Abstract

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.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
    [CrossRef]
  6. V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
    [CrossRef]
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    [CrossRef]
  8. W. Tape and G. P. Konnen, “A general setting for halo theory,” Appl. Opt. 38, 1552-1625 (1998).
    [CrossRef]
  9. F.-M. Bréon and B. Dubrulle, “Horizontally oriented plates in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
    [CrossRef]
  10. R. Greenler, Rainbows, Halos, and Glories (Cambridge University, 1989).
  11. A. G. Borovoi, A. V. Burnashov, and A. Y. S. Cheng, “Light scattering by horizontally oriented ice crystal plates,” J. Quant. Spectrosc. Radiat. Transfer 106, 11-20 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. J. I. Katz, “Subsuns and low Reynolds number flow,” J. Atmos. Sci. 55, 3358-3362 (1998).
    [CrossRef]
  16. E. Trankle and R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591-599 (1987).
    [CrossRef]
  17. M. Pekkola, M. Riikonen, J. Moilanen, and J. Ruoskanen, “Halo arcs From airborne, pyramidal ice crystals falling with their c axes in vertical orientation,” Appl. Opt. 37, 1435-1440(1998).
    [CrossRef]
  18. K. Sassen, “Halos in cirrus clouds: why are classic displays so rare?,” Appl. Opt. 44, 5684-5687 (2005).
    [CrossRef] [PubMed]
  19. Y. Takano and K. N. Liou, “Halo phenomena modified by multiple scattering,” J. Opt. Soc. Am. A 7, 885-889 (1990).
    [CrossRef]
  20. K. Sassen, “Polarization and Brewster angle properties of light pillars,” J. Opt. Soc. Am. 4, 570-580 (1987).
    [CrossRef]
  21. L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211-216 (1990).
  22. K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422-429 (1980).
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    [CrossRef]
  25. S. Klotzsche and A. Macke, “Influence of crystal tilt on solar irradiance of cirrus clouds,” Appl. Opt. 45, 1034-1040 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  27. V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystal,” J. Atmos. Sci. 63, 1513-1525 (2006).
    [CrossRef]
  28. M. I. Mishchenko, D. J. Wielaard, and B. E. Carlson, “T-matrix computation of zenith-enhanced lidar backscatter from horizontally oriented ice plate,” Geophys. Res. Lett. 24, 771-774 (1997).
    [CrossRef]
  29. M. Born and E. Wolf, Principles of Optics : Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
    [PubMed]
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    [CrossRef]
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    [CrossRef]
  33. H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
    [CrossRef]
  34. V. Noel and K. Sassen, “Study of planar ice crystal orientations in Ice Clouds from sacking polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
    [CrossRef]

2007 (1)

A. G. Borovoi, A. V. Burnashov, and A. Y. S. Cheng, “Light scattering by horizontally oriented ice crystal plates,” J. Quant. Spectrosc. Radiat. Transfer 106, 11-20 (2007).
[CrossRef]

2006 (2)

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystal,” J. Atmos. Sci. 63, 1513-1525 (2006).
[CrossRef]

S. Klotzsche and A. Macke, “Influence of crystal tilt on solar irradiance of cirrus clouds,” Appl. Opt. 45, 1034-1040 (2006).
[CrossRef] [PubMed]

2005 (2)

K. Sassen, “Halos in cirrus clouds: why are classic displays so rare?,” Appl. Opt. 44, 5684-5687 (2005).
[CrossRef] [PubMed]

V. Noel and K. Sassen, “Study of planar ice crystal orientations in Ice Clouds from sacking polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

2004 (2)

F.-M. Bréon and B. Dubrulle, “Horizontally oriented plates in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

2000 (1)

1999 (2)

H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
[CrossRef]

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

1998 (3)

1997 (1)

M. I. Mishchenko, D. J. Wielaard, and B. E. Carlson, “T-matrix computation of zenith-enhanced lidar backscatter from horizontally oriented ice plate,” Geophys. Res. Lett. 24, 771-774 (1997).
[CrossRef]

1996 (2)

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813-2825 (1996).
[CrossRef]

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Clim. 9, 2058-2081 (1996).
[CrossRef]

1995 (1)

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276-2285 (1995).
[CrossRef]

1994 (1)

1990 (2)

Y. Takano and K. N. Liou, “Halo phenomena modified by multiple scattering,” J. Opt. Soc. Am. A 7, 885-889 (1990).
[CrossRef]

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211-216 (1990).

1989 (1)

1987 (2)

E. Trankle and R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591-599 (1987).
[CrossRef]

K. Sassen, “Polarization and Brewster angle properties of light pillars,” J. Opt. Soc. Am. 4, 570-580 (1987).
[CrossRef]

1986 (1)

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167-1199 (1986).
[CrossRef]

1984 (1)

1981 (1)

R. F. Coleman and K.-N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos. Sci. 38, 1260-1271 (1981).
[CrossRef]

1980 (1)

K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422-429 (1980).

1978 (1)

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

1970 (1)

A. H. Auer and D. L. Veal, “Dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919-926 (1970).
[CrossRef]

1969 (1)

A. Ono, “Shape and riming properties of ice crystals in natural clouds,” J. Atmos. Sci. 26, 138-147 (1969).
[CrossRef]

Liou, K. N.

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167-1199 (1986).
[CrossRef]

Abshire, N. L.

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Auer, A. H.

A. H. Auer and D. L. Veal, “Dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919-926 (1970).
[CrossRef]

Baker, B.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystal,” J. Atmos. Sci. 63, 1513-1525 (2006).
[CrossRef]

Blasband, C. B.

J. G. Shanks, F. C. Mertz, C. B. Blasband, and T. Kassal, “Specular scattering from cirrus clouds: a first-order model,” in Proceedings of the Cloud Impact, Department of Defense Operations and Systems 1991 , D. Grantham and W. Snow, eds. (U.S. Government Printing Office, 1991), p. 207.

Born, M.

M. Born and E. Wolf, Principles of Optics : Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

Borovoi, A. G.

A. G. Borovoi, A. V. Burnashov, and A. Y. S. Cheng, “Light scattering by horizontally oriented ice crystal plates,” J. Quant. Spectrosc. Radiat. Transfer 106, 11-20 (2007).
[CrossRef]

Breon, F. M.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Bréon, F.-M.

F.-M. Bréon and B. Dubrulle, “Horizontally oriented plates in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

Brogniez, G.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
[CrossRef]

Burnashov, A. V.

A. G. Borovoi, A. V. Burnashov, and A. Y. S. Cheng, “Light scattering by horizontally oriented ice crystal plates,” J. Quant. Spectrosc. Radiat. Transfer 106, 11-20 (2007).
[CrossRef]

Carlson, B. E.

M. I. Mishchenko, D. J. Wielaard, and B. E. Carlson, “T-matrix computation of zenith-enhanced lidar backscatter from horizontally oriented ice plate,” Geophys. Res. Lett. 24, 771-774 (1997).
[CrossRef]

Cartwright, J. C.

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211-216 (1990).

Cheng, A. Y. S.

A. G. Borovoi, A. V. Burnashov, and A. Y. S. Cheng, “Light scattering by horizontally oriented ice crystal plates,” J. Quant. Spectrosc. Radiat. Transfer 106, 11-20 (2007).
[CrossRef]

Chepfer, H.

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
[CrossRef]

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Coleman, R. F.

R. F. Coleman and K.-N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos. Sci. 38, 1260-1271 (1981).
[CrossRef]

Dubrulle, B.

F.-M. Bréon and B. Dubrulle, “Horizontally oriented plates in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

Flamant, P. H.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
[CrossRef]

Fraser, A. B.

Fu, Q.

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Clim. 9, 2058-2081 (1996).
[CrossRef]

Gayet, J.-F.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystal,” J. Atmos. Sci. 63, 1513-1525 (2006).
[CrossRef]

Gedzelman, S. D.

Goloub, P.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Greenler, R.

R. Greenler, Rainbows, Halos, and Glories (Cambridge University, 1989).

Greenler, R. G.

Kassal, T.

J. G. Shanks, F. C. Mertz, C. B. Blasband, and T. Kassal, “Specular scattering from cirrus clouds: a first-order model,” in Proceedings of the Cloud Impact, Department of Defense Operations and Systems 1991 , D. Grantham and W. Snow, eds. (U.S. Government Printing Office, 1991), p. 207.

Katz, J. I.

J. I. Katz, “Subsuns and low Reynolds number flow,” J. Atmos. Sci. 55, 3358-3362 (1998).
[CrossRef]

Klett, J. D.

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276-2285 (1995).
[CrossRef]

Klotzsche, S.

Konnen, G. P.

Lawson, P.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystal,” J. Atmos. Sci. 63, 1513-1525 (2006).
[CrossRef]

Liou, K. N.

Liou, K. N.

K. N. Liou, Radiation and Cloud Processes in the Atmosphere, Theory, Observation and Modelling (Oxford University, 1992).

Liou, K.-N.

R. F. Coleman and K.-N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos. Sci. 38, 1260-1271 (1981).
[CrossRef]

Lynch, D. K.

Macke, A.

S. Klotzsche and A. Macke, “Influence of crystal tilt on solar irradiance of cirrus clouds,” Appl. Opt. 45, 1034-1040 (2006).
[CrossRef] [PubMed]

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813-2825 (1996).
[CrossRef]

McNice, G. T.

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Mertz, F. C.

J. G. Shanks, F. C. Mertz, C. B. Blasband, and T. Kassal, “Specular scattering from cirrus clouds: a first-order model,” in Proceedings of the Cloud Impact, Department of Defense Operations and Systems 1991 , D. Grantham and W. Snow, eds. (U.S. Government Printing Office, 1991), p. 207.

Mishchenko, M. I.

M. I. Mishchenko, “Calculation of the amplitude matrix for a nonspherical particle in a fixed orientation,” Appl. Opt. 39, 1026-1031 (2000).
[CrossRef]

M. I. Mishchenko, D. J. Wielaard, and B. E. Carlson, “T-matrix computation of zenith-enhanced lidar backscatter from horizontally oriented ice plate,” Geophys. Res. Lett. 24, 771-774 (1997).
[CrossRef]

Moilanen, J.

Mueller, J.

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813-2825 (1996).
[CrossRef]

Noel, V.

V. Noel and K. Sassen, “Study of planar ice crystal orientations in Ice Clouds from sacking polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

Ono, A.

A. Ono, “Shape and riming properties of ice crystals in natural clouds,” J. Atmos. Sci. 26, 138-147 (1969).
[CrossRef]

Pekkola, M.

Pelon, J.

H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
[CrossRef]

Platt, C. M. R.

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Raschke, E.

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813-2825 (1996).
[CrossRef]

Riikonen, M.

Rockwitz, K.-D.

Ruoskanen, J.

Sassen, K.

K. Sassen, “Halos in cirrus clouds: why are classic displays so rare?,” Appl. Opt. 44, 5684-5687 (2005).
[CrossRef] [PubMed]

V. Noel and K. Sassen, “Study of planar ice crystal orientations in Ice Clouds from sacking polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

K. Sassen, “Polarization and Brewster angle properties of light pillars,” J. Opt. Soc. Am. 4, 570-580 (1987).
[CrossRef]

K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422-429 (1980).

Sauvage, L.

H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
[CrossRef]

Shanks, J. G.

J. G. Shanks, F. C. Mertz, C. B. Blasband, and T. Kassal, “Specular scattering from cirrus clouds: a first-order model,” in Proceedings of the Cloud Impact, Department of Defense Operations and Systems 1991 , D. Grantham and W. Snow, eds. (U.S. Government Printing Office, 1991), p. 207.

Shcherbakov, V.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, “Light scattering by single natural ice crystal,” J. Atmos. Sci. 63, 1513-1525 (2006).
[CrossRef]

Takano, Y.

Tape, W.

Thomas, L.

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211-216 (1990).

Trankle, E.

Trouillet, V.

H. Chepfer, G. Brogniez, L. Sauvage, P. H. Flamant, V. Trouillet, and J. Pelon, “Remote sensing of cirrus radiative parameters during EUCREX'94. Case study of 17 April 1994. Part II : Microphysical models,” Mon. Weather Rev. 127, 504-518 (1999).
[CrossRef]

Veal, D. L.

A. H. Auer and D. L. Veal, “Dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919-926 (1970).
[CrossRef]

Wareing, D. P.

L. Thomas, J. C. Cartwright, and D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211-216 (1990).

Warren, S. G.

Wielaard, D. J.

M. I. Mishchenko, D. J. Wielaard, and B. E. Carlson, “T-matrix computation of zenith-enhanced lidar backscatter from horizontally oriented ice plate,” Geophys. Res. Lett. 24, 771-774 (1997).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics : Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

Appl. Opt. (8)

Geophys. Res. Lett. (1)

M. I. Mishchenko, D. J. Wielaard, and B. E. Carlson, “T-matrix computation of zenith-enhanced lidar backscatter from horizontally oriented ice plate,” Geophys. Res. Lett. 24, 771-774 (1997).
[CrossRef]

J. Appl. Meteorol. (2)

V. Noel and K. Sassen, “Study of planar ice crystal orientations in Ice Clouds from sacking polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

J. Atmos. Sci. (9)

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

A. Ono, “Shape and riming properties of ice crystals in natural clouds,” J. Atmos. Sci. 26, 138-147 (1969).
[CrossRef]

F.-M. Bréon and B. Dubrulle, “Horizontally oriented plates in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276-2285 (1995).
[CrossRef]

J. I. Katz, “Subsuns and low Reynolds number flow,” J. Atmos. Sci. 55, 3358-3362 (1998).
[CrossRef]

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813-2825 (1996).
[CrossRef]

A. H. Auer and D. L. Veal, “Dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919-926 (1970).
[CrossRef]

R. F. Coleman and K.-N. Liou, “Light scattering by hexagonal ice crystals,” J. Atmos. Sci. 38, 1260-1271 (1981).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Geometry of the single crystal diffraction case. ( θ 1 , φ 1 ) is the direction of the incident radiation, and ( θ 2 , φ 2 ) is the direction of the diffracted and reflected radiation.

Fig. 2
Fig. 2

Comparison between the phase function calculated around the direction of specular reflection by the T-matrix method [30] and our method taking into account diffraction effect and geometric considerations for two angles of solar incidence θ 1 equal to (a)  50 ° and (b)  10 ° at a wavelength of 3.7 μm and for a size parameter of 34.

Fig. 3
Fig. 3

Comparison between the phase function calculated around the direction of specular reflection by the T-matrix method [30] and our method taking into account the diffraction effect and geometric considerations for two angles of solar incidence θ i equal to (a)  50 ° (b)  10 ° at a wavelength of 0.55 μm and for a size parameter of 34.

Fig. 4
Fig. 4

Comparison between crystal phase functions in the plane of specular reflection taking into account tilt and diffraction effects for particles with radius equal to (a)  20 μm , (b)  50 μm , and (c)  150 μm at a wavelength of 3.7 μm . The solar zenith angle is taken to be 50 ° .

Fig. 5
Fig. 5

Comparison between the phase function obtained by integration over three kinds of Fu size distributions at λ = 3.7 μm : distribution 13 (FIRE I, 28 October 1986) with a mean effective size D e equal to 122.14 μm , distribution 14 (cirrostratus) with D e equal to 50.15 μm and distribution 22 (CEPEX IWC = 2.68 10 2 g m 3 ) with D e equal to 89.88 μm . The solar zenith angle is equal to 50 ° .

Fig. 6
Fig. 6

Phase function around the direction of specular scattering at 3.7 μm taking into account the diffraction effect and tilt orientation of the crystal for two solar zenith angles, (a)  θ i = 10 ° and (b)  θ i = 50 ° . Crystal properties are integrated over a size distribution of Fu (FIRE I, 28 October 1986, distribution 13) with a mean effective size D e equal to 122.14 μm .

Fig. 7
Fig. 7

Influence of the solar disk width on the phase function obtained by averaging crystal properties over the distribution 13 of Fu [3] at a wavelength of 3.7 μm and for a solar zenith angle equal to 50 ° .

Fig. 8
Fig. 8

Geometry of solar scattering detection from an airborne sensor. θ i is the solar zenith angle, and σ S is the solar disk deviation.

Fig. 9
Fig. 9

Radiance scattered by a cirrus cloud in case of oriented crystals for a sensor FOV equal to 10 ° (a) at a wavelength of 0.55 μm and (b) at a wavelength of 3.7 μm . Sensor and cirrus altitudes are respectively equal to 14 and 11 km , and a solar zenith angle of 50 ° is taken into account. Crystals properties have been averaged over Fu distribution number 13, and thickness of the specular layer is taken to be 150 m.

Tables (3)

Tables Icon

Table 1 Maximum of the Phase Function ( sr 1 ) of a Cirrus Layer Around the Direction of Specular Scattering in Case of Oriented Crystals for Three Wavelengths λ and Four Solar Zenith Angles Crystals a

Tables Icon

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 Angles a

Tables Icon

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 Angles a

Equations (17)

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R 1 2 = ( cos θ i u ) 2 + v 2 ( cos θ i + u ) 2 + v 2 ,
R 2 2 = [ ( m r 2 m i ) 2 cos θ i u ] 2 + ( 2 m r m i cos θ i v ) 2 [ ( m r 2 m i 2 ) cos θ i + u ] 2 + ( 2 m r m i cos θ i + v ) 2 ,
u 2 = 1 2 { m r 2 m i 2 sin θ i + [ ( m r 2 m i 2 sin 2 θ i ) 2 + 4 m r 2 m i 2 ] 1 / 2 } ,
v 2 = 1 2 { ( m r 2 m i 2 sin 2 θ i ) + [ ( m r 2 m i 2 sin 2 θ i ) 2 + 4 m r 2 m i 2 ] 1 / 2 } .
I n ( θ 1 , φ 1 , θ 2 , φ 2 ) = ( 2 J 1 ( k a ω ) k a ω ) 2 ,
ω 2 = sin 2 θ 1 + sin 2 θ 2 + 2 sin θ 1 sin θ 2 cos ( φ 1 φ 2 ) ,
P diff ( θ 2 θ 1 ) = I n ( θ 1 , φ 1 , θ 2 ) Σ θ 2 I n ( θ 1 , φ 1 , θ 2 ) Δ Ω ( θ 2 θ 1 ) ,
P scatt ( θ ) = β P diff ( θ 2 θ 1 ) .
L = 2.02 d 0.449 ,
p tilt ( θ c ) = exp ( θ c 2 / 2 σ c 2 ) 2 π σ c ,
P ( N ( r ) , θ i , θ ) = N ( r ) × P ( θ i , θ , r ) d r N ( r ) d r .
d F + d τ = α F + + β F β F + + t F + , d F d τ = α F + β F + β F + t F ,
ρ = β α + β sinh ( φ τ ) sinh ( φ τ ) + φ α + β cosh ( φ τ ) , φ 2 = 4 α 2 + 3 β 2 + 8 α β 4 α 4 β + 1.
ρ = β τ 1 + τ ( α + β ) β τ .
L scat ( θ i , θ r ) τ = β × I S un cos θ i × T atm × P ( N ( r ) , θ i , θ , φ = π ) , P ( N ( r ) , θ i , θ , φ ) d Ω = 1.
p S un ( θ i , θ r ) = Ω s P ( N ( r ) , θ r , θ , φ ) d Ω ,
L tot ( θ i , θ r ) = β × I S un × T atm × cos θ i × p S un ( θ i , θ r ) × τ Ω s ,

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