AN ARCHETYPAL LINEAR PROGRAMMING MODEL FOR OPTIMAL INTERTEMPORAL ALLOCATION OF GROUNDWATR TO AGRICULTURAL ACTIVITIES1

ABSTRACT: In the past, researchers have applied a variety of analytical techniques for maximizing the present value of a stock resource - simulation, calculus of variations, stochastic dynamic programming, and optimal control theory. This paper presents a more operational approach - linear programming. A simplified, broadly drawn example from Southwest agriculture is used for demonstrating the model's structure and output. The method is based on a set of state transformation operations that prevent the additivity assumption of linear programming from being violated.     

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.     

FACTUAL INPUTS FOR ALLOCATION DECISIONS CONCERNING SCARCE WATER RESOURCES1

ABSTRACT: Factual inputs which may be useful for completing first-order assessments to aid decision-making on the allocation of scarce water resources are compiled. Water needs of major manufacturing industry groups and of minerals industries show wide variations in several measures of water use intensity. The chemicals and allied products and primary metals industries dominate the total water intake and consumptive water use by manufacturing industries. Consumptive use per employee for the petroleum and coal products industry group is nearly 2.5 times higher than that for any other industry group. Estimates of the water requirements per unit energy output for energy-processing systems vary by as much as an order of magnitude. Agricultural water use is larger than that of any other industry but water use for irrigation is not expected to increase significantly by the year 2020. In California, the production of crop calories and proteins per unit of irrigation water applied may vary by more than an order of magnitude. Crops which offer larger monetary returns per acre are irrigated most frequently.     

APPLICATION OF LINEAR SYSTEM'S THEORY AND LINEAR PROGRAMMING TO GROUND WATER MANAGEMENT IN KANSAS1

ABSTRACT: A ground water management model based on the linear systems theory and the use of linear programming is formulated and solved. The model maximizes the total amount of pound water that can be pumped from the system subject to the physical capability of the system and institutional constraints. The results are compared With analytical and numerical solutions. Then, this model is applied to the Pawnee Valley area of south-central Kansas. The results of this application support the previous studies about the future ground water resources of the Valley. These results provide a guide for the ground water resources management of the area over the next ten years.     

COST MINIMIZATION OF NUTRIENT REDUCTION IN WATERSHED MANAGEMENT USING LINEAR PROGRAMMING1

ABSTRACT: Linear programming is applied to identify the least cost strategy for reaching politically specified phosphorus and total suspended solids reduction targets for the Fox-Wolf river basin in Northeast Wisconsin. The programming model uses data collected on annualized unit reduction costs associated with five categories of sources of phosphorus and total suspended solids discharge in each of the 41 sub-watersheds in the basin to determine the least cost management strategy. Results indicate that: (1) cost-effective nutrient reduction requires careful selection of geographic areas and source categories to address throughout the watershed; (2) agricultural sources are the most cost-effective to address in the basin; and (3) care should be exercised in setting nutrient reduction targets, given that there are likely to be significantly increasing marginal costs of nutrient reduction; the model predicts that lowering the most restrictive target by 33 percent would cut reduction expenditures by about 75 percent. Policy implications of the model include support for the investigation and potential development of institutional arrangements that enable cost-effective nutrient reduction activities to occur, such as the creation of an agency with authority over a given watershed, coordinated watershed management activities, or nutrient trading programs.     

SOLUTION OF A WATER RESOURCES PROBLEM WITH ECONOMIES OF SCALE BY LINEAR PROGRAMMING1

ABSTRACT Both because of its effectiveness and ease in use, linear programming has become progressively popular in water resources planning problems. Yet, the assumptions of linear construction costs can be misleading. Diseconomies of scale in construction can be handled by successive approximations to the cost function but problems with economies of scale yield paradoxical results when piecewise approximations are used. If significant economies of scale exist in only one facility, the solution to problems of this nature can be found using normal linear programming codes by successively adjusting the unit construction cost on that single facility to iteratively work toward the true optimal solution.     

COST SHARING AND IMPLEMENTATION OF NATIONAL WATER RESOURCES POLICY1

ABSTRACT: In this article a managerial approach to developing and implementing National Water Resources policy is suggested. Proper consideration can be given to national economic development (NED), environmental quality (EQ) and conservation and still result in an implementable policy at the operational level if proper incentives are built into the process with proper attention to alternate non-Federal cost sharing rates. Not only can these multiple objectives be entertained but the Administration and Congress will have a management tool that should ensure a certain probability of success.     

COMPROMISE PROGRAMMING METHODOLOGY FOR DETERMINING INSTREAM FLOW UNDER MULTIOBJECTIVE WATER ALLOCATION CRITERIA1

ABSTRACT: This paper presents a quantitative assessment framework for determining the instream flow under multiobjective water allocation criteria. The Range of Variability Approach (RVA) is employed to evaluate the hydrologic alterations caused by flow diversions, and the resulting degrees of alteration for the 32 Indicators of Hydrologic Alteration (IHAs) are integrated as an overall degree of hydrologic alteration. By including this index in the objective function, it is possible to optimize the water allocation scheme using compromise programming to minimize the hydrologic alteration and water supply shortages. The proposed methodology is applied to a case study of the Kaoping diversion weir in Taiwan. The results indicate that the current release of 9.5 m³/s as a minimum instream flow does not effectively mitigate the highly altered hydrologic regime. Increasing the instream flow would reduce the overall degree of hydrologic alteration; however, this is achieved at the cost of increasing the water supply shortages. The effects on the optimal instream flow of the weighting factors assigned to water supplies and natural flow variations are also investigated. With equal weighting assigned to the multiple objectives, the optimal instream flow of 26 m³/s leads to a less severely altered hydrologic regime, especially for those low‐flow characteristics, thereby providing a better protection of the riverine environment.     

ALLOCATION MODEL FOR IRRIGATION WATER COST: CASE STUDY OF THE NILE VALLEY IN EGYPT1

ABSTRACT: An allocation model for irrigation water cost, based on the Use of Facilities method, is presented. The model is developed for large-scale irrigation systems which may include multipurpose reservoirs, irrigation control works, pump stations and irrigation canals of various orders. The model accounts for the water conveyance losses as well as the water gains in the irrigation canals, and their effects on irrigation cost. It is applied to the irrigation distribution system of the Nile Valley in Egypt, which contains the High Aswan Dam, 16 irrigation structures, 12 pump stations, and numerous irrigation canals. The irrigation water cost at 29 areas representing the Nile Valley is determined.     

A MODEL FOR ACHIEVING CONSISTENCY FOR COST SHARING IN WATER RESOURCE PROGRAMS1

ABSTRACT: Three basic principles of responsibility have influenced the Federal/non-Federal cost sharing rates for water resources programs (1) full payment by beneficiaries (2) exclusive Federal assumption of costs and (3) joint Federal/non-Federal sharing. The efforts to determine appropriate cost sharing rates have resulted in several hundred complex arrangements involving contributions, user charges and direct sales based on many variations of payment terms. This basic present value model was developed to determine the non-Federal cost shares which are expected to be paid for 32 different functional purposes emanating from Federal water resources programs and projects for both implementation and OMR stages. The model introduces the concept of a composite (implementation plus OMR) cost share as a focus developing appropriate cost sharing rates for the private, public and mixed outputs produced through public water resources investments. The model can be used as a focus for policy decisions on cost sharing which seek to achieve consistent and equitable cost shares for purposes provided while maintaining an efficient allocation of resources within water programs.     

NORMALIZED AGRICULTURAL PRICES AND WATER RESOURCES PLANNING1

ABSTRACT: Short-term fluctuations in agricultural markets necesitate adjustments in market prices for use in water resources planning. Two procudures for this price normalizing are described and evaluated. The linear treand and weighted average normalizing procedures perform reasonably well, except in cases of dramatic price oscillations.     

POTENTIAL WATER USE AND AGRICULTURAL PRODUCTION PATTERNS UNDER ALTERNATIVE WATER PRICES1

Out study deals with the demand for water and alternative agricultural production and land use patterns under varying prices for both surface and ground water. We derive irrigation water demands for both the United States and regions of it. Not only is a different amount of water used at each set of water prices but also a different mix of crops, livestock, and production technology develops among the different regions. Under the highest set of prices used, more than fourteen million acres are converted into dryland farming. Total irrigated water use decreases by more than 25 million acre-feet. Irrigated crop yields are reduced and cropping patterns shift away from irrigation. Commodity shadow prices increase as much as 15 percent under high prices for both surface and ground water. A redistribution of farm income occurs between irrigated and dryland regions.     

A NET BENEFIT MODEL FOR RECREATION PLANNING AT DRINKING WATER RESERVOIRS1

A management model was developed for determining levels of recreation activities at public drinking water reservoirs. Quabbin Reservoir, located in central Massachusetts, served as a case study for the model. An interdisciplinary research team was formed to study the impact of selected recreation activities on water quality, public demand and willingness to pay for selected recreation activities, carrying capacity constraints, and the economic cost/benefits associated with increases in recreation at the Quabbin Reservation. Study variables were integrated into a quadratic programming model, producing the number of participants that corresponds to maximum net benefits for specific development packages on design days. The recreation mix associated with maximum net economic benefits was found to be cost-effective (assuming the use of reasonable entrance fees) and not deleterious to water quality. However, as a result of the findings of a related study, it was recommended that nutrients, particularly from wastewater, not be permitted to enter the reservoir, since the current phosphorous level may be at a critical point. Management techniques that would safeguard against this occurrence were recommended. The model was sensitive to management objectives; recommendations were limited to activities that would not lower the existing high quality of Quabbin water.     

CURRENT USE OF WATER SURFACE ZONING FOR RECREATION1

ABSTRACT: As the many recreational uses of waterways have intensified, management agencies have increasingly turned to water surface zoning techniques to provide safe, equitable opportunities while also protecting aquatic habitats. Other publications have described the concept of water surface zoning; the study reported on was conducted to determine its current use nationwide. Depending on jurisdiction of the water surface in question and state legislation to zone water surfaces, nonfederal zoning regulations sometimes emanate directly from state government, and sometimes involve direct state and local government cooperation. Results of a national survey show that water surface zoning techniques employed by state and local governments in 1976–77 fall into five broad categories: restrictions on boat speed and horsepower, special use zoning, time zoining, protective space zoning, and limited density zoning. Examples of each are reported on in this paper.     

COST EFFECTIVE OPERATION OF URBAN WATER SUPPLY SYSTEM USING DYNAMIC PROGRAMMING1

ABSTRACT: Efficient operation of a city water supply system is an important goal of all municipalities. Efficient operation should result in minimum operation cost through reduction in total energy use and/ or reduction in on-peak energy consumption. An optimization model was designed for operating the water supply systems of cities using groundwater. The Newton-Raphson pipe network was used for network analysis and a dynamic programming optimization algorithm was used for determining a schedule for pump operation in the pipe network system. The model is most suitable for use in small cities with up to 45,000 in population, but with large-scale disintegration techniques may also be used for larger cities. The savings in operation costs are a function of energy cost and energy use pattern and water use pattern in the area.     

A SCREENING MODEL FOR WATER RESOURCES PLANNING1

ABSTRACT: Techniques of optimization and simulation are merged to select the most efficient arrangement of components for regional water resources development and management. Application is made to the Elkhorn River Basin in Nebraska. The Basin extends over 7,000 square miles and includes 184 proposed reservoirs. Structure sizes, locations and operating policies are selected for optimal plans based on economic efficiency and regional development. Results indicate that substantial savings in time and costs over conventional planning techniques are effected. Agreement between model output and agency design values was noted.     

AN APPLICATION OF MATHEMATICAL PROGRAMMING TO WATER RESOURCES PLANNING: AN ECONOMIC VIEW1

ABSTRACT: Individuals involved in state water resource planning generally have avoided any development of a comprehensive public water planning investment model that would set the stage for quantitative recommendations of a “what ought to be” tone for future water strategies. Three New Hampshire towns were selected to illustrate the usefulness of a mixed integer multiperiod programming model that utilizes hydrologic and economic data for identifying the discounted least cost of water supply, distribution, and scheduling. Comparisons are made regarding the feasibility of a regional water system approach versus independent “town by town” water supplies that presently prevail. To analyze the sensitivity of optimal water planning solutions to projected water demands, variations in these demands are made.     

OPTIMIZATION OF WATER RESOURCES FOR IRRIGATION IN EAST JORDAN1

The paper describes an approach towards optimal allocation of surface and ground water resources to three agricultural areas in the Jordan Valley under conditions of scarce water supply. The optimizing model allocates water from three main rivers, each with reservoir storage, and from two ground water sources to three irrigation regions. Productivity of irrigation water, expressed as the net present value of the regional agricultural output, but allowing for crop water deficits, is first maximized using nonlinear programming. The allocation process then adopts techniques of linear programming to determine the least cost alternative based on the unit cost of water from each resource at each destination, as it varies with time.     

CONJUNCTIVE USE OF SEA AND FRESH WATER RESOURCES: AN INTEGER PROGRAMMING APPROACH1

ABSTRACT Mathematical models are formulated for selection of water resources projects to meet the future additional water requirements of a given region at the minimum present worth cost. The projects available are surface water reservoirs and desalination plants. The modles are used for selecting both the development sequence of projects and their optimum sizes. Decisions with regard to planning time horizon and discount rates are made outside of the mathematical model. The algorithm used for solving these models is an integer programming routine using the implicit enumeration technique. Some computational results are presented for a hypothetical case.     

SURFACE WATER WITHDRAWAL ALLOCATION AND TRADING SYSTEMS FOR TRADITIONALLY RIPARLAN AREAS1

ABSTRACT: There is a growing need for water regulations in states traditionally managed by the riparian doctrine. Several states have passed water laws to control withdrawals from streams. Few, if any, however, have set up consistent and defensible methods for allocating water to users. This paper explores several methods for such allocations, examining each in detail and offering numerical examples that compare each on the basis of economic efficiency and effectiveness for maintaining critical stream‐flow standards. This work is part of a study to assess the vulnerability of Midwestern streams to climate change and, especially, surface supplied irrigation spawned by such climate change. The results suggest that it is possible to implement regulations that at once (1) are consistent with the riparian doctrine; (2) control the hydrological and ecological impacts of off stream withdrawals effectively; and (3) preserve the primary economic functions of those withdrawals, including minimizing economic risk. The results further suggest that trading of water permits improves the latter two objectives, but only if both the regulatory system and permit are well‐designed. On the other hand, in the absence of regulations, or under poorly designed regulations, streamflows, and therefore aquatic ecosystems, could be quite vulnerable.