On the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres

Abstract

The difficulties inherent in the conventional numerical implementation of the discrete ordinate method (following Chandrasekhar’s prescription) for solving the radiative transfer equation are discussed. A matrix formulation is developed to overcome these difficulties, and it is specifically shown that the order of the algebraic eigenvalue problem can be reduced by a factor of 2. This results in considerable reduction of computing time, especially if high-order discrete ordinate solutions are desired. A new expression for the source function is derived and used to obtain angular distributions. By appealing to the reciprocity principle it is shown that substantial computational shortcuts are possible if only integrated quantities such as albedo and transmissivity are required. Comparison of fluxes calculated by the present approach with those obtained by other methods shows that low-order discrete ordinate approximations yield very accurate results. Thus, the present approach offers an efficient and reliable computational scheme that lends itself readily to the solution of a variety of radiative transfer problems in realistic planetary atmospheres.