A hybrid TFN-LSTM model for groundwater level forecasting in Rhode Island, USA.

Performance and Limitations of Machine Learning Models for Groundwater Level Prediction Using Hydro-Climatic Variables

Accurate groundwater level (GWL) prediction is essential for sustainable groundwater management and resource planning. However, it is challenging in heterogeneous hydrogeological settings for physics-based models, particularly under limited subsurface characterisation. Machine learning (ML) techniques can capture complex spatio-temporal groundwater dynamics, complementing conventional modelling approaches. This study systematically evaluates the performance and limitations of ML models for GWL prediction in sandstone and mudstone formations, with emphasis on the influence of local hydrogeological conditions. Artificial Neural Network (ANN), Long Short-Term Memory (LSTM), Support Vector Regression (SVR), and Random Forest (RF), along with their wavelet-enhanced counterparts, were applied to monthly hydro-climatic data from 11 observation wells in the Lower Otter Catchment, UK, covering 2011–2023. The final four years were reserved for validation. Time-series predictors were used because time-invariant and sparsely available geological parameters provide limited explanatory power for local-scale GWL dynamics. Their influence is implicitly reflected in observed GWL responses. Model performance was assessed using statistical criteria, including the coefficient of determination (R 2 ). Additionally, a new metric, the Data Difference and Trend Index (DDTI), was introduced to measure the proportion of simulated values matching observed trends within a predefined threshold (e.g. 0.5 m). Model performance was site-specific, with validation R 2 ranging from < 0.1 to > 0.9. This indicates the dominant influence of local hydrogeological conditions, with lower accuracy observed in partially confined, non-recharge-dominated, and river-disconnected wells. A 2-month time lag produced optimal model performance, reflecting the catchment’s characteristic response time to infiltration processes. Individual models occasionally outperformed ensemble averages, which showed fewer outliers. Wavelet transforms did not consistently enhance performance. Model efficacy varied seasonally, with validation R 2 markedly lower in summer (e.g. < 0.1) and higher in autumn (e.g. > 0.9). This emphasises key limitations of ML-based GWL prediction, including reduced reliability near lithological boundaries and strong sensitivity to hydro-climatic conditions, constraining model transferability. Overall, the findings highlight the value of moving beyond performance benchmarking to explicitly identify hydro-climatic and hydrogeological conditions under which ML models lose reliability, informing groundwater modelling and sustainable water management. Graphical Abstract This study evaluates the performance and limitations of machine learning (ML) models for predicting groundwater levels (GWL) in sandstone and mudstone formations using hydro-climatic variables across 11 observation wells in the Lower River Otter Water Body, UK. Four ML models, i.e. Artificial Neural Networks (ANN), Long Short-Term Memory (LSTM), Support Vector Regression (SVR), and Random Forest (RF), along with their wavelet-enhanced versions, were applied to monthly hydro-climatic data from 2011 to 2023, with the last four years reserved for validation. Model performance was assessed using the coefficient of determination (R 2 ), Root Mean Square Error (RMSE), and Nash-Sutcliffe Efficiency (NSE), and a novel Data Difference and Trend Index (DDTI), which quantifies the proportion of simulated data following observed trends within a defined threshold. Results indicate that predictive accuracy is highly site-specific, with local hydrogeological conditions strongly influencing outcomes. No model consistently captured GWL near interior boundaries where sandstone is confined by mudstone, and neither wavelet transforms nor model ensembles reliably improved performance. Seasonal variability also affected model efficacy, with the highest accuracy in autumn and the lowest in summer. Overall, the workflow highlights the limitations of ML for GWL prediction and provides insights for future hydrogeological modelling.

Understanding Long-Term Groundwater Storage Variability Using GRACE Data and Explainable Machine Learning

The decline in groundwater storage (GWS) poses a critical threat to water security in semi-arid regions where increasing agricultural water demand and climate variability are increasing pressure on aquifers. This study presents a novel hybrid modeling framework integrating multi-source satellite and climate data (GRACE, GLDAS, TerraClimate, and MODIS) with machine learning and explanatory artificial intelligence techniques for the long-term assessment and interpretation of GWS anomalies in the data-poor Iğdır Basin. Three different modeling approaches were developed: XGBoost, Long Short-Term Memory (LSTM) networks, and their combined model, and interpreted using the Shapley Additive Explanations (SHAP) method. The results showed a significant long-term decreasing trend in groundwater storage anomalies at a rate of −0.87 mm per month during the 2002–2016 period, indicating continuous depletion. The LSTM model demonstrated the best performance with R2 of 0.59, RMSE of 19.5 mm, and MAE of 15.1 mm, revealing the dominant role of temporal dependencies in groundwater systems. SHAP analysis identified lagged groundwater anomalies (especially GWS_lag3) as the most effective predictors; this may reflect the memory effect and lagged response specific to semi-arid aquifer systems, but this interpretation needs to be validated in different study areas. Snow water equivalent and total water storage anomalies also emerged as significant determinants, while the direct effect of instantaneous precipitation was found to be limited. This study addresses significant gaps in the literature by combining sequence-based modeling with model interpretability in a semi-arid closed basin. The findings highlight the necessity of using system memory and explainable artificial intelligence together for reliable groundwater prediction. While the proposed hybrid approach has the potential for application in other semi-arid regions, its broader usability needs to be supported by independent validation studies under different hydrogeological and climatic conditions.

Improved water-level predictions using hybrid long short-term memory networks and random forest techniques

Robust Short-Term Multivariate Water-Level Forecasting Using a Hybrid LSTM–EnKF Model Under White-Noise Disturbances

Short-term multivariate forecasting of hydrological variables remains challenging because river systems exhibit nonlinear and time-dependent dynamics, complex relationships among water level, flow, and precipitation, and uncertainty arising from measurement errors and external disturbances. Although neural network models can learn nonlinear relationships among hydrological variables, their predictive performance often deteriorates in the presence of noise. Moreover, existing approaches rarely integrate the learning of long-term temporal dependencies and cross-variable relationships with a data assimilation mechanism capable of recursively updating state estimates and reducing forecast uncertainty. This limitation reveals the need for a robust forecasting framework that combines both capabilities. Therefore, this study aimed to develop and evaluate a hybrid Long Short-Term Memory–Ensemble Kalman Filter (LSTM–EnKF) model for short-term multivariate water-level forecasting under noisy conditions. The proposed framework extends a previously developed NARX–EnKF approach by replacing the NARX network with an LSTM architecture capable of learning nonlinear temporal patterns and relationships among water level, flow, and precipitation. The model was implemented using data from two hydrological stations located along the Atrato River in Colombia and configured to generate water-level forecasts with a two-day prediction horizon. The LSTM network generated the initial forecasts, whereas the EnKF assimilated the available observations to recursively update the estimated states and reduce forecast uncertainty. Model robustness was examined by introducing Gaussian white noise with variance levels of 0.001, 0.05, 0.10, and 0.20 to represent measurement uncertainty and external disturbances. Performance was evaluated using the root mean square error (RMSE), mean absolute error (MAE), and Nash–Sutcliffe efficiency (NSE). Across all evaluated noise levels, the LSTM–EnKF model outperformed the standalone LSTM model. Its total RMSE ranged from 0.1009 to 0.1929 m, compared with 0.1740 to 0.2356 m for the standalone LSTM, representing reductions of approximately 18.1–42%. The hybrid model achieved NSE values ranging from 0.9760 to 0.9992, whereas the standalone LSTM produced values between 0.9200 and 0.9776. Furthermore, the LSTM–EnKF reduced the MAE by approximately 51.9–56.2% across both outputs. These results indicate that integrating LSTM-based temporal learning with EnKF-based data assimilation improves short-term forecasting accuracy and robustness under noisy conditions. The developed framework provides a promising tool for supporting flood early-warning systems, flood-risk management, and the protection of riverine communities.

Interpretable Groundwater-Level Prediction in an Arid Inland Basin by Integrating Dempster–Shafer Feature Screening with a Stacking Ensemble

Daily groundwater-level prediction in arid inland basins is driven by complex meteorological–hydrological conditions, water supply, pumping, and irrigation demand. Using data from the Zhangye Basin (2018–2025), this study selected 10 representative wells from 51 candidates to build a one-day-ahead framework with a 60-day input window. Dempster–Shafer evidence theory fused five criteria (Pearson, Spearman, lagged correlation, mutual information, and tree-model importance) to screen external variables. Long short-term memory network (LSTM), temporal convolutional network (TCN), and Transformer served as first-level sequence models; extreme gradient boosting (XGBoost) as the second-level stacking learner; and SHapley Additive exPlanations (SHAP) to quantify feature contributions. Dempster–Shafer evidence theory (D-S evidence theory) results indicated that groundwater pumping proxy variable (GPV), irrigation water-demand intensity proxy variable (IWD), surface-water supply proxy variable (SWS), canal-diversion proxy variable (CDV), air temperature (AT), runoff, vapor pressure deficit (VPD), and canal irrigation supply–demand coupling intensity (CISDCI) exhibited high process-representation relevance. During the 90-day test period, Stacking achieved the lowest RMSE for six of 10 wells. Regional average RMSE, MAE, and NSE values were 0.1596 m, 0.0772 m, and 0.9326 for the Zhangye group, and 0.0185 m, 0.0133 m, and 0.9177 for the Gaotai group. SHAP showed historical groundwater-level data dominated contributions, accounting for 64.17% and 43.96% in the Zhangye and Gaotai groups, respectively, and indicating model dependence rather than direct hydrological causality. This framework provides a cautious reference for short-term groundwater forecasting and input selection under the given data conditions.

Time‐Varying Hydroclimatic and Oceanic Controls on Arctic Submarine Groundwater Discharge Inferred Using Explainable AI

Submarine groundwater discharge (SGD), an important component of coastal water and nutrient budgets, is challenging to monitor and predict in the Arctic given the remoteness and harsh conditions. Here, we used explainable artificial intelligence to quantify the time‐varying importance of hydroclimatic and oceanic drivers of SGD at an Arctic beach from the early thaw period to late summer. Deep learning models were trained on in situ observations and reanalysis data, and feature contributions to model prediction were quantified using SHAP (Shapley Additive Explanations). We learned the following: potential evaporation is the dominant control on groundwater storage and SGD over seasonal scales; winds regulate short‐term groundwater levels and intermediate‐term discharge; soil temperature modulates groundwater storage via thaw‐driven processes; and precipitation is important for short‐term groundwater flushing and seasonal‐scale storage. These insights on the scale‐dependent SGD controls establish a framework for hindcasting and forecasting groundwater dynamics in remote Arctic environments.