Reduction of the Equations of Radiative Transfer for a Plane-Parallel, Planetary Atmosphere

Part II

by Zdenek Sekera


Download eBook for Free

FormatFile SizeNotes
PDF file 1.5 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.


Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback72 pages $25.00 $20.00 20% Web Discount

A presentation of mathematical techniques necessary in unique solution of equations of radiative transfer in a homogeneous atmosphere with Rayleigh scsattering. The singular linear integral equations for the X-and Y-matrices appearing in the azimuth-independent terms of the reflection and transmission matrices for the emerging radiation from a homogeneous, plane-parallel atmosphere with Rayleigh scattering are reduced to four pairs of scalar equations of the forms discussed by T. W. Mullikin. The nonuniqueness in the solutions of one of these pairs of equations is removed by using linear constraints. The solutions are finally expressed as linear combinations of Chandrasekhar's functions and are brought to the same form as that derived by Chandrasekhar, but by completely different methods. The new forms of the solutions are particularly suitable from the computational point of view when large optical thicknesses are involved. Mathematical expressions corresponding to physical quantities such as directional radiation and total fluxes emerging from a Rayleigh scattering atmosphere are also derived.

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.