A Novel Reservoir Ensemble Forecasting Method Based on Constrained Multi-Model Weight Optimization

Accurate runoff forecasting is vital yet challenged by the increasing non-stationarity of hydrological systems, which often exceeds the capacity of traditional single models. Ensemble forecasting, as an effective approach, integrates multiple models’ information to enhance forecasting performance and assess uncertainty. However, existing methods (such as Bayesian Model Averaging and BMA) still have limitations in dealing with complex hydrological scenarios, particularly in the construction and optimization of forecast intervals. This paper proposes a novel hydrological ensemble interval forecasting method based on constrained multi-model weight optimization (Constrained Multi-Model Weight Optimization, CMWO). CMWO utilizes a set of heterogeneous deterministic models to generate members, assigns dynamic optimization weight intervals to enhance flexibility, and employs a multi-objective framework to minimize interval width and errors subject to a ≥95% coverage constraint. Taking the Huangjinxia Reservoir in the upper reaches of the Hanjiang River as a case study, the CMWO method was systematically applied and evaluated for decadal-scale runoff forecasting and comprehensively compared with widely used BMA methods and individual models. The results show that CMWO significantly outperforms in improving point forecast accuracy (measured by RMSE, KGE, etc.) and interval forecast quality (evaluated by PICP, PIAW, CRPS, etc.), especially in generating narrower, more informative prediction intervals while ensuring high reliability. The CMWO method proposed in this study provides a competitive new tool for the effective management of forecasting uncertainty in complex hydrological systems.