As a complex hydrological problem, rainfall-runoff (RR) modeling is of importance in runoff studies, water supply, irrigation issues, and environmental management. Among the variety of approaches for RR modeling, conceptual approaches use physical concepts and are appropriate methods for representation of the physics of the problem while may fail in competition with their advanced alternatives. Contrarily, machine learning approaches for RR modeling provide high computation ability however, they are based on the data characteristics and the physics of the problem cannot be completely understood. For the sake of overcoming the aforementioned deficiencies, this study coupled conceptual and machine learning approaches to establish a robust and more reliable RR model. To this end, three hydrological process-based models namely: IHACRES, GR4J, and MISD are applied for runoff simulating in a snow-covered basin in Switzerland and then, conceptual models' outcomes together with more hydro-meteorological variables were incorporated into the model structure to construct multilayer perceptron (MLP) and support vector machine (SVM) models. At the final stage of the modeling procedure, the data fusion machine learning approach was implemented through using the outcomes of MLP and SVM models to develop two evolutionary models of fusion MLP and hybrid MLP-whale optimization algorithm (MLP-WOA). As a result of conceptual models, the IHACRES-based model better simulated the RR process in comparison to the GR4J, and MISD models. The effect of incorporating meteorological variables into the coupled hydrological process-based and machine learning models was also investigated where precipitation, wind speed, relative humidity, temperature and snow depth were added separately to each hydrological model. It is found that incorporating meteorological variables into the hydrological models increased the accuracy of the models in runoff simulation. Three different learning phases were successfully applied in the current study for improving runoff peak simulation accuracy. This study proved that phase one (only hydrological model) has a big error while phase three (coupling hydrological model by machine learning model) gave a minimum error in runoff estimation in a snow-covered catchment. The IHACRES-based MLP-WOA model with RMSE of 8.49 m3/s improved the performance of the ordinary IHACRES model by a factor of almost 27%. It can be considered as a satisfactory achievement in this study for runoff estimation through applying coupled conceptual-ML hydrological models. Recommended methodology in this study for RR modeling may motivate its application in alternative hydrological problems.
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