Zdunkowski W., Trautmann T., Bott A. Radiation in the atmosphere: A course in Theoretical Meteorology
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Index
absorption, 17
absorption coefficient, 23, 359, 374
generalized, 236
gray, 196
monochromatic, 303
of the Doppler line, 214
of the Lorentz line, 184, 208
of the Voigt line, 215
spectral, 302
absorption cross-section, 360
absorption function, 126
monochromatic, 204, 218
absorption probability, 23
actinic flux, 95
addition theorems, 85
adjoint linear differential operator, 135
adjoint radiance, 135
adjoint solution techniques, 133
albedo, 4
global, 4, 444
of the ground, 77
of the Lambertian ground, 433
amplitude spectrum, 206
anisotropic media, 24
aphelion, 8
associated Legendre equation, 312
asymmetry parameter, 167
atmospheric window region, 51, 176
attenuation coefficient, 374
azimuth angle, 13
azimuthally integrated form, 45
Babinet’s principle, 370
backscattered fraction, 162
backscattering coefficient, 162, 367
band models, 217
Beer’s law, 34, 66, 121, 303, 332
Bessel functions, 220
modified of the first kind, 220
of the first kind, 221
spherical, 340
spherical of the first kind, 349
Bessel’s differential equation, 340
bidirectional reflection function, 130
black body, 38, 185
black body emission of the Earth’s surface,
193, 415
black body radiation, 1, 192
Boltzmann constant, 20, 211
Boltzmann distribution, 302
Bouguer–Langley method, 406
budget equation for photons, 28
Chandrasekhar’s X- and Y-functions, 80
characteristic energy levels, 292
characteristic function, 80
characteristic state, 289
circle of precession, 16
classical emissivity method, 184
cloud forcing, 445
coherence time, 393
coherent state, 289, 290
collision broadening, 205
collision cross section, 210
complex index of refraction, 40, 333, 335, 346
concept of a supermatrix, 397
conservative scattering, 26
continuity equation for the mass, 29
cooling to space term, 188
correlated k-distribution, 240
Curtis–Godson approximation, 256
curve of growth, 218
(2J + 1) degeneracy, 313
degenerate state, 300
depolarization correction, 366
dielectric constant, 329
differential absorbing mass, 303
diffuse solar radiation, 34
dipole moment, 284
direct solar beam, 34
DISORT, 104, 437
distribution function of photons, 18
Dobson Network for total ozone measurements, 408
Doppler broadening, 205, 421
Doppler effect, 205
478
Index 479
Doppler line, 211
Doppler shift, 211
double-Gaussian quadrature, 99
E-state, 385
eccentricity, 15
Eddington approximation, 167
classical, 167
δ-, 169
effective particle radius, 372
effective variance, 372
efficiency factor, 360
for absorption, 360
for extinction, 360
for scattering, 360
eigenfrequency, 278
eigenstate, 289
eigenvibration, 278
Einstein coefficient, 301
of absorption, 301
of induced emission, 301
of spontaneous emission, 301
Einstein’s mass–energy relation, 291
elastic scattering, 17
electric dipole moment transition, 297
electric field vector, 294
electric susceptibility, 329
electrical conductivity, 329
emission, 2, 26, 32, 204
of an isothermal layer, 192
emission coefficient, 26
monochromatic, 204
emission source function, 38
emissivity of the ground, 114
energy, 276
electronic, 276
rotational, 276
vibrational, 276
energy density, 19
energy state, 2
rotational, 2
vibrational, 2
equation of time, 9, 11
equatorial bulge, 15
equinox points, 9
equivalent width, 218
excited state, 204
exponential integral, 61, 62
exponential matrices, 53
exponential sum-fitting of transmissions, 237
extinction coefficient, 25, 359, 374
extinction cross-section, 360
extinction paradox, 370
extraterrestrial solar flux, 35
feedback process, 446
field of view, 401
field theory, 334
figure axis of the molecule, 325
first law of thermodynamics, 37
flux-emissivity equations, 186
flux-emissivity function, 186
flux-transmission function, 60, 184
forbidden transitions, 303
formal solutions of the RTE, 53
forward method, 133
forward problem, 400
Fraunhofer diffraction theory, 370
Gauss–Legendre quadrature formulas, 47
generalized coordinate, 277
generalized velocity, 277
geographical coordinates, 13
Godson’s inverse power model, 228
Goody, 64, 196, 199, 209, 226
Goody’s exponential model, 226
gray absorber, 190
greenhouse gases, 4
Greenwich mean time, 12
H-function, 70
half-day length, 14
half-width, 208
of the Doppler line, 214
of the Lorentz line, 208
of the Voigt line, 216
Hamilton function, 293
Hamilton operator, 293
classical, 293, 328
quantum mechanical, 293
Hankel functions, 350
spherical of the first kind, 350
harmonic oscillator, 304
heat flux, 37
Heaviside step function, 144
Heisenberg’s uncertainty principle, 289, 306
Helmholtz’s principle of reciprocity, 65
Henyey–Greenstein phase function, 167, 255
Hermite polynomials, 306
recursion formula, 317
Hermite’s differential equation, 306
Hooke’s law, 276
Hopf–Bronstein relation, 81
hour angle of the Sun, 12
hyperfine structure, 304
ill-posed inverse problem, 400
index of refraction, 30, 331
inelastic scattering, 17
infrared radiation spectrum, 2
inner product, 134
inscattering, 29
instrument signal, 401
intensity, 331
interaction Hamiltonian, 296
internuclear axis, 285
inverse problem, 400
irradiance, 331
isotropic media, 24
isotropic scattering process, 25
Jordan matrix, 107
480 Index
k-distribution method, 240
correlated, 237, 248
Kirchhoff’s law, 1, 38, 62
L-state, 385
Ladenburg and Reiche function, 221
Lagrange’s equation of motion, 277
Lagrangian function, 277
Lambert’s law, 75
Lambertian surface, 75, 139
Laurent series, 269
law of darkening
Legendre polynomials, 40
addition theorem, 42
associated, 40, 313
orthogonality relation, 41
Legendre’s differential equation, 349
lidar, 399
limb sounding, 403
line broadening, 204, 241, 421
line intensity, 208
of the Lorentz line, 208
line overlap, 218
line strength, 208
line-by-line integration, 237
line-by-line models, 217
line-shape factor, 209
for monochromatic emission, 213
of the Doppler line, 214
of the Lorentz line, 209
of the Voigt line, 215
linear differential operator, 134
linear interaction principle, 84
linear polarization, 378
local mean time, 11
local standard time, 13
local thermodynamic equilibrium, 1, 61
long-wave radiation, 2
Lorentz, 205
Lorentz broadening, 205, 421
Lorentz force, 294
Lorentz line, 205
Loschmidt’s number, 246
magnetic field vector, 294
magnetization, 328
Marshak boundary condition, 109
mass absorption coefficient, 24, 184
matrix operator method, 82
matrix–vector form of the RTE, 50
maximum overlap, 179
Maxwell’s equations, 5, 328, 333, 334
Maxwell–Boltzmann distribution, 320
Mayer–Goody model, 226
mean solar day, 11
microwave emission, 399
Mie calculations, 333
Mie intensity functions, 363
Mie phase function, 167, 255
Mie scattering, 17, 254
Mie size parameter, 40
Mie theory, 40, 333
Mie–Debye theory, 167
Milankovitch theory, 446
modal matrix, 107
momentum, 16
monochromatic light, 393
monochromatic line, 213
monochromatic radiative equilibrium, 197
monochromatic source, 393
Morse function, 307
multiplication property of the transmissions, 218
nadir-looking mode, 403
natural broadening, 205
natural light, 393
net radiative flux density, 2
monochromatic, 196
net radiative flux density vector, 22
spectral, 22
net sensitivity coefficient, 444
noise, 401
nondegenerate energy levels, 300
normal coordinates, 281
normal mode of vibration, 278
nuclear spin, 304
nutation, 16
one-parameter scaling, 256
optical air mass, 405
optical depth, 24, 39
for absorption, 24
for scattering, 24
orthogonality relations of the trigonometric
functions, 43
outscattering, 28
overlap effects, 189
P branch, 316
P-state, 385
partial polarization, 394
partially polarized light, 393
partition function, 321
perfect scattering, 371
perfect thermodynamic equilibrium, 19
perihelion, 8
permeability, 328
permittivity, 328
perturbation integral, 149
perturbation technique, 133
perturbation theory, 147
phase function, 25, 31, 51, 68, 96, 135, 255
δ-scaled, 97, 158
phase matrix, 396
phase space, 134
photon, 16, 28
Planck function, 19, 33, 178, 418
Planck’s constant, 16, 204, 289
Planck’s radiation law, 1, 302
Planck’s relation, 204
Planckian black body radiation, 54, 394
Planckian emission, 176, 395, 413
Index 481
plane–parallel approximation, 37
planetary problem, 75
Poincar´e sphere, 384
polar night, 14
polarization, 284, 328
polarization ellipse, 378
polarized light, 393
power spectrum, 206
Poynting vector, 331
practical improved flux method, 170
pressure scaling factor, 258
pressure broadening, 205, 212
principal axes, 323
principle of invariance, 64, 69
probability density, 289
probability distribution function, 289
pseudo-radiance, 136, 435
pseudo-source, 136
Q branch, 316
quadratically integrable normalized functions, 289
quantum number, 313
magnetic, 313
rotational, 313
R branch, 316
R-state, 385
radar, 399
radiance, 18
radiation chart, 190
radiative effect, 143, 434
radiative equilibrium, 36, 195
radiative temperature change, 59, 145, 194
radiative transfer equation, 28, 82, 395
adjoint form, 135
nonstationary form, 33
vector form, 395
radiative–convective equilibrium, 201
Raman scattering, 17
random overlap, 179
Rayleigh, 355
Rayleigh scattering, 17, 80, 254, 355, 396
Rayleigh–Jeans distribution, 27
reduced absorber mass, 184, 257
reduced parallel solar flux density, 66
reflection coefficient, 176
for diffuse radiation, 176
for primary scattered solar radiation, 176
reflection matrix, 89
reflectivity, 83
regular method, 133
relative permeability, 329
relative permittivity, 329
remote sensing, 399
active, 399
airborne, 400
ground-based, 400
spaceborne, 400
passive, 399
resonance case, 174
response function, 144, 401, 418
restricted problem, 64
retrieval process, 400
Riccati–Bessel functions, 352
Robert’s approximation, 202
rotational constant, 321
rotational partition function, 321
60 GHz O
2
complex, 416
scaling parameter, 257
scaling path length, 257
scattering albedo, 119
scattering angle, 24
scattering coefficient, 24, 359, 366, 374
scattering cross-section, 360
of an air molecule, 407
scattering function, 24, 64, 366
scattering matrix, 392
scattering phase function, 25, 36, 254, 366
scattering plane, 354, 386
scattering process, 17
Schr¨odinger equation, 291
time-dependent, 293
Schwarzschild equation, 202
Schwinger functional, 150
Schwinger’s variational principle, 149
semi-classical treatment, 297
sensitivity coefficient, 444
for long-wave radiation, 444
for solar radiation, 444
short-wave radiation, 2
sidereal day, 11
single scattering albedo, 26, 34, 254
slit function, 401
sodar, 399
solar aureole observation, 413
solar constant, 4, 9, 35
solar day, 11
solar declination, 9
solar height, 13
solar radiation spectrum, 2
solar zenith angle, 13
solid angle element, 18
solution methods of the RTE, 82
quasi-exact, 82
sonar, 399
source function, 33, 83, 176, 395
for true emission, 33, 134
spaceborne solar occultation measurements,
408
space quantization, 325
specific enthalpy, 37
specific heat at constant pressure, 37
specific internal energy, 37
spectral black body radiance, 19
spectral lines, 204
spectral window region, 5
speed of light, 16
spontaneous emission, 300
square-root law, 222
standard problem, 64, 138
star-product algorithm, 89
482 Index
Stark effect, 325
state function, 288
statement of the invariance, 67
stationary state, 289
statistical weight, 300
Stefan–Boltzmann constant, 8, 21
Stefan–Boltzmann law, 8, 27
stimulated emission, 301
Stokes integral theorem, 338
Stokes parameters, 383
modified, 391
Stokes vector, 385, 395
streaming term, 135
strong encounter, 205
strong line approximation, 222
successive order of scattering, 93
symmetry properties of the phase
function, 111
tangent height, 408
thermal broadening, 205, 215
thermal emission, 2, 45
of the ground, 91
thermal radiation, 1
thermal source vector, 89
thermodynamic equilibrium, 1, 196
thermodynamic heat equation, 161
total solar radiation field, 34
translational energy, 2
transmission, 35, 122, 419
mean, 418
monochromatic, 417
transmission coefficient, 176, 352
for diffuse radiation, 176
for direct solar radiation, 176
for primary scattered solar radiation, 176
transmission function, 35, 56, 64, 183, 224, 237
for nonoverlapping lines, 236
transmission matrix, 89
transmissivity, 83
true solar time, 11
two-stream methods, 82, 162
Twomey effect, 451
universal time, 12
unpolarized light, 393
vacuum boundary conditions, 130, 138, 434
vector wave functions, 341
vibration, 282
ν
1
-, 282, 288
ν
2
-, 283, 288
ν
3
-, 282, 288
parallel, 284
perpendicular, 284
vibrational ground state, 306
vibrational quantum number, 309
vibrational transitions, 276
Voigt line, 214
Voigt profile, 205
wave equation, 339
scalar form, 339
vector form, 339, 341
wave function, 288
weak line approximation, 221
weighting function, 402, 414
Wien distribution, 27
Wien’s displacement law, 20
Zeeman effect, 325
zero point energy, 306