Correction to: A new strategy for groundwater level prediction using a hybrid deep learning model under Ecological Water Replenishment

Accurate prediction of the groundwater level (GWL) is crucial for sustainable groundwater resource management. Ecological water replenishment (EWR) involves artificially diverting water to replenish the ecological flow and water resources of both surface water and groundwater within the basin. However, fluctuations in GWLs during the EWR process exhibit high nonlinearity and complexity in their time series, making it challenging for single data-driven models to predict the trend of groundwater level changes under the backdrop of EWR. This study introduced a new GWL prediction strategy based on a hybrid deep learning model, STL-IWOA-GRU. It integrated the LOESS-based seasonal trend decomposition algorithm (STL), improved whale optimization algorithm (IWOA), and Gated recurrent unit (GRU). The aim was to accurately predict GWLs in the context of EWR. This study gathered GWL, precipitation, and surface runoff data from 21 monitoring wells in the Yongding River Basin (Beijing Section) over a period of 731 days. The research results demonstrate that the improvement strategy implemented for the IWOA enhances the convergence speed and global search capabilities of the algorithm. In the case analysis, evaluation metrics including the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and Nash–Sutcliffe efficiency (NSE) were employed. STL-IWOA-GRU exhibited commendable performance, with MAE achieving the best result, averaging at 0.266. When compared to other models such as Variance Mode Decomposition-Gated Recurrent Unit (VMD-GRU), Ant Lion Optimizer-Support Vector Machine (ALO-SVM), STL-Particle Swarm Optimization-GRU (STL-PSO-GRU), and STL-Sine Cosine Algorithm-GRU (STL-SCA-GRU), MAE was reduced by 18