Analyzing the spatial distribution of PCB concentrations in soils using below-quantification limit data.

Polychlorinated biphenyls (PCBs) are highly toxic environmental pollutants that can accumulate in soils. We consider the problem of explaining and mapping the spatial distribution of PCBs using a spatial data set of 105 PCB-187 measurements from a region in the north of France. A large proportion of our data (35%) fell below a quantification limit (QL), meaning that their concentrations could not be determined to a sufficient degree of precision. Where a measurement fell below this QL, the inequality information was all that we were presented with. In this work, we demonstrate a full geostatistical analysis-bringing together the various components, including model selection, cross-validation, and mapping-using censored data to represent the uncertainty that results from below-QL observations. We implement a Monte Carlo maximum likelihood approach to estimate the geostatistical model parameters. To select the best set of explanatory variables for explaining and mapping the spatial distribution of PCB-187 concentrations, we apply the Akaike Information Criterion (AIC). The AIC provides a trade-off between the goodness-of-fit of a model and its complexity (i.e., the number of covariates). We then use the best set of explanatory variables to help interpolate the measurements via a Bayesian approach, and produce maps of the predictions. We calculate predictions of the probability of exceeding a concentration threshold, above which the land could be considered as contaminated. The work demonstrates some differences between approaches based on censored data and on imputed data (in which the below-QL data are replaced by a value of half of the QL). Cross-validation results demonstrate better predictions based on the censored data approach, and we should therefore have confidence in the information provided by predictions from this method.

Which persistent organic pollutants can we map in soil using a large spacing systematic soil monitoring design? A case study in Northern France.

Persistent organic pollutants (POPs) impact upon human and animal health and the wider environment. It is important to determine where POPs are found and the spatial pattern of POP variation. The concentrations of 90 molecules which are members of four families of POPs and two families of herbicides were measured within a region of Northern France as part of the French National Soil Monitoring Network (RMQS: Réseau de Mesures de la Qualité des Sols). We also gather information on five covariates (elevation, soil organic carbon content, road density, land cover and population density) which might influence POP concentrations. The study region contains 105 RMQS observation sites arranged on a regular square grid with spacing of 16 km. The observations include hot-spots at sites of POP application, smaller concentrations where POPs have been dispersed and observations less than the limit of quantification (LOQ) where the soil has not been impacted by POPs. Fifty nine of the molecules were detected at less than 50 sites and hence the data were unsuitable for spatial analyses. We represent the variation of the remaining 31 molecules by various linear mixed models which can include fixed effects (i.e. linear relationships between the molecule concentrations and covariates) and spatially correlated random effects. The best model for each molecule is selected by the Akaike Information Criterion. For nine of the molecules, spatial correlation is evident and hence they can potentially be mapped. For four of these molecules, the spatial correlation cannot be wholly explained by fixed effects. It appears that these molecules have been transported away from their application sites and are now dispersed across the study region with the largest concentrations found in a heavily populated depression. More complicated statistical models and sampling designs are required to explain the distribution of the less dispersed molecules.