Optimal Flood Pre-releases - Flood Hedging for A Single Reservoir

摘要

Hedging for flood reservoir operations involves making releases in advance of a storm to make additional storage capacity available in the reservoir, as a way of reducing the probability of more severe flooding. Such pre-releases can involve the likely loss of water which would have value for water supply and might also involve pre-releases large enough to create small floods or small increases in downstream levee failures under some conditions. This paper explores some sufficient theoretical conditions needed for flood hedging to be optimal. In all cases, a necessary condition for flood hedging is that the overall expected damage from flood pre-release decisions is convex. The convexity in flood risk can arise from convex levee failure probability function, convex flood damage functions, and the probability distribution of possible storms. Extremely large storms that overwhelm the systems, and small storms that are handled relatively easily, do not encourage flood hedging operations. The likelihood of intermediate storms that are large but not overwhelming, where the additional flood storage capacity from pre-releases is likely to reduce overall flood damage, drives the optimality of flood hedging pre-releases operations. The ideal theoretical condition for optimal flood hedging is that current marginal damages from prereleases equal future marginal expected damages from later storm releases.