Accurate medium- to long-term runoff forecasting is crucial for flood control, drought resilience, water resources development, and ecological improvement. Traditional statistical methods struggle to utilize multifaceted variable information, leading to lower prediction accuracy. This study introduces two innovative coupled models—SRA-SVR and SRA-MLPR—to enhance runoff prediction by leveraging the strengths of statistical and deep learning approaches. Stepwise Regression Analysis (SRA) was employed to effectively handle high-dimensional data and multicollinearity, ensuring that only the most influential predictive variables were retained. Support Vector Regression (SVR) and Multi-Layer Perceptron Regression (MLPR) were chosen due to their strong adaptability in capturing nonlinear relationships and extracting latent hydrological patterns. The integration of these methods significantly improves prediction accuracy and model stability. By integrating 80 atmospheric circulation indices as teleconnection variables, the models tackle critical challenges such as high-dimensional data, multicollinearity, and nonlinear hydrological dynamics. The Yalong River Basin, characterized by complex hydrological processes and diverse climatic influences, serves as the case study for model validation. The results show that: (1) Compared to baseline single models, the SRA-MLPR model reduced RMSE (from 798.47 to 594.45) by 26% and MAPE (from 34.79 to 22.90%) by 34%, while achieving an NSE (from 0.67 to 0.76) improvement of 13%, particularly excelling in extreme runoff scenarios. (2) The inclusion of teleconnection indices not only enriched the predictive feature set but also improved model stability, with the SRA-MLPR demonstrating enhanced capability in capturing latent nonlinear relationships. (3) A one-month lag in atmospheric circulation indices was identified as the optimal predictor for basin-scale runoff, providing actionable insights into temporal runoff dynamics. (4) To enhance model interpretability, SHAP (SHapley Additive exPlanations) analysis was employed to quantify the contribution of atmospheric circulation indices to runoff predictions, revealing the dominant climate drivers and their nonlinear interactions. The results indicate that the Northern Hemisphere Polar Vortex and the East Asian Trough exert significant control over runoff dynamics, with their influence modulated by large-scale climate oscillations such as the North Atlantic Oscillation (NAO) and Pacific Decadal Oscillation (PDO). (5) The models’ scalability is validated through their modular design, allowing seamless adaptation to diverse hydrological contexts. Applications include improved flood forecasting, optimized reservoir operations, and adaptive water resource planning. Furthermore, the study demonstrates the potential of coupled models as generalizable tools for hydrological forecasting in basins with varying climatic and geographic conditions. This study highlights the potential of coupled models as robust and generalizable tools for hydrological forecasting across diverse climatic and geographic conditions. By integrating atmospheric circulation indices, the proposed models enhance runoff prediction accuracy and stability while offering valuable insights for flood prevention, drought mitigation, and adaptive water resource management. These methodological advancements bridge the gap between statistical and deep learning approaches, providing a scalable framework for accurate and interpretable hydrological, climatological, and environmental predictions. Given the escalating challenges brought about by climate change, the findings of this study make contributions to sustainable water management, interpretable decision-making support, and disaster preparedness at a global level.
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