Analytical Methods in Radiative Transfer

by Alexander Kokhanovsky, Vijay Natraj, Dmitry Efremenko

Overview

Provides in-depth knowledge of the physics of radiative transfer

In Analytical Methods in Radiative Transfer, a team of distinguished researchers delivers a comprehensive exploration of solutions to practical problems of modern atmospheric optics related to solar light interaction with the terrestrial atmosphere and the remote sensing of clouds, aerosols, and gases. The authors describe analytic methods in radiative transfer that help explain atmospheric phenomena.

The book includes discussions on the interaction of solar light with the atmosphere. Readers will also benefit from thorough reviews of various analytical radiative transfer techniques, for various turbid media, including media with phase functions extended in the forward direction, and also semi-infinite, non-absorbing, weakly absorbing, and strongly absorbing light scattering media.

Analytical Methods in Radiative Transfer also includes:

• A thorough introduction to exact solutions of the radiative transfer equation, including situations of single scattering, as well as isotropic and Rayleigh scattering
• A comprehensive exploration of approximate solutions for scalar radiative transfer, including single and multiple light scattering separation and the case of semi-infinite media such as snow
• In-depth examinations of the applications of analytical methods in atmospheric radiative transfer, including aerosol remote sensing, cloud remote sensing, and the remote sensing of trace gases

Perfect for meteorologists, climatologists and graduate students studying physics, Analytical Methods in Radiative Transfer is also an indispensable resource for geophysicists seeking a practical exploration of modern atmospheric optics.

Product Details

ISBN-13:	9783527698974
Publisher:	Wiley
Publication date:	09/04/2025
Series:	Wiley Series in Atmospheric Physics and Remote Sensing
Sold by:	JOHN WILEY & SONS
Format:	eBook
Pages:	192
File size:	13 MB
Note:	This product may take a few minutes to download.

About the Author

Alexander Kokhanovsky, PhD, is a scientist at the Department of Geography, Marburg University, Germany. He has authored over 350 scientific publications and is the author or editor of six books.

Vijay Natraj, PhD, is a scientist at the Jet Propulsion Laboratory, California Institute of Technology (JPL), USA. His research focuses on polarization, aerosol and cloud modeling, fast radiative transfer computations, and information theoretical analysis.

Dmitry Efremenko, PhD, is scientist at the German Aerospace Center (DLR). His research is focused on remote sensing of atmospheric processes.

Table of Contents

Preface ix

Acknowledgments xi

1 Introduction 1

1.1 Historical Background 1

1.2 What Is Radiative Transfer About and What Is It Good For? 6

1.3 Phenomenological Radiative Transfer 7

1.4 Microphysical Approach 8

1.5 Atmospheric Remote Sensing 10

1.6 Radiative Transfer Models in Atmospheric Remote Sensing 13

1.7 Electromagnetic Spectrum 15

1.8 Why Do We Need Analytical Models in Radiative Transfer? 17

1.9 Radiative Transfer and Climate Modeling 19

1.10 Remote Sensing of Trace Gases 21

1.11 Remote Sensing of Clouds 24

1.12 Remote Sensing of Atmospheric Aerosol 26

2 Radiative Transfer Equation 29

2.1 Introduction to Radiative Transfer Theory 29

2.2 Formulation of the RTE 30

2.3 RTE with Thermal Source 34

2.4 Optical Thickness and Single-scattering Albedo 35

2.5 Single-scattering Phase Function 36

2.6 Orders of Scattering 39

2.7 One-dimensional RTE 41

2.8 Formal Solution of the RTE 42

2.9 RTE for Azimuthal Harmonics of the Intensity 43

2.10 Radiance Moments 45

2.11 Light Reflection from Layered Media 46

3 Optically Thin Media and Media with Strongly Anisotropic Scattering 49

3.1 Single-scattering Approximation 49

3.2 Second-order Scattering Approximation 52

3.3 Small-angle Approximation 57

4 Semi-infinite Media 63

4.1 Milne Problem 63

4.2 Light in Deep Layers of Semi-infinite Turbid Media 65

4.3 Light Reflection from Semi-infinite Media 70

4.3.1 Invariant Imbedding 70

4.3.2 H-functions 72

4.3.3 Nonabsorbing Media 73

4.3.4 Weakly Absorbing Media 75

5 Optically Thick Media 79

5.1 Nonabsorbing Media 79

5.2 Weakly Absorbing Media 81

5.3 Optically Thick Turbid Media with an Arbitrary Level of

Light Absorption 83

5.4 Asymptotic Equations 91

6 Turbid Media with Arbitrary Optical Thickness 93

6.1 Sobolev Approximation 93

6.2 Two-stream Approximation 99

6.3 Four-stream Approximation 105

6.4 The Spherical Harmonics Method 111

6.5 Phase Function Truncation Methods 112

7 Radiative Transfer in Gaseous Absorption Bands 117

7.1 k-Distribution and Correlated-k Methods 117

7.2 Exponential Sum Fitting of Transmittances 119

7.3 Spectral Mapping 120

7.4 Optimal Spectral Sampling 121

7.5 Double-k, Linear-k, and Low-streams Interpolation Techniques 122

7.6 Computations in a Broad Spectral Range: 400–2500 nm 126

7.7 Concept of Dimensionality Reduction 130

7.8 Principal Component Analysis of Spectral Radiances 131

7.9 Principal Component Analysis for Differential Optical Absorption Spectroscopy 134

7.10 Principal Component Analysis of Optical Parameters 135

7.11 Neural Networks 138

A Legendre Polynomials 143

B Computations of Local Optical Parameters 145

Bibliography 155

Index 167