Differential properties of H-functions with applications to optically thick planetary atmospheres and spherical clouds

Details Differential properties of H-functions with applications to optically thick planetary atmospheres and spherical clouds Differential properties of H-functions with applications to optically thick planetary atmospheres and spherical clouds

Dec 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988a%26a...207..194h&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 207, no. 1, Dec. 1988, p. 194-203.

Statistics

Computation

9

Atmospheric Models, Computational Astrophysics, Optical Thickness, Planetary Atmospheres, Radiative Transfer, Angular Distribution, Light Scattering, Reflectance

Scientific paper

Integral expressions are derived for the first two derivatives of H-functions with respect to the directional variable. Assuming isotropic scattering these expressions are used to develop algorithms for numerical computation. Some results are presented in figures and tables with five decimal accuracy. The precise nature of the angular distribution of light emerging from a homogeneous semi-infinite plane-parallel planetary atmosphere is established. Several functions occurring in the asymptotic theory of isotropic scattering in spherical clouds are numerically evaluated. To clarify their nature when the albedo of single scattering is close to zero or one, expansions for H-functions and related functions are derived.

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