A Hybrid Forecasting Model to Simulate the Runoff of the Upper Heihe River

River runoff simulation and prediction are important for controlling the water volume and ensuring the optimal allocation of water resources in river basins. However, the instability of medium- and long-term runoff series increases the difficulty of runoff forecasting work. In order to improve the prediction accuracy, this research establishes a hybrid deep learning model framework based on variational mode decomposition (VMD), the mutual information method (MI), and a long short-term memory network (LSTM), namely, VMD-LSTM. First, the original runoff data are decomposed into a number of intrinsic mode functions (IMFs) using VMD. Then, for each IMF, a long short-term memory (LSTM) network is applied to establish the prediction model, and the MI method is used to determine the data input lag time. Finally, the prediction results of each subsequence are reconstructed to obtain the final forecast result. We explored the predictive performance of the model with regard to monthly runoff in the upper Heihe River Basin, China, and compared its performance with other single and hybrid models. The results show that the proposed model has obvious advantages in terms of the performance of point prediction and interval prediction compared to several comparative models. The Nash–Sutcliffe efficiency coefficient (NSE) of the prediction results reached 0.96, and the coverage of the interval prediction reached 0.967 and 0.908 at 95% and 90% confidence intervals, respectively. Therefore, the proposed model is feasible for simulating the monthly runoff of this watershed.