A Bayesian Ensemble Learning-Based Scheme for Real-Time Error Correction of Flood Forecasting

To address the critical demand for high-precision forecasts in flood management, real-time error correction techniques are increasingly implemented to improve the accuracy and operational reliability of the hydrological prediction framework. However, developing a robust error correction scheme remains a significant challenge due to the compounded errors inherent in hydrological modeling frameworks. In this study, a Bayesian ensemble learning-based correction (BELC) scheme is proposed which integrates hydrological modeling with multiple machine learning methods to enhance real-time error correction for flood forecasting. The Xin’anjiang (XAJ) model is selected as the hydrological model for this study, given its proven effectiveness in flood forecasting across humid and semi-humid regions, combining structural simplicity with demonstrated predictive accuracy. The BELC scheme straightforwardly post-processes the output of the XAJ model under the Bayesian ensemble learning framework. Four machine learning methods are implemented as base learners: long short-term memory (LSTM) networks, a light gradient-boosting machine (LGBM), temporal convolutional networks (TCN), and random forest (RF). Optimal weights for all base learners are determined by the K-means clustering technique and Bayesian optimization in the BELC scheme. Four baseline schemes constructed by base learners and three ensemble learning-based schemes are also built for comparison purposes. The performance of the BELC scheme is systematically evaluated in the Hengshan Reservoir watershed (Fenghua City, China). Results indicate the following: (1) The BELC scheme achieves better performance in both accuracy and robustness compared to the four baseline schemes and three ensemble learning-based schemes. The average performance metrics for 1–3 h lead times are 0.95 (NSE), 0.92 (KGE), 24.25 ${\mathrm{m}}^3/\mathrm{s}$ (RMSE), and 8.71% (RPE), with a PTE consistently below 1 h in advance. (2) The K-means clustering technique proves particularly effective with the ensemble learning framework for high flow ranges, where the correction performance exhibits an increment of 62%, 100%, and 100% for 1 h, 2 h, and 3 h lead hours, respectively. Overall, the BELC scheme demonstrates the potential of a Bayesian ensemble learning framework in improving real-time error correction of flood forecasting systems.