Combining two-stage decomposition based machine learning methods for annual runoff forecasting

•Two-stage Decomposition Based SVMs are combined for Annual Runoff Forecasting.•The IMFs by EEMD are further decomposed by VMD.•All the decomposition based SVM models are averaged by the simple average method.•Annual runoff data of Pingshi station in 1964–2012 are used for model development.•Combined models outperform member models based on two-stage decomposition. Accurate annual runoff forecasting is of great significance for water resources management and timely flood control. However, nonlinear and non-stationary runoff series and the complexity of hydrological processes make it difficult. To improve the forecast accuracy, a hybrid model based on two-stage decomposition, the support vector machine (SVM), and the combined method is proposed. Firstly, the original annual runoff is decomposed into a series of components (IMFs) by the ensemble empirical mode decomposition (EEMD). The high frequency components of IMFs are further decomposed into multiple components (VMFs) by the variational mode decomposition (VMD). Then, the SVM is applied to predict all the components. The sum of the forecast VMFs is the forecast of each high frequency IMF and the forecast annual runoff is obtained by summarizing the forecast IMFs. Finally, all the member models are averaged by the simple average method (SAM), which is the combining model. To evaluate the proposed model, the Pingshi Station in the Lechangxia Basin, China is selected. The results show that the two-stage decomposition enormously enhances the forecasting ability. The validation R of the optimal EEMD-VMD-SVM increases by 20%, 11% and 11% compared with the optimal SVM, EEMD-SVM and VMD-SVM, respectively. The validation MSE decreases by 58%, 45% and 47%, respectively. The optimal combined model outperforms the optimal member model because the validation R and MSE increase and decrease by 3% and 28%, respectively. The optimal combined model consists of four member models based on the EEMD-VMD and one member model based on the EEMD. This study highlights that combining machine learning methods based on two-stage decomposition can effectively improve the forecast accuracy of annual runoff.