A multi-scale machine learning framework for interpretable groundwater level prediction

Accurate prediction of groundwater level variations remains challenging in intensively exploited aquifers, particularly where recharge processes operate at daily scales while pumping activities are recorded at coarser temporal resolutions. Conventional data-driven models often struggle to reconcile these mismatched time scales and provide limited physical interpretability. This study aims to develop an interpretable, multi-scale machine learning framework that explicitly separates recharge-driven dynamics from pumping-induced impacts, thereby facilitating both predictive performance and enhanced hydrological insight. A two-stage, multi-scale modeling framework is proposed for a catchment-scale groundwater monitoring network consisting of nine monitoring wells. Daily groundwater levels and rainfall data were used alongside monthly electricity consumption records from surrounding pumping wells, disaggregated by pumping purpose. In Stage A, a monthly-scale model was constructed to capture long-term groundwater trends driven by aggregated rainfall and pumping intensity. Monthly groundwater levels were modeled using gradient boosting with rainfall sums, purpose-specific pumping electricity consumption, and optional autoregressive terms. Out-of-fold (OOF) predictions were generated using a five-fold time-series cross-validation scheme, and monthly predictions were subsequently upsampled to daily resolution. In Stage B, daily-scale residuals were defined as the difference between observed groundwater levels and Stage A monthly predictions. A residual learning model was then developed to represent short-term recharge responses using daily autoregressive information (with a 7-day lag), cumulative rainfall indices (7- and 14-day sums), and antecedent dry-day counts. To enhance robustness against extreme fluctuations, a pseudo-Huber loss function was adopted within an XGBoost regression framework. A small nested time-series grid search was employed to tune key hyperparameters, thereby balancing model stability and the risk of overfitting. Model performance was evaluated using OOF predictions across all wells. Interpretability was assessed through SHAP value analysis, rainfall event-aligned composite response analysis, and lag-to-peak diagnostics. Additional scenario-based comparisons were conducted to contrast observed responses, no-pumping counterfactual predictions, and simulations that included pumping. The proposed multi-scale framework achieved stable and physically consistent groundwater level predictions across the monitoring network. Stage B residual modeling substantially improved daily-scale performance relative to autoregressive-only baselines, particularly during recharge events. SHAP analysis confirmed that short-term rainfall accumulation and antecedent wetness were the dominant drivers of residual groundwater responses, while autoregressive terms captured local memory effects. Event-aligned composite analyses revealed heterogeneous lag-to-peak responses among wells, reflecting spatial variability in hydrogeological connectivity and the influence of pumping. While incorporating pumping information improved monthly trend representation in Stage A, scenario comparisons indicated that pumping effects on event-scale dynamics were well-separated from recharge-driven responses. The pseudo-Huber loss function provided marginal but consistent gains in robustness, particularly for wells exhibiting heavy-tailed residual behavior, without compromising interpretability. This study demonstrates that a multi-scale, residual-based machine learning framework can effectively reconcile disparate temporal resolutions in groundwater datasets while preserving hydrological interpretability. By explicitly decoupling long-term pumping impacts from short-term recharge dynamics, the proposed approach provides a transparent and extensible foundation for groundwater management applications. The framework is well-suited for exploratory analysis and international knowledge exchange, with future work focusing on refined representations of pumping and extended scenario-based assessments.