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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. In other words, the two-stream approximation assumes the intensity is constant with angle in the upward hemisphere, with a different constant value in the downward hemisphere. It was first used by [[Arthur Schuster]] in 1905.<ref>{{cite book|title=An Introduction to Atmospheric Radiation|first=K. N.|last=Liou|date=2002-05-09|url=https://books.google.com/books?id=mQ1DiDpX34UC&q=schuster+two+stream+climate+model|page=106|publisher=Elsevier |isbn=9780080491677|accessdate=2017-10-22}}</ref> The two ordinates are chosen such that the model captures the essence of [[Radiative transfer|radiative transport]] in light scattering atmospheres.<ref name="meador80a">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</ref> 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 climate model|global circulation models]] and in [[Numerical weather prediction|weather forecasting models]], such as the [[Weather Research and Forecasting model|WRF]]. There are 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.<ref>Bohren, Craig F., 1987, Multiple scattering of light and some of its observable consequences, American Journal of Physics, 55, 524-533.</ref> The two-stream approximation comes in many variants, such as the Quadrature, and Hemispheric constant models.<ref name="meador80a" /> Mathematical descriptions of the two-stream approximation are given in several books.<ref>{{cite book|author=G. E. Thomas and K. Stamnes|title=Radiative Transfer in the Atmosphere and Ocean|publisher=Cambridge University Press.|year=1999|isbn=0-521-40124-0}}</ref><ref>{{cite book|title=A First Course In Atmospheric Radiation (2nd Ed.)|author=Grant W. Petty|publisher=Sundog Publishing, Madison, Wisconsin|year=2006|isbn=0-9729033-0-5}}</ref> The two-stream approximation is separate from the [[Radiative transfer#The Eddington approximation|Eddington approximation]] (and its derivatives such as Delta-Eddington<ref>{{Cite journal |last1=Joseph |first1=J. H. |last2=Wiscombe |first2=W. J. |last3=Weinman |first3=J. A. |date=December 1976 |title=The Delta-Eddington Approximation for Radiative Flux Transfer
==See also==
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