Jump to ContentJump to Main Navigation
Atmospheric RadiationTheoretical Basis$
Users without a subscription are not able to see the full content.

R. M. Goody and Y. L. Yung

Print publication date: 1989

Print ISBN-13: 9780195051346

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195051346.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 05 December 2021

Radiative Transfer in a Scattering Atmosphere

Radiative Transfer in a Scattering Atmosphere

Chapter:
(p.330) 8 Radiative Transfer in a Scattering Atmosphere
Source:
Atmospheric Radiation
Author(s):

R. M. Goody

Y. L. Yung

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195051346.003.0010

The source function for scattering, (2.32), is more complicated than a thermal source function on two accounts: it is not a function of local conditions alone, but involves conditions throughout the atmosphere, through the local radiation field, and the phase function, Pij(s, d), may be an extremely complex function of the directions, s and d, and the states of polarization, i and j. The general solution, (2.87), is still valid, but it is now an integral equation, involving the intensity both on the left-hand side and under the integral on the right-hand side. Successive approximations, starting with the first-order scattering term [third term on the right-hand side of (2.116)], are an obvious approach, and would lead to a solution, but there are more efficient and more accurate ways to solve the problem. Many methods are available because their fundamental theory has proved to be mathematically interesting and because there are important applications in neutron diffusion theory and astrophysics. These motivations are extraneous to atmospheric science, but the availability of the methodology has led to its adoption and extension to atmospheric problems. Many methods are available because their fundamental theory has proved to be mathematically interesting and because there are important applications in neutron diffusion theory and astrophysics. These motivations are extraneous to atmospheric science, but the availability of the methodology has led to its adoption and extension to atmospheric problems. Solutions to scattering problems can be elaborate and mathematically elegant; they can also be numerically onerous but, with access to modern computers, “exact” solutions are feasible, given the input parameters τv, av (=sv/ev), and Pi j. For monochromatic calculations with simple phase functions, numerical solutions present few difficulties. Nevertheless, the combination of unfamiliar formalism with inaccessible and undocumented algorithms can be daunting for those with only a peripheral interest in radiation calculations. It is, therefore, relevant to note that available data are imprecise and virtually never require the accuracy available from exact methods. Easily visualized two-stream approximations, combined with similarity relations to handle complex phase functions (see §§8.4.4 and 8.5.6), are often more than adequate, and some angular information can be added, if required, from the use of Eddington’s second approximation (§ 2.4.5).

Keywords:   Aircraft measurements, Babinet's principle, Diffusivity factor, Emergent radiation, Four-stream approximation, Gaussian quadrature, Haze, Interaction principle, Multistream solutions

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .