Abstract
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.
Highlights
Estimating rainfall-runoff relationship and streamflow accurately is a significant element which should be considered for managing water resources effectively [1,2]
Wang et al [47] proposed a coupling of ensemble EMD (EEMD), particle swarm optimization (PSO) and support vector machines (SVMs) for forecasting annual rainfall-runoff and concluded that the hybrid approach could improve the accuracy of annual runoff forecasting significantly
As stated in the Introduction chapter, this study aims at examining the performances of variational mode decomposition (VMD)-based machine learning models (MLMs) for daily rainfall-runoff modeling and comparing them with those of discrete wavelet transform (DWT)-based and single MLMs
Summary
Estimating rainfall-runoff relationship and streamflow accurately is a significant element which should be considered for managing water resources effectively [1,2]. Hydrologic practices, including water supply and allocation, reservoir planning and operation, flood and drought management, and other hydrological applications, can be conducted successfully only when the rainfall-runoff relationship and streamflow behavior in a river watershed are estimated accurately. Atmosphere 2018, 9, 251 based on the physical interpretation of watershed system. These models are formulated utilizing complex physical equations and parametric assumptions [2]. The data-driven models characterize the relationship between input and output, not describing the natural watershed process [2,5]
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