Abstract: To improve the accuracy of runoff forecast, we construct combined prediction models by integrating gradient lifting tree regression (GBDT), back propagation algorithm (BP), and with differential evolution Grey Wolf algorithm (HGWO) support vector regression (SVR) algorithm optimized using the variational mode decomposition (VMD) and the extreme-point symmetric mode decomposition (ESMD), and apply them to the monthly runoff series measured at the Tangnaihai station and Lanzhou station of the Yellow River. The results show the combined model VMD-HGWO-SVR gives the best predictions compared with other models. Its average absolute error in predicting monthly runoff at the two stations is decreased by 53.38%, 14.27% and 6.8% compared with ESMD-HGWO-SVR, VMD-BP and VMD-GBDT, respectively. On average, its root-mean-square error is decreased by 53.66%, 22.0% and 11.54%, average relative error by 54.92%, 12.0% and 3.67%; its Nash efficiency coefficient is increased by 17.09%, 3.26% and 1.36%, respectively. This verifies our new method achieves satisfactory effects in predicting monthly runoff time series.

Key words: variational mode decomposition, monthly runoff prediction, Gray Wolf algorithm, differential evolution algorithm, Tangnaihai station, Lanzhou station