A Deep Ensemble Learning Framework with Interpretability for Long-Term Streamflow Forecasting under Multiple Uncertainties

Accurate and reliable long-term streamflow forecasting plays a crucial role in sustainable water resource management and risk mitigation. However, forecast performance is often constrained by multiple sources of uncertainty and the limited interpretability of deep learning models. To address these challenges, this study proposes an explainable hierarchical optimisation framework for long-term streamflow forecasting based on ensemble learning. The proposed framework systematically integrates a Dempster–Shafer (DS) evidence theory-based predictor selection strategy to reduce input uncertainty, an improved loss function designed to enhance model sensitivity to extreme flow events, and a Stacking ensemble scheme that combines the complementary strengths of multiple deep learning models, thereby overcoming the limitations of individual models in complex hydrological systems. In addition, SHapley Additive exPlanations (SHAP) are employed to improve model interpretability and to quantify the contributions of different predictors.

The effectiveness of the proposed framework is demonstrated through long-term streamflow forecasting at Hongze Lake. The results indicate that: (1) the DS-based predictor selection method substantially enhances both forecasting accuracy and stability, with Nash–Sutcliffe efficiency (NSE) values increasing by 0.10–0.18; (2) the improved loss function significantly strengthens model robustness under extreme high-flow conditions, reducing the mean absolute percentage error (MAPE) by 63.11%, 55.33%, and 23.6% for the MLP, LSTM, and Transformer models, respectively; (3) the Stacking ensemble model consistently outperforms individual base models by reducing forecast errors (RMSE decreased by 17–25%), improving the representation of large-scale variability (MAPE reduced by 21.6–26.8%), and more accurately capturing streamflow dynamics (NSE increased by 0.12–0.20), effectively mitigating multi-source uncertainties; and (4) SHAP-based interpretability analysis reveals pronounced monthly variations in predictor importance and confirms the dominant influence of antecedent streamflow on long-term forecasts. Overall, the proposed framework markedly improves the accuracy, robustness, and transparency of long-term streamflow forecasting and shows strong potential for application in other data-driven hydrological forecasting tasks.