An analytic operating rule for reservoirs under the Budyko “supply–demand” framework

•Theoretically formulated a hedging function consistent with the Budyko framework.•The derived function outperforms commonly-used rules.•The derived function depicts a general non-linear “supply–demand” relationship. Operating rules play an important role in enhancing the water utilization of reservoirs. Previous studies on hedging investigated the operating rules between water release (R) and available water (AW) based on minimizing the normalized shortage index, and applied the rules to optimization. However, seldom considered a realistic economic objective function to form a more general “supply–demand” relationship. To address this issue, this study formulated a theoretical function by a two-period reservoir operation model with the goal of minimizing the sum of economic loss from the current release and carryover storage targets. The derived function that guides the water supply was numerically validated to obtain the optimal time-varying hedging rules by non-dominated sorting genetic algorithm Ⅱ. The water-supply system of Dongwushi Reservoir in Hebei Province, China was selected as a case study. The results show that (1) The derived function depicts the relationship between “R-AW ratio” and “D-AW ratio”, which is consistent with the Budyko “supply–demand” framework. (2) The optimized results using the derived Budyko hedging function outperform those using two-point hedging rule (TPH) and standard operating policy (SOP). (3) The derived function depicts a general non-linear “supply–demand” relationship rather than the linear one contained in commonly-used TPH. The derived function could be used for varied demands, indicating broader applications than TPH.