Numerical smearing, ray effect, and angular false scattering in radiation transfer computation

Solutions of the integro-differential equation of radiation transfer via numerical methods were well known to suffer from two “separate” shortcomings: (1) numerical smearing error due to spatial domain discretization, and (2) ray effect error due to angular discretization. In this study, proportionality expressions for various orders of numerical smearing errors are derived, and the inherent dependence of such errors on both spatial and angular discretization is found. Ray effect is categorized into two components: local and propagation errors; and they are not independent of spatial discretization. Using DOM solution, the individual and combined impacts of the above-mentioned numerical errors together with the recently discovered angular false scattering error are examined for various spatial and angular discretizations and medium optical properties. The dependence of numerical errors on scattering anisotropy is investigated. It is found that, for low scattering anisotropy, either numerical smearing or ray effect errors dominate, depending on optical thickness and scattering albedo. For high scattering anisotropy, however, the ray effect and angular false scattering dominate.