Prediction of Groundwater Burial Depth Based on an HO-LSTM-GPR Hybrid Deep Learning Model

Groundwater in Zhengzhou has experienced substantial changes under the combined effects of long-term abstraction, water-source substitution by the South-to-North Water Diversion Project, and ecological replenishment. During the 13th Five-Year Plan period, shallow and middle-deep groundwater levels in Zhengzhou recovered by 2.83 m and 6.46 m, respectively; nevertheless, extensive groundwater depression cones remained, highlighting the need for reliable groundwater burial-depth prediction to support dynamic monitoring and water-resource management. Aiming to address the limitations of the single long short-term memory (LSTM) network in groundwater burial depth prediction, including insufficient accuracy, tendency to fall into local optima, and difficulty in adaptive hyperparameter optimization, this study constructs a hybrid deep learning model (HO-LSTM-GPR). The Hippopotamus Optimization (HO) algorithm is employed to search for an appropriate parameter configuration of the LSTM network, and Gaussian Process Regression (GPR) is subsequently introduced to correct the residual deviations of the preliminary predictions. Four groundwater monitoring wells in Zhengzhou City, including the shallow wells Q1 and Q8 and the middle-deep wells Z14 and Z30, are selected to evaluate groundwater burial-depth prediction using historical input sequence lengths ranging from 1 to 30 days. The results show that the HO-LSTM-GPR model can significantly reduce prediction errors, and the Nash–Sutcliffe Efficiency (NSE) of all monitoring points exceeds 0.92, with the most prominent improvement observed at the Q1 site. The model can accurately characterize the high-frequency fluctuations of shallow groundwater levels and the slow variation characteristics of middle-deep groundwater levels, and effectively capture extreme points and mutation nodes. Within the comparison conducted in this study, the HO-LSTM-GPR model achieves higher fitting accuracy and prediction stability than the baseline LSTM model. Under the present dataset and model configuration, the HO-LSTM-GPR model achieves the best overall predictive performance when the historical input sequence length is 19 days. Overall, the HO-LSTM-GPR model exhibits relatively stable predictive performance for the investigated aquifers under different historical input sequence lengths.