Approximated expression of the hygroscopic growth factor for polydispersed aerosols

Hygroscopic growth of aerosols plays an important role in the characterization of atmospheric aerosols. Physico-chemical and optical properties of aerosols are dependent on relative humidity (RH) as well as on their size and composition. In this study, scattering enhancement factors, f(RH), for polydispersed aerosols were approximated. f(RH) of ammonium sulfate and ammonium nitrate (AS) and NaCl aerosols (ss) were considered under the assumption of externally mixed aerosols. f(RH) was calculated using the Mie theory for polydispersed aerosols at a given RH and corresponding water uptake (denoted as fMie(RH)). f(RH) was approximated as a quadratic function of RH (denoted as fapp(RH)). The obtained approximated f(RH) or fapp(RH)) values were compared with the values based on the Mie theory and showed a reasonable agreement between them. To the best of our knowledge, this is the first study that parametrizes the size dependency of f(RH) for log normally distributed aerosols. •Hygroscopic scattering enhancement factor f(RH) for polydispersed aerosols are approximated.•f(RH) for polydispersed aerosols was approximated as a simple formula of quadratic function of RH.•The obtained results were compared with the original results that showed good agreement.•The obtained formula estimates f(RH) and related optical properties, such as aerosol extinction coefficient with confidence.