46:. 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. The two-stream approximation comes in many variants, such as the Quadrature, and Hemispheric constant models. Mathematical descriptions of the two-stream approximation are given in several books. The two-stream approximation is separate from the
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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
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in light scattering atmospheres. 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
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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
50:(and its derivatives such as Delta-Eddington), 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.
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Bohren, Craig F., 1987, Multiple scattering of light and some of its observable consequences, American
Journal of Physics, 55, 524-533.
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237:"The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation"
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42:. There are a large number of applications of the two-stream approximation, including variants such as the
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http://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%281980%29037%3C0630%3ATSATRT%3E2.0.CO%3B2
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in 1905. The two ordinates are chosen such that the model captures the essence of
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Joseph, J. H.; Wiscombe, W. J.; Weinman, J. A. (December 1976).
188:"The Delta-Eddington Approximation for Radiative Flux Transfer"
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10.1175/1520-0469(1970)027<1048:ttosit>2.0.co;2
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10.1175/1520-0469(1976)033<2452:tdeafr>2.0.co;2
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163:A First Course In Atmospheric Radiation (2nd Ed.)
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235:Shettle, E. P.; Weinman, J. A. (October 1970).
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138:Radiative Transfer in the Atmosphere and Ocean
60:List of atmospheric radiative transfer codes
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165:. Sundog Publishing, Madison, Wisconsin.
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81:An Introduction to Atmospheric Radiation
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16:In models of radiative transfer, the
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78:Liou, K. N. (2002-05-09).
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84:. Elsevier. p. 106.
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161:Grant W. Petty (2006).
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