Probabilistic assessment of spatial heterogeneity of natural background concentrations in large-scale groundwater bodies through Functional Geostatistics

We propose and exemplify a framework to assess Natural Background Levels (NBLs) of target chemical species in large-scale groundwater bodies based on the context of Object Oriented Spatial Statistics. The approach enables one to fully exploit the richness of the information content embedded in the probability density function (PDF) of the variables of interest, as estimated from historical records of chemical observations. As such, the population of the entire distribution functions of NBL concentrations monitored across a network of monitoring boreholes across a given aquifer is considered as the object of the spatial analysis. Our approach starkly differs from previous studies which are mainly focused on the estimation of NBLs on the basis of the median or selected quantiles of chemical concentrations, thus resulting in information loss and limitations related to the need to invoke parametric assumptions to obtain further summary statistics in addition to those considered for the spatial analysis. Our work enables one to (i) assess spatial dependencies among observed PDFs of natural background concentrations, (ii) provide spatially distributed kriging predictions of NBLs, as well as (iii) yield a robust quantification of the ensuing uncertainty and probability of exceeding given threshold concentration values via stochastic simulation. We illustrate the approach by considering the (probabilistic) characterization of spatially variable NBLs of ammonium and arsenic detected at a monitoring network across a large scale confined groundwater body in Northern Italy.