A semi-analytic method to speed up the convergence of successive order of scattering model

While the successive order of scattering (SOS) method is used to solve the radiative transfer equation, however, for the large optical depth with a high single scattering albeldo, the slow convergence will spend a lot of computing time. To speed up the convergence of SOS method, an improved semi-analytic model is developed and the two notes fitting method is used to get the ratio of two successive scattering radiances after the thirteenth scattering. The new semi-analytic model is accurate and efficient and makes the SOS method applicable for optically thick scattering media. With the improved semi-analytic model, the efficiency of the SOS method can be greatly improved.