Factorial-based response-surface modeling with confidence intervals for optimizing thermal-optical transmission analysis of atmospheric black carbon

Thermal-optical transmission (TOT) analysis measures black carbon (BC) in atmospheric aerosol on a fibrous filter. The method pyrolyzes organic carbon (OC) and employs laser light absorption to distinguish BC from the pyrolyzed OC; however, the instrument does not necessarily separate the two physically. In addition, a comprehensive temperature protocol for the analysis based on the Beer-Lambert Law remains elusive. Here, empirical response-surface modeling was used to show how the temperature protocol in TOT analysis can be modified to distinguish pyrolyzed OC from BC based on the Beer-Lambert Law. We determined the apparent specific absorption cross sections for pyrolyzed OC (σ_Char) and BC (σ_BC), which accounted for individual absorption enhancement effects within the filter. Response-surface models of these cross sections were derived from a three-factor central-composite factorial experimental design: temperature and duration of the high-temperature step in the helium phase, and the heating increase in the helium-oxygen phase. The response surface for σ_BC, which varied with instrument conditions, revealed a ridge indicating the correct conditions for OC pyrolysis in helium. The intersection of the σ_BC and σ_Char surfaces indicated the conditions where the cross sections were equivalent, satisfying an important assumption upon which the method relies. 95% confidence interval surfaces defined a confidence region for a range of pyrolysis conditions. Analyses of wintertime samples from Seattle, WA revealed a temperature between 830 °C and 850 °C as most suitable for the helium high-temperature step lasting 150 s. However, a temperature as low as 750 °C could not be rejected statistically.