Astrophysics and Space Science

, Volume 232, Issue 1, pp 37–48 | Cite as

Average photon path-length of radiation emerging from finite atmospheres

I Henyey-Greenstein Phase Function
  • Tõnu Viik


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.


Computing Time Radiation Field Phase Function Multiple Scattering Optical Thickness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Tõnu Viik
    • 1
  1. 1.W.Struve Tartu Astrophysical ObservatoryTõravereEstonia

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