MODELING OF ESTUARINE WATER QUALITYINTRODUCTION Estuarine water quality is a term used to describe doc

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MODELING OF ESTUARINE WATER QUALITY
INTRODUCTION
Estuarine water quality is a term used to describe the quality
of characteristics of the water in estuaries. Although the term
implies quality in a physical-chemical sense, its use has been
extended to include also the acceptability of water in a socio-
economic sense. The term “water quality,” like environmental
quality and air quality, has to do with the quality of the water
or the environment wherever it is found and wherever it is
used or encountered. The high chemical and bacteriological
quality of the water supplies has become an almost matter-
of-fact part of any American’s life, but the quality of waters
in which man recreates has become of greater concern with
man’s awareness of degradation of the quality of the waters
around him.
Estuarine water quality has become a major focus of the
U.S. Environmental Protection Agency with passage of the
Water Quality Act of 1987 establishing the National Estuary
Program with the goal of identifying nationally significant estu-
aries, protecting and improving their water quality, and enhanc-
ing their living resources. The original four estuaries selected
in 1985 for study were Narragansett Bay in Rhode Island,
Long Island Sound in New York and Connecticut, Buzzards
Bay in Massachusetts, and Puget Sound in Washington. Within
a year, Albemarle-Pamlico Sounds in North Carolina and the
San Francisco Bay/Sacramento-San Jacinto Delta system in
California were added, and most recently Galveston Bay in
Texas, among others, has been added.
A thoroughly technical description of water quality
would require several volumes to cover the physical, chemi-

cal, and biological characteristics of water and how these
characteristics change in different environments, how they
interact, and how they influence the many ways water is
used by plants, animals, and especially man. This would be
true even though this article is limited to estuaries, which are
among the most complex natural systems known and which
feel the impact of man perhaps more than any other natural
aquatic system. Suffice it to say that estuarine water qual-
ity will be examined in a broad way only, and the reader is
referred to the books and articles cited in the bibliography
for further discussions on the topics covered herein.
Use Context for Water Quality
Quality of water may be discussed most usefully in the context
of water use. That is, for certain uses of water, whether they be
recreation, drinking, navigation, or some other use, some level
of water quality is required or desired for that particular use.
Some uses, such as drinking, will require a much higher level
of water quality than will another use such as swimming, and
swimming may require a higher quality of water than naviga-
tion. The important point is that for desired uses of bodies or
areas of water, certain levels of water quality are desired, and
if the quality of the water desired or needed to support that
use is not present, the use may not be sustained. The concept
of use applies not only to man’s direct uses of the water, but
applies also to biological uses of bodies of water such as fish
spawning grounds, shrimp nursery areas, and so forth. Indeed,
the history of setting levels of desired water quality for par-
ticular uses has shown that following the setting of levels for
water quality for drinking and swimming, levels of water qual-
ity were set for protecting and enhancing the survival of fish

and other organisms in streams. Levels of dissolved oxygen
in streams, which are in state and federal water quality stan-
dards, are there to protect fish in those streams.
As uses for bodies of water become more numerous,
a competition for use of the water begins to develop. Uses
such as navigation, swimming, recreational fishing, fish and
shellfish nursery areas, and other uses are not uncommon
competing uses for a body of water. The quality of water
required to support each of these uses is different as noted
above, and because of this, some uses may or may not be
sustained, depending on which use is the most “beneficial”
of that particular body of water.
The Federal Water Quality Act of 1965 stated that
water quality standards were to be adopted by all the states
by June, 1967, and in preparation of these standard public
hearings were to be held to determine the desired uses of
all the waters of the state which were under federal jurisdic-
tion. Although many states had already determined uses of
their waters, particularly for streams, this was the first time
that a nation-wide effort was made to determine desired uses
of waters and to set water quality standards for them. The
hearings, the water quality standards developed, and the sub-
sequent implementation and enforcement of the standards
showed the very real problems which arise when competing
uses of the water resource become very strong and intense.
One or two particular uses become dominant, and the water
quality for a particular use is set to meet that use. Other uses
which require a higher level of water quality may or may not
be sustained, while levels of water quality required for other
uses may be more than adequately met.

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MODELING OF ESTUARINE WATER QUALITY 715
This use context has been supported in subsequent leg-
islation, particularly the 1972 Water Pollution Control Act,
which required that water quality criteria be updated periodi-
cally by the U.S. Environmental Protection Agency as well
as by the states.
Estuaries
The estuary is one of those bodies of water which is the
focus of intense competing uses. Estuaries comprise one of
the most important resources of any country for the support
of such uses as navigation, recreation, nursery and resting
grounds for waterfowl and wildlife, nursery and spawning
areas for fish and shellfish, and particularly sites for urban
growth and the consequences or byproducts of urban growth.
It is estimated that about 75% of the entire population of the
U.S. lives within 50 miles of the nation’s coasts (USEPA
1987), and such a large urban population presents heavy use
pressures on coastal areas, particularly estuaries.
Estuaries are semi-enclosed coastal bodies of water having
a free connection with the open sea and within which the sea
water is measurably diluted with fresh water derived from land
drainage (Pritchard, 1967). Along the coasts of the United
States alone some 45,832 square miles of estuarine waters
exist. Of this total, 17,058 square miles are found along the
Atlantic Coast, while along the Pacific Coast south of Alaska
but including the Pacific Islands some 14,353 square miles
exist, 2760 square miles are found along the Coast of Alaska,
and 11,661 square miles are found in the Gulf of Mexico and

Caribbean Islands (National Estuarine Study, 1971). Of the
total, less than 30% is water less than six feet deep, vulnerable
to filling, as well as especially productive of fish, shellfish
and wildlife. At least 6.8% of the latter have been obliterated
through filling, most in the last 50 years (Stroud, 1971).
Development of estuary shorelines indicate some of the
uses of the estuaries. Of the 89,571 statute miles of tidal
shoreline in the United States estuaries, some 17,853 miles
can be described as recreation shoreline, that is, accessible
and useful for recreational pursuits. Of this shoreline, 16,559
miles are privately owned and 1,294 miles are publicly
owned; however, only 770 miles may be considered rec-
reation areas. Marine transportation terminal facilities are
users of a portion of the shoreline estuaries. In 1966, there
were 1,626 marine terminals providing deep water berths in
132 ports on the Atlantic, Gulf, and Pacific Coasts. Industries
use estuarine waters for cooling and return a heated effluent.
Industries and cities use estuaries as disposal sites for their
wastes. With a third of the United States population located
in the estuarine zone, the impact of man on estuaries must
necessarily be quite high (National Estuarine Study, 1971).
Biological uses of estuaries are also quite high. It has
been estimated that nearly 63% of the commercial catch on
the Atlantic Coast is made up of species of fish believed to be
estuarine dependent. Assuming that this applies equally to the
combined catches by foreign nationals as to the US domestic
catch, the fisheries yield to the US Atlantic continental shelf
and present levels of development of the fishery is equivalent
to about 535 pounds per acre of estuaries (McHugh, 1966).
Similar but somewhat smaller estimates have been made for

the Gulf of Mexico estuaries based on commercial catches
in the Gulf of Mexico and for the Chesapeake Bay estuary
based on catches within the estuary itself (McHugh, 1967).
Factors Influencing Estuarine Water Quality
What are the factors that control the quality of waters in estu-
aries? The predominant factors are the hydraulic (transport)
characteristics of the estuary, the inputs or sources of materi-
als which make up elements of the quality of the water, and
the sinks present in estuaries—those physical, chemical and
biological phenomena which cause materials in the water to
change in concentration or to be altered chemically to a dif-
ferent form than when originally introduced.
The hydraulic regime of an estuary is dependent upon
three particular factors: the physiography of the bay—its
size, area in relation to volume, depth, and shoreline devel-
opment; the amount and seasonability of river inflow to the
estuary; and the wind and tidal mixing which takes place in
the estuary on each tidal excursion. The latter factor is depen-
dent upon the tidal range, the configuration of the entrance
to the estuary, the volume of the river inflow and the peri-
odicity of the tides. The impact of sources of material to an
estuary are dependent upon the character and amount of the
material and the location in the estuary where the material
enters. Materials which enter with the river inflow will very
likely reach broad areas in the estuary due to mixing within
the estuary and the fact that the material will pass through the
estuary on its way to the ocean. On the other hand, material
discharged near the mouth of the estuary will travel only a
short distance into the estuary and most likely be transported
out of the estuary rather quickly. This generalization does not

apply to all estuaries, particularly those which are strongly
stratified. This type of estuary will be discussed in more detail
later on. The size of the sinks for materials in estuaries is
dependent on the conservative or non-conservative nature of
the material, that is, whether the material can be broken down
into by-products or whether it remains in essentially the same
form throughout its history within the estuary. Conservative
and nonconservative materials may both be removed from
the water column due to flocculation or sedimentation within
the estuary, in which case materials may become part of the
bottom sediments and lost from the water column unless the
sediments are disturbed.
Because of the intimate tie between water quality and
estuarine hydraulics, they will be examined below as well
as the sources and sinks for materials within estuaries, both
natural and man-made materials, before discussing water
quality-estuarine use interactions.
ESTUARINE HYDRAULICS
A spectrum of hydraulic types may occur or exist in an estu-
ary. These may range from the situation in an estuary in
which the river flow dominates to the estuary in which the
river flow is negligible and the hydraulic regime is dependent
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716 MODELING OF ESTUARINE WATER QUALITY
on the tidal mixing. Naturally, in a river flow dominated estu-
ary, the water quality in the estuary is most similar to that
of the river, whereas in the tidal mixing dominated estuary,
its water quality is more like that of the off-shore waters.
The other factor greatly influencing the hydraulic regime in

an estuary is the physiography of the estuary which is very
greatly dependent on the origin of the estuary and the subse-
quent natural events which have taken place in geologic time
and man-made events in contemporary time to modify the
original shape of the estuary.
Origins of Estuaries
From a geomorphological standpoint, there are four primary
subdivisions of estuaries: (1) drowned river valleys; (2) fjord
type estuaries; (3) bar-built estuaries; and (4) estuaries pro-
duced by tectonic processes (Pritchard, 1967). Each of these
types of estuaries is characterized by the fact that at some
point in geologic time, it has been inundated with ocean
water due to the rise in the sea level. During the last glacial
stage, sea level was about 450 feet below its present level,
and the shorelines of the continent were at or near the present
continental slopes. Within the last 50,000 years, the sea level
has risen from that stage to the present with the last changes
in sea level occurring about 3,000 years ago (Russell, 1967).
As the name implies, drowned river valley estuaries are
river valleys found along a coastline with a relatively wide
coastal plain, which were inundated with ocean water as
the sea level rose. The Chesapeake Bay is a prime example
of this type of estuary. During the last glacial period, the
Susquehanna River reached the ocean about 180 kilometers
seaward of the present shoreline; the York River and the
other rivers now entering the bay to the north of the York
were then tributaries of the Susquehanna River. The rise in
sea level flooded the valleys of these rivers to form the pres-
ent Chesapeake Bay system. The drowned river valleys, or
as they are more commonly called, coastal plain estuaries,

extend up river to a point approximately where the floor of
the river rises above sea level. This is also the point at which
a major change in water quality occurs from the ocean and
estuary type water quality to that of the river. This geograph-
ical point may be downstream from parts of the river which
are still influenced by the oscillation of the tidal currents.
The fjord type estuary is that formed by glaciers. These
estuaries are generally U-shaped in cross section, and
they frequently have a shallow sill formed by terminal gla-
cial deposits at their mouths. The basins inside these sills
are often quite deep, reaching depths of some 300 or 400
meters. Most fjords have rivers entering at the head and
exhibit estuary features in the upper water layers. The sill
depths in Norwegian fjords are often so shallow that the
estuarine features develop from the surface to the sill depth
while the deeper basin waters remain stagnant for prolonged
periods.
Bar-built estuaries are those formed in an offshore area
where sand is deposited as a sand island and sand pit built
above sea level, and they extend between the headlands in
a chain broken by one or more inlets. Such bays often occur
in areas where the land is emerging geologically. The area
enclosed by the barrier beaches is generally parallel to the
coast line. Frequently, more than one river enters the estu-
ary, though the total drainage area feeding a bar-built estuary
is seldom large. The lower valleys of such rivers have fre-
quently been drowned by the rising sea level, and hence the
bar-built estuary might be considered as a composite system,
part being an outer embayment partially enclosed by the bar-
rier beaches, and part being a drowned river valley or valleys.

Tidal action is usually considerably reduced in such estuar-
ies. These systems are usually shallow, and the wind provides
the important mixing mechanism (Pritchard, 1967). Several
of the North Carolina estuaries and most of those along the
Texas Gulf Coast are examples of this type of estuary.
Estuaries produced by tectonic processes are those
formed by faulting or by local subsidence, and they usually
have an excess supply of freshwater inflow. San Francisco
Bay is an example of such an estuary.
Circulation in Estuaries
Other than the physiography of estuaries, the dominant
physical processes associated with movement of water and
mixing in an estuary are the wind, tides, and the inflow of
river water. Extensive analysis of these processes has been
presented in Fischer et al. (1979), Fisher (1981), Thomann
and Mueller (1987), and others. The composite actions of
these processes produce a variable interaction or interfacing
of fresh water from the river and salt water from the ocean.
Because these two sources of water have very different den-
sities, the less dense fresh river water will tend to float on top
of the dense salt water, and the extent that the two types of
water mix is dependent on the strength of the mixing mecha-
nisms. In an estuary with no tides or wind and a steady river
inflow, the fresh water inflow would ride on top of the salt
water from sea level in the estuary or river bed to the ocean.
Because in a real system friction is present, the fresh water
will force sea water some distance downstream from the sea
level point in the river and the interface between the salt and
fresh water layers will tilt downward in the upstream direc-
tion in a wedge shape. The friction between the layers will

also cause an exchange of water from one layer to another,
generally from the salt water, or “salt wedge,” to the fresh
water. The amount of exchange depends strongly on the
mixing mechanisms, wind, tides, and river inflow.
In a wind dominated estuary, wind provides most of the
energy for moving and mixing the water. In a tide domi-
nated estuary, turbulence associates with the tidal currents
results in mixing between the salt and fresh water, which
in turn produces the density gradients associated with the
non-tidal circulation pattern. In a river dominated estuary,
such as the Mississippi River estuary, water movement is
predominantly related to riverflow and mixing is caused
mostly by the breaking of unstable interfacial waves at the
upper boundary between the fresh river water and the salt
water from the ocean.
In an estuary in which a salt wedge occurs distinctly
the river flow completely dominates the circulation. The
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salt water extends as a wedge into the river and the inter-
face between the fresh and salt water slopes slightly down-
ward in the upstream direction. The steep density gradient
at the interface, amounting to a discontinuity, reduces the
turbulence and mixing to a very low level. The effect of
the Coriolis force causes the interface to slope downward
to the right in the northern hemisphere looking toward
the sea. In the moderately stratified estuary, the dominant
mixing agent is turbulence caused by tidal action, rather
than velocity shear at the interface between the salt water

and overlying fresh water layer as in the previous case.
With a tide of moderate amplitude, random water move-
ments at all depths occur and turbulent eddies transport
fresh water downward and carry salt water upward, in con-
trast to the dominantly upward advection of salt across the
interface which constitutes the vertical flux of salt in the
river dominated estuary. The result of this two way mixing
is that the salt content of both the upper and lower layers
increases toward the sea. At any given point the bottom
layer is always higher in salt content than the lower layer.
The boundary between the seaward flowing upward layer
and the counter flowing lower layer occurs with a mid-
depth region of relatively rapid increase in salt content
with depth, compared to the vertical gradient in either the
upper or lower layers. This type of mixing contributes a
greater volume of salt water to the upper, seaward flowing
layer than in the salt wedge estuary. The rate of flow in the
upper layer of the moderately stratified estuary is therefore
much greater in volume than in the highly stratified estu-
ary, necessitating a correspondingly larger compensating
up estuary flow in the lower layer.
When tidal mixing is sufficiently vigorous, the vertical
salinity stratification breaks down, and the estuary approaches
true vertical homogeneity. The type of circulation which
exists in a vertically homogeneous system depends upon the
amount of lateral homogeneity. Owing to the Coriolis force in
the northern hemisphere, the water on the right of an observer
looking seaward may be lower in salinity than the water to his
left. A cyclonic circulation pattern is developed, with fresher,
seaward flowing water concentrated to the right of center and

a compensating up estuary flow of higher salinity water to the
left of center. Although a vertical salinity gradient is absent
in a vertically homogeneous estuary, vertical transfer of salt
is not lacking. There is also a strong lateral transfer of salt
which represents the dominant circulation pattern in this type
of estuary.
Certain vertically homogeneous estuaries, particularly
those which are relatively deep and narrow, do not exhibit
these cyclonic circulation patterns. The direction of water
movement is symmetrical about the longitudinal axis, and
fluctuations in velocity are related to the tides and the net
flow averaged over several tidal cycles is directed seaward at
all depths. There is a tendency for salt to be driven out of the
estuary by the action of the advective process. There must
be a compensating non-advective longitudinal flux of salt
directed toward the head of the estuary (Pritchard, 1967).
It is very important to note that the quality or character
of the water at any point in the stratified, partially stratified,
or vertically homogeneous estuary will be strongly corre-
lated with the salinity content of the water. For example, the
high salinity, bottom water in a stratified estuary will have a
quality much like that of the offshore ocean water. The water
at the geographical midpoint of a vertically homogeneous
estuary will be a mixture of river and ocean waters. Also,
materials introduced into an estuary will be influenced at
any point in time or space by the circulation patterns in the
estuary. Estuaries which have not felt man’s influence either
in the estuarine zone or the fresh waters which flow into them
have biological systems adapted to whatever water quality
patterns exist. Since these water quality patterns are strongly

influenced by the circulation patterns and/or introduction
or removal of materials, they will have a beneficial or del-
eterious effect on the biota of the estuary depending on the
extent of the change or the nature of the material introduc-
tion or removal. Thus, it is important to examine the circula-
tion patterns of estuaries as well as the material introduced
or removed to understand the water quality and biota of the
estuary and the uses which may be made of the estuary.
Estuarine Circulation Models
Numerous attempts have been made to model the hydraulic
processes which occur in estuaries. Originally, these models
were developed to determine circulation modifications
which might occur because of physical modifications to the
estuary. These models have been extended in recent years
to include constituents of water and the prediction of their
transport and fate in estuaries.
One of the first type of models developed for estuaries
was the hydraulic model. This type of model is a physical
representation of an estuary on a small scale. Such models
are usually distorted in the vertical direction so that water
depth may be represented on a larger scale than a lateral
dimension. For example, if an estuary were modeled on a
scale of 1:100, the width of the estuary, if it were 10 miles,
would be 0.1 miles in the model, but the depth of the water,
if it were 10 feet, would be 0.01 feet which would be not
much more than a film of water in the model. To avoid this
situation which would make the model unusable, the ver-
tical scale is reduced to a lesser extent than the horizontal
scale such that the 10 foot depth of water mentioned above
would be about 1 foot. While the hydraulic models are capa-

ble of representing tidal currents, momentum entrainment,
and gravitational circulation, they are not able to represent
local currents and turbulent eddies. For this reason, there is
considerable distortion of diffusive processes in the physi-
cal model that makes its utility in quantitative concentra-
tion distribution studies dubious (Ward and Especy, 1971).
From a qualitative standpoint, the physical model possesses
an excellent demonstration capability for the visualization
of flow patterns in resultant concentration distributions, and
this capability should not be under-rated.
The other types of models developed for estuaries are
mathematical models which may be intended to model tidal
currents, net advective movement, or tidal stage in an estu-
ary, or they may be intended to model the transport of salt
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718 MODELING OF ESTUARINE WATER QUALITY
in the water or other chemical forms. Such models may be
three dimensional to represent transport of material down
the estuary as well as laterally and vertically, or they may
be two dimensional to represent transport of material down
the estuary and laterally or vertically, or they may be one
dimensional to represent transport of material down the
estuary. Because the complexity of developing and solving
mathematical models decreases as the number of dimen-
sions included are decreased, the one dimensional model
has received the widest attention in terms of development
and use. This type of model is most advantageously applied
to linear type estuaries, that is, estuaries which have little
or limited variation in cross sectional area and depth with

distance down the estuary. Examples of such models include
the model of the Thames River in England, the Delaware
River in New Jersey, the Potomac River in Maryland, and the
excellent introduction to such models).
Water quality models are usually derived from the fol-
lowing basic three dimensional continuity equation:



Ѩ
Ѩ
ϭ
Ѩ
Ѩ
Ѩ
Ѩ
ϩ
Ѩ
Ѩ
Ѩ
Ѩ
ϩ
Ѩ
Ѩ
Ѩ
Ѩ
Ϫ
Ѩ
Ѩ
C

t x
E
C
xy
E
C
yz
E
C
z
x
u
xyz
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠

⎟
( CC
y
vC
z
wc S)()()Ϫ
Ѩ
Ѩ
ϪϮ
∂
∂
∑
where
E ϭ dispersion coefficient along each of the three axes
x , y , and z
u , v , w ϭ velocity in x , y , or z direction respectively
S ϭ source or sink for material
C ϭ concentration of material.
This equation expresses a relationship between the flux
of mass caused by circulation and mixing in the estuary and
the sources and sinks of mass. In the one-dimensional form
in which the assumptions have been made that concentra-
tions of some material are of homogeneous concentration
laterally and vertically (the y and z directions, respec-
tively) and that the net transport of the material through
the estuary is of concern, then the following equation has
been used (O’Connor and Thomann, 1971; Thomann and
Mueller 1987):

Ѩ
Ѩ
ϭ
Ѩ
Ѩ
Ѩ
Ѩ
Ϫ
Ѩ
Ѩ
Ϯ
C
tAx
EA
xAx
QC S
11
⎛
⎝
⎜
⎞
⎠
⎟
where
A ϭ cross sectional area of estuary
Q ϭ freshwater inflow
E ϭ dispersion coefficient in x direction
and other terms are the same as above. Such models may
be used to determine changes in material concentration with

time for materials whose rate of entry to the estuary and/or
loss from the estuary in a sink are steady or only slightly vari-
able. A further assumption is to select the steady state situa-
tion, the condition in which the concentration of the material
does not change with time. For this condition ѨC / Ѩt in the
above equation is to set to zero and the equation solved.
Recently two dimensional models have been developed.
These models often assume that vertical stratification does
not occur in the water column and that lateral stratification
does occur. Such models are most appropriately applied to
estuaries with large surface areas and shallow waters. Such
models have been developed for many estuarine systems.
Feigner and Harris (1970) describe a link-node model devel-
oped specifically for the Francisco Bay-Delta Estuary, but
applicable elsewhere. It models the two-dimensional flow
and dispersion characteristics of any estuary where strati-
fication is absent or negligible. Hydrological parameters of
tidal flow and stage are computed at time intervals ranging
from 0.5 to 5.0 mins and at distance intervals ranging from
several hundred to several thousand feet. Predictions of qual-
ity levels are computed on the same space scale, but on an
expanded time scale, ranging from 15 to 60 mins. The model
is thus truly dynamic in character. It predicts fluctuating
tidal flows and computes tidally varying concentrations of
constituents, in contrast to a non-tidal model based on the
net flow through the estuary such as that developed for the
Delaware estuary. It can also accommodate both conserva-
tive and non-conservative constituents.
First, the hydraulic behavior of the estuary is modeled.
Having established channel directions both in the actual

prototype channels and (artificially) in the bay areas, the
authors use one dimensional equations based on the follow-
ing assumptions :
a) Acceleration normal to the x -axis is negligible.
b) Coriolis and wind forces are negligible.
c) The channel is straight.
d) The channel cross-section is uniform throughout
its length.
e) The wave length of the propagated tidal wave is
at least twice the channel depth.
f) The bottom of the channel is level.
Equations of motion and continuity are, respectively



Ѩ
Ѩ
ϭϪ
Ѩ
Ѩ
ϭϪ
Ѩ
Ѩ
u
t
u
u
x
Ku u g
H

x
and



Ѩ
Ѩ
ϭϪ
Ѩ
Ѩ
H
tbx
uA
1
()
where
u ϭ velocity along the x -axis
x ϭ distance along the x -axis
H ϭ water surface elevation
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Hudson in New York (see Thomann and Mueller 1987 for an
MODELING OF ESTUARINE WATER QUALITY 719
g ϭ acceleration of gravity
K ϭ frictional resistance coefficient
t ϭ time
b ϭ mean channel width
A ϭ cross-sectional area of the channel.
The terms on the right hand side of the equation of
motion are, in sequence, the rate of momentum change by

mass transfer, the frictional resistance (with the absolute
value sign to assure that the resistance always opposes the
direction of flow), and the potential difference between the
ends of the channel element. In the continuity equation the
right hand side represents the change in storage over the
channel length per unit channel width. To minimize com-
putation, the equation of motion is applied to the channel
elements and the continuity equation to the junctions.
Both equations are rendered into partial difference form
and solved for each channel element and junction, using a
modified Runge-Kutta procedure. The results comprise the
predicted channel velocities, flows, and cross-sectional areas
and the predicted water surface elevations at each junction
for each time interval. These data are then input to the water
quality component of the model. The equations are put into
finite difference form and solved to give the concentration of
the substance at each junction.
Ward and Espey (1971) and Masch and Brandes (1971)
describe a segmented hydrodynamic and water quality model
which has been applied to Texas estuaries. Each segment is
a square one nautical mile on each side, and the estuary is
divided into these segments. Hydrodynamic transport across
segment boundaries is represented much as the equations
given above and occurs in response to forcing flows from
river inflow at the head of the estuary and tidal exchange
at the lower end. The model is able to simulate water stage
change within each segment and flows between segments
with change in tides, and the averages of the flows are used
in conjunction with the water quality portion of the model to
forecast concentrations of conservative and nonconservative

constituents.
A third type of two-dimensional model is that of
Leendertse (1970) who developed a water-quality simula-
tion model for well-mixed estuaries and coastal seas (i.e.,
no stratification) and applied it in Jamaica Bay, New York.
Leendertse and Gritton, 1971, have extended the model
to include the transport of several dissolved waste con-
stituents in the water, including any interactions among
them. The changing tide level influences the location of
the land-water boundaries in the shallow areas of coastal
waters. To simulate this process, procedures were devel-
oped in the model to allow for time-dependent boundary
changes. Large amounts of numerical data are generated
by the computer program developed from the simulation
model. To assist the investigator in extracting important
and meaningful results from these data, machine-made
drawings were used to graphically present the results of
the computation.
The basic mass-balance equation for 2-dimensional trans-
port of waste constituents in a well mixed estuary (uniform
concentration in the vertical directions) is given in Leendertse
(1970) as:



Ѩ
Ѩ
ϩ
Ѩ
Ѩ

ϩ
Ѩ
Ѩ
Ϫ
Ѩ
Ѩ
Ѩ
Ѩ
Ѩ
Ѩ
Ѩ
Ѩ
t
HP
x
HUP
y
HVP
x
HD
P
xy
HD
P
y
xy
() ( ) ( )
⎛
⎝
⎜

⎞
⎠
⎟
−
⎛
⎝
⎜
⎞
⎠
⎟⎟
ϪϭHS
A
0
where
P ϭ integrated average over the vertical of the waste
constituents mass concentration
U and V ϭ vertically averaged fluid velocity (compo-
nents in the x (eastward) and y (northward) directions
respectively)
S
A
ϭ source function
D
x
and D
y
ϭ dispersion coefficients
H ϭ instantaneous depth at a point.
The generalized mass-balance equation for n constitu-
ents is written in matrix notation as

Ѩ
Ѩ
ϩ
Ѩ
Ѩ
ϩ
Ѩ
Ѩ
Ϫ
Ѩ
Ѩ
Ѩ
Ѩ
Ϫ
Ѩ
Ѩ
Ѩ
Ѩ
t
HP
x
HUP
y
HVP
x
HD
P
x
y

HD
P
y
x
y
() ( ) ( )
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟⎟
ϩϩϭ[]KHP HS D

where
P
Ϫ


ϭ mass-concentration vector with n elements
[ K ] ϭ reaction matrix


S

Ϫ

ϭ source and sink vector.
The reaction matrix [ K ] in its most general form can give
rise to a non-linear transport equation. This occurs because
the individual elements of the matrix can be defined as func-
tions of their own concentration, or that of other constitu-
ents or both. Since the elements of [ K ] are multiplied by the
elements of the concentration vector, such non-linear terms
imply kinetics of an order higher than first.
Point sources, such as occur at the location of sewage
discharges into the estuary, are simulated by adding delta-
function source terms to the source vector.
For two-dimensional flow in a well-mixed estuary, verti-
cal integration of the momentum and continuity equations
yields the following basic equations for the flow model

Ѩ
Ѩ
ϩ
Ѩ
Ѩ
ϩ
Ѩ
Ѩ
Ϫϩ
ϩ
ϩ
Ϫϭ
ϩ

U
t
U
U
x
V
u
y
fV g
x
g
UU V
CH
H
V
t
U
V
x
s
Ѩ
Ѩ
Ѩ
Ѩ
Ѩ
z
r
t
()
/2212

2
1
0
ѨѨ
Ѩ
Ѩ
Ѩ
Ѩx
V
V
y
fU g
y
g
VU V
CH
H
y
s
ϩϩϩ
ϩ
ϩ
Ϫ
z
r
t
()
/2212
2
1

0=



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720 MODELING OF ESTUARINE WATER QUALITY

Ѩ
Ѩ
Ѩ
Ѩ
Ѩ
Ѩ
z
tx
HU
y
HVϩϩϭ() ()0
where
f ϭ Coriolis parameter
g ϭ Acceleration of gravity
C ϭ Chezy coefficient


t
x
s

ϭ Component of the wind stress in the x direction

t
y
s

ϭ Component of the wind stress in the y direction
r ϭ Water density
z ϭ water level elevation relative to the reference
plane.
The wind stress components are given by



tur w
tur w
x
s
y
s
ϭ
ϭ
a
a
W
W
2
2
sin
cos
where
u ϭ wind stress coefficient ≈ 0.0026

r
a
ϭ atmospheric density
W ϭ wind velocity
w ϭ angle between the wind direction and the y axis.
In the finite difference approximations of these equations,
the discrete values of the variables are described on a space-
staggered grid. The position and time coordinates (x, y, t)
are represented on the finite grid by (j ∆ x, k ∆ y, n ∆ t), for j, k,
n ϭ 0,

Ϯ1/2, Ϯ1, Ϯ3/2, K.
Water levels and pollutant concentrations are computed
at integer values of j and k (x and y directions). Water depths,
obtained from a field survey, are given at half-integer values
of j and k. The velocity component U (x directed) is com-
puted at half integer values of j and integer values of k, and
the velocity component V (y directed) is computed at integer
values of j and half-integer values of k.
The set of finite different equations used to approxi-
mate the momentum and mass-balance equations are then
presented at two adjacent time levels, n and

(n ϩ 1/2).
Numerical computation of the reaction matrix terms in the
mass-balance equations is accomplished by a sequential
use of forward and backward information. If M constitu-
ents are transported, then for constituent i(1 Ͻ i Ͻ M), in
the first operation at time level n (going from t to t ϩ 1/2⌬t),
information is used in the reaction matrix terms on the level

(t ϩ ∆ t) for all constituents for which the sequence num-
bers m is smaller than i. Information at the level t is used
for which m Ͼ i. In this step, the constituents are computed
is ascending order, from 1 to M.
In the second operation, at time level n ϩ 1/2

(going
from t

ϩ 1/2 ∆t to t ϩ ∆ t), the constituents are computed in
descending order, M to 1. Information on the level

t ϩ 1/2⌬t
is used for all constituents whose m Ͻ i, and information on
the level

t ϩ 1/2⌬t

is used for all constituents whose m Ͼ i.
This procedure centers the reaction matrix information of the
mass-balance equations within the time interval t to t ϩ ∆ t.
The reaction matrix terms which involve the ith constituent
itself are taken centered over each half time step.
The sequential use of finite-difference approximations
for the continuity equations at n and n ϩ 1/2

results in
alternating forward and backward differences. This means
that over a full time step the terms are either central in time
or averaged over the time interval. In the first operation at

time level n (going from t to

t ϩ 1/2⌬t), the momentum and
continuity equations are solved first for the water levels
and x-directed velocities at time level

n ϩ 1/2. The infor-
mation generated is then used in the mass balance equa-
tions to obtain the constituent concentrations at time level

n ϩ 1/2.
The results of this first operation are then used at time level

n ϩ 1/2 to determine the unknowns in the second half timestep,
going from

t ϩ 1/2⌬t to t ϩ ∆ t. Again, the momentum and con-
tinuity equations are solved first, but this time the water levels
and y-directed velocities at time level n ϩ 1 are obtained. This
new information is then used in the mass balance equation to
obtain pollutant concentrations at time level n ϩ 1.
This procedure is then repeated for each succeeding full
time step. The model can be used to investigate the influence
of wind on low and circulation in the area covered, together
with its effect on water levels and distribution of pollutants.
This was the first time that real wind effects were investi-
gated in detail.
The need for three dimensional models has been rec-
ognized for salt wedge type and moderately stratified
estuaries, and three dimensional mathematical models

of real estuaries have been developed. Leedertse and Liu
(1975) developed a three dimensional code for water
movements, salinity, and temperature which was applied
to San Francisco and Chesapeake Bays and later to the
Bering Sea, Chukchi Sea, the Beaufort Sea, and the Gulf
of Alaska (Liu and Leendertse 1987). Other three dimen-
sional models include that of Oey (1985) who modeled the
Hudson-Raritan estuary.
SOURCES AND SINKS
In addition to the hydraulic regime of an estuary, the other
factors which have great influence on the water quality of
estuaries are the sources and sinks of the materials. The cir-
culation patterns and water movement in estuaries will dic-
tate the distribution of fresh and salt water in the estuary.
Superimposed on this distribution is another pattern made up
of materials introduced by sources and lost to sinks.
In all these equations, the source and sink terms become
zero for conservative substances. For non-conservative sub-
stances, reactions that take place may usually be represented
by first-order kinetics, i.e., the rate of reaction is propor-
tional to the concentration of the material. In some cases the
reaction term defines the fundamental reaction mechanism,
whereas in other uses it is an empirical approximation to the
phenomenon.
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MODELING OF ESTUARINE WATER QUALITY 721
While as a general rule the modeling of the hydrody-
namic transport of a constituent in an estuary is much fur-
ther advanced than the modeling of its reaction kinetics,

the most commonly unsatisfactory aspect of present water
quality models is the specification of the source and sink
terms. Many of the physical-chemical processes affecting
the concentration of parameters lack adequate formulation.
These include sedimentation and deposits of particulate
matter, non-linear reaction kinetics, surface exchange of
gaseous constituents, and chemical and biological reactions.
Modeling of the relation of water quality and estuarine biota
is not well advanced. Models of phytoplankton production,
of nitrogen cycling, and of gross ecological parameters have
been attempted with limited success.
Sources
Sources for the materials which are found in the waters of
estuaries include two major sources, river inflow and ocean
water inflow. The concentrations (or ranges) of selected
chemical constituents of fresh and ocean waters are given in
Table 1. Fresh waters may have large ranges of concentra-
tions of the lands which they drain. These ranges are quite
different from those of oceanic waters. In fresh waters, cal-
cium is usually the most abundant cation and sulfate is the
most abundant anion although carbonate may also be quite
high in concentration. In sea water, on the other hand, chlo-
ride is the most abundant constituent and anion followed by
sulfate and bicarbonate. Sodium and magnesium constitute
the majority of the cations. Depending on the relative balance
of river inflow and the incursion of seawater brought in by
tidal action, the quality of the water in the estuary assumes a
composition in proportion to the two sources. However, the
location of constituents from the various sources either later-
ally in the estuary or vertically in the water column is highly

dependent on the circulation patterns existing in the estuary
which were discussed earlier.

Although in relation to river and tidal flows, direct pre-
cipitation is a small hydraulic input to an estuary, its water
quality cannot be ignored. In shallow bays with little river
inflow and a restricted opening to the ocean such as bar-built
estuaries, rainfall directly on the estuary may be an impor-
tant source of fresh water.
Waste discharges may exert a dominant influence on
the water quality of estuaries depending on the amount of
material discharged and its character. Because urbaniza-
tion typically occurs around estuaries, waste discharges
are usually directed to the estuaries since they are the most
convenient waste disposal site. Domestic wastes, wastes
derived from municipalities and ultimately humans, con-
tains large amounts of organic and nutrient (nitrogen,
phosphorus, trace) materials. Some typical concentration
rial discharged to estuaries or other bodies of water may be
estimated by knowing the population served by a sewerage
system and mass discharge coefficients. These coefficients
indicate the amount of material discharged per person per
day. Such coefficients are also given in Table 2.
Industrial wastes also reach estuaries either as a direct
discharge to the estuary, as spills from vessels carrying mate-
rials to or from the industries, as the result of dredging activ-
ities, as the discharge of heated effluents from power plants
and heated effluents from nuclear power plants which also
carry radioactive materials, and in other forms. Most indus-
trial activities involve the use of and/or the disposal of water.

Such waters usually contain the by-products of the industrial
process and are characteristic of the process. For example in
manufacturing steel, a certain amount of water is required
for cooling and washing purposes. The amount of water used
to produce a ton of steel by a given process is fairly consis-
tent and the quality of the water resulting from the process is
activities, the amount of water used in the activity, and the
pounds of oxygen required to oxidize the organic material
in the wastewater as well as the pounds of suspended solids
produced in making some unit amount of product.
Another source of waste material is urban and rural
runoff. Urban runoff may consist of storm water runoff from
the streets and gutters which is routed to the nearest water-
way by storm water pipes, or it may consist of a mixture of
storm water runoff and sanitary sewage in what is called a
combined sewer system. Such systems are typical of older
cities in the United States and other countries which built one
pipe to carry both sanitary wastes and storm water wastes.
TABLE 1
Quality of fresh and ocean water
(Concentration units are mg/L)
Constituent Fresh Ocean
Chloride 1.0–1,000 18,980
Sodium 1.0–1,000 10,560
Sulfate 1.0–1,000 2,560
Magnesium 1.0–1,000 1,272
Calcium 1.0–1,000 400
Potassium 0.01–10.0 —
Bicarbonate 1.0–1,000 142
Carbonate 0.01–10.0 —

Bromide 0.0001–0.1 65
Strontium 0.01–10.0 65
Boron 0.01–10.0 4.6
Fluoride 0.01–10.0 1.4
Aluminum 0.0001–0.1 0.16–1.9
Iodide 0.0001–0.1 0.05
Silicate 1.0–1,000 0.04–8.6
Nitrogen 0.01–10.0 0.03–0.9
Zinc 0.0001–0.10 0.005–0.014
Lead 0.0001–0.1 0.004–0.005
Iron 0.01–10.0 0.002–0.02
Phosphorus 0.0001–0.1 0.001–0.10
Mercury — 0.0003
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© 2006 by Taylor & Francis Group, LLC
also fairly consistent. Table 3 lists various types of industrial
values are given in Table 2. The relative amounts of mate-
722 MODELING OF ESTUARINE WATER QUALITY
TABLE 2
Quality of domestic wastes (Concentration units are mg/L)
Constituent Strong Medium Weak
Mass discharge coefficients
(9 lbs/person/day)
Solids, Total 1,000 500 200 —
Volatile 700 350 120 —
Fixed 300 150 80 —
Suspended, Total 500 300 100 0.23
Volatile 400 250 70 —
Fixed 100 50 30 —
Dissolved, Total 500 200 100 —

Volatile 300 100 50 —
Fixed 200 200 50 —
BOD (5-Day 20°C) 300 200 100 0.2
Dissolved Oxygen 0 0 0 —
Nitrogen, Total 86 50 25 0.06
Organic 35 20 10 0.035
Ammonia 50 30 15 —
Nitrites (NO
2
) 0.10 0.25 0 0.025
Nitrates (NO
3
) 0.40 0.20 0.10 —
Chlorides 175 100 15 —
Alkalinity 200 100 50 —
Fats 40 20 0 0.03
Phosphorus — — — 0.012
Flow — — — 135 gal/person/day
Source: Water Encyclopedia, 1971.
TABLE 3
Industrial wastes characteristies
Industry
(Unit)
Flow
(gal/unit)
BOD
(lb/unit)
Suspended solids
(lb/unit)
Brewery (Barrel) 370 1.9 1.03

Cannery (Case) 75 0.7 0.8
Dairy (100 LB.)
Butter 410–1,350 0.34–1.68 —
Cheese 1,290–2,310 0.45–3.0 —
Ice Cream 620–1,200 0 —
Milk 200–500 0.05–0.26 —
Meat Packing (100 LB.
live wt. killed)
1,294 14.4 —
Poultry Proc.
(1000 birds)
10,400 26.2 —
Petrol, Ref. (Barrel) 100 0.1 —
Pulp and Paper (ton)
Bleached kraft 45,000 120 170
Bleached sulfite 55,000 330 100
Steel Mill (Injet Ten) 10,000 — 100
Tannery (100 LB.) 660 6.2 13.0
Textile (LB. Cloth)
Wool 63 0.30 —
Cotton 38 0.16 0.07
Synthetics 15 0.07–0.10 0.02–0.07
Source: Malina, 1970.
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© 2006 by Taylor & Francis Group, LLC
MODELING OF ESTUARINE WATER QUALITY 723
TABLE 4
Combined sewer overflow and urban storm runoff characteristics
Constituent
Flow wtd. conc.

(mg/l)
b
Mass discharge
(lb/acre/in. runoff)
c
Coefficients
(lb/acre/ year)
d
BOD 150 30 125
SS 325 70 600
VSS 200 45 180
HEM 50 10 38
TKN 12 3 13
NH
3
N5——
NO
3
˜
N 0.2 — —
Total
ϳ
P 5.0 1 3
Total coli
a
5 ϫ 10
5
——
Fecal coli
a

0.5 ϫ 10
5
——
Urban Runoff
Mass discharge
Coefficients
(lb/acre/in.
runoff)
b
Constituent
Flow wtd.
conc. (mg/l) (lb/acre/year)
b
(lb/acre/in.
runoff)
b
BOD 18 33 2.0 4.1
SS 77 730 45.6 17.4
VSS 25 160 10.0 5.7
HEM 2.8 — — —
TKN 1.2 9 0.56 0.26
TP 0.3 2.5 0.05 0.07
TC
a
9 ϫ 10
3
FC
a
3 ϫ 10
3

a
Units are MPN/ml.

b
Data from Weibel et al., 1964.

c
Data from Spring Creek Project, 1970.

d
Data from San Francisco, 1967.
Because of economics the pipe could be built just so big,
and at the size it could carry all the domestic wastes during
dry weather but only a portion of the wastes during wet
weather. During a large storm, the pipe would fill to capac-
ity and the flow would have to be diverted to a waterway to
insure that backups did not occur in the sewage system. For
such drainage systems, each large rainfall results in a certain
amount of material being washed into the nearest waterway.
The amount of material produced is highly dependent on the
drainage system itself, on the use of land in the drainage
TABLE 5
Quality of rural runoff
Source
Total nitrogen
(lb/acre/year)
Total phosphorus
(lb/acre/year)
Forest Runoff 1.3–3.0 0.3–0.8

Surface Irrigation
Return flow 2.45–24.0 0.92–3.88
Subsurface
Irrigation
Return flow 38.0–66.0 2.5–8.1
Urban Runoff 8.5 0.8
Source: Fruh, 1968.
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724 MODELING OF ESTUARINE WATER QUALITY
area, and for some systems on the stage of the tide when the
overflow occurs. The quality of such wastewater is given in
detailed discussion of this type of wastewater is given in

Rural runoff, though less innocuous than urban runoff,
cannot be disregarded as a wastewater source. Mass dis-
charge coefficients relating to quality of the runoff water
Miscellaneous waste discharges occur into estuaries which
cannot be quantified in the way done for other types of
waste discharges. These include such waste as oil spills,
spills of toxic or hazardous materials waste from houseboats
or larger vessels with quarters for crew for living purposes,
dredging spoils, heat from power or nuclear plants, and other
sources.
Another source of material in estuaries is biological recy-
cling. Although biological recycling may also be considered
as a sink and will be discussed as such later, recycling of
material is extremely important in transforming waste mate-
rials from man-made waste discharges (or waste discharges
from other lower animals or even dead organisms) to a chem-

ical form in which it may be used again by the biological
system. For example, organic material in a domestic waste
discharge is oxidized at least partially by bacteria to carbon
dioxide and water. Carbon dioxide is a necessary constitu-
ent for the growth of plants in conjunction with light. The
process of photosynthesis using light reduces carbon dioxide
in an organic material which is incorporated in the tissues of
the plant. Since plants comprise the basic food stuff for all
organisms, the recycling of carbon from the organic form to
the inorganic form as carbon dioxide is vitally important.
Similarly, nitrogen, which may be in an organic form in a
waste discharge, is oxidized by plants for growth. In both
cases the organic form acts as a sink while concurrently the
inorganic form becomes the source.

Sinks
There are several types of water quality sinks in estuaries.
Water withdrawal from an estuary is one type of sink; with-
drawals may be made for industrial uses such as salt produc-
tion or for cooling purposes. In the latter case, some water may
be returned to the estuary in a heated condition, but the water
withdrawn which is lost in the cooling process as evaporation
is lost to the estuary. Sedimentation becomes another sink as
molecules of material which were in the water column sorb
into the particulate matter which settles out and becomes part
of the bottom sediment. Unless the bottom sediment is dis-
turbed, eroded or dredged, this material is essentially lost to
the water column. Precipitation may also occur to tie up sev-
eral minerals which then settle out on the bottom and as with
sedimentation are lost from the water column. Precipitation

quite commonly occurs in estuaries which have little fresh
water inflow but a high evaporation rate. These estuaries are
known as hypersaline estuaries because the salinity content
rises to levels above that of normal sea water. In the Laguna
Madre Bay of Texas, salinity levels reach two or three times
that of normal sea water. In this bay, crystals of gypsum are
found on the shores.
Another type of sink which is tied intimately to the bio-
logical system of the estuary is the degradation of materials,
that is, the change from one chemical form to another by
biological action. Above, the process of oxidation of organic
material was mentioned. This is one form of oxidation in
which organic material is oxidized to smaller molecular mate-
rial, which is further oxidized to carbon dioxide and water as
the ultimate inorganic products. Oxygen is consumed in the
process and is lost to the water. Another oxidation process is
nitrification. In this process, nitrogen in the organic form is
oxidized to ammonia which is then further oxidized by the
bacterium, Nitrosomonus to nitrite and further to nitrate by
the bacterium, Nitrobacter. Under low oxygen or anaerobic
conditions, the nitrate or nitrite may be reduced by bacteria
to elemental nitrogen gas which may then be removed from
the system according to the solubility of the nitrogen gas.
QUALITY NEEDED FOR ESTUARY USE
SUSTENANCE
Now that some of the hydraulic, biological, and man-made
mechanisms which influence water quality in estuaries have
been described, the use concept for estuaries and the water
quality needed to sustain uses should be considered.
As an example, the San Francisco Bay-Delta Study

Report (1969) listed some of the uses which can be made of
varied and in some cases would be competing uses if applied
to the same part of an estuary. For combinations of uses for a
given area in an estuary, usually one use will require a water
quality higher than the other uses, and this use will dictate
the water quality needed in that particular area. Some of the
uses listed are not really dependent on water quality such as
shipping, unless the quality is particularly adverse (very acid
water or large floating material).
The general philosophy of estuary use in particular or
resource use in general is that a range of uses may exist
bounded by two extreme views. These views are: (1) a
resource may be used indiscriminately without regard to
the consequences (e.g., total consumption, contamination,
etc.) of that use; and (2) a resource should be preserved with
no interaction with man. Both views, despite being held
by some are recognized as incompatible, and the concept
of sustained use, the designation of some use or uses for
a resource area and management of the system to support
that use best, is favored. As mentioned at the beginning of
this article, the designation of uses for estuarine areas in
all states through public hearings was a recognition of the
sustained use concept. However, subsequent attempts to
manage waste inputs to estuarine systems and the estuarine
systems themselves have shown how difficult management
is. The difficulties lie in the technical aspects of manage-
ment (the interrelatedness of water quality with estuarine
circulation and sources and sinks), the economic aspects
(the cost of management systems directly and indirectly),
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Table 4 as well as some mass discharge coefficients. A more
to the land use and amount of rainfall are given in Table 5.
estuaries, and these are given in Table 6. These uses are quite
another part of this Encyclopedia (see Urban Runoff ).
MODELING OF ESTUARINE WATER QUALITY 725
and the socio-political-legal aspects (the interrelatedness of
social desires and political decisions and the lack of ade-
quate pollution control laws).
For each of the uses listed in Table 6, a list of physical,
chemical and/or biological properties or constituents may be
compiled. This list would indicate the levels of the proper-
ties or constituents which have to be provided or cannot be
exceeded if that use is to be sustained. These constituent lists
have changed as they have been found to be unimportant
or found to be needed, and as the levels have changed new
knowledge has been gained about how the levels more spe-
cifically affect the desired use. The extension of water quality
criteria to toxic materials in recent years (U.S. Environmental
Protection Agency 1976, 1986) indicates how emphasis has
shifted from one set of criteria for which waste discharge
problems have been solved essentially to another set which
is comprised of substances of major concern today.
Unfortunately at this time, very little is known about the
bases for many levels set. For example, good epidemio-
logical evidence relating fecal or total coliform organism
concentrations in swimming areas to disease is still lacking.
A larger gap, however, is the criteria list for the fish and wild-
life of estuaries and the organisms they feed on. For these
organisms the best information available pertains to tem-

perature, dissolved oxygen, pH and salinity. Beyond these
criteria, the levels set for other materials such as toxic sub-
stances are being developed (U.S. Environmental Protection
Agency 1986).
The reader may obtain more specific information about
water quality in general and estuarine water quality in partic-
ular by referring to the bibliography references and to other
related material. Of special interest might be the reports
of studies on major estuaries such as San Francisco Bay,
Galveston Bay, Delaware Bay, and Jamaica Bay. The studies
include not only the theory of water quality but the practical
techniques for and applications of its management.
REFERENCES
1. Characterization and treatment of combined sewer outflows, report
to Federal Water Pollution Control Admin. by City of San Francisco.
Prepared by Engineering-Science, Inc., November, 1967.
2. Feigner, K.D. and H.S. Harris, “Documentation Report—FWQA
Dynamic Estuary Model,” U.S. Department of the Interior, FWQA,
1970.
3. Fischer, H.B. Transport Models for Inland and Coastal Waters, Aca-
demic Press, 1971.
4. Fischer, H.B., E.J. List, R.C.Y. Koh, J. Imberger, and N.H. Brooks,
Mixing in Inland and Coastal Waters, Academic Press, 1979.
5. Fruh, E.G., in Advances in Water Quality Improvement, Eds. E.F.
Gloyna and W.W. Eckenfelder, Jr., Univ. of Texas Press, Austin, 1968.
6. Geyer, R.A., in The Biological Significance of Estuaries, Sport Fishing
Institute, March, 1971.
7. Leendertse, J.J., RM-6230-RC, The Rand Corporation, February,
1970.
8. Leendertse, J.J., Rand Corp. Publication RM-6230-RC, Febr. 1970.

9. Leendertse, J.J. and E.C. Gritton, The New York City Rand Institute,
R-708/6-RC, July 1971.
10. Leendertse, J.J. and S-K. Liu, A Three Dimensional Model for Estuar-
ies and Coastal Seas: Vol. II, Aspects of Computation, R-1764-OWRT,
The Rand Corporation, June 1975.
11. Liu, S-K. and J.J. Leendertse, Modeling the Alaskan Continental Shelf
Waters, R-3567-NOAA/RC, October 1987.
12. Malina, J.F., Jr., Report No. CRWR 69, Center for Research in Water
Resources, University of Texas, October, 1970.
13. Masch, F.D. and R.J. Brandes, Tech. Rept. HYD 12-7102, Hydraulic
Engineering Laboratory, University of Texas, August 1971.
14. McHugh, J.L., in A Symposium on Estuarine Fisheries, Special Publ.
No. 3, 133154. Amer. Fish. Soc., Wash., D.C., 1966.
15. McHugh, 1967, in Estuaries, Pub. No. 83, AAAS, 1967.
16. National Estuarine Pollution Study, U.S. Gov’t. Printing Office, 1971.
17. O’Connor, D.J. and R.V. Thomann, in Estuarine Modeling: An Assessment,
Environmental Protection Agency, Project 16070 DZV, February, 1971.
18. Oey, L-Y., A three-dimensional simulation of the Hudson-Raritan
estuary, J. Phy. Ocean. 15(12), 1985.
19. Pritchard, D.R., in Estuaries, Pub. No. 83, AAAS, 1967.
20. Russell, J.J., in Estuaries, Pub. No. 83, AAAS, 1967.
21. San Francisco Bay-Delta Water Quality Control Program, final report
to the State of California by Kaiser Engineers and Associated Firms,
March 1969.
22. Stroud, R.H., in The Biological Significance of Estuaries, Sport Fishing
Institute, March, 1971.
23. Thomann, R.V. and J. Mueller, Principles of Surface Water Quality
Modeling and Control, Harper & Row, 1987.
24. U.S. Environmental Protection Agency, Quality Criteria for Water, 1976.
25. U.S. Environmental Protection Agency, Quality Criteria for Water,

1986.
TABLE 6
Beneficial uses to be protected in San Francisco Bay
Municipal Supply (seasonal)
Industrial Supply
Boiler
Cooling
Rinsing
Processing
Agricultural Supply (some seasonal)
Irrigation
Liverstock
Fish and Wildlife Propogation and Aquatic Growth
Fish habitat, migration, spawning
Shrimp and crab habitat
Shellfish habitat
Waterfowl habitat
Mammal rookery
Kelp
Comercial Fishing and Shellfishing
Recreation
Swimming, waterskiing, skindiving, picnicking
Surface, beachcombing, sunbathing
Pleasure boating
Fishing
Shellfishing
Hunting
Enjoyment of Esthetic Values
Tidepool and Marine Life Study
Navigation

Resource Extraction
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726 MODELING OF ESTUARINE WATER QUALITY
26. U.S. Environmental Protection Agency, The National Estuary Program,
1989.
27. Ward, G.H. and W.H. Especy, in Estuarine Modeling: An Assessment,
Environmental Protection Agency, Project 16070 DZV, February
1971.
28. Water Quality Criteria, Report of the National Technical Advisory
Committee of the Federal Water Pollution Control Administration to
the Department of the Interior, April, 1968.
29. Weibel, S.R., R.J. Anderson, and R.L. Woodward, J. Wat. Poll Contr.
36(7), 914, 1964.
30. Water Encyclopedia, David K. Todd, Water Information Center, Port
Washington, N.Y., 1970.
NEAL E. ARMSTRONG
University of Texas at Austin

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