A finite difference method of solving anisotropic scattering problems.
Abstract
A new method of solving radiative transfer problems is described including a comparison of its speed with that of the doubling method, and a discussion of its accuracy and suitability for computations involving variable optical properties. The method uses a discretization in angle to produce a coupled set of firstorder differential equations which are integrated between discrete depth points to produce a set of recursion relations for symmetric and antisymmetric angular sums of the radiation field at alternate depth points. The formulation given here includes depthdependent anisotropic scattering, absorption, and internal sources, and allows arbitrary combinations of specular and nonLambertian diffuse reflection at either or both boundaries. Numerical tests of the method show that it can return accurate emergent intensities even for large optical depths. The method is also shown to conserve flux to machine accuracy in conservative atmospheres
 Publication:

Journal of Quantitative Spectroscopy and Radiative Transfer
 Pub Date:
 September 1976
 DOI:
 10.1016/00224073(76)900017
 Bibcode:
 1976JQSRT..16..725B
 Keywords:

 Anisotropic Media;
 Atmospheric Scattering;
 Finite Difference Theory;
 Scattering Functions;
 Atmospheric Optics;
 Diffuse Radiation;
 Radiative Transfer;
 Specular Reflection;
 Physics (General)