- Email: [email protected]
Appendix E. Glossary of Symbols
APPENDIX E. GLOSSARY OF SYMBOLS WILBER B. HUSTON 'OAO Corporalion Greenbelt, Maryland
GLOSSARY OF SYMBOLS Radius of earth; absorption coefficient Fraction of storm covered by the kth temperature Component of long ocean wave orbital acceleration along the radial direction Maximum radial acceleration due to the long wave Area of a storm as defined by the -20°C isotherm Backscattering coefficient Empirical weighting function of the (4)pixel Empirical weighting coefficient corresponding to the kth temperature Planck blackbody radiation function Azimuthal radar bandwidth Radar system bandwidth Velocity of light; phase speed of the short waves Actual group speed, nonlinear waves Small-amplitude, linear internal wave group speed Shallow-water phase (and group) velocity Cross-correlation function Ice concentration; pigment concentration; wave velocity (C = w/k = velocity bunching parameter Drag coefficient Specific heat of air at constant pressure Water depth Decibel Interpacket distance; difference Mean of a set of differences Absolute value of a difference Rainfall rate in the (ij) pixel of a grid Total energy of a wave field Mean of differences Mean of absolute value of differences Systematic component of radial ephemeris error Electromagnetic bias Coriolis parameter (f = - 2Rsin A) at latitude A Spectral peak frequency Fraction of ice which is multiyear; earth crust flexural rigidity Solar irradiance at wavelength 1, Acceleration due to gravity
a):
499 ADVANCES IN GEOPHYSICS,VOLUME 21
Copyright @ 1985 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-018827-9
500
WILBER B. HUSTON Area (km') of the (ij)pixel of a grid Two-way antenna gain pattein, normalized so that it is unity at its maximum (accounts for pointing error)
B(J5m)
Antenna pattern RMS wave height; altitude; satellite elevation above the sea surface; radial distance of the satellite from the instantaneous sea surface N + (height of surface above ellipsoid) Satellite height; heat flux H(l + H/a), "extended" satellite height H/(l + H/a), reduced satellite height Significant wave height Height of a rain cell Hertz Point target intensity response along slant range direction Point target intensity response along flight direction Image intensity caused by moving ocean waves Zero-order modified Bessel function of the first kind with argument z Downward component of radiation Rainfall rate for tropical storms (set equal to 1.2 mm hr-') Index for each temperature increment in the IR data equal to or greater than -20°C; ocean wavenumber (2nlA)); diffuse attenuation coefficient (CZCS) Wavenumber of the long ocean waves Vector wavenumber = (k,,k,) Radar wavenumber (241) Linear wavenumber (2n/A) One-way signal attenuation rate due to rain Absorption coefficient Kilometer Kelvin; Karman constant; diffuse attenuation coefficient Upwelled spectral radiance Diffuse attenuation coefficient for pure sea water Corrected radiance; leading crest length of an internal wave Radiance contribution due to aerosol scattering Radiance contribution due to Rayleigh scattering Radiance received at sensor Water-leaving radiance In a surface wave field, wavelengths of the short and long waves Argument of the complete elliptic integral of the first kind; modulation level Number of points Number of pairs Geoid elevation relative to the ellipsoid; number of multiple looks; gate numbers; Brunt-Vaisala frequency; geoid height Pre-leading-edge average noise level Degree and order of spherical harmonic expansion Pressure Denotes surface Joint height-slope probability density function of surface height (positive upward) of the waves above a mean local surface, and wave s l o p corresponding to specular angle 8. Legendre polynomial of the first kind
APPENDIX E. GLOSSARY OF SYMBOLS
PCA r
501
One-way range resolution Effective pulse shape at receiver output, normalized to unity at its maximum, vs spatial propagation distance, x = 4 2 Point of closest approach Geocentric satellite position; linear-regression coefficient; correlation coefficient; radar slant range Mean earth equatorial radius Geocentric radius of reference ellipsoid, rainfall rate, reflectance Equatorial radius of earth Volumetric output of rain Fresnel reflection coefficient of sea surface at normal incidence Fresnel reflection coefficient for smooth sea water Standard error of estimate Total ocean wave slope RMS ocean wave slopes along any two orthogonal axes tangent to the mean sphere Cross spectrum One-dimensional ocean wave-height spectrum Sea surface height Significant wave height Epoch time; echo time; earth crust thickness Temperature; coherent integration time; period (2xlw); period (T = l/w) Brightness temperature Downward component of radiation Physical temperature of ice Transmitted pulse width Swell period (sec) Physical temperature of surface Integration time Ocean temperature field (scalar) Wind speed; a variable of integration a24'/2H" Horizontal component of surface water velocity Row Ocean current field (vector) Wind speed at reference height of 10 m above sea level Ocean current vector in the direction of the wind Wind-friction velocity Unit-step function Radar platform velocity; velocity Complex surface current vector Eckman transport vector Group velocity ( s ; f m f o r deep water) Meteorologically measured wind Radar-measured wind Synoptic wind Earth gravitational potential Vertical-wind velocity Vertical velocity; white-noise power Wind speed at 10 m height Vertical-structure function Distance traversed by radar pulse; fetch Radar wind direction
502
WILBER B. HUSTON X.
Synoptic wind directipn Three-dimensional directional wave spectrum Radar-reflectivity factor; altitude Slope of the water surface relative to the marine geoid; Phillips constant Speed-correction factor Attitude relative to nadir, pointing error Peak-enhancernent factor Delta function; relative phase of a point target Radial ephemeris error Spacing between observations Emissivity Nondimensional fetch parameter; height of the sea; wave surface height above a mean local surface (positive upward); total instantaneous sea surface height referenced to geoid; [, I, Wave amplitude Time-average sea surface Time-varying surface topography Three-dimensional spatial and temporal displacement wave field specifying the sea surface Long-wave amplitude, wavelength and direction referred to azimuth Wave amplitude, vertical displacement Angle of incidence (20" for Seasat SAR); latitude; wave direction (0 = arctan ky/k,); angle of radiation Local angle of incidence Wave-propagation direction relative to flight direction Nondimensional wind shear Dominant wave direction Partitioning wavenumber Ocean wavelength; elastic modulus Radar wavelength Wave-height skewness coefficient Skewness coefficient between wave height and wave slope squared Vertical diffusion coet€lcient; elastic modulus Relaxation-time constant Component of orbital velocity along the radial direction Nondimensional peak frequency; kinematic viscosity; frequency of radiation Random component of radial ephemeris error Density Theoretical azimuthal resolution for a stationary target Resolution of a point target degraded due to motion of the long ocean waves Slant range resolution Coherence power spectrum Correlation coefficient of wave slopes Atmospheric density as function of altitude Peak width Amplitude of the radar return; normalized radar backscatter coefficient; nadir backscattering cross section Average backscattering cross section per unit area at normal incidence Backscattering cross section per unit area of ocean surface at normal or vertical incidence
+
00
a"(0")
APPENDIX E. GLOSSARY OF SYMBOLS
503
The amount (in space) by which a pulse is stretched by scattering from waves of RMS height h Normalized radar cross section Density anomaly Average radar cross section for a short-pulse altimeter as function of time Total wind stress; atmospheric transmittance; temporal half-power width of a Gaussian pulse Complex surface wind-stress vector Zonal component of T Wave-induced Reynolds stress Angle at earth center from satellite to point [ on ocean surface; longitude Angle between direction of travel of ocean wave field and flight direction Nondimensional wind shear Error function of argument y Angle at antenna from nadir to point [ on ocean surface Two-dimensional wave-height spectrum as function of wavenumber Frequency (o= 1/T) Frequency of long ocean waves Dispersion relation Rotation speed of the earth Ensemble average
GLOSSARY OF SYMBOLS Radius of earth; absorption coefficient Fraction of storm covered by the kth temperature Component of long ocean wave orbital acceleration along the radial direction Maximum radial acceleration due to the long wave Area of a storm as defined by the -20°C isotherm Backscattering coefficient Empirical weighting function of the (4)pixel Empirical weighting coefficient corresponding to the kth temperature Planck blackbody radiation function Azimuthal radar bandwidth Radar system bandwidth Velocity of light; phase speed of the short waves Actual group speed, nonlinear waves Small-amplitude, linear internal wave group speed Shallow-water phase (and group) velocity Cross-correlation function Ice concentration; pigment concentration; wave velocity (C = w/k = velocity bunching parameter Drag coefficient Specific heat of air at constant pressure Water depth Decibel Interpacket distance; difference Mean of a set of differences Absolute value of a difference Rainfall rate in the (ij) pixel of a grid Total energy of a wave field Mean of differences Mean of absolute value of differences Systematic component of radial ephemeris error Electromagnetic bias Coriolis parameter (f = - 2Rsin A) at latitude A Spectral peak frequency Fraction of ice which is multiyear; earth crust flexural rigidity Solar irradiance at wavelength 1, Acceleration due to gravity
a):
499 ADVANCES IN GEOPHYSICS,VOLUME 21
Copyright @ 1985 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-018827-9
500
WILBER B. HUSTON Area (km') of the (ij)pixel of a grid Two-way antenna gain pattein, normalized so that it is unity at its maximum (accounts for pointing error)
B(J5m)
Antenna pattern RMS wave height; altitude; satellite elevation above the sea surface; radial distance of the satellite from the instantaneous sea surface N + (height of surface above ellipsoid) Satellite height; heat flux H(l + H/a), "extended" satellite height H/(l + H/a), reduced satellite height Significant wave height Height of a rain cell Hertz Point target intensity response along slant range direction Point target intensity response along flight direction Image intensity caused by moving ocean waves Zero-order modified Bessel function of the first kind with argument z Downward component of radiation Rainfall rate for tropical storms (set equal to 1.2 mm hr-') Index for each temperature increment in the IR data equal to or greater than -20°C; ocean wavenumber (2nlA)); diffuse attenuation coefficient (CZCS) Wavenumber of the long ocean waves Vector wavenumber = (k,,k,) Radar wavenumber (241) Linear wavenumber (2n/A) One-way signal attenuation rate due to rain Absorption coefficient Kilometer Kelvin; Karman constant; diffuse attenuation coefficient Upwelled spectral radiance Diffuse attenuation coefficient for pure sea water Corrected radiance; leading crest length of an internal wave Radiance contribution due to aerosol scattering Radiance contribution due to Rayleigh scattering Radiance received at sensor Water-leaving radiance In a surface wave field, wavelengths of the short and long waves Argument of the complete elliptic integral of the first kind; modulation level Number of points Number of pairs Geoid elevation relative to the ellipsoid; number of multiple looks; gate numbers; Brunt-Vaisala frequency; geoid height Pre-leading-edge average noise level Degree and order of spherical harmonic expansion Pressure Denotes surface Joint height-slope probability density function of surface height (positive upward) of the waves above a mean local surface, and wave s l o p corresponding to specular angle 8. Legendre polynomial of the first kind
APPENDIX E. GLOSSARY OF SYMBOLS
PCA r
501
One-way range resolution Effective pulse shape at receiver output, normalized to unity at its maximum, vs spatial propagation distance, x = 4 2 Point of closest approach Geocentric satellite position; linear-regression coefficient; correlation coefficient; radar slant range Mean earth equatorial radius Geocentric radius of reference ellipsoid, rainfall rate, reflectance Equatorial radius of earth Volumetric output of rain Fresnel reflection coefficient of sea surface at normal incidence Fresnel reflection coefficient for smooth sea water Standard error of estimate Total ocean wave slope RMS ocean wave slopes along any two orthogonal axes tangent to the mean sphere Cross spectrum One-dimensional ocean wave-height spectrum Sea surface height Significant wave height Epoch time; echo time; earth crust thickness Temperature; coherent integration time; period (2xlw); period (T = l/w) Brightness temperature Downward component of radiation Physical temperature of ice Transmitted pulse width Swell period (sec) Physical temperature of surface Integration time Ocean temperature field (scalar) Wind speed; a variable of integration a24'/2H" Horizontal component of surface water velocity Row Ocean current field (vector) Wind speed at reference height of 10 m above sea level Ocean current vector in the direction of the wind Wind-friction velocity Unit-step function Radar platform velocity; velocity Complex surface current vector Eckman transport vector Group velocity ( s ; f m f o r deep water) Meteorologically measured wind Radar-measured wind Synoptic wind Earth gravitational potential Vertical-wind velocity Vertical velocity; white-noise power Wind speed at 10 m height Vertical-structure function Distance traversed by radar pulse; fetch Radar wind direction
502
WILBER B. HUSTON X.
Synoptic wind directipn Three-dimensional directional wave spectrum Radar-reflectivity factor; altitude Slope of the water surface relative to the marine geoid; Phillips constant Speed-correction factor Attitude relative to nadir, pointing error Peak-enhancernent factor Delta function; relative phase of a point target Radial ephemeris error Spacing between observations Emissivity Nondimensional fetch parameter; height of the sea; wave surface height above a mean local surface (positive upward); total instantaneous sea surface height referenced to geoid; [, I, Wave amplitude Time-average sea surface Time-varying surface topography Three-dimensional spatial and temporal displacement wave field specifying the sea surface Long-wave amplitude, wavelength and direction referred to azimuth Wave amplitude, vertical displacement Angle of incidence (20" for Seasat SAR); latitude; wave direction (0 = arctan ky/k,); angle of radiation Local angle of incidence Wave-propagation direction relative to flight direction Nondimensional wind shear Dominant wave direction Partitioning wavenumber Ocean wavelength; elastic modulus Radar wavelength Wave-height skewness coefficient Skewness coefficient between wave height and wave slope squared Vertical diffusion coet€lcient; elastic modulus Relaxation-time constant Component of orbital velocity along the radial direction Nondimensional peak frequency; kinematic viscosity; frequency of radiation Random component of radial ephemeris error Density Theoretical azimuthal resolution for a stationary target Resolution of a point target degraded due to motion of the long ocean waves Slant range resolution Coherence power spectrum Correlation coefficient of wave slopes Atmospheric density as function of altitude Peak width Amplitude of the radar return; normalized radar backscatter coefficient; nadir backscattering cross section Average backscattering cross section per unit area at normal incidence Backscattering cross section per unit area of ocean surface at normal or vertical incidence
+
00
a"(0")
APPENDIX E. GLOSSARY OF SYMBOLS
503
The amount (in space) by which a pulse is stretched by scattering from waves of RMS height h Normalized radar cross section Density anomaly Average radar cross section for a short-pulse altimeter as function of time Total wind stress; atmospheric transmittance; temporal half-power width of a Gaussian pulse Complex surface wind-stress vector Zonal component of T Wave-induced Reynolds stress Angle at earth center from satellite to point [ on ocean surface; longitude Angle between direction of travel of ocean wave field and flight direction Nondimensional wind shear Error function of argument y Angle at antenna from nadir to point [ on ocean surface Two-dimensional wave-height spectrum as function of wavenumber Frequency (o= 1/T) Frequency of long ocean waves Dispersion relation Rotation speed of the earth Ensemble average