Daily Runoff Series Prediction Using GWO Optimization and Secondary Decomposition: A Case Study of the Xujiang River Basin

Runoff time series often exhibit nonlinear and fluctuating characteristics, and their complexity has further increased with the intensification of global climate change; high-precision daily-scale forecasting remains a core challenge in the field of hydrological forecasting. Addressing the shortcomings of existing methods in terms of runoff feature extraction capabilities and limited forecasting accuracy, this paper aims to improve the accuracy of daily runoff forecasting in small watersheds by constructing a hybrid forecasting model that integrates optimization algorithms, signal decomposition, and deep learning models. Specifically, the original runoff data is first preliminarily decomposed using a variational mode decomposition (VMD) method optimized by the grey wolf optimization (GWO) algorithm. The mode components obtained from the decomposition are evaluated using Fuzzy Entropy (FE), and the selected high-entropy components (IMFs) are then input into a second-order decomposition using an optimized Wavelet Transform (WT) to further extract latent features. After decomposition, the mode components are reassembled; second, a bidirectional long short-term memory (BiLSTM) model for daily runoff prediction is constructed for each subcomponent, and the model’s hyperparameters are optimized using an optimization algorithm; finally, the prediction results are reconstructed to obtain the final output. Case studies were conducted using three hydrological stations—Nanfeng, Baiquan, and Shaziling—in the Xujiang River basin of the Fuhe River. The experimental results indicate that by incorporating an optimization mechanism and a two-stage decomposition strategy, the proposed model achieved an NSE of over 0.95 at all three stations. Compared to the baseline BiLSTM model, the proposed model reduced the RMSE by 76.69%, 75.82%, and 65.92% at the three stations, respectively, and reduced the MAE by 64.77%, 73.54%, and 50.46%, and NSE increased by 27.82%, 40.06%, and 38.02%, respectively. This demonstrates that the model exhibits excellent reliability and superiority in daily-scale runoff forecasting for small watersheds.