A Comparative Study of VMD-Based Hybrid Forecasting Model for Nonstationary Daily Streamflow Time Series

Data-driven methods are very useful for streamflow forecasting when the underlying physical relationships are not entirely clear. However, obtaining an accurate data-driven model that is sufficiently performant for streamflow forecasting remains often challenging. This study proposes a new data-driven model that combined the variational mode decomposition (VMD) and the prediction models for daily streamflow forecasting. The prediction models include the autoregressive moving average (ARMA), the gradient boosting regression tree (GBRT), the support vector regression (SVR), and the backpropagation neural network (BPNN). The latest decomposition model, the VMD algorithm, was first applied to extract the multiscale features from the entire time series and to decompose them into several subseries, which were predicted after that using forecast models. The ensemble forecast was finally reconstructed by summing. Historical daily streamflow series recorded at the Wushan and Weijiabao hydrologic stations from 1 January 2001 to 31 December 2014 in China were investigated using the proposed VMD-based models. Three quantitative evaluation indexes, including the Nash–Sutcliffe efficiency coefficient (NSE), the root mean square error (RMSE), and the mean absolute error (MAE), were used to evaluate and compare the predicted results of the proposed VMD-based models with two other models such as nondecomposition method (BPNN) and BPNN based on ensemble empirical mode decomposition (EEMD-BPNN). Furthermore, a comparative analysis of the performance of the VMD-BPNN model under different forecast periods (1, 3, 5, and 7 days) was performed. The results evidenced that the proposed VMD-based models could always achieve good performance in the testing stage and had relatively good stability and representativeness. Specifically, the VMD-BPNN model considered both the prediction accuracy and computation efficiency. The results show that the reliability of the forecasting decreased as the foresight period increased. The model performed satisfactorily up to 7-d lead time. The VMD-BPNN model could be applied as a promising, reliable, and robust prediction tool for short-term streamflow forecasting modelling.