An interpretable model for efficient and robust runoff forecasting via causal-linear attention and adaptive KAN decoding

Accurate runoff prediction is essential for water resources management, flood control, and disaster mitigation. However, existing deep learning models often face challenges in efficiently modeling long sequences, representing nonlinear runoff responses, and providing interpretable predictions. To address these issues, this study proposes LiTKAN, a hybrid runoff forecasting model integrating Temporal Causal Encoding (TCE), Global Linear Attention (GLA), and a KAN-based Nonlinear Decoder (KND). The proposed model combines temporal information representation, efficient long-range dependency modeling, and adaptive nonlinear mapping. Specifically, TCE incorporates temporal structural information into runoff sequences; GLA reduces the computational complexity of attention-based dependency modeling from O(N²) to O(N), enabling efficient long-sequence feature extraction; and KND employs learnable B-spline basis functions to characterize nonlinear runoff responses and provide data-driven interpretability. To evaluate LiTKAN under different forecasting configurations, this study conducted experiments across dual temporal scales and four representative basins with different hydrological characteristics, including multi-source meteorological-driven forecasting and univariate runoff forecasting scenarios. Results show that LiTKAN achieved competitive prediction performance under the evaluated conditions, with NSE values ranging from 0.878 to 0.994 across the four basins. The model also demonstrated improved representation of extreme runoff variations compared with baseline models. In terms of computational efficiency, the linear attention mechanism reduced runtime and GPU memory consumption compared with the standard Transformer while maintaining high prediction accuracy. Ablation experiments and interpretability analyses revealed that different model components contribute differently under different forecasting scenarios, and the nonlinear response patterns extracted by KND were generally consistent with known hydrological characteristics. Overall, this study demonstrates the potential of integrating efficient sequence modeling, nonlinear representation, and data-driven interpretability for multi-timescale runoff forecasting.