A study on the convergence property of successive orders of scattering method

The successive orders of scattering method is a useful means to solve the radiative transfer in the atmosphere. For the optically thick scattering media, a semi-empirical model can be used to speed up the convergence. In this paper, the key features of successive orders of scattering method are discussed, as well as the convergence properties of this method are studied. With the two-stream and four-stream approximation, the corresponding parameters' influence on the convergence of the ratio of two successive scattering radiances I
n
/ I
n−1
are analyzed, some function relations about the case of conservative and nonconservative scattering are also obtained. Base on the convergence property and those function relations, the semi-empirical model can better applied to the successive orders of scattering method for the optically thick scattering media.