A MATHEMATICAL MODEL FOR EVALUATING THE POTENTIAL OF DESALTING1

ABSTRACT The Office of Saline Water, which has federal responsibility for developing low-cost, saline sources of fresh water, has recognized the need for an improved method of forecasting the future potential of desalting in this country. The magnitude of the role of desalting will influence the plans of federal, state, and local water resource agencies and the research and development programs of manufacturers. A dynamic simulation model has been developed by Arthur D. Little, Inc. under contract by OSW to translate relevant factors of water supply and demand into a forecast of desalting potential. The model projects the needs for desalting in 20 hydrologic regions of the U.S. Model performance has thus far been demonstrated by the development of a forecast and a battery of related sensitivity tests. Current results indicate the following potential desalting capacities: 225 MGD in 1980; 2,250 MGD in 2000; and 7,000 MGD in 2020. Significant improvements in desalting economics promise to increase these potentials by a factor of four or five by 2000-2020. Model inputs and results are continuing to be refined. When completed, OSW will have a dynamic tool with which to guide its R&D program.     

A MODELLING METHOD FOR EVALUATING WATER QUALITY POLICIES IN NONSERIAL RIVER SYSTEMS1

ABSTRACT: This paper describes a modelling method which simplifies the evaluation of water quality policies for nonserial (branching) river systems. The method introduces dummy facilities at the junctions of the major tributary branches with the mainstream as replacements for the facilities and activities on the tributaries. The cost functions for the dummy facilities and the DO and BOD concentrations at the junctions as determined for each tributary are introduced into the mainstream serial system model which is then solved for the optimal values of the mainstream treatment plant efficiencies, the dummy facility effeciencies, and the tributary system DO and BOD concentrations using nonlinear programming. Given the optimum values for the dummy facility efficiencies and the values for the tributary system DO and BOD concentrations, the optimum values for the tributary treatment plant efficiencies are found using nonlinear programming. The method is applied to a river system with a mainstream and one major tributary which contain industrial and municipal organic and thermal polluters and their associated wastewater treatment plants.     

A WATER QUALITY MODEL FOR A CONJUNCTIVE SURFACE-GROUNDWATER SYSTEM: AN OVERVIEW1

ABSTRACT. A mathematical model to predict water quality in a surface-groundwater system is under development. This project is being sponsored by the Environmental Protection Agency. The ultimate goal of this study is to obtain cause and effect relationships between pollutant sources and the ensuing concentrations at different locations in a basin. Several programs are used to model the various hydrologic processes occurring in nature, namely: rainfall, runoff, flow in surface bodies of water, infiltration, and groundwater flow. At every time step in the simulation, the water quantity computations for the above hydrologic models are performed first. Subsequently, the results of these computations, typically in the form of flow velocities, are used as input to the water quality calculations. The water quality routines involve the modeling of the associated physical, chemical, and biological processes. In this study, emphasis is being placed on pollution in agricultural areas. Accordingly the Lake Apopka basin in Central Florida is being used as the application site.     

TECHNIQUES FOR DETECTING TRENDS IN LAKE WATER QUALITY1

ABSTRACT: With the advent of standards and criteria for water quality variables, there has been an increasing concern about the changes of these variables over time. Thus, sound statistical methods for determining the presence or absence of trends are needed. A Trend Detection Method is presented that provides: 1) Hypothesis Formulation - statement of the problem to be tested, 2) Data Preparation - selection of water quality variable and data, 3) Data Analysis - exploratory data analysis techniques, and 4) Statistical Tests - tests for detecting trends. The method is utilized in a stepwise fashion and is presented in a nonstatistical manner to allow use by those not well versed in statistical theory. While the emphasis herein is on lakes, the method may be adopted easily to other water bodies.     

WATER QUALITY MANAGEMENT: THE CASE FOR RIVER BASIN AUTHORITIES1

ABSTRACT: There is a lamentable absence of comprehensive planning in the current cursade to improve water quality. A serious shortcoming is the lack of evaluation of the effects of waste water treatment upon environmental quality. At some point in time the public may ask what they have obtained for their money. The nature of pollution in a river basin demands a coordinated attack against it. Engineering and economic criteria suggest that a properly empowered river basin authority would be the logical organization to plan and operate a water quality management system. Several forms of such authorities have operated effectively and efficiently for many years in the United States and other industrialized countries. Examples of successful river basin authorities and their advantages and methods of operation are discussed.     

A MULTIOBJECTIVE MODEL FOR REGIONAL WATER QUALITY MANAGEMENT1

ABSTRACT: Linear programming is the simplest of all the optimization techniques used in regional water quality management studies; but the technique can optimize only one goal. When there are multiple goals with the same or different priorities, goal programming is a useful decisionmaking tool. This paper illustrates the application of goal programming to a regional water quality management problem where the following two goals are considered: (1) minimize the total cost of waste treatment, and (2) maintain the water quality goals (dissolved oxygen) close to the minimum level stated in the stream standards.     

IMPACT OF DROUGHT ON QUALITY IN A NEW JERSEY WATER SUPPLY SYSTEM1

ABSTRACT. New Jersey, together with other states in the northeast, was stricken with drought during 1961-66. The effect of this drought was most severe in the northern part of the State. The water quality of the Passaic River, which drains the urban, industrialized northeast, perhaps deteriorated the most among the major drainage systems. This river system is used as a raw-water source by 10 water suppliers. The impact of the drought upon the water supply of the Passaic Valley Water Commission, the most downstream of the basin's suppliers, which supplies an average of about 90 million gallons a day to more than 650,000 persons, is evaluated herein. The drought's impact on the raw-water quality is appraised by the comparison of before-and-after qualities of dissolved solids, dissolved oxygen, biochemical-oxygen demand, turbidity, and hardness. For example, at the worst point during the drought, monthly average dissolved-solids content in the raw water were about 210 percent, hardness, about 167 percent, and biochemical-oxygen demand about 270 percent higher than antecedent values. In general, the study concludes that the drought produced a deterioration in both raw and finished water quality, and is estimated to have increased chemical-treatment costs during the drought by about $650,000.     

DISPERSION MODEL FOR A STREAM WITH SEVERAL WASTE INPUTS AND WATER INTAKES1

An analytical solution is developed to predict the BOD and DO profiles in a stream having several outfalls of waste and intakes of water. The model also incorporates continuous addition and removal of BOD and DO along the stream. A steady state one dimensional dispersion model is used to describe the transport of BOD and DO in a stream. Changes in stream properties along the length are considered by dividing the stream into several segments and changing the parameters of the BOD and DO equations as needed in each segment. By applying continuity equations at the boundaries of these segments and equilibrium conditions at either ends of the infinitely long stream, the arbitrary constants in the solutions to the differential equations for BOD and DO can be determined. Some applications of the results in studying water pollution problems are illustrated.     

IMPACT OF DROUGHT ON QUALITY OF POTENTIAL WATER SUPPLY SOURCES IN THE SANGAMON RIVER BASIN1

ABSTRACT: The analysis of stream flow and several water quality parameters in six Illinois rivers showed both deterioration and improvement in quality indicators during 1976–1977 drought. The adverse impacts were an increase of ammonia and manganese concentrations and, to a lesser degree, increased concentrations of phenol and specific conductance. At the worst point during the drought, the 12-month moving average of monthly ammonia concentration in the Sangamon River was about 620 percent higher than the antecedent value. On the other hand, average concentrations of nitrites and nitrates, total iron, and the number of coliform bacteria significantly decreased. This positive response suggests that streams which are considered unsuitable for municipal supply due to high levels of these quality indicators may be used as emergency sources during droughts.     

A STATISTICAL MODEL FOR SMALL LAKE WATER QUALITY MANAGEMENT1

ABSTRACT: Phosphorus loading tolerances of small lakes are analyzed by means of a statistical model of lake eutrophication based upon the work of Vollenweider and Dillon. Using a sample of 195 midwestern and eastern U. S. lakes, it was found that Vollenweider and Dillon's method of predicting the trophic status of relatively deep, slow-flushing lakes can be applied to shallower lakes with much shorter retention times. The statistical model used to replicate the results of Vollenweider and Dillon is stated in detail, for convenience of application to small lake water quality management problems. The model extends the Vollenweider and Dillon results by associating each alternative phosphorous loading with a probability that a given lake can achieve or maintain noneutrophis status. It is applicable to lakes for which only minimal data are available. The major policy conclusion is that the highly variable tolerance for phosphorus loading must be considered in legislating efficient effluent limitations. The paper concludes with a comparison to a recent contribution employing a similar approach.     

LINEAR PROGRAMMING APPLICATIONS IN WATER RESOURCES1

Applications of linear programming to water quality and water quantity problems are discussed, and a fairly comprehensive sample of recent literature in these areas is reviewed. Basic elements of linear programming are also discussed. Emphasis is placed on the elements of linear programming that make it a useful tool for analyzing water resource problems and the basic features of various water resource problems that render them amenable to meaningful analysis by linear programming.     

PHOSPHORUS MANAGEMENT TO PROTECT LAKE WATER QUALITY1

ABSTRACT: The Hallett Quarry gravel pit lakes are an active sand and gravel extraction operation located 0.4 km north of the City of Ames, Iowa. During periods of drought, these lakes serve as a supplemental water supply for Ames. A modified version of the Vollenweider input-output model was used to predict future water quality under various watershed land use, drainage, and lake configurations. The dominant factor controlling the future water quality of the lakes was found to be the nutrient input. It is recommended that a management plan to protect the future water quality should be oriented towards reducing the sources of phosphorus to the lakes.     

A VERIFICATION OF THE QUAL-1 WATER QUALITY MODEL FOR THE LOWER MISSISSIPPI RIVER1

ABSTRACT: This paper describes the verification of the QUAL-1 mass transport model for the lower Mississippi River between St. Francisville and Point a la Hache using dye studies conducted by the U. S. Geological Survey. QUAL-1 is a one-dimensional steady-state model for rivers and is capable of predicting longitudinal profiles of soluble materials entering rivers from point sources. Both conservative and nonconservative parameters of water quality can be considered. The major problems surmounted were the determination of a diffusion coefficient and the use of transient data to verify a steady state model.     

WATER QUALITY PREDICTION WITHIN AN INTERBASIN TRANSFER SYSTEM1

ABSTRACT A methodology for predicting the spatial and temporal levels of conservative water quality constituents within a multibasin water resource system is presented. Dissolved solids, sulfates, and chlorides are the constituents used during this investigation; however, any other conservative ion or mineral can be incorporated into the simulation model. The methodology is tested on the proposed Texas Water System. The water quality model, QNET-I, utilizes monthly canal and river flows and reservoir storage levels calculated by the Texas Water Development Board's systems simulation model. Discharge-concentration relationships are developed for each source of water in the system, including significant waste-water discharges. Reservoirs in the system are assumed to be completely mixed with respect to conservative constituents. A mass balance analysis is performed for each node and each month during the simulation period. The output from the water quality simulation is a table of the concentrations of the conservative water quality constituents at each demand point in the system and in each reservoir and canal for every month the system is in operation. The desired quality of the water at the demand locations is used to determine the economic utility of transporting and mixing water from various sources.     

A COMPARATIVE STUDY OF LINEAR AND NONLINEAR TIME SERIES MODELS FOR WATER QUALITY1

ABSTRACT: Surface water quality data are routinely collected in river basins by state or federal agencies. The observed quality of river water generally reflects the overall quality of the ecosystem of the river basin. Advanced statistical methods are often needed to extract valuable information from the vast amount of data for developing management strategies. Among the measured water quality constituents, total phosphorus is most often the limiting nutrient in freshwater aquatic systems. Relatively low concentrations of phosphorus in surface waters may create eutrophication problems. Phosphorus is a non-conservative constituent. Its time series generally exhibits nonlinear behavior. Linear models are shown to be inadequate. This paper presents a nonlinear state-dependent model for the phosphorous data collected at DeSoto, Kansas. The nonlinear model gives significant reductions in error variance and forecasting error as compared to the best linear autoregressive model identified.     

MULTIVARIATE NONPARAMETRIC TESTS FOR TREND IN WATER QUALITY1

ABSTRACT: National and state fixed station stream quality monitoring networks have now been in existence for over ten years. The resulting data bases provide opportunities and challenges for statistical trend assessment. Although nonparametric tests have been developed that are well suited to such problems, the interpretation of variations in trend significance between seasons and variables remains a problem. One recently developed test is based on the sum of Mann-Kendall statistics over seasons or variables, with the test statistic variance computed as the sum of the covariances of the individual Mann-Kendall statistics. In this method, up- and downtrends can cancel, giving an overall indication of no trend. A related test which is sensitive to trend regardless of direction has been shown to behave poorly for typical stream quality record lengths. An alternative formulation which is sensitive to up- and downtrends and has power approaching that of the covariance sum method, is described. In addition, a variation of a contrast test for discriminating trend directions and magnitudes among variables or seasons where correlation between seasons or variables is present is described, and tests of its performance reported.     

A WATER QUALITY ASSESSMENT OF DEVELOPMENT IN THE SENEGAL RIVER BASIN1

A study was made to determine the impact on water quality due to water resource development in a large river basin in a semi-arid region of West Africa. Mathematical modeling and the examination of case histories were used to project impacts. The impacts associated with changes in water quality were shown to be slight assuming that modern basin and agricultural management practices are adopted. Analytical techniques normally implemented in studies of more highly developed basins are useful for analysis of water quality impacts in relatively undeveloped basins.     

WATER SUPPLY FORECASTING IN REAL-TIME1

ABSTRACT: A strategy is developed for making seasonal water supply forecasts in real time. It links the traditional regression based forecasting techniques to real-time data acquired by systems such as the Soil Conservation Service SNOTEL and the U.S. Bureau of Reclamation Hydromet networks. The concept is based on interpolating between the forecast values obtained by using real-time data in the forecast equations that bracket the real time. Different interpolation procedures were examined and the procedure for calculating confidence intervals about the forecast estimates is developed. The entire conceptual procedure is demonstrated using data from the Reynolds Creek, Idaho, experimental watershed maintained by the USDA-ARS Northwest Watershed Research Center in Boise, Idaho.     

A PARTITIONING PROCEDURE FOR WATER QUALITY MANAGEMENT MODELS1

ABSTRACT: An improved computational procedure for solving water quality management models containing interacting pollutants and control policies is presented. The method is developed with respect to the specific problem of minimizing the costs of basin-wide thermal and organic pollution control to meet water quality standards. It views the problem in partitioned form where a master problem is used to find cooling levels for thermal polluters while subproblems determine optimal organic pollutant reductions for fixed cooling levels. A gradient based search procedure is used to solve the master problem. Computational results for several river systems are presented. Application of the method to other water quality management models is suggested.