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

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 (σChar) and BC (σBC), 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 σBC, which varied with instrument conditions, revealed a ridge indicating the correct conditions for OC pyrolysis in helium. The intersection of the σBC and σChar 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.