[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.
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, such as the Quadrature, and Hemispheric constant models.
[4][5] The two-stream approximation is separate from the Eddington approximation (and its derivatives such as Delta-Eddington[6]), which instead assumes that the intensity is linear in the cosine of the incidence angle (from +1 to -1), with no discontinuity at the horizon.