A new approach of direction discretization and oversampling for 3D anisotropic radiative transfer modeling

In radiative transfer modeling, the angular variable Ω discretization can strongly influence the radiative transfer simulation, especially with small numbers of discrete directions. Most radiative transfer models use discrete ordinate method or finite volume method for solving the transport equation. Both of the methods have their own algorithms to discretize the 4π space, under the constraint of satisfying geometric symmetry and specific moments. This paper introduces a new direction discretization and oversampling scheme, IUSD, and compares it with the other methods in simulating satellite signals. This method considers the constraint of geometric shape of angular sector, and iteratively discretizes the 4π space under this constraint. The result shows that IUSD is quite competitive in the accuracy of simulating remote sensing images. Furthermore, the new method provides a flexibility for adding any oversampling angular region, with any number of additional directions, using an optimal approach in terms of the total number of directions. Several case studies are presented. It turns out that the regional oversampling has significant influence for strong anisotropic scattering. This method has been implemented in the latest code of DART 3D radiative transfer model. DART is available for scientific purpose upon request.