Sustainable Management of a Water Reservoir System Facing Climate Uncertainty

Abstract

Water scarcity is a growing global issue. It affects even highly developed regions like California, the world's fifth largest economy, where years of severe droughts interspersed with unusually wet seasons have caused societal debates over the management of the water resources stored in the state's extensive reservoir system. This paper presents a strategic optimization model for the long-term, sustainable management of such a system. Introducing a new modeling paradigm based on cycles of stochastic length, defined by the event when all reservoirs are simultaneously full, we avoid the limitations of traditional models and obtain sustainable management policies. To address the unpredictable effect of climate change on future water supply, we adopt a distributionally robust framework where nature chooses adverse inflow distributions. This leads to a stochastic shortest path problem under distributional ambiguity. Using tools from stochastic dynamic programming and aggregation methods, we obtain policy insights and overcome the curse of dimensionality typically associated with systems models. In a case study for California's Sacramento River Basin, we report suboptimality gaps between 3% and 15%, with our sustainable management policy reducing average cycle shortage costs by 40% compared to the current policy, demonstrating the significant cost saving potential.

Keywords: Water resource management, distributionally robust optimization, stochastic shortest path