Uncertainty-Aware Geostatistical Reconstruction of Regional Groundwater Hydraulics under Sparse Monitoring Conditions: A Case Study of the Evergreen Underground Water Conservation District (EUWCD), Texas, USA

Abstract

Adequate estimation of hydraulic head fields in regional aquifers is critical for sustainable groundwater management, but in rural aquifers monitoring networks are often sparse, uneven, and temporally irregular, leading to large and poorly quantified interpolation uncertainty. This study proposes and tests an uncertainty-aware geostatistical approach to reconstruct the regional potentiometric surface of the Carrizo–Wilcox aquifer under the Evergreen Underground Water Conservation District (EUWCD) in South-Central Texas. A total of 180 monitoring wells provided 4,872 hydraulic head observations from 2005 to 2022 that were analyzed. The following six spatial predictors were contrasted: ordinary kriging (OK), universal kriging (UK), kriging with external drift (KED) (with land-surface elevation as the external drift variable), Bayesian kriging (BK), sequential Gaussian simulation (SGSIM) (with 500 realizations), and a combination of Random Forest and krigged residuals (RFK). Leave-one-out cross-validation and independent hold-out testing (22 wells) were used to evaluate model performance, whilst predictive uncertainty was evaluated using kriging variance, Bayesian posterior variance, and ensemble standard deviation. The omnidirectional spatial structure was best represented by a spherical variogram with a nugget of 18 m2, a partial sill of 105 m2 and a range of 22 km, while a moderate geometric anisotropy (ratio 1.44) was found, consistent with the regional dip. RFK produced the lowest overall error (RMSE = 2.68 m, R² = 0.934), followed by KED (RMSE = 2.91 m). SGSIM realizations reproduced the observed head statistics while providing spatially explicit uncertainty maps; the mean ensemble standard deviation was 4.7 m across the domain but exceeded 8.5 m in downdip sub-regions with < 0.15 wells km⁻². Based on a sensitivity analysis of well density and the resulting uncertainty in prediction, the well density range of 0.6–1.0 wells km−² was determined to be an efficient design envelope. The framework offers EUWCDs and similar rural watermanagement entities a clear, defensible and replicable process for regional groundwater characterization and prioritization of monitoring investments.