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Accurate modeling for nonlinear and nonstationary rainfall-runoff processes is essential for performing hydrologic practices effectively. This paper proposes two hybrid machine learning models (MLMs) coupled with variational mode decomposition (VMD) to enhance the accuracy for daily rainfall-runoff modeling. These hybrid MLMs consist of VMD-based extreme learning machine (VMD-ELM) and VMD-based least squares support vector regression (VMD-LSSVR). The VMD is employed to decompose original input and target time series into sub-time series called intrinsic mode functions (IMFs). The ELM and LSSVR models are selected for developing daily rainfall-runoff models utilizing the IMFs as inputs. The performances of VMD-ELM and VMD-LSSVR models are evaluated utilizing efficiency and effectiveness indices. Their performances are also compared with those of VMD-based artificial neural network (VMD-ANN), discrete wavelet transform (DWT)-based MLMs (DWT-ELM, DWT-LSSVR, and DWT-ANN) and single MLMs (ELM, LSSVR, and ANN). As a result, the VMD-based MLMs provide better accuracy compared with the single MLMs and yield slightly better performance than the DWT-based MLMs. Among all models, the VMD-ELM and VMD-LSSVR models achieve the best performance in daily rainfall-runoff modeling with respect to efficiency and effectiveness. Therefore, the VMD-ELM and VMD-LSSVR models can be an alternative tool for reliable and accurate daily rainfall-runoff modeling.

Machine Learning Models Coupled with Variational Mode Decomposition: A New Approach for Modeling Daily Rainfall-Runoff