GAMA Data

Figure 1: This figure shows a map of the 8018 GAMA Program wells in California.

Industry Sites

Figure 2: This figure shows a map of the 20077 industry facilities that are the potential PFAS sources.

River Connectivity

Figure 3: Map of HUC polygons and well locations.

Source Apportionment Model

• Y_i is observed concentration of a type of PFAS at well \boldsymbol s_i
• The model relating the sources to the concentrations is

Y_i = \left(C_0(\boldsymbol s_i) + \sum_{k=1}^K C_k(\boldsymbol s_i) \right) \exp\left\{\varepsilon_i - \frac{\sigma^2}{2} \right\}

• C_0 is the baseline amount of PFAS (i.e. not from these industry sites)
• C_k is the contribution of industry sites from industry k.
• Note that \varepsilon_i \overset{iid}{\sim} N(0, \sigma^2) and E[\exp\{\varepsilon_i - \sigma^2/2\}] = 1

Source Contributions

We model the source contribution [3] from each industry sector k, summed across the m_k industry sites as

C_k(\boldsymbol s_i) = \sum_{j=1}^{m_k} f(\boldsymbol s_i, \boldsymbol t_{jk}) V_{jk} where our transfer function f is defined as

f(\boldsymbol s_i, \boldsymbol t_{jk}) = \exp \left\{- \left(\frac{d(\boldsymbol s_i,\boldsymbol t_{jk})}{\phi} \right)^2\right\}

Extended Generalized Pareto Distribution

Figure 4: This figure shows how the EGPD changes with differing \kappa values.

Bayesian Hierarchical Model

• We use a spike-and-slab setup [5] to help reflect the prior belief that many sources emit little PFAS, i.e., below the detection limit.
• The “slab” distribution (b = 1) models the V_{jk} values that we expect to be above the detection limit. EGPD(\kappa, \xi, \tau_k)
  • The shape parameters being the same across industries while scale parameter varies by industry.
• The “spike” distribution (b = 0) models the V_{jk} values that are close to the detection limit. EGPD(1, 0, \tau_{DL})
  • \tau_{DL} is set so that the 95th percentile is the detection limit.

Posterior Means of V_{jk}’s

Figure 5: These maps show the log-posterior means of the industry site contributions.

Proportion of PFOS Contributed

Figure 6: This forest plot shows the posterior mean and corresponding 95% credible intervals for the proportion of PFOS contributed by that industry.

PFOS Contributed by Ecoregion

Figure 7: This plot looks at the proportion of PFOS contributed across 8 different ecoregions.

Conclusion

• Our method is able to attribute PFAS to potential industry sources via source apportionment modeling.
• This is accomplished through our Bayesian hierarchical model which incorporates the EGPD into a mixture model prior.
• We see that chemical plants and waste management sites are the primary sources, although it varies across different regions.

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