Photon transport in vegetation canopies with anisotropic scattering Part IV. Discrete-ordinates/exact-kernel technique for two-angle photon transport in slab geometry

Abstract

A computational technique for two-angle photon transport in vegetation canopies involving anisotropic scattering is discussed. The exact-kernel method of evaluating the distributed and the first-collision source terms eliminates the need for Legendre polynomial expansion and thus the inherent expansion errors. The phase function now takes the form of a transfer matrix, whose elements are the actual phase function evaluated at discrete quadrature angles. To use the non-expanded scattering cross-sections in transport calculations, a slightly modified discrete-ordinates finite-difference method is formulated. The negative flux fixup procedure employed is a modified diamond difference relation with a step function. The code was tested for photon conservation and also by comparisons with results from neutron transport theory. The method showed good correspondence with measured directional reflectance data collected on two different vegetation canopies.