Claire Lavigne,1,*
Antoine Roblin,1
and Patrick Chervet1
1Applied and Theoretical Optics Department, Office National d’Etudes et de Recherches Aérospatiales, The French Aerospace Lab, Chemin de la Hunière, 91761 Palaiseau cedex, France
Solar scattering on oriented cirrus crystals near the specular reflection direction is modeled using a mix method combining geometric optics and diffraction effects at three wavelengths in the visible and infrared domains. Different potential sources of phase function broadening around the specular direction, such as multiple scattering, solar disk, or tilt effects, are studied by means of a Monte Carlo method. The radiance detected by an airborne sensor located a few kilometers above the cirrus cloud and pointing in the specular scattering direction is calculated at four solar zenith angles showing a dramatic increase of the signal in relation to the usual assumption of random crystal orientation.
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Maximum of the Phase Function () of a Cirrus Layer Around the Direction of Specular Scattering in Case of Oriented Crystals for Three Wavelengths λ and Four Solar Zenith Angles Crystalsa
Solar Zenith Angle )
10
191
14.1
6.9
30
155
13.6
6.5
50
171
13.5
6.7
70
255
16.6
9.1
Properties have been averaged over distribution 13 of Fu, and the specular layer thickness is equal to . A Gaussian fit has been applied to the initial function.
Table 2
Standard Deviation of the Phase Function of a Cirrus Layer Around the Direction of Specular Scattering in Case of Oriented Crystals for Three Wavelengths λ and Four Solar Zenith Anglesa
Solar Zenith Angle
10
0.50
0.75
0.82
30
0.50
0.75
0.86
50
0.50
0.85
0.98
70
0.55
1.20
1.46
Crystals properties have been averaged over distribution 13 of Fu, and the specular layer thickness is equal to . A Gaussian fit has been applied to the initial function.
Table 3
Comparison Between the Radiance Obtained at the Center of a Sensor Taking Into Account Oriented and Nonoriented Crystals at Three Wavelengths and Four Solar Zenith Anglesa
Wavelength ()
Solar Zenith Angle
Solar Scattered Radiance for Oriented Crystals ()
Solar Scattered Radiance for Non- oriented Crystals ()
Thermal Radiance ()
0.55
10
0
30
0
50
0
70
0
3.7
10
30
50
70
5.0
10
30
50
70
Clouds properties are taken from Fu distribution number 13. The cloud altitude and sensor are respectively equal to 11 and . Thickness of the whole cloud layer is equal to . 10% of the crystals are supposed to be oriented, and the thickness of the specular layer is .
Tables (3)
Table 1
Maximum of the Phase Function () of a Cirrus Layer Around the Direction of Specular Scattering in Case of Oriented Crystals for Three Wavelengths λ and Four Solar Zenith Angles Crystalsa
Solar Zenith Angle )
10
191
14.1
6.9
30
155
13.6
6.5
50
171
13.5
6.7
70
255
16.6
9.1
Properties have been averaged over distribution 13 of Fu, and the specular layer thickness is equal to . A Gaussian fit has been applied to the initial function.
Table 2
Standard Deviation of the Phase Function of a Cirrus Layer Around the Direction of Specular Scattering in Case of Oriented Crystals for Three Wavelengths λ and Four Solar Zenith Anglesa
Solar Zenith Angle
10
0.50
0.75
0.82
30
0.50
0.75
0.86
50
0.50
0.85
0.98
70
0.55
1.20
1.46
Crystals properties have been averaged over distribution 13 of Fu, and the specular layer thickness is equal to . A Gaussian fit has been applied to the initial function.
Table 3
Comparison Between the Radiance Obtained at the Center of a Sensor Taking Into Account Oriented and Nonoriented Crystals at Three Wavelengths and Four Solar Zenith Anglesa
Wavelength ()
Solar Zenith Angle
Solar Scattered Radiance for Oriented Crystals ()
Solar Scattered Radiance for Non- oriented Crystals ()
Thermal Radiance ()
0.55
10
0
30
0
50
0
70
0
3.7
10
30
50
70
5.0
10
30
50
70
Clouds properties are taken from Fu distribution number 13. The cloud altitude and sensor are respectively equal to 11 and . Thickness of the whole cloud layer is equal to . 10% of the crystals are supposed to be oriented, and the thickness of the specular layer is .