Predicting Groundwater Depth Using Historical Data Trend Decomposition: Based on the VMD-LSTM Hybrid Deep Learning Model

Groundwater is a critical natural and strategic economic resource, and the accurate prediction of groundwater depth dynamics is essential for the rational development and utilization of water resources. However, under the combined influence of climate variability, human activities, and complex hydrogeological conditions, groundwater level time series exhibit strong nonlinear and non-stationary characteristics, posing great challenges to the accurate prediction of groundwater level dynamics. Most existing prediction models rely on sufficient hydro-meteorological and exploitation data that are difficult to obtain in water-scarce regions, or fail to effectively decouple the multi-scale features of non-stationary groundwater level signals, resulting in limited prediction accuracy and insufficient generalization ability. To address these research gaps, this study takes Zhengzhou, a typical water-deficient city in the Yellow River Basin, as the study area, and proposes a hybrid deep learning framework combining Variational Mode Decomposition (VMD) and Long Short-Term Memory (LSTM) neural network for predicting shallow and intermediate-deep groundwater level changes. Kolmogorov–Arnold Networks (KANs) and Gated Recurrent Units (GRUs) are selected as benchmark models to verify the superior performance of the proposed framework. In this framework, the non-stationary groundwater level signal is adaptively decomposed into Intrinsic Mode Functions (IMFs) with distinct frequency characteristics via VMD. An independent LSTM model is constructed for each IMF to capture its unique temporal variation pattern, and the final groundwater level prediction is obtained by linearly reconstructing the predicted results of all IMFs. The results show that the coefficient of determination (R2) of the VMD-LSTM model exceeds 0.90 for all monitoring datasets, with low Mean Absolute Error (MAE) and Mean Squared Error (MSE). It significantly outperforms the benchmark models in handling nonlinear and non-stationary time series features. Using only historical groundwater level data as input, the proposed framework effectively overcomes the limitation of insufficient driving variables in data-scarce regions and fully explores the multi-scale evolution of groundwater dynamics through the synergistic effect of multi-scale decomposition and deep learning. The method presented in this study provides a novel and reliable technical approach for groundwater level prediction in water-deficient and data-limited areas, and also offers scientific support for the rational management and sustainable utilization of regional groundwater resources. Future research will incorporate driving factors such as meteorology and exploitation to further improve the model’s ability to capture abrupt changes in groundwater level dynamics.