriptions of phytoplankton kinetics.
              Simulation  of ammonia-nitrogen is also necessary in
              studies  involving ammonia-toxicity. Sources of
              nutrients include bottom sediments, point source load-
                                              2-23

-------
   PARTICULATE
   REFRACTORY
      ORG-P
PARTICULATE
   LABILE
   ORG-P
                                                                                            NO,
I

PARTICULATE
REFRACTORY
ORQ-N
H@H
1
i
PARTICULATE
LABILE
ORG-N
	 1
-^
v
) 
 
1

DISSOLVED
LABILE
ORG-N
-SH
i

 	 	 	

DISSOLVED
NH4*

.'


SORBED
NH4*
                                                                                            w
                            SETTLINQ 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 variable* and process** for nutrient Interaction.
ings, non-point loadings from the watershed, and at-
mospheric deposition.

Atmospheric deposition has been implicated  as  a
major source of nutrients in some large estuaries.

For the simplified DO-BOO modeling, as illustrated by
Figure 2-6, it  may  be sufficient to consider only
nitrogenous  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 com-
plexity, as illustrated by the nutrients considered in the
eutrophication model illustrated in Rgure 2-7 as com-
pared  to that illustrated  in Rgure 2-9. The primary
nutrients  considered to Impact  eutrophication are
nitrogen, phosphorus, and silica.

Nitrogen is present in  paniculate 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 paniculate 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 (NHa). 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

-------
              BENTHIC DECOMPOSITION

              DENITRIFICATION

         : 7 )  DEPOSITION OF ORGANIC MATERIAL
         : 9 )  DEPOSITION OF PHYTOPLANKTON
Figure 2-1 0.  Benthle Interactions for nutrients and DO.
     [A4 *]
                                         (232)
and that the total ammonia-nitrogen present or
predicted (NHr) is the unionized ammonia plus the
ionized ammonia (NH4 + ), (NHj = NHa + NH4+ ) the
portion occurring as NHa can then be estimated from
         1 +
                                         (233)
Some caution needs to be exercised concerning the
reporting of units of nitrogen (i.e.1 as nitrogen or as
ammonia). Speciation is also effected by temperature
and the  distribution of  cations  and anions. The
aqueous 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 am-
monia speciation. The speciation of ammonia may also
be estimated using equilibrium speciation models such
as MINTEQA1 (Brown and Allison 1987).
     (15) BENTHIC REMINERALIZATION
     (17) DIFFUSION

      8) SORPT1ON, DEPOSITION
         OF INORGANIC MATERIAL
         NITRIFICATION
Phosphorus may also occur In the water column in
organic or  inorganic, paniculate  or dissolved forms
(Figure  2-9). Phosphorus  is released during
phytoplankton respiration and death in either organic
or inorganic form. Phosphorus  is utilized in algal
growth as indicated in Equation 2.29.  Dissolved inor-
ganic phosphorus sorbs to suspended paniculate mat-
ter in the water  column, coming to  an equilibrium
expressed either with a partition coefficient or as  a
calibrated fraction dissolved:
   /DIP
             KripSS
(234)
where foiP is the fraction inorganic phosphorus dis-
solved, SS is the suspended sediment concentration
(kg/L). and  KPIP Is the partition coefficient in (I/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 predic-
tion of this important variable significantly. Phosphorus
loss mechanisms are generally described  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
results 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).

VIM. 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 = Kz(C-Ct)                         (2J5)
        where Kg is a reaeration rate, C is the water concentra-
        tion, and Cs  the saturation concentration. The satura-
        tion 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
        fflm 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
occur through resuspension. Chemical transforma-
tions may result from hydrolysis, photolysis, oxidation
and reduction and ionization. Biological transformation
and loss can  result from bacterial degradation and
accumulation  in  biota. Additional differences result
where materials do not mix, or only partially mix, with
the mean flow, such as some oils. The mathematical
treatment 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=-KrC
(236)
where KT Is the observed loss coefficient (day*1). C is
the total chemical concentration (g/m3) 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, sediment
concentrations, or pH can affect the total loss rate in
ways that can not be considered using this approach
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
(1963), Thomann and Mueller (1987) and elsewhere.

A method to complement field survey data is the chemi-
cal 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 T;

   Ki  (*,<)=*, E\ (r.O                  (237)
where Ki Is a laboratory measured second order rate
constant and Ei (x,t) is the intensity of the relevant
                                                2-26

-------
DISSOLVB)
NEUTRAL



* t


DISSOLVED
IONIZED
                          SOKBED
                         NEUTRAL
                                                       SOKBED
                                                       IONIZED
             
                                    		
                                                                               G)>-
                                   PROCESSES
       HYDROPHOBIC SORPTION/DESORPTION
       IONIC SORPTION/DESORPTION
       IONI2ATION
       VOLATILIZATION
       HYDROLYSIS
                                                              OXIDATION
                                                              REDUCTION
                                                              BENTHIC BIODEGRADAT10N
                                                              WATER  BIODECRADATION
                                                         (17)   PHOTOLYSIS
                                    PARAMETERS
Ddepth
Cair
S
Toe
       = air temperature
       = wind speed
       = water velocity
       = water depth
       = atmospheric concentration
       = Solids concentration
       = fraction organic carbon
Tw     = water temperature
Ro     = concentration of oxidant
CEC   = cation exchange capacity
Rr     = concentration of reductant
Bs     = bacterial concentration in sediment
Bw    = bacterial concentration in water
I      = incident light
Ke     = extinction coefficient
figure 2-11.  Basle variable* and processes for reactive organic chemical*.
                                            2-27

-------
environmental parameter. If  more  than one  loss
process 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 en-
vironmental 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 = *v (Cw - Ca)                         (238)
where kv is the  transfer rate.  Cw the dissolved  con-
centration of the chemical in water, and Ca the satura-
tion dissolved concentration,  dependent upon the
atmospheric partial pressure and Henry's Law  con-
stant 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 paniculate), the  concentration must
also be adjusted for the fraction dissolved (Id) as

   5v = *v /d Ctw                           (239)
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
        (/?L +
                  -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 (Uss 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 estlmates.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
paniculate 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-Si.

   S, + C=C-S,                         (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), equi-
librium sorption is linear with dissolved chemical con-
centration (Karickhoff 1984) or

   Ci = Kpi Ci                            (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 Kp, 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 hydrophoblcity 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 coefficient
of the chemical has yielded successful predictive tools
for incorporating the hydrophobicity of the chemical 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
hydrophilic contributions to adsorption. Large  non-
polar molecules with high octanol/water partition coef-
ficients 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 instantaneous
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 equi-
librium,  implicit in the  use of  Equation 2.42  is the
assumption of reversibility. Laboratory data for very
hydrophobic chemicals suggest,  however,  that  a
hysteresis 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 concentra-
tion. 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:
*HNi
                                           (2.43)
where  kHAi is  the acid hydrolysis rate constant for
phase i (L mole"1 see"1'. kHNi is the neutral hydrolysis
rate constant for phase I (sec*1), kna  is the alkaline
hydrolysis rate constant for phase I (mole"1 sec"1 ) . [H * ]
is the hydrogen ion concentration (moles L ). 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  unaf-
fected by the hydrolysis reaction because of the low
concentration of the toxic chemical present and react-
ing.

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 Qine 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 paniculate
material in  the water column. A  comprehensive
framework 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.


where KPQ is the observed rate coefficient (s'1) for a
reference light Intensity. [L] is the fraction of the refer-
ence light Intensity averaged through the water
column. 


-------
The ability to simulate lonizatlon. the disassoclation 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 varia-
tions In toxic effects. Increases In observed toxicity of
hydrogen cyanide (HCN) above pH 9 correlate well
with the fraction in the anionlc form (CN), (Bums 1985).
Ionization was described previously for ammonia (Sup-
plement III. part V).

IV. Biological Loss Mechanisms

A. Biodegradation
Biodegradation  is  generally assumed to follow
Mlchaelis-Menten enzyme kinetics. Values for the half
saturation constant  Km  and the maximum rate  of
degradation are not easily measured. Toxic chemical
models generally assume the chemical concentration
is  much less than the half saturation constant and
simplify the Michaelis-Menten equation to:
         - B max Km ~l B = -
                 (2.47)
                     -1
where KB is the second order rate coefficient (mL cells
day*1). The bacterial activity, B (cells mL'1), 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
                         biological 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 bac-
                         teria, the toxicity of the chemical to  the degrading
                         bacteria, and the possibilities  of adaptation to the
                         chemical or co-metabolism  make  quantification of
                         changes in the  population difficult as well as the ex-
                         trapolation of laboratory to field conditions ques-
                         tionable. 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 experi-
                         ments that then require the additional estimation of field
                         bacterial concentrations (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. Present-
ly, only approximate methods are available for estimat-
ing the dynamic  mass transport of metals  in
complicated natural environments. The sorptrve inter-
actions of metals with paniculate  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) utilizes
this approach and was used to analyze metal con-
tamination in the Hint River, Michigan as described by
Delos et al. (1984) and Mills et al. (1985). Thomann and
Meuller (1987) described the simulation of sediment
cadmium concentrations in the Sajo River. Hungary,
using  a partition  coefficient which varied with
suspended solids concentrations. Mills et al. (1985)
describes several screening level approaches con-
                         sidering  sorption. These methods may also be ap-
                         propriate for some estuarine waste load allocations for
                         metals. 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. Equi-
                         librium speciation models, such as MINTEQA1 (Brown
                         and Allison 1987) may provide estimates of equilibrium
                         aqueous speciation. adsorption, gas phase partition-
                         ing, solid phase saturation states, and precipitation-
                         dissolution for  multimetal,  multiligand  systems. For
                         waste load allocation purposes, equilibrium speciation
                         models must then be run in conjunction with transport
                         and transformation models, such as WASP4 (Ambrose
                         etal. 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. OK. CO32-. SO42-, CT. F, NH3."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(j).
where X(J) 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

   a X (1) + b X (2) = X (l)a X (2)b         (2.48)
Assuming equilibrium, the reaction may be written as
and then



where C(i) is the activity of the complex (X(1)aX(2)t>)
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,l)andb= a(i,2)) then the reaction may be written
in more general form as

                                          (2JO)
where N is the total number of components (metals and
ligands) in complex I (2 In the above example) . and a 0,1)
is the stoichiometric coefficient for the jth component
of the ith complex.
A mass balance may be written for any given com-
ponent distributed among all of the complexes. For
example the amount of a component X(j) in a complex
C(i) is a(l.j)C(I). The total amount of the component
among all complexes may be written as-
              M
             i-I
where M is the total number of complexes. Substituting
from Equation 2.50, Equation 2.51 may be rewritten as


       *T 0') - 5  0V) * (O fi *0')" f'J}  (2^2)
               -1           j-l
The  solution procedure, used in such models as
MINEQL (Westall etal. 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 (DQ)) 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 numerically
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, CuSO) or through coprecipitation where a major
ion  precipitate is formed  which binds metals in the
process (Medineand McCutcheon 1989). The possible
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   +e   M  ,Kti                  (2.53)
                                               2-31

-------
where M + "*" Is oxidized metal, M * is reduced metal, e*
is an electron, and Kn is the equilibrium coefficient for
reaction I. Oxidation-reduction reactions exert  sig-
nificant  controls on  the chemistry of major ions  and
trace  metals and their mobility, particularly between
suspended and  bed solids forms (Medine and  Mc-
Cutcheon 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. Sorption.
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, sorptlon 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 = MS
and
         [M] (5m)
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 MINTEQAi code are
activity Langmuir sorption, activity Freundlich, ion ex-
change sorption, constant capacitance and triple-layer
surface complexation models (Medine and  Mc-
Cutcheon 1989. Brown and Allison 1987).
2.9. References
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Ambrose, R.B. Jr., Connoly. J.P., Southeriand, E.,
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Ariathural, R.  1982. Two and Three-Dimensional
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Ariathurai, R. and Krone,  R.B. 1976. Finite  Element
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Bedford, K.W. 1985. Selection of Turbulence and
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Bowden. K.F. 1967. Circulation and Diffusion. In Es-
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Bowie, G.L et al. 1985. Rates. Constants, and Kinetics
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Brown. D.S. and Allison. J.D.  1987.  MINTEQA1, An
Equilibrium Metal Speciation Model:  User's Manual,
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Chapra. S.C. and Reckhow, K.H.  1983. Engineering
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Chen, R.L, Brannon, J.M., and Gunnison. D.  1984.
Anaerobic and Aerobic Rate  Coefficients for Use in
CE-QUAL-R1, Waterways Experiment Station, Miscel-
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Churchhill.  MA,  Smith, D.J.,  and Lee, S.  1962. The
Prediction of Stream Reaction Rates, ASCE, J. Sanitary
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Delos, C.G., Richardson, W.L,  DePinto, J.V., Ambrose.
R.B.. Rogers, P.W., Rygwelskl, K.. and  St. John, J.P.
1984. Technical  Guidance Manual for Performing
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Dietrich, W.E. 1982. Settling Velocities Of Natural Par-
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Di Tore, D.M. 1985. A Particle Interaction  Model of
Reversible Organic Chemical Sorption,  Chemosphere
14(10). pp.  1503-1538.

Di Toro, D.M. 1986. A Diagenetic Oxygen Equivalents
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Oxygen Demand: Processes. Modeling, and Measure-
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GA., pp. 171-208.
                                                2-32

-------
Emerson. K., Russo, R.C., Lund. R.E.. and Thurston.
R.V. 1975.  Aqueous Ammonia Equilibrium  Calcula-
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Canada. 32(12): 2379-2383.

Environmental and Hydraulics Laboratories. 1986. CE-
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Hydrodynamics and Water Quality, User's Manual, In-
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Station. Vicksburg. MS.

Fischer, H.B. et al. 1978. Mixing In Inland and Coastal
Waters. Academic Press, N.Y. 483 pp.

Ford, D.  and Thornton. K.W. 1989. Time and Length
Scales for One-dimensional  Assumptions and Its
Relationship to Ecological Models, Water Resources
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Gantzer.  C.J.. Kolig. H.P.. Rittmann. B.R.. and Lewis.
D.L 1988. Predicting the Rate of Trace-organic Com-
pound  Removal by Natural Biofilms, Water Research.
22(2). pp. 191-200.

Gibbs.  R.J.. Matthews.  M.D.. and Link. D.A. 1971. The
Relationship Between  sphere  Size and  Settling
Velocity, Jour. Sedimentary Petrology. 41 (1).

Gill. A.E. 1982. Appendix 3. Properties of Seawater, in
Atmospheric-Ocean Dynamics, Academic Press, New
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Golterman.  H.L, Sly, P.G., and Thomas. R.C. 1983.
Study of the Relationship Between Water Quality and
Sediment Transport,  WNESCO, Tech. Papers in
Hydrology No. 26.

Hansen, D.V. and Rattray, M. 1966. New Dimension in
Estuary Classification.  Limno and Oceanography 11,
319-325.

Hatcher, K.J. (ed.) 1986. Sediment Oxygen Demand;
Processes,  Modeling,  and Measurement,  Univ. of
Georgia, Athens. GA.

Imboden, D.M. et. al. 1983. Mixing Processes in Lakes:
Mechanisms and Ecological  Relevance.  Scherz. Z.
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Ives, K.J. 1973. The Scientific Basis of Filtration. Nato
Advanced study Inst., Cambridge, UK, D. Reidel
Publishing Co., 1973.

Karickhoff. S.W. 1981.  Semi-Emperical Estimation of
Sorption of Hydrophobic Pollutants on Natural Sedi-
ments and Soils, Chemosphere 10, pp 833-846.
Karickhoff. S.W. 1984. Organic Pollutant Sorption in
Aquatic Systems. Jour-. Hydraulic Engineering, ASCE,
110(6). pp. 707-735.

Lai, D. 1977. The  Oceanic Microcosm of Particles,
Science. 198(4321). pp. 997-1009.

Large Lakes Research Station. 1987. U sere's Manual
for the Transport and Fate Model MICHRIV. USEPA
Large Lakes Research Station. Grosse He, MI.

Lewis. WX and Whitman, W.C. 1924. Principles of Gas
Adsorption, Industrial & Engineering Chemistry, 16.

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phase Michaells-Menten Kinetics to Predictive Model-
ing for Aquatic Ecosystems, Environ. Tox. Chem., 3(4),
pp. 563-574.

Lick. W.. Ziegler, K,. and Tsai. C. 1987. Resuspension.
Deposition and Transport of Fine-grained Sediments in
Rivers and Near-shore Areas, Prepared for the USEPA
Large Lakes Research Station. Grosse He. Ml.

Uss, P.S. and Slater, P.G. 1974. Flux of Gases Across
the Air-Sea Interface. Nature, 247,  pp. 181-184.

Lung, W.S. 1987.  Advective Acceleration and  Mass
Transport in Estuaries, ASCE J. Hydraulic Engr. 112(9),
874-878.

Lung, W.S. and O'Connor. D.J. 1984. Two-Dimensional
Mass Transport In Estuaries, ASCE J. Hydraulic Engr.
110(10). 1340-1357.

Lung, W.S. andTesterman, N. 1989. Modeling Fate and
Transport of Nutrients in the James Estuary, ASCE J.
Environ. Engr. Div.  (In Print).

Lung. W.. Mackay. D..'and Yeun, A.T.K. 1983  Mass
Transfer Coefficient Correlations for Volatilization of
Organic Solutes from Water, Environ. Sci. Technol.,
17(4). pp. 211-217.

Medine. A.J. and McCutcheon. S.C. 1989. Fate and
Transport of Sediment-Associated Contaminants,  in
Hazard Assessment  of Chemicals  (ed. J. Saxena).
Hemisphere Publ. Corp.. New York. pp. 225-291.

Megard. R.O.. Tonkyn. D.W.. and Senft. W.H. II. 1984.
Kinetics of Oxygen  Photosynthesis in Planktonic
Algae, Jour, of Plankton Research, 6(4), pp. 325-337.

Mehta. A., ed. 1986. Estuarine Cohesive  Sediment
Dynamics, Springer Verlag, 486 pp.

Miller. S. 1983. Photochemistry of Natural Water Sys-
tems. Environ. Sci. Technol., 19(12). pp. 558-570A.
                                              2-33

-------
Mills, W.,  et al. 1985. Water Quality Assessment: A
Screening Procedure for Toxic and Conventional Pol-
lutants, Parts 1 and 2. US EPA Athens, Ga, EPA/600/6-
85/002.

Morel, F.M.M.  1983. Principles of Aquatic Chemistry.
Wiley. New York.

Munk, W. and Anderson, E.R. 1948. Notes on a Theory
of the Thermocline. J. Marine Res. 7, 276-295.

Nihoul and Jamarf. 1987. Three-Dimensional Models of
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of Reaeration in Natural Streams, ASCE Transactions,
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O'Connor. D.J. 1983. Wind Effects on Gas-liquid Trans-
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109(3). pp. 731-752.

Officer,  C.B. 1976. Physical Oceanography of Es-
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Officer, C.B. 1977. Longitudinal Circulation and Mixing
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Orlob. G.T. and Selna. LG. 1970. Temperature Varia-
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Orlob, G.T.  1983.  Mathematical Modeling of Water
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Owens.  M.. Edwards, R.W.. nd  Gibbs. J.W..  1984.
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3-D Variable-Density Hydrodynamic Rows: Documen-
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Pritchard.  D.W. 1967. Observations on Circulation in
Coastal Plain Estuaries, in Estuaries (G.H. Lauft. ed.)
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Rodney, M. and Stefan. H. 1987. Conceptual Model for
Wind-generated Sediment  Resuspension in Shallow
Ponds. Proceedings, 1987 National  Symposium on
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                                               2-34

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School of Engineering. The University of Mississippi,
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                                              2-35

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                     3. Model Identification and Selection
                                     Robert B. Ambrose, Jr., P.E.
                              Center tor 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
problems are identified and study objectives are set.
The goals are to identify the simplest conceptual model
that includes all the important estuarine phenomena
affecting  the water quality problems, and to select the
most useful analytical formula or computer model for
calculating waste load allocations.  Selection of too
simple a  model can result in inaccurate predictions of
future water quality under hypothetical load  reduc-
tions. 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 underprotective 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 available
data. Study costs will increase because of the addition-
al data requirements and the expanded computer 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 pic-
ture 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
regulation 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

-------
estuarine-wlde, 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/or season of the
year. The modeler can use this  information to deter-
mine the temporal  resolution (steady-state, tidally
averaged, real time) and the important pollution sour-
ces (point source, nonpoint source) that must be in-
cluded  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 infor-
mation collected on the water quality problems will help
determine 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.

3.2.2. 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 in-
directly link the pollutants  to be controlled  with the
primary water quality indicators. All other interacting
water quality constituents  thought to be significant
should be included at this point. This can best be done
in a diagram or flow chart  representing the mass
transport  and transformations of water quality con-
stituents in a defined segment of water. Rgures 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, however, should  be considered exter-
nally and parameterized in the coefficients. Figure 2-4
covered sediment transport.  Figures 2-5  through 2-9
illustrated conventional pollutant interactions  affecting
dissolved  oxygen,  nutrient enrichment, and
Table 3-1.   General Scale* of Interact
Problem Context
Salinity
5AGIfY)0flt
Bacteria
Heat
O.O. Depletion
Nutrient Enrichment
Toxictty
Human Exposure
metals
volatile organic*
-hydrophobia organic*
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
eutrophication. Rgure 2-10 dealt with toxicants, such
as organic chemicals.

Each water quality constituent must be examined to
determine the important forcing functions and boun-
daries, such as the air-water or water-benthic sediment
interfaces. For example,  dissolved  oxygen is in-
fluenced 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
parameters. 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
specified 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 calculation^ 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 start-
ing point from which systematic reductions  in com-
plexity can be Identified that will provide an adequate
representation of the system, while meeting the objec-
tives of the study.
                                                 3-2

-------
3.23. Spatial Extent and Scale
The general area affected by the waste load allocation
and the significant water quality reactions were Iden-
tified 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 boun-
daries of the study area, then specifying the required
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
dimensions over which these gradients significantly
affect  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)
dimension 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 at. (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 buoyan-
cy 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/nr),
   g  = acceleration of gravity, (about 9.81 m/sec2),
   and
   QR = freshwater river flow, m3/sec
The tide on the other hand Is a source of kinetic energy.
equal to:

   Kinetic energy = pWUt3                    (3-2)
where

   p = the seawater density, about 1.025 kg/in3,
   W  o 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 = *pgQ*/pWUt*                     (3-3)
If R is very  large (above  0.8). the estuary is typically
considered to be strongly  stratified and the  flow
dominated 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 de-
gree of stratification in the estuary is to use a stratifica-
tion-circulation diagram (Hansen and Rattray, 1966).
The diagram (shown In Figure 3-1) is based on meas-
urements from  a  number of estuaries with  known
degrees of stratification. Its use requires the calculation
of the
   Stratification Parameter
and the

   Circulation Parameter =
where
                                             (3-4)
                                              (3-5)
   AS = time averaged difference between salinity
   levels at the surface and bottom of the estuary.
   So =  cross-sectional mean salinity,
                                                  3-3

-------
              10-3
             o
                    10
                  10
                    -*
                  10
                         '
                       *',
                                       ''/
"
                                         ,


                        Hi
                               10
    10*
    u./u,
                                                 10
                                                           10*
                                                                    10<
                (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,
                Sliver Bay. Subscripts h and I refer to high and low
                river discharge; numbers Indicate distance (In miles) from
                mouth of the James River estuary.
Flgurt 3-1.  Stratification circulation diagram and example*.
                                          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
parameters  of Equations 3-4 and  3-5, and  plot the
resulting point on the diagram. Type 1 estuaries have
seaward  flows at all depths, and the upestuary salt
intrusion is due to tidal diffusion. Type la 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 ap-
propriate to model at least two layers. The approach
for a partially-mixed system is  not so clear and judg-
ment must  be exercised. For a recent toxics study
(O'Connor 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,

   PI = tidal prism volume, m ,

   Ud  = densimetric velocity, m/sec,
   Ap = the density difference between river water
   and sea water (about 0.025 kg/m3),
   p  = density of sea water (about 1.025 kg/in3),
   Uo = maximum velocity at  mouth of estuary, m/sec
   D = depth, m,
   g  = acceleration due to gravity (9.81 m/sec2), 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 dimen-
     sion 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 dimen-
     sion, unless water quality processes dictate ver-
     tical resolution

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 ver-
     tical 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 '
     responding 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,

  o  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

-------

       a) Tidal Velocity Reversal
      b) RetMual Velocity Rvrul
      e) No Obsvrvabl* Rvr*ate
Figure 3-2.  Vertical velocity profile*.
O. Geomorphological Classification.

Over the years, a systematic geomorphologicat 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  Tit the first three  das*
     sifi cations

Typical examples  of North American estuaries are
presented in Tables 3-2 and 3-3. The characteristics of
each geomorphological classification were discussed
in Section 2-1. Using  these classifications, the ap-
proach is  to estimate the degree of stratification from
known conditions in a geomorphologically simitar 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 dis-
charge 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-flow-
ing, riverine reaches. Downstream boundaries are best
located at the mouth of an estuary, or even nearby in
                                                          s) Cloud Separates
                                                                                L
                                                                                    Injection Point
    b) Non-Gaussian Spreading
                              Injection Point
                           L,
                              Injection Point

    e) Gaussian Spreading with Downstream Movement

Figure 3-3.  Vertical dye concentration profile*.
                                                   3-6

-------
Table 3-2.  Topographic Estuarine ClaMfficatlon
Type / Vertical De- Lateral
Dominant gree of Variability
Long Term Stratification
Process
Coastal Plain / Moderate Moderate
River
Row


Bar Built / Vertically Well High
Wind Mixed


Fjords / Tide High Small
Other Various Various
Estuaries/
Various
Example
Chesapeake
Bay
James River
Potomac River
Delaware Es-
tuary
Now i one
Bight
Utlle Sarasota
Bay
Apalachicola
Bay
Galveston Bay
Albemarle
Sound
Palmico
Sound
Pugent Sound
Aiberni Inlet
Silver Bay
San Francisco
Columbia
River
the ocean. For large estuaries with relatively unaffected
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
simplifications in dimensionality may be possible. 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.
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 con-
stituents. For example, an estuarine reach that mixes
laterally In 1 day can be laterally averaged for pollutants
with characteristic reaction  times of days (such as
BOD). This same reach, however, should not be lateral-
ly 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 centeriine and  side  discharges,
respectively, the mixing length U is given by

   Lc = Q.luW2/Ey                          (3-7)

   Le = 0.4u W*/Ey                          (3-8)
where

   u = mean downstream velocity, in/day
   W = channel width, m
   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 U/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 Claaarfleatlon
Type
Highly
Stratified
Partially Mixed
Vertically

Lateral Type River Dis-
charge
Laterally Large
Homogeneous
Partially Mixed Medium
Moderate to Small
High
Variability
Example
Mississippi
River
Mobile River
Chesapeake
Bay
James Estuary
Potomac River
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 (Le/u) can be usefully com-
pared to reaction half lives (A f vi) 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:
0.693/JT
                                             (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.
Numerical  models should be composed of computa-
tional elements with short length A x and width A y:
                                            (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 determined.
Dye studies can give important information about the
advective velocities and flushing times  through the
study area. The rate of downstream transport must be
compared with water quality reaction rates to deter-
mine  if longitudinal gradients are to be expected for
particular constituents. Steeper water quality gradients
require more detailed spatial resolution. The length of
model computational elements should be significantly
less than that required for concentrations to halve:
         uAfn                             (3-12)
The characteristic velocity can be either tidal or tidal-
averaged,  depending upon the type of simulation
chosen. This decision is discussed in the next section.

Other considerations may affect the choice of spatial
scale and the actual layout of the model network. One
is the desired spatial  resolution in critical areas to be
protected, as along a public beach or around a water
intake. Computational elements should be centered on
these features, so that predicted concentrations can
be  related directly to appropriate standards or goals
set to protect these resources. Likewise, computation-
al elements should be centered on monitoring stations
and important  discharges. The  model network may
also have to account for unique features of the study
area, such as embayments,  marshes and tidal flats,
channels, and islands. If the required spatial resolution
is  much  larger than these features, they may be ig-
nored. They should be accounted for when the re-
quired spatial resolution is of a similar size or less.
Another set of considerations affecting spatial scale is
the required time resolution and the dynamics of the
loading, transport, and kinetic processes. The need for
monthly or seasonal average concentrations  may
allow quite large computational elements. 1f high or low
tidal concentrations are needed, however, computa-
tional elements must be a fraction (say 20% or less) of
the length of a tidal excursion. Predicting the effects of
a steady discharge may  allow large computational
elements, while tracking the direct effects of batch
discharges or storm  runoff with characteristic times
(AtE) constrains the computational lengths:

   AxSuAfE                            (3-13)
Direct effects include such problems as acute toxicity
and bacterial exposure. Indirect effects from unsteady
discharges, such  as the  impact of nutrients on
eutrophication and  dissolved oxygen, generally don't
constrain the computational lengths. An exception is
when load  is correlated with tidal transport, such as
batch discharges into ebb tide only.

It is dear that choice of spatial scale and layout of the
model network  requires considerable judgment.
Knowledge of the regulatory problem must be com-
bined with  knowledge of the loading, transport, and
transformation processes and an understanding of the
WLA model chosen to perform the simulations. Com-
peting factors must often be balanced, such as
precision and cost, or better fitting one section of the
network versus another. For best results, the modeler
should retain the flexibility to refine the model network
during the  calibration phase of the WLA study. Ex-
amples of 6 different model networks applied in actual
case studies are given in Part 4 of this manual.

3.24. Temporal Extent and Scale
The WLA problem context and its general time scale
were identified in step 1. The purpose of this step is to
specify the duration  and  temporal resolution of the
WLA model.

3.2.4.1. Duration of WLA Simulations

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
regulatory requirements. One  basic guideline applies
in all cases - the simulations should be long enough to
eliminate the effect of initial conditions on important
water quality constituents at critical locations. This will
ensure that errors in the initial conditions do not sig-
nificantly affect predicted  concentrations upon which
the WLA is being based.
                                                  3-8

-------
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 loca-
tion in an estuary. Factors that control flushing include
tidal action, freshwater Inflow, and wind stress. All of
these forcing functions are time variable. Rushing 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 unambiguous point at
which the original water and pollutants are completely
replaced. Rushing 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, et al.. (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.

Rushing times give the minimum duration for simula-
tions of dissolved, non-reactive pollutants. Reaction
kinetics affect the required duration for those 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
diagenesis models should be helpful  in analyzing
chemical 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
eutrophication  simulations range from seasons to
years.

The final factor affecting the duration of simulations is
the strategy for relating  simulation  results to the
regulatory requirements. Sometimes a set of "design
conditions" can be defined, allowing for shorter simula-
tions. Care must be taken to ensure that a particular
combination of design conditions,  such  as flow,
temperature, and nonpoint source loads, does not
reflect an unreasonably low probability of occurrence
and thus an overly restrictive 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 concentrations are expressed as a frequen-
cy 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 out-
put 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 forc-
ing functions such as freshwater inflow, pollutant load-
ing, 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. Dynamic models are necessary for
analysis of control options for complex  situations in
estuaries. Predicting the upstream migration of pol-
lutants 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 dynamic simulation.

On the  other hand, quasidynamic and steady state
models  are currently more practical  for long term
analysis of water quality response. Predicting  the year
to year eutrophication response or the accumulation
of hydrophobic organic chemicals in the benthic sedi-
ments of large  estuaries  is best accomplished  by
quasidynamic simulations. In general, if the regulatory
                                                3-9

-------
 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
 quasidynamic simulation. Some experts assert that
 even for long term analyses where only average predic-
 tions are  needed, dynamic  simulations are practical
 and more desirable.  Dynamic simulations can be ex-
 pected to more accurately  account for interactions
 among the important tidal and diurnal forcing functions
 controlling average water quality conditions. Calcu-
 lated maxima and minima at a location can account for
 the major tidal and diurnal processes; calculated con-
 centrations, 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 predicted 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 neces-
 sary.

 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 exten-
 sive data  base is necessary  to calibrate the dynamic
 calculations. Quasidynamic simulations cost less be-
 cause of  their longer time steps and less  use of
 hydrodynamic simulation. The lower costs allow for
 longer simulations than dynamic models, and  thus
 greater ability to explore seasonal and yearly  trends.
The  lower costs  also allow for  more water  quality
variables and processes 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 f'-e.. solutions remain within  bounds
and do not "blow up"). Furthermore, satisfying these
conditions 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)

      A t S A x /v#i u                      (3-14)
    mass transport, dispersion, and kinetic condi-
     tions
                                          (3-15)
where
   u = maximum tidal velocity, m/sec
   g = gravitational acceleration, 9.81 m/sec2
   h = hydraulic radius, or depth, m
   EL = longitudinal dispersion coefficient, m2/sec
   K =  first order decay rate, I/sec
   a = finite difference weight, (1 for backward dif-
   ferences, 14 for central differences)
Similar  conditions exist for 2 and 3-dimensional
models, and other conditions, such as a friction term
criterion, may also be required. Chemical and biologi-
cal components of the WLA model may cause restric-
tions in the time step if reaction kinetics are rapid. In
that case, the reaction is often written as an equilibrium
relationship, which does not affect the time step. The
most stringent condition is usually the Courant condi-
tion (unless vertical diffusion and/or momentum trans-
fer is explicitly treated, in which case a criterion like
Equation 3-15 is required with Az replacing Ax). Many
models  solve for the mass transport equations  in a
separate model, or at a different time step than the
hydrodynamic solution.  In these cases, all the above
criteria should be checked.

Dynamic models are governed by equations 3-14 and
3-15 where u is the maximum tidal velocity. Time steps
are on  the order of seconds  to minutes for the
hydrodynamic component or model, and minutes to
an hour  for the mass transport (and water quality)
model. Quasidynamic models are governed by equa-
tion 3-15 where u and EL are tidal-averaged values (u
being smaller and EL being larger than nonaveraged
values). Time steps are on the order of one to several
hours.

Some models, particularly current  hydrodynamic
programs, use an implicit technique to approximate the
                                                3-10

-------
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, calcula-
tions 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
mode! is used. Nevertheless, while selection of an
appropriate model will not guarantee success,  it will
help.  Selection of an inappropriate model will not
guarantee 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 or-
ganization should also  be considered. The  models
summarized 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. Gassffication of Models by Transport
Complexity
Estuarine WLA models consist of two components-
hydrodynamic and water quality. In the simplest case.
hydrodynamics may  be represented in a  model by
user-supplied velocity and flow data. In a more com-
plex model,  hydrodynamics may be represented by
numerical solution  of the equations of motion and
continuity. In either case, water quality conservation-
of-mass equations are executed using  the
hydrodynamic output of water volumes and flows. The
water quality component of the model calculates pol-
lutant dispersion and  transformation 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 predic-
tion of DO concentrations. The more comprehensive
models include nutrient-algal relationships and benthic
source/sink terms. A few estuarine models that include
reaction rate coefficients and transformation proces-
ses for toxic  materials also are  available.

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 etal. (1981).

Level I Includes desktop screening methodologies that
calculate seasonal or annual  mean  pollutant con-
centrations  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
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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 tidaliy
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
averaged 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 tidaliy
averaged concentrations overtime. 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 employ
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  models
will calculate hour-to-hour changes in water quality
variables,  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. In this case, model results
should be averaged to obtain mean diurnal variability
over a minimum of 1 week intervals within the simulated
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 required data
and modeling effort are usually not mobilized in stand-
ard 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 tidaliy
averaged temporal scale. When hydrodynamics and
pollutant Inputs are rapidly  varying,  steady state
models are difficult to properly calibrate. Consequent-
ly, these models are less satisfactory in short estuaries
or when waste load, river inflow, or tidal  range vary
appreciably with a period dose to the flushing time of
the water body. Steady state and tidaliy averaged
models require calibration 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 Wallls (1975) explain, dispersion is
caused by the combined  action of turbulence and a
nonuniform velocity profile.  Nonuniform velocities
elongate a wastewater slug, whereas turbulence,  ac-
ting 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 tempera-
ture Induced density currents,  and wind-induced cur-
rents, 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)

      4- Tidal dispersion                       (2)

      + Net transverse gravitational circulation   (3)

      + Net vertical gravitational circulation      (4)

      + Transverse oscillatory shear            (5)

      -i- Vertical oscillatory shear               (6)

      + Turbulent or eddy diffusion             (7)

One-dimensional,  tidaliy  averaged or steady state
models calculate term 1 directly but represent terms 2
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through 7 with a tidal average or steady state lon-
gitudinal dispersion coefficient In contrast, the Level
IIM -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 lon-
gitudinal and lateral diffusion coefficients only to rep-
resent terms 4,6 and  7.

As a model Is  simplified from Level IV to Level  II, the
dispersion coefficients become larger and more uni-
que to each flow situation. The steady state or tidally
averaged Level II models require the dispersion coeffi-
cient to Include the effects of tidal mixing. As a result.
the coefficient  must be calibrated using salinity meas-
urements, and it cannot be used to predict the water
quality effects of projected changes in estuarine topog-
raphy 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  ad-
vantages  over steady state and tidally averaged
models in representing mixing in partially mixed es-
tuaries because advection is so much better repre-
sented. Although 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 violations
depends upon both the accuracy and resolution of the
loading and environmental data, and the model's treat-
ment of short time scale kinetics such as desorptlon or
diurnal fluctuations In temperature, pH, or sunlight.
While dynamic models are capable of predicting diur-
nal and transient fluctuations -in  water quality
parameters,  the input data requirements  are  much
greater. Lack of detailed data or process descriptions
often render their real 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 con-
centrations for estuaries with fairly regular channels
that are much longer than they are wide. Near points
of waste injection, however, model predictions can be
significantly in error due to lateral variations in con-
centrations. The quasi 2-d approach can solve this
problem, but the difficulty In estimating effective disper-
sion coefficients still remains. The Level IV longitudinal
and lateral 2-d models have the advantage of repre-
senting the lateral variations in  velocity and waste
concentrations that arise in all estuaries and bays
because of the nonuniformity of  cross-sections, em-
bayments. 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-longitudinal models
assume an estuary is vertically well-mixed. This as-
sumption  can lead to significant errors In predictions
for stratified estuaries.

3.32. Level I Models
The purpose of modeling at Level  I is to screen trouble
spots  for more detailed analysis. Level I  desktop
methodologies may  be done with a hand held cal-
culator and are based on steady state conditions, first
order decay coefficients, simplified estimates  of flush-
ing time, and  seasonal pollutant concentrations.

Level I  screening of a given waterbody may entail
selected 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
phosphorus loading), or it may entail a comprehensive
examination of the estuary. A comprehensive  analysis
may be accomplished with models such as the
Simplified Estuary Model (SEM) or the Water Quality
Assessment Methodology (WQAM). SEM and WQAM
both require only hand calculations and are used chief-
ly for  preliminary assessments of  estuarine water
quality. Documentation 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
ranges set for each estuarine classification.

WQAM includes calculations to estimate the transport
of BOD,  DO, pH, arbitrary conservative substances,
thermal  pollution, turbidity, sediment, and organic
chemicals in an estuary. Pollutant distribution can be
estimated using either a far field or a near field method
of analysis. The near field technique  predicts initial
dilution of submerged discharges through the use of
tabulated data  from MERGE, a computerized plume
model. For well-mixed estuaries, far field pollutant dis-
tributions can be predicted using the fraction of fresh-
water method, modified tidal prism method, or
one-dimensional advection-dlspersion equations. For
partially mixed and stratified estuaries, WQAM far field
analysis  uses Prrtchard's two-dimensional  box model
approach, which represents the estuary as a series of
longitudinal segments with a  surface  and a bottom
layer. The analysis is performed by solving a system of
simultaneous linear equations for pollutant concentra-
tions in each layer. WQAM consists of a number of
individual analyses, listed in Table 3-4 (Mills et al. 1985).
The document is available from the Center for  Ex-
posure Assessment Modeling in Athens, Georgia.

3.3.2.2. Simplified Estuarine  Model

SEM is a one-dimensional steady state desktop model
capable of simulating water quality in tidal rivers and
non-stratified estuaries (Hydroscience 1971). Coupled
BOD-DO reactions, arbitrary conservative substances,
and uncoupled nonconservatives with first order decay
(nutrients and coliforms) are represented in SEM. The
model is based on user-specified hydraulics that con-
sider only longitudinal variations and handle only point
source inputs. Advection Is represented in the form of
freshwater flow velocity and dispersion in the form of a
Table 3-4.  Summary of Methodology for Estuarine Water Quality Assessment
Calculations
Estuarine Classification
Rushing Time
Pollutant Distribution
Thermal Pollution
Turbidity
Sedimentation
Methods
* Hansen & Rattray
* Row ratio
* Fraction of freshwater
* Modified tidal pnsm
* Fraction of freshwater (conservative pollutants +)
* Modified tidal pnsm (conservative or first-order decay pol-
lutants)
* 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 (con-
servative pollutants + , pH, dissolved oxygen)
* Farfield distribution (conservative and first-order pol-
lutants + . 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 Ini'rtiai dilution
* Ught 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
10
2D
1 D/2D
1 D/2D
20
N/A
N/A
1D/2D
10/2D
10/2D
1 012 D
1 D/2D
1 D/2D
ID/20
1 D/2D
1D/2D
20
0 One dimensional (ID) means a vertically well-mixed system.
A two dimensional (2 D) estuary is vertically stratified.
+ These methods aoply 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 loca-
tion and to characterize the reach as either tidal river
or estuarine segment. The estuarine number  (N) is
calculated from the values of the dispersion coefficient
(E). the freshwater flow velocity (V) and the deoxygena-
tion  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. Level II 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
hydrodynamics and pollutant releases are rapidly vary-
ing. Consequently, these models are less appropriate
when  waste load,  river inflow, or tidal range vary ap-
preciably 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,
calibrated 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
models. A variation of this strategy is to use compart-
ment models with net advecth/e flows calculated from
measured vertical and  longitudinal  salinity distribu-
tions.  An iterative calculation  has  been  published by
Lung and O'Connor (1984)  and Lung (1986) for two-
dimensional estuaries characterized  by  a horizontal
seaward velocity 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 analysis 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
eutrophication programs TOXI4 and EUTRO4.  Other
models described here include  HAR03, FEDBAK03,
and AUTOQUAL

3.3.3.1. QUAL2E

QUAL2E is a  steady state one-dimensional model
designed 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 vari-
ables simulated include  conservative substances,
temperature,  bacteria, BOO,  DO, ammonia, nitrite.
nitrate, and organic nitrogen, phosphate and organic
phosphorus, and algae. 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. OUAL2E Version 3
incorporates several uncertainty analysis techniques
useful in risk assessment. This model can be obtained
from the Center for Exposure 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
dispersion 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 eutrophication, bacterial con-
tamination,  and toxic chemical movement  (DiToro,
1981).  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).

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-N 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.
oxidants, depth,  velocity, and wind  speed. Internal
transport and export of organic chemicals occur via
advective and dispersive movement of dissolved, sedl-
ment-sorbed,  and biosorbed  materials, and  by
volatilization 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 between
the water column and the bed can occur by settling or
resuspension of particulates, diffusion of dissolved pol-
lutants  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 horizontally with
bed load transport.

S. EUTRO4

EUTRO4 is a version  of WASP4 that is designed to
simulate conventional pollutants. EUTRO4 combines a
kinetic  structure adapted  from  the Potomac
Eutrophication Model with the WASP transport struc-
ture. EUTRO4 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
deposition  and resuspension velocities  for organic
solids,  inorganic solids, and phytoplankton. The frac-
tion of  each water quality variable  associated with
these solids also must be given. Rate constants and
half-saturation 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 ben-
thic 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 segmenta-
tion is used with each segment having up to six Inter-
faces. The model Includes the effect of net advection
and  dispersive 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 photosynthetic  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
dispersive 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 (Crim and
Lovelace 1973. Lovelace 1975). Transport is calculated
from user-specified flow and dispersion. Water quality
variables simulated  include  carbonaceous  BOD,
nitrogenous oxygen demand, DO. total  phosphorus,
and total nitrogen.

3.3.4. Level HI Models
Level III includes  computerized 1-d and  quasi 2-d
models that simulate variations  in tidal height and
velocity throughout each tidal cycle. Level  III models
are generally composed of separate but compatible
hydrodynamic 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 char-
acterization of phenomena rapidly varying within each
tidal cycle, such as pollutant spills, stormwater runoff,
and  batch  discharges. Level III models also are
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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) modeis 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 subsequent
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
throughout 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
response 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.
Homogeneity 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
nitrogen, ammonia, nitrite and nitrate; algal growth and
respiration; and DO. These models also include settling
rates and benthic flux rates for several different con-
stituents such as phosphorus, nitrogen and sediment
oxygen demand. Only one model is designed to simu-
late the  physiochemical processes affecting organic
chemicals 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 as-
sociated 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
carbon,  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
                                              3-17

-------
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
exist.  One  version is limited to steady inflows and
constantly  repetitive  tide. The steady inflow version
cannot explicitly  handle  short-term stochastic tran-
sients 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 inflow pattern. Consequently, this version is
most reliable when predicting high and low values for
diurnal or tidal cycles, or both, averaged over a rela-
tively  steady 2-week period (Ambrose and Roesch.
1982). Real time simulations of water quality are pos-
sible with the steady inflow version of DEM, but with
some inaccuracies. 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 com-
    prehensive version of the model currently avail-
    able (Chen and Orlob 1972). The model has the
    capability of representing 22 coupled biotic and
    abiotic constituents including: temperature, pes-
    ticides, heavy metals, CBOD, DO, phosphate.
    ammonia, nitrite, nitrate, total dissolved solids,
    alkalinity, pH, carbon dioxide, phytoplankton,
    zooplankton, fish, benthic animals, suspended
    detritus, and sediment detritus.

   DEM, Pearl Harbor version. Is limited to steady
    Inflows and constantly repetitive tide (Genet et
    at. 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 han-
    dling only steady inflows and constantly repeti-
    tive tide, but a newer version is available that Is
    capable of handling variable inflows (Roesch et
    al. 1979). The model simulates CBOD, DO, am-
    monia, 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
regime 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
col'rforms. Two versions  of the model are currently
available, and are described below.

   MIT-DNM. Potomac version, includes nutrient
    modeling and algal growth, photosynthesis.
    and respiration and represents bacterially
    mediated reactions for ammonia, nitrite, nitrate,
    phytoplankton-N, zooplankton-N, paniculate or-
    ganic N, and dissolved organic N (Najarian and
    Harleman 1975).

   MIT-DNM. St. Lawrence version, includes
    nutrient modeling and algal growth, photosyn-
    thesis, and respiration, and represents CBOD,
    DO,  Inorganic phosphorus, organic phos-
    phorus, inorganic nitrogen, organic nitrogen,
    phytoplankton, and zooplankton (Thatcher et al.
    1975).

3.3.4.4. EXPLORE-I

EXPLORE-! 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.
EXPLORE-I has the capability of simulating DO, con-
servatives,  toxic pollutants, conforms, sedimentary
phosphorus,  soluble  phosphorus, organic  phos-
phorus, organic  nitrogen, ammonia, nitrite, nitrate,
total organic carbon, refractory organic carbon,
phytoplankton, zooplankton, CBOD, and benthic BOD.
Sedimentation and scour of organic matter is  repre-
sented In the model as well as algal growth, photosyn-
thesis, and respiration.

3.3.5. Level IV Models
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-dif-
ference or finite-element hydrodynamic programs
exist, relatively 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 tempera-
ture but very few include nonconservath/e constituents
or water quality routines. Models in this category simu-
                                                3-18

-------
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
mode! 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 hydrodynamtc output of a Level  IV
hydrodynamic model. In particular, these models will
be selected for Investigations where dlumal and tidal
fluctuations 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
tidally 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
supercomputers, 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 varying
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,
flexibility, 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 dif-
ferent time steps or on-a coarser grid, the user must
still calibrate horizontal and vertical dispersion coeffi-
cients to observed salinity or tracer data.

The criteria for the specification  of time and space
scales for Level IV models are similar to those  dis-
cussed 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 coeffi-
cients.

At present, no Level IV model Is supported by CEAM.
A variety  of these models currently being  used is
described 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  inertia! forces,
corrective forces, hydrostatic pressure, wind forces,
Coriolis forces, bottom friction,  and  internal water
column forces  due to eddies. The parameters simu-
lated by the model include the following:  conserva-
tives, coliforms,  chlorophyll-a,  organic nitrogen,
ammonia, nitrite, nitrate, organic phosphorus,  inor-
ganic 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. Equa-
tions are solved by a finite element technique.

3.3.5.2. FETRA

FETRA 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 EX-
PLORE-I. FETRA consists of three submodels linked to
simulate the transport and transformation of sediments
and contaminants by the processes of advection, dif-
fusion/ dispersion, adsorption/ desorption,  and
degradation/decay. The sediment transport submodel
simulates advection 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 contaminant transport submodel  predicts
advection and diffusion/dispersion of dissolved pol-
lutants, adsorption by both moving and stationary sedi-
ments, desorption from sediments, and degradation or
radionuclide  decay. The paniculate contaminant
                                                3-19

-------
transport submodel includes advection and dispersion
of sediment-attached contaminants,  adsorp-
tion/desorptlon  with sediment,  degradation or
radionuclide decay; and settling/resuspension.

3.3.5.3. TABS-2

TABS-2 is a generalized numerical modeling system for
open-channel flows,  sedimentation, and constituent
transport developed and supported by the U.S. Army
Engineers Waterways Experiment Station. Hydraulics
Laboratory (Thomas and McAnally, 1985). It consists
of more than 40 computer programs to perform model-
ing and related tasks. The major modeling  com-
ponent S--RMA-2V, STUDH. and  RMA-4~calculate
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
generation 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 Engineers,
Waterways Experiment Station. Units of measure 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 capability In con-
junction 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-
dimensional 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 motion and continuity for model horizon-
tal velocity components and flow depths. The effects
of bottom, Internal and surface shear stresses and the
Coriolis force are represented in the equations of mo-
tion. CSTM-H is a cohesive sediment transport model
that solves the advection-dispersion equation for nodal
depth-averaged  concentrations  of suspended  sedi-
ment and bed surface  elevations. The processes of
erosion, dispersion, aggregation, deposition and con-
solidation are simulated. A layered bed modef 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 follow-
ing 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 calcu-
lated for each element: sediment bed structure (bed
density and shear strength profiles, bed thickness and
elevation), 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 suspension, and the downward flux of
sediment onto the bed. These parameters are essential
in estimating the bed-water exchange of chemicals
adsorbed onto cohesive 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 extrapola-
tion 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, I984a, I984b).
CE-QUAL-W2  consists  of  directly  coupled
hydrodynamic and water quality transport models.
Hydrodynamic computations are influenced by vari-
                                               3-20

-------
able water density caused by temperature, salinity, and
dissolved and suspended solids. Developed for reser-
voirs and narrow, stratified estuaries. CE-QUAL-W2
can handle a branched and/or looped system with flow
and/or head boundary  conditions. With two dimen-
sions depicted, point and non-point loadings can be
spatially distributed. Relative to other 2-d models, CE-
OUAL-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,
convectrve  mixing, wind  and flow  induced  mixing,
entrapment 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.
Major chemical and biological processes in CE-QUAL-
W2 include: the  effects on DO of atmospheric  ex-
change, photosynthesis, respiration, organic  matter
decomposition, nitrification, and chemical oxidation of
reduced substances; uptake, excretion, and regenera-
tion of phosphorus  and  nitrogen and nitrification-
denitrification under aerobic and anaerobic conditions;
carbon cycling and  alkalinity-pH-COz interactions;
trophic relationships for total phytoplankton; ac-
cumulation and decomposition of detritus and organic
sediment; and  conform bacteria mortality.

3.3.5.7. EHSM3D

The EHSM3D model was developed by Y. P. Sheng at
University of Florida calculates three-dimensional un-
steady currents and sediment dispersion in estuaries
and lakes (Sheng. et al.. 1987, Sheng. 1989). Given
proper boundary and initial conditions, the code can
calculate the three-dimensional time-dependent dis-
tributions 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 pressure 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 Mode! 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 ap-
plication. For complete information, the potential user
must consult the appropriate user's manuals, the sup-
porting 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 per-
sonal 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
specifying  appropriate boundaries, loads, and  first
order decay constants for another state variable. Sedi-
ment may be modeled using calibrated deposition and
scour velocities (1), or by using functional relationships
with shear stress and shear strength to predict these
velocities (2). Dissolved oxygen may be modeled along
with total BOD (1), with CBOD, NBOD. and  prescribed
sediment oxygen  demand (SOD) and net photosyn-
thetic production (2). or with CBOD nitrification, SOD.
and simulated nutrients and  phytoplankton  (3).
Nutrient enrichment and eutrophication may be simu-
lated 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 original chemical plus reaction
products (3). Metals may be modeled as dissolved and
paniculate fractions with calibrated partition coeffi-
cients (1),  or as  multiple species predicted with a
thermodynamic data base and process models (2).
                                               3-21

-------
Table 3-5.  Basle Modal Feature*
Model
SEM
WQAM
HARO3
FEDBAKO3
OUAL2
AUTOOUAL/OD
WASP4:
stand atone
with DYNHYO4
DEM
EXPLORE-)
MIT-DNM
Chen
FETRA
CE-OUAL-W2
TABS-2
WIFM-SAL
FCSTM-H
EHSM3D
J PAUL
D-dynamic
O-quasidynamic (tidal-
averaged)
SS-sleady state




Time Scale Spatial Dimension Hydrodynamics
SS x
S3 x
SS 8
SS B
SS x
Q x

Q B
D xx
D xx
D xx
D x
0 xy
D xy
0 xz
0 xy
D xy
D xy
D xyz
D xyz
x-1 dimensional
xy-2 dimensional, lon-
gitudinal-lateral
xz-2 dimensional, lon-
gitudinal-vertical
jcyz-3 dimensional
B-compartment or box 3D
xx-)ink node branching 20







I
S
S
S
S
S
1
S
S
S
S
S
S
Miydrodynamics input
S-hydrodynamics simu-
lated





Solution Tech.
A
A
FD
FD
FD
FD

FD
FD
FD
FD
FD
FE
FE
FD
FE
FE
FE
FO
FO
A-analytical solution
FD-finrte difference
solution
FE-finite element solu-
tion



Computer
_
_
M
M
M.PC
M, PC

M, PC
M.PC
M
M
M
M
M
M
M
M
M
M
M
M-mainframe computers
PC-personal computers






Table 3-6.  Water Qualm/ Probleme Addreuad
Model
SEM
WQAM
HARO3
FEDBAKO3
OUAL2
AUTOOUAL
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
Sedi-
ment

1




1




2
1
2

2
2

DO
2
2'
2
2
3
2
3
3
3
3
3

3





Eutro-
phica-
tion




1

1
1
3
1
1

1





Org.
Chem.

1




1.2.3











Me-
tals






1




1






                                                    3.4. References
                                                    Ambrose, R.B., Najarian, T.O., Bourne, G., Thatcher,
                                                    M.L  1981. Models for Analyzing Eutrophication  in
                                                    Chesapeake Bay Watersheds: A Selection Methodol-
                                                    ogy.  USEPA. Office of Research and Development,
                                                    Chesapeake Bay Program, Annapolis. MD.

                                                    Ambrose, R.B. and Roesch, S.E. 1982. Dynamic Es-
                                                    tuary Model Performance. Journal of the Environmen-
                                                    tal Engineering Division, American Society of  Civil
                                                    Engineers, 108(EE1).

                                                    Ambrose. R.B. Jr. et a!. 1987. WASP4, A General Water
                                                    Quality Model for Toxic and Conventional Pollutants,
                                                    U.S. Environmental Protection Agency, Athens, Geor-
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                                                    Blumberg, A.F. 1975. A Numerical Investigation intothe
                                                    Dynamics of  Estuarine Circulation. Chesapeake Bay
                                                    Institute, Johns Hopkins University, Baltimore  MD.
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                                                    Bowie. G.L et. a!. 1985. Rates, Constants, and Kinetics
                                                    Formulations in Surface Water Quality Modeling
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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. I984a. Generalized,
Longitudinal-vertical  Hydrodynamics and Transport:
Development, Programming And Applications, Docu-
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Vicksburg, Mississippi.

Buchak, E. M. and Edinger, J.E I984b. Simulation of
a Density Underflow into Wellington Reservoir using
Longitudinal-vertical Numerical Hydrodynamics,
Document No. 84-18-R, U.S. Army Corps of Engineers,
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
Hydraulics Division Specialty Conference on Verifica-
tion of Mathematical and Physical Models in Hydraulic
Engineering, American Society of Civil Engineers. New
York. NY.

Chen. C.W. and Orlob, G.T. December, 1972. Ecologi-
cal Simulation for Aquatic Environments. NT1S Doc. PB
218828. Water Resources Engineers, Inc..  Walnut
Creek. California, for Office of Water Resources Re-
search. U.S. Department of the Interior, Washington.
D.C.

Crim. R. and Lovelace. N.L 1973. AUTO_QUAL Model-
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Washington, D.C. EPA-440/9-73-004.

Di Toro. D.M., 1986. A Diagenetic Oxygen Equivalents
Model of Sediment  Oxygen Demand. In  Sediment
Oxygen Demand; Processes, Modeling, and Measure-
ment, editor K. J. Hatcher. Univ. of Georgia. Athens,
GA. pp 171-208.

Di Toro. D.M., Fitzpatrick. J.J.. and Thomann. R.V.
1981. Water Quality  Analysis Simulation Program
(WASP) and Model  Verification Program  (MVP)-
Documentation. Hydroscience, Inc., Westwood, New
Jersey, for  U.S.  Environmental Protection Agency.
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 in
LARM2: A Longitudinal-vertical, Time-varying
Hydrodynamic Reservoir Model, Technical  Report E-
83-1, USAE Waterways Experiment Station, Vicksburg.
MS.
Elliott, A.J. 1976. A Numerical Model of the Internal
Circulation in a Branching Tidal Estuary. Chesapeake
Bay  Institute, Johns Hopkins University,  Baltimore,
MD, Special Report 54.

Environmental and Hydraulics Laboratories. 1986. CE-
OUAL-W2. A Numerical Two-Dimensional Model of
Hydrodynamics and Water Quality, User's Manual. In-
struction 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.

Fisher, J.S., Ditmars, J.D.. and Ippen, A.T. 1972. Math-
ematical Simulation of Tidal Time-Averages of Salinity
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