Estimation of fugitive lead emission rates from secondary lead facilities using hierarchical Bayesian models

Fugitive emissions from secondary lead recovery facilities are difficult to estimate and can vary significantly from site to site. A methodology is presented for estimating fugitive emissions using back inference from observed ambient concentrations at nearby monitors, in conjunction with an atmospheric transport and dispersion model. Observed concentrations are regressed against unit source-monitor transfer terms computed by the model, and the fitted parameters of the regression equation include the background ambient lead concentration, the fugitive lead emission rate, and (when stack emissions are assumed to be unknown) the stack lead emission rate. The methodology is implemented at three sites, one each in Florida, Texas, and New York. A hierarchical Bayesian method is used to estimate the parameters of the model, allowing inferences to be made for both site-specific values and multisite (national) distributions of fugitive emissions and background concentrations. Informed prior distributions must be specified for the background lead concentrations and for fugitive and stack emission rates in order to obtain stable estimates. Sensitivity analyses with alternative priors indicate that posterior estimates of background concentrations and fugitive emission rates are relatively insensitive to the assumed priors, although estimated stack emission rates can vary with alternative priors, especially for the New York facility, where the stack emission rate is highly uncertain and poorly resolved by the model. The fugitive lead emission rates estimated for the sites are comparable to, or in some cases (especially Texas and New York) likely larger than the stack emissions that are determined for these facilities. An aggregate predictive distribution is derived for the average fugitive lead emission rate from secondary lead smelting facilities, with a median value of 9.2 x 10(-7) g Pb/m2/sec, and a 90% credible interval from 2.1 x 10(-7)-5.3 x 10(-6) g Pb/m2/sec. This wide range reflects both the variation in fugitive lead emissions from site to site and the high degree of uncertainty resulting from an estimate based on only a very small sample of sites. As such, the primary contribution of this study is methodological, demonstrating how information from multiple sites can be combined and considered simultaneously for the estimation of fugitive emission rates, but recognizing that additional sites must be included to obtain a more precise characterization.