Geostatistical Modeling of Uncertainty Attached to the Spatial Distribution of Arsenic in Groundwater of Southeast Michigan

Assessment of the health risks associated with exposure to elevated levels of arsenic in drinking water has become the subject of considerable interest and some controversy in both regulatory and public health communities. The objective of this research is to explore the factors that have contributed to the observed geographic co-clustering in bladder cancer mortality and arsenic concentrations in drinking water in Michigan. A corner stone is the building of a probabilistic space-time model of arsenic concentrations, accounting for information collected at private residential wells and the hydrogeochemistry of the area. Because of the small changes in concentration observed in time, the study has focused on the spatial variability of arsenic, which can be considerable over very short distances. Various geostatistical techniques, based either on lognormal or indicator transforms of the data to accommodate the highly skewed distribution, have been compared using a cross validation procedure. The most promising approach involves a soft indicator coding of arsenic measurements, which allows one to account for data below the detection limit and the magnitude of measurement errors. Prior probabilities of exceeding various arsenic thresholds are also derived from secondary information, such as type of bedrock and surficial material, well casing depth, using logistic regression. Both well and secondary data are combined using kriging, leading to a non-parametric assessment of the uncertainty attached to arsenic concentration at each node of a 500m grid. This geostatistical model can be used to map either the expected arsenic concentration, the probability that it exceeds any giventhreshold, or the variance of the prediction indicating where supplementary information should be collected. The accuracy and precision of these local probability distributions is assessed using cross validation.