U.S. ENVIRONMENTAL PROTECTION AGENCY
CONTRACT NO. 68-01-6403
SELECTING ESTUARINE
MODELS
Raymond Walton
Thomas S. George
Larry A. Roesner
Camp Dresser 4 McKee
7630 Little River Turnpike, Suite 500
Annandale, Virginia 22003
(703) 642-5500
September 1984
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CONTENTS
Section Page
LIST OF FIGURES Hi
LIST OF TABLES 1v
I. INTRODUCTION 1-1
1.1 Purpose 1-1
1.2 Relation to Other Books and Chapters 1-1
1.3 Scope of Chapter 1-1
1.3.1 Importance of Nutrients and Toxics 1-1
1n the Estuary
1.3.2 Beneficial Uses 1n the Estuary 1-3
1.3.3 Objectives of Chapter 1-5
I.4 Overview of Criteria for Selection of a Model 1-5
II. HYDRODYNAMIC AND MASS TRANSPORT PROCESSES II-l
II.1 General II-l
11.2 Physical Processes II-2
11.2.1 Introduction II-2
11.2.2 Tides II-2
11.2.3 Wind II-4
11.2.4 Freshwater Inflows 11-4
11.2.5 Friction II-6
11.2.6 CoHolis Effect II-8
11.2.7 Vertical Mixing 11-8
11.2.8 Horizontal Mixing 11-11
11.3 Estuarine Classification 11-11
11.3.1 Introduction 11-11
11.3.2 Geomorphological Classification 11-11
11.3.3 Stratification 11-14
11.3.4 Circulation Patterns 11-17
11.4 Time Scales 11-18
11.5 Governing Equations 11-20
11.6 Reducing Dimensions 11-21
11.7 Tidal Averaging 11-24
11.8 Dispersion Coefficients 11-25
11.9 Decay Coefficients 11-32
U S EPA LIBRARY REGION 10 MATERIALS
RXO
b302
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ill. WATER QUALITY PROCESSES III-l
111.1 General III-l
111.2 Biochemical Processes III-3
111.2.1 Conservative Substances II1-3
111.2.2 Biochemical Oxygen Demand III-4
111.2.3 Fecal Conforms III-5
111.2.4 Phosphorus III-5
111.2.5 Nitrogen IIIt8
111.2.6 Nitrogen and Phosphorus Without Algae, 111-12
Settling or Benthlc Sources
111.2.7 Algae 111-12
111.2.8 Dissolved Oxygen 111-15
111.2.9 Toxicants 111-18
111.2.10 Aquatic Ecosystem 111-20
111.3 Reaction Rates and Constants II1-23
111.3.1 Reaeratlon Rate 111-25
111.3.2 Temperature Dependence 111-26
111.4 Time and Space Scales II1-27
111.4.1 Time Scales 111-27
111.4.2 Space Scales II1-30
IV. FRAMEWORK FOR MODEL SELECTION IV-1
IV. 1 Conceptual Model IV-3
IV.2 Definition of Complete Mixing IV-3
IV.3 Far Field Dimension Reduction IV-7
IV.3.1 Vertical Dimension IV-8
IV.3.2 Lateral Dimension IV-17
IV.4 Process Time and Space Scales IV-18
IV.4.1 Flushing Time IV-18
IV.4.2 Decay or Dleoff Rates IV-22
IV.5 Regulatory Scales IV-22
IV.6 Study Scale Dimension Reduction IV-23
IV.7 Dynamic or Steady-State IV-29
IV.8 Spatial and Temporal Resolution IV-31
IV.8.1 Resolution IV-31
IV.8.2 Stability IV-32
IV.9 Diffusion Coefficients IV-34
IV.10 Data Availability IV-36
IV.11 Model Selection IV-37
V. REFERENCES V-l
1i
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LIST OF TABLES
Table
Page
1-1
Organization of Guidance Manual for Performance of
1-2
Waste Load Allocations
II-l
Topographic Estuarlne Classification
11-12
11-2
Stratification Classification
11-16
11-3
Time Scales of Major Processes
11-19
III-l
Reaction Rates and Constants for Conventional Pollutants
II1-24
IV-1
Topographic Estuarlne Classification
IV-16
IV-2
Stratification Classification
IY-16
IV-3
Observed Longitudinal Dispersion Coefficients
IV-21
IV—4
Example Model Selection Checklist
IV-38
iv
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SECTION I
INTRODUCTION
1.1 PURPOSE
This chapter on selection of estuarlne models is one in a series of manuats
whose purpose is to provide technical Information and policy guidance for
the preparation of Waste Load Allocations (WLAs). The objective of such
waste load allocations 1s to ensure that water quality conditions are
achieved that protect the designated beneficial uses of the receiving
water. An ancillary benefit of a technically sound WLA Is that excessive
degrees of treatment which are not necessary and that do not yield
proportionate Improvements 1n water quality, can be avoided.
1.2 RELATION TO OTHER BOOKS AND CHAPTERS
The various books and chapters that make up the set of technical guidance
manuals on Waste Load Allocation are summarized 1n Chapter 1-1. These
technical chapters should be used in, conjunction with the material of Book
I which provides background information applicable to all types of water
bodies and to all contaminants that must be considered in the Waste Load
Allocation process.
1.3 SCOPE OF CHAPTER
1.3.1 IMPORTANCE OF NUTRIENTS AND TOXICS IN THE ESTUARY
The most significant anthropogenic Impacts on estuaries stem from the
release of nutrients and toxic chemicals to feeder streams and to the
estuary Itself. Nutrients appear to present the greatest threat to the
estuary because of their role 1n supporting and promoting the widespread
growth of algae. Algal growths are Important because they act to diminish
the penetration of sunlight into the water. Submerged aquatic vegetation
1-1
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TABLE 1-1
ORGANIZATION OF GUIDANCE MANUAL FOR PERFORMANCE OF WASTE LOAD ALLOCATIONS
BOOK I GENERAL GUIDANCE
(Discussion of overall WLA process, procedures and
considerations)
BOOK II STREAMS AND RIVERS
(Specific technical guidance for these water bodies)
Chapter 1 - BOD/Dissolved Oxygen Impacts and Ammonia Toxicity
2 - Nutrient/Eutrophlcatlon Impacts
3 - Toxic Substances Impacts
BOOK III ESTUARIES
Chapter 1 - BOD/Dissolved Oxygen Impacts
2 - Nutrient/Eutrophication Impacts
3 - Toxic Substances Impacts
BOOK IV LAKES, RESERVOIRS, AND IMPOUNDMENTS
Chapter 1 - BOD/Dissolved Oxygen Impacts
2 - Nutr1ent/Eutroph1cat1on Impacts
3 - Toxic Substances Impacts
Note: Other water bodies (e.g., groundwaters, bays, and oceans) and other
contaminants (coliform bacteria and virus, TDS) may subsequently be
incorporated into the manual as need for comprehensive treatment is
determined.
1-2
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(SAV) is dependent upon _ inlight for pnw. -ynthesls, and when light
penetration is diminished too much by algal growths, the SAV will be
affected.
SAV serves an Important role as habitat and food source for much of the
biota of the estuary. Major estuary studies, Including an Intensive
years-long study of the Chesapeake Bay, have shown that the health of SAV
communities serves as an important Indication of estuary health. When SAV
conmunlties are adversely affected by nutrients and/or toxics, the aquatic
life use of the estuary will also be affected.
1.3.2 BENEFICIAL USES IN THE ESTUARY
Our national management strategy for surface waters 1s based upon the
specification, by each State, of a water quality standard for Individual
water bodies or portions of a water body within that State. Once
specified, the standard becomes the gage against which general water
quality is assessed for the specified water body.
A standard is made up of two components: an aquatic life protection use,
and water quality criteria that will protect that use. The starting point
in the specification of a standard is the definition of attainable uses for
the water body 1n question. The basic precepts for the specification of
uses in an estuary are discussed in two documents Issued by the U.S.
Environmental Protection Agency, Office of Water Regulations and Standards:
Water Quality Standards Handbook (December, 1983) and Technical Support
Manual: Water Body Surveys and Assessments for Conducting Use Attain-
ability Analyses, Volume II, Estuaries (June, 1984).
'Cold water fishers,' 'warm water fishers,' or 'fish maintenance' are
examples of aquatic life protection uses. The use most commonly found in
State standards *nat 1s applicable to the estuary Is generally phrased 1n
terms of the protection and propagation of fish and shellfish. For the
simple estuary with few freshwater sources, the delineation of a zone whose
salinity range will support the protection and propagation of fish and
shellfish may be straightforward. For the larger, more complex estuary,
1-3
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however, the physiography of Individual embayments, and the presence of
regionalized water chemistry-water quality characteristics may require
greater specificity In the establishment of uses. Uses are protected by
criteria, the levels of various water quality constituents that will
support (In the case of dissolved oxygen) or not Interfere (1n the case of
pH, temperature, ammonia, chlorine, ca
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1.3.3 OBJECTIVES OF CHAPTER
The objective of this Chapter 1s to provide the reader with explicit
guidance In the selection of a model that best satisfies the requirements
of a specific waste load allocation study, and that best represents the
conditions 1n the estuary of concern.
1.4 OVERVIEW OF CRITERIA FOR SELECTION OF A MODEL
There are numerous publications that competently describe the
characteristics and capabilities of Individual models that nay be used 1n
an estuarine study, and other publications that compare the attributes of
these models, one with another, but little Indeed In the literature that
provides systematic guidelines for the selection of an appropriate model.
The appropriateness of a model Is determined by examining the estuary 1n
terns of spatial and temporal characteristics in order to decide whether a
zero, one, two or three dimensional analysis 1s required; to decide the
time scale of the analysis and which temporal processes (the most important
of which is tide in a short scale, or seasonal freshwater flows on a longer
scale, etc.) are important.
1-5
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SECTION II
HYDRODYNAMIC AND MASS TRANSPORT PROCESSES
II.1 GENERAL
The term estuary Is generally used to denote the lower reaches of a river
where tide and river flows Interact. The generally accepted definition for
an estuary was provided by Prltchard In 1952: "An estuary Is a semi-
enclosed coastal body of water having a free connection with the open sea
and containing a measureable quantity of seawater." This description has
remained remarkably consistent with time and has undergone only minor
revisions (Emery and Stevenson, 1957; Cameron and Prltchard, 1963). To
this day, such qualitative definitions are the most typical basis for
determining what does and what does not constitute an estuary.
Estuaries are perhaps the most Important social, economic, and ecologic
regions in the United States. For example, according to the Department of
Commerce (DeFalco, 1967), 43 of the 110 Standard Metropolitan Statistical
Areas are on estuaries. Furthermore, recent studies Indicate that many
estuaries, Including Delaware Bay and Chesapeake Bay, are on the decline.
Thus, the need has arisen to better understand their ecological functions
to define what constitutes a "healthy" system, to define actual and
potential uses, to determine whether designated uses are Impaired, and to
determine how these uses can be preserved or maintained.
As part of such a program, there Is a need to define Impact assessment pro-
cedures that are simple, 1n light of the wide variability among estuaries,
yet adequately represent the major features of each system studied.
Estuaries are three-dimensional waterbodles which exhibit variations 1n
physical and chemical processes 1n all three directions (longitudinal,
vertical, and lateral) and also over time. However, following a careful
consideration of the major physical and chemical processes and the time
scales Involved 1n a particular study one can often define a simplified
version of the prototype system for study.
II-l
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In this chapter, a discussion is presented of the Important estuarine
features and major physical processes. From this background, guidance for
model selection is given which considers the various assumptions that may
be made to simplify the complexity of the analysis, while retaining an
adequate description of the system. Finally, a framework for selecting
appropriate computer models 1s outlined 1n Chapter IV.
II.2 PHYSICAL PROCESSES
11.2.1 INTRODUCTION
Estuarine flows are the result of a complex Interaction of:
o ti des,
o wind,
o freshwater inflow,
o bottom friction,
o Rotational effect of the earth (Coriolis effect),
o vertical mixing, and
o horizontal mixing.
In performing a modeling study, one tries to simplify the complex prototype
system by determining which of these effects or combination of effects is
most important at the time scale of the evaluation. To do this, 1t is
necessary to understand each of these processes and their Impacts on the
evaluation. A complete description of all of the above 1s beyond the scope
of this chapter. Rather, illustrations are provided of some of the
features of each process, which emphasize considerations of magnitude and
time scale.
11.2.2 TIDES
Tides are highly variable throughout the United States, both in amplitude
and phase. Figure II-l (NOAA, 1983) shows some typical tide curves along
the Atlantic, Gulf of Mexico, and Pacific Coasts. Tidal amplitude can vary
from 1 foot or less along the Gulf of Mexico (e.g., Pensacola, Florida) to
11-2
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III!*!!!!
MAWPTO* MAM
ItMn in apegr*
latt quarter
Moon on Equator
0 • nr« Noon
A iliiruMiM ol the(# rurvn ts given mi iIii* pn,t»i«ior
Q - >.r. *
Figure 11-1. Typical Tide Curves for United States Ports
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over 30 feet in parts of Alaska (e.g., Anchorage) and the Maritime
Provinces of Canada (e.g., the Bay of Fundy). Tidal phasing 1s a
combination of many factors with differing periods. However, 1n the United
States, most tides are based on 12.5-hour (semidiurnal), 25-hour (diurnal)
and 14-day (semi-lunar) combinations. In some areas, such as Boston
(Figure II-l), the tide 1s predominantly semidiurnal with 2 high tides and
2 low tides each day. In others, such as along the Gulf of Mexico, the
tides are more typically mixed.
Tidal power 1s directly related to amplitude. This potential energy source
can promote Increased mixing through Increased velocities and interactions
with topographic features.
11.2.3 WIND
In many exposed bays or estuaries, particularly those In which tidal
forcing is smaller, wind shear can have a tremendous Impact on circulation
patterns at time scales of a few hours to several days. An example is
Tampa Bay on the West Coast of Florida, where tidal ranges are
approximately 3 feet, and the terrain 1s generally quite flat. Wind can be
produced from localized thunderstorms of a few hours duration, or from
frontal movements with durations on the order of days. Unlike tides, wind
is unpredictable in a real time sense. The usual approach to studying wind
driven circulation is to develop a wind rose (Figure 11-2) from local
meteorological data, and base the study of Impacts on statistically
significant magnitudes and directions, or on winds that might produce the
most severe impact.
11.2.4 FRESHWATER INFLOWS
Freshwater Inflows from a major riverine source can be highly variable from
day to day and season to season. At the shorter time scale, the river may
be responding to a localized thunderstorm, or the passage of a front. In
many areas, however, the frequency of these events tends to group into a
season (denoted the wet season) which is distinct from the remainder of the
year (the dry season). The average monthly streamflow distributions 1n
11-4
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MBUAOT MM
CiaCiaa*"
ii« vcm'omi
•0«
*H.» i
Ciociaaan
HO TMM'MU)
*
•0%
11-5
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Figure 11-3 Illustrate that 1n Virginia the wet season is typically from
December to May and comes mainly from frontal systems. In Florida,
however, where the wet season coincides with the simmer months when
localized thunderstorms predominate, the trend 1s reversed.
It is important to consider the effect of freshwater flows on estuarfne
circulation because streamflow 1s the only major mechanism which produces a
net cross-sectional flow over long averaging times. A common approach 1s
to represent the estuary as a system driven by net freshwater flows In the
downstream direction with other effects averaged out and lumped Into a
dispersion-type parameter. When using this approach to evaluate the
estuary system, one must weigh the consequences very carefully.
Freshwater is less dense and tends to "float" over seawater. In some
cases, freshwater may produce a residual 2-layer flow pattern (such as In
the James Estuary, Virginia, or Potomac River) or even a 3-layer flow
pattern (as in Baltimore Harbor). The danger Is to treat such a distinctly
2-layer system as a cross-sectionally averaged, river driven system, and
then try to explain why pollutants are observed upstream of a discharge
point when no advective mechanism exists to produce this effect using a
one-dimensional approach.
II.2.5 FRICTION
The estuary's topographic boundaries (bed and sides) produce frictional
resistance to local currents. In some estuaries with highly variable
geometries, this can produce a number of net nontldal (or tidally-averaged)
effects such as residual eddies near headlands or tidal rectification.
Pollutants trapped 1n residual eddies, perhaps from a wastewater treatment
plant outfall, may have very large residence times that are not predictable
from cross-sectionally averaged flows before such pollutants are flushed
from the system.
II-6
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0 1 667 500-Rapidan River mi. Culpeper, va. Drainage aria. 472 so mi
13
Z
o
O 02030500-Siat# Rivtr near Arvonia, Va.
1 0 C '
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a:
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CL
I. 226 tQ.mi.
Lj
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02045500-Nottoway River near Stony Creek, Va. Drainage area. 579 $a mi
1 1
11
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1
!
r,.^ r
C3J98000-N.F. Holston River near S a 11 v • 11 e. Va. D r j i» a ; e )r«a, 222 53 mi.
i :•;
-m
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H
iff
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP YEAR
n - ¦ •
1 : r .. a : r
Figure 11-3. Monthly Average Streamflows for Locations in
Virginia, (from U. S. Geological Survey 1982)
11-7
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II.2.6 CORIOLIS EFFECT
In wide estuaries, the Cor1ol1s effect can cause freshwater to move to the
right-hand bank (facing the open sea) so that the surface slopes upward to
the right of the flow. The Interface has an opposite slope to maintain
geostrophlc balance. For specific configurations and corresponding flow
regimes, the boundary between outflow and Inflow nay actually cut the
surface (Figure II-4a). This 1s the case In the lower reaches of the St.
Lawrence estuary, for example, where the well-defined Gaspe Current holds
against the southern shore and counter flow 1s observed along the northern
side. This effect is augmented by tidal circulation which forces ocean
waters entering the estuary with the flood tide to adhere to the left side
of the estuary (facing the open sea), and the ebb flow to the right side.
Thus, as 1s often apparent from the surface salinity pattern 1n an estuary,
the outflow 1s stronger on the right-hand side (Figure II-4b). The exact
location and configuration of the saltwater/freshwater Interface depends on
the relative magnitude of the forces at play. Quantitative estimates of
various mixing modes in estuaries are discussed below.
II.2.7 VERTICAL MIXING
All mixing processes are caused by local differences 1n velocities and by
the fact that liquids are viscous (i.e., possess internal friction). In
the vertical direction, the most common mixing occurs between riverine
fresh waters and the underlying saline ocean waters.
If there were no friction, freshwater would flow seaward as a shallow layer
on top of the seawater. The layer would become shallower and the velocity
would decrease as the estuary widened toward Its mouth. However, the fact
of friction between the two types of water requires a balancing pressure
gradient down-estuary, explaining the salt wedge formation which deepens
toward the mouth of the estuary, as seen 1n Figure II-5. Friction also
causes mixing along the Interface. A particularly well-defined salt wedge
1s observed 1n the estuary of the Mississippi River.
11-8
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MOUTH
a. Cross-section A-A looking
Down-estuary.
HEAD
b. Surface Salinity Distribu-
tion (ppt).
Figure II-4. Net Inflow and Outflow in a Tidal Estuary, Northern
Hemisphere.
HEAD
MOUTH
SALINITY
DISTRIBUTION (S)
Figure II-5. Layered Flow in a Salt-wedge Estuary (Longitudinal Profile).
11-9
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If significant mixing does not occur along the freshwater/saltwater inter-
face, the layers of differing density tend to remain distinct and the
system 1s said to be highly stratified 1n the vertical direction. If the
vertical mixing is relatively high, the mixing process can almost
completely break down the density difference, and the system 1s called
well-mixed or homogeneous.
In sections of the estuary where there Is a significant difference between
surface and bottom salinity levels over some specified depth (e.g., differ-
ences of about 5 ppt or greater over about a 10 foot depth), the water
column 1s regarded as highly stratified. An Important Impact of vertical
stratification is that the vertical density differences significantly
reduce the exchange of dissolved oxygen and other constituents between
surface and bottom waters. Consequently, persistent stratification can
result in a depression of dissolved oxygen (DO) 1n the high salinity bottom
waters that are cut off from the low salinity surface waters. This is
because bottom waters depend upon vertical mixing with surface waters,
which can take advantage of reaeratlon at the e1r-water Interface, to
replenish DO that is consumed as a result of respiration and the decay of
organic materials within the water column and bottom sediments. In
sections of the estuary exhibiting significant vertical stratification,
vertical mixing of DO contributed by reaeratlon 1s limited to the low
salinity surface waters. As a result, persistent stratified conditions can
cause the DO concentration in the bottom waters to fall to levels that
cause stress on or mortality of the resident communities of benthic
organlsms.
Another potential impact of vertical stratification is that anaerobic con-
ditions in bottom waters can result 1n increased release of nutrients such
as phosphorus and ammonia-nitrogen from bottom sediments. During later
periods or in sections of the estuary exhibiting reduced levels of
stratification, these increased bottom sediment contributions of nutrients
can eventually be transported to the surface water layer. These Increased
nutrient loadings on surface waters can result In higher phytoplankton con-
centrations that can exert diurnal DO stresses and reduced light penetra-
tion for rooted aquatic plants. In summary, the persistence and area!
11-10
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extent of vertical stratification is an important determinant of mixing
within an estuary.
II.2.8 HORIZONTAL MIXING
Mixing also occurs in the horizontal direction, although It 1s often
neglected in favor of vertical processes. As with vertical nixing,
horizontal mixing is caused by localized velocity variations and Internal
friction, or viscosity. The velocity variations are usually produced by
the Interactions between the shape of the system and friction, resulting in
eddies of varying sizes. Thus, horizontal constituent distributions tend
to be broken down by differential advection, which when viewed as an
average advection (laterally, or cross-sectionally) Is called dispersion.
II.3 ESTUARINE CLASSIFICATION
11.3.1 INTRODUCTION
It is often useful to consider some broad classifications of estuaries,
particularly in terms of features and processes which enable us to analyze
them in terms of simplified approaches. The most conroonly used groupings
are based on geomorphology, stratification, circulation patterns, and time
scales.
11.3.2 6E0M0RPH0L0GICAL CLASSIFICATION
Over the years, a systematic structure of geomorphological classification
has evolved. Dyer (1973) and Fischer, et al. (1979) Identify four groups:
o Drowned river valleys (coastal plain estuaries),
o Fjords
o Bar-built estuaries, and
o Other estuaries that do not fit the first three classifications.
Typical examples of North American estuaries are presented 1n Table II-l.
11-11
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TABLE II-l. TOPOGRAPHIC ESTUARINE CLASSIFICATION
Type
Dominant Degree of
Long-Term Process Stratification
Examples
Coastal Plain
River Flow
Moderate Chesapeake Bay, MD/VA
James River, VA
Potomac River, MD/VA
Delaware Estuary, DE/NJ
New York Bight, NY
Bar Built
Wind
Vertical Little Sarasota Bay, FL
Apalachlcola Bay, FL
Galveston Bay, TX
Roanoke River, VA
Albemarle Sound, NC
Pamlico Sound, NC
Fjords
Ti de
Hi gh
Alberni Inlet, B.C.
Silver Bay, AL
Puget Sound, WA
Other Estuaries
Various
Various San Francisco Bay, CA
Columbia River, WA/OR
11-12
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Coastal plain estuaries are generally shallow with gently sloping bottoms,
and depths Increasing uniformly towards the mouth. Such estuaries have
usually been cut by erosion and are drowned river valleys, often displaying
a dendritic pattern fed by several streams. A well-known example 1s
Chesapeake Bay. Coastal plain estuaries are usually Moderately stratified
(particularly 1n the old river valley section) and can be highly Influenced
by wind.
Bar built estuaries are bodies of water enclosed by the deposition of a
sand bar off the coast through which a channel provides exchange with the
open sea, usually servicing rivers with relatively small discharges. These
are usually unstable estuaries, subject to gradual seasonal and cata-
strophic variations in configuration. Many estuaries in the Gulf Coast and
Lower Atlantic Regions fall into this category. They are generally a few
meters deep, vertically well mixed and highly Influenced by wind.
Fjords are characterized by relatively deep water and steep sides, and are
generally long and narrow. They are usually formed by glaclatlon, and are
more typical in Scandinavia and Alaska than the contiguous United States.
There are examples along the Northwest Pacific Coast such as Alberni Inlet
in British Columbia and Puget Sound. The freshwater streams that feed a
fjord generally pass through rocky terrain. Little sediment Is carried to
the estuary by the streams, and thus the bottom 1s likely to be a clean
rocky surface. The deep water of a fjord is distinctly cooler and more
saline than the surface layer, and the fjord tends to be highly stratified.
The remaining estuaries not covered by the above classification are usually
produced by tectonic activity, faulting, landslides, or volcanic eruptions.
An example 1s San Francisco Bay which was formed by movement of the San
Andreas Fault System (Dyer, 1973).
11-13
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II.3.3 STRATIFICATION
A second method of classifying estuaries is by the degree of observed
stratification, and was developed originally by Pritchard (1955) and
Cameron and Pritchard (1963). They considered three groupings (Figure
11-6):
o The highly stratified (salt wedge) type
o Partially mixed estuary
o Vertically homogeneous estuary
Such a classification is Intended for the general case of the estuary
influenced by tides and freshwater inflows. Shorter term events, such as
strong winds, tend to break down highly stratified systems by Inducing
greater vertical mixing. Examples of different types of stratification are
presented in Table 11-2.
In the stratified estuary (Figure II-6a), large freshwater inflows ride
over saltier ocean waters, with little mixing between layers. Averaged
over a tidal cycle, the system usually exhibits net seaward movement 1n the
freshwater layer, and net landward movement In the salt layer, as salt
water is entrained into the upper layer. The Mississippi River Delta 1s an
example of this type of estuary.
As the interfacial forces between the saltwater and overlying freshwater
become great enough to partially break down the density differences, the
system becomes partially stratified, or partially well-mixed (Figure
II-6b). Tidal flows are now usually much greater than river flows, and
flow reversals in the lower layer may still be observed, although they are
generally not as large as for the highly stratified system. Chesapeake Bay
and the James River estuary are examples of this type.
In a well mixed system (Figure II-6c), the river Inflow 1s usually very
small, and the tidal flow 1s sufficient to completely break down the
stratification and thoroughly mix the system vertically. Such systems are
11-14
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VELOCITY 15
A A
• k
SALINITY
(b) Partially mixed
(c) Well-mixed
Figure 11-6. Classification of Estuarine Stratification.
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TABLE 11-2. STRATIFICATION CLASSIFICATION
Type
Highly Stratified
Partially Mixed
Vertically Homogeneous
River Discharge
Large
Medium
Small
Examples
Mississippi River, LA
Mobile River, AL
Puget Sound, WA
Chesapeake Bay, MD/VA
Jaaes Estuary, VA
Potomac River, MD/VA
Del aware Bay, DE/NJ
Rarltan River, NJ
Blscayne Bay. FL
Tampa Bay, FL
San Francisco Bay, CA
San Diego Bay, CA
11-16
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generally shallow, so that the tidal amplitude to depth ratio is large and
mixing can easily penetrate throughout the water column. The Delaware and
Raritan River estuaries are examples of well-mixed systems.
11.3.4 CIRCULATION PATTERNS
Circulation 1n an estuary (I.e., the velocity patterns as they change over
time) Is primarily affected by the freshwater outflow, the tidal Inflow,
and the effect of wind. In turn, the difference In density between outflow
and inflow sets up secondary currents that ultimately affect the salinity
distribution across the estuary. The salinity distribution 1s Important 1n
that 1t affects the distribution of fauna and flora within the estuary. It
is also important because It Indicates the mixing properties of the estuary
as they may affect the dispersion of pollutants and flushing properties.
Additional factors such as friction forces and the size and geometry of the
estuary contribute to the circulation patterns.
The complex geometry of estuaries, 1n combination with the presence of,
wind, the effect of the earth's rotation (Coriolis effect), and other
effects, often results in residual currents (i.e., of longer period than
the tidal cycle) that strongly influence the mixing processes in estuaries.
For example, a uniform wind over the surface of an estuary produces a net
wind drag which may cause the center of mass of the water in the estuary to
be displaced toward the deeper side. Hence a torque is induced causing the
water mass to rotate.
In the absence of wind, the pure interaction of tides and estuary geometry
may also cause residual currents. For example, flood flows through narrow
inlets set up so-called tidal jets, which are long and narrow as compared
to the ebb flows which draw from a larger area of the estuary, thus forcing
a residual circulation from the central part of the estuary to the sides
(Stommel and Farmer, 1952). The energy available In the tide is 1n part
extracted to drive regular circulation patterns whose net result 1s similar
11-17
-------
to what would happen if pumps and pipes were Installed to move water about
in circuits. This is why this type of circulation is referred to as "tidal
pumping" to differentiate from wind and other circulation (Fisher, et al.,
1979).
Tidal "trapping" 1s a mechanism — present In long estuaries with side
embayments and small branching channels — that strongly enhances
longitudinal dispersion. It 1s explained as follows. The propagation of
the tide in an estuary -- which represents a balance between the water mass
Inertia, the hydraulic pressure force due to the slope of the water
surface, and the retarding bottom friction force — results 1n aaln channel
tidal elevations and velocities that are not In phase. For example, high
water occurs before high slack tide and low water before low slack tide
because the momentum of flow In the main channel causes the current to
continue to flow against an opposing pressure gradient. In contrast, side
channels which have less momentum can reverse the current direction faster,
thus "trapping" portions of the main channel water which are then available
for further longitudinal dispersion during the next flood tide.
II.4 TIME SCALES
A time scale is defined as the period of time over which physical/chemical/
biological processes act to produce a condition. The consideration of the
time scales of the physical processes being evaluated 1s very important for
any water quality study. Short-term conditions are much more influenced by
a variety of short-term events which perhaps have to be analyzed to
evaluate a 'worst case" scenario. Longer term (seasonal) conditions are
influenced predominantly by events which are averaged over the duration of
that time scale.
The key to any study is to identify the time scale of the Impact being
evaluated and then analyze the forcing functions over the same time scale.
As an example, circulation and mass transport In the upper part of
Chesapeake Bay can be wind driven over a period of days, but 1s river
driven over a period of one month or more. Table II-3 lists the major
types of forcing functions on most estuarine systems and gives some idea of
their time scales.
11-18
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TABLE I1-3. TIME SCALES OF MAJOR PROCESSES
Forcing Function
Time Scale
TIDE
One cycle
Neap/Spring
0.5-1 day
14 days
WIND
Thunderstorm
Frontal Passage
1-4 hours
1-3 days
RIVER FLOW
Thunderstorm
Frontal Passage
Wet/Dry Seasons
0.5-1 day
3-7 days
4-6 months
11-19
-------
II.5 GOVERNING EQUATIONS
The equations that describe the dynamics of water circulation and mass
transport 1n an embayment, estuary, bay or coastal sea are the momentim
equation, the continuity equation, the mass transport equations for
salinity and temperature, and an equat1on-of-state relating the density of
seawater to the local salinity concentration and/or temperature. The fate
of water quality constituents 1s also governed by the mass transport
equation, with the addition of terms to handle chemical kinetics.
Two basic assumptions usually govern the form of these equations: (1) the
fluid may be assumed to be Incompressible; and (2) flows are nearly
horizontal. These assunptlons Imply that the modeler may neglect
compressible effects and vertical accelerations, and may specify the
vertical momentun balance by the hydrostatic pressure equation. With these
assumptions, and using the Bousslnesq approximation applied to the pressure
term, the equations may be formed as follows (Leendertse, et al., 1973):
the momentum equations:
_?u 3(u2)
3t 3x
oV
at
a (uv)
ax
3( UV) 3(UW)
3y 3z
2
3(V ) + 3(vw)
sy sz
- *» ~ i- If - i (¦
P dX p
f „ ~ i 12 . i (
c sy c
9t
XX
3x
3t
sx
3t 3t
+ *Z + _«
By n
3t 3t
~ _J£ + _ZZ)
sy sz
) (II-l)
(11-2)
+ pg = o (n-3)
the continuity equation:
LH + iv + 3w = 0 (IM)
3 x 3y 3 z
the mass transport equation:
+ a(uc) + B(vc> + 9(wc) = a(Dx ?x) + 5(Dy ^y) + a(Dz 3z) + (II_5)
3t 3 X 3y 3 z 3 x 3y 3z p
11-20
-------
and an equation of state in the general form:
p = function (s, T) (II-6)
where x,y,z = right-hand Cartesian coordinates, with z directed
upward (I.e., "x" Indicates longitudinal direction,
"y" Indicates lateral direction, and "z" Indicates
vertical direction),
t = time, (T),
u, v, w ¦ x, y, z components of the Instantaneous velocity,
(L/T),
f = Coriolls parameter, (1/T),
p = density, (M/L3),
Tij = 1j component of stress tensor where 1, j « x, y, 2,
(M/LT2),
J
p = pressure, (M/LT ),
p
g = acceleration due to gravity, (L/t ),
3
c = constituent concentration, (M/L ),
o
Dx,Dy,Dz = components of diffusion coefficient, (L /T),
rp = source/sink^term, (M/TL3),
s = salinity, ( /••), and
T = temperature, (degrees).
II.6 REDUCING DIMENSIONS
Solutions of the full three-dimensional governing equations of motion and
mass transport are always expensive In terms of computer time and other
resources, and frequently are more elegant than Is necessary to simulate
the system being analyzed. Most numerical models simplify these equations
either by eliminating spatial dimensions considered not to be Important, by
time averaging (usually over a tidal cycle), or else by neglecting some of
the terms, such as the non-11 near convectlve acceleration terms. The most
frequent simplification is a reduction 1n the number of spatial dimensions
modelled. One of three simplifications are used:
11-21
-------
0
0
0
vertical averaging,
lateral averaging, or
cross-sectional averaging.
In addition, there are variations to these, such as layer averaging 1n
which the vertical (or lateral) direction 1s divided Into a series of
layers over which solution variables are assuned to be constant.
As an example, the most common form of estuarlne aodel simplification Is
vertical averaging. Equations (11-1)-(11-5) become
momentivn equations:
3(qxu) 3(qu)
T"»
(II-7)
3x
(11-8)
sy
continuity equation:
(11-9)
and mass transport equation:
a (he) , 8|V' , 3
-------
where
?
qy,q « x-, y-components of flow per unit width, (L /T),
u,v = x-, y- components of velocity, (l/T),
f « Coriolls parameter, (l/T),
p » density, (M/L^),
p = pressure, (M/LT ),
2
t ,Ttft e x-, y-components of surface shear, (M/LT ),
' 2i
Txb,Tyb * *"• ^components of bottom shear, (M/LT ),
Nh « horizontal momentum transfer coefficient, (lVt),
n s surface elevation above datum, (L).
c « constituent concentration,
2
Eh e horizontal dispersion coefficient, (L A),
K = decay coefficient, (l/T),
x.y = horizontal directions, (L), and
t = time, (T).
In Equation (11-10), the variable, c, can represent salinity, temperature,
non-conservative constituents, or water quality variables.
In reducing dimensions, it is important to remember what the solution
variables represent. Any form of numerical integration, or averaging,
produces variables which are averaged over the dimension of integration. In
the above example, Equations (II-7MII-10), the resulting velocities are
depth-averaged, and as such exhibit no variation with depth. If the system
being modelled exhibits vertical variability that is considered to be
significant, then it is inappropriate to use this type of model.
More often than not, field data can guide the modeler as to the
appropriateness of the simplification used. As an example, many river
estuaries are simulated using one-d1mens1onal (cross-sectional average)
models. These types of models assume that velocities are cross-sectionally
uniform. However, comparisons with field data may show observed velocities
which are 2 or 3 times greater than those simulated (e.g., Aldrlch, et al.,
11-23
-------
1963). This is because current meters are usually placed in the deeper,
swifter parts of the river and may measure maximum flow, rather than
average flows as predicted by the models.
II.7 TIDAL AVERAGING
A different reduction in numerical model complexity 1s found by performing
time averages over the tidal cycle period, T. This ellalnates the
unsteady, non-uniform flows in the estuary, and replaces them with
non-tidal or residual flows. This process 1s sumarlzed In Harleman
(1971).
Consider, for example, the unsteady, non-uniform, one-dimensional, mass
transport equation:
(11-11)
where
o
A = cross sectional area, (L ),
Q = flow, (L3/T),
El = longitudinal dispersion coefficient, (L A), and
K = decay coefficient.
This equation can be time averaged to give (Harleman, 1971):
(11-12)
where
3 river flow, (L^/T), and
overbar = time average over a tidal cycle.
11-24
-------
For a steady-state river flow (Q^ = constant) and a conservative substance
(r =0), the steady-state flow of Equation (11-12) 1s (Stommel, 1953):
P
«»Si• h (5fL it'
Another way to consider Equation (11-12) Is as a slack water approximation -
(O'Connor and D1 Toro, 1964; O'Connor, 1965) in which the concentration, 1s
calculated at successive high or low water slack tides:
As rr * qr rr " h <\E, rr1'+ VP" W (IM4)
where the subscript, denotes values at slack water.
In each of these approaches, 1t Is Important to understand what 1s, and
what 1s not represented by the equations. Both approaches are essentially
the same, with the exception of the time varying term 1n Equation (11-14),
and represent time averages over the tidal cycle, T. This means that
fluctuations of transport phenomena within the tidal cycle cannot be
resolved, and as such are treated -using the dispersion term, E^ or Eg, both
of which must be larger than the unsteady coefficient, E^» Equation
(11-11).
This can be a very useful approach, and not just in terms of computational
savings, provided that the system responds in an appropriate manner and
important information is not lost. At one extreme, consider the case of a
tidal regime with no river flow, = 0. Then all advectlve processes are
lost and replaced with a tidally-averaged dispersion coefficient.
II.8 DISPERSION COEFFICIENTS
The mass transport equation, Equation (11-5) contains dispersion
coefficients, D , D , D , which represent a combination of sub-grid
x y z
processes within the numerical discretization In the three principle
directions. The common forms of these coefficients and their
11-25
-------
representations after spatial and temporal averaging 1s worth some
discussion. We will also discuss briefly their relative Impacts within
more common numerical model schemes. An excellent background discussion of
mixing processes can be found In Fischer et al. (1979).
In three-dimensional models, one of two approaches Is often used. For
near-field models, such as close to ocean outfalls, it Is common to assign
constant values to the coefficients:
Dx c Cl» Dy * C2» Dz " C3 (11-15)
Further, at least horizontal isotropy Is often assumed, Cj » C2> In far
field models, where the entire depth of flow and perhaps stratification
become Important, the vertical coefficient may be made a function of
Internal flow parameters, usually characterized by the local or bulk
Richardson numbers:
e.g., (Leendertse et al., 1975)
Dz = Do e"3Rl {II-15)
where D„ = vertical dispersion coefficient for neutral
0 ?
stability condition, (L /T), and
R.j = local Richardson number
_ g(sp/sz)
2
p(3U/3Z)
For two-dimensional, 1aterally-averaged models, the approach is usually to
use a three dimensional formulation, and simply drop the lateral
coefficient. Model calibration provides any further adjustment to
coefficient values that reflect lateral averages.
In most two-dimensional, vertically-averaged models, the horizontal
coefficients are usually specified as constants, and 1n many cases,
Isotropy 1s assumed.
Perhaps the most critical selection for model dispersion coefficients is
the category of one-dimensional models—both dynamic and steady-state. For
11-26
-------
models that Include a dynamic description of one-dimensional hydrodynamic
processes, most coefficients are based on a formulation of the form:
El = KR|u|
(11-17)
2
where EL » longitudinal dispersion coefficient, (I A),
K = dlmenslonless dispersion coefficient,
R = hydraulic radius, (L), and
u « velocity, (LA)
that follows from the work of Taylor (1954) and Elder (1959). Similar
forms have been derived by Harleman (1964 and 1971, respectively):
where n = Manning's roughness coefficient (0.02-0.035, typically),
and
umav = maximum tidal velocity, (LA).
ma a
When the modeler applies time-averaging in the governing equations,
however, the choice of dispersion coefficients becomes much more difficult.
This is because the dispersive terms in the resulting time-average
mass-transport equation now contain representations of processes whose time
scales are less than the time over which averaging 1s performed. The most
conr.c: form of time averaging is over tiit tidal period, T. In this case,
the dispersive terms contain tidal fluctuations of velocity and constituent
mass.
Selection of dispersion coefficients, eJ, in one-dimensional, tldally-
averaged models is usually performed in one of three ways:
1. eJ ¦ constant (space, time) (11-19)
2. E^ = constant (time) (II-20)
El = 77 n|u|R5/6
(11-18)
3.
eJ = krqr/a
(11-21)
11-27
-------
In the first method, a uniform coefficient Is selected over time and space,
and calibrated to best fit observations. This is usually done when there
1s little data for calibration, and often leads to poor results when
adequate data become available for comparison.
In the second method, the coefficient is allowed to vary space only, and
Is held constant through time. Using this approach increases the number of
unknown coefficients to the number of boxes or nodes In the system,
resulting in Increased difficulty 1n calibration, though generally more
accurate calibrations.
The third approach, or variations thereof, attempts to reduce the number of
unknowns again to one—that is, the dlmenslonless coefficient, K. In doing
this, the approach is to relate the coefficient, eJ, to some property
(e.g., RQr/A in Equation (11-21)) that describes the variability found in
the system in trying to match the form of Equation (11-20). The objective
is to reduce the number of unknowns and yet achieve accurate calibrations
as is theoretically possible with Equation (11-20). In fact, even more
accurate calibrations may result 1f multiple data sets are available,
because the form of Equation (11-21) is also variable through time as QR
varies.
Unfortunately, in many systems, coefficients based on the form of Equation
(11-12) fail to achieve satisfactory results because the form of explicit
dependence (river flow, QR, in this case) is the wrong measure of system
variability. Such an approach works well for rivers where it was
originally conceived and tested, and probably works well for river
dominated tidal estuaries. However, let us explore the case in which the
tidal estuary Is dominated by the tide. To simplify the analysis, we will
make the following assumptions:
o the estuary is short enough that the water surface is almost
horizontal,
o the form of E^ by Equation (11-17) 1s adequate to describe
tidally-varying coefficients, and
o tidal forcing given by:
11-28
-------
n = a cos(wt)
(11-22)
where n = tidal elevation above MSL, (L),
a = tidal amplitude, (L)
w » tidal frequency = 2VT, (1/T),
T = tidal period, (T), and
t = time, (T).
These assumptions are generally reasonable for an estuary In which a
one-dimensional, mass transport model can be applied. From these
assumptions, the cross-sectional averaged velocity (u, positive downstream)
can be found from the continuity equation alone (Walton, 1978):
U = (Qr + Aws )/A = (Qr - Aws aw s1n(wt))/A (11-23)
2
where = upstream area of water surface, (L ), and
2
A = cross-sectional area, (L ).
The time-varying dispersion coefficient, E^, from Equation (11-17) Is then:
El = KR|Qr - Aws aw sin(wt)|/A (11-24)
This distribution is shown schematically in Figure II-7, along with the
resulting velocity distribution.
The further assumption is now made that the tidal-time average of the
unsteady mass transport equation leads to a dispersion coefficient, E^,
that Is proportional to the time average of E^ from Equation (11-24) (the
coefficient of proportionality reflects the effects of the constituent
gradient, ac/ax over the tidal cycle). This Is reasonable when one
considers the form of the coefficients chosen for nany one-dimensional,
steady-state models. From Figure 11-7, the velocity goes to zero at
t,and t0 = r: sin
1 L W
awAw;
for 0 - t < T
(11-25)
11-29
-------
Figure 11-7 TIME VARYING AND
RESIDUAL TIDAL FLOWS
11-30
-------
and thus:
f ^1 *2 P
ll ¦ T l/o ELdt -/tj ELdt + /t2ELdtJ »'-26'
" Til VT+2tr 2t2* + 2aAws(ltcos (wtj) -cos(wtj))]
If Qr Is sufficiently large that the velocity Is always positive
(downstream), then tj and t2 do not exist, and the steady-state dispersion
coefficient Is given by:
eJ = KRQr/A (11-27)
At the other extreme, if QR 1s small, then tj = 0, t2 s T/2 and Equation
(11-26) reduces to:
T 4aAws KR
E^ = (11-28)
Examining the results of Equations (11-26)-(11-28), one can see the
difficulty in obtaining dispersion coefficients for a steady-state model
(even assuming that such a model is a true representation of natural
processes). If the river flow dominates the system everywhere, then the
use of Equation (11-27) is justified. However, even 1n cases where there
1s a strong river Inflow, such as in the Potomac River, this formulation
may only apply 1n the upstream portion where QR dominates. In the
downstream section of the Potomac, tidal flows dominate and one might
expect the relationship of Equation (11-28) to hold. Between these two
sections, In which Equation (11-25) is satisfied, one might expect a
balance between river and tidal Influences. In this region, Equation
(11-26) could be used as a guide to coefficient selection, or a laborious
calibration could be followed with coefficients specified at each node or
box of the system.
11-31
-------
11.9 DECAY COEFFICIENTS
Non-conservative mass transport and water quality models contain a decay or
reaction kinetics term, of the form -Kc, where K is a decay coefficient and
c is the constituent concentration. A non-conservative mass transport
model takes the form:
|| + R « -Kc (11-29)
and a water quality model may have the general form:
+ R = -Ks (11-30)
0 *
where c = constituent concentration,
R = other terms of the equation,
K = decay rate, (1/T), and
s = constituent influencing decay.
These foTis are termed "first order" reactions and serve to describe such
processes in the majority of numerical models. Higher order reaction
kinetics are occasionally used in more complex water quality models.
Formulation of decay or reaction kinetics relationships 1n non-steady
models is generally not a problem. Usually, the main concern is over
numerical stability, through the selection of a time step, At, 1n an
explicit model simulation (most models use explicit schemes allowable time
step In which there is a maximum for numerical stability). If we neglect R
1n Equation (11-29) for the moment, an explicit approximation to the
remaining terms 1s:
cn+1 = cn(l - KAt) (11-31)
where n denotes time level.
11-32
-------
From Equation (11-31) one can see an obvious stability condition, often
overlooked, that:
t£l/K (11-32)
It 1s also Interesting to note that Equation (11-29), with R * 0, can be
solved directly:
cn+1 - cne"KAt (11-33)
which will always be stable. Unfortunately, the stability condition on
Equation (11-30) is not as obvious, but the condition of Equation (11-32)
should serve as a general guide.
There is a more fundamental problem when one looks at steady-state models,
particularly for high decay rates. Consider the problem of fecal coliform
fate modeling in which the decay coefficient represented by Tg0 (« 2.3A)
was much less than the tidal period T. Tidally averaged models could not
produce the same pattern of maximum conform values, and certainly not
their occurrence through time, as for an unsteady model.
Intuitively, one might expect a criterion, D, to be based on a ratio of the
T90 value of the non-conservative constituent or critical water quality
parameter, to the flushing time, F:
T90/F
(11-34)
As D —> 0 for a conservative substance, a steady-state nodel might be
applicable. As D >_ Dc, where Dc 1s a threshold value to be determined,
decay becomes important, and an unsteady model should be used. At present,
there Is no means to determine appropriate values of 0£ for given
tolerances of solutions.
11-33
-------
SECTION III
WATER QUALITY PROCESSES
III.l GENERAL
There are many chemical and biological actions and Interactions that
constitute water quality processes. The following section will describe a
variety of biochemical processes, however, the aost critical water quality
parameters to be considered as part of the wasteload allocation process are
dissolved oxygen, nutrients, chlorophyll-a, collforms and toxicants.
Dissolved oxygen (DO) is an Important water quality Indicator for all
fisheries uses. The DO concentration In bottom waters Is the most critical
indicator of survival and/or density and diversity for most shellfish and
an Important indicator for finfish. DO concentrations at mid-depth and
surface locations are also important Indicators for finfish. Assessments
of DO impacts should consider the relative contributions of three different
sources of oxygen demand: (a) net photosynthesis/respiration demand from
phytoplankton, perripbyton and rooted aquatic plants; (b) water column
demand due to decay of suspended organic matter and chemical reactions; er,d
(c) benthic oxygen demand. Assessments of the significance of each oxygen
sink can be used to evaluate the requirements for achieving the required
degree of pollution control.
The nutrients of concern in the estuary are nitrogen and phosphorus. Their
sources typically are discharges from sewage treatment plants and Indus-
tries, and runoff from urban and agricultural areas. Increased nutrient
levels lead to phytoplankton blooms and a subsequent reduction in DO
levels. In addition, algal blooms decrease the depth to which light is
able to penetrate, thereby adversely affecting submerged aquatic vegetation
populations in the estuary. Nutrient enriched waters can also produce
Increased perriphyton growth on submerged aquatic vegetation which blocks
the light and kills the vegetation.
III-l
-------
Sewage treatment plants are typically the major source of nutrients to
estuaries 1n urbanized areas. Agricultural land uses and urban land uses,
however, represent significant nonpoint sources of nutrients. Often
wastewater treatment plants are the major source of phosphorus loadings
while nonpoint sources tend to be major contributors of nitrogen. In
estuaries located near highly urbanized areas, aunlclpal discharges
probably will dominate the point source nutrient contributions. Thus, It.
Is Important to base control strategies on an understanding of the sources
of each type of nutrient, both In the estuary and 1n Its feeder streams.
The method of choice for controlling primary productivity In the tidal
fresh zone of an estuary (upper estuary), which is phosphorus United, 1s
phosphorus removal from municipal discharges, because point sources of
nutrients are typically much more amenable to control than nonpoint
sources, and because phosphorus removal from municipal wastewater
discharges 1s less expensive than nitrogen removal. However, the nutrient
control programs for the upper estuary can have an adverse effect on
control of phytoplankton growth 1n the lower estuary (i.e., near the mouth)
where nitrogen is typically the critical nutrient for eutrophication
control. This is because the reduction of phytoplankton concentrations 1n
the upper estuary will reduce the uptake and settling of the non-11miting
nutrient which is typically nitrogen, thereby resulting In increased
transport of nitrogen through the upper estuary to the lower estuary where
1t 1s the limiting nutrient for algal growth. The result 1s that reduc-
tions in algal blooms within the upper estuary due to the control of one
nutrient (phosphorus) can result in increased phytoplankton concentrations
in the lower estuary due to higher levels of the uncontrolled nutrient
(nitrogen). Thus, tradeoffs between nutrient controls for the upper and
lower estuary should be considered 1n performing wasteload allocations.
Chlorophyll-a, because It 1s easy to measure, 1s the most popular Indicator
of algal concentrations and nutrient overenrlchment which In turn can be
related to diurnal DO depressions due to algal respiration. Typically, the
control of phosphorus levels can limit algal growth 1n the upper end of the
estuary, while the control of nitrogen levels can limit algal growth near
the mouth of the estuary. However, these relationships are dependent upon
111-2
-------
factors such as N:P ratios and light penetration potential, which can vary
from one estuary to the next due to natural or man-generated turbidity in
the water column, thereby producing different limiting conditions within a
given estuary. Excessive phy topiankton concentrations, as indicated by
chlorophyll-a levels, can cause adverse DO Impacts such as: (a) wide
diurnal variations 1n surface DO's due to daytime photosynthetlc oxygen
production and nighttime oxygen depletion by respiration; and (b) depletion
of bottom DO's through the decomposition of dead algae. Thus, excessive
chlorophyll-a levels can deplete the oxygen resources required for bottom
water fisheries, exert stress on the oxygen resources of surface water
fisheries, and upset the balance of the detrltal foodweb In the seagrass
community through the production of excessive organic matter. Excessive
chlorophyll-a levels also result in shading which reduces light penetration
for submerged aquatic vegetation.
The transport, fate, and impact on biota of toxicants such as pesticides,
herbicides, heavy metals, and chlorinated effluents are also Important
factors to consider. The presence of certain toxicants 1n excessive
concentrations in the water column or within bottom sediments can impact
fisheries propagation/harvesting and seagrass habitat. This can occur in
estuary segments which satisfy water quality criteria for DO, chlorophyll-a,
nutrient enrichment, and fecal coliforms.
III.2 BIOCHEMICAL PROCESSES
Several biological and chemical parameters or constituents can be
investigated separately because their concentrations are Independent of
other constituent concentrations. Other constituent concentrations,
however, are dependent on the concentrations of other constituents. The
following discussion begins with those parameters which are Independent and
proceeds toward those which are most Interdependent.
111.2.1 CONSERVATIVE SUBSTANCES
Conservative substances neither react with other constituents nor do they
decay. They are only dependent on the loads from the headwater and tidal
111-3
-------
boundaries,, and from the point and nonpoint contributions to the estuary.
Such substances Include chlorides, alkalinity, total dissolved solids,
total nitrogen, total phosphorus, and sometimes heavy metals. The
processes surrounding heavy metals can be very complicated. In model
applications, however, they are usually considered as conservative
substances»
The kinetic representation for a conservative substance Is:
II1.2.2 BIOCHEMICAL OXYGEN DEMAND
The ultimate biochemical oxygen demand (BOD) includes carbonaceous and
nitrogenous BOD. Most model applications break up this total Into Its
i
carbonaceous and nitrogenous components. The nitrogenous component 1s
accounted for within the analysis of the nitrogen series. The change in
BOD concentration can be represented by a first order decay rate. If the
total carbonaceous and nitrogenous BCD is being considered as one con-
stituent, then the decay rate must reflect the carbonaceous and nitrogenous
processes- On the other hand, if nitrogenous BOD is considered separately,
then the appropriate carbonaceous rate constant must be selected. BOD
decreases can also be attributed to the rate of loss due to settling. The
BOD reduced as a function of the decay rate exerts an oxygen demand on the
dissolved toxygen in the water column while the BOD loss due to settling
becomes a teenthic oxygen demand.
The rate crt* change of BOD is formulated as a first order reaction. If
carbonaceous BOD and settling are considered the representation of the BOD
decay and settling 1s:
(III-l)
where
s = conservative substance
d(BOD)
dt
= - K.(BOD) - K3 (BOD)
1 T
(III-2)
111-4
-------
where
BOD = concentration of carbonaceous BOD,
Kj = rate of decay of carbonaceous BOD,
* settling rate of BOD,
d = depth.
111.2.3 FECAL COLIFORMS
Fecal conforms are affected only by waste Input strength and a decay rate.
The reduction in fecal conforms 1s a function of the coll form die-off rate
and the concentration of the coliforms 1n the water column. The equation
that describes the die-off of fecal coliforms (first order kinetics) is:
^=-K4E (II1-3)
where
E = concentration of coliforms,
K, = coliform die-off rate.
H
111.2.4 PHOSPHORUS
Sources of phosphorus include wasteload, incremental inflows and benthic
deposits. The phosphorus cycle is less complicated than the nitrogen cycle
because for a simplistic representation, its only Interaction 1s with
algae. This representation does not include Interactions with fish,
zooplankton, benthic animals, organic sediment and detritus. One approach
Is to consider only the dissolved orthophosphorus and relate Its concen-
tration change to algae growth and respiration, and a benthic source rate.
Another approach would be to consider two components of phosphorus: the
non-living organic phosphorus and the orthophosphorus. In this scheme,
111-5
-------
organic phosphorus 1s decomposed with first order kinetics to ortho-
phosphorus. Organic phosphorus can also be lost due to settling where it
becomes a benthic source of phosphorus. The source of organic phosphorus
1s from algal respiration. For the second component, orthophosphorus, the
source 1s the decomposed organic phosphorus and the uptake Is due to algal
growth. Another source of orthophosphorus which could be considered 1s the
release from sediment.
A graphic example of the phosphorus cycle Is shown In Figure I INI. The
figure presents the various actions and Interactions of phosphorus,
Including not only algae or phytoplankton as discussed above, but also the
link to zooplankton which 1s discussed 1n a subsequent section.
The decomposition of organic phosphorus to orthophosphorus 1s represented
with first order kinetics; additional loss can be attributed to settling.
The source of organic phosphorus 1s algal respiration. The general
formulation is thus:
ORGP = concentration of organic phosphorus,
K5 = rate of decomposition of organic phosphorus,
Kg = settling rate of organic phosphorus,
d = depth,
f#p c fraction of algal blomass which is phosphorus,
r. = respiration rate of algae,
a
A s algal blomass concentration.
Orthophosphorus does not decay. However, its sources and sink can be
represented by the following formula:
d(ORGP)
dt
- K,(0RGP) - K6 (ORGP) +
5 T
(III-4)
where
(111-5)
III-6
-------
Sinking
r~
PHYTOPLANKTON
Growth
Respiration
TOTAL
NONACCESSIBLE
PHOSPHORUS
Sinking
PHOSPHORUS
DETRITUS
A
ORGANIC
PHOSPHORUS
INORGANIC
PHOSPHORUS
SEDIMENTS
ZOOPLANKTON
T T t_
c
o
~-
VI
o<
Ul
o
z
o
Q
Respiration
Figure 111 -1. Phosphorus Cycle (modified .lfter Canalc, et aj_., 197G).
-------
where
P = concentration of orthophosphorus,
Kg = rate of decomposition of organic phosphorus,
ORGP * concentration of organic phosphorus,
f a fraction of algal blooass which Is phosphorus,
9a = specific growth rate of algae,
A » algae concentration,
*7 * benthlc source rate of orthophosphorus,
d ¦ depth.
III.2.5 NITROGEN
The nitrogen cycle can be analyzed simply as Its two najor components
ammonia and nitrate or with more detail considering all four components.
For this first case, only ammonia nitrogen and nitrite-nitrate nitrogen are
considered. Ammonia nitrogen decays with a first order rate to the sum of
nitrite + nitrate and by doing so produces an oxygen demand. This approach
»
1s feasible because nitrite serves only as an intermediate product and its
oxidation to nitrate is rapid. Under this scheme, a source of ammonia is
from respired (dead) algal blomass which 1s resolublllzed as ammonia
nitrogen by bacterial action. Another source of ammonia that can be
considered is the benthlc source. The nitrite-nitrate which 1s produced
from the ammonia decay is reduced as a function of the algal growth.
In a more extensive scheme, organic nitrogen, ammonia nitrogen, nitrite
nitrogen, and nitrate nitrogen can be considered separately. Organic
nitrogen 1s decomposed to ammonia using first order kinetics. Settling can
also be considered as a loss of organic nitrogen from the water column.
The source of ammonia nitrogen 1s from the decomposed organic nitrogen In
the water column and from the benthos. Ammonia Is lost through a first
order decay rate, settling and uptake during algal growth. (Note that in
this scheme, algal growth relies on ammonia as well as nitrate.) Nitrite's
source 1s the decayed ammonia and the nitrite 1s decayed to nitrate by
first order kinetics. The source of nitrate 1s then a function of the
111-8
-------
amount of nitrite decayed, and the benthlc source rate for nitrate. A sink
or reduction of nitrate is the nitrate uptake during algal growth.
An example of the nitrogen cycle is presented In Figure I11-2. The figure
shows the relationships of the various forms of nitrogen and their link to
phytoplankton (algae) as discussed above. Figure III-2 also shows the
links to nitrogen detritus and zooplankton which are discussed In a
subsequent section.
For the scheme where all four forms of nitrogen are to be considered, the
governing transformations are given below.
For Organic Nitrogen:
= - KgORGN - K90RGN + f r A (III-6)
ot o -g— an a
where
For Ammonia:
ORGN = organic nitrogen,
Kg = rate of decomposition of organic nitrogen,
Kg = settling rate of organic nitrogen,
d = depth,
fan = fraction of algal biomass which is nitrogen,
r, = respiration rate of algae,
0
A = concentration of algae.
dNH3 - K10 - K..NH3 - K
~r~ 11 ~r
-7— - Kft0RGN + 10 - K..NH3 - "12 NH3 - P.f_9,A (III-7)
ot o —t~ li —a— a an a
II1-9
-------
Growth
SinKinq
total
NONACCESSI0LE
NITROGEN
I
SEOIMENTS
I F
"• PHYTOPLANKTON •
Growth
Respirotion
Sinking
NITROGEN
DETRITUS
4
c
o
o«
UJ
ZOOPLANKTON
T
o
%-
3
o
2
o
at
o
organic
NITROGEN
Respiration
Respiration
AMMONIA)
NITRATES
Figure 111-2. nitrooen Cycle (r,;or!if ied after Carrnlo, et a]^., 197C).
-------
where
NH3 = anmonia,
Kg = rate of decomposition of organic nitrogen,
ORGN « organic nitrogen,
K^q * benthlc source rate of amonla,
d * depth,
*11 s rate b^olo91ca1 oxidation of amonla,
*12 * settlIng rate of anmonia,
P# « fraction of algae blonass that prefers NH3 for growth,
f.„ * fraction of algal bloaass which 1s nitrogen,
an
ga c specific growth rate of algae,
A = concentration of algae.
For Nitrite:
d(N02) =
-------
fan = fraction of algae biomass which 1s nitrogen,
q. * specific growth rate of algae,
Q
A = algae,
= benthic source rate of nitrate.
111.2.6 NITROGEN AND PHOSPHORUS WITHOUT ALGAE, SETTLING OR BENTHIC SOURCES
If algal growth and respiration are not a Major concern, then the factors
which act as sources or sinks within the nitrogen cycles can be deleted.
As for phosphorus, If algal blomass, settling, or benthic release are not
considered, then for studying only orthophosphorus It would be considered a
conservative substance. If organic phosphorus and orthophosphorus are
considered, then the only action would be the loss of organic phosphorus
due to its decay rate and the Increase of orthophosphorus from the decayed
organic phosphorus.
Likewise, if algae, settling or sediment release, which govern the various
species of nitrogen are not Included, then only the ammonia and nitrite
decay rates will produce the different components of the nitrogen cycle.
111.2.7 ALGAE
In many studies, chlorophyl1-a is used as an indicator of algal blomass.
In modeling, the chlorophyl1-a concentration Is converted by a factor to
the algal blomass concentration. The change 1n algal blomass concentration
can be represented simply by the algal growth as a source, which adds
oxygen to the system, and by algal respiration as a loss, which depletes
the oxygen in the water column. In addition to these two main processes,
algal settling and predation can be considered as sinks for the algal
biomass.
Algal production is coupled to the available nutrient supply and the light
intensity. In some formulations, to determine the growth rate, a maximum
growth rate is multiplied by a light limitation factor, a nitrogen limi-
tation factor, and a phosphorus limitation factor. In others, the maximum
111-12
-------
growth rate is multiplied by the light limitation factor and the minimum of
the nitrogen and phosphorus limitation factors.
The discussion above pertains mainly to green and blue-green algae. In
some cases, diatoms may be an important factor 1n the oxygen balance and
the food chain. Diatoms are algae whose cell walls contain silica. They
require much more silica than do the other types of algae. The diatoms
will uptake dissolved silicon during the growth period and will release
silicon during respiration.
A simple equation that governs the growth and production of algae is
formulated as follows:
H " r,A ««-"»
where
A = algae concentration,
ga = specific growth rate of algae,
= respiration rate of algae.
Two additional processes can be added to account for the loss of algae due
to settling and predation. With these two terms, the expanded equation is:
J = g A - r A - K15 A - K..A (III-ll)
at a a —g— 10
where (in addition to the terms above)
K15 = settling rate for algae
*16 = Preda^on rate
As discussed above, the specific growth rate of algae Is coupled to the
availability of required nutrients and light.
111-13
-------
The specific growth rate (ga) can be determined by the following equation:
ga = specific growth rate of algae,
gamax B maximum specific growth rate of algae,
LL * light limitation factor,
MIN (L , L_) = the minimum value of L_, the nitrogen limitation
p factor, and Lp, the phosphorus limitation factor.
The light limitation factor 1s defined as:
h • W LL MIN (Ln. V
(111-12)
where
(111-13)
where
x = light extinction coefficient,
d = depth,
*L = empirical half saturation constant for light,
L = light intensity.
The nitrogen limitation factor is defined as:
Ln s (NH3+ N03)
(NH3 + N03) + K
n
(III-14)
where
NH3 = ammonia concentration,
NO3 = nitrate concentration,
Kn = empirical half saturation constant for nitrogen.
111-14
-------
The phosphorus limitation factor is defined as:
Lp = — (111-15)
P + KP
where
P » orthophosphate concentration,
Kp = empirical half saturation constant for nitrogen.
III.2.8 DISSOLVED OXYGEN
A simplistic approach to the analysis of dissolved oxygen (DO) concentra-
tions would be to consider the DO reaeration process at the water surface
and the DO uptake from the 800 decay. If this approach Is used, then the
reaeration rate and BOD decay rate are actually representing all the other
water quality actions and reactions which may be adding to or depleting the
supply of DO in the estuary. If the nitrogen cycle Is considered, then 1n
addition to the BOD uptake, the oxidation of amnonla to nitrite, and
nitrite to nitrate will deplete the supply of oxygen. For those cases
where sludge deposits or other sediment conditions which exert an oxygen
demand on the water column above the sediment bed, a benthic oxygen demand
can be included in the processes to describe the dissolved oxygen
concentration. Where algal blomass 1s considered 1n the water quality
processes of the estuary, DO is supplied to the system during algal growth
and DO is taken from the system during algal respiration.
The change 1n dissolved oxygen concentration, as discussed above, Is a
function of many other water quality parameters. Figure II1-3 demonstrates
graphically the Interrelationship and mechanisms of change formulated as
part of one water quality model, the Dynamic Estuary Model (Genet, et al.,
1974). This diagram which shows the relationships of BOD, nitrogen, and
algae to dissolved oxygen, also displays the models mechanism of change for
phosphorus, pesticides, and heavy metals.
III-15
-------
A Afl'triON - OE AERATION R RCSOLUBfLIZEO OURIMC RESPIRATION
BO Bl'K hi MIC At OXIDATION RD RESOLUBHI2EO WITH DECAY
G CC'J i'Mf.O DURING S REMOVED BY SETTLING
Al' r' r,w*'™ UO UPTAKE WITH DECAT
° a*','m'",*rS«HU'"NC UR UPTAKE WITH respiration
P PHI ' I'llATION
Figure 111-3. Interrelation -ins and Mechanises of Change in the Dynar.:ic Estuary
Model (Genet ( I .11, 1374).
-------
Many actions and reactions of water quality constituents increase or
decrease the dissolved oxygen concentration in the water body. The rate of
change of dissolved oxygen can be described in the following form:
^ - K2(0*-0) + (kjga - k2r#)A - K^BOD)
- *17 - k3Kn(NH3) - k4K13(N02) (111-16)
d
where
0 * dissolved oxygen concentration,
0* » saturation concentration of dissolved oxygen at the
local temperature, pressure and chloride
concentration,
*2 = reaeratlon rate,
k, = rate of oxygen production per unit of algae during
photosynthesis,
ga = specific growth rate of algae,
k2 = rate of oxygen uptake per unit of algae respired
>*a = respiration rate of algae,
A = concentration of algae,
= rate of decay of carbonaceous BOD,
BOD = carbonaceous biochemical oxygen demand,
Ki7 = benthic oxygen demand,
d = depth,
k3 * rate of oxygen uptake per unit of amnonla oxidation,
K11 = rate biolo9^ca1 oxidation of ammonia,
NH3 * ammonia concentration,
k^ « rate of oxygen uptake per unit of nitrite oxidation,
k13 = rate °* ox*dat^on nitrite,
N02 = nitrite concentration.
III-17
-------
III.2.9 TOXICANTS
The transport and transformations (I.e., the fate) of toxic substances can
be very complex. However, many heavy metals are considered as conserva-
tives and organic chemicals are considered to decay using first order
kinetics. Toxic substances are not only transported and transformed 1n the
water column, but bottom sediment Is also a transport Medium for toxicants
which can remain 1n the sediment for years.
Unlike many conventional pollutants, such as BOD, toxic substances are not
necessarily transformed Into harmless substances. In soae cases, they are
tranformed Into equally toxic substances or Into a substance which Is more
toxic than the original substance. The primary transformation processes
Include photolysis, hydrolysis, and blodegradatlon.
Photolysis
Photolysis Is the process in which the absorbtlon of light causes chemical
decomposition of the toxicant. There are two general types of photolysis;
direct and sensitized (Tetra Tech, 1982). Direct photolysis occurs when
the toxic substance reacts to direct light which it has absorbed. Sensi-
tized photolysis, or photosensitization, occurs when a molecule which has
absorbed light transfers Its excess energy to another molecule which
absorbs the energy. The overall rate of photolysis Is the sum of the two
types. The reaction kinetics can be expressed as a first order decay as
follows:
f--KpC (111-17)
where
C * toxicant concentration,
Kp = sum of photolysis rates,
III-18
-------
= Kd + Ks
where
Kd « direct rate,
Ks s sensitized rate.
Hydrolysls
The toxicant may also react chemically with the H+ and OH* Ions of water to
form a weaker substance. This process Is known as hydrolysis. Hydrolysis
can occur by microbial meditated reactions or abiotic reactions (Tetra
Tech, 1982). The microbial actions become part of the process of blo-
degradatlon as discussed below. Abiotic hydrolysis can be expressed as a
first order decay as follows:
H - - Kh C (111-18)
where
C = concentration of toxicant,
Kh = specific hydrolysis rate constant.
Biodegradation
Many toxic substances are transformed by microbial organisms. In this
process of biodegradation, the organisms metabolize the substance and
change Its form and level of toxicity. There are two metabolic patterns 1n
the process of biodegradation (Tetra Tech, 1982). The first, growth
metabolism, occurs when an organic toxicant Is used as a food source by the
microorganism. The second, called cometabolIsm, occurs when the organic
toxicant is transformed by the microorganism but the organism does not
derive any benefit for growth from the reaction. These two processes have
different rates of degradation.
Ill—19
-------
For growth metabolism, first order decay can be applied to describe the
kinetics in the aquatic environment. The formula is:
(111-19)
where
C * concentration of toxicant,
KB s biodegradation rate constant
For cometabollsm, the rate 1s directly proportional to the size of the
microbial population. The process can be represented as a second order law
as follows:
111.2.10 AQUATIC ECOSYSTEM
In addition to the processes discussed above, other processes of an eco-
system can affect and be affected by the water quality in an estuary. A
conceptual model of an aquatic ecosystem Is given In Figure III-4 (Chen and
Orlob, 1971).
An aquatic ecosystem is comprised of water, Its chemicals and various life
forms: bacteria, algae, zooplankton, benthos, and fish, among others.
Biota respond to nutrient availability and to other environmental con-
ditions that affect growth, respiration, decay, mortality, and predation.
Abiotic substances, derived from air, soil, tributary waters and the
(111-20)
where
C = concentration of toxicant,
Kb2 = second-order biodegradation rate,
B = bacterial population.
Ill-20
-------
is ^
3ENTHIC
FISH
ANIMAL
FOOD
Figure 111-4. Conceptual Model of an Aquatic Ecosystem
(Chen and Orlob, 1977)
II1-21
-------
activities of man, are inputs to the system that exert an influence on the
estuary life structure.
The fundamental building blocks for all living organisms are nutrients.
With solar radiation as the energy source, these Inorganic nutrients are
transformed Into complex organic materials by photosynthetlc organisms.
The organic products of photosynthesis serve as food sources for aquatic
animals. It 1s evident that a natural succession up the food chain occurs
whereby inorganic nutrients are transformed to blomass and ultimately are
passed to man.
Biological activities generate wastes, consisting of respired nutrients,
dead cell material and excrete, which Initially are suspended but settle to
the bottom to become organic sediments. Detritus and organic bottom
sediments decay with the attendant release of the original abiotic sub-
stances. These transformations Include the nitrogen and phosphorus cycles
and result in a natural "recycling" of nutrients within an aquatic eco-
system.
Specific processes not discussed in the previous sections are presented
below:
Zooplankton
Zooplankton feed on the phytoplankton (algae) depending on the abundance of
the algae and the zooplankton's preference for various types of algae. The
concentrations of zooplankton depend on their growth rate, mortality rate,
respiration rate and fish predation.
Benthic Animals
Benthic animals use organic sediment as a food source and are grazed by
fish. The benthic animal density 1s a function of the benthos growth,
mortality and respiration rates, and fish predation.
Ill-22
-------
F1 sh
F1sh growth, respiration and mortality are a function of the dissolved
oxygen concentration and food availability. F1sh are typically divided
into herbivores and carnivores. Herbivores feed principally on living
plants, while carnivores feed principally on anlaals that they kill.
Another type, omnlvore, feeds on plants and animals alike. F1sh popu-
lations can be reduced by the top-carnivores and by fish harvest by man.
Detritus
Detritus consists of dead zooplankton and suspended excreta derived from
zoopl ante ton and fish. Detritus 1s removed from the system by sedimentation
and decay.
Organic Sediment
Organic sediment is the food source for benthlc animals and 1s composed of
dead biota. Algae and detritus are converted to organic sediment when they
settle to the estuary bottom. Sediment decay serves both as a dissolved
oxygen sink and a source of inorganic nutrients.
III.3 REACTION RATES AND CONSTANTS
The chemical and biological reactions that occur in the biochemical
processes are dependent on various reaction rates and physical constants.
Some of these coefficients are constant and some are temperature dependent.
Table III-l lists several of the more commonly used conventional
parameters, gives the units and possible ranges of the reaction rates for
each parameter. Care must be taken In applying these coefficients. Some
are highly variable and the values and units of others are dependent on the
particular formulation in a given estuary model. A more extensive
literature review of rate parameters used In surface water quality models
can be found in "Rates, Constants, and Kinetics Formulations In Surface
Water Quality Modeling" (Zison, et al., 1978).
II1-23
-------
TABLE III-1
REACTION r'Tr". AND CONSTanTS FOR CONVENTIONAL POLLUTANTS
RANGE OF TEMPERATURE
DESCRIPTION UNITS VALUES DEPENDENT RELIABILITY
Fraction of algae blomass mg N 0.07-0.09 No Good
which 1s N mg A
Fraction of algae blomass mg P 0.012-0.015 No Good
which 1s P mg A
02 production per unit of mg 0 1.4-1.8 No Good
aigae growth mgT
0» production per unit of mg 0 1.6-2.3 No Fair
algae respired mgT
0? uptake per unit of NH, mg 0 3.0-4.0 No Good
oxidation mgR"
Op uptake per unit of N0~
oxidation
mg
mg 0 1.0-1.5 No Good
mg N
Maximun specific growth 1 1.0-6.0 Yes Good
rate of algae day
Algae respiration rate 1 0.01-0.5 Yes Fair
day
Rate constant for biological 1 ,0.05-0.5 Yes Fair
oxidation of NH.J-NO2 Bay
Rate constant for biological 1 0.5-2.0 Yes Fair
oxidation of N02-N03 Hay
Local settling rate for ft 0.5-6.0 No Fair
algae (lay
Carbonaceous BOD decay rate 1 0.05-2.0 Yes Poor
day
Reaeratlon rate 1 0.0-100 Yes Good
day
CoHform die-off rate _1 0.5-4.0 Yes Fair
day
Nitrogen half-saturation mg 0.1-0.4 No Fair to Good
constant for algae growth 1
Phosphorus half-saturation mg 0.03-0.05 No Fair to Good
constant for algae growth 1
Light half-saturation Kcal/m^/sec 0.002-0.006 No Good
constant for algae growth
rrr^
-------
Toxicant reaction rates are highly variable and depend on the particular
pollutant under consideration, and on the transformation process or
processes being simulated by the model. For example, 1f for a particular
toxicant the abiotic hydrolysis rate Is 20 times faster than the bio-
degradation rate, then the simulation of the transformation can neglect the
blodegradatlon process without significantly Impacting the model result. A
good source of reaction rates for a wide range of compounds for blode-
gradatlon, near-surface direct photolysis and hydrolysis Is available in
"Water Quality Assessment: A Screening Procedure for Toxic and Convent-
ional Pollutants - Part 1 (Mills, et al., 1982).
The references cited for Information on reaction rates (Zlson, et al.,
1978; and Mills, et al., 1982) provide a basic starting point for selecting
various reaction rates and constant. Documentations and users manuals for
estuary models may also contain ranges of the reaction rates applied In the
particular model. The final selection of the values for many of the
reaction rates and constant should be made during model calibration and
verification.
111.3.1 REAERATION RATE
It is important to obtain good estimates of all the reaction rates. Many
initial estimates of the rates can be obtained from the analysis of field
and laboratory water quality data. In most model formulations the reaction
rates are input directly Into the model.
In this section additional discussion is provided concerning the reaeration
rate because 1t 1s highly dependent on the hydrodynamlc properties of the
estuary, and some models Include formulas which calculate the K2 rate.
There have been a variety of studies which have produced equations for
determining the reaeration rate. Many of them rely on the velocity and
depth to calculate the reaeration coefficient. Most of these formulations
have been developed from river and stream studies, and they may not be
applicable to estuary studies. Zlson, et al. (1978) relate that for
modeling non-stratified estuaries, the equation by O'Connor (1960) has
III-25
-------
probably been the most widely used formulation which contains velocity and
depth. O'Connor's expression is:
0.5
(111-21)
where
*2 " reaeratlon rate,
Dm e molecular d1ffus1v1ty of oxygen,
UQ = mean tidal velocity over a complete tidal cycle,
H = average depth at a section over the tidal cycle,
and any consistent units are used.
Several estuary models include this formulation. However, models also
allow for user input of the reaeration coefficients. Therefore, like all
other reaction rates, the final Kg rate will be determined during the
process of model calibration and verification.
111.3.2 TEMPERATURE DEPENDENCE
All reaction rate constants and some other factors (except the saturation
concentration of oxygen) that are known to be temperature dependent are
usually formulated by applying an exponential temperature adjustment factor
to the reaction rate at 20#C. The equation is:
(I II-22)
where
Kj » reaction rate at temperature T,
T = ambient temperature of water body 1n #C,
*2q = reaction rate at 20°C,
6 = empirical constant for a given reaction rate.
111-26
-------
The temperature adjustment factor, 0, varies for different reaction rates.
Different Investigators have used different adjustment factors for the same
reaction rate. Values of the temperature adjustment factors are presented
by Zlson, et al. (1978).
III.4 TIME AND SPACE SCALES
The time and space scales as they relate to water quality processes depend
on the problem being addressed. Time scales relate to the time cycle being
simulated and the duration of the total simulation. Space scales relate to
the longitudinal, lateral, and vertical definitions required.
III.4.1 TIME SCALES
The major temporal dimensions are those considered by steady state, t1dally
averaged and real time models. The selection of a time scale will depend
on, for example, whether the problem 1s to predict the summer chlorophyll-a
concentration from the spring load of nutrients or the diurnal dissolved
oxygen variation as a function of algae photosynthesis and respiration.
Real time models which simulate the tidal cycle are appropriately used for
analyzing changes which occur within a tidal cycle. These models can
simulate the estuary response over short durations of nonpolnt source loads
from a storm event and point source spills. Whenever 1t Is desirable to
simulate the concentration and location of a waste plume, In a tidal
estuary, a real time model must be used. Where minimum or maximum water
quality criteria are given at any time in addition to a dally average
value, then a real time model can simulate the variations over the tidal
cycle and predict the minimum or maximum constituent concentration that
occurred during the day.
If diurnal variations are Important to the wasteload allocation study, then
real time models must be used. They can be used to predict the diurnal
dissolved oxygen variation as a function of algal photosynthesis and
respiration.
III-27
-------
Figure 111-5 Illustrates a typical pattern of diurnal DO response. The
primary points of interest on this curve are the points labeled A and £.
The value of the dissolved oxygen at point A 1s taken to represent the
"average" DO concentration, Ignoring the diurnal effects produced by plant
comnun1t1es. The dissolved oxygen deficit, C-A, represents the deficit
caused by BOD exertion. The DO at point Bis the minimum DO for the day.
The dissolved oxygen deficit at this point, C-D, represents the net total
community respiration on the stream oxygen resources. The magnitude of the
deficit, A-D, can be considered to represent the maximum deficit over the
dally cycle attributable to aquatic plant respiration.
Steady state or tidally averaged models cannot predict the water quality
variation over a tidal cycle. They are useful in predicting larger term
(daily or seasonal) effects of the actions and interactions of the water
quality constituents. For example, they can be used to predict the growth
of algal blooms which may take several days.
It is also important to consider the total duration of the model simula-
tion for temporal dimensions other than steady state. The model must
simulate a long enough period of time so that the water quality parameters
have had enough time to react and reach their minimum or maximum values. A
large oxygen consuming load from a localized storm event In one part of the
estuary watershed may take several days to produce the minimum dissolved
oxygen concentration in another, downstream, part of the estuary. The
simulation period must be long enough to show the beginning of the
dissolved oxygen recovery In order to demonstrate that the minimum
dissolved oxygen sag value has occurred. As another example, consider the
simulation of fecal conform die-off from a storm or point source by-pass.
If the investigator 1s Interested 1n the time when 90 percent of the
coliform population has died-off (T90), then the duration of the simulation
may have to be half a day or several days, depending on the die-off rate
used.
In the above discussions of biochemical processes, reaction kinetics were
frequently described by a decay rate or reaction rate, K. This can be
111-28
-------
TIME (hrs.)
Figure 111-5. Diurnal Dissolved Oxygen Variation
-------
converted to a process rate time scale characterized by the time to achieve
90 percent reduction, T90, by:
T90 = 2.3/K {III-23)
This biochemical time scale can then be compared with physical time scales
to select appropriate processes.
111.4.2 SPACE SCALES
Space scales are determined to adequately model the longitudinal, lateral
and vertical dimensions. Models are usually developed along the horizontal
with various segments or 1n a node-link manner. The longitudinal distance
between nodes or segments where water quality calculations are made must be
spaced so that they will adequately simulate the spatial variability 1n the
water quality and biological communities. The distance must be small
enough to simulate the actual maximum or minimum constituent concentrations
of concern. For example, If under certain conditions the dissolved oxygen
sag occurs a distance of 2 km from the point of discharge, then the
distance between water quality computations cannot be greater than 2 km or
the model would inaccurately locate the point of minimum dissolved oxygen.
In addition to defining the proper longitudinal scale for water quality
computational purposes, it is Important to design the length of the
segments or links in order to adequately receive Important point and
nonpoint sources of pollution as Input to the model. This 1s not usually a
problem if variable length segments or links can be accommodated by the
model.
For a very wide estuary or wide segments of an estuary, It may be important
to show the lateral variations of water quality constituent, thus requiring
a two-dimensional network. Concentration will vary laterally 1n a wide
estuary especially near the major points of discharge where the pollution
load has not been completely mixed across the estuary. It Is possible that
a stream standard could be violated on one side of the estuary but not on
the other side. The physical properties such as depth and velocity may
III-30
-------
also vary laterally across the estuary. This can affect the prediction of
the reaeration rates which are a function of velocity and depth, and
thereby affect the dissolved oxygen prediction.
Vertical space scales can also be Important In those estuaries which
stratify, that 1s, where a large density gradient exists between the upper
freshwater and the lower saltwater region of an estuary* At the depth of
the greatest gradient difference (pycnocllne), transfer of water quality
constituents from the freshwater layer to the saltwater 1*yer and vice
versa Is Inhibited. One major factor In this phenomenon Is the variability
of the dissolved oxygen on the vertical scale. The reaerated surface
waters cannot mix with the bottom waters and, therefore, the dissolved
oxygen concentrations 1n bottom waters becomes depleted by the oxygen
consuming constituents and benthos. Major changes can occur In the aquatic
ecosystem if the dissolved oxygen concentrations approach or go to zero in
the bottom waters. Models which can formulate networks with vertical
slices or levels instead of a system which 1s completely mixed vertically
can be applied for those estuaries which are highly stratified.
280/3
III-31
-------
SECTION IV
FRAMEWORK FOR MODEL SELECTION
The approach to numerical model selection In the past has been essentially
Intuitive, with a tendency to ush one's own model rather than choose the
best model to do the job. In this section, we will 1«y out a stepwise
framework which can be used as a basis for model selection.
The rationale behind the framework Is to Identify and evaluate the
Importance of physical/chemical/biological characteristics of the study
area and to define a set of objectives for the study. The method of
selecting an appropriate model Is then to Identify the set of available
models that can simulate the Important processes within the time and
spatial scales of the study. These scales define bounds with which the
study Is performed. These scales are then divided into time and space
Intervals which provide resolution within the study bounds.
The proposed framework has eleven steps (see Figure IV-1):
1. Develop a conceptual model;
2. Develop a definition of complete mixing;
3. Define far-field dimensions which cannot be reduced;
4. Determine time and spatial scales of processes and constituents;
5. Determine time and spatial scales of regulations;
6. Determine which spatial scales can be neglected at the study scale;
7. Determine whether a fully dynamic model Is needed;
8. Determine desired spatial and temporal resolution;
9. Select form of the dispersion coefficient;
10. Check data availability; and
11. Select appropriate model(s).
IV-1
-------
Figure IV-1 FRAMEWORK FOR MODEL SELECTION
IV-2
-------
IV.1 CONCEPTUAL MODEL
A useful starting point for numerical model selection is to conceptualize
the system being studied. This can be done either as a set of equations
describing the various physical/chemical/b1olog1cal processes, a written
description of them, or perhaps, most usefully, a schematic representation
of them. The figure 1s perhaps the most useful form, as one can readily
visualize the system's processes. The schematic representation can be 1n
the form of a diagram of the system and Its processes (Figure IV-2) or else
In the form of relationship charts of parts of the system (Figure IV-3).
The purpose of this step is to assimilate and present all the available
knowledge of a system In a way that major processes and ecologic
relationships can be evaluate for Inclusion 1n the numerical model
description. The conceptual model Is the starting point from which
systematic reductions 1n complexity can be made which will provide an
adequate representation of the system, while meeting the objectives of the
study.
IV.2 DEFINITION OF COMPLETE MIXING
Complete mixing in a numerical model 1s a theoretical concept only. This
1s because given any model with spatial resolution, dispersion 1s treated
as a gradient process. Only in the limit as t can complete mixing be
achieved numerically. It thus becomes necessary, 1n a practical sense, to
develp some definition of complete mixing over a spatial dimension that
provides an acceptable point at which uniformity In that spatial dimension
can be assumed and that dimension neglected. For example, if we wish to
use a one-dimensional, cross-sectlonally averaged, mass transport model,
the assumption 1s Implicitly made that actual concentration deviations from
the cross-sectional mean are acceptable within an error tolerance.
There are several way 1n which a definition might be established over the
dimension being analyzed. Consider the definition sketch of an actual
distribution over the lateral dimension, y, shown 1n Figure IV-4. One
definition might be:
IV-3
-------
«WC02
7/1
QoutL*C0? / /
Of*co2
REEF FLATS
7
C0? (photosynthesis) \
1 '
/
Variables affecting CO;
concentration in the water column
temperature
total alkalinity
P«
plant/animal respiration
surface turbulence
photosynthesis (light)
relative rate of water
exchange between reef
tract cells
^inxC02
1C02 (respl.ptlon)
_ \
photoplankton-) \
1 EUPHOfTIC 20Ht \
C0? (reef respiration)
CO,
coralline algae
-------
Figure IV-3 Major Constituent Interactions
IV-5
-------
y
XJ
r\
c i .1
i
5 -i /
y
A
-Profiling Cross Section
Figure IV-4 LATERAL CONCENTRATION
DISTRIBUTION
IV-6
-------
(IV-1)
where
c
max
maximum concentration deviation
c « average concentration over dimension, y, and
Tj^ « acceptable error tolerance.
A second definition might be:
The crux of the problem is to assign suitable values to Tj or Tg* Factors
Involved in choosing these values are errors 1n field measurements, errors
in simulated values, and acceptable deviation from the mean value, c.
IV.3 FAR FIELD DIMENSION REDUCTION
It is usually practical to choose a numerical model with as simple a
description of the prototype physical/chemical/biologlcal processes as will
yield sufficiently accurate results. A common approach to simplifying the
analysis is to neglect one or more spatial dimensions (usually the vertical
and/or lateral) over which the constituent being modeled can be assumed to
be completely well-mixed from the definition developed. Reductions in
dimensionality, when justifiable, can realize considerable savings in model
development/modification and simulation costs. As a first step to reducing
dimensionality, one can consider the Inverse condition - which dimensions
cannot be neglected in the far field (at distances a long way away from the
po1nt(s) of discharge(s)). Considerations here Include whether the system
Is stratified, 1n which case the vertical dimension must be Included,
whether flow reversal are observed, etc. This step 1s often straight-
forward, and simplifies later analysis in which finer-scale fields are
analyzed because it will limit such analyses to those dimensions over which
the system might be considered to be well mixed.
(IV-2)
where
c_,w * maximum concentration value, and
nwX
T2 = acceptable error tolerance.
IV-7
-------
For estuarine modeling, we will assume that the longitudinal (x) dimension
cannot be neglected (as 1s sometimes the case for reservoir modeling). The
objective of this step, then, is to evaluate whether the lateral (y) or
vertical (z) dimensions must be retained.
IV.3.1 VERTICAL DIMENSION
The most frequent cause of variations 1n the vertical direction Is density
stratification. This can be observed In one of several w*ys:
o salinity and/or temperature gradients,
o tidal or residual velocity reversals,
o dye cloud splitting and differential advectlon, and/or
o geomorphological classification.
Degree of Stratification.
Freshwater is lighter than saltwater. This produces a buoyance of amount:
Buoyancy = Ap g 0R UV-3)
where Ap = the difference in density between sea and river water,
(M/L3) „
g ® acceleration of gravity, LL/T ), and
Qr = freshwater river flow, (LA)
The tide on the other hand is a source of kinetic energy, equal to:
kinetic energy = WU^3 (IV-4)
where p = the seawater density,
W the estuary width
= the square root of the averaged squared velocities.
The ratio of the above two quantities, called the "Estuarine Richardson
Number" (Fischer, 1972), 1s an estuary characterization parameter which 1s
indicative of the vertical mixing potential of the estuary:
IV-8
-------
ap g QR
R ¦ (IV-5)
P wut 3
If R 1s very large (above 0.8), the estuary is typically considered to be
strongly stratified and the flow dominated by density currents. If R 1s
very small, the estuary 1s typically considered to be well-nixed and the
density effects to be negligible.
Another desktop approach to characterizing the degree of stratification 1n
the estuary 1s to use a stratiflcatlon-clrculatlon diagram (Hansen and
Rattray, 1966). The diagram (shown 1n Figure IV-5) requires the calcula-
tion of two parameters:
Stratification Parameter = (IV-6)
^o
Us
and Circulation Parameter = tt-
where aS = time averaged difference between salinity levels at
the surface and bottom of the estuary,
SQ = cross-sectional mean salinity,
Us = net non-t1dal surface velocity, and
Uf = mean freshwater velocity through the section.
To apply the stratification-circulation diagram in Figure IV-5, which is
based on measurements from a number of estuaries with known degrees of
stratification, calculate the parameters of Equation (IV-6) and plot the
resulting point on the diagram. Type la represents slight stratification
as In a laterally homogeneous, well-mixed estuary. In Type lb, there 1s
strong stratification. Type 2 Is partially well-mixed and shows flow
reversals with depth. In Type 3a the transfer 1s primarily advectlve, and
In Type 3b the lower layer 1s so deep, as 1n a fjord, that circulation does
not extend to the bottom. Finally, Type 4 represents the salt-wedge type
with intense stratification (Dyer, 1973).
IV-9
-------
10*
\Sh
X
NM*
2o 3o
X
15
10
"io5 io5"
V"r
*>~
10s
(Station code: M, H1ss1ss1ppt River mouth; Ct Colunbla
River estuary; J, Janes River estuary; NM, Narrows of
the Mersey estuary; JF, Strait of Juan.de Fuca; S,
Silver Bay. Subscripts h and 1 refer to high and low
river discharge; numbers indicate distance (In miles)
JFrom^outho^hejJame^lverjjstuary^^^^^^^^^^
Figure IV-5. Stratification Circulation Diagram and Examples.
IV-10
-------
The purpose of the analysis is to examine the degree of vertical resolution
needed for the analysis. If the estuary 1s well-mixed, the vertical dimen-
sion may be neglected, and all constituents in the water column assumed to
be dispersed evenly throughout. If the estuary is highly stratified, at
least a 2-layer analysis must be used. For the case of a parti ally-mixed
system, a judgment call must be made. The Janes River any be considered as
an example which is partially stratified but was treated as a 2-layer
system for a recent toxics study (O'Connor et al., 1983).
A final desktop method for characterizing the degree of stratification 1s
the calculation of the estuary number proposed by Thatcher and Harleman
(1972):
P F^
E = ——- /1 v-7)
d Q,T U '
where E, = estuary number,
3
P^ = tidal prism volume, (L )
F . = densimetric Froude number,
3
Qf = freshwater inflow,.(L /T), and
T = tidal period, (T).
Again, by comparing the calculated value with the values from known
systems, one can infer the degree of stratification present.
Once the degree of stratification is determined by one of the above
methods, we recommend the following criteria:
strongly stratified
moderately stratified
vertically well-mixed
- include the vertical dimension in at
least a 2-layer model
- Include the vertical dimension in a
multi-layered model, or reserve
judgment to the calculations in
Step 6, and
- could neglect vertical dimension
after calculation 1n Step 6.
IY-11
-------
Tfda1 or Residual Yelocfty 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 IV-6):
tidal velocity reversals
residual velocity reversals
no observable reversals
- Include vertical dimension 1n at
least a 2-layer model,
- Include the vertical dimension 1n a
multl-layered model or reserve
judgment to the calculation In
Step 6, and
- could neglect vertical dimension
after calculation In Step 6.
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 difficult, but the following criteria seem reasonable (Figure IV-7):
Dye cloud separates and moves
Dye cloud spreads in non-Gaussian
manner
Dye cloud moves downstream and
diffuses in a Gaussian manner
cloud 1s 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,
some differential shearing is
present and system should be studied
using a multl-layer model, or
reserve judgment to the calculations
1n Step 6, and
little differential shearing 1s
present and system could be modeled
neglecting vertical dimension after
calculations 1n Step 6.
IV-12
-------
7
j
€
a) Tidal Velocity Reversal
WW
b) Residual Velocity Reversal
c) No Observable Reversals
Figure IV-6 VERTICAL VELOCITY PROFILES
IV-13
-------
a) Cloud Seperates
c) Gaussian Spreading with Downstream Movement
Figure IV-7 VERTICAL DYE CONCENTRATION
PROFILES
IV-14
-------
Geomorphological Classification
If little or no data is present, one can try to categorize the estuary
within the basic definitions of Dyer (1973). Over the years, a systematic
structure of geomorphological classification has evolved. Dyer (1973) and
Fischer et al. (1979) Identify four groups:
o Drowned river valleys (coastal plain estuaries),
o Fjords
o Bar-bu1lt estuaries, and
o Other estuaries that do not fit the first three classifications.
Typical examples of North American estuaries are presented 1n Tables IV-1
and IV-2.
Coastal plain estuaries are generally shallow with gently sloping bottoms,
and depths increasing uniformly towards the mouth. Such estuaries have
usually been cut by erosion *nd are drowned river valleys, often displaying
a dendritic pattern fed by several streams. A well-known example 1s
Chesapeake Bay. Coastal plain estuaries are usually moderately stratified
(particularly in the old river valley section) and can be highly Influenced
by wind over short time scales.
Bar built estua-ies are bodies of water enclosed by the deposition of a
sand bar off the coast through which a channel provides exchange with the
open sea, usually servicing rivers with relatively small discharges. These
are often unstable estuaries, subject to gradual seasonal and catastrophic
variations in configuration. Many estuaries In the Gulf Coast and Lower
Atlantic Regions fall Into this category. They are generally a few meters
deep, vertically well mixed and highly Influenced by wind.
Fjords are characterized by relatively deep water and steep sides, and are
generally long and narrow. They are usually formed by glaclatlon, and are
more typical in Scandinavia and Alaska than the contiguous United States.
There are examples along the Northwest Pacific Coast, such as Alberni Inlet
IV-15
-------
TABLE IV-1. TOPOGRAPHIC ESTUARINE CLASSIFICATION
Type
Coastal
Plain
Bar Built
Fjords
Dominant
Long-Term Process
River Flow
Wind
Tide
Other Estuaries Various
Vertical
Degree of
Stratification
Moderate
Vertically
well mixed
High
Various
Lateral
Variability
Moderate
High
Small
Various
Examples
Chesapeake Bay, MD/VA
James River, VA
Potomac River, MD/VA
Delaware Estuary, DE/N
New York Bight, NY
Little Sarasota Bay, F
Apalachlcola Bay, FL
Galveston Baty, TX
Roanoke River, VA
Albemarle Sound, NC
Pamlico Sound, NC
Puget Sound, UA
Albernl Inlet, B.C.
Silver Bay, AL
San Francisco Bay, CA
Columbia River, WA/OR
TABLE IV-2. STRATIFICATION CLASSIFICATION
Vertical Type
Highly Stratified
Lateral Type
Laterally
homogeneous
River Discharge
Large
Examples
Mississippi River, LA
Mobile River, AL
Partially Mixed
Partially
mixed
Medium
Chesapeake Bay, MD/YA
James Estuary, VA
Potomac River, MD/VA
Vertically
Homogeneous
High
Variability
Small
Delaware Bay, DE/NJ
Rarltan River, NJ
Biscayne Bay, FL
Tampa Bay,FL
San Francisco Bay, CA
San Diego Bay, CA
IV-16
-------
in British Columbia. The freshwater streams that feed a fjord generally
pass through rocky terrain. Little sediment is carried to the estuary by
the streams, and thus the bottom is likely to be a clean rocky surface.
The deep water of a fjord is distinctly cooler and more saline than the
surface layer, and the fjord tends to be highly stratified.
The remaining estuaries not covered by the above classification are usually
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 (Dyer, 1973).
Using this classification, the approach is to estimate the degree of
stratification from known conditions 1n a geomorphologlcally similar
estuarine and use the criteria under a "degree of stratification" given
above.
IV.3.2 LATERAL DIMENSION
Neglecting the lateral dimension in the far field 1s more difficult to
estimate than for the vertical dimension, although the same features can be
considered. These are:
o salinity and/or temperature gradients,
o tidal or residual velocity reversals,
o dye cloud splitting and differential advection, and/or
o geomorphological classification.
The analyses in this step are the same as for the vertical dimension
analyses (no equivalent to the stratification diagram exists) except that
we are looking for lateral gradients and reversals. Using the geo-
morphological classification, the reader should refer to Tables IV-1 and
IV-2.
IV-17
-------
IV. 4 PROCESS TIME AND SPACE SCALES
At this point we begin to narrow our attention to tine and spatial scales
compatible with physical/chemical/biological processes and at which
resolution of predicted results Is desired. It Is Important at this step
to refer to the conceptual model, developed In Step 1, of the Important
processes which should be Included In the numerical model. This 1s
necessary for two reasons. Firstly, 1t provides a checklist of processes
or variables Included 1n the final numerical model selected. If the
checklist 1s not completely satisfied, the shortfall can be used to assess
the need for further model modification/development, or a comprise achieved
and a revised conceptual model developed. Secondly, It can be used as a
base to estimate rate coefficients used In defining process linkages 1n the
numerical model. As we have said, an Important consideration 1n selecting
an appropriate numerical model 1s the question of dynamic versus steady-
state modeling. It 1s Intuitively evident that some measure of the ratio
of phys1cal-to-biochemical rates (perhaps defined by flushing time divided
by a measure of kinetic rates, such as the smallest Tgo) can be used to
make this assessment.
In order to more closely investigate the possibility of reducing model
dimensionality, we must be able to understand the time and space scales of
the physical/chemical/biological processes Included 1n the conceptual model
of the prototype system, and their interrelationships. To do this, we will
define only physical and chemical time and space scales as:
o physical - flushing time
o biochemical - biochemical reaction, decay, and dleoff rate.
IV.4.1 FLUSHING.TIME
The time that 1s required to remove pollutant mass from a particular point
1n an estuary (usually some upstream location) 1s called the flushing time.
Long flushing times are often Indicative of poor water quality conditions
due to long residence times for pollutants. Flushing time, particularly in
a segmented estuary, can also be used In an Initial screening of alternate
IV-18
-------
locations for facilities which discharge constituents detrimental to
estuarine health 1f they persist 1n the water column for lengthy periods.
Factors Influencing flushing times are tidal ranges, freshwater Inflows,
and wind. All of these forcing functions vary over tine, and way be
somewhat unpredictable (e.g., wind). Thus, flushing tine calculations are
usually based on average conditions of tidal range and freshwater Inflows;
with wind effects neglected.
The Fraction of Fresh Water Method for flushing tine calculation 1s based
upon observations of estuarine salinities:
where F = flushing time in tidal cycles,
S = salinity of ocean water, and
Se = mean estuarine salinity.
The tidal prism method for flushing time calculation considers the system
as one unit with tidal exchange being the dominant process:
V. + P
F = -t-p— (IV-9)
where F = flushing time in tidal cycles,
VL = low tide volume of the estuary, and
P = tidal prism volume (volume between low and high tides).
The Tidal Prism technique was further nodlfled by Ketchum (1951) to segment
the estuary Into lengths defined by the maximum excursion of a particle of
water during a tidal cycle. This technique can now Include a freshwater
Inflow:
IV-19
-------
F =
n
z
1=1
'LI
+ pi
(IV-10)
where F * flushing time 1n tidal cycles,
1 = segment nunber,
n * ntnber of segments
V,1 8 low tide volune In segment 1, and
Pj ¦ tidal prism volume 1n segment.
Riverine Inflow, QR, 1s accounted for by setting the upstream length equal
to the river velocity multiplied by the tidal period, and setting:
P„ = QrT (IV-11)
where P = tidal prism volune in upstream segment,
Q° = freshwater flow, and
T = tidal period.
Finally, the replacement time technique is based upon estuarlne geometry
and longitudinal dispersion:
tR = 0.4 L2/El (IY-12)
where tp = replacement time,
L = length of estuary, and
El = longitudinal dispersion coefficient.
This technique requires knowledge of a longitudinal dispersion coefficient,
E^, which may not be known from direct estuarlne measurements. A coeffici-
ent based upon measured data from a similar estuary may be assumed (see
Table IV-3 for typical values In a number of U.S. estuaries) or It nay be
estimated from empirical relationships, such as the one reported by
Harleman (1964):
EL = 77 n u R5/6 (IV-13)
IV-20
-------
TABLE IV-3
OBSERVED LONGITUDINAL DISPERSION COEFFICIENTS
Estuary
Delaware River (DE/NJ)
Hudson River (NY)
East River (NY)
Cooper River (SC)
Savannah River (GA, SC)
Lower Raritan River (NJ)
South River (NJ)
Houston Ship Channel (TX)
Cape Fear River (NC)
Potomac River (MD/VA)
Compton Creek (NJ)
Wappinger and Fishkill Creek (NY)
San Francisco Bay (CA):
Southern Arm
Northern Arm
SOURCE: From Hills et al. (1982).
River Flow Dispersion Coefficents
(cfs)
(n^/sec)
(ft2/sec)
2500
150
1600
5000
600
6500
0
300
3250
10000
900
9700
7000
300-600
3250-6500
150
150
1600
23
150
1600
900
800
8700
1000
60-300
650-3250
550
30-300
325-3250
10
30
325
2
15-30
160-325
18-180 200-2000
46-1800 500-20000
IV-21
-------
or Harleman (1971):
EL * 100 " umax r5/6 (iv"14)
2
where E, = longitudinal dispersion coefficient (ft /sec),
n = Manning's roughness coefficient (0.028-0.035, typically),
u « velocity (ft/sec),
u.., = maximum tidal velocity (ft/sec), and
R = hydraulic radius ¦ A/P (ft)
where A « cross sectional area (ft),
P = wetted perimeter (ft).
Y.4.2 DECAY OF DIEOFF RATES
A measure of biochemical process time scales is given by the decay
or the dleoff rate, usually denoted by T^q. Tqq 1s defined as the
reduce the constltutent concentration by an order of magnitude, or
percent. The relationship between the two 1s:
T90 = 2.3A
where Tg0 = dieoff rate in hours, and
K = decay rate in 1/hours.
Of critical concern in selecting a water quality model 1s the ability to
resolve the most rapid constituent dieoff. Thus, from a knowledge of the
system chemistry, select the minimum dieoff rate T^q0 as the biochemical
process time scale. If there 1s a large difference between two rates (e.g.,
10 mins versus 24 hours), we may want to consider neglecting one or the
other of the processes in the conceptual model (Section IV.l).
IV.5 REGULATORY SCALES
It 1s important to make a clear statement of the purpose and objectives of a
study. Frequently, such a statement 1s bound to local/state/federal
regulations which, in turn may Imply time and spatial scales that must be
resolved by the model description. An example of this Is the concept of an
rate, K,
time to
90
(IY-15)
IY-22
-------
"allowable mixing zone" frequently defined 1n the vicinity of an outfall.
The regulation may be so written that the numerical model must have
sufficient spatial resolution to determine that the mixing zone length 1s
not exceeded (thus requiring distance steps at least an order-of-magn1tude
less than this length) and that no violations occur at any time, which may
necessitate a dynamic rather than steady state approach to modeling.
More often than not, the purpose of modeling 1s to evaluate compliance with
Federal or State regulations. Many of these regulations define time and
space scales beyond which violations will not be permitted. For example,
the regulation for a thermal outfall may state that waters must return to
within 2°C of the ambient temperature after 100 m downstream 1n the river.
This clearly defines a length scale of 100 m, and a time scale of 100 m
divided by the ambient river velocity.
Thus, if regulatory standards are a consideration 1n the model selection
process, we will define a regulatory length scale, LR as:
lR = the minimum of the specified distance if known (IV-16)
from regulations, length of system wished to be
modeled, or total length of system,
and a time scale, TR as:
Tr = Lr/u (IV-17)
where u = velocity averaged over time and space scales.
IV.6 STUDY SCALE DIMENSION REDUCTION
Based on the information of Steps 1-5, we can now develop a more refined
conceptual model that Incorporates all the Information of these steps. The
emphasis in this step is to determine whether spatial dimensions, other
than those determined non-negligible in Step 3, can be neglected and yet
IV-23
-------
resolve all necessary physical/chemical/biological processes at the
regulatory spatial scale.
As an example of this, consider wastewater discharged into a stratified
estuary. Step 3 may show that stratification 1s Important and thus the
vertical variation cannot be neglected (or Integrated). However, the
question may still remain whether It Is reasonable to neglect lateral
variations and assume a laterally well-nixed system. If the regulations
reviewed 1n Step 5 require a mixing zone of not nore than 1000 m downstream
of the outfall, we would wish to determine from this step whether the
laterally well-mixed condition is reached before or after this distance.
If it Is reached before 1000 m, for example, 1t way be reasonable to
neglect lateral variations, However, 1f 1t Is reached afterwards, the
lateral dimension 1s still required to be able to adequately compare
simulated results with the regulatory standard.
In Step 3 (Section IV.3), we looked at the IrreducablHty of dimensions at
the far field scale. This Included analyses and subjective Indications
that considered:
o Density stratification,
o Velocity data,
o Dye studies, and
o Topographic characteristics.
These were included at the far field level because such data are usually
either unavailable 1n the potential study area or are inadequate to make a
reliable determination of dimension reductions at this scale. Normally any
data 1n the study area will be part of a larger data set covering a much
wider area.
Having identified the dimensions we should not neglect, from Step 3, 1n
this step we wish to determine whether any of the other dimensions can be
neglected. Having probably exhausted our supply of data to make such
determinations, we will rely on simple analytic solutions.
IV-24
-------
At this stage, we should have a fairly complete conceptual nodel of the
system to be studied. This should Include a definition of the minimum
study spatial resolution, Ls, defined as the minimum of the process space
scale, Lp, and the regulatory space scale, LR:
There are three dimension reductions we will consider here:
1. Cross-sectional area,
2. Vertical dimension, and
3. Lateral dimension.
There are several techniques that can be used to make these assessments:
o Fischer's mixing length, and
o Analytic transport models.
Fischer's Mixing Length
A frequently used technique described by Fischer et al. (1979) 1s to use a
definition of the convective length, Lc, over which the discharge plume 1s
completely mixed laterally, so that "the concentration is within 5 percent
of its mean value everywhere in the cross section" for a centerline
discharge:
Ls * m1n (Lp, LR)
(IY-18)
Lc = 0.1 u W*/Ey
(IV-19)
where u = mean velocity, (LA)
W = channel width, (L), and
Ey = lateral diffusion coefficient.
For a side discharge, W 1s replaced with 2W for symmetry:
Lc = 0.4 u W2/Ey
(IV-20)
IY-25
-------
A good estimate (Fisher et al., 1979) for the lateral diffusion
coefficient, Ey, is:
Ey s 0.6 R u* = 0.06 R u
(IV-21)
where R ¦ hydraulic radius, (L), and
u* * bed shear velocity, (LA)
Thus, for a center!ine discharge:
Lc « 6.67W2/R
(IV-22)
and for a side discharge:
Lc = 26.67W2/R
(IV-23)
If the convective length, Lc, is less than the study space scale, L^, a
cross sectionally averaged model can be selected.
Analytical Model
A second technique, which is actually more general In the sense that 1t can
be directly related to the definition of complete mixing (Step 2), is to
use a closed form (analytic) solution to the governing three-dimensional
mass transport equation (Eq. 11-5). To obtain a closed form solution, the
following assumptions are made:
1. the velocity, u, is steady and uniform over the entire cross
section (or layer 1f analyzed specifically as such),
2. the load 1s either (a) an Instantaneous point source, or (b) a
continuous point source,
3. the diffusion coefficients, Ex, Ey, Ez are constant 1n space and
time, and
4. reflections of the solution at solid and surface boundaries can be
accounted for using a series of Image sources (Figure IV-8),
IV-26
-------
Q
2h<
2W
o o-
Note:
• - Source
O - Image Source
0
\\wv;w
2W
2h,
-Cll-
w
mw
2W
2h/
6
2h,
O
2W
-O
Figure IV-8 SCHEMATIC OF SOURCE AND IMAGE SOURCES
-------
Then (using Fisher et al., 1979) the Instantaneous point source
distribution 1s:
c(x,y,z,t) * i i
j=-J k=-K
exp -
(4*t)3/2 (ExEyE2)1/Z
(IV-24)
(x-xrut)2 + (y-yi)2 + (2-Zi)2 -KDt
4Ex*
4Eyt
4Ez*
M =
o =
where c(x,y,z,t) * concentration at location x,y,z (within the channel)
at time t,
mass load (M),
mass density, (M/L3)
longitudinal, lateral, and vertical diffusion
coefficients, (L2/T)
j = -J, J 1s number of lateral Image sources (Figure IV-8)
k = -K, K 1s number of vertical Image sources (Figure IV-8)
location of each image (or actual source), and
decay coefficient, (1/T).
Ex'EyEz
V*i'zi
Kn
Similarly, the steady-state concentration distribution, c(x,y,z), for a
continuous point source is:
c(x,y,z) = ^ *
j=-J k=-K
exp -
4-p (^yEz)1/2 ((x-Xj)2 + (y-yi)2 + (z-Zi)2)1/2 {IV"
((x-Xi)2 + (y-y^2 + (Z-Z1)2)1/2 (u2 + »(EyEz)1/2KD)1/2 - u(x-Xl)'
2(EyE2)
T7T
where q s mass loading rate, (M/T)
If the diffusion coefficients are unknown, they can be estimated from
(Fischer et al., 1979):
Ex = 0.6 R u (assumed equal to the lateral coefficient)
Ey = 0.6 R u* - 0.06 R u (IV-26)
IV -28
-------
Ez = 0.067 R u* = 0.0067 R u
*
where u = bed shear velocity
The procedure 1s to:
1. Select either an Instantaneous point source or a continuous point
source,
2. estimate velocity, loads, and diffusion coefficients,
3. select a number of Image sources (usually J * K » 3 will be adequate),
4. use the appropriate equation above (IV—24 or IV-25) and calculate
cross-sectional distribution,
5. find the closest sections (both vertically and laterally) that satisfy
the definition of complete mixing from Step 2, and
6. compare those distances, L, to the. sections with the minimum spatial
resolution needed (Eq. IV-18). If L < L$ the dimension considered can
be assumed to be well mixed and neglected for model selection purposes.
If L < Ls, the section will not be completely well-mixed, and the
dimension must be included in the selected model description.
IV.7 DYNAMIC OR STEADY-STATE
Again based on the Information of Steps 1-6, we further wish to make a
decision whether a steady-state model can be used or whether a dynamic model
1s required to achieve the required temporal resolution. An example of this
1s that the dissolved oxygen (DO) standard In many states requires no oxygen
depletion below a given level at any time. In a tidal river, for example,
in which processes can occur within or at the same period as a tidal cycle
(many constituents will exhibit diurnal variations which are not 1n phase
with the tidal cycle) a dynamic model may be required to provide adequate
temporal resolution to make such a determination.
IY-29
-------
Steady-state modeling is Inherently more economical than dynamic modeling.
Another advantage is that it can perhaps be adapted to run on a micro-
computer for relatively simple kinetic descriptions, thus making the
approach more readily available to groups with severe computer hardwater
limitations. Finally, steady-state models are usually less complex, because
the cumbersome hydrodynamlc equations have been greatly simplified to
include only the continuity equation.
There 1s a great danger, however, of choosing such an approach without
considering the Implications of the selection. It Is Intuitively argued
that a steady-state approach 1s of little use In a closed-end canal system,
for example, because there is no (or at least, very little) net advectlon
towards the mouth. By contrast, one would frequently choose such an
approach for a stream with no tidal effect. But what about the systems in
between — those that have both net downstream advection and tidal
oscillations?
Unfortunately, there is no hard and fast rule that can be applied. Rather
we must rely on our experience, plus some obvious physical/chemical process
limits. It seems reasonable that a decision criteria would depend on the
time scales of both physical and biochemical rates, most likely as a ratio.
Physical time scales, T , will be defined as the minimum of the tidal
period, T, and the flushing time, F:
The biochemical process time scale, Tc, 1s defined as the minimum of the
kinetic rates, using the concept of an order-of-magn1tude or 90% reduction,
Tqq, and any regulatory time scale, TR, defined In Step 5:
T
min (T,F)
(IV-27)
P
Tc = min (Tg0, TR)
(IV-28)
Defining the ratio:
R = VTc
(IV-29)
IV—30
-------
we would recommend the following criteria:
o If R > 0.5
o If R < 0.1
use a dynamic model
use a steady-state model
o If 0.1
-------
adequate representation results. The minimum spatial resolution required,
Ax . , can be determined from the resulting construction (Figure IV-9).
mm
IV.8.2 STABILITY
Most computer waste load allocation models use explicit schewes—that Is,
variables at the new time level are calculated using known values at
previous time levels. This leads to several coanon conditions that must be
satisfied to ensure model stability (I.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.
These conditions, or criteria for a one-dimensional are usually, a hydro-
dynamic criterion (Courant condition):
a< {vi-31)
ZgF + u
a mass transport condition:
At £ & * (VI —32)
and a dispersion condition:
A x2
At 1-^— (VI -33)
lL
Similar conditions exist for 2 and 3-d1mens1onal models, and other
conditions, such as a friction term criterion, may also be required. The
most stringent condition is usually the Courant condition (unless vertical
diffusion and/or momentum transfer 1s explicitly treated, In which case a
criterion like Equation (IV-32) 1s required withAz replacing Ax). Some
IV-32
-------
"A Xmin
DISTANCE, X
Figure IV-9 APPROXIMATION TO CONCENTRATION
GRADIENT
IV-33
-------
models may solve for the mass transport In a separate model, or at a
different time step than the hydrodynamic solution. In these cases, all the
above criteria should be checked.
Some models exist which use an implicit technique to approximate the
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 considerations. Here, the time step should be chosen to provide
adequate resolution of temporal processes.
IV.9 DIFFUSION COEFFICIENTS
In dynamic modeling, the choice of the form to describe the diffusion
process 1s fairly standard, as discussed 1n Section II.9. As further
discussed in that Section, the selection of diffusion coefficients for
steady-state models is much less well-defined, and frequently In error, or
at least not well based. In this Step, we will recommend an approach to
diffusion coefficient selection for steady-state models, based on some
physical aspects of the system being studied.
Diffusion coefficient selection for dynamic models 1s both straightforward,
1n that the form used in any particular model selected will probably be
adequate, and yet, at the same time, to establish rigorous guidelines as to
the most appropriate form 1s very difficult. Our advice here Is to follow
the discussion of Section II.9 and ensure that the form used 1n a
particular model has a reasonably sound basis. In most cases, as a dynamic
model 1s complex, and usually well reviewed (choosing well-known models or
agency-supported models can lead to increased confidence), one may
generally assume that 1t contains an adequate description of the diffusion
processes. Furthermore, diffusion In a dynamic model is not as critical as
dispersion 1n a steady-state model, In which neglected processes are
Inherently lumped into the dispersion mechanism.
More care must be exercised when selecting the appropriate dispersion
coefficient description to be used in a steady-state model. Such a
selection, as has frequently been stated in this report, must be based on a
IV-34
-------
sound knowledge of the physical/chemical processes at work and the Inherent
assumptions made when the hydrodynamic equations are simplified or time
Integrated.
Following the discussion of Section II.9, there are three types of tldally-
averaged dispersion coefficients, eJ, commonly used In steaty-state models:
1. E^ ¦ constant (space, time) (IV-34)
2. E^ = constant (time) (IV-35)
3. eJ = KRQr/A (IV-36)
Selection of the most appropriate form will be based on a consideration of
the respective Influences of river and tidal flows. In general, we would
recommend that Eq. (IV-35) be used for tldally dominated flows, Eq. (IV-35)
bee used for river dominated flows, and Eq. (IV-35) be used as little as
possible or when no data is available for a more rational selection.
More specifically, we propose the following criteria:
o If river flow is strong enough that the estuarlne flow 1s always
unidirectional i.e. (from Eq. 11-24):
Qr > A^aw (IV-37)
where QR = river flow, (L^/T),
Aws = upstream water surface area, (L2),
a = tidal amplitude, (L), and
w = 2 ir/T, ( 1/T),
where T = tidal period,
then use:
EI = KRQr/A (IV-38)
IV-35
-------
where A =
cross-sectional area.
o If the tidal flows dominate, such that the river flow Is less than
10% of the maximim tidal flow:
QR < 0,1 Aws8*
(IV-39)
then use:
r-T . 4#AWSKR
EL TT~
(IV—40)
If the flow 1s some Intermediate combination of river and tidal
flows:
0.1 < Qp/A^aw < 1.0
(IV-41)
then Eqs. (11-25) and (11-26) can be used as a guide for coefficient
form selection, for:
tj and t2 = ^ sin
ft M
L ~ TA
awAws
for 0 < t < T
Qr (T + 2tj - 2t2) + 2aAws d + cosfwtj) - cos(wt2))
(IV-42)
(IV-43)
It should be noted that the above analyses may not apply everywhere 1s a
given system. Consider the Potomac River, for example. Upstream, the river
Is strongly tidal and Eq. (IY-38) can be applied. Downstream, the river may
dominate and Eq. (1V-40) can be applied. In the middle reaches, there 1s a
balance between river and tidal flows, and thus Eq. (IV-43) can be used as a
guide.
IV.10 DATA AVAILABILITY
At this point, the model selection procedure should have arrived at the
point where the processes, dimensionality, and time scales are determined.
IV-36
-------
The next step is then to consider whether sufficient data exist to run the
model.
These data are required for two purposes—calibration and verification.
Calibration is a process of adjusting model coefficients, until good
agreement 1s achieved between simulation and observations. The neasures of
"goodness-of-fit" may be either judgmental or statistical, using such
approaches as relative errors, root-mean-square errors, and tests of
statistical significance of variations, etc. Model verification then
requires that a second data set be simulated, without adjusting model
coefficients, to demonstrate that the model can accurately reproduce a
(preferably) different set of conditions.
If sufficient data do not exist, a decision must be made to (a) collect
additional data to supplement existing data, or (b) to use the existing data
to perform model calibration only. This latter condition 1s not desirable
because it must reduce confidence in the model's ability to accurately
simulate conditions other than those found during calibration. Perhaps the
most desirable situation is to have three of four data sets covering a wide
range of conditions to be used for calibration and verification.
IV.11 MODEL SELECTION
Having completed Steps 1-10 (Section IV.1-IV.10), the system to be studied
should be comprehensively conceptualized. At this point, we are able to
select the most appropriate model to do the job. As a basis for model
selection, a "check 11st" should be prepared of desired model features,
with room to evaluate the features of several candidate models. A sample
list 1s shown 1n Table IV-4 as a guide.
The ability to perform this model selection does not only depend on one's
capability of evaluating Steps 1-10, but also on the knowledge of available
numerical models that are possible candidates. Host "experienced" modelers
will process this knowledge, and one commonly held view is that only
experieced modelers should use models. Certainly there is a great danger
in an inexperienced modeler or team of modelers performing a study.
IV-37
-------
TABLE IV-4
EXAMPLE MODEL SELECTION CHECKLIST
Category
Item
Conceptual
Model
Model 1
Model 2
Model'3
Dimensions
Longitudinal (x)
lateral (y)
vertical (z)
Time
Integration
Dynamic
steady-state
Dispersion
Coff1c1ent
Constant (x, t)
tidal dominated
river dominated
Physical
features
Coriolls
nonlinear ac-
celeration
bottom friction
wind shear
variable water
surface
density
Chemical
constituent
Constituent a
Constituent b
Chemical
kinetics
Kinetic 1
Kinetic 2
Solutlon
scheme
Finite difference
Finite element
link node
IV-38
-------
However, the current trend 1s to consider the model as a "black box" and to
use 1t with as much guidance as can be provided In reports such as this,
authored by experienced modelers.
To those Inexperienced in model use or those who are unfamiliar with models
1n a certain area of estuarlne hydraulics/water quality modeling, there 1s
no one central agency to which one can turn to provide a complete summary
of available models. Such a mechanism does exist In groundwater Modeling
through the Holcomb Research Institute at Butler University In
Indianapolis. Termed "a clearing house", one of Its functions 1s to
provide a library service of available software for groundwater modeling.
Such a mechanism Is being considered for hydraulics/hydrology by the
American Society of Civil Engineers Task Committee on the Documentation of
Hydraulic Software, but the implementation of any such recommendation is
still some time away.
There are several ways one might approach the task of actual model
selection:
1. Use models that are readily available to the user or lie within
their realm of experience,
2. Perform a library search, perhaps using a computerized database,
such as DIALOG,
3. Seek the advise of a knowledgeable modeler, and
4. Reference bibliographic and/or model specific reports and papers.
Most model users usually have both a basis of experience and access to
knowledgeable modelers. Once Steps 1-10 have been performed, and several
candidate models identified, final model selected Is based on previous
experience with various models. Factors such as ease of use, reliability,
accuracy, availability, and economy can be weighed In choosing the model.
IV-39
-------
Without such a basis of knowledge, or when a particular study 1s beyond
one's previous experience, model selection follows ways 2-4, above. In
particular, there are a nunber of bibliographic and model selection suimary
reports that one might turn to for Information (e.g., EPA, 1979; Versar,
1983; JRB, 1984; Ambrose et al., 1981; etc.).
A good example of a comprehensive discussion of estuarlne waste load
allocation models 1s the study by Ambrose et al. (1981). They divided
estuarlne waste load allocation models Into four levels according to the
following definitions:
Level I Includes desktop screening methodologies which calculate seasonal
or annual mean pollutant concentrations based on steady state conditions,
simplified flushing time estimates, and first order decay coefficients.
These models are designed to examine an estuary rapidly to Isolate trouble
spots for more detailed analyses. They should be used to highlight major
water quality issues and Important data gaps.
Level II Includes computerized steady state or tidally averaged planning
models which generally use a box or compartment-type network. Steady state
models use an unvarying flow condition which 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 1n tidally averaged concentra-
tions over time. Level II models can predict slowly changing seasonal
water quality with an effective time resolution of two weeks to a month.
Level III includes computerized one-dimens1nal (1-D) and quasi two-
dimensional (2-D), real time planning models. These real time models
simulate variations In tidal heights and velocities throughout each tidal
cycle. 0ne-d1mens1onal models treat the estuary as well-mixed vertically
and laterally.
Quasi 2-D models employ a link-node approach which describes water quality
in two dimensions (longitudinal and lateral) through a network of 1-D nodes
IV-40
-------
and channels. The 1-D equation of motion 1s applied to the channels while
the continuity equation 1s applied at nodes between channels, where all the
storage Is assumed to be concentrated. Tidal Movement Is simulated with a
separate hydrodynamlc package In these models. Although the Level III
models will calculate hour-to-hour changes 1n water quality variables,
their effective time resolution 1s usually limited to one week because
tidal input parameters generally consist of only average or slowly varying
values. Model results should be averaged to obtain aean diurnal
variability over a minimini of one week Intervals within the simulated time
period (Ambrose and Roesch, 1982).
Level IV consists of computerized 2-D and 3-0 real time design models.
Dispersive mixing and seaward boundary exchanges are treated more realisti-
cally than In the Level III 1-0 models. At the present time, there are no
well-docunented three-dimensional water quality models which include
coupled constituent Interactions and feedback reactions. The only 3-D
models currently reported In the literature are hydrodynamic models that
Include simple first order decay rates for uncoupled nonconservatlves
(Swanson and Spaulding, 1983). The only well-docunented 2-D estaurlne
water quality models simulate quality and hydrodynamics 1n the lateral and
longitudinal directions, but It 1s also possible to develop a fully two-
dimensional model in the longitudinal and vertical directions. The
effective time resolution of the Level IV models 1s less than one day with
a good representation of diurnal water quality and 1ntrat1dal variations.
JRB (1983) provides a discussion of the advantages and disadvantages of
Level I-IV models. However, the aim of the model selection process
described 1n this section, 1s to choose the model with the mlnlmun set of
features that adequately describes the prototype situation. This
automatically leads to the selection of the most appropriate and most
economic model, based on the assunptlon (usually true) that more complex
models are more costly.
The procedure discussed in Steps 1-10 above, can be tied Into the Levels of
Ambrose et al. (1981), quite simply through the required dimensionality and
IV -41
-------
time Integration required 1n the study. The classification of Level I-IV
models 1s purely based on model dimensions and whether the model 1s
steady-state or dynamic.
In sunmary, the model selection procedure Is:
1. Perform the analyses of Steps 1-10 (Sections IV.1-IY.1Q) and compile
a model feature "checklist", such as Table IV-4,
2. Identify a nunber or source of relevent models,
3. List these models features on the "checklist" (Table IV-4),
4. List those models which provide the required features and make a
final decision based on such factors as availability, previous
experience, training, docmentation, cost, compatibility with
computers, etc, and
5. If no such model exists, decide to (a) modify the most appropriate
model to include the missing features, or (b) redefine the
objectives, and thus the conceptual model, or the study to fit the
most appropriate model found.
IV-42
-------
SECTION V
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Ambrose, R.B. and S.E. Roesch, "Dynamic Estuarlne Model Performance," ASCE,
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Ambrose, R.8., T.O. Najarlan, G. Bourne, and M.L. Thatcher, "Models for
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V-l
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V-2
-------
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Palisades, N.Y., September 1964.
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