Journal of Water Resources Planning and Management

The importance of water distribution network rehabilitation, replacement, and expansion is discussed. The problem of choosing the best possible set of network improvements to make with a limited budget is presented as a large optimization problem to which conventional optimization techniques are poorly suited. A multiobjective approach is described, using capital cost and benefit as dual objectives, enabling a range of noninferior solutions of varying cost to be derived. A structured messy genetic algorithm is developed, incorporating some of the principles of the messy genetic algorithm, such as strings that increase in length during the evolution of designs. The algorithm is shown to be an effective tool for the current optimization problem, being particularly suited both to the multiobjective approach and to problems that involve the selection of small sets of variables from large numbers of possibilities. Two examples are included that demonstrate the features of the method and show that the algorithm performs much better than a standard genetic algorithm for a large network.

Fuzzy set theory provides a useful model to address imprecision in interpreting linguistically described objectives for reservoir management. Fuzzy membership functions can be used to represent degrees of objective satisfaction for different values of management variables. However, lack of background information, differing experiences and qualifications, and complex interactions of influencing factors can contribute to significant variability among membership functions derived from surveys of multiple experts. In the present study, probabilistic membership functions are used to model variability in experts' perceptions of satisfaction of objectives for hydropower generation, fish habitat, kayaking, rafting, and scenery preservation on the Green River through operations of Flaming Gorge Dam. Degree of variability in experts' perceptions differed among objectives but resulted in substantial uncertainty in estimation of optimal reservoir releases.

Imprecise and noncommensurable objectives for reservoir operation are addressed through fuzzy dynamic programming using an implicit stochastic approach. Fuzzy membership functions for evaluating the achievement of a linguistically described operational goal and linguistically described constraints are estimated from surveys of decision makers. Summary statistics of the membership function values for optimal operation provide easily interpreted measures of degree of satisfaction among diverse objectives. An example application to the proposed Grey Mountain Reservoir on the Cache la Poudre River in northern Colorado showed that the expected degree of satisfaction for water supply objectives (constraints) would exceed 70% in six of 12 months, while 90% satisfaction of the flood control objective could be expected throughout the year. Expected degrees of satisfaction for storage, recreational, fish habitat, and hydropower objectives are substantially lower. Relative variability in predicted degrees of satisfaction is high. The average composite degree of satisfaction for the project is moderate, has a general seasonal trend, and is substantially variable in late summer and early fall.

A mixed integer chance constrained optimization model was developed to determine design and rehabilitation management strategies for storm-water drainage systems conditioned on the likelihood of exceeding the system's conveyance capacity. The model is multiobjective in nature and capable of considering multiple design or rehabilitation alternatives. Model objectives include the minimization of cost and probability of system failure. The probability that storm-water flows exceed the conveyance capacity of any network segment within the system is expressed as a chance constraint. The model combines kinematic wave routing methods and second-moment analysis to formulate the chance constraint. In this manner, only the mean, variance, and form of the distribution of the storm-water flows are needed to formulate the deterministic equivalent optimization model. To illustrate the model, an example is presented using an existing storm-water drainage network at Duke University, Durham, North Carolina. Results of this example specify the most cost-effective storm-water network design at varying system reliabilities. These results define trade-off relationships between total system cost and the probability of system failure.

The use of event trees and subjective probabilities in risk analysis is illustrated via a case study: the estimation of the probability of closure of Poe Lock on St. Marys River (Sault Ste. Marie, Mich.) because of vessel accidents and other nonstructural failures. The risk of closure is needed to determine the benefits of building a second Poe-class lock at that location. An event tree structures the risk analysis. Probabilities associated with the branches of the tree were developed from a combination of historical data and subjective probabilities. The latter were obtained in workshops with navigation experts. This paper summarizes the risk analysis, and discusses the difficulties associated with obtaining the necessary probabilities. It was found that a 30-day closure could occur about once every 50 years. The results are most sensitive to assumptions concerning how often ships hit lock gates.

In work sponsored by the U.S. Army Corps of Engineers (USACE), Pacific Northwest Laboratory (PNL), Richland, Wash., has performed a frequency analysis regarding the nonroutine closure of water flow through the turbines of powerhouses along the Columbia and Snake Rivers. The analysis involved developing a frequency analysis model capable of producing frequency profiles of overspeed and flooding events as a function of time and the associated component importance rankings. Data regarding hydropower equipment failures from a previous study were used to estimate component failure rates within the model. The present paper summarizes the model development and quantification, and calculation of component importance measures. The results of this analysis can be used as input to further analyses to evaluate economic consequences of overspeed and flooding events and to provide policy recommendations for operations of hydroelectric generating stations.

By the year 2010 southern Nevada, which is one of the fastest-growing urban centers in the West, will have committed nearly 100% of its water resources. Early in its history, Las Vegas developed a reputation for high per capita water use compared to other major cities in the arid West. This arose from a belief by its residents that the valley was situated on an inexhaustible supply of water, enticements by the state to drill wells for urban development, the attraction of tourists, and a lack of enforcement of passed or existing laws. The first water crisis in the 1940s was averted by allowing the principal aquifer to be overdrafted. Overdrafting of the aquifer has led to geologic problems for the valley and its residents. The second major water crisis was averted in the 1970s by the increasing availability of Colorado River water to area residents. Metering, local ordinances, research, and educational programming are impacting water use by addressing the problems of overdrafting and conservation.