Reliable conjunctive use rules for sustainable irrigated agriculture and reservoir spill control

We develop optimal conjunctive use water management strategies that balance two potentially conflicting objectives: sustaining irrigated agriculture during droughts and minimizing unnecessary spills and resulting water losses from the reservoir during wet periods. Conjunctive use is specified by a linear operating rule, which determines the maximum surface water release as a function of initial reservoir storage. Optimal strategies are identified using multiobjective interannual optimization for sustainability and spill control, combined with gradient-based annual profit maximization. Application to historical conditions in the irrigated system of the Yaqui Valley, Mexico, yields a Pareto curve of solutions illustrating the trade-off between sustaining agriculture and minimizing spills and water losses. Minimal water losses are obtained by maximizing surface water use and limiting groundwater pumping, such that reservoir levels are kept sufficiently low. Maximum agricultural sustainability, on the other hand, results from increased groundwater use and keeping surface water reservoir levels high during wet periods. Selected optimal operating rules from the multiobjective optimization are tested over a large number of equally probable streamflow time series, generated with a stochastic time series model. In this manner, statistical properties, such as the mean sustainability and sustainability percentiles, are determined for each optimal rule. These statistical properties can be used to select rules for water management that are reliable over a wide range of streamflow conditions.