Estimating the economic value of inter‐annual reservoir storage in water resource systems

Reservoir operators face pressures on timing releases of water. Releasing too much water immediately can threaten future supplies and costs, but not releasing enough creates immediate economic hardship downstream. This paper examines how the economic valuation of end‐of‐year carry‐over storage can lead to optimal amounts of carry‐over storage in complex large water resource systems. Economic carry‐over storage value functions (COSVF) are developed to represent the value of storage in the face of inter‐annual inflow uncertainty and variability within water resource optimization models. The approach divides a perfect foresight optimization problem into year‐long (limited foresight) sub‐problems solved sequentially by a within‐year optimization engine to find optimal short‐term operations. The final storage state from the previous year provides the initial condition to each annual problem, and end‐of‐year COSVFs are the final condition. Here, the COSVF parameters that maximize the inter‐annual benefits from river basin operations are found by evolutionary search. This generalized approach can handle non‐convexity in large‐scale water resources systems. The approach is illustrated with a regional model of the California Central Valley water system including 30 reservoirs, 22 aquifers, and 51 urban and agricultural demand sites. Head‐dependent pumping costs make the optimization problem non‐convex. Optimized inter‐annual reservoir operation improves over more cautious operation in the historical approximation, reducing the average annual scarcity volume and costs by 80% and 98%, respectively, with more realistic representation of hydrologic foresight for California's Mediterranean climate. The economic valuation of storage helps inform water storage decisions.