Modeling of atmospheric radiative transfer with polarization effects using scattering phase matrix

Solar radiation will be scattered by atmospheric molecules and aerosol particles when it transfers through the Earth atmosphere. The scattered radiance with different polarization state can be used to characterize atmospheric components. Based on the BHU-ATM presented in our previous work, an atmospheric radiative transfer model considering the polarization effects is developed in this paper, in which the parameter discretization method is used. To this end, the radiative transfer equation is adapted into the Stokes vector form, while the impacts of atmospheric molecules and aerosols on the polarization state of the scattered radiance are represented by means of the scattering phase matrix. The Curtis-Godson approximation and the two-stream approximation are used to obtain the analytical solution of the adapted radiative transfer equation. As the precise calculation of the scattering phase matrix varying with the scattering angle and the radiant wavelength is inefficient for the calculation of spectral path radiance, a novel aspect of this work is the efficient computation of the scattering phase matrix through a two-dimensional interpolation method, significantly reducing computational complexity while maintaining accuracy across a broad range of angles and wavelengths. The simulation results of the atmospheric transmittance, the spectral radiance and the degree of polarization (DOP) for an arbitrarily selected transfer path are given. As it can be seen, in the spectrum from the visible through the near infrared (VNIR), the polarization modeling showed a maximum transmittance difference of 0.0007 and a spectral radiance difference of 0.3 W/m²/μm/sr. The DOP varied significantly, with a difference of up to 0.12 between urban and ocean aerosols. The developed polarization model can improve aerosol component identification in satellite-based remote sensing applications, aiding in more accurate air quality monitoring and enhancing climate models that account for aerosol scattering effects.