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

Part I

Zdenek Sekera

ResearchPublished 1966

A discussion of the reduction of the equations of radiative transfer when the phase matrix is "separable." A separable matrix is one that can be expressed as the product of two matrices, one whose elements depend on the directional parameters of the incident beam alone, and the other whose elements depend on the directional parameters of the scattered and incident beams and each term of this series is separable, the radiative transfer equations have "series" solutions with each term of this series is separable, the radiative transfer equations have "series" solutions with each term in these series being given by a product of three matrices; one of these is azimuth-independent, the other two, which post- and pre-multiply this matrix, are the same matrices whose product forms the corresponding term in the phase matrix.

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1966
  • Pages: 87
  • Document Number: RM-4951-PR

Citation

Chicago Manual of Style

Sekera, Zdenek, Reduction of the Equations of Radiative Transfer for a Plane-Parallel, Planetary Atmosphere: Part I. Santa Monica, CA: RAND Corporation, 1966. https://www.rand.org/pubs/research_memoranda/RM4951.html.
BibTeX RIS

This publication is part of the RAND research memorandum series. The research memorandum series, a product of RAND from 1948 to 1973, included 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 www.rand.org/pubs/permissions.

RAND 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.