Two-stream approximation of the radiative transfer equation is an approximation of the radiative transfer equation in which radiation is propagating in only two discrete directions.
This approximation captures essence of the radiative transport in light scattering atmosphere. Two-stream approximation is commonly used in parameterizations of radiative transport in global circulation models and in weather forecasting models such as WRF. There is a surprisingly large number of applications of the two-stream approximations, including variants such as Kubelka-Munk approximation. The two-stream approximation is the simplest approximation which can be used to explain common observation 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, the darkening of sand upon wetting. The two-stream approximation comes in many variants, including Eddington approximation, Modified Eddington, Quadrature, Hemispheric constant models. Modern mathematical description of the two-stream approximation is given in several books. 
Notes and references
- W.E. Meador and W.R. Weaver, 1980, Two-Stream Approximations to Radiative Transfer in Planetary Atmospheres: A Unified Description of Existing Methods and a New Improvement, 37, Journal of the Atmospheric Sciences, 630–643 http://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%281980%29037%3C0630%3ATSATRT%3E2.0.CO%3B2
- Bohren, Craig F., 1987, Multiple scattering of light and some of its observable consequences, American Journal of Physics, 55, 524-533.
- G. E. Thomas and K. Stamnes (1999). Radiative Transfer in the Atmosphere and Ocean. Cambridge University Press. ISBN 0-521-40124-0.
- Grant W. Petty (2006). A First Course In Atmospheric Radiation (2nd Ed.). Sundog Publishing, Madison, Wisconsin. ISBN 0-9729033-0-5.