Improving Daily Runoff Forecasting with VMD-VPPSO-LSTM

To further improve prediction accuracy, a VMD-VPPSO-LSTM model is proposed in this study, which combines Variational Mode Decomposition (VMD) for signal decomposition, Velocity-Pause Particle Swarm Optimization (VPPSO) for parameter optimization, and Long Short-Term Memory (LSTM) for runoff prediction. The model was evaluated at Huangtaiqiao station in the Xiaoqing River Basin, Dawenkou station in the Dawen River Basin, and Tangnaihai station in the source region of the Yellow River Basin. The proposed model achieved the best overall performance among all comparison models, with Nash–Sutcliffe Efficiency (NSE) values of 0.970, 0.962, and 0.994 and Root Mean Square Error (RMSE) values of 1.357, 0.989, and 46.804 at the three stations, respectively. Compared with VMD-LSTM, VPPSO further reduced the RMSE at all stations and maintained training-test NSE gaps below 0.006, indicating strong generalization performance. The model also achieved the lowest Peak Percent Standard Deviation (PPSD) values for high-flow events, reaching 9.03%, 14.42%, and 3.88% at the three stations, respectively. These results demonstrate that VMD-VPPSO-LSTM is a reliable and effective model for daily runoff prediction.