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

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Abstract
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. Graphical Abstract

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