Comparisons and improvement of parameterization schemes for the scattering phase function of atmospheric particles

The parameterization of the scattering phase function of atmospheric particles is an important part of the radiative transfer parameterization. The accuracy of Henyey-Greenstein (HG) scheme and Double Henyey-Greenstein (DHG) scheme are examined systematically. These two schemes are applied in the four-stream spherical harmonic expansion adding method to calculate the reflection/transmission/absorption of aerosols, clouds and haze particles. Results show that the HG scheme cannot realistically describe the backscattering pattern of the phase function, thereby reducing the accuracy of the calculated reflection and transmission of atmospheric particles.The peak of forward scattering and backscattering can be well represented by the DHG scheme in some cases. However, the DHG scheme often leads to abnormal backscattering peak or negative values of the phase function, which is unrealistic. In this case, the accuracy of reflection and transmission calculated by the DHG scheme are lower than those by the HG scheme.For this reason, a modified DHG scheme (MDHG) is proposed in this study to improve the phase function parameterization.The modified scheme is stable, and the traits of forward scattering and backscattering are well characterized.In addition, errors of reflection and transmission calculated by the improved scheme are smaller. Results of the study indicate that the MDHG scheme is appropriate for parameterizing the phase function.