Two-stream approximation

In models of radiative transfer, the two-stream approximation is a discrete ordinate approximation in which radiation propagating along only two discrete directions is considered. It was first used by Arthur Schuster in 1905.[1] The two ordinates are chosen such that the model captures the essence of radiative transport in light scattering atmospheres.[2] A practical benefit of the approach is that it reduces the computational cost of integrating the radiative transfer equation. The two-stream approximation is commonly used in parameterizations of radiative transport in global circulation models and in weather forecasting models, such as the WRF. There is a large number of applications of the two-stream approximation, including variants such as the Kubelka-Munk approximation. It is the simplest approximation that can be used to explain common observations inexplicable by single-scattering arguments, such as the brightness and color of the clear sky, the brightness of clouds, the whiteness of a glass of milk, and the darkening of sand upon wetting.[3] The two-stream approximation comes in many variants, including the Eddington approximation, as well as the modified Eddington, Quadrature, and Hemispheric constant models.[2] Mathematical descriptions of the two-stream approximation are given in several books.[4][5]