The traditional water-supply planning problem is characterized by two main steps: (1) project future water requirements based on present rates of economic growth, 'and (2) schedule water development projects to be introduced into the system on time to meet these predicted requirements. If alternative projects are thought to exist, the one thought to cost the least amount is selected. As project costs rise and actual new water availabilities become less, there is a growing awareness that more new water is not necessarily the only answer. Increased efficiency in water use through conservation, reuse, transfer to less consumptive and higher valued applications, and improved management techniques are becoming practical alternatives. These alternatives lead to a need for a restatement of water-supply planning objectives in more precise forms than have heretofore been put forth. The various water- supply planning objective functions including the traditional one are all expressions which maximize the difference between gains and los se s involved with water development. They can be expressed mathematically and differentiated on the basis of how these gains and losses are defined. In the traditional sense, gains derived from meeting projected requirements are assumed to be infinite, and losses are taken to be actual project costs; therefore, maximization of net gains is accomplished by minimizing project costs and gains do not even have to be expressed. Consideration of alternatives, however, requires that gains be expressed quantitatively as benefits to individuals, communities, or regions, i. e. , primary, secondary, or tertiary benefits. The same thing holds for the expression of total costs. An objective function used to express the water-supply problem in the Tucson Basin, Arizona, considers gains as cash revenue to a hypothetical central water-control agency which sells water to the users within the basin. Losses are considered as marginal costs to the agency for producing, treating, and distributing water. The concept of economic demand is used to estimate the amount of water that municipal, agricultural, and industrial users will purchase at different prices. The possible sources of supply considered are groundwater from within the basin, groundwater from the neighboring Avra Valley Basin, reclaimed waste water, and Central Arizona Project water from the Colorado River. Constraints are formulated in order to determine optimal allocations of water under different conditions. The model used is referred to as a pricing model and is optimized by first decomposing the objective function into component parts, each part representing terms involving only one source of water. Then in instances involving inequality constraints, quadratic programming is used. In other instances where equality constraints or unconstrained conditions exist, Lagrangian multipliers and the calculus are used. The se latter conditions arise when it is determined at which point certain constraints become inactive. In the completely general case, this type of decomposition is not possible, but it appears that in many specific uses objective functions of this nature can be profitably decomposed. and optima determined much more conveniently than otherwise possible.

No description available.

The traditional metropolitan water -supply planning problem is characterized by two main steps: (a) project future water requirements based on present rates of economic growth,, and (b) schedule water development projects to be introduced into the system on time to meet these predicted requirements. The City of Tucson plans its water supply essentially in this manner. The prime objective of this phase of our research was to formally review the above problem and to formulate it in terms of concepts of management science. Implied commitments to accept Colorado River water and gradual changes in quality of Tucson's groundwater force serious consideration of the economic tradeoffs between alternative sources and uses of water. These alternatives lead to a need for a restatement of water - supply planning objectives in more precise forms than have heretofore been put forth. The doctoral dissertation by G. Clausen addresses itself to the above restatement with actual data on the Tucson basin. The various water -supply planning objective functions including the traditional one are all expressions which maximize the difference between gains and losses involved with water development. They can be expressed mathematically and differentiated on the basis of how these gains and losses are defined. In the traditional sense, gains derived from meeting projected requirements are assumed to be infinite, and losses are taken to be actual project costs and not social costs associated with undesirable economic growth. Therefore, maximization of net gains is accomplished by minimizing project costs, and gains do not even have to be expressed. Consideration of alternatives, however, requires that gains be expressed quantitatively as benefits to individuals, communities, or regions, i.e., primary, secondary, or tertiary benefits. The same logic holds for the expression of total costs. An objective function, used to express the water- supply problem in the Tucson Basin, considers gains as cash revenue to a hypothetical central water - control agency which sells water to the users within the basin. Losses are considered as marginal costs to the agency for producing, treating, and distributing water. The concept of economic demand is used to estimate the amount of water that municipal, industrial, and agricultural users will purchase at different prices. Linear demand functions are postulated. The possible sources of supply considered are groundwater from within the basin, groundwater from the neighboring Avra Valley Basin, reclaimed waste water, and Central Arizona Project water from the Colorado River. Constraints are formulated to allow for limits on water availability, for social limits on water prices, and for minimal requirements of each user over a specified time period; these permit a determination of optimal allocations of water under different conditions to answer "what if' questions, given the assumptions of the model. The resulting static model is termed a pricing model and is optimized by first decomposing the objective function into component parts with each part representing terms involving only one source of water. In instances involving inequality constraints, quadratic programming is used. In other instances where equality constraints or unconstrained conditions exist, Lagrange multipliers and calculus methods are used. These latter conditions arise when it is determined at which point certain constraints become inactive. In the completely general case, this type of decomposition is not possible, but it appears that in many specific uses objective functions of this nature can be profitably decomposed and optima determined much more conveniently than otherwise possible. The model clearly identifies the opportunity costs associated with the required use of Colorado River water in lieu of the cheaper Tucson groundwater.

With the population of urban areas rapidly increasing, a much greater demand is being placed on existing water supplies. The arid southwestern region of the United States, in particular, is experiencing large population increases while possessing limited water resources. Tucson is a representative city in the region facing problems of providing an adequate water supply to the public in the future. Presently, Tucson is being supplied entirely with groundwater. Increases in population and industrial activities, however, have caused a steady decline of the groundwater table in the Tucson Basin. The reclamation of wastewater and the importation of water have been studied as alternatives in alleviating the annual decline of the groundwater table. Problems still exist, however, preventing the immediate use of both aforementioned supplies of water. In developing the water resources of an area, every possible source of water must be evaluated. A source which has not received much attention, but which merits much attention, is the water occurring as urban runoff following intense storms. In order to evaluate the potential of urban runoff as a water supply, the study includes investigations of water quality, water treatment through storage and coagulation, and problems involved with the utilization of storm water. Samples of runoff from three diversified urban watersheds in the Tucson area were analyzed for bacterial, mineral, pesticide, solids, and chemical oxygen demand concentrations. The watersheds were characterized according to the percentage of the total area devoted to a particular land use. In addition, the hydrologic characteristics of each storm were tabulated. Correlation coefficients were determined between the quality parameters and the watershed and hydrological characteristics. Development of regression equations equating quality parameters as a function of both watershed and hydrological characteristics was also undertaken. The final analysis of the quality study involved the determination of relationships between quality parameters of chemical oxygen demand, total coliforms and suspended solids and the point of time on the hydrograph at which runoff was sampled. Prior to beneficial use of the urban runoff, treatment to varying degrees will be required. In the second phase of this study, the efficiency of treatment by the simple methods of storage and alum coagulations was studied. Five gallon samples were collected from randomly selected storms and used either in the storage or coagulation study. Changes in chemical oxygen demand, solids and bacterial concentrations were evaluated at selected intervals during storage for a period of a week. Jar test studies utilizing varying doses of alum were undertaken on water collected from each of the watersheds, determining the efficiency of chemical oxygen demand, turbidity, and total coliform removals. The final phase of the study involved discussion of the problems attendant with the planning and design of treatment facilities. Included in this phase were sections involving water quality standards and the related treatment processes, waste sludge production and treatment methods, and costs pertaining to treatment. Legal aspects of appropriating the urban runoff were considered and the possible conflicts between upstream and downstream interests noted. The study concluded with a demonstration of the application of dynamic programming for optimally planning the location and capacity of storage treatment facilities at urban sites.

No description available.

United States Army Corps of Engineers, Los Angeles District, Tucson Urban Study, Eastern Pima County, Regional Water Supply Element / Final Report / The Feasibility of Utilizing Remote Sources of Water to Augment the Natural Supply of the Tucson Area, Pima County Arizona / DACW09-79-M-1223 / April 1980

Tucson, Arizona is often said to have a water problem. The water table is falling, giving rise to concern on the part of the public and conflicts between water users in the Basin. Many see the problem as a shortage of water to be solved by bringing more water to Tucson by means of the Central Arizona Project. This dissertation examines the occurrence and use of water in the region in order to determine the real nature of Tucson's water problem. First, the institutions governing the use of water in the Basin are described and the disputes between the local water users are discussed. Next, an account is given of the use of water by businesses and residences in Tucson, by the copper mines to the south of Tucson, and by the farms in the Basin. The effect of changes in the cost and availability of water on each of these classes of water user is investigated and the effect that changes in water use could have on the region's economy is discussed. Next, an account is given of the water available for use in the Basin. The occurrence of groundwater in the region is described and the merits of the proposed Central Arizona Project are investigated. The information on the use of water in the Basin and the information on the sources of water available for use in the Basin are then combined to forecast the depletions of groundwater that will take place under various circumstances. Various ways of balancing the region's water budget are described and an assessment is made of the effect that curtailing the use of water in the region would have upon the local water users and the region's economy. The principal conclusions of this study are as follows. First, there is no danger of the supply of water in the Basin becoming exhausted in the near future. The economic and physical effects of the continuing fall in the level of the water table are unlikely to be serious. The second main conclusion is that the region's water budget could be balanced very economically by retiring all agriculture in the region and making modest reductions in the amount of water consumed by urban water users and the copper mines. Given suitable institutional arrangements, curtailing the use of water in the Basin would be a much more economical way of balancing the region's water budget than building the Central Arizona Project. The final conclusion is that the real water problem is an institutional problem. The threat of the Indians' claims to the groundwater of the Tucson Basin, together with the difficulty of resolving the continual disputes between the mines, the farms, and the City of Tucson over water puts all of the local water-using interests in a position where they see the provision of more supplies of water as the only cure to their woes. The remedy to the region's water problem is not the provision of more supplies of water, but a settlement of the Indians' claims and a reform of Arizona's groundwater law to enable a resolution of the conflicts between the water users in the Tucson Basin.

A survey methodology was developed to measure the consumer welfare loss associated with various municipal water shortages. The methodology was designed to provide monetary estimates of consumer welfare loss and was tested on 644 households in the Tucson metropolitan area in February, 1981. The methodology was based on welfare economic theory and used two types of welfare measures: willingness to pay and willingness to accept. Respondents were presented with two hypothetical water shortage situations and asked to estimate their welfare loss according to prepared bidding schedules. The results of the survey, although biased by bidding behavior, indicate that consumers place a low value on the welfare loss associated with water shortages. The bidding behavior can be explained in part by the bidding mechanics and in part by the inability of the respondents to know their true response to possible water shortages.