In this case, the characteristics of the data, including periodicity, trends and noises, are identified and directly provided to the models. Streamflow series could be divided into multiple sub-series using these approaches. Machine learning models based on fundamental decomposition approaches have been developed to overcome this challenge. Human activities and climate changes are among the challenges that have a significant impact on machine learning methods performance with increasing non-stationarity in hydrological data (Meng et al. 2022) and the K-star algorithm (KS) (Salih et al. 2020 Achieng and Zhu 2019), random forests (RF) (Ahmadi et al. 2021), Bayesian regression (BR) (Wagena et al. 2022), gene expression programming (GEP) (Mehdizadeh et al. Support vector machine (SVM) (Essam et al. The following are some of the machine learning algorithms that have been frequently employed in hydrological modeling. Unlike time-series models, machine learning approaches are better at recognizing complex relationships among the components of phenomenon and have been proposed as a feasible alternative method for estimating streamflow. Due to the trend, climate change, and other elements impacting streamflow, the stationarity criteria are critical to satisfying (Ghimire et al. In addition, the stationarity of the recorded data is a fundamental assumption in their implementation. In streamflow forecasting, time-series models imply a linear connection between inputs and outputs, which is harder to accomplish. Autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), and autoregressive vector (VAR) models are popular types of these models. Time-series models are one type of data-driven strategy that has been widely utilized to forecast river flow in many regions of the world (Adnan et al. These techniques require less inputs, are less parameter-dependent, simpler to debug, and practical (Meng et al. In recent years, data-driven strategies have made tremendous progress in overcoming the limitations of physical models. In other words, the presence of high uncertainty in the data required by physical models can lead to inaccurate predictions of complicated variables like streamflow (Lin et al. Furthermore, one of these models’ shortcomings is the requirement for extensive hydrological data. As can be recognized in physical models, there are several aspects that influence the model’s outputs. Soil texture, land use, and vegetation cover in the basin are only a few data points (Beven 2020). Physical models are created from field data and are based on pre-existing mathematical correlations between various hydrological processes. Various equations and models for forecasting streamflow have been developed so far, including conceptual rainfall-runoff methods, time-series models, and hybrid techniques, all of which can be classified into two categories: physical models and data-driven models (Kartzert et al. Streamflow forecasting is an important issue for water resource management, since it is necessary to develop flood warning systems, the optimal operation of dam reservoirs, and hydropower generation (Lin et al. The VMD-RF model is proposed as a superior method based on root mean square error (RMSE = 13.79), mean absolute error (MAE = 8.35), and Kling–Gupta (KGE = 0.89) indices. The findings demonstrated that data preprocessing enhanced standalone models’ performance, and those hybrid models developed based on VMD performed best in terms of increasing the accuracy of monthly streamflow predictions. Other hybrid models, such as EDM-RF, EMD-KS, CEEMD-RF, and CEEMD-KS, were also developed in this research in order to assess the performance of VMD-RF and VMD-KS hybrid models. The ensemble forecasting result is then accomplished by adding the IMFs’ forecasting outputs. The following step models the IMFs obtained by the VMD approach using the RF and KS methods. The streamflow data were initially decomposed into intrinsic modes functions (IMFs) using the VMD approach up to level eight to develop the hybrid models. The monthly data obtained between 19 at the Iranian Bibijan Abad station on the Zohreh River were used for this purpose. In this study, hybrid models based on variational mode decomposition (VMD) and machine learning models such as random forest (RF) and K-star algorithm (KS) were developed to improve the accuracy of streamflow forecasting. Therefore, researchers have become interested in the development of hybrid approaches in recent years to enhance the performance of modeling techniques for predicting hydrological variables. The optimal management of water resources depends on accurate and reliable streamflow prediction.
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