Intensity of radiation reflected by a vertically inhomogeneous medium through multiple scattering

Details Intensity of radiation reflected by a vertically inhomogeneous medium through multiple scattering Intensity of radiation reflected by a vertically inhomogeneous medium through multiple scattering

Feb 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985ap%26ss.109..345k&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 109, no. 2, Feb. 1985, p. 345-356.

Astronomy and Astrophysics

Astrophysics

1

Inhomogeneity, Light Scattering, Radiant Flux Density, Albedo, Fourier Analysis, Numerical Integration, Optical Thickness

Scientific paper

In order to compute the radiative intensity reflected, upon multiple scattering, by a vertically inhomogeneous medium, a numerical integration scheme for solving the invariant imbedding equation for the Fourier-analyzed reflection function, is developed. The equation is solved by approximating the height variations of the single-scattering albedo and the phase function characterizing the degree of inhomogeneity, by piece-wise linear functions of optical height tau, and by approximating the reflection function by a piece-wise quadratic polynomial in tau over each integration step. The method is capable of handling cases where the single-scattering albedo and the phase function show variations with height in an arbitrary manner. To facilitate the computations for high-order Fourier terms of the reflection function, the single-order and second-order scattering equations are solved in the form applicable to inhomogeneous media.

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