Study On Spherical Harmonics Discrete Ordinate Method For Radiative Transfer

Radiative process is one of the most important processes in the atmospheric physics. These years, the development of the computer provides a possibility to improve the numerical calculation of the atmospheric radiative process. The Spherical Harmonics Method is first used in the interstellar radiative field in the early 20th century, then it's widly used in the neutron transfer field. But the combination between the Spherical Harmonics and other numerical method is developed these couple of years. The Spherical Harmonics Discrete Ordinate Method is provided by Evens in order to deal with the three-dimensional atmospheric radiative transfer. The SHDOM combines the benefit of the Spherical Method and the Discrete Ordinate Method. Comparing with the original Spherical Harmonics Method, it has the advantage of clear in the signification, simple in the math model, and its calculation is more effective and accurate.This article has a study on the fundamental of the Spherical Harmonics Discrete Ordinate Method. Comparing the results between the SHDOM programs and the BMC programs in several situations fallowed: (1) Isotropic scattering, fixed wavelength and extinction, varying albedo; (2) Isotropic scattering, fixed wavelength and albedo, varying extinction; (3) Anisotropic scattering, fixed wavelength and extinction, varying albedo, and fixed wavelength and albedo, varying extinction. Using the typical Gamma distribution parameters of the stratus to get its scattering properties, and then the result is used in the SHDOM programs, to calculate the two-dimensional atmospheric radiative transfer model.According to the 1D results, the relative error is increasing with the increase of the albedo or the extinction. Using the typical parameters of the Gamma distribution, there is a peak value on the curve of the albedo and extinction varing with the effiective radius, which is appear near the effective value 3. In the 2D atmospheric radiative transfer model, the outgoing radiance on the top plane has some peak value, which have two kind of reasons:one is caused by the direct radiation of the bottom plane; the other is caused by the strong scattering to the radiation come from the top plane.