Optimized decomposition and deep learning with bias correction for reliable runoff point-interval prediction

Accurate runoff prediction is critical for flood risk management and water resources regulation. This study proposes a probabilistic runoff forecasting framework that integrates optimized signal decomposition, deep learning, bias correction, and uncertainty quantification. Variational Mode Decomposition optimized by the Whale Optimization Algorithm (WVMD) is first applied to decompose non-stationary runoff series into stable intrinsic mode functions, which are then modeled using a hybrid Temporal Convolutional Network and Bidirectional Gated Recurrent Unit (TCN-BiGRU) with optimized hyperparameters. A Bias Correction (BC) strategy is further incorporated to improve point prediction accuracy. Based on the runoff point prediction residuals generated by the WVMD-TCN-BiGRU-BC model, Kernel Density Estimation (KDE) is applied to characterize the error distribution and construct probabilistic prediction intervals, with the Normal and Gumbel distributions adopted as parametric benchmarks. Experimental results at the Yangtze River Basin demonstrate that the proposed framework significantly improves both deterministic and probabilistic forecasting performance. The BC strategy reduces RMSE by 68.0% at Yichang and 73.2% at Jianli station compared with the WVMD-TCN-BiGRU model, while the KDE based interval prediction yields an approximately 5% improvement in the F score at the 90% confidence level, confirming the reliability of the proposed runoff probabilistic forecasting framework.