Comprehensive objective function- guided decomposition-prediction co-optimization framework: Enhanced Transformer model for high-accuracy forecasting of non-stationary runoff

Study focus: This study proposes a novel monthly runoff forecasting framework that integrates a Comprehensive Objective Function (COF) to guide the optimization of a hybrid model combining Sequential Variational Mode Decomposition (SVMD) and an enhanced Transformer (BGST). The framework addresses the nonlinearity and non-stationarity of runoff data by first employing the Walrus Optimizer (WO) to fine-tune SVMD parameters for effective signal decomposition, then leveraging a Bidirectional GRU and Squeeze-and-Excitation Network to enhance the Transformer’s ability to capture temporal dependencies and feature interactions. The study emphasizes systematic validation through multi-metric evaluation, objective function comparison, ablation studies, and model evaluations across three hydrological stations of Fen River Basin in China, aiming to improve forecasting accuracy for water resource management under climate change and human activity impacts. The results show: (1) COF outperformed NSE and KGE, increasing them by 1.43 % and 3.69 % at Lancun; (2) BGST improved Transformer’s NSE and KGE by 74.21 % and 91.44 %; (3) BGST achieved optimal metrics (NSE=0.993, KGE=0.984), surpassing other models. Consistent outcomes across three stations validated the framework’s superiority for runoff forecasting, which provides critical technological support for water resource planning and management. • Novel comprehensive objective function enhances monthly runoff forecasting. • Enhanced BGST model boosts performance, validated by ablation tests. • Proposed forecasting framework effectively reduces peak flow errors.