Spatial Inference of Nitrate Concentrations in Groundwater
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We develop a method for multiscale estimation of pollutant concentrations, based on a nonparametric spatial statistical model. We apply this method to estimate nitrate concentrations in groundwater over the mid-Atlantic states, using measurements gathered during a period of 10 years. A map of the fine-scale estimated nitrate concentration is obtained, as well as maps of the estimated county-level average nitrate concentration and similar maps at the level of watersheds and other geographic regions. The fine-scale and coarse-scale estimates arise naturally from a single model, without refitting or ad hoc aggregation. As a result, the uncertainty associated with each estimate is available, without approximations relying on high spatial density of measurements or parametric distributional assumptions.
Several risk measures are also obtained, including the probability of the pollutant concentration exceeding a particular threshold. These risk measures can be obtained at the fine scale, or at the level of counties or other regions.
The nonparametric Bayesian statistical model allows for this flexibility in estimation while avoiding strong assumptions. This method can be applied directly to estimate ozone concentrations in air, pesticide concentrations in groundwater, or any other quantity that varies over a geographic region, based on approximate measurements at some locations and perhaps of associated covariates. An S-PLUS package with this capability is provided as supplemental material.
Key WordsBayesian Geostatistics Kriging Lévy processes Nonparametrics Response surface Spatial moving average
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