Risk‐Reliability Programming for Optimal Water Quality Control

Abstract

A risk‐reliability programming approach is developed for optimal allocation of releases for control of water quality downstream of a multipurpose reservoir. Additionally, the approach allows the evaluation of optimal risk/reliability values. Risk is defined as a probability of not satisfying constraints given in probabilistic form, e.g., encroachment of water quality reservation on that for flood control. The objective function includes agricultural production losses that are functions of water quality, and risk‐losses associated with encroachment of the water quality control functions on reservations for flood control, fisheries, and irrigation. The approach is demonstrated using data from New Melones Reservoir on the Stanislaus River in California. Results indicate that an optimum water quality reservation exists for a given set of quality targets and loss functions. Additional analysis is presented to determine the sensitivity of optimization results to agricultural production loss functions and the influence of statistically different river flows on the optimal reservoir storage for water quality control. Results indicate the dependence of an optimum water quality reservation on agricultural production losses and hydrologic conditions.