Improving River-Stage Forecasting Using Hybrid Models Based on the Combination of Multiple Additive Regression Trees and Runge–Kutta Schemes

Over the last 50 years, physics-based numerical and machine learning (ML) models have been the two major tools for river-stage forecasting—the former are more accurate but time-consuming in model construction and computation, whereas the latter are faster but lack of physical backup. To extract the advantages and avoid the shortages of the two models in isolation, four hybrid ML models were developed in this study for river-stage forecasting using multiple additive regression trees (MART) driven under different orders of Runge–Kutta (RK) numerical schemes. The models are trained and tested using 13 typhoon events between 2015 and 2019 in the Keelung River Basin, Taiwan. Compared with the original MART without RK schemes, the hybrid models greatly reduce the errors by 29% and 53% in the predictions of mean and peak river stages, respectively. Meanwhile, the patterns of the river stages predicted by the hybrid models fluctuate less and are more accurate when lead time increases. Requiring fewer training times than the original MART models, and less computation time than pure numerical models, the hybrid models are more economical and efficient in the application of real-time river-stage forecasting. The positive results show that the combination of different ML models and numerical schemes has great potential for improving hydrological forecasting that requires further studies in the future.