The accumulation mode with a lognormal size distribution was considered with different refractive indices. The obtained analytic expression was compared with the different size distributions for geometric mean diameters of 0.05–1 mm with geometric standard deviations of 1.3–1.9 using Mie theory.
Subsequently, this study showed that the analytical expression of the scattering enhancement factor can express polydispersed aerosol optical properties as a function of size distribution along with the refractive index, and the results showed that the relationship between hygroscopic parameter-scattering enhancement factors depends on the size distribution. The obtained analytical expression can be efficiently used for 3D models with reduced computational burden.

