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

INTRODUCTION Estuarine water quality is a term used to describe the quality of characteristics of the water in estuaries.. That is, for certain uses of water, whether they be recreatio

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 livenhanc-ing 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

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

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 fricdirec-tion 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

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 distribuconcentra-tion 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

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:





C

C

C

C z

x u

⎛

( C C

∂

where

E  dispersion coefficient along each of the three axes

x , y , and z

u , v , w  velocity in x , y , or z direction respectively

S  source or sink for material

C  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):



C

⎝⎜ ⎞⎠⎟

where

A  cross sectional area of estuary

Q  freshwater inflow

E  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
C /
t 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-conservaconserva-tive 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



u

u

H x

and

H

1

where

u  velocity along the x -axis

x  distance along the x -axis

H  water surface elevation

g  acceleration of gravity

K  frictional resistance coefficient

t  time

b  mean channel width

A  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:



P

P y

⎛

⎛

⎝⎜

⎞

⎠⎟⎟HS A0 where

P  integrated average over the vertical of the waste

constituents mass concentration

U and V  vertically averaged fluid velocity

(compo-nents in the x (eastward) and y (northward) directions

respectively)

S A  source function

D x and D y  dispersion coefficients

H  instantaneous depth at a point

The generalized mass-balance equation for n

constitu-ents is written in matrix notation as



P x

P y

x

y

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟⎟[ ]K HPHSD

where

P

  mass-concentration vector with n elements

[ K ]  reaction matrix

S

  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 elemconstitu-ents 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







U

U

u

V

V

x s

z

r t

( 2 2 1 2)/ 2

1 0

V

s

z

r t

( 2 2 1 2)/ 2

1 0

=

z

t  x(HU) y(HV)0

where

f  Coriolis parameter

g  Acceleration of gravity

C  Chezy coefficient

t x s  Component of the wind stress in the x direction

t y s

 Component of the wind stress in the y direction

r  Water density

z  water level elevation relative to the reference

plane

The wind stress components are given by

t ur w

t ur w

x s

y s



 a a

W W

2 2

sin cos

where

u  wind stress coefficient ≈ 0.0026

ra  atmospheric density

W  wind velocity

w  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

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  0, 1/2, 1, 3/2, 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  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  i  M), in

the first operation at time level n (going from t to t  1/2t),

information is used in the reaction matrix terms on the level

(t  ∆ 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  i In this step, the constituents are computed

is ascending order, from 1 to M

In the second operation, at time level n  1/2 (going

from t  1/2 ∆t to t  ∆ t), the constituents are computed in

descending order, M to 1 Information on the level t  1/2t

is used for all constituents whose m  i, and information on

the level t  1/2t is used for all constituents whose m  i

This procedure centers the reaction matrix information of the mass-balance equations within the time interval t to t  ∆ 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  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  1/2t), the momentum and

continuity equations are solved first for the water levels and x-directed velocities at time level n  1/2 The

infor-mation generated is then used in the mass balance equa-tions to obtain the constituent concentraequa-tions at time level

n  1/2

The results of this first operation are then used at time level

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

going from t  1/2t to t  ∆ 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  1 are obtained This

new information is then used in the mass balance equation to obtain pollutant concentrations at time level n  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

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 verticlater-ally 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)

also fairly consistent Table 3 lists various types of industrial

values are given in Table 2 The relative amounts of

TABLE 2 Quality of domestic wastes (Concentration units are mg/L)

Mass discharge coefficients (9 lbs/person/day)

Source: Water Encyclopedia, 1971

TABLE 3 Industrial wastes characteristies Industry

(Unit)

Flow (gal/unit)

BOD (lb/unit)

Suspended solids (lb/unit)

Dairy (100 LB.)

Meat Packing (100 LB

live wt killed)

Poultry Proc.

(1000 birds)

Pulp and Paper (ton)

Textile (LB Cloth)

Source: Malina, 1970

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

Urban Runoff

Mass discharge

Coefficients (lb/acre/in

runoff) b Constituent

Flow wtd

(lb/acre/in.

runoff) b

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)

Surface Irrigation

Subsurface Irrigation

Source: Fruh, 1968