A Hybrid Model Based on Variational Mode Decomposition and Gradient Boosting Regression Tree for Monthly Runoff Forecasting

Accurate and reliable monthly runoff forecasting is of great significance for water resource optimization and management. A neoteric hybrid model based on variational mode decomposition (VMD) and gradient boosting regression (GBRT) called VMD-GBRT was proposed and applied for monthly runoff forecasting. VMD was first employed to decompose the original monthly runoff series into several intrinsic mode functions (IMFs). The optimal number of input variables were then chosen according to the autocorrelation function (ACF) and the partial autocorrelation function (PACF). The trained GBRT model was used as a forecasting instrument to predict the testing set of each normalized subsequence. The ensemble forecasting result was finally generated by aggregating the prediction results of all subsequences. The proposed hybrid model was evaluated using an original monthly runoff series, from 1/1969 to 12/2018, measured at the Huaxian, Lintong and Xianyang hydrological stations in the Wei River Basin (WRB), China. The EEMD-GBRT, the single GBRT, and the single SVM were adopted as comparative forecast models using the same dataset. The results indicated that the VMD-GBRT model exhibited the best forecasting performance among all the peer models in terms of the coefficient of determination (R² = 0.8840), mean absolute percentage error (MAPE = 19.7451), and normalized root-mean-square error (NRMSE = 0.3468) at Huaxian station. Furthermore, the model forecasting results applied at Lintong and Xianyang stations were consistent with those at Huaxian station. This result further verified the accuracy and stability of the VMD-GBRT model. Thus, the proposed VMD-GBRT model was effective method for forecasting non-stationary and non-linear runoff series, and can be recommended as a promising model for monthly runoff forecasting.