Hybridization of stochastic hydrological models and machine learning methods for improving rainfall-runoff modeling

Abstract

Accurately simulating river discharge remains a challenge. Hybrid models combining hydrological models with machine learning improve discharge simulation and offer better interpretability than standalone machine learning models. However, the commonly used models are deterministic. This study introduces an innovative extension to stochastic hydrological models, offering a novel combination that has not been previously explored. The proposed approach predicts discharge by integrating the simulated statistical properties of daily discharge probability distributions, derived from a stochastic rainfall-runoff model, into machine learning frameworks. This integration allows the machine learning models to incorporate insights from the uncertainties in discharge, thereby enhancing predictive accuracy of discharge simulations. The hybridization presented combines the physically-based stochastic HyMoLAP (Sto. HyMoLAP) model with machine learning techniques, including Wavelet-based eXtreme Gradient Boosting (WXGBoost) and Wavelet-based Gated Recurrent Unit (WGRU). Evaluated on the Ouémé at Bonou river basin, Benin, the Sto. HyMoLAP-WGRU model shows the best predictive performance, especially for low and high discharges. It achieves an overall Nash-Sutcliffe Efficiency (NSE) of 0.896, which is 7.30% higher than the NSE of HyMoLAP, and 29.67% and 259.71% higher than those of the standalone machine learning models. The Combined Accuracy (CA) is 38.11, reflecting reductions of 19.81%, 42.30%, and 62.41% compared to the standalone models. The analyses show that the performance of hybrid models depends on the simulated discharge distribution properties used as input. They suggest that the hybridization approach could be particularly beneficial for runoff simulations in catchments subject to significant random fluctuations where point discharge simulation is challenging.