The Neumann solution of the multiple scattering problem in a plane-parallel medium—I. The infinite medium

1985 ◽  
Vol 33 (4) ◽  
pp. 373-380 ◽  
Author(s):  
B. Rutily ◽  
J. Bergeat
Keyword(s):  
Multiple Scattering ◽  
Scattering Problem ◽  
Infinite Medium ◽  
Plane Parallel

scholarly journals Some Effects of Multiple Scattering on the Distribution of Solar Radiation in Snow and Ice

1972 ◽  
Vol 11 (63) ◽  
pp. 357-368 ◽  
Author(s):  
Bruce R. Barkstrom
Keyword(s):  
Solar Radiation ◽  
Multiple Scattering ◽  
Specular Reflection ◽  
Scattering Problem ◽  
Solar Flux ◽  
Isotropic Scattering ◽  
Solar Altitude ◽  
Exponential Decrease ◽  
The Antarctic ◽  
Upward Flux

AbstractMultiple scattering of the solar flux in snow and “bubbly” ice can account for the variable albedo, the non-specular reflection, the non-exponential flux decrease near the surface, and the large upward flux within the medium. The scattering problem has been formulated and solved exactly, assuming isotropic scattering in a plane-parallel, semi-infinite, grey medium. The solution shows a non-exponential flux decrease near the surface and an exponential decrease deep in the medium. For such a medium, the albedo will increase with decreasing solar altitude in a manner which agrees to within one per cent of observed snow albedos in the Antarctic.

A note on the enhancement of J values in optically thick scattering atmospheres

1991 ◽  
Vol 69 (8-9) ◽  
pp. 1166-1174 ◽  
Author(s):  
Jacek W. Kaminski ◽  
John C. McConnell
Keyword(s):  
Multiple Scattering ◽  
Rayleigh Scattering ◽  
Large Fraction ◽  
Coherent Scattering ◽  
Single Scattering ◽  
Average Density ◽  
Infinite Medium ◽  
Scattering Medium ◽  
Surface Reflection ◽  
Thick Medium

In a planetary atmosphere the J value is determined by the angular-averaged radiance, or the average density of photons in an element of volume. The average density may be enhanced by multiple scattering of photons in a conservative, or near-conservative scattering atmosphere. We show that in a conservative semi-infinite medium this enhancement will be a factor of 5, for optical depths greater than about 20 for coherent scattering. We investigate the modification of the J values owing to multiple scattering in an optically thick medium of various optical depths, various single-scattering albedos of the scattering medium, and a range of surface albedos. We have applied the results to the calculation of J values in clouds in the terrestrial atmosphere and in the Rayleigh-scattering atmosphere of Uranus. We note that J values in a realistic atmosphere may be enhanced by as much as a factor of 5 throughout a large fraction of the atmosphere over those calculated without multiple scattering and surface reflection.

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