Two-stream approximation
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.[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. The two-stream approximation is commonly used in parameterizations of radiative transport in global circulation models and in weather forecasting models, such as the 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.[3] The two-stream approximation comes in many variants, such as the Quadrature, and Hemispheric constant models.[2] Mathematical descriptions of the two-stream approximation are given in several books.[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.[7]
See also
Notes and references
- ^ Liou, K. N. (2002-05-09). An Introduction to Atmospheric Radiation. Elsevier. p. 106. ISBN 9780080491677. Retrieved 2017-10-22.
- ^ a b 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.
- ^ Joseph, J. H.; Wiscombe, W. J.; Weinman, J. A. (December 1976). "The Delta-Eddington Approximation for Radiative Flux Transfer". Journal of the Atmospheric Sciences. 33 (12): 2452–2459. Bibcode:1976JAtS...33.2452J. doi:10.1175/1520-0469(1976)033<2452:tdeafr>2.0.co;2. ISSN 0022-4928.
- ^ Shettle, E. P.; Weinman, J. A. (October 1970). "The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation". Journal of the Atmospheric Sciences. 27 (7): 1048–1055. Bibcode:1970JAtS...27.1048S. doi:10.1175/1520-0469(1970)027<1048:ttosit>2.0.co;2. ISSN 0022-4928.