Geostatistical modeling of the spatial variability of arsenic in groundwater of southeast Michigan

During the last decade one has witnessed an increasing interest in assessing healthrisks caused by exposure to contaminants present in the soil, air, and water. A keycomponent of any exposure study is a reliable model for the space-time distribution ofpollutants. This paper compares the performances of multi-Gaussian and indicator krigingfor modeling probabilistically the spatial distribution of arsenic concentrations ingroundwater of southeast Michigan, accounting for arsenic data collected at privateresidential wells and the hydrogeochemistry of the area. The arsenic data set, which wasprovided by the Michigan Department of Environmental Quality (MDEQ), includesmeasurements collected between 1993 and 2002 at 8212 different wells. Factorial krigingwas used to filter the short-range spatial variability in arsenic concentration, leading to asignificant increase (17–65%) in the proportion of variance explained by secondaryinformation, such as type of unconsolidated deposits and proximity to Marshall Sandstonesubcrop. Cross validation of well data shows that accounting for this regional backgrounddoes not improve the local prediction of arsenic, which reveals the presence ofunexplained sources of variability and the importance of modeling the uncertaintyattached to these predictions. Slightly more precise models of uncertainty were obtainedusing indicator kriging. Well data collected in 2004 were compared to the predictionmodelandbestresultswerefoundforsoftindicatorkrigingwhichhasameanabsoluteerrorof 5.6 mg/L. Although this error is large with respect to the USEPA standard of 10 mg/L,it is smaller than the average difference (12.53 mg/L) between data collected at the samewell and day, as reported in the MDEQ data set. Thus the uncertainty attached to thesampled values themselves, which arises from laboratory errors and lack of informationregarding the sample origin, contributes to the poor accuracy of the geostatisticalpredictions in southeast Michigan.