Theory of atmospheric radiative transfer : a comprehensive introduction

Aimed at the senior undergraduate and graduate level, this textbook fills the gap between general introductory texts offering little detail and very technical, advanced books written for mathematicians and theorists rather than experimentalists in the field.
The result is a concise course in atmospheric radiative processes, tailored for one semester. The authors are accomplished researchers who know how to reach their intended audience and provide here the content needed to understand climate warming and remote sensing for pollution measurement. They also include supplementary reading for planet scientists and problems.
Equally suitable reading for geophysicists, physical chemists, astronomers, environmental chemists and spectroscopists.
A solutions manual for lecturers will be provided on www.wiley-vch.de/supplements.

Author Notes

Manfred Wendisch is a full professor and director of the Institute of Meteorology at the University of Leipzig, Germany, and holds a permanent guest professor appointment at the Chinese Academy of Sciences in Beijing. His teaching expertise includes the fields of atmospheric radiative transfer, cloud physics, atmospheric dynamics, and synoptic meteorology, and he is actively involved in numerous research projects focusing on airborne measurements and impacts of atmospheric clouds and their radiative properties. In 2011, Professor Wendisch was elected as a member of the Saxonian Academy of Sciences.
Ping Yang is a professor and the holder of the David Bullock Harris Chair in Geosciences, the Department of Atmospheric Sciences, Texas A M University, USA. His research interests cover the areas of remote sensing and radiative transfer. He has been actively conducting research in the modeling of the optical and radiative properties of clouds and aerosols, in particular cirrus clouds, and their applications to space-borne and ground-based remote sensing. Professor Yang received a Best Paper Award from the Climate and Radiation Branch, NASA Goddard Space Center in 2000 and the U.S. National Science Foundation CAREER grant award in 2003. He was elected a fellow of the Optical Society of America (OSA) in 2010.

Preface	p. XI
1 Introduction	p. I
1.1 Brief Survey of Atmospheric Radiation	p. 1
1.2 A Broadbrush Picture of the Atmospheric Radiation Budget	p. 3
1.3 Solar and Terrestrial Thermal Infrared Spectra in a Cloudless Atmosphere	p. 6
1.4 The Greenhouse Effect	p. 7
1.5 Relevance to the Interpretation of Spaceborne Observations	p. 9
2 Notation and Math Refresher	p. 11
2.1 Physical Dimensions and Prefixes	p. 11
2.2 Some Rules and Conventions	p. 13
2.3 Vector Algebra Brief	p. 13
2.3.1 Major Vector Operations	p. 13
2.3.2 Use of Index Notation	p. 15
2.4 Dirac ¿5-Function	p. 18
2.5 Geometry	p. 20
2.5.1 Directions	p. 20
2.5.2 Solid Angle	p. 20
2.5.3 Angle between Two Directions	p. 22
2.6 Orthogonal Functions	p. 22
2.6.1 Legendre Polynomials	p. 23
2.6.2 Legendre Functions	p. 24
2.7 Quadrature Formula	p. 26
Problems	p. 27
3 Fundamentals	p. 29
3.1 Electromagnetic (EM) Radiation	p. 29
3.1.1 Maxwell's Equations and Plane-Wave Solutions	p. 29
3.1.2 Wavelength, Frequency, Wavenumber, Dispersion Relation, and Phase Speed	p. 31
3.1.3 Coherence, Incoherence, and Polarization	p. 32
3.1.4 Wave-Particle Duality	p. 33
3.1.5 Atmospheric EM Radiation Spectrum	p. 34
3.2 Basic Radiometric Quantities	p. 36
3.2.1 Radiant Energy Flux, Flux Density, and Radiance	p. 36
3.2.2 Radiant Energy Density and Radiance	p. 38
3.2.3 Irradiance, Emittance, Exitance, and Actinic Radiation	p. 40
3.2.4 Relation between Upward, Downward, and Net Actinic Flux Densities and Radiance	p. 41
3.2.5 Isotropic Radiation Field	p. 43
3.2.6 Reflectivity, Absorptivity, and Transmissivity	p. 43
3.3 Blackbody and Graybody Radiation: Basic Laws	p. 43
3.3.1 Planck's Law	p. 43
3.3.2 Wien's Displacement Law	p. 45
3.3.3 Stefan-Boltzmann Law	p. 47
3.3.4 Rayleigh-Jeans and Wien's Approximations	p. 48
3.3.5 Emissivity and Kirchhof s Law	p. 48
Problems	p. 51
4 Interactions of EM Radiation and Individual Particles	p. 59
4.1 Overview	p. 59
4.2 Complex Index of Refraction	p. 60
4.3 Decomposition of Electric Field Vector	p. 62
4.4 Complex Amplitude Scattering Matrix	p. 63
4.5 Stokes Vector	p. 64
4.6 Degree of Polarization	p. 66
4.7 Mueller Matrix	p. 67
4.8 Optical Properties of Individual Particles	p. 70
4.8.1 Optical Parameters	p. 70
4.8.2 Optical Theorem	p. 73
4.9 Spherical Particles (Lorenz-Mie Theory)	p. 75
4.9.1 Assumptions and Goals	p. 75
4.9.2 Efficiency Factors: Q ext,Mie , Q sca,Mie , Q abs,Mie	p. 76
4.9.3 Single-Scattering Albedo:¿ Mie	p. 78
4.9.4 Elements of the Complex Amplitude Scattering Matrix	p. 78
4.9.5 Elements of the Mueller Matrix	p. 79
4.9.6 Polarization	p. 80
4.9.7 Phase Function for Unpolarized Incident Radiation: P unp,Mie	p. 82
4.9.8 Asymmetry Factor: g unp,Mie	p. 83
4.10 Rayleigh Scattering and Oscillating Electric Dipole	p. 84
4.10.1 Amplitudes Scattering Matrix and Mueller Matrix	p. 84
4.10.2 Degree of Polarization	p. 86
4.10.3 Rayleigh Phase Function for Unpolarized Incident Radiation: P unp,Rayl	p. 86
4.10.4 Scattering Cross Section and Efficiency Factor	p. 88
4.10.5 Extinction and Absorption Cross Sections and Efficiency Factors	p. 88
4.10.6 Rayleigh Scattering as an Approximation of Lorenz-Mie Theory	p. 89
4.10.7 Rayleigh Scattering in the Atmosphere	p. 91
4.11 Scattering by Nonspherical Individual Particles	p. 93
4.11.1 Analytical Approaches	p. 93
4.11.2 Mueller Matrix	p. 94
4.11.3 Phase Function	p. 95
4.11.4 Integrated Optical Properties	p. 97
4.12 Geometric-Optics Method for Light Scattering by Large Particles	p. 99
4.12.1 Directional Changes Due to Reflection and Transmission (Refraction) at a Plane Interface: Snel's Law	p. 101
4.12.2 The n 2 Law	p. 105
4.12.3 Fresnel Formulas for Reflection and Transmission	p. 106
4.12.4 Radiant Energy Changes for Transmission (Plane Interface)	p. 109
4.12.5 Radiant Energy Changes for Reflection (Plane Interface)	p. 111
4.12.6 Ray-Tracing Technique	p. 114
4.12.7 Diffraction	p. 116
4.13 Rainbow and Halo	p. 122
Problems	p. 125
5 Volumetric (Bulk) Optical Properties	p. 133
5.1 Particle Size Distribution	p. 133
5.1.1 Analytical Descriptions	p. 133
5.1.2 Integrated Microphysical Parameters	p. 134
5.1.3 Parameterizations	p. 135
5.2 Volumetric (Bulk) Scattering, Absorption, and Extinction	p. 136
Problems	p. 140
6 Radiative Transfer Equation	p. 143
6.1 Optical Thickness	p. 144
6.2 Lambert-Bouguer Law	p. 144
6.2.1 Differential and Exponential Forms	p. 144
6.2.2 Application to Direct Solar Irradiance dir,¿	p. 146
6.3 General Formulation of the RTE	p. 147
6.3.1 Spectral Photon Density Function	p. 147
6.3.2 Radiative Transfer Equation in Scattering Media	p. 149
6.3.3 Photon Budget Equation	p. 153
6.3.4 3D Time-Dependent and Stationary RTE for Total Radiance	p. 153
6.3.5 3D Stationary RTE for Diffuse Radiance	p. 254
6.4 ID RTE for a Horizontally Homogeneous Atmosphere	p. 156
6.4.1 Independent Variables	p. 156
6.4.2 Standard Form of ID RTE for Diffuse Radiance	p. 157
6.4.3 Downward Diffuse Radiance	p. 161
6.4.4 Upward Radiance	p. 165
Problems	p. 169
7 Numerical and Approximate Solution Techniques for the RTE	p. 173
7.1 Legendre and Fourier Expansions	p. 173
7.1.1 Expansion of Phase Function in Terms of Legendre Polynomials	p. 173
7.1.2 Truncation of Phase Function and Similarity Principle	p. 175
7.1.3 Atmospheric Angular Coordinates	p. 178
7.1.4 The Delta-M Method (DMM) and Delta-Fit Methods (DFM)	p. 181
7.1.5 Fourier Expansions of Diffuse Radiance and Irradiance	p. 185
7.2 Equations for Fourier Modes of Diffuse Radiance	p. 187
7.2.1 Net Radiative Flux Density in a Nonabsorbing Atmosphere	p. 188
7.3 Method of Successive Order of Scattering (MSOS)	p. 191
7.4 Adding-Doubling Method (A-DM)	p. 193
7.4.1 Simplified Example	p. 193
7.4.2 Generalization for Radiances	p. 196
7.4.3 Application to Flux Densities	p. 202
7.5 Discrete Ordinate Method (DOM)	p. 205
7.6 Spherical Harmonics Method (SHM)	p. 209
7.7 Monte Carlo Method (MCM)	p. 212
7.7.1 Basic Principle	p. 213
7.7.2 Backward (Inverse) Monte Carlo Method (BMCM)	p. 216
7.8 Two-Stream Approximation (TSA)	p. 222
7.8.1 Classical Approach	p. 222
7.8.2 TSA Based on RTE	p. 227
Problems	p. 230
8 Absorption and Emission by Atmospheric Gases	p. 233
8.1 Interactions of Photons and Gas Molecules	p. 233
8.1.1 Types of Molecular Energy E mol	p. 233
8.1.2 Photon Absorption and Emission	p. 234
8.1.3 Allowed Quantized Energies and Frequencies (Wavelengths)	p. 235
8.1.4 Energy Level Probability in Thermal Equihbrium	p. 235
8.2 Examples of Energy Transitions	p. 237
8.2.1 Structure of Gas Molecules	p. 237
8.2.2 Molecular Rotational Energy E n rot	p. 238
8.2.3 Molecular Vibrational Energy E n vib	p. 238
8.3 Line Spectra for Single-Atomic Gases	p. 239
8.3.1 Molecular Electron Orbital Energy E n orb	p. 239
8.3.2 Line Spectrum of the Hydrogen Atom	p. 240
8.4 Molecular Absorption/Emission Line Spectra	p. 244
8.4.1 Molecular Rotational Spectra	p. 244
8.4.2 Ratio of Molecular Electron Orbital and Rotational Energies	p. 246
8.4.3 Vibrational Spectra of Diatomic Molecules	p. 247
8.4.4 Combined Molecular Vibration-Rotation Spectra	p. 248
8.5 Examples of Atmospheric Gas Spectra	p. 252
8.5.1 Three General Types of Spectra	p. 252
8.5.2 Infrared (IR) - Combined Vibrational and Rotational Transitions	p. 252
8.5.3 Near Infrared (NIR) to Visible (VIS)	p. 253
8.5.4 Visible (VIS) to Ultraviolet (UV)-Electron Orbital Transitions	p. 254
8.6 Approximations of Absorption/Emission line Shapes	p. 256
8.6.1 Lorentz Line Shape of the Absorption Coefficient Collision Broadening	p. 257
8.6.2 Thermal Doppler Line Shape	p. 258
8.6.3 Voigt Line Shape-Combined Collision and Doppler Broadening	p. 259
8.7 Spectral Transmissivity and Absorptivity	p. 260
8.7.1 Weak-Line and Strong-Line Approximations	p. 261
8.7.2 Line-By-Line Method (LBLM)	p. 264
8.7.3 Band Models	p. 264
8.7.4 Scaling Techniques for Inhomogeneous Path	p. 266
8.7.5 The k-Distribution Method	p. 267
8.7.6 The Correlated k-Distribution Method (CKDM)	p. 270
8.7.7 Application of the CKDM to Satellite Remote Sensing	p. 271
Problems	p. 272
9 Terrestrial Radiative Transfer	p. 275
9.1 Downward Spectral Radiation	p. 276
9.1.1 Diffuse Downward Radiance I diff.¿ ↓	p. 276
9.1.2 Diffuse Downward Irradiance F diff,¿ ↓	p. 282
9.2 Upward Terrestrial Spectral Radiation	p. 287
9.2.1 Diffuse Upward Radiance I diff,¿ ↑	p. 287
9.2.2 Diffuse Upward Irradiance F diff,¿ ↑	p. 288
9.3 Example of Simulated Spectra	p. 288
9.3.1 Downward and Upward Radiances	p. 288
9.3.2 Influence of Cirrus on Terrestrial Spectral Irradiance	p. 289
9.4 Broadband Terrestrial Radiative Transfer	p. 291
9.4.1 Impact of Cirrus on Irradiance	p. 291
9.4.2 Radiative Cooling and Heating	p. 293
Problems	p. 298
Appendix A Abbreviations, Symbols, and Constants	p. 301
A.1 Acronyms	p. 301
A.2 Subscripts and Superscripts	p. 302
A.3 Greek Symbols	p. 305
A.4 Latin Symbols	p. 306
A.5 Physical Constants	p. 309
A.6 Mathematical Constants	p. 309
References	p. 311
Index	p. 319

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