Object oriented spatial analysis of natural concentration levels of chemical species in regional-scale aquifers

We address the problem of characterizing spatially variable Natural Background Levels (NBLs) of concentrations of chemical species of environmental concern in a large-scale groundwater body. Assessment of NBLs is critical to identify significant trends of (possibly hazardous) chemical concentrations in aquifer systems, the latter being typically associated with spatially heterogeneous hydrogeochemical characteristics. Our study considers the entire probability density function (PDF) of the concentration of the chemical species of interest as atom of the statistical analysis. These PDFs are estimated across a network of observation boreholes in the investigated spatial domain, and modeled as random points in a Bayes Hilbert space, in the context of Object Oriented Data Analysis. This approach enables one to take advantage of the entire information content provided by these objects for the purpose of spatial prediction and uncertainty quantification. As a key element of innovation, we investigate the use of depth measures for distributional data with the distinctive aims of (i) detecting central and outlying NBL distributions in the dataset, and (ii) building prediction regions for NBL distribution at unsampled locations. We illustrate the results of the proposed approach to the analysis of NBLs of a selected chemical species detected at an environmental monitoring network within a large-scale alluvial aquifer in Northern Italy.