Geodesic
System ``ATRAD'' for calculations of atmospheric radiation: calculation of solar radiation transport in mid-latitude summer atmosphere
Matematičeskoe modelirovanie, Tome 11 (1999) no. 5, pp. 117-125.

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This paper is one of a series of reports describing the Database and Computer Code System ATRAD (Atmospheric Radiation) designed for high precision calculations of Earth atmospheric radiation for climate studies. The results of transport equation calculations by Lebesque averaging method for solar radiation in mid-latitude summer atmosphere for the whole spectrum are presented. Good agreement with the results of “line-by-line” calculations for purely absorbing atmosphere is achieved. Amount of numerical operations by Lebesque averaging method without optimization of parameters is at least four orders less than in “line-by-line” calculations. We don't know about compatible “line-by-line” results for scattering atmosphere. 
@article{MM_1999_11_5_a4,
     author = {E. N. Aristova and V. Ya. Gol'din and A. V. Shilkov and S. V. Shilkova},
     title = {System {``ATRAD''} for calculations of atmospheric radiation: calculation of solar radiation transport in mid-latitude summer atmosphere},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {117--125},
     publisher = {mathdoc},
     volume = {11},
     number = {5},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1999_11_5_a4/}
}
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E. N. Aristova; V. Ya. Gol'din; A. V. Shilkov; S. V. Shilkova. System ``ATRAD'' for calculations of atmospheric radiation: calculation of solar radiation transport in mid-latitude summer atmosphere. Matematičeskoe modelirovanie, Tome 11 (1999) no. 5, pp. 117-125. http://geodesic.mathdoc.fr/item/MM_1999_11_5_a4/