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
Keywords:
Geostatistics, hydraulic head, kriging, sequential Gaussian simulation, Bayesian, Random Forest, uncertainty quantification, Carrizo–Wilcox aquifer, Texas, sparse monitoring.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 water-management entities a clear, defensible and replicable process for regional groundwater characterization and prioritization of monitoring investments.
References
[1] S. Jasechko and D. Perrone, "Global groundwater wells at risk of running dry," Science, vol. 372, no. 6540, pp. 418–421, Apr. 2021.
[2] B. Bruun, "Commentary: The regional water planning process: A Texas success story," Texas Water Journal, vol. 8, no. 1, p. 1, 2017.
[3] C. Wang and W. A. Illman, "Hydraulic tomography estimates improved by zonal information from the clustering of geophysical survey data," Water Resources Research, vol. 59, no. 9, Art. no. e2023WR035191, 2023.
[4] E. A. Varouchakis, C. Guardiola-Albert, and G. P. Karatzas, "Spatiotemporal geostatistical analysis of groundwater level in aquifer systems of complex hydrogeology," Water Resources Research, vol. 58, no. 3, Art. no. e2021WR029988, 2022.
[5] A. Pavlides, E. A. Varouchakis, and D. T. Hristopulos, "Geostatistical analysis of groundwater levels in a mining area with three active mines," Hydrogeology Journal, vol. 31, no. 6, pp. 1425–1441, 2023.
[6] D. R. Kitanidis, Introduction to Geostatistics: Applications in Hydrogeology. Cambridge, U.K.: Cambridge Univ. Press, 1997.
[7] Y. Zha, T. C. J. Yeh, W. A. Illman, H. Onoe, C. M. W. Mok, J. C. Wen, et al., "Incorporating geologic information into hydraulic tomography: A general framework based on geostatistical approach," Water Resources Research, vol. 53, no. 4, pp. 2850–2876, 2017.
[8] S. Banerjee, B. P. Carlin, and A. E. Gelfand, Hierarchical Modeling and Analysis for Spatial Data, 2nd ed. Boca Raton, FL: CRC Press, 2015.
[9] H. Chihi and I. Ben Cheikh Larbi, "Spatial prediction of groundwater levels using machine learning and geostatistical models: A case study of coastal faulted aquifer systems in southeastern Tunisia," Hydrogeology Journal, vol. 31, no. 6, pp. 1387–1404, 2023.
[10] P. Renard, "Stochastic hydrogeology: What professionals really need?," Ground Water, vol. 45, no. 5, pp. 531–541, Sep. 2007.
[11] T. Hengl, M. Nussbaum, M. N. Wright, G. B. M. Heuvelink, and B. Gräler, "Random forest as a generic framework for predictive modeling of spatial and spatio-temporal variables," PeerJ, vol. 6, e5518, Aug. 2018.
[12] D. Sekulić, M. Kilibarda, G. B. M. Heuvelink, M. Nikolić, and B. Bajat, "Random forest spatial interpolation," Remote Sens., vol. 12, no. 10, art. 1687, May 2020.
[13] M. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning. Cambridge, MA: MIT Press, 2006.
[14] G. B. M. Heuvelink and D. J. Brus, "Machine learning in space and time for modelling soil organic carbon change," Eur. J. Soil Sci., vol. 72, no. 4, pp. 1607–1623, Jul. 2021.
[15] A. Nussbaum et al., "Evaluation of digital soil mapping approaches with large sets of environmental covariates," SOIL, vol. 4, no. 1, pp. 1–22, Jan. 2018.
[16] M. Bierkens, "Global hydrology 2015: State, trends, and directions," Water Resour. Res., vol. 51, no. 7, pp. 4923–4947, Jul. 2015.
[17] R. G. Taylor et al., "Ground water and climate change," Nature Clim. Change, vol. 3, no. 4, pp. 322–329, Apr. 2013.
[18] M. Ohmer, T. Liesch, and A. Wunsch, "Spatio-temporal optimization of groundwater monitoring networks using data-driven sparse sensing methods," Hydrology and Earth System Sciences Discussions, pp. 1–29, 2022.
[19] N. K. Christensen, B. J. Minsley, and S. Christensen, "Generation of 3-D hydrostratigraphic zones from dense airborne electromagnetic data to assess groundwater model prediction error," Water Resources Research, vol. 53, no. 2, pp. 1019–1038, 2017.
[20] P. Xue, Z. Wen, E. Park, H. Jakada, D. Zhao, and X. Liang, "Geostatistical analysis and hydrofacies simulation for estimating the spatial variability of hydraulic conductivity in the Jianghan Plain, central China," Hydrogeology Journal, vol. 30, no. 4, pp. 1135–1155, 2022.
[21] M. Siena and M. Riva, "Impact of geostatistical reconstruction approaches on model calibration for flow in highly heterogeneous aquifers," Stochastic Environmental Research and Risk Assessment, vol. 34, no. 10, pp. 1591–1606, 2020.
[22] D. Rambourg, R. Di Chiara, and P. Ackerer, "Three-dimensional hydrogeological parametrization using sparse piezometric data," Hydrology and Earth System Sciences, vol. 26, no. 23, pp. 6147–6162, 2022.
[23] J.-P. Nicot and B. R. Scanlon, "Water use for shale-gas production in Texas, U.S.," Environ. Sci. Technol., vol. 46, no. 6, pp. 3580–3586, Mar. 2012.
[24] R. C. Reedy, B. R. Scanlon, S. Walden, and G. Strassberg, "Naturally occurring groundwater contamination in Texas," TWDB Contract Rep. 1004831125, 2011.
[25] M. Milmo, J. McDowell, M. Yesildirek, and G. Harwell, "The use of historical data and global climate models to assess historical and future surface water and groundwater availability in the Trinity River Basin in Texas," Texas Water Journal, vol. 14, no. 1, pp. 34–61, 2023.
[26] R. G. Anaya and I. Jones, "Groundwater availability model for the Edwards-Trinity (Plateau) and Pecos Valley aquifers of Texas," TWDB Numerical Modeling Rep. 373, 2009.
[27] K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. New York, NY: Springer, 2002.
[28] J. Doherty, Calibration and Uncertainty Analysis for Complex Environmental Models. Brisbane, Australia: Watermark Numerical Computing, 2015.
[29] G. Evensen, Data Assimilation: The Ensemble Kalman Filter, 2nd ed. Berlin, Germany: Springer, 2009.
[30] K. Varouchakis, D. T. Hristopulos, and G. Karatzas, "Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application," Hydrol. Sci. J., vol. 57, no. 7, pp. 1404–1419, Oct. 2012.
[31] R. M. Neuman, "Maximum likelihood Bayesian averaging of uncertain model predictions," Stoch. Environ. Res. Risk Assess., vol. 17, no. 5, pp. 291–305, Nov. 2003.
[32] M. Marini, F. Felletti, G. P. Beretta, and J. Terrenghi, "Three geostatistical methods for hydrofacies simulation ranked using a large borehole lithology dataset from the Venice Hinterland (NE Italy)," Water, vol. 10, no. 7, Art. no. 844, 2018.
[33] S. Janardhanan, D. Gladish, D. Gonzalez, D. Pagendam, T. Pickett, and T. Cui, "Optimal design and prediction-independent verification of groundwater monitoring network," Water, vol. 12, no. 1, Art. no. 123, 2019.
[34] L. M. Nunes, M. C. Cunha, and L. Ribeiro, "Groundwater monitoring network optimization with redundancy reduction," J. Water Resour. Plann. Manage., vol. 130, no. 1, pp. 33–43, Jan. 2004.
[35] L. Fienen, R. J. Hunt, D. Krabbenhoft, and T. Clemo, "Obtaining parsimonious hydraulic conductivity fields using head and transport observations: A Bayesian geostatistical parameter estimation approach," Water Resour. Res., vol. 45, no. 8, W08405, Aug. 2009.
[36] S. De Iaco, D. E. Myers, and D. Posa, "Space-time analysis using a general product-sum model," Stat. Prob. Lett., vol. 52, no. 1, pp. 21–28, Mar. 2001.
[37] E. Varouchakis and D. T. Hristopulos, "Comparison of stochastic and deterministic methods for mapping groundwater level spatial variability in sparsely monitored basins," Environ. Monit. Assess., vol. 185, no. 1, pp. 1–19, Jan. 2013.
[38] B. R. Scanlon et al., "Global models underestimate large decadal declining and rising water storage trends relative to GRACE satellite data," Proc. Natl. Acad. Sci. USA, vol. 115, no. 6, pp. E1080–E1089, Feb. 2018.
[39] G. Evensen, "The ensemble Kalman filter: Theoretical formulation and practical implementation," Ocean Dyn., vol. 53, no. 4, pp. 343–367, Nov. 2003.
[40] A. Doucet, N. de Freitas, and N. Gordon, Eds., Sequential Monte Carlo Methods in Practice. New York, NY: Springer, 2001.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Mir Akib Jawed (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
