Hybrid forecasting model for non-stationary daily runoff series: A case study in the Han River Basin, China

Accurate and reliable short-term runoff prediction is of great significance to the management of water resources optimization and reservoir flood operation. In order to improve the accuracy of short-term runoff forecasting, a hybrid model-based feature decomposition-learning reconstruction named VMD-DBN-IPSO was proposed. In this paper, variational mode decomposition (VMD) is first used to decompose the original daily runoff series into a set of sub-sequence for improving the frequency resolution. Partial autocorrelation function (PACF) is then applied to determine the input variables of each sub-sequence. The improved particle swarm optimization (IPSO) algorithm is combined with the deep belief network (DBN) model to predict each sub-sequences and finally reconstruct the ensemble forecasting result. Three quantitative evaluation indicators, mean absolute error (MAE), root mean square error (RMSE) and Nash-Sutcliffe efficiency coefficient (NSE), were used to evaluate and compare the established models using the historical daily runoff data (1/1/1988-31/12/2017) at Yangxian and Ankang hydrological station in the Han River Basin of China. Meanwhile, a comparative analysis of the performance of VMD-DBN-IPSO model under different forecast periods (1-, 3-, 5- and 7-day lead time) was performed. In addition, the prediction ability of peak runoff of the VMD-DBN-IPSO model is further verified by analyzing the 10 peak flows during the testing data-series. The results indicate that the VMD-DBN-IPSO model can always achieve the best performance in the training and testing stage, and has good stability and representativeness, the NSE coefficient remains above 0.8, and the prediction error of peak flow is within 20%. It is a preferred data-driven tool for forecasting daily runoff.