Abstract: The mechanisms behind medium and long-term runoff are complex, making errors in deterministic prediction models inevitable. Exploring the runoff characteristics within these errors can further improve the prediction accuracy of the models. This study proposes an integrated monthly runoff forecasting model based on Long Short-Term Memory (LSTM) neural networks with error correction using Extreme Gradient Boosting (XGBoost). Transfer Entropy (TE) analyses were conducted in three directional pairs: upstream to midstream, midstream to downstream, and upstream to downstream. Meteorological factors highly correlated with monthly runoff, identified via Pearson correlation, were selected as inputs to the LSTM model for initial runoff prediction. The residual errors were further modeled with XGBoost, and SHAP analysis was applied to interpret error sequences. Results show that meteorological variables such as air temperature, ground temperature, and air pressure—excluded in the first-stage LSTM prediction—were effectively exploited in the secondary error modeling. Combining XGBoost-predicted errors with LSTM outputs yielded the final predictions of the LSTM-XGBoost integrated model.Results show that the LSTM-XGBoost hybrid model achieved Nash-Sutcliffe efficiency coefficients of 0.82, 0.81, and 0.82 at the upstream, midstream, and downstream stations, respectively. Compared to models such as Random Forest, Back Propagation Neural Network (BP), standalone LSTM, and standalone XGBoost, the proposed LSTM-XGBoost model exhibited superior forecasting accuracy and reliability.

Key words: XGBoost, error correction, LSTM, ensemble prediction, transfer entropy