Numerical investigation on retrieval errors of mixing states of fractal black carbon aerosols using single-particle soot photometer based on Mie scattering and the effects on radiative forcing estimation

The mixing state of black carbon (BC) aerosols, which is the diameter ratio of coated particle to BC core (Dp/Dc), can be retrieved by the single-particle soot photometer (SP2). However, the retrieved Dp/Dc contains errors, because the core-shell model and Mie scattering calculation are normally employed in the retrieval principle of SP2 and the spherical core-shell structure seriously deviated from the real morphology of coated BC. In this study, fractal models are constructed to represent thinly and thickly coated BC particles for optical simulations, the differential scattering cross-sections are selected as references to conduct optical retrieval of particle diameter (Dp) based on Mie theory, just like the retrieval principle of SP2, and the volume equivalent diameter of BC core (Dc) is the same for fractal and spherical models. Then, the retrieval errors of the mixing state (Dp/Dc) of BC are investigated from numerical aspects, and the estimation accuracy of BC radiative forcing is analyzed through the simple forcing efficiency (SFE) equation with SP2 retrieval results taken into consideration. Results show that SP2 retrieved Dp/Dc based on Mie theory underestimates the realistic Dp/Dc of coated BC at most particle sizes. The retrieval errors of Dp/Dc of thinly coated BC for both single particles and particle groups are larger than those of thickly coated BC. In addition, evaluation errors of radiative forcing of coated BC caused by retrieval errors of SP2 are up to about 55 % and 95 % at 1064 and 532 nm, respectively. This study provides meaningful referential understandings of the retrieved Dp/Dc of SP2 based on Mie scattering.