William Kirby

Bio: William Kirby is an academic researcher. The author has contributed to research in topics: Decision rule & Poisson distribution. The author has an hindex of 4, co-authored 4 publications receiving 393 citations.

The Linear Decision Rule in Reservoir Management and Design: 1, Development of the Stochastic Model

Abstract: With the aid of a linear decision rule, reservoir management and design problems often can be formulated as easily solved linear programing problems. The linear decision rule specifies the release during any period of reservoir operation as the difference between the storage at the beginning of the period and a decision parameter for the period. The decision parameters for the entire study horizon are determined by solving the linear programing problem. Problems may be formulated in either the deterministic or the stochastic environment.

Linear Decision Rule in Reservoir Management and Design: 2. Performance Optimization

Abstract: The application of linear decision rules to reservoir management and design is extended in two directions. First, an improved linear decision rule is derived for reservoirs suffering evaporation losses. Release commitments generated by this rule are based on the storage at the beginning of the period, the predicted evaporation depth in the period, and the linearized storage area curve of the reservoir. A clearer and more rigorous derivation of the chance constraints, including the effects of both evaporation losses and possible failures to meet previous commitments, is presented. Second, several reservoir performance measures are formulated as objective functions that can be optimized by linear programing. These performance measures include expected and reliable values of storages and releases, deviations from targets, and reliabilities of achieving stated goals.

On the Random Occurrence of Major Floods

Abstract: Plausible hydrologic arguments imply that floods can be represented as the successes or exceedances in a sequence of randomly spaced Bernoulli trials representing the occurrence of hydrograph peaks. This representation generalizes existing flood occurrence models by admitting an arbitrary probability distribution of the times between trials and an arbitrary criterion for distinguishing between floods and ordinary hydrograph peaks. Analysis of this model shows that at sufficiently small exceedance probabilities the probability distributions and moments of the interexceedance time, the waiting time to the next exceedance, and the number of exceedances approach those implied by the occurrence of trials in a Poisson process. This theory therefore constitutes a rational justification of Poisson models of flood occurrence as well as a rational explanation of empiric observations.

Optimal Operation of Multireservoir Systems: State-of-the-Art Review

Abstract: With construction of new large-scale water storage projects on the wane in the U.S. and other developed countries, attention must focus on improving the operational effectiveness and efficiency of existing reservoir systems for maximizing the beneficial uses of these projects. Optimal coordination of the many facets of reservoir systems requires the assistance of computer modeling tools to provide information for rational management and operational decisions. The purpose of this review is to assess the state-of-the-art in optimization of reservoir system management and operations and consider future directions for additional research and application. Optimization methods designed to prevail over the high-dimensional, dynamic, nonlinear, and stochastic characteristics of reservoir systems are scrutinized, as well as extensions into multiobjective optimization. Application of heuristic programming methods using evolutionary and genetic algorithms are described, along with application of neural networks and fuzzy rule-based systems for inferring reservoir system operating rules.

Reservoir Management and Operations Models: A State‐of‐the‐Art Review

Abstract: The objective of this paper is to review the state-of-the-art of mathematical models developed for reservoir operations, including simulation. Algorithms and methods surveyed include linear programming (LP), dynamic programming (DP), nonliner programming (NLP), and simulation. A general overview is first presented. The historical development of each key model is critically reviewed. Conclusions and recommendations for future research are presented.

Dynamic programming applications in water resources

Abstract: The central intention of this survey is to review dynamic programming models for water resource problems and to examine computational techniques which have been used to obtain solutions to these problems. Problem areas surveyed here include aqueduct design, irrigation system control, project development, water quality maintenance, and reservoir operations analysis. Computational considerations impose severe limitation on the scale of dynamic programming problems which can be solved. Inventive numerical techniques for implementing dynamic programming have been applied to water resource problems. Discrete dynamic programming, differential dynamic programming, state incremental dynamic programming, and Howard's policy iteration method are among the techniques reviewed. Attempts have been made to delineate the successful applications, and speculative ideas are offered toward attacking problems which have not been solved satisfactorily.

A Programming Model for Analysis of the Reliability, Resilience, and Vulnerability of a Water Supply Reservoir

Abstract: Reliability in water supply reservoir operation is commonly thought of as the probability of failing to achieve some target release. Here we explore two additional proposed descriptions of reservoir performance: the maximum shortfall from the target (system vulnerability) and the maximum number of consecutive periods of deficit during a record (system resilience). The larger the maximum shortfall, the greater the vulnerability. The shorter the maximum length of deficits, the more resilient the system. Using multiobjective mixed-integer, linear programming, the tradeoffs between reliability, vulnerability, and resilience are examined. It is found that as reliability is increased or as the maximum length of consecutive shortfalls decreases (resilience increases), the vulnerability of the water system to larger deficits increases.

A Stochastic Model for Flood Analysis

Abstract: A stochastic model, based on the recent developments in the theory of extreme values, is presented to describe and analyze excessive streamflows. The model is a particular stochastic process x(t) defined as the maximum term among a random number of random observations in an interval of time [0, t]. Since the number of hydrograph peaks in [0, t] that exceed a certain level x0 and the magnitudes of these peaks are random variables, the foregoing model seems to conform well to the flood phenomenon. The passage time T(x) of the process x(t) relevant to the risk evaluation in the design of hydraulic structures is also considered. The results obtained are applied on the 72-year record of the Susquehanna River at Wilkes-Barre, Pennsylvania. Theoretical and observed results agree reasonably well.