Accurate prediction of daily streamflow plays an essential role in various applications of water resources engineering, such as flood mitigation and urban and agricultural planning. This study investigated a hybrid ensemble decomposition technique based on ensemble empirical mode decomposition (EEMD) and variational mode decomposition (VMD) with gene expression programming (GEP) and random forest regression (RFR) algorithms for daily streamflow simulation across three mountainous stations, Siira, Bilghan, and Gachsar, in Karaj, Iran. To determine the appropriate corresponding input variables with optimal lag time the partial auto-correlation function (PACF) and auto-correlation function (ACF) were used for streamflow prediction purpose. Calibration and validation datasets were separately decomposed by EEMD that eventually improved standalone predictive models. Further, the component of highest pass (IMF1) was decomposed by the VMD approach to breakdown the distinctive characteristic of the variables. Results suggested that the EEMD-VMD algorithm significantly enhanced model calibration. Moreover, the EEMD-VMD-RFR algorithm as a hybrid ensemble model outperformed better than other techniques (EEMD-VMD-GEP, RFR and GEP) for daily streamflow prediction of the selected gauging stations. Overall, the proposed methodology indicated the superiority of hybrid ensemble models compare to standalone in predicting streamflow time series particularly in case of high fluctuations and different patterns in datasets.

Hydrological modeling is one of the important subjects in managing water resources and the processes of predicting stochastic behavior. Developing Data-Driven Models (DDMs) to apply to hydrological modeling is a very complex issue because of the stochastic nature of the observed data, like seasonality, periodicities, anomalies, and lack of data. As streamflow is one of the most important components in the hydrological cycle, modeling and estimating streamflow is a crucial aspect. In this study, two models, namely, Optimally Pruned Extreme Learning Machine (OPELM) and Chi-Square Automatic Interaction Detector (CHAID) methods were used to model the deterministic parts of monthly streamflow equations, while Autoregressive Conditional Heteroskedasticity (ARCH) was used in modeling the stochastic parts of monthly streamflow equations. The state of art and innovation of this study is the integration of these models in order to create new hybrid models, ARCH-OPELM and ARCH-CHAID, and increasing the accuracy of models. The study draws on the monthly streamflow data of two different river stations, located in north-western Iran, including Dizaj and Tapik, which are on Nazluchai and Baranduzchai, gathered over 31 years from 1986 to 2016. To ascertain the conclusive accuracy, five evaluation metrics including Correlation Coefficient (R), Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency (NSE), Mean Absolute Error (MAE), the ratio of RMSE to the Standard Deviation (RSD), scatter plots, time-series plots, and Taylor diagrams were used. Standalone CHAID models have better results than OPELM methods considering sole models. In the case of hybrid models, ARCH-CHAID models in the validation stage performed better than ARCH-OPELM for Dizaj station (R = 0.96, RMSE = 1.289 m³/s, NSE = 0.92, MAE = 0.719 m³/s and RSD = 0.301) and for Tapik station (R = 0.94, RMSE = 2.662 m³/s, NSE = 0.86, MAE = 1.467 m³/s and RSD = 0.419). The results remarkably reveal that ARCH-CHAID models in both stations outperformed all other models. Finally, it is worth mentioning that the new hybrid “ARCH-DDM” models outperformed standalone models in predicting monthly streamflow.