714 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. C013_006_r03.indd 714C013_006_r03.indd 714 11/18/2005 12:49:00 PM11/18/2005 12:49:00 PM © 2006 by Taylor & Francis Group, LLC 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 C013_006_r03.indd 715C013_006_r03.indd 715 11/18/2005 12:49:00 PM11/18/2005 12:49:00 PM © 2006 by Taylor & Francis Group, LLC 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 C013_006_r03.indd 716C013_006_r03.indd 716 11/18/2005 12:49:00 PM11/18/2005 12:49:00 PM © 2006 by Taylor & Francis Group, LLC MODELING OF ESTUARINE WATER QUALITY 717 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 C013_006_r03.indd 717C013_006_r03.indd 717 11/18/2005 12:49:01 PM11/18/2005 12:49:01 PM © 2006 by Taylor & Francis Group, LLC 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 C013_006_r03.indd 718C013_006_r03.indd 718 11/18/2005 12:49:01 PM11/18/2005 12:49:01 PM © 2006 by Taylor & Francis Group, LLC 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= C013_006_r03.indd 719C013_006_r03.indd 719 11/18/2005 12:49:01 PM11/18/2005 12:49:01 PM © 2006 by Taylor & Francis Group, LLC 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. C013_006_r03.indd 720C013_006_r03.indd 720 11/18/2005 12:49:01 PM11/18/2005 12:49:01 PM © 2006 by Taylor & Francis Group, LLC 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 C013_006_r03.indd 721C013_006_r03.indd 721 11/18/2005 12:49:02 PM11/18/2005 12:49:02 PM © 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. C013_006_r03.indd 722C013_006_r03.indd 722 11/18/2005 12:49:02 PM11/18/2005 12:49:02 PM © 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. C013_006_r03.indd 723C013_006_r03.indd 723 11/18/2005 12:49:02 PM11/18/2005 12:49:02 PM © 2006 by Taylor & Francis Group, LLC [...]... 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...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 Table 4 as well as some mass discharge coefficients A more detailed discussion of this type of wastewater is given in another part of this Encyclopedia (see Urban Runoff) Rural runoff, though less innocuous than urban runoff, cannot be disregarded... disregarded as a wastewater source Mass discharge coefficients relating to quality of the runoff water to the land use and amount of rainfall are given in Table 5 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... 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 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... 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. .. other materials such as toxic substances 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 particular 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... this bay, crystals of gypsum are found on the shores Another type of sink which is tied intimately to the biological 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... lower animals or even dead organisms) to a chemical 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 constituent for the growth of plants in conjunction with light The process of photosynthesis using light reduces carbon dioxide in an... Processing Agricultural Supply (some seasonal) Irrigation Liverstock Fish and Wildlife Propogation and Aquatic Growth Fish habitat, migration, spawning 725 A larger gap, however, is the criteria list for the fish and wildlife of estuaries and the organisms they feed on For these organisms the best information available pertains to temperature, dissolved oxygen, pH and salinity Beyond these criteria, the... 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 . 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. 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. 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