Optimal Hedging Rule for Reservoir Refill

Abstract

AbstractIn this study, an optimal reservoir refill hedging rule (RHR) is developed under hydrologic uncertainty using a two-stage model. Based on the probability distribution of the maximum refill water availability at the end of refill season, three possible cases exist: unfilled without flood damage, complete filling without flood damage, and complete filling with flood damage. These cases are characterized based on relationships among storage capacity, expected storage buffer, and maximum safe excess discharge. Karush–Kuhn–Tucker (KKT) conditions for the two-stage model show that the optimal refill operation equates the expected marginal loss of conservation benefit from not complete filling (i.e., ending storage of refill period less than storage capacity) and the expected marginal flood damage from levee overtopping downstream, unless constrained by capacity constraints. A RHR curve, which is analogous to water supply hedging and flood hedging rules, is drawn and shows the trade-off between the two o...