Constructing regional groundwater level prediction models considering spatial heterogeneity

Groundwater table prediction can play an essential role in agricultural production, drainage engineering, and water-resources regulation in arid and semi-arid regions. Particularly, shallow groundwater dynamics can also respond rapidly to climate forcing and anthropogenic disturbances. In this study, a groundwater dynamics model was constructed to predict the regional level using spatial heterogeneity. 23 daily monitoring stations were selected in Linwei District, Weinan City, Shaanxi Province, China, a typical semi-arid region with complex non-linear interactions between meteorological forcing and human activities. A prediction framework was also developed for the regional groundwater level. Site-specific explanatory variables were integrated with Long Short-Term Memory (LSTM) networks and intelligent hyperparameter optimization. An independent modeling strategy was adopted for spatial heterogeneity in the study area. A customized prediction model was constructed for each individual observation well. The localized hydrogeological features were implicitly captured in response to external stressors, rather than the explicit spatial parameterization. A standard score outlier detection was applied to the daily water level series after data preprocessing. The 3 $\sigma$ criterion of standard deviations was utilized to identify and then remove anomalous data points. Missing values were subsequently filled using linear interpolation. Feature screening was conducted for the effectiveness of model inputs using Pearson correlation analysis. Eight candidate variables were evaluated, including meteorological and environmental indicators, such as reference crop evapotranspiration, daily maximum and minimum temperatures, precipitation, relative humidity, sunshine hours, wind speed, and soil heat flux. Input features were selected for the absolute correlation coefficient greater than 0.30 with the localized groundwater level. Site-adaptive input selection effectively reduced data redundancy and overfitting. Weakly correlated noise was removed after selection. A systematic investigation was implemented to compare manual hyperparameter tuning, the Salp Swarm Algorithm (SSA), and Bayesian Optimization (BO). The swarming behavior of Salp chains was then simulated to explore the parameter space using a leader-follower mechanism. In contrast, a Gaussian Process was employed as a surrogate model to estimate the distribution of the objective function. An Upper Confidence Bound acquisition function was utilized to balance exploration and exploitation. These optimizers were used to determine the optimal configuration of the model structures. The results demonstrated that intelligent optimization significantly enhanced the predictive accuracy and robustness of the baseline LSTM models. The benchmark LSTM models achieved average Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Nash-Sutcliffe Efficiency (NSE) of 0.15, 0.24, and 0.71, respectively. The SSA reduced the average MAE and RMSE to 0.14 and 0.22, respectively. The LSTM network with BO (LSTM-BO) exhibited the most superior performance, with the average MAE and RMSE decreasing to 0.13 and 0.20, respectively. Crucially, the average NSE reached 0.85 for the LSTM-BO models. All individual stations maintained an efficiency score above 0.61. A more stable and reliable parameter search was obtained in the BO, compared with the SSA, particularly in complex stations where the baseline models previously failed or significantly degraded. The framework was combined with site-specific feature selection with probabilistic hyperparameter optimization. The findings can also offer a powerful and practical tool for groundwater resources of agricultural drainage engineering in semi-arid environments.