Preface |
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xi | |
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1 | (10) |
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1.1 Brief Survey of Atmospheric Radiation |
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1 | (2) |
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1.2 A Broadbrush Picture of the Atmospheric Radiation Budget |
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3 | (3) |
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1.3 Solar and Terrestrial Thermal Infrared Spectra in a Cloudless Atmosphere |
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6 | (1) |
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1.4 The Greenhouse Effect |
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7 | (2) |
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1.5 Relevance to the Interpretation of Spaceborne Observations |
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9 | (2) |
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2 Notation and Math Refresher |
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11 | (18) |
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2.1 Physical Dimensions and Prefixes |
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11 | (2) |
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2.2 Some Rules and Conventions |
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13 | (1) |
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13 | (5) |
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2.3.1 Major Vector Operations |
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13 | (2) |
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2.3.2 Use of Index Notation |
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15 | (3) |
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18 | (2) |
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20 | (2) |
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20 | (1) |
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20 | (2) |
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2.5.3 Angle between Two Directions |
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22 | (1) |
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22 | (4) |
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2.6.1 Legendre Polynomials |
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23 | (1) |
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24 | (2) |
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26 | (3) |
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27 | (2) |
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29 | (30) |
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3.1 Electromagnetic (EM) Radiation |
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29 | (7) |
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3.1.1 Maxwell's Equations and Plane-Wave Solutions |
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29 | (2) |
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3.1.2 Wavelength, Frequency, Wavenumber, Dispersion Relation, and Phase Speed |
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31 | (1) |
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3.1.3 Coherence, Incoherence, and Polarization |
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32 | (1) |
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3.1.4 Wave-Particle Duality |
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33 | (1) |
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3.1.5 Atmospheric EM Radiation Spectrum |
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34 | (2) |
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3.2 Basic Radiometric Quantities |
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36 | (7) |
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3.2.1 Radiant Energy Flux, Flux Density, and Radiance |
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36 | (2) |
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3.2.2 Radiant Energy Density and Radiance |
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38 | (2) |
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3.2.3 Irradiance, Emittance, Exitance, and Actinic Radiation |
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40 | (1) |
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3.2.4 Relation between Upward, Downward, and Net Actinic Flux Densities and Radiance |
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41 | (2) |
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3.2.5 Isotropic Radiation Field |
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43 | (1) |
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3.2.6 Reflectivity, Absorptivity, and Transmissivity |
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43 | (1) |
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3.3 Blackbody and Graybody Radiation: Basic Laws |
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43 | (16) |
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43 | (2) |
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3.3.2 Wien's Displacement Law |
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45 | (2) |
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3.3.3 Stefan-Boltzmann Law |
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47 | (1) |
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3.3.4 Rayleigh-Jeans and Wien's Approximations |
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48 | (1) |
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3.3.5 Emissivity and Kirchhoff's Law |
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48 | (3) |
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51 | (8) |
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4 Interactions of EM Radiation and Individual Particles |
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59 | (74) |
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59 | (1) |
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4.2 Complex Index of Refraction |
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60 | (2) |
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4.3 Decomposition of Electric Field Vector |
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62 | (1) |
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4.4 Complex Amplitude Scattering Matrix |
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63 | (1) |
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64 | (2) |
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4.6 Degree of Polarization |
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66 | (1) |
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67 | (3) |
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4.8 Optical Properties of Individual Particles |
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70 | (5) |
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70 | (3) |
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73 | (2) |
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4.9 Spherical Particles (Lorenz-Mie Theory) |
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75 | (9) |
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4.9.1 Assumptions and Goals |
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75 | (1) |
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4.9.2 Efficiency Factors: Qext,Mie, Qsca,Mie, Qabs,Mie |
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76 | (2) |
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4.9.3 Single-Scattering Albedo: ωMie |
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78 | (1) |
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4.9.4 Elements of the Complex Amplitude Scattering Matrix |
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78 | (1) |
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4.9.5 Elements of the Mueller Matrix |
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79 | (1) |
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80 | (2) |
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4.9.7 Phase Function for Unpolarized Incident Radiation: Punp,Mie |
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82 | (1) |
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4.9.8 Asymmetry Factor: gunp,Mie |
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83 | (1) |
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4.10 Rayleigh Scattering and Oscillating Electric Dipole |
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84 | (9) |
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4.10.1 Amplitudes Scattering Matrix and Mueller Matrix |
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84 | (2) |
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4.10.2 Degree of Polarization |
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86 | (1) |
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4.10.3 Rayleigh Phase Function for Unpolarized Incident Radiation: Punp,Rayl |
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86 | (2) |
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4.10.4 Scattering Cross Section and Efficiency Factor |
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88 | (1) |
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4.10.5 Extinction and Absorption Cross Sections and Efficiency Factors |
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88 | (1) |
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4.10.6 Rayleigh Scattering as an Approximation of Lorenz-Mie Theory |
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89 | (2) |
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4.10.7 Rayleigh Scattering in the Atmosphere |
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91 | (2) |
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4.11 Scattering by Nonspherical Individual Particles |
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93 | (6) |
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4.11.1 Analytical Approaches |
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93 | (1) |
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94 | (1) |
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95 | (2) |
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4.11.4 Integrated Optical Properties |
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97 | (2) |
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4.12 Geometric-Optics Method for Light Scattering by Large Particles |
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99 | (23) |
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4.12.1 Directional Changes Due to Reflection and Transmission (Refraction) at a Plane Interface: Snel's Law |
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101 | (4) |
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105 | (1) |
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4.12.3 Fresnel Formulas for Reflection and Transmission |
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106 | (3) |
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4.12.4 Radiant Energy Changes for Transmission (Plane Interface) |
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109 | (2) |
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4.12.5 Radiant Energy Changes for Reflection (Plane Interface) |
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111 | (3) |
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4.12.6 Ray-Tracing Technique |
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114 | (2) |
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116 | (6) |
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122 | (11) |
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125 | (8) |
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5 Volumetric (Bulk) Optical Properties |
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133 | (10) |
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5.1 Particle Size Distribution |
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133 | (3) |
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5.1.1 Analytical Descriptions |
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133 | (1) |
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5.1.2 Integrated Microphysical Parameters |
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134 | (1) |
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135 | (1) |
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5.2 Volumetric (Bulk) Scattering, Absorption, and Extinction |
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136 | (7) |
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140 | (3) |
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6 Radiative Transfer Equation |
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143 | (30) |
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144 | (1) |
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144 | (3) |
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6.2.1 Differential and Exponential Forms |
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144 | (2) |
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6.2.2 Application to Direct Solar Irradiance Sdir,λ |
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146 | (1) |
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6.3 General Formulation of the RTE |
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147 | (9) |
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6.3.1 Spectral Photon Density Function |
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147 | (2) |
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6.3.2 Radiative Transfer Equation in Scattering Media |
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149 | (4) |
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6.3.3 Photon Budget Equation |
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153 | (1) |
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6.3.4 3D Time-Dependent and Stationary RTE for Total Radiance |
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153 | (1) |
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6.3.5 3D Stationary RTE for Diffuse Radiance |
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154 | (2) |
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6.4 1D RTE for a Horizontally Homogeneous Atmosphere |
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156 | (17) |
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6.4.1 Independent Variables |
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156 | (1) |
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6.4.2 Standard Form of 1D RTE for Diffuse Radiance |
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157 | (4) |
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6.4.3 Downward Diffuse Radiance |
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161 | (4) |
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165 | (4) |
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169 | (4) |
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7 Numerical and Approximate Solution Techniques for the RTE |
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173 | (60) |
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7.1 Legendre and Fourier Expansions |
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173 | (14) |
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7.1.1 Expansion of Phase Function in Terms of Legendre Polynomials |
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173 | (2) |
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7.1.2 Truncation of Phase Function and Similarity Principle |
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175 | (3) |
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7.1.3 Atmospheric Angular Coordinates |
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178 | (3) |
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7.1.4 The Delta-M Method (DMM) and Delta-Fit Methods (DFM) |
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181 | (4) |
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7.1.5 Fourier Expansions of Diffuse Radiance and Irradiance |
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185 | (2) |
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7.2 Equations for Fourier Modes of Diffuse Radiance |
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187 | (4) |
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7.2.1 Net Radiative Flux Density in a Nonabsorbing Atmosphere |
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188 | (3) |
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7.3 Method of Successive Order of Scattering (MSOS) |
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191 | (2) |
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7.4 Adding-Doubling Method (A-DM) |
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193 | (12) |
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193 | (3) |
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7.4.2 Generalization for Radiances |
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196 | (6) |
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7.4.3 Application to Flux Densities |
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202 | (3) |
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7.5 Discrete Ordinate Method (DOM) |
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205 | (4) |
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7.6 Spherical Harmonics Method (SHM) |
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209 | (3) |
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7.7 Monte Carlo Method (MCM) |
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212 | (10) |
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213 | (3) |
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7.7.2 Backward (Inverse) Monte Carlo Method (BMCM) |
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216 | (6) |
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7.8 Two-Stream Approximation (TSA) |
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222 | (11) |
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222 | (5) |
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227 | (3) |
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230 | (3) |
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8 Absorption and Emission by Atmospheric Gases |
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233 | (42) |
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8.1 Interactions of Photons and Gas Molecules |
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233 | (4) |
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8.1.1 Types of Molecular Energy Emol |
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233 | (1) |
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8.1.2 Photon Absorption and Emission |
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234 | (1) |
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8.1.3 Allowed Quantized Energies and Frequencies (Wavelengths) |
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235 | (1) |
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8.1.4 Energy Level Probability in Thermal Equilibrium |
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235 | (2) |
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8.2 Examples of Energy Transitions |
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237 | (2) |
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8.2.1 Structure of Gas Molecules |
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237 | (1) |
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8.2.2 Molecular Rotational Energy Enrot |
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238 | (1) |
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8.2.3 Molecular Vibrational Energy Envib |
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238 | (1) |
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8.3 Line Spectra for Single-Atomic Gases |
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239 | (5) |
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8.3.1 Molecular Electron Orbital Energy Enorb |
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239 | (1) |
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8.3.2 Line Spectrum of the Hydrogen Atom |
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240 | (4) |
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8.4 Molecular Absorption/Emission Line Spectra |
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244 | (8) |
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8.4.1 Molecular Rotational Spectra |
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244 | (2) |
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8.4.2 Ratio of Molecular Electron Orbital and Rotational Energies |
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246 | (1) |
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8.4.3 Vibrational Spectra of Diatomic Molecules |
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247 | (1) |
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8.4.4 Combined Molecular Vibration-Rotation Spectra |
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248 | (4) |
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8.5 Examples of Atmospheric Gas Spectra |
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252 | (4) |
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8.5.1 Three General Types of Spectra |
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252 | (1) |
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8.5.2 Infrared (IR) - Combined Vibrational and Rotational Transitions |
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252 | (1) |
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8.5.3 Near Infrared (NIR) to Visible (VIS) |
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253 | (1) |
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8.5.4 Visible (VIS) to Ultraviolet (UV) - Electron Orbital Transitions |
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254 | (2) |
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8.6 Approximations of Absorption/Emission Line Shapes |
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256 | (4) |
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8.6.1 Lorentz Line Shape of the Absorption Coefficient - Collision Broadening |
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257 | (1) |
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8.6.2 Thermal Doppler Line Shape |
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258 | (1) |
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8.6.3 Voigt Line Shape - Combined Collision and Doppler Broadening |
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259 | (1) |
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8.7 Spectral Transmissivity and Absorptivity |
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260 | (15) |
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8.7.1 Weak-Line and Strong-Line Approximations |
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261 | (3) |
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8.7.2 Line-By-Line Method (LBLM) |
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264 | (1) |
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264 | (2) |
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8.7.4 Scaling Techniques for Inhomogeneous Path |
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266 | (1) |
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8.7.5 The k-Distribution Method |
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267 | (3) |
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8.7.6 The Correlated k-Distribution Method (CKDM) |
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270 | (1) |
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8.7.7 Application of the CKDM to Satellite Remote Sensing |
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271 | (1) |
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272 | (3) |
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9 Terrestrial Radiative Transfer |
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275 | (26) |
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9.1 Downward Spectral Radiation |
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276 | (11) |
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9.1.1 Diffuse Downward Radiance I↓diff,λ |
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276 | (6) |
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9.1.2 Diffuse Downward Irradiance I↓diff,λ |
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282 | (5) |
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9.2 Upward Terrestrial Spectral Radiation |
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287 | (1) |
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9.2.1 Diffuse Upward Radiance I↓diff,λ |
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287 | (1) |
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9.2.2 Diffuse Upward Irradiance F↓diff,λ |
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288 | (1) |
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9.3 Example of Simulated Spectra |
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288 | (3) |
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9.3.1 Downward and Upward Radiances |
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288 | (1) |
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9.3.2 Influence of Cirrus on Terrestrial Spectral Irradiance |
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289 | (2) |
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9.4 Broadband Terrestrial Radiative Transfer |
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291 | (10) |
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9.4.1 Impact of Cirrus on Irradiance |
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291 | (2) |
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9.4.2 Radiative Cooling and Heating |
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293 | (5) |
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298 | (3) |
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Appendix A Abbreviations, Symbols, and Constants |
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301 | (10) |
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301 | (1) |
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A.2 Subscripts and Superscripts |
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302 | (3) |
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305 | (1) |
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306 | (3) |
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309 | (1) |
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A.6 Mathematical Constants |
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309 | (2) |
References |
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311 | (8) |
Index |
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