Comparison and integrated application of medium- and long-term runoff forecasting models

To improve the accuracy and robustness of medium- and long-term runoff forecasting, nine major river control stations in Sichuan Province were selected to systematically evaluate the application performance of various models and explore ensemble methods.Six medium- and long-term runoff forecasting models were first selected, including linear model (Generalized Linear Model, GLM), machine learning models (Random Forest, RF; Boosted Regression Trees, BRT; Cubist model), and neural network models (Long Short-Term Memory, LSTM; Back Propagation Neural Network, BP).Using observed runoff, precipitation data (1980~2024), along with 88 atmospheric circulation indices and 26 sea surface temperature (SST) indices, we calibrated model parameters via Bayesian optimization combined with 10-fold cross-validation to assess model generalization capability.Subsequently, we integrated high-performance models using Bayesian Model Averaging (BMA), Quantile Averaging, and Ensemble Selection methods, followed by feature importance analysis to reveal key drivers influencing runoff.The results indicated that: ① The LSTM, RF, BRT, and Cubist models outperformed the traditional linear model (GLM) and the shallow neural network model (BP) in comprehensive multi-index performance.② During the calibration period, the RF model exhibited the optimal performance, with a median Nash-Sutcliffe Efficiency (NSE) coefficient of 0.91 and a Mean Absolute Percentage Error (MAPE) of 13.7%.During the validation period, the LSTM and BRT models demonstrated strong generalization ability, with the median NSE of LSTM decreasing from 0.79 to 0.63, while the median MAPE of BRT increased from 21.7% to 25.2%.③ Feature importance analysis indicated that the Tibetan Plateau -1 Index and the Asian Polar Vortex Intensity Index were the dominant controlling factors for runoff at the Wutongqiao Station on the Minjiang River.Furthermore, the impact of the same index at different time lags on runoff could be contrasting, and such nonlinear effects were closely related to the adjustment of water vapor transport pathways.④ The BMA ensemble model demonstrated a relative advantage in comprehensive performance, achieving a median NSE of 0.67 during the validation period (ranking first jointly with the RF model) and a median MAPE of 25.7% (slightly higher than the BRT model), effectively constraining hydrological uncertainty.The findings of this study can provide optimization schemes for runoff simulation in complex basins, and the proposed hybrid modeling strategy can enhance the robustness of predictions.