Probabilistic Interval Forecasting Method Based on Game-Theoretic Combinations: A Case Study of the Wei River Basin

With global climate change and population growth, water scarcity issues are intensifying, severely limiting the accuracy of hydrological forecasting in river basins. Against this backdrop, this paper addresses key challenges in runoff forecasting-nonlinearity, nonstationarity, and uncertainty quantification by integrating point-interval collaborative learning concepts. It proposes a hybrid modeling framework to systematically enhance model stationarity, generalization capability, and evaluation comprehensiveness. This framework integrates deep learning, decomposition-reconstruction techniques, and multitask learning mechanisms to balance forecasting accuracy with interval stability, forming a probabilistic interval forecasting model. Validation at representative sections like Huaxian and Linjiacun in the Wei River Basin demonstrates that the proposed Pyraformer-BiLSTM-LSS model effectively captures both global and local dynamic characteristics of runoff sequences. The adaptive decomposition method based on a binary local search optimizer with variational modal decomposition (BLSO-VMD) significantly enhances denoising performance and model robustness. The interval forecasting scheme, combining multitask learning with game-theoretic composite weighting evaluation, generates coverage-reasonable and structurally stable forecast intervals at different confidence levels, markedly improving uncertainty quantification capabilities. This study provides a systematic technical pathway for probabilistic runoff forecasting under complex hydrological scenarios, offering significant theoretical value and broad application prospects.