Optimization of environmental water purchases with uncertainty

Water managers are turning increasingly to market solutions to meet new
environmental demands for water in fully allocated systems. This paper presents a three-stage probabilistic optimization model that identifies least cost strategies for staged seasonal water purchases for an environmental water acquisition program given hydrologic, operational, and biological uncertainties. Multistage linear programming is used to minimize the expected cost of long-term, spot, and option water purchases used to meet uncertain environmental demands. Results prescribe the location, timing, and type of optimal water purchases and illustrate how least cost strategies change as information becomes available during the year. Results also provide sensitivity analysis, including shadow values that estimate the expected cost of additional dedicated environmental water. The model’s application to California’s Environmental Water Account is presented with a discussion of its utility for planning and policy purposes. Model limitations and sensitivity analysis are discussed, as are operational and research recommendations.