A successive-order-scattering solution of the hemispherical harmonic decomposed radiative transfer equations

Abstract

In this work, we applies the successive-order-scattering (SOS) method to the generally decomposed radiative transfer equations (GD-RTEs). The basic equations is presented and a numerical model is developed specifically to solve the hemispherical harmonic components of radiance. The numerical results are checked against those of the hemispherical harmonics method to validate the model and to investigate the factors influencing the accuracies of the new algorithm, including the optical depth of the sublayers and the criterion for convergence. We find that the trend to more isotropic of the scattered radiance and the additivity of the hemispherical harmonic components of radiance lead to a more efficient criterion of convergence, which allows the order of the decomposed equations reduced with the increasing order of scattering, while limiting the error caused by the reduction below the prescribed level. With the new criterion, the computation time can be saved by typically from a half of to an order of magnitude less than that with the conventional criterion, in presence of multiple scattering.