Wavelet Bootstrap Multiple Linear Regression Based Hybrid Modeling for Daily River Discharge Forecasting

Abstract

A new hybrid model, the wavelet–bootstrap–multiple linear regression (WBMLR) is proposed to explore the potential of wavelet analysis and bootstrap resampling techniques for daily discharge forecasting. The performance of the developed WBMLR model is also compared with five more models: multiple linear regression (MLR), artificial neural network (ANN), wavelet-based MLR (WMLR), wavelet-based ANN (WANN) and wavelet–bootstrap–ANN (WBANN) models. Seven years of discharge data from seven gauging stations in the middle reaches of Mahanadi river basin in India are applied in this study. Significant input vectors are decomposed into discrete wavelet components (DWCs) using discrete wavelet transformation (DWT) to generate wavelet sub time series that are used as inputs to the MLR and ANN models to develop the WMLR and WANN models, respectively. Effective wavelets are selected by considering several types of wavelets with different vanishing moments. WBMLR and WBANN models are developed as ensemble of different WMLR and WANN models, respectively, developed using different realizations of the training dataset generated using bootstrap resampling technique. The results show that the wavelet bootstrap hybrid models (i.e. WBMLR and WBANN) produce significantly better results than the traditional MLR and ANN models. Hybrid models based on MLR (WMLR, WBMLR) perform better than the ANN based hybrid models (WBANN, WANN). The WBMLR and WMLR models simulate the peak discharges better than the WBANN, WANN, MLR and ANN models, whereas the overall performance of WBMLR model is found to be more accurate and reliable than the remaining five models.