|
In models of radiative transfer, the '''Twotwo-stream approximation''' ofis thea radiativediscrete transferordinate equationapproximation in which radiation propagating along only two discrete directions is anconsidered. In other words, the two-stream approximation ofassumes the radiativeintensity transferis equationconstant with angle in whichthe radiationupward ishemisphere, propagatingwith a different constant value in onlythe twodownward discrete directionshemisphere. 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&dqq=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> TwoA 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 isare a surprisingly large number of applications of the two-stream approximationsapproximation, including variants such as the [[Kubelka-Munk approximation]]. The two-stream approximationIt is the simplest approximation whichthat can be used to explain common observationobservations 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, includingsuch [[Radiativeas transfer#Thethe Eddington approximation|Eddington approximation]]Quadrature, Modified Eddington, Quadrature,and Hemispheric constant models.<ref name= "meador80a " /> ModernMathematical mathematical descriptiondescriptions of the two-stream approximation isare 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 |journal=Journal of the Atmospheric Sciences |volume=33 |issue=12 |pages=2452–2459 |doi=10.1175/1520-0469(1976)033<2452:tdeafr>2.0.co;2 |bibcode=1976JAtS...33.2452J |issn=0022-4928|doi-access=free }}</ref>), 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.<ref>{{Cite journal |last1=Shettle |first1=E. P. |last2=Weinman |first2=J. A. |date=October 1970 |title=The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation |journal=Journal of the Atmospheric Sciences |volume=27 |issue=7 |pages=1048–1055 |doi=10.1175/1520-0469(1970)027<1048:ttosit>2.0.co;2 |bibcode=1970JAtS...27.1048S |issn=0022-4928|doi-access=free }}</ref> ▼
This approximation captures essence of the [[Radiative transfer|radiative transport]] in light scattering atmosphere.<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> 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 [[Weather Research and Forecasting model|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.<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, including [[Radiative transfer#The Eddington approximation|Eddington approximation]], Modified Eddington, Quadrature, Hemispheric constant models.<ref name=meador80a/> Modern mathematical description of the two-stream approximation is 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>
==See also==
|
