COMPARISON OF RESERVOIR LINEAR OPERATION RULES USING LINEAR AND DYNAMIC PROGRAMMING1

ABSTRACT: Mathematical optimization techniques are used to study the operation and design of a single, multi-purpose reservoir system. Optimal monthly release policies are derived for Hoover Reservoir, located in Central Ohio, using chance-constrained linear programming and dynamic programming-regression methodologies. Important characteristics of the former approach are derived, discussed, and graphically illustrated using Hoover Reservoir as a case example. Simulation procedures are used to examine and compare the overall performance of the optimal monthly reservoir release policies derived under the two approaches. Results indicate that, for the mean detention time and the corresponding safe yield target water supply release under existing design of Hoover Reservoir, the dynamic programming policies produce lower average annual losses (as defined by a two-sided quadratic loss function) while achieving at least as high reliability levels when compared to policies derived under the chance-constrained linear programming method. In making this comparison, the reservoir release policies, although not identical, are assumed to be linear. This restricted form of the release policy is necessary to make the chance-constrained programming method mathematically tractable.     

USE OF RADAR TO DERWE A STORM INTENSITY-DURATION CURVE1

ABSTRACT: Rainstorms which exceed the design capacity of conveyance systems and cause extensive damage to structures and property, occur frequently in Alberta. After such a severe storm, an early and quick assessment of the storm's location and magnitude and the corresponding frequency for various duration (storm intensity-duration curve) is often required to estimate the damage. The storm intensity-duration curve is produced with information obtained from a sparse network of recording raingages, thus, creating a high degree of uncertainty in the result. Short-duration precipitation is usually quite variable in Alberta; hencea very dense network of recording precipitation stations would be required to provide precise measurements of the storm intensity-duration curve at all locations. Such a dense network does not exist in Alberta; it would be very expensive to install, maintain, and thus difficult to justify financially. One solution for obtaining a large amount of closely spaced in-intensity-duration values is to use weather radar. Using weather radar data, intensity-duration curves could be produced routinely for any set of prespecified locations. The radar data thus have the potential for facilitating the identification of the return period of rainfall events quickly, cheaply, and precisely when the long-term intensity-duration curves are available. As a pilot project to demonstrate the feasibility of the method and the potential of the radar data, computer software was developed to derive from archived radar data, intensity-duration values for up to a 2,500 2 area for a given storm.     

MULTICRITERION ANALYSIS OF FOREST WATERSHED MANAGEMENT ALTERNATIVES1

ABSTRACT: The impacts of alternative forest watershed management practices are examined from a multicriterion viewpoint in order to select the most satisfactory management scheme. The selection process is carried out using two types of multicriterion decision making techniques: the outranking types of ELECTRE I and II, and the distance-based type of compromise programming (CP). The process is illustrated using the U.S. Forest Service Beaver Creek Experimental Watershed in the Salt-Verde River Basin of Arizona as an example. The desired objectives of the experimental study and the alternative forest watershed resources management schemes are transformed into an evaluation matrix of alternatives versus criteria array. Analyses of the matrix using the aforementioned techniques result in a complete preference ordering of the feasible alternatives in the cases of ELECTRE LI and CP and a partial ordering when ELECTRE I is used. In addition, some sensitivity analyses have been performed and showed ELECTRE II and CP to be fairly robust with respect to parameter changes, while ELECTRE I being highly sensitive to changes in threshold levels. Overall the three techniques pointed out that 65 percent vegetation cut is the best management scheme, while the next best is shown to be 50 percent vegetation cut.     

WATER POLICIES FOR ENERGY DEVELOPMENT1

ABSTRACF: Examination of a series of studies of the economically efficient water allocations in the Upper Colorado River, Yellowstone River, and Great Basins indicate that water is not a serious general physical constraint on the development of energy resources, so long as public institutions do not hinder the exchange of water rights in markets. Energy development will cause limited impacts on other water-using sectors, principally agriculture. There appears to be little reason to develop large-scale water storage facilities, even during periods of reduced water production. Water storage developments appear to be necessary only when institutional constraints severely restrict water rights markets and transfers.     

DERIVING THE NONLINEAR RISK-BENEFIT ALGORITHM FOR RESERVOIRS1

ABSTRACT: The Nonlinear Risk-Benefit (NRB) Algorithm includes risk as one of the objectives in a multiple-objective optimization problem. The NRB Algorithm is derived by extending the Surrogate Worth Trade-Off method to quadratic programming. This category of problem is common in water resources planning and design, especially multipurpose reservoir systems. Consequently, an example is given using the algorithm for optimally operating a multipurpose reservoir.     

A dynamic model for intertemporal allocation of old-growth forests in the Pacific Northwest

Across the globe, continued policy debates regarding the management of old-growth forests center around the difficult task of balancing economic and ecological considerations. Though the forests of the Pacific Northwest United States are among the most studied old-growth ecosystems, ecological and economic analyses have yielded public land management directives that remain controversial. Specifically, the recently adopted Northwest Forest Plan lacks explicit goals for maintaining intergenerational equity for the use of forest resources and the diversity of old-growth ecosystems. Unlike previous studies which rely on monetary quantification of costs and benefits, this study develops and applies a conceptual framework for evaluating socially optimal Pacific Northwest old-growth forest utilization strategies. Conditions for the optimal management of old-growth forests are derived using dynamic programming. The objective function synthesizes relevant biological and economic attributes of the old-growth allocation problem. Results in the form of extraction paths are compared given social pressure for consumptive and non-consumptive benefits, as well as different planning horizons, rates of social time preference, and environmental variance. Lengthening the planning horizon results in a vast divergence of optimal policies in the absence of discounting. Extraction rates appear to approach zero as the planning horizon approaches infinity. While higher rates of social time preference increase the rate of extraction, forest stocks remaining at the terminal time period equal levels remaining with a lower discount rate. Increasing environmental variance results in a higher level of stock remaining at the terminal time period. This analysis, while specific to the old-growth controversy of the Pacific Northwest, does provide general guidelines for addressing similar problems of multiple uses of natural areas, particularly where such uses are mutually incompatible, or where one use may be irreversibly destructive to another.     

MULTICRITERIA PROGRAMMING OF WATER SUPPLY SYSTEMS FOR RURAL AREAS1

ABSTRACT: The aim of this paper is to present a multicriteria methodology for decision aid at the stage of programming a water supply system (WSS) for a rural area. The programming stage is an intermediate one between planning and designing water supply facilities, and can be decomposed into two problems: (a) setting up a priority order of water users, taking into account socio-economic criteria; and (b) choosing the best technical variant of the WSS. Among the criteria considered for the latter problem, there is a criterion of distance between the socio-economic priorities of users and the precedence orders of users according to the technical programming, which plays a coordinating role between problems (a) and (b). All steps of the presented methodology are illustrated by a real case study.     

MULTIOBJECTWE OPTIMIZATION OF RESERVOIR SYSTEMS OPERATION1

ABSTRACT: Development of optimal operational policies for large-scale reservoir systems is often complicated by a multiplicity of conflicting project uses and purposes. A wide range of multiobjective optimization methods are available for appraising tradeoffs between conificting objectives. The purpose of this study is to provide guidance as to those methods which are best suited to dealing with the challenging large-scale, nonlinear, dynamic, and stochastic characteristics of multireservoir system operations. As a case study, the selected methodologies are applied to the Han River Reservoir System in Korea for four principal project objectives: water supply and low flow augmentation; annual hydropower production, reliable energy generation, and minimization of risk of violating firm water supply requirements. Additional objectives such as flood control are also considered, but are imposed as fixed constraints.     

IMPROVED RIVER BASIN UTILIZATION THROUGH SYSTEMS ANALYSIS1

ABSTRACT. Theoretical and practical results are summarized for a study to determine optimal water resource allocation in a proposed water conservancy district. The area of this district, which covers several river basins, contains a large number of existing and proposed facilities such as reservoirs and diversions. The operation of all of these facilities was to be determined along with the sizing of the proposed facilities in order to optimize given objective functions. Related efforts in optimal river basin utilization were surveyed, and linear programming was selected as an expedient optimization technique. The problem is formulated by identifying time stages which together constitute a repetitive cycle such as a year. With these stages, it is possible to associate operational and capacity variables with network components, which are branches and nodes. Objective functions are assembled for the component variables. Constraint equations are written in terms of the variables to reflect network nodal continuity, capacity restrictions, and adjudications such as water rights. A numerical example is considered in which the existing and proposed facilities are aggregated to produce a small, tractable number of facilities. This paper examines the example results and suggests future improvements for models of this type.     

SOME CONJUNCTIVE DESALTING STUDIES EN THE UNITED KINGDOM1

ABSTRACT .Operating rule procedures are developed for the optimal use of desalination in conjunction with surface water impoundments. Results obtained from the use of hill-climbing and dynamic programming methods are compared. Benefits to be obtained from the integrated use of desalination are demonstrated through a case study for the Barcelona area of Spain.