A fast, exact code for scattered thermal radiation compared with a two-stream approximation

For radiative transfer in plane-parallel emitting, absorbing, and scattering media, the two-stream approximation, and its various modifications or related methods, is probably mathematically the most simple to use. Unfortunately this physical approximation produces errors that are neither analytically known nor controllable. For externally (Sun) driven problems, many error studies exist for reflectivity, transmissivity, and certain defined albedos. A two-stream accuracy study for internally (thermal) driven problems is presented in this paper by comparison with a recently developed “exact” adding/doubling method. The resulting errors in external (or boundary) radiative intensity and flux are usually larger than those for the externally driven problems and vary substantially with the radiative parameters. Error predictions for a specific problem are difficult. An unexpected result was that the exact method is computationally as fast as the two-stream approximation for nonisothermal media. Although the adding/doubling method is mathematically and conceptually more complex, it may be used as a developed code with no essential sacrifice in computing time.