Decomposition ensemble model based on variational mode decomposition and long short-term memory for streamflow forecasting

Reliable and accurate streamflow forecasting is vital for water resource management. Many streamflow prediction studies have demonstrated the excellent prediction ability of decomposition ensemble models. Several studies first extracted subsignals from a streamflow series and then split subsignals into training and validation sets to build prediction models, capturing some future information not available in practical streamflow forecasting. Alternatively, dividing a time series into training and validation sets first and later decomposing them into subsignals can expose the subsignals to the boundary effect, making predicting streamflow difficult. Furthermore, building one model for each subsignal is laborious and can cause error accumulation. Therefore, establishing a robust and efficient decomposition ensemble model without future information to predict highly nonstationary and nonlinear streamflow is challenging. Hence, a single-model forecasting (SF) scheme that assesses the validation distribution during the training stage to adapt to the boundary effect was designed. A SF scheme based on variational mode decomposition (VMD) and long short-term memory (LSTM), namely, SF-VMD-LSTM, was proposed to predict daily streamflow 1-7 days ahead. Non-decomposition-based and decomposition-ensemble-based LSTM models established using SF, multi-model ensemble forecasting (MEF) and SF with the most influential subsignals (SFMIS) and the ensemble empirical mode decomposition (EEMD) and discrete wavelet transform (DWT) were compared. Additionally, multi-model ensemble hindcasting (MEH), single-model hindcasting (SH) and SH with the most influential subsignals (SHMIS) were used as benchmarks to evaluate the forecasting schemes' adaptability to the boundary effect. Two daily streamflow series from Han River and Jing River, China, were investigated. The results indicate that (1) SF is more robust and efficient than MEF and SFMIS; (2) VMD performs better than EEMD and DWT; (3) SF-VMD-LSTM, with NSE values larger than 0.8 for almost all the prediction scenarios, outperformed other comparative models. Therefore, SF-VMD-LSTM is robust and efficient for forecasting highly nonstationary and nonlinear streamflow.