Monthly runoff prediction using the VMD-LSTM-Transformer hybrid model: a case study of the Miyun Reservoir in Beijing

Abstract

Abstract Accurate runoff prediction is of great significance for flood prevention and mitigation, agricultural irrigation, and reservoir scheduling in watersheds. To address the strong non-linear and non-stationary characteristics of runoff series, a hybrid model of monthly runoff prediction, variational mode decomposition (VMD)–long short-term memory (LSTM)–Transformer, is proposed. Firstly, VMD is used to decompose the runoff series into multiple modal components, and the sample entropy of each modal component is calculated and divided into high-frequency and low-frequency components. The LSTM model is then used to predict the high-frequency components and the transformer to predict the low-frequency components. Finally, the prediction results are summed to obtain the final prediction results. The Mann–Kendall trend test method is used to analyze the runoff characteristics of the Miyun Reservoir, and the constructed VMD–LSTM–Transformer model is used to forecast the runoff of the Miyun Reservoir. The prediction results are compared and evaluated with those of VMD–LSTM, VMD–Transformer, empirical mode decomposition (EMD)–LSTM–Transformer, and empirical mode decomposition (EMD)–LSTM models. The results show that the Nash–Sutcliffe efficiency coefficient (NSE) value of this model is 0.976, mean absolute error (MAE) is 0.206 × 107 m3, mean absolute percentage error (MAPE) is 0.381%, and root mean squared error (RMSE) is 0.411 × 107 m3, all of which are better than other models, indicating that the VMD–LSTM–Transformer model has higher prediction accuracy and can be applied to runoff prediction in the actual study area.