Monthly runoff prediction based on a coupled VMD-SSA-BiLSTM model

The accurate prediction of monthly runoff in the lower reaches of the Yellow River is crucial for the rational utilization of regional water resources, optimal allocation, and flood prevention. This study proposes a VMD-SSA-BiLSTM coupled model for monthly runoff volume prediction, which combines the advantages of Variational Modal Decomposition (VMD) for signal decomposition and preprocessing, Sparrow Search Algorithm (SSA) for BiLSTM model parameter optimization, and Bi-directional Long and Short-Term Memory Neural Network (BiLSTM) for exploiting the bi-directional linkage and advanced characteristics of the runoff process. The proposed model was applied to predict monthly runoff at GaoCun hydrological station in the lower Yellow River. The results demonstrate that the VMD-SSA-BiLSTM model outperforms both the BiLSTM model and the VMD-BiLSTM model in terms of prediction accuracy during both the training and validation periods. The Root-mean-square deviation of VMD-SSA-BiLSTM model is 30.6601, which is 242.5124 and 39.9835 lower compared to the BiLSTM model and the VMD-BiLSTM model respectively; the mean absolute percentage error is 5.6832%, which is 35.5937% and 6.3856% lower compared to the other two models, respectively; the mean absolute error was 19.8992, which decreased by 136.7288 and 25.7274 respectively; the square of the correlation coefficient (R(2)) is 0.93775, which increases by 0.53059 and 0.14739 respectively; the Nash–Sutcliffe efficiency coefficient was 0.9886, which increased by 0.4994 and 0.1122 respectively. In conclusion, the proposed VMD-SSA-BiLSTM model, utilizing the sparrow search algorithm and bidirectional long and short-term memory neural network, enhances the smoothness of the monthly runoff series and improves the accuracy of point predictions. This model holds promise for the effective prediction of monthly runoff in the lower Yellow River.