Analytical discrete ordinate method for radiative transfer in dense vegetation canopies

The radiative transfer (RT) in dense vegetation canopies can be approximated via linear Boltzmann equation. However, the directionality of the basic scattering element (i.e. the canopy leaf) makes the medium inherently anisotropic and introduces special features in the definition of both scattering kernel and total cross section. In this paper, a classical methodology for the solution of transport problem, namely the analytical discrete ordinate (ADO) method, is extended to account for the peculiarities of photon transport into dense vegetation canopies. It is demonstrated that the special symmetries arising from modeling the leaf as a bi-Lambertian scatterer, enable the derivation of the ADO equations for canopy transport. Several numerical tests have been performed to evaluate the accuracy of ADO against numerical benchmarks available in the literature. The results show that the proposed methodology is highly accurate, computationally efficient and may set future standards for numerical transport in dense vegetation canopies.