Multiple-scaling method for anisotropic scattering and its applications to radiance calculations

Radiative transfer (RT) equation for anisotropic light scattering due to large particles is often solved using so-called truncation approximation, which accelerates computation by approximating the phase function by a finite series truncated at a limited number of terms or by a geometrically-truncated function. The approximation produces bias in computed radiance. This study devoted to reduce the bias. It is shown that different truncation approximations can be used for each order of scattering and that accurate radiance can be obtained by using exact phase function for the first- order scattering and truncated, approximated function for multiple scattering. If the degree of approximation is small for the first three or four scattering events, highly accurate radiance can be calculated even if higher-order scattering is treated with scaled properties with a smooth phase function. The multiple-scaling method has been implemented in a new linearized radiative transfer model, which has been developed for the purposes of remote sensing of the atmosphere. The model is especially efficient for quickly calculating a hyper-spectrum and Jacobian matrices.