Optimal Hedging Rule for Reservoir Refill

Abstract

In 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 objectives. The optimal refill hedging release decision shows a linear relationship with expected current water availability for a wide range of water conservation benefit functions (linear, concave, or convex). Several operational results are derived. A large downstream flood conveyance capacity and remaining storage capacity allow for a smaller current release and greater storage of water. Relative economic drivers are important; a greater economic potential for flood damage drives a greater release of water in the current stage, and vice versa. Below a critical forecast uncertainty value, improving forecasts reduces the volume of water released, although the opposite effect occurs above this critical value. Finally, the Danjiangkou Reservoir case shows that the RHR, combined with a rolling horizon decision approach, performs better than current rule curves and leads to a gradual dynamic refilling based on forecast information, indicating its potential for practical use.