Developing optimal operating rules for a multi-reservoir system with multi-objective water utilization and multi-year carryover storage: A case study of the Upper Yellow River

Study region The multi-reservoir system on the Upper Yellow River, China, comprising Longyangxia, Laxiwa, Lijiaxia, Gongboxia, Jishixia, and Liujiaxia. Study focus To address the difficulty of directly translating optimal operation results under multi-reservoir, multi-objective, and multi-year regulation conditions into operating rules that can guide reservoir operation, this study develops an integrated framework for cascade reservoir operating rule derivation. The framework constructs optimization-based samples considering different scenarios, performs key factor mining, derives operating rules using data-driven methods, and validates their applicability under broader inflow conditions using stochastic runoff preserving multisite temporal and spatial dependence. New hydrological insights for the region (1) An optimization-based framework transformed optimal operation results under multi-reservoir, multi-objective, and multi-year regulation conditions into rule-learning samples while preserving principal cascade operating features. (2) Key factor mining reduced 59 candidate factors to 29–31, decreasing input dimensionality by 48%-51% while maintaining prediction accuracy close to the full factor sets. (3) Under historical runoff conditions, the derived operating rules generated reservoir operation trajectories close to direct optimization results, with energy production reaching at least 87% and water supply reaching at least 94% of the direct optimization results. (4) Under stochastic runoff conditions, the historical-runoff-derived rules remained effective without retraining, generating operation trajectories close to direct optimization results, with energy production reaching at least 85% and water supply exceeding 90% of the direct optimization results for most combinations.