Parameterization of the Aerosol Upscatter Fraction as Function of the Backscatter Fraction and Their Relationships to the Asymmetry Parameter for Radiative Transfer Calculations Atmosphere

Simple analytical approximations for aerosol radiative forcing generally contain the aerosol upscatter fraction (the fraction of scattered light that is scattered into the upper hemisphere), while ambient measurements generally yield the backscatter fraction, and theoretical calculations of scattering phase functions often yield the asymmetry parameter. Therefore, simple analytical relationships and parameterizations relating these three parameters are very valuable for radiative transfer calculations. Here, we review published parameterizations, mostly based on the Henyey-Greenstein phase function, and evaluate their goodness and range of validity. In addition, we give new parameterizations that are valid over the full range of backscatter fractions that are possibly encountered in the ambient atmosphere (i.e., 0 to 0.5).