Real-time error correction for flood forecasting based on machine learning ensemble method and its uncertainty assessment

Real-time error correction is an effective measure to improve forecast accuracy. This paper develops a real-time error correction model based on machine learning (ML) ensemble method, including the establishment of base learners, heterogeneity test, and Stacking combination. Then the Copula-based Bayesian processor of forecast (BPF) is adopted for probabilistic forecasts, which quantitatively describes the uncertainty of the correction results. Finally, the model performance is comprehensively evaluated from accuracy and stability, with deterministic metrics used to evaluate the correction effect and uncertain metrics for assessing probabilistic forecasts. The proposed model is applied to the multireservoir system in the Huai River Basin, and the results reveal the following: (1) Unlike the single ML algorithm with the performance of oscillations, the Stacking ensemble method can aggregate the advantages of multiple learners, showing robust correction effect and high adaptability across all data samples. (2) The forecasting error is significantly reduced by the Stacking method, with the average Nash–Sutcliffe efficiency coefficient (NSE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NSE$$\end{document}) value increasing above 0.9, which is 4.93% higher than that of the autoregressive (AR) method. The greater superiority is also shown in the remaining evaluation metric values. Moreover, as the lead time increases, the performance of the stacking method tends to have a slower decline trend than the AR method. (3) The changes in the structure of the Stacking method have a relatively small influence on the forecast uncertainty, with all the Containing ratio (CR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CR$$\end{document}) values over 80% for different samples. The flexible combination of ML algorithms in the ensemble method will not add additional uncertainty factors and ensure the stability of the correction performance. The framework for real-time error correction and its uncertainty assessment has overall optimal correction performance with less observed data and lower computational cost required, which is promising for further improving the accuracy and reliability of real-time flood forecasting.