Multivariate Geostatistical Model for Groundwater Constituents in Texas


Although many studies have explored the quality of Texas groundwater, very few have investigated the concurrent distributions of more than one pollutant, which provides insight on the temporal and spatial behavior of constituents within and between aquifers. The purpose of this research is to study the multivariate spatial patterns of seven health-related Texas groundwater constituents, which are calcium (Ca), chloride (Cl), nitrate (NO3), sodium (Na), magnesium (Mg), sulfate (SO4), and potassium (K). Data is extracted from Texas Water Development Board’s database including nine years: 2000 through 2008. A multivariate geostatistical model was developed to examine the interactions between the constituents. The model had seven dependent variables—one for each of the constituents, and five independent variables: altitude, latitude, longitude, major aquifer and water level. Exploratory analyses show that the data has no temporal patterns, but hold spatial patterns as well as intrinsic correlation. The intrinsic correlation allowed for the use of a Kronecker form for the covariance matrix. The model was validated with a split-sample. Estimates of iteratively re-weighted generalized least squares converged after four iterations. Matern covariance function estimates are zero nugget, practical range is 44 miles, 0.8340 variance and kappa was fixed at 2. To show that our assumptions are reasonable and the choice of the model is appropriate, we perform residual validation and universal kriging. Moreover, prediction maps for the seven constituents are estimated from new locations data. The results point to an alarmingly increasing levels of these constituents’ concentrations, which calls for more intensive monitoring and groundwater management.

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Anderson, F. (2014) Multivariate Geostatistical Model for Groundwater Constituents in Texas. International Journal of Geosciences, 5, 1609-1617. doi: 10.4236/ijg.2014.513132.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Texas Water Development Board (TWDB) (2007) Water for Texas 2007. Volume II, p. 161.
[2] Sansom, A., Armitano, E.R. and Wassenich, T. (2008) Water in Texas: An Introduction. UT Press.
[3] Westlake, K. (1995) Landfill Waste Pollution and Control. Horwood Publishing.
[4] Szekely, G.J. and Rizzo, M.L. (2013) Energy Statistics: A Class of Statistics Based on Distances. Journal of Statistical Planning and Inference, 143, 1249-1272.
[5] Piegorsch, W.W. and El-Sharaawi, A.H. (2002) Encyclopaedia of Environmentrics. John Wiley and Sons, Hoboken, 1368.
[6] Wackernagel, H. (2003) Multivariate Geostatistics: An Introduction with Applications. 3rd Edition, Springer.
[7] Waller, L.A. and Gotway, C.A. (2004) Applied Spatial Statistics for Public Health Data. Wiley-IEEE.
[8] Schabenberger, O. and Gotway, C.A. (2005) Statistical Methods for Spatial Data Analysis. Chapman & Hall/CRC Press.
[9] United States Environmental Protection Agency (EPA) (2014) Drinking Water Contaminants.
[10] Chaudhuri, S. and Ale, S. (2014) Long Term (1960-2010) Trends in Groundwater Contamination and Salinization in the Ogallala Aquifer in Texas. Journal of Hydrology, 513, 376-390.

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