Application of Gaussian mixture models to quantify the upper background threshold for perfluorooctane sulfonate (PFOS) in U.S. surface soil.

Studies on the occurrence and environmental distribution of per- and polyfluoroalkyl substances (PFAS) have clearly demonstrated their ubiquity in surface soil as a result of historic and ongoing emissions from various manufacturing and industrial activities worldwide. Given global efforts to characterize and mitigate risk from point source-impacted sites, there is, thus, an urgent need to quantify nonpoint source threshold concentrations (i.e., background) to support site management decisions particularly for perfluorooctane sulfonate (PFOS) as a top priority. Accordingly, this study evaluated the application of Gaussian mixture models (GMMs) fitted to log-transformed PFOS concentrations using nation-wide metadata consisting of thousands of surface soil samples representative of both background and aqueous film-forming foam (AFFF) impacts with unknown proportion. Multiple GMMs were fitted for a given number of components using different methods to account for bias associated with a marginal non-detect fraction (n = 8%) including exclusion, substitution, and imputation. Careful evaluation of the rate of change among multiple goodness-of-fit measures universally justified fitting a 2-component GMM; thus, discriminating between background and AFFF-impacted samples among the metadata. Background threshold PFOS concentrations were defined as the intersection of the probability density functions and ranged between 1.9 and 13.8 µg/kg within a broader concentration range extending up to ~ 50,000 µg/kg reflecting AFFF impacts. By demonstrating an innovative statistical approach that intelligently incorporates different criteria for model selection, this research makes significant contributions to risk mitigation efforts at point source-impacted sites and lays the groundwork for future targeted regulatory actions.