Diffraction Decomposition Order Method for Solving the Vector Radiative Transfer Equation in the Multi-Layer Atmosphere

The scattering phase function of atmospheric particle usually has a strong forward peak due to the diffraction effect so that the scattering energy spans large order differences of magnitude in all scattering directions. Correspondingly, the accurate computation of multiple scattering processes in the radiative transfer is high resolution required and time-consuming. A decomposition method is described in this study for the separation of radiative transfer into a rapidly-varying process (RVP) and a slowly-varying process (SVP). The proposed diffraction decomposition order (DDO) method is developed by considering the difference between a delta function and the RVP in a series order of radiative transfer equations, and is generalized to solve the radiative transfer equation in a multi-layer atmosphere. The zeroth-order equation has the forward phase function reduced to the delta function, and the high-order equations successively consider the contribution of the RVP. In this study, the DDO radiative transfer calculation is realized by successive order of scattering approximation and is derived for the multi-layer polarized scenario. By considering the convergences in the orders of both scattering and decomposition, the radiative results are obtained efficiently and accurately as the sum over all order. Finally, numerical simulations are verified using the successive order of scattering method and their accuracy variation associated with orders is discussed.