Average Photon Path-Length of Radiation Emerging from Finite Atmospheres. I. Henyey-Greenstein Phase Function

Details Average Photon Path-Length of Radiation Emerging from Finite Atmospheres. I. Henyey-Greenstein Phase Function Average Photon Path-Length of Radiation Emerging from Finite Atmospheres. I. Henyey-Greenstein Phase Function

Oct 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995ap%26ss.232...37v&link_type=abstract

Astrophysics and Space Science, Volume 232, Issue 1, pp.37-48

Astronomy and Astrophysics

Astrophysics

1

Scientific paper

The determination of the average path-length of photons emerging from a conservative finite plane-parallel atmosphere is discussed. The multiple scattering in the atmosphere obeys the Henyey-Greenstein phase function and only the axial radiation field is considered. In order to obtain the average path-length we need to know the derivatives of the scattering and transmission functions with respect to the albedo of single scattering and the optical thickness. As a starting point we use the integro-differential equations of Chandrasekhar for the diffuse scattering and transmission functions. By differentiation of these equations with respect to the albedo of single scattering we obtain new equations the solution of which gives us the derivatives of the intensities of the emergent radiation at the boundaries. In the case of large asymmetry parameters these equations tend to be rather stiff and the computing time may be prohibitive. To overcome this difficulty we propose an adding scheme based on the principles of invariance by Chandrasekhar. The application of a scheme of numerical integration is discussed and some numerical results are given.

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