Mathematical Geology

, Volume 37, Issue 6, pp 587–613 | Cite as

Estimating Regional Hydraulic Conductivity Fields—A Comparative Study of Geostatistical Methods

  • Delphine Patriarche
  • Maria Clara Castro
  • Pierre Goovaerts
Article
Received:
Accepted:

Abstract

Geostatistical estimations of the hydraulic conductivity field (K) in the Carrizo aquifer, Texas, are performed over three regional domains of increasing extent: 1) the domain corresponding to a three-dimensional groundwater flow model previously built (model domain); 2) the area corresponding to the 10 counties encompassing the model domain (County domain), and; 3) the full extension of the Carrizo aquifer within Texas (Texas domain). Two different approaches are used: 1) an indirect approach where transmissivity (T) is estimated first and K is retrieved through division of the T estimate by the screen length of the wells, and; 2) a direct approach where K data are kriged directly. Due to preferential well screen emplacement, and scarcity of sampling in the deeper portions of the formation (> 1 km), the available data set is biased toward high values of hydraulic conductivities. Kriging combined with linear regression, simple kriging with varying local means, kriging with an external drift, and cokriging allow the incorporation of specific capacity as secondary information. Prediction performances (assessed through cross-validation) differ according to the chosen approach, the considered variable (log-transformed or back-transformed), and the scale of interest. For the indirect approach, kriging of log T with varying local means yields the best estimates for both log-transformed and back-transformed variables in the model domain. For larger regional scales (County and Texas domains), cokriging performs generally better than other kriging procedures when estimating both (log T)∗ and T∗. Among procedures using the direct approach, the best prediction performances are obtained using kriging of log K with an external drift. Overall, geostatistical estimation of the hydraulic conductivity field at regional scales is rendered difficult by both preferential well location and preferential emplacement of well screens in the most productive portions of the aquifer. Such bias creates unrealistic hydraulic conductivity values, in particular, in sparsely sampled areas.

Key Words

kriging cross-validation lognormal kriging transmissivity specific capacity 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aboufirassi, M., and Marino, M. A., 1984, Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity: Math. Geol., v. 16, no. 1, p. 19–35.CrossRefGoogle Scholar
  2. Ahmed, S., and de Marsily, G., 1987, Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity: Water Resour. Res., v. 23, no. 9, p. 1717–1737.Google Scholar
  3. Anderson, M. P., 1997, Characterization of geological heterogeneity, in Dagan, G., and Neuman, S. P., eds., Subsurface flow and transport; a stochastic approach, International Hydrology Series: Cambridge University Press, Cambridge, U.K., v. 5, p. 23–43.Google Scholar
  4. Armstrong, M., 1994, Is research in mining geostats as dead as a dodo? in Dimitrakopoulos, R., ed., Geostatistics for the next century, Quantitative Geology and Geostatistics: Kluwer Academic, Dordrecht, The Netherlands, v. 6, p. 303–312.Google Scholar
  5. Bleines, C., Deraisme, J., Geffroy, F., Jeannée, N., Perseval, S., Rambert, F., Renard, D., and Touffait, Y., 2002, ISATIS Software Manual, 4th ed.: Géovariances, Fontainebleau, France, 645 p.Google Scholar
  6. Bredehoeft, J. D., and Papadopulos, S. S., 1980, A method for determining the hydraulic properties of tight formations: Water Resour. Res., v. 16, no. 1, p. 233–238.Google Scholar
  7. Castro, M. C., and Goblet, P., 2003, Calibration of regional groundwater flow models: Working toward a better understanding of site-specific systems: Water Resour. Res., v. 39, no. 6, art. 1172, doi: 10.1029/2002WR001653.Google Scholar
  8. Castro, M. C., Goblet, P., Ledoux, E., Violette, S., and de Marsily, G., 1998b, Noble gases as natural tracers of water circulation in the Paris Basin 2. Calibration of a groundwater flow model using noble gas isotope data: Water Resour. Res., v. 34, no. 10, p. 2467–2483.CrossRefGoogle Scholar
  9. Castro, M. C., Jambon, A., de Marsily, G., and Schlosser, P., 1998a, Noble gases as natural tracers of water circulation in the Paris Basin 1. Measurements and discussion of their origin and mechanisms of vertical transport in the basin: Water Resour. Res., v. 34, no. 10, p. 2443–2466.CrossRefGoogle Scholar
  10. Chiles, J.-P., and Delfiner, P., 1999, Geostatistics. Modeling spatial uncertainty: Wiley, New York, 695 p.Google Scholar
  11. Christensen, S., 1997, On the strategy of estimating regional-scale transmissivity fields: Ground Water, v. 35, no. 1, p. 131–139.CrossRefGoogle Scholar
  12. Davis, J. C., 2002, Statistics and data analysis in geology, 3rd ed.: Wiley, New York, 638 p.Google Scholar
  13. Delhomme, J. P., 1974, La cartographie d'une grandeur physique à partir de données de différentes qualités (A cartographic method for assessing data with different reliabilities): Mémoires: Association Internationale des Hydrogéologues (Memoires: International Association of Hydrogeologists), v. 10, no. 1, p. 185–194.Google Scholar
  14. Delhomme, J. P., 1979, Spatial variability and uncertainty in groundwater flow parameters; a geostatistical approach: Water Resour. Res., v. 15, no. 2, p. 269–280.Google Scholar
  15. de Marsily, G., 1986, Quantitative hydrogeology: Academic Press, San Diego, 440 p.Google Scholar
  16. Fabbri, P., 1997, Transmissivity in the geothermal Euganean Basin; a geostatistical analysis: Ground Water, v. 35, no. 5, p. 881–887.CrossRefGoogle Scholar
  17. Goovaerts, P., 1997, Geostatistics for natural resources evaluation: Oxford University Press, New York, 483 p.Google Scholar
  18. Goovaerts, P., 1998, Ordinary cokriging revisited: Math. Geol., v. 30, no. 1, p. 21–42.CrossRefGoogle Scholar
  19. Goovaerts, P., 2000, Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall: J. Hydrol., v. 228, no. 1–2, p. 113–129.Google Scholar
  20. Hamlin, H. S., 1988, Depositional and ground-water flow systems of the Carrizo–Upper Wilcox, South Texas, Report of Investigations 175: Bureau of Economic Geology, Austin, 61 p.Google Scholar
  21. Hughson, L., Huntley, D., and Razack, M., 1996, Cokriging limited transmissivity data using widely sampled specific capacity from pump tests in an alluvial aquifer: Ground Water, v. 34, no. 1, p. 12–18.CrossRefGoogle Scholar
  22. Huntley, D., Nommensen, R., and Steffey, D., 1992, The use of specific capacity to assess transmissivity in fractured-rock aquifers: Ground Water, v. 30, no. 3, p. 396–402.CrossRefGoogle Scholar
  23. Isaaks, E. H., and Srivastava, R. M., 1989, An introduction to applied geostatistics: Oxford University Press, New York, 561 p.Google Scholar
  24. Journel, A. G., 1980, The lognormal approach to predicting local distributions of selective mining unit grades: Math. Geol., v. 12, p. 285–303.CrossRefGoogle Scholar
  25. Journel, A. G., 1993, Geostatistics; roadblocks and challenges, in Soares, A., ed., Geostatistics Tróia '92, Quantitative Geology and Geostatistics: Kluwer Academic, Dordrecht, The Netherlands, v. 5, p. 213–224.Google Scholar
  26. Journel, A. G., and Huijbregts, C. J., 1978, Mining geostatistics: Academic Press, London, 600 p.Google Scholar
  27. Koltermann, C. E., and Gorelick, S. M., 1996, Heterogeneity in sedimentary deposits; a review of structure-imitating, process-imitating, and descriptive approaches: Water Resour. Res., v. 32, no. 9, p. 2617–2658.CrossRefGoogle Scholar
  28. Lavenue, M., and de Marsily, G., 2001, Three-dimensional interference test interpretation in a fractured aquifer using the pilot point inverse method: Water Resour. Res., v. 37, no. 11, p. 2659–2675.CrossRefGoogle Scholar
  29. Mace, R. E., 1997, Determination of transmissivity from specific capacity tests in a karst aquifer: Ground Water, v. 35, no. 5, p. 738–742.CrossRefGoogle Scholar
  30. Mace, R. E., and Smyth, R. C., 2003, Hydraulic properties of the Carrizo–Wilcox aquifer in Texas: Information for groundwater modeling, planning, and management, Report of Investigations 269: University of Texas at Austin, Bureau of Economic Geology, New Orleans, 40 p.Google Scholar
  31. Neuman, S. P., 1982, Statistical characterization of aquifer heterogeneities; an overview, in Narasimhan, T. N., ed., Geol. Soc. Amer. Spectral Paper 189, p. 81–102.Google Scholar
  32. Neuzil, C. E., 1994, How permeable are clays and shales?: Water Resour. Res., v. 30, no. 2, p. 145– 150.Google Scholar
  33. Patriarche, D., Castro, M. C., and Goblet, P., 2004, Large-scale hydraulic conductivities inferred from three-dimensional groundwater flow and 4He transport modeling in the Carrizo aquifer, Texas: J. Geophys. Res., v. 109, no. B11, art. B11202, doi: 10.1029/2004JB003173.Google Scholar
  34. Payne, J. N., 1972, Geohydrologic significance of Lithofacies of the Carrizo Sand of Arkansas, Louisiana, and Texas and the Meridian Sand of Mississippi, U. S. Geological Survey, Professional Paper 569-D: Washington, DC, 15 p.Google Scholar
  35. Razack, M., and Huntley, D., 1991, Assessing transmissivity from specific capacity in a large and heterogeneous alluvial aquifer: Ground Water, v. 29, no. 6, p. 856–861.CrossRefGoogle Scholar
  36. Saito, H., and Goovaerts, P., 2000, Geostatistical interpolation of positively skewed and censored data in Dioxin-contaminated site: Environ. Sci. Technol., v. 34, no. 19, p. 4228–4235.CrossRefGoogle Scholar
  37. Wierenga, P. J., Hills, R. G., and Hudson, D. B., 1991, The Las-Cruces Trench site— Characterization, experimental results, and one-dimensional flow predictions: Water Resour. Res., v. 27, no. 10, p. 2695–2705.CrossRefGoogle Scholar
  38. Wladis, D., and Gustafson, G., 1999, Regional characterization of hydraulic properties of rock using air-lift data: Hydrogeol. J., v. 7, no. 2, p. 168–179.CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geology 2005

Authors and Affiliations

  • Delphine Patriarche
    • 1
  • Maria Clara Castro
    • 1
  • Pierre Goovaerts
    • 2
  1. 1.Department of Geological SciencesUniversity of MichiganAnn Arbor
  2. 2.BioMedwareAnn Arbor

Personalised recommendations