An Interpretable Gated Convolutional Transformer Optimized by an Improved Black Kite Algorithm for Runoff Prediction

Accurate runoff forecasting serves as a fundamental basis for the scientific management of water resources and flood and drought risk mitigation. Owing to the nonlinearity, non-stationarity, and multi-scale temporal characteristics of runoff series, existing deep learning models still exhibit notable limitations in capturing long-term trends, responding to abrupt hydrological events, and ensuring model interpretability. The original Transformer relies on global self-attention, whose computational complexity increases quadratically with sequence length; it also has limited capacity to capture short-term local temporal dependencies such as rainfall–runoff relationships, and lacks prior constraints tailored to hydrological processes. To address these challenges, this study proposes a collaborative forecasting framework that integrates a gated convolutional Transformer (GCTrans) with an improved black kite algorithm (IBKA), enabling accurate, stable, and interpretable daily-scale runoff prediction. The GCTrans model consists of three customized modules: convolution-enhanced positional encoding (CEPE), which combines learnable positional encoding with local causal convolution to strengthen the temporal association of adjacent rainfall–runoff events, thereby providing a hydrologically meaningful positional reference for the attention mechanism; gated convolutional attention (GCA), which adopts a dual-path parallel architecture comprising global self-attention and local causal convolution to adaptively fuse long-term seasonal patterns with short-term storm-induced variations, thus capturing both baseflow evolution and flood peak responses; and a temporal gated output layer (TGOL), which performs adaptive feature weighting along the temporal dimension to selectively enhance the contribution of critical driving periods associated with extreme flood events, thereby improving the flood peak prediction accuracy. In addition, an improved black kite algorithm (IBKA) was developed by incorporating Tent chaotic initialization to enhance initial population diversity and introducing cosine adaptive inertia weights to dynamically balance global exploration and local exploitation, effectively alleviating premature convergence in high-dimensional hyperparameter spaces. Validation using data from the ME-Inland snowmelt-dominated watershed and the OR-Coastal storm-driven coastal watershed in the United States demonstrated that the GCTrans model consistently outperformed benchmark models including TCN, LSTM, Transformer, and Informer. After synergistic optimization with IBKA, both prediction accuracy and stability were further improved. SHAP-based interpretability analysis revealed that the model’s feature response patterns are statistically consistent with the rainfall–runoff generation mechanisms of the study basins: temperature-related drivers dominate in the inland watershed, while precipitation plays a dominant role in the coastal watershed, confirming the hydrological plausibility of the model’s decision-making logic. The integrated framework—encompassing model architecture, optimization algorithm, and interpretability—offers a valuable methodological reference for deep learning-based runoff forecasting in complex hydrological settings.