Water Qual Expo Health DOI 10.1007/s12403-014-0154-2 ORIGINAL PAPER Spatial Interpolation of Sulfate Concentration in Groundwater Including Covariates Using Bayesian Hierarchical Models Ijaz Hussain · Naima Mubarak · Javid Shabbir · Tajammal Hussain · Muhammad Faisal Received: 18 August 2014 / Revised: 25 November 2014 / Accepted: 26 November 2014 © Springer Science+Business Media Dordrecht 2014 Abstract Sulfate is a key parameter for water quality and is commonly used in manufacturing of fertilizers, soaps, glass, papers, and common household items. If sulfate quantity is more than a threshold, it is hazardous for health. In the present paper, we use Bayesian kriging with external drift and Gaussian spatial predictive process model to analyze the spa- tial behavior of response variable (Sulfate). Different infor- mative and non-informative priors are utilized to estimate the correlation parameters. The performance of these mod- els are compared by means of twofold cross validation with deviance information criterion, and root mean square pre- diction as criterion. In summary, the inclusion of covariates plays an important role in minimizing the mean square pre- diction error. Bayesian kriging with external drift performs better than Gaussian spatial predictive process. The predic- tive distribution of Bayesian kriging with external drift is also applicable for interpolation of sulfate concentration at unobserved locations. Keywords Bayesian kriging with external drift · Cross val- idation · Gaussian spatial predictive process · Groundwater · Punjab · Sulfate I. Hussain (B ) · N. Mubarak · J. Shabbir Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan e-mail: ijaz@qau.edu.pk M. Faisal National Center for Bio-informatics, Quaid-i-Azam University, Islamabad, Pakistan T. Hussain Department of Statistics, COMSATS Institute of Information Technology, Lahore, Pakistan Introduction Nowadays, deterioration in water quality is a major issue and increasing rapidly. It is important to analyze a source of this problem and its causes using different chemical and physical properties of water. Geostatistical tools are used to analyze the spatial distribution of the water quality parameters such as, nitrate, sulfate, sodium, turbidity, etc. Sulfate naturally occurs in water, but it can also occur in soil, rocks, miner- als, food, and plants. Its high concentration in water causes catharsis, dehydration, diarrhea, and gastrointestinal irrita- tion. It is a combination of sulfur and oxygen which are the part of minerals that naturally occur in soil and rocks. When water moves through soil and rock formations, some sul- fates get dissolved into water. High concentration of sulfate present in water is harmful for humans and animals. Ata- soy and Yesilnacar (2010) investigate destructive effects of ground water. The maximum contaminant level of sulfates set by World Health Organization (WHO 2006) and Envi- ronmental Protection Agency (Awwa et al. 1998) are 250 and 500 mg/l respectively, Adhikary et al. (2010). If sulfate concentration exceeds 250 mg/l, then it gives a bitter and medicinal taste to water, which may make water unpleas- ant to drink. High concentration of sulfate in water causes diseases like dehydration and diarrhea in humans. Animals are also sensitive to high levels of sulfate. High sulfate con- centration also destroys plumbing, particularly copper pip- ing. The spatial behavior of groundwater properties can be modeled and nowadays, it is a burning issue for scientists (Atasoy and Yesilnacar 2010; Adhikary et al. 2010; Nas and Berktay 2010). Geostatistical models could capture the spa- tial behavior of groundwater quality parameters efficiently. In geostatistics, the spatial variation of data is quantified by var- iogram modeling, and it plays vital role in the precise spatial 123