Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The radiative transfer equation
- 3 Principles of invariance
- 4 Quasi-exact solution methods for the radiative transfer equation
- 5 Radiative perturbation theory
- 6 Two-stream methods for the solution of the radiative transfer equation
- 7 Transmission in individual spectral lines and in bands of lines
- 8 Absorption by gases
- 9 Light scattering theory for spheres
- 10 Effects of polarization in radiative transfer
- 11 Remote sensing applications of radiative transfer
- 12 Influence of clouds on the climate of the Earth
- Answers to problems
- List of frequently used symbols
- References
- Index
5 - Radiative perturbation theory
Published online by Cambridge University Press: 18 December 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The radiative transfer equation
- 3 Principles of invariance
- 4 Quasi-exact solution methods for the radiative transfer equation
- 5 Radiative perturbation theory
- 6 Two-stream methods for the solution of the radiative transfer equation
- 7 Transmission in individual spectral lines and in bands of lines
- 8 Absorption by gases
- 9 Light scattering theory for spheres
- 10 Effects of polarization in radiative transfer
- 11 Remote sensing applications of radiative transfer
- 12 Influence of clouds on the climate of the Earth
- Answers to problems
- List of frequently used symbols
- References
- Index
Summary
Adjoint formulation of the radiative transfer equation
Problems in radiative transfer theory can be solved by various solution methods. In the previous chapter we have discussed a number of these which we will classify as the forward or the regular methods. In addition to applying the forward solutions, it is also possible to use the so-called adjoint solution techniques which offer the decisive advantage that for certain types of transfer problems the numerical effort can be drastically reduced.
In this section we will formulate the adjoint technique. It will be necessary to introduce a new terminology involving expressions such as the radiative effect and the atmospheric response due to the presence of energy sources. By means of an important but simple example we will demonstrate the numerical advantage that the adjoint technique offers in comparison to the forward formulation. In Section 5.2 we will introduce the perturbation technique and show how to apply it to the forward as well as to the adjoint formulation.
The adjoint method originated as a purely mathematical tool for the solution of linear operator equations. Discussions on this subject can be found in textbooks on principles of applied mathematics such as Courant and Hilbert (1953), Friedman (1956) and Keener (1988).
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- Radiation in the AtmosphereA Course in Theoretical Meteorology, pp. 133 - 157Publisher: Cambridge University PressPrint publication year: 2007