Analytic expression for the aerosol mass efficiencies for polydispersed accumulation mode

Aerosol mass efficiencies for extinction, scattering, and absorption are important parameters to understand aerosol optical properties. Although the mass efficiency is functions of the refractive index and particle size distribution, due to the complexity of the efficiency, mass efficiency parameters are usually regarded as a size independent and assumed to depend mainly on the chemical composition of aerosols. In this study, we calculated the mass efficiencies of polydispersed aerosols based on different aerosol types. An analytical approach to the approximated formula of the mass efficiency of each chemical species was developed and evaluated by fitting the results to those of the Mie theory that calculated the optical properties of chemical species based on the refractive index and size. We used the lognormal size distributions and external mixture approximations that represent the polydispersity of aerosol particles. Size ranges of 0.5–2.5 µm in the geometric mean diameter were considered for five different chemical species. The parameters of fitting curves were generalized for polydispersed aerosols as functions of the geometric mean diameter and the geometric standard deviation. The results of the newly developed analytic approach showed a good agreement with those of the Mie theory. The proposed approach provides an effective means to estimate the mass extinction efficiency of polydispersed multi-component aerosols.