| In this study, Variational Mode Decomposition (VMD) and Long Short-Term Memory neural network (LSTM) were integrated to establish a hybrid prediction model, named VMD-LSTM, for reducing the prediction error caused by the nonlinearity and non-stationarity of the runoff series and for improving the accuracy of monthly runoff prediction results under various forecast periods, and some highly correlated atmospheric circulation factors were selected as the additional term of the model input, then the monthly runoff was predicted for 1~ 3 lead months. The performance of VMD-LSTM in predicting monthly runoff at the Tangnaihai, Minhe, Xiangtang, Hongqi and Zheqiao stations at the upper reaches of the Yellow River Basin was verified. And the VMD-LSTM model was compared with VMD-BP(BP neural network), VMD-SVR(support vector regression) and the single LSTM model for evaluating its applicability. The results show that the VMD-LSTM model exhibits the best forecasting performance, compared with the single LSTM model, and its Nash efficiency coefficient (NSE) is substantially improved from 0.6~0.7 to above 0.9; when putting atmospheric circulation factors, the accuracy of VMD-LSTM model is further improved, with NSE remaining at 0.91~0.96; with the increase of lead time, the precision attenuation of VMD-LSTM model becomes slower than VMD-BP and VMD-SVR model, and its NSE can still remain at 0.84~0.95 when the forecast period is 3 months. The VMD-LSTM model is an effective method for monthly runoff prediction, and the results can provide guidance for monthly runoff prediction in the study area. |