Determination of the multi-scattered solar radiation from a leaf canopy for use in climate models

The terrestrial component of climate models requires computationally efficient algorithms for determining the multi-scattered radiation contributing to its heating from solar radiation. Much of the vegetated land cover has strong 3D controls on its radiation. The scattering from a 3D object of isotropic scatters is formulated abstractly and an approach to solution is described in the context of a spherical object. A Laplace integral representation of the 3D integral equation for radiative transfer is discretized. Such discretization provides the solution in terms of solutions to 3D Helmholtz equations, a single such equation in the lowest order approach. A Green’s function approximate solution along the paths of entering and exiting radiation is integrated over such radiation for the paths assumed to coincide except for direction. The resulting approximate description of multi-scattered radiation corresponds to replacing the 3D scattering paths with a 1D path with attenuation amplified by a diffusivity factor. This description combines with previously derived analytic solutions for single scattered radiation to provide an efficient representation of the bidirectional scattering from the 3D object, intended for use in climate models and remote sensing.