Cambridge University Press 978-0-521-88916-2 — Light Scattering by Ice Crystals Kuo-Nan Liou , Ping Yang Index More Information

Index

120° parhelion, 133, 134, see also halo A-Train satellite constellation, 259, 260 1-D climate model, 365 cloud and aerosol interactions, 366 1-D model, 51, 361, 363, 364 deposition, 192, 193 detection of thin cirrus, 286, 287 22° halo, 133, 134, see also halo direct and indirect effect of, 361, 362, 380 22° parhelion, 130, 133, see also halo historical review of polarization measurements, 302 2-D climate model, 366 radiative transfer, 332 radiative transfer results compared with satellite 46° halo, 128, 132, 134, 186, 189, 220, 233, 268, 269, observations, 346, 348 see also halo soot and sulfate aerosols, 379, 380 view from satellite instruments, 14, 16 absorbing boundary conditions, 204 Aerosol Polarimetry Sensor, 302 absorptance, 80, 255 AGCM, 366, 370, see also GCM absorption aggregate, 20, 32, 35, 38, 39, 42, 43, 47, 49, 216, 218, coefﬁcient, 77, 78, 80, 325, 335, 336, 337 233, 234, 239, 271, 273, 303 cross-section, 55, 56, 156, 157, 175, 176, 330 Airborne Visible/Infrared Imaging Spectrometer, 286 efﬁciency, 168 AIRS, 11, 259, 277, 279, 280, 281, 300, see also line, 250, 252, 279, 321, 323, 328, 333, 335, 336, Atmospheric Infrared Sounder 338 Airy function, 167 spectrum albedo CH4, 250 cloud, 344, 351, 361 CO, 250 global, 293, 390 CO2, 250 planetary, 346 H2O, 250 shortwave, 349 N2, 250 single-scattering, see single-scattering albedo N2O, 250 solar, 341, 342, 344, 359, 360, 361, 362, 364, 373, O2, 250 374, 377 O3, 250 surface, 254, 255, 257, 263, 266, 291, 293, 295, Ac, see altocumulus 305, 321, 322, 341, 342, 344, 353, 355, 366, accretion, 29, 33, 47, 192, 277, 360 373, 384 ACCRI, 375, 377, 380, see also Aviation Climate TOA, 347, 348 Change Research Initiative total-sky, 348 ADDA, 212, 234, 243, 246 altocumulus, 2 adding method, 112, 339 altostratus, 2 ADEOS, 302, 303, 304 AMSR2, see Advanced Microwave Scanning Advanced Earth Observing Satellite, see ADEOS Radiometer 2 Advanced Microwave Scanning Radiometer 2, 259 AMSR-E, see Advanced Microwave Scanning Advanced Microwave Scanning Radiometer-EOS, 259 Radiometer-EOS Advanced Microwave Sounding Unit, 11, 259, 279 Amsterdam DDA, 212, see also ADDA Advanced Very High Resolution Radiometer, 5, 6, 286 AMSU, 280, see also Advanced Microwave Sounding aerosol Unit as atmospheric composition, 249 AMSU-A, 259

427

428 Index

analyzer, 92 BDC, see Brewer–Dobson circulation anomalous dispersion, 77 Beer’s law, 79 anthelion, 131, 134, see also halo Bessel function, 68, 71, 74, 136, 141, 144, 223 anvil, 5, 42, 50, 279, 306, 382, 383, see also tropical bidirectional reflectance anvil climate studies, 327 APS, see Aerosol Polarimetry Sensor ice spectral, 257 Aqua, 14, 258, 259, 269, 279, 283, 285, 376, see also reflected line spectra in 1.38 and 0.76 µm bands, MODIS, A-Train 318, 319, 324 ARM, 13, 42, 43, 49, 287, 288, 292, 295, 300, 346, reflected polarization from ice clouds, 305 348, see also Atmospheric Radiation relative position of sun–satellite system, 254 Measurement remote sensing, 248, see also remote sensing As, see altostratus retrieval associated Legendre function, 73 algorithm for vertical sizing, 293 asymmetry factor of cirrus cloud parameters, 325 comparison with FDTD and DDA, 173 single-scattering properties of ice spheres, 102 current MODIS operation program, 273 birefringence, 78, 79, 147 effect of ice crystal shape on cloud radiative Bishop’s ring, 117 forcing, 367 black carbon, see also BC FDTD 1-D cloud–precipitation–climate model, 362 and DDA, 174 application to climate studies, 341 and PSTD, 220 cirrus radiative forcing, 355 for ice sphere and circular cylinder, 102 contrail cirrus, 370 invariant imbedding T-matrix method, 237 high thin clouds, 391 Koch snowflake, 184 Rayleigh–Gans–Debye approximation, 176 radiative forcing of cirrus clouds, 350 single-scattering parameterization for ice crystals, RGD approximation, 175 333 single-scattering parameterization for ice crystals, snow grains contaminated by, 192 333 unified theory for light scattering, 180, 184 snow grain contaminated by BC and dust, 192 blackbody, 285, 342, 383, 384 surface wave approach for sphere, 167, 168, 169, blue sky, 1, 5, 6 171 BRDF (bidirectional reflectance distribution two-channel inversion, 264 function), 254, 255, 256, 257 unified theory, 178, 179, 181, 184 Brewer–Dobson circulation, 382 asymmetry parameter, 306, 331, 348, see also brightness temperature, 270, 274, 281, 285, 307, see asymmetry factor also temperature atmospheric composition, 248, 357, 375 difference, 13, 15, 274, 280, 287, 288, see also Atmospheric Infrared Sounder, 11 BTD Atmospheric Radiation Measurement, 13, 42, 295, broadband emissivity, 336 346 BTD, 13, 15, 16, 274, 287, see also brightness A-Train, 13, 14, 257, 275, 292, 302, 316, 386 temperature attenuation, 59, 123, 252, 315, 339 bullet rosette Aura, 258, 259, 386 depolarization ratio, 316 AVHRR, 5, 279, 286, 374, see also Advanced Very FDTD method, 215 High Resolution Radiometer improved geometric optics approach, 163 Aviation Climate Change Research Initiative, 375 in contrails and contrail cirrus, 370 AVIRIS, 286, 318, see also Airborne Visible/Infrared invariant imbedding T-matrix method, 234 Imaging Spectrometer phase function, 268 azimuthal angle, definition of, 107 snow grains, 193 unified theory for light scattering, 182 Babinet’s principle, 117, 134, 148, 155, 170, 171, 178 backscattering, 11, 12, 14, 45, 104, 112, 117, 147, CAGEX (CERES/ARM/GEWEX Experiment), 346, 163, 176, 247, 267, 288, 306, 308, 310, 311, 347, 348, 349, 350 312, 313, 314, 315, 316 CALIOP, 14, 16, 259, 288, 306, 316, 318, see also backscattering depolarization ratio, see depolarization Cloud-Aerosol Lidar and Infrared Pathfinder ratio Satellite Observations band model, 336 CALIOP/IIR, 259 BC, 180, 192, 193, 195, 196, 355, 357, 362, see also CALIPSO, see Cloud-Aerosol Lidar and Infrared black carbon Pathfinder Satellite Observations

Index 429

A-Train satellite constellation, 259, 260 aerosol–cloud interactions, 361 backscattering depolarization, 306, 316 anthropogenic, 277 contrails and contrail cirrus, 376 clouds and cloud feedback, 327 high thin clouds, 387, 390 contrails and contrail cirrus, 371 mechanism of stratosphere dehydration, 386 detection of thin cirrus, 285 role of cirrus in UTLS exchange, 382 greenhouse gases, 248 view from satellite instruments, 14 impacts of aviation soot on cirrus, 380 CAM, 370, 377, 378, 387, see also Community natural variability and anthropogenic perturbations, Atmosphere Model 357 carbon dioxide, 248, 255, 359, 371 physical and microphysical properties of contrails, carbon monoxide, 248, 259 374 CART, 346, 348, see also Cloud and Radiation RFs resulting from aviation produced contrails, Testbed 377 Cartesian coordinate, 38, 72, 90, 94, 107, 168, 311 role of cirrus in UTLS exchange, 380 Cb, 3, 5, see also cumulonimbus role of ice clouds, 390 Cc, 2, see also cirrocumulus climate model CCN, 180, 359, 360, 361, see also cloud condensation 1-D climate–cirrus cloud model, 363, 364 nuclei 1-D cloud–precipitation–climate model, 359, 360, Central Equatorial Pacific Experiment, 42, see also 361 CEPEX cirrus cloud vertical profile effect, 289 CEPEX, 42, 46, 47, 266, 267, 292, see also Central cirrus radiative forcing, 351, 353 Equatorial Pacific Experiment comparison with satellite observations, 346 CERES, 11, 259, 277, 283, 346, 389, see also Clouds contrails and contrail cirrus, 373 and the Earth’s Radiant Energy System detection of thin cirrus, 286 CERES/ARM/GEWEX Experiment, 347, see also effect of interactive ice crystal size on precipitation, CAGEX 365 CESM, see Community Earth System Model energy balance climate model, 373 CF2Cl2, 339 general circulation model, 45, 289, 332 CF3Cl, 339 high thin ice clouds, 390 CFC, 249, 339 MODIS C6 products, 277 CFCl3, 339 one-dimensional, 358, 359 CFL, 204, 216, see also Courant–Friedrichs–Lewy radiative forcing of cirrus clouds, 350 condition radiative transfer, 340 CGOM, 162, 178, see also conventional geometric single-scattering parameterization for ice crystals, optics 332 CH4, 101, 248, 249, 251, 252, 335, 338, 339, 343, see thin cirrus detection and comparison with GCM, also absorption spectrum; methane 386 chemical composition cloud of atmosphere, 380, 386 absorptance, 283, 342 of particles, 239 condensation nuclei, 180, 360, see also CCN chlorine, 259 cover, xiv, 9, 275, 285, 348, 351, 355, 363, 371, chlorofluorocarbon, see CFC 373, 386, 389, 390 Christiansen effect, 102, 333 overlap, 348, 377, 385, 389 Ci, 2, see also cirrus radar system, 306 circular polarization, 86, 90, 91, 92 radiative forcing, 321, 328, 350, 351, 355, 362, 370, circumzenithal arc, 133, 134, see also halo 389, 390, see also CRF cirrocumulus, 2, 41, see also Cc reflection, 262, 351 cirrostratus, 2, 41, 43, 57, 103, 104, 114, 319, 320, see resolving model, 51 also Cs water content, 29, 365 cirrus, 2 Cloud and Radiation Testbed, 346 CIRRUS, 323 Cloud Particle Imager, 33 cirrus radiative forcing, 351, 355 Cloud Profiling Radar, 259, 295, 387, see also CPR CKD, 337, 338, see also correlated k-distribution Cloud-Aerosol Lidar and Infrared Pathfinder Satellite method Observations, 14, see also CALIPSO Clausius–Clapeyron equation, 22, 24 Cloud-Aerosol Lidar with Orthogonal Polarization, climate change 14, 259, 316, see also CALIOP 3-D cloud structure, 365 Clouds and the Earth’s Radiant Energy System, 11, ACCRI program, 375 259, see also CERES

430 Index

CloudSat, 13, 259, 260, 295, 386, 387, 389 continuum absorption, 338 coccolith, 237 contrails and contrail cirrus coccolithophore, 237 CALIOP, 14 column climate issues, 370 ADDA, PSTD, and EGOH, 246 contaminated ice particles in, 192 backscattered depolarization, 312, 313 contemporary programs, 374, 375, 380 backscattering depolarization, 309 early studies, 371 classification, 32, 33 ice crystal size and shape spectra, 42, 43 comparison of GOS with FDTD and DDA, 173, 174 introduction to clouds, 5 computer-generated, 35, 38 lidar, 316 crystal size and shape distribution, 271, 272, 277, radiative forcing, 333 292 solar heating rate, 355 depolarization ratio, 316 SUCCESS, 51 effect of size distribution, 267, 268 UTLS, 380 extinction cross-section, 330 convection, 2, 8, 9, 42, 46, 50, 52, 358, 359, 366, 380, FDTD, 214 385, 387 and PSTD, 220 convective adjustment, 359 generalized parameterization, 332 conventional geometric optics, 159, 162, 180, 325, geometric ray-tracing, 124, 146 330, 331, 333 GOS, 173 convolution PML, 198 growth by riming, 29 coordinates horizontal orientation, 112, 114, 129, 132, 303, body-framed, 137 310, 311 Cartesian, see Cartesian coordinate ice crystal cylindrical, 68, 70 habits, 25 polar, 135 shape, 41 pressure, 335 IGOM, 163 rectangular, 118 II-TM right-handed, 150 and DDA, 233 spherical, 65 and IGOM, 238 spheroidal, 72 in contrails and contrail cirrus, 370 corona, 116, 117, 134, 136 measured and computed BRDF, 257 correlated k-distribution method, 257, 279, 319, see metamorphism, 193 also CKD; k-distribution MPACE observations, 49 Courant–Friedrichs–Lewy condition, 204 NaF, 186 CPI, 33, 42, see also Cloud Particle Imager polarization measurements, 303 CPML, 198, see also convolution PML pristine habit model, 269 CPR, 259, 295, see also Cloud Profiling Radar PSTD and IGOM, 219 CRF, 321, 323, see also cloud radiative forcing ray-by-ray and FDTD, 214 critical lapse rate, 359 relation between maximum size and width, 43 CRM, 51, see also cloud resolving model retrieved asymmetry parameter, 306 CRS, 306, 307, see also cloud radar system scattering and absorption properties, 344 CRYSTAL-FACE (Cirrus Regional Study of Tropical single-scattering input to radiative transfer, Anvils and Cirrus Layers – Florida Area 264 Cirrus Experiment), 47, 292, 306 single-scattering parameterization, 328 Cs, 2, see also cirrostratus smooth-solid crystal distributions, 283 Cu, 2, see also cumulus unified theory, 182 cumulative probability, 257, 319, 336, 338 video cloud-scope image, 189 cumulonimbus, 3, 8, 41, 51, 249, 360, 383, see also Cb volume and geometric cross-section, 329 cumulus, 2, 3, 9, 22, 41, 42, 46, 50, 358, 366, 382, Community Atmosphere Model, 370, 387 387, see also Cu Community Earth System Model, 376 Curtis–Godson approximation, see two-parameter complex angular momentum theory, 166, 168 Curtis–Godson approximation complex refractive index, 61, 73, 77, 115, 121, CWC, 29, see also cloud water content 165, 175, 200, 203, 255, see also refractive cylindrical coordinates, see coordinates index conductivity, 24, 61, 198, 200, 203, 363, see also D4S, 279, 280, 281, see also delta-four-stream specific conductivity; thermal conductivity approximation

Index 431

DDA, 173, 178, 182, 197, 212, 233, 234, 237, 239, homogeneous and heterogeneous nucleation, 19 241, 243, 244, 246, see also discrete dipole laboratory scattering for, 186 approximation supercooled water, 22 degree of linear polarization, 93, 103, 176, 183, 225, two-channel inversion technique, 262, 264 237, 301, 302 dust dehydration, 50, 382, 383, 386 atmospheric composition, 249 delta cloud configurations and dynamic and circulation four-stream approximation, 341 patterns, 341 function, 110, 158, 206, 242 DDA, 239 transmission, 134, 157, 158 detection of thin cirrus, 287 dendrite, 24, 29, 35, 39, 41, 58, 125 mineral, 362 depolarization snow grains contaminated by, 192, 193, 195, 196 ratio, 104, 112, 235, 310, 311, 313, 314, 315, 316, view from satellite, 14, 16 318 technique, 11, 14, 16, 112, 315 Earth radiation budget, 345, 389 deposition, 5, 19, 20, 53, 56, 192, 193 Earth System Science Pathfinder Project, 258, 323 Descartes, 31, 117 Earth’s atmosphere, 1, 12, 46, 50, 106, 115, 116, 118, dichroism, 113 134, 146, 175, 182, 247, 248, 250, 301, 323, dielectric medium, 160 333, 350, 366, 390 dielectrics, 61 Earth’s orbit, 357 diffraction EBCM, 222, 223, 225, 228, 243, see also extended Babinet, 117, see also Babinet’s principle boundary condition method circular aperture, 134, 135, 141, 144, 171 ECMWF, see European Centre for Medium-Range Fraunhofer, 134, 148, 155, 158, 171, 235 Weather Forecasts hexagonal cylinder, 139, 140, 143, 144 Eddington’s approximation, 340 rectangular parallelepiped, 138, 143, 144 edge effect, 116, 117, 167, 170, 173, 214, see also sphere, 135, 136, 144, 145 surface wave spheroid, 140, 142, 144 effective emittance, 285 three-axis ellipsoid, 142, 144 effective particle size, 16, 264, 283, 296, 305, see also diffusion, 22, 25, 29, 47, 53, 54, 56, 277, 360, 363, mean effective radius 366 effective size, see also mean effective size dimethyl sulfide, 360 cirrus radiative forcing, 351 dipole moment, 75, 239, 240, 253 cloud-top and cloud-base, 289, 295 direct effect, 362 dispersion, 301 discrete dipole approximation, 173, 238, see also phase matrix, 182 DDA validation of retrieval technique, 266 discrete-ordinates method, see radiative transfer variance, 268 dispersion effective variance, 260, 263, 267 of light, 115, 333 efficiency factor, 172, 261 of size distribution, 272, 301 efficient geometric optics hybrid, 245, see also divergence theorem, 242 EGOH DMS, see dimethyl sulfide EGOH, 245, 246 DOE (Department of Energy), 13, 43, 49 electric Doppler, 11, 335 charge density, 60 doubling method, 196, 264 current density, 60 droplet, see also water droplet dipole moment, 239, 240, see also dipole moment 1-D climate model, 357 displacement, 60, 75, 76 1-D cloud–precipitation–climate model, 359, field, 59, 75, 83, 86, 87, 91, 93, 96, 112, 118, 122, 361 149, 151, 152, 153, 159, 178, 201, 202, 206, application to lidar, 315 222, 228, 239, 242, 308 backscattering depolarization, 309 vector, 60, 62, 68, 71, 77, 84, 87, 91, 93, 95, 122, classification of ice crystals, 32 151, 207, 240, 307, 308, 310, 312, 313 contrails and contrail cirrus, 370 electromagnetic definition of optical depth and mean effective size, equivalence theorem, 159 260, 261 field, 60, 158, 199, 201, 205 growth by accretion, 29 wave, 58, 61, 68, 76, 77, 83, 85, 86, 120, 121, 149, growth by diffusion, 24 159, 197, 203, 205, 220

432 Index

electronic, 251, 253, 323 cross-section, 95, 97, 98, 107, 148, 157, 160, 161, elevation angle, 130, 131 180, 189, 199, 261, 330 elliptical polarization, 87, 90, 91 efficiency, 75, 101, 148, 158, 162, 168, 173, 178, ellipticity, 24, 87, 88, 89, 91, 93, 109, 301 184, 213, 237, 272, 333 Elsasser, 336 extraordinary wave, 78, 79 emission absorption line, see absorption FAA, 374, 375, 380, see also Federal Aviation absorption spectrum, 250, 251 Administration AIRS, 280 fair-weather cumulus, 2 A-Train, 259 far field, 68, 71, 93, 96, 134, 135, 139, 146, 147, 158, by non-black cirrus clouds, 350 159, 171, 178, 199, 207 cirrus cloud vertical profile, 293 far-infrared spectra, 210 clouds, 342 FDTD, 163, 173, 178, 180, 197, 199, 200, 201, 204, dimethyl sulfide, 360 206, 207, 208, 209, 212, 214, 215, 218, 221, downward thermal IR from high clouds, 244, 246, see also finite-difference time 373 domain from underlying surface, 383 Federal Aviation Administration, 374, see also line spectra for Earth remote sensing, 319 FAA microwave, 386 feedback, 50, 51, 300, 327, 333, 351, 357, 359, 361, NOx, 374 364, 365, 370, 373, 374, 377, 380, 382, 386, radiative transfer equation, 107, 108, 254 390 water vapor from aircraft, 370 finite-difference time domain, 162, 163, 174, 198, emissivity 292, see also FDTD broadband, 336 FIRE, 41, 51, 264, 292, 341, 343, 344, see also First cirrus, 373 ISCCP Regional Experiment cirrus cloud, 259 first indirect effect, 361 cloud, 344 First ISCCP Regional Experiment, 41, 341 CO2 slicing method, 9 flux 346, see also flux density downward, 343 broadband, 343, 346 infrared, 341 downward, 348, 357 k-coefficient, 280 eddy, 363 surface albedo at 3.75 µm, 293 forward calculation, 348 upward, 343 in the g space, 338 emittance, 283, 285 infrared, 335, 377 energy balance climate model, see climate interpretation of observed data, 344 model IR, 250, 341, 367 energy conservation principle, 107, 209 mass, 386 Environmental Protection Agency, 375 net, 355 EPA, see Environmental Protection Agency Poynting vector, 83, 120 equilibrium temperature, 250, 327, 336, 373, precipitation, 359 383 radiative, xiv, 50, 56, 102, 259, 331, 340, 341, 350, ERB, 346, 389, see also Earth radiation budget 374, 382 ESSP, 258, 323, see also Earth System Science radiative transfer, 339 Pathfinder Project sensible and latent heat, 358 EUCREX (European Cloud and Radiation solar, 109, 110, 250, 254, 293, 332, 367 Experiment), 51, 303, 305 surface, 350 European Centre for Medium-Range Weather TOA, 328 Forecasts, 387 vertical profiles, 346 expansion coefficient, 55, 73, 222, 225, 230, 328, 331, water vapor, 383 333, 338, 340, 353 flux density, 55, 96, 339, see also flux extended boundary condition method, 222 Forward Scattering Spectrometer Probe, 42 external reflection, 104, 114, 120, 146, 148, 151, 159, fossil fuel, 248, 249 162, 237 fountain theory, 382, 383 extinction Fourier coefficient, 55, 113, 192, 261, 264, 281, 288, 299, spectral variable, 215 315, 318, 325, 329, 330, 331, 333, 341, 350, spectrometer, 319 353 terms, 283

Index 433

transform, 199, 206, 207, 210, 216 generalized, 146 transform spectrometer, 324 GOS approach, see GOS four-stream approximation, see delta-four-stream ice optics, 127, 132 approximation IGOM, see improved geometric optics Fraunhofer diffraction, see diffraction localization principle, see localization principle freezing, 2, 19, 20, 22, 29, 53, 180, 382 modified, 292 frequency near-IR, 283 circular, 61, 76, 84 radiation pressure, see radiation pressure CKD, 338 efficiency, 171 cloud formation, 371 radiative transfer, 266 constant, 58, 59 ray-by-ray approach, see ray-by-ray domain, 205, 210 Snell’s and Fresnel’s laws, 118 electromagnetic wave, 203 surface wave, see surface wave ice cloud, 281, 283 surface-integral, 147 in GHz, 252 unified theory, 178 microwave, see microwave geometric ray tracing, 124, 127, 133, 147, 313 near-field, 207 geometric shadow, 125, 136, 137, 138, 139, 140, of all clouds and high clouds, 9 170 optical constants of H2O, 80 geometric-optics and surface-wave, 168, 173, 195, see resonant, 77 also GOS response of scattering particle, 199, 206 Geophysical Fluid Dynamics Laboratory, 387 thin cirrus occurrence, 389 GEOS, see Goddard Earth Observing System Model Fresnel Geostationary Operational Environmental Satellite, 5 coefficient, 121, 151, 165 GEWEX (Global Energy and Water cycle Exchanges), formula, 120, 151 348 law, 118, 121 GFDL, see Geophysical Fluid Dynamics Laboratory ray, 156, 158 Gibbs phenomenon, 216 reflection, 123, 126, 158, 159 global albedo, see albedo Fresnelian interaction, 147 Global Change Observation Mission, 258 FSSP, see Forward Scattering Spectrometer Probe global climate model, xiv, 363, 364, 386 FTS, see Fourier transform spectrometer glory, 103, 104, 117, 127, 391 Glory satellite, 259, 302 g function, 321, see also correlated k-distribution Goddard Earth Observing System Model, 387 method GOES, 5, 347, 348, see also Geostationary gamma size distribution, 103, 263, 273 Operational Environmental Satellite gaseous profile, 108 GOS, see also geometric-optics and surface-wave Gauss’ divergence theorem, 63, 161 comparison with FDTD and DDA, 173 Gaussian comparison with Lorenz–Mie, 169 probability function, 45, 127 conceptual ray-by-ray approach, 166 pulse, 206 coupled with Rayleigh–Gans–Debye, 173 system of units, 60 for ice crystals, 169 GCM, 46, 300, 332, 333, 340, 341, 350, 353, 361, for non-spherical particles, 171 365, 366, 367, 377, 380, 386, 387, 389, see for snow grains contaminated by BC and dust, also general circulation model 195 GCOM-W1, see Global Change Observation Mission for spheres, 168 general circulation model, 45, 289, 332, see also radiation pressure, 168 GCM; climate model unified theory, 178, 184 geometric optics graupel, 22, 29, 30, 32, 315 absorption effects, 120 greenhouse effect, 350, 351, 360, 361, 362, 364, 373, asymptotic approximation, 147, 149, 151, 153, 155, 377, 389, 390, see also IR greenhouse effect 157, 159, 161, 163, 165, 167, 169, 171, 173, greenhouse gas, xii, 248, 252, 346, 351, 357 175, 177 ground state, 253 asymptotic extinction efficiency, 237 CGOM, 162, 180, see also conventional geometric H2O, 12, 17, 80, 248, 250, 253, 257, 264, 300, 319, optics 323, 335, 338, 342, 350, 364, 379, 380 EGOH, see efficient geometric optics hybrid hail, 3, 29, 249 for ice crystals, 391 half-width, 77, 215, 335, 336

434 Index

halo polarization ratio and BRDF, 306 120° parhelion, 133 PSTD and FDTD, 217 22°, 117, 128 homogeneous 22° parhelion, 134 deposition, 20 46°, 117, 128 freezing, 19, 20, 53 anthelion, 133 nucleation, 19, 20, 51 circumhorizontal arc, 133 horizontal orientation, 59, 147, 303 circumzenithal arc, 133 Huygens surface, 199 diamond shape, 132 hydrogen, 17, 19 helic arc, 134 hydrological cycle, xii, 2, 248 infralateral arc, 134 lower tangent arc, 133 ICAO (International Civil Aviation Organization), Parry arc, 133 375 Parry infralateral arc, 133 ice crystal Parry supralateral arc, 133 habit, 25, see also ice crystal shape subhelic arc, 133 morphology, 30, see also ice crystal shape subsun, 132 ice crystal shape sundog, 58, 131, 135 aggregate, see aggregate supralateral arc, 133 as a function of temperature, 26 upper tangent arc, 134 bullet rosette, see bullet rosette Wegener arc, 133 classification of ice crystals, 32, 33 Hankel function, 68, 74, 223 column, see column harmonic wave, 160, 206 computer generation of 3-D ice crystals, 35, 41 He, see helium crystal size and shape distribution, 41 heat budget, 327 dendrite, see dendrite heating rate, 50, 53, 192, 340, 355, 356, 382, 384 effect on GCM simulation, 367 helic arc, see halo growth of ice crystals, 22 helium, 313 hexagonal structure, 25, 31 Helmholtz equation, 223 historical perspective, 30 Henyey–Greenstein function, 331 hollow column, see hollow column heterogeneous ice crystal size distribution, 41 deposition, 21, 54, see also deposition Koch snowflake, see Koch snowflake freezing, 53, see also freezing needle, see needle nucleation, 19, 20, 46, 366, 371 observed at South Pole, 33 processes, 363 observed from aircraft, 33 high cloud, xiv, 2, 5, 9, 247, 271, 286, 357, 362, 371, plate, see plate 372, 373, 389 ice nuclei, 2, 19, 20, 21, 22, 31, 53, 115, 175, 178, High Resolution Infrared Spectrometer, 9, see also 180, 249 HIRS ice water content, see also IWC High Spectral Resolution Infrared Spectrometer, 319 cirrus cloud vertical profiles, 288 HIRS, 9, 11, 389, see also High Resolution Infrared CloudSat, 13 Spectrometer correlation HIS, see High Spectral Resolution Infrared analysis, 46 Spectrometer with ice crystal size, 45, see also IWC hollow column with mean effective ice crystal size, 47, 48, 49, classification of ice crystals, 32 353 computer generation of 3-D ice crystals, 35, 38, 41 definition of, 261 crystal size and shape distribution, 42, 43, 49, 266, reflected line spectra in the 0.76 µm band, 325 271, 292, 319, 344 single-scattering parameterization of ice crystals, depolarization ratio, 316 329 geometric ray-tracing, 125 surface temperature deviation due to CO2 doubling, ice optical property library, 277 365 IGOM and FDTD, 163 ice water path, xiv, 55, 255, 261, 332, 343, 345, 352, II-TM and ADDA, 234 see also IWP laboratory scattering, 189 IGOM, see improved geometric optics phase matrix, 182 imaginary refractive index, 77, 80, 156, 330, 333, see polarization measurement, 303 also refractive index

Index 435

improved geometric optics, xiii, 158, 173, 178, 219, vertical 229, 266, 277, 350 profile of extinction coefficient, 299 incident field, 118, 152, 199, 225, 239, 240, 242 sizing, 292 independent scattering, 58, 59, 100, 106, 112, 228 IWC–De correlation, 47, 368 indirect effect, 46, 366, 379, 380 IWP, 343, 344, 351, 353, 355, 362, 363, 364, 389, see infralateral arc, see halo also ice water path infrared flux, 250, 335, 358, 363, 377, see also flux jet fuel consumption, 372 radiation, xiii, 319, 350, see also thermal infrared radiation k-distribution, 336, see also CKD; correlated radiative transfer, 112, 336, 340 k-distribution method spectrum, 302, 331, 335 Kepler, 31 Infrared Radiation Interferometer Spectrometer, 319, Kirchhoff thermodynamic equilibrium, 342, see also see also IRIS thermodynamic equilibrium insolation, 348, 349 Koch snowflake, 35, 39, 40, 184, 316 integral equation, 138, 160, 207, 225, 228, 241 Kramers–Kronig relationship, 80 intensity function, 136, 139, 142, 145 Intergovernmental Panel on Climate Change, 371 laboratory scattering, 186, 192 internal reflection, 104, 114, 117, 124, 132, 146, 149, Lambert, 301, 341 159, 183, 237, 308, 310, 313, 315 land surface, 2, 252, 270, 271, 286, 301, 366, 386 International Satellite Cloud Climatology Program, Landsat, 262 11, see also ISCCP lapse rate, 359, 363, 382, see also critical lapse Intertropical Convergence Zone, 8, see also ITCZ rate invariant imbedding T-matrix method, 226 laser radar, see lidar inversion, see retrieval; remote sensing latent heat, 23, 24, 46, 53, 358, 360, 363 IPCC, 5, 371, 375, 377, 380, 391, see also law of reciprocity, 98, 100, 101, 113, 154 Intergovernmental Panel on Climate Change Legendre polynomial, 67, 283, 331, 340 IR flux, 250, 341, 346, 357, 367, see also flux lidar IR greenhouse effect, 360, 361, 364, 373, 377, 390, 3-D backscattering image of cirrus, 12 see also greenhouse effect active remote sensing, 247 IRIS, 319, see also Infrared Radiation Interferometer backscattering technique, 11 Spectrometer CALIOP, 259, 316 irradiance, 250, see also solar irradiance CALIPSO, 14, 376, 381, 382 ISCCP, 11, 41, 43, 51, 341, see also International cloud base height, 347 Satellite Cloud Climatology Program cloud geometric thickness, 267 ITCZ, 8, 9, 279, 281, 285, see also Intertropical depolarization technique, 14, 16 Convergence Zone detection of cirrus clouds microphysics, 184 IWC, see also ice water content differentiation of ice and water, 306, 316 1-D climate–cirrus cloud model, 362, 363, 364, equation, 315 365 from aircraft, 257 2-D cirrus cloud formation model, 55, 56 ground-based, 45, 279, 316 as a function of cirrus cloud temperature, 357, 358 II-TM, 235 cirrus radiative forcing, 353, 355 laboratory (laser) and field studies, 315 correlation with ice crystal size, 45, 46, 49 laser radar, 314 definition of, 261 MicroPulse, 348 effect of interactive ice crystal size on precipitation, orientation of ice particles, 112 365, 366, 367 PARASOL, 259 feedback, 374 retrieval of re, 283 generalized single-scattering parameterization, 332 subvisible cirrus, 383 high thin clouds, 388, 389 theoretical depolarization ratio, 316 radiative transfer versus aircraft observations, 343 vertical inhomogeneity, 288 retrieval of cirrus cloud parameters, 325, 326, see limb, 5, 114, 259, 386 also retrieval line single-scattering parameterization of ice crystals, intensity, 335 328, 330, 331 overlap, 338, 339 thin cirrus detection and comparison with GCM, shape, 335, 336 386, 387 strength, 77, 318, 335, 336

436 Index

linear polarization, 77, 90, 110, 184, 301, 302, 303, 1-D climate–cirrus cloud model, 364 304, see also degree of linear polarization asymmetry factor, 273 linearly polarized radiance, 276 bi-spectral correlation technique, 264 line-by-line, 336 BRDF in the 1.38 µm band, 319 liquid cirrus cloud climatology, 386, 389 water content, 260, 359, 360, see also LWC construction of look-up tables, 267 water path, 260, see also LWP correlation to IWC, 353 local thermodynamic equilibrium, 109 CRF localization principle, 146, 158, 164 at TOA, 352, 354 longwave radiation, 346, see also outgoing longwave in the 1.38 µm band, 321 radiation definition of, 42, 261, 329 Lorentz–Lorenz, 240 emissivity and solar albedo, 344 Lorenz–Mie, 216 global retrieval, 277 amplitude scattering matrix, 224 ice crystal surface roughness, 269 bidirectional reflectance, 257 in GCMs, 46, 366 comparison with linear contrails, 376 DDA, 243, 244 radiation parameterization, 55 experimental results, 186, 187 radiative heating rate, 384 FDTD, 210, 211 relation to IWC,47 GOS, 169 retrieval, 261 PSTD, 216 single-scattering parameterization, 334 exact “solution,” 115, 118, 128, 166, 168, 171, 178, solar albedo, 344 197 spectral BRDF and absorptance, 255 invariant imbedding T-matrix method, 227 tropical ice crystal size distribution, 264 polarization of Venus, 301 UCLA GCM, 289 single-scattering properties of ice spheres, 102, mean effective radius, 188, 260, 262, 264, 277, 279, 103 289, 329, 360, see also effective size; effective spherical coordinates, 64, 68 particle size spheroidal coordinates, 72 mean effective size, 47, 55, 56, 101, 187, 257, 263, water droplets, 350 271, 274, 282, 295, 305, 322, 330, 333, 343, low cloud, 2, 271, 288, 359, 389 356, 359, 363, 365, see also effective size; lower effective particle size; mean effective ice atmosphere, 2, 249, 251 crystal size tangent arc, 114, 132, see also halo meridional plane, 253 LWC, 260, 360, 361, see also liquid water content Mesoscale Atmospheric Prediction System, 346, see LWP, 260, 261, 361, see also liquid water path also MAPS METEOR, 319 magnetic, 118, 201 Meteosat, 377 component, 120 methane, 248, 259, see also CH4 current, 159 MFRSR, 348, see also Multi Filter Rotating dipole, 253 Shadowband Radiometer field, 60, 65, 68, 73, 76, 113, 134, 159, 160, 201, microwave, 11, 83, 211, 247, 250, 252, 259, 279, 205, 225 386 induction, 60, 62 Microwave Limb Sounder, 259, 386, see also MLS permeability, 61, 62 middle cloud, 2, 5, 8, 357, 360, 371, 372, 373 poles, 60 Miller indices, 17, 19, 25 vector, 60, 62, 70, 83, 106, 115, 311 millimeter wave cloud radar, 295 MAPS, 346, 347, 348, 349, see also Mesoscale millimeter-wave radar, see radar, mm-wave Atmospheric Prediction System Mixed-Phase Arctic Cloud Experiment, 43 MAS, 264, 266, 267, 271, 286, 306, 307, see also mixing ratio, 52, 53, 343, 360, 366, 384 MODIS Airborne Simulator MLS, 259, 386, 387, 388, 389, 390, see also mass extinction cross-section, 107 Microwave Limb Sounder Maxwell Garnett mixing rule, 165, 180 MMCR, 295, 297, 299, 300, see also millimeter wave Maxwell’s equations, 58, 61, 75, 160, 199, 215, 223, cloud radar 391 mm-wave radar, see radar, mm-wave mean effective ice crystal size, see also mean effective MODerate-resolution Imaging Spectroradiometer, 11, size 14, see also MODIS

Index 437

MODIS, see also MODerate-resolution Imaging multiple scattering, xiii, 58, 59, 79, 106, 107, 108, Spectroradiometer 109, 110, 112, 188, 257, 263, 281, 301, 314, 1.38 µm reflectance, 8.6–11 µmBTD,13 319, 321, 323 1.9 µm water vapor absorption channel, 286 N2O, 249, 251, 252, 335, 338, 339, 343, see also Aqua, 259 nitrous oxide A-Train, 14 Nakaya diagram, 32, see also ice crystal shape BTD National Polar-orbiting Operational Environmental between 11 and 12 µm channels, 14 Satellite System, 295, see also NPOESS between 8.5 and 11 µm channels, 275 natural light, 93, 97 C5 and C6 models, 273 near field, 147, 160, 198, 205, 207 C6 model, 275 near infrared, xiii, 261, 344 CERES, 283 near-to-far-field mapping, 207 cirrus cloud vertical sizing, 289 needle, 24, 29, 32 cirrus scenes, 295 nephelometer, 187, 188, 190, 191 cloud climatology, 11 nimbostratus, 3, 4 cloud effective particle size, 17 Nimbus, 319 cloud retrieval algorithm, 294 nitrogen, 186, 193, 248 Collection 4 products, 271 nitrogen oxides, 249, 259 collocation scheme with MMCR, 299 nitrous oxide, 248 detection of thin cirrus, 287 NO, 249 difference in cloud particle size derived from NO2, 249, 339 MMCR, 300 NOAA, 5, 9, 301, 302, 346, 374, 375, 389 differences in ice cloud optical depth derived from normal dispersion, 77 PARASOL, 302 NOx, 249, 374, 380, see also nitrogen oxide false-color RGB image, 270 NPOESS, 295, 303, see also National Polar-orbiting generation of look-up library, 292 Operational Environmental Satellite global cloud climatology, 277 System input parameters extracted from, 291 Ns, see nimbostratus IR optical properties of cirrus, 280 nucleation, 5, 19, 20, 31, 51, 53, 56, 186, 187, 192, linear contrails, 375 310, 363, see also heterogeneous nucleation; MMCR observation, 299 homogeneous nucleation optical depth and ice crystal size, 260 nuclei, 5, 20, 21, 51, 178, see also cloud condensation product evolution (C6 versus C5), 388 nuclei; ice nuclei retrieval of contrail properties, 376 seasonal ice cloud optical depth and ice crystal O2, 12, 247, 248, 249, 251, 252, 258, 264, 323, 324, mean effective radius, 279 335, 338, 339 solar channels, 263 O3, 249, 250, 251, 257, 335, 338, 339, 346, 374, 379, surface albedo at 3.75 µm, 293 380 Terra, 269 OCO, 251, 258, 319, 323, see also Orbiting Carbon tropical ice crystal size distribution, 264 Observatory two-channel inversion, 262 OLR, 346, 348, 350, 367, 368, 377, see also outgoing validation of cloud product, 296 longwave radiation water clouds, 264 OMI, 259, see also Ozone Monitoring Instrument weighting function, 290 one-parameter scaling approximation, 336 MODIS Airborne Simulator, 393 optical depth, definition of, 260 modulator, 92 OPTRAN, 279 monochromatic intensity, 107 Orbiting Carbon Observatory, 258, 323, see also OCO monochromatic radiative transfer, 321, 338 ordinary wave, 78, 79 Monte Carlo, xiii, 124, 126, 127, 146, 147, 155, 170, outgoing longwave radiation, 346, 349, see also OLR 195 outgoing wave, 199, 204 MPACE, 43, 49, see also Mixed-Phase Arctic Cloud overtone, 318 Experiment oxygen, xiv, 17, 19, 248, 249, 319, 323, 325, see also Mueller matrix, 92 O2 Multi Filter Rotating Shadowband Radiometer, ozone, 249, 255, 259, 336, 343, 355, 366, 384, 390, 348 see also O3 multiple reflection, 293 Ozone Monitoring Instrument, 259

438 Index

PARASOL, 259, 275, 302, see also Polarization & plane wave, 68, 71, 84, 87, 118, 119, 135, 136, 139, Anisotropy of Reflectances for Atmospheric 198 Sciences coupled with Observations from a plane-parallel atmosphere, xiv, 106, 108, 339 Lidar planetary albedo, see albedo parhelic circle, see halo planetary boundary layer, 250, 363, 366, see also PBL parhelion, see halo plate Parry arc, 131, 133, 134, see also halo backscattering depolarization, 312 particle size distribution, 271, 272, 329, 359, see also classification, 32, 33 size distribution comparison of GOS with FDTD and DDA, 173 PARTNER, 374 comparison with Partnership for AiR Transportation Noise and experiment, 189 Emissions Reduction, see PARTNER Koch snowflake, 184 PBL, 250, 366, see also planetary boundary layer computer generation of 3-D ice crystals, 35, 39 perfectly matched layer, 198, 204 contrails and contrail cirrus, 371 permeability, 61, 75, 198, see also magnetic correlation between BRDF and polarization ratio, permeability 305 permittivity, 61, 62, 75, 77, 165, 198, 200, 203, 204, crystal size and shape distribution, 41, 42, 43, 49, 241 266, 268, 271, 272, 292, 319, 344 phase function, see also scattering phase function depolarization ratio, 316 3-D distribution of scattered intensity, 108 detailed drawing, 31 ADDA, 243 extinction cross-section, 330 backscattering, 315 FDTD, 214 bullet rosette, 214 and PSTD, 220 columns and plates, 189 for snow grains, 195 delta-function adjustment, 340 Fraunhofer diffraction, 148 enhancement of 22° halo, 235 generalized parameterization, 332 FDTD, 215 geometric ray-tracing, 124 and Lorenz–Mie, 210 geometrical similarity with column, 311 for horizontally oriented ice particles, 111 GOS, 171 for polydisperse ice spheres, 103 coupled with RGD, 173 for randomly oriented spheroids, 104 growth by riming, 29 four size distributions, 267 halos and arcs, 132 Henyey–Greenstein function, 331 horizontal orientation, 45, 112, 114, 129, 131, 303, IGOM and FDTD, 163 310 II-TM and DDA, 233 ice crystal habit, 25, see also ice crystal shape importance of ice crystal, 267 ice optical property library, 277 laboratory measurements, 186 ice particle surface roughness, 269 Legendre polynomial expansion, 331 IGOM, 163 MODIS C5 and C6 models, 273 II-TM, see invariant imbedding T-matrix method normalization, 188 II-TM and ADDA, 234 optically thin cirrus, 254 measured and computed BRDF, 257 particle-ensemble-averaged, 271 phase matrix, 182 PSTD, 216, 220 polarization measurements, 303 Rayleigh scattering, 338 polarization ratio and BRDF, 305 ray-tracing technique, 146 relation between maximum size and length, 45 RGD approximation, 176 scattering and absorption properties, 344 rough surfaces, 183, 269 single-scattering input to radiative transfer, 264 smooth surfaces, 182 spectral single-scattering, 328, 333, 334 three effective variances, 268 sundog, 130 three habit models, 268 unified theory, 182 T-matrix, 225 volume and geometric cross-section, 329 phase matrix, see scattering phase matrix PML, 198, 199, 204, 205, see also perfectly matched photon, 125, 126, 170, 195, 196, 289, 291, layer 323 Poincare´ sphere, 90 Planck, 107, 108, 110, 250 polar nephelometer, see nephelometer function, 55, 109, 280, 335, 336 polar stratospheric cloud, 5 plane of stratification, 108 polarizability, 75, 175, 238, 240, 243

Index 439

Polarization & Anisotropy of Reflectances for budget, 14, 327, 345, 346, 373, 390 Atmospheric Sciences coupled with pressure, 165, 167, 168, 171 Observations from a Lidar, 259 radiative equilibrium, 383 POLarization and Directionality of the Earth’s radiative forcing, 192, 251, 286, 328, 333, 344, 351, Reflectances, 259 353, 355, 358, 359, 360, 362, 365, 375, 376, polarized light, 93, 236, 312 377, 386, 389, 390, see also cloud radiative polarizer, 92, 313 forcing POLDER, 259, 275, 276, 301, 302, 303, 304, 305, see radiative heating, 50, 53, 57, 289, 355, 359, 382, 384, also POLarization and Directionality of the 385 Earth’s Reflectances radiative transfer polydisperse, 103, 146 1.38 µmH2O band, 319 potential temperature, 52, 366, see also temperature AIRS data, 279 Poynting vector, 84, 120, 156, 160, 209, 310, 311 bi-spectral correlation technique, 264 precipitation, xiv, 2, 5, 8, 56, 192, 248, 249, 259, 327, CAGEX, 346 355, 359, 360, 361, 362, 365, 367, 380, 387, CAGEX biases for LW flux, 349 390 CERES-2, 283 principle of reciprocity, 229, see also law of cirrus cloud formation, 55 reciprocity cirrus radiative forcing, 351 PSC, see polar stratospheric cloud correlated k-distribution method, 257 pseudo-spectral time domain method, 215, see also delta-four-stream approach, 332 PSTD discrete-ordinates method, 339 PSTD, 215, 216, 217, 220, 221, 244, 245 Eddington’s approximation, 340 equation, 108 quarter-wave plate, 92, 301 flux gain at the surface, 374 for oriented and complex ice crystals, 339 radar for tropical anvil, 382 94-GHz, 259, see also CloudSat Fu–Liou code, 348 Cloud Profiling Radar, see Cloud Profiling Radar in horizontally oriented ice particles, 112 cloud radar system, see cloud radar system in plane-parallel atmosphere, 108 cloud reflectivity, 13, 307, 387 in the g-domain, 321 CloudSat k-coefficient approach, 280 vertical inhomogeneity, 295 Legendre polynomial, 331 lidar (or radar) equation, 315 model results compared with satellite observations, mm-wave, 11, 12, 13, 287, 295, 297, 299, 389, see 345 also millimeter-wave radar model results versus aircraft observations, 341 retrieval of re, 283 MODIS channels, 265 validation, 280 multiple scattering, 106 vertical inhomogeneity, 288 offline simulation, 370 windows, 12 radiative forcing analysis, 389 radiance radiative heating, 53 3.75 µm, 291, 294 reflected a look-up library, 293 intensity, 254 clear, 281 polarization, 303 cloud-cleared, 279, 280 retrieval of cirrus cloud parameters, 326 cloudy, 279, 280 solar reflection techniques, 254 incident, 280 vector, 109 Level-1B, 275 vertical sizing algorithm, 296 measured, 294 radiative–convective model, 362, 363, 365, see also polarized, 276, 301 climate model simulated, 293, 295 radiometer, 247, 257, 259, 262, 275, 302, 323, 346, solar, 285, 289, 293 386, 389 spectral, 280, 346 rainbow, 31, 103, 104, 116, 117, 127, 188, 257, 303 total, 291, 293 random orientation, 129, 154, 177, 214, 224, 310, transmitted, 280 311, 313 upwelling, 280, 319 ray tracing, see geometric ray tracing radiation ray-by-ray, 160, 163, 168, 170, 213, 245 balance, 285 Rayleigh scattering, 175, 177, 252, 289, 293, 301, 337

440 Index

Rayleigh–Gans–Debye approximation, 173, see also rotational RGD band, 251, 336 Rayleigh–Wait theory, 72 matrix, 151, 153, 308 RBRI, see ray-by-ray RSP, 302, 306, see also Research Scanning real refractive index, 77, 80, 115, 169, 175, 180, see Polarimeter also refractive index reciprocity, see law of reciprocity; principle of SARB, 346, see also surface and atmospheric reciprocity radiation budget rectangular parallelepiped, 136, 138, 139, 144, 171 SARTA, 280, see also Stand-Alone clear-radiance reflected intensity, 254 Radiative Transfer Algorithm reflection Sc, see stratocumulus coefficient, 126 scaling approximation, see one-parameter scaling function, 253, 254, 325 approximation matrix, 151, 309 scattering amplitude matrix, 208, 209, 224 reflectivity, 13, 262, 276, 280, 287, 306 scattering angle, definition of, 92 refraction matrix, 152 scattering matrix, 152, 155, 163, 207, 208, 209, 224 refractive index, 79, 80, 81, 117, 118, 119, 120, 128, scattering phase function, 214, 267, 283, 325, see also 149, 152, 156, 168, 180, 186, 210, 211, 212, phase function 216, 223, 225, 227, 228, 236, 237, 240, 243, scattering phase matrix 244, 261, 301, see also complex refractive 10 independent parameters, 229, 233 index; imaginary refractive index; real ADDA, PSTD, and EGOH, 246 refractive index circular-polarization representation, 229 remote sensing, see also retrieval contribution of diffraction, 156 active, 247 definition, 94 AIRS, 279 FDTD, 212 atmospheric absorption spectrum, 250 for an ensemble of ice crystals, 97, 99, 100, 101, atmospheric composition and structure, 250 146, 157, 182 A-Train satellite constellation, 257 for horizontally oriented ice particles, 113 CALIPSO, see Cloud-Aerosol Lidar and Infrared for randomly oriented soot aggregates, 176 Pathfinder Satellite Observations IGOM, 229 CloudSat, see CloudSat II-TM method, 229, 230 delta-four-stream, 279 near-to-far-field, 207, 209 ice clouds, 248, 254 RGD approach, 177 ice crystal phase function, 268 vector radiative transfer, 109, 110 lidar, 11 scattering plane, 92, 107, 152, 153, 154, 207, 241, MODIS, 275 276, 308 optical depth and mean effective size, 260 Schelkunoff, see electromagnetic equivalence passive, 247 theorem POLDER, 302 Schuster, 106, 340 radiative transfer, 254 Schwarzschild, 106, 340 reflected line spectra, 324, 326 sea surface temperature, 259, 300, 366, see also SST reflected polarization, 248, 301, 303 second indirect effect, 361, 362 satellite, 259 semiconductors, 61 validation of the vertical sizing, 300 semi-direct effect, 362 vertical sizing, 292 sensible heat, 363 representation of a light beam, 301 separation of variables, 228 Research Scanning Polarimeter, 302, see also shortwave radiation, 370 RSP SIM, 207, 208, see also surface-integral method resonance, 180, 253 similarity, 32, 103, 308, 311, 332, 340 retrieval, 253, 260, 262, 263, 264, 266, 267, 268, 271, single-scattering albedo 275, 277, 279, 280, 281, 283, 286, 289, 291, aerosol, 348 292, 293, 295, 296, 297, 300, 302, 303, 306, combined ice crystals and absorbing gases, 338 326, 348, 386, 387, 388, 390, see also remote comparison with FDTD and DDA, 173 sensing conventional geometric optics, 331 RGB (red, green, blue), 14, 16, 269, 270, 271 definition of, 101, 330 RGD, 176, 177, 178, 180, 184, see also effect of water vapor, 325 Rayleigh–Gans–Debye approximation FDTD, 199

Index 441

and ray-by-ray, 213 spectrum, 250, 285, 333, 338, 339 and PSTD, 220 zenith angle, 114, 131, 255, 257, 263, 276, 283, functions of only De, 353 293, 304, 305, 321, 323, 324, 325, 341, 344, generalized single-scattering parameterization, 333 352, 353, 355, 384 geometric ray tracing, 127 solid angle, 95, 106, 108, 109, 127, 159, 316, 346 Glory satellite, 259 soot, 147, 176, 180, 193, 362, 370, 379, 380, see also GOS, 169, see also geometric-optics and BC; black carbon surface-wave source function, 107, 108, 109, 110 horizontal orientation, 113 specific conductivity, 61 ice sphere, 102 specific humidity, 52, 360, 363, 373 II-TM and IGOM, 237 spectral single-scattering parameterization, 328 Koch snowflake, 184 spectral transmittance, 335, 336, 337 N homogeneous layers, 341 spectrometer, 247, 258, 319, 323 normalized phase function, 158 spherical parameterization using mean effective size, albedo, 264, 293 55 coordinates, see coordinates particle-ensemble-averaged, 272 harmonic, 67 radiative particle, 31, 94, 95, 100, 101, 110, 115, 165, 166, forcing of cirrus clouds, 350 167, 175, 184, 261, 301, 344, 362 transfer equation, 108, 254 wave function, 223, 225 surface wave, 172 spheroidal coordinates, see coordinates; Lorenz–Mie two-channel inversion, 264 split-window, 283 unified theory, 178, 179, 181, 184 SST, 366, see also sea surface temperature size distribution, 42, 56 St, 2, see also stratus aerosol, 348 Stand-Alone clear-radiance Radiative Transfer analytic, 268 Algorithm, 280, see also SARTA counted crystals, 189 standard atmosphere, 2, 251, 252, 255, 355, 359, see droplet, 187, 260, 360 also U.S. Standard Atmosphere dust aerosol, 193 STEP, 382, see also Stratosphere-Troposphere for contrail, 43 Exchange Project for spherical particles, 145 Stefan–Boltzmann constant, 383 gamma, see gamma size distribution Stokes parameters, 86, 87, 89, 90, 91, 93, 94, 95, 99, ice crystal, 41, 46, 47, 51, 52, 53, 55, 114, 261, 264, 100, 109, 155, 157, 301, 303 267, 292, 319, 329, 330, 332, 344, 351, 362, stratocumulus, 2, 262, 341 363 Stratosphere-Troposphere Exchange Project, 382 in situ,49 stratus, 2, 52, 289, 359, see also St log-normal, 188 subhelic arc, see halo particle, see particle size distribution sublimation, 19, 53, 56, 289, 367 vertical, 296 Subsonic Aircraft: Contrail and Cloud Effect Special size parameter, definition of, 102 Study, 370, see also SUCCESS Snell’s law, 118, 120, 123, 126, 128, 129, 148, 149, subsun, 114, 131, 303, see also halo 310 SUCCESS, 42, 51, 266, 370, 374, see also Subsonic snow grain, 192, 193, 196 Aircraft: Contrail and Cloud Effect Special snowflake, 21, 29, 30, 31, 32, 39, 145, 184, 249, 315, Study see also Koch snowflake sulfur dioxide, 249 S-NPP (Suomi-National Polar-orbiting Operational sundog, see halo Environmental Satellite System (NPOESS) supralateral arc, see halo Preparatory Project), 280, 295, 296, 305 surface SO2, 249, 339, see also sulfur dioxide albedo, see albedo solar and atmospheric radiation budget, 346 albedo effect, 360, 361, 364, 365 flux, see flux flux, 339, 341, 342, 346, 358 integral method, 134, 207 heating rate, 355, see also heating rate reflection, 262, 319 insolation, 357, 371 temperature, see temperature irradiance, 276, 323, 346, see also irradiance wave, 116, 117, 118, 166, 168, 170, 171, 172, 180, radiation, 111, 113, 180, 255, 257, 280, 293, 339, 308, 350 342, 352, 353, 356, 359, 362, 367 susceptibility, 240

442 Index

temperature radiative balance equation, 383 1-D climate–cirrus cloud model, 364 rate coefficients, 360 2-D cirrus cloud model, 53 Rayleigh optical depth, 338 at crystal surface, 24 reference, 336 atmospheric, 259, 343, 359 sea water, 259 brightness, 270, 271 secondary ice particle production, 22 classification of ice crystals, 32, 33, 41 slope of linear fit of, 373 cloud, 285 snowflake shape, 31 cloud top, 11, 271, 277 sounding, 346 cloud–climate model, 373 standard atmosphere, 364, see also standard correlation with De,49 atmosphere crystal size versus temperature range, 42 stratosphere dehydration, 386 decreasing with height, 5 surface, 8, 24, 250, 291, 293, 350, 359, 360, 364, dependence of 365, 371, 373, 390 conductivity on, 61 to determine De,46 depolarization ratio on, 316 triple point, 23 ice crystal size on, 358, 367 tropopause, 383 ice refractive index on, 80, 83 tropopause layer, 380 IWC on, 357 tropopause region, 383 line profile on, 337 upper atmosphere, 250 line strength on, 335 vapor pressure over ice at, 25 dependent contrail parameterization, 376 Terra, 11, 13, 14, 269, 277, 283, 284, 285, 296, 297, depolarization as a function of, 316 376, see also MODIS depolarization in relation to, 315 TES, see Tropospheric Emission Spectrometer differential between cloud and surface, thermal 357 conductivity, 24, 363 distributions, 353 equilibrium, 107 field, 355 infrared radiation, 57, 106, 112, 350, 371, see also freezing, 2 infrared radiation greenhouse radiative perturbation, 358 thermodynamic equilibrium, 336, 342, see also heterogeneous nucleation, 20 Kirchhoff thermodynamic equilibrium homogeneous thin cirrus clouds, 386 freezing, 22 Tibetan Plateau, 193 nucleation, 19 time harmonic, 84, 87 horizontal averages, 363 T-matrix, 176, 178, 197, 216, 222, 223, 224, 225, 226, horizontal distribution, 381 227, 228, 237, 243 ice crystal, 54 TOA, 250, 254, 276, 280, 281, 283, 285, 328, 339, ice crystal habit, 25 345, 348, 350, 351, 352, 354, 358, 370, 373, ice crystal shape, 55 389, see also albedo; flux ice crystal size, 42 total reflection, 124, 149 ice crystal size and shape, 33 transformation matrix, 92, 94, 95, 98, 99, 109, 139, ice nuclei concentration, 54 153, 154, 156, 307, 308, 311 infrared flux as a function of, 363 transmission, 79, 80, 113, 123, 126, 155, 226, 251, land surface, 366 252, 293, 308, 341, 357 linear contrails, 376 function, 292, 325 moderated, 371 matrix, 308 negative correlation with depolarization, 317 transmissivity, 281 nucleation, 19, 186 transmittance, 279, 280, 325, 335, 336 nucleation threshold, 20 transverse vector, 149 of planetary atmosphere, 336 triple point, 23 photospheric, 250 TRMM, 11, 42, 283, see also Tropical Rainfall plate habit, 189 Measuring Mission positive correlation with IWC, 389 tropical anvil, 42, 50, 382, see also anvil potential, 52, see also potential temperature Tropical Rainfall Measuring Mission, 11, 42, see also pristine and irregular habits, 49 TRMM probability of adhesion, 29 tropopause, 249, 250, 357, 380, 382, 383, 385, 386, profile, 250 387

Index 443

troposphere, 3, 5, 249, 250, 252, 300, 323, 328, 335, VIM, 207, 208, see also volume-integral method 346, 355, 357, 359, 371, 373, 380, 382, 383, VIPS, 42, 47, see also video ice particle sampler 385, 386, 387, 389 VIRS, 283, 285, see also Visible and Infrared Tropospheric Emission Spectrometer, 259 Scanner two-parameter Curtis–Godson approximation, 336 visibility, 3, 250 two-stream approximation, 340 Visible and Infrared Scanner, 11, 283, see also VIRS U.S. Standard Atmosphere, 293, 343, see also visible spectrum, 59, 262 standard atmosphere Visible-Infrared Imaging-Radiometric Suites, 295 UCLA AGCM, 341, 366 VISST (Visible Infrared Shortwave-infrared ultraviolet radiation, 249, see also UV Split-window Technique), 283 uncinus, 43, 264 volcanic dust, 249, see also dust uniaxial crystal, 78, 79 volume-integral method, 207 unified theory for light scattering by ice crystals, 178, 179, 181, 184, 186, 192, 316 water droplet, xiv, 2, 59, 134, 184, 187, 188, 248, 260, unit vector, 36, 63, 65, 73, 118, 121, 148, 149, 150, 261, 264, 279, 283, 308, 314, 315, 329, 350, 152, 153, 159, 160, 162, 207, 208 359, 362, see also droplet unpolarized light, 93, 313 wave equation, 59, 115, 122, 205 upper scalar, 65, 66, 68, 70, 71, 73 atmosphere, 5, 50, 383 vector, 58, 62, 64, 73 tangent arc, see halo wave vector, 121, 122 troposphere and lower-stratosphere, 380 wavelength, 61 upwelling radiance, 280, 281, 319 wavenumber, definition of, 61 UTLS, 371, 380, 383, 386, see also upper-troposphere Weather Research Forecast, 341 and lower-stratosphere Wegener arc, see halo UV, 59, 252, 257, see also ultraviolet radiation weighting function, 290, 291 wet deposition, 192 velocity of light, 60, 75, 76, 77 window, 9, 12, 253, 275, 279, 280, 281, 289, 319, 327, vibrational 339 mode, 17 WRF, see Weather Research Forecast rotational transition, 17, 323 Wu-Shing, 30 transition, 251, 318 video ice particle sampler, 42 Yin-Yang, 30 VIIRS, 295, 296, see also Visible-Infrared Imaging-Radiometric Suites zenith angle, definition of, 107