Abstract

A general view of the backscattering Mueller matrix for the quasi-horizontally oriented hexagonal ice crystals of cirrus clouds has been obtained in the case of tilted and scanning lidars. It is shown that the main properties of this matrix are caused by contributions from two qualitatively different components referred to the specular and corner-reflection terms. The numerical calculation of the matrix is worked out in the physical optics approximation. These matrices calculated for two wavelengths and two tilt angles (initial and present) of CALIPSO lidar are presented as a data bank. The depolarization and color ratios for these data have been obtained and discussed.

© 2012 OSA

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  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(8), 1220–1224 (1978).
    [CrossRef]
  2. K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci.58(15), 2103–2112 (2001).
    [CrossRef]
  3. V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
    [CrossRef]
  4. M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt.45(20), 4878–4887 (2006).
    [CrossRef] [PubMed]
  5. W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
    [CrossRef]
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    [CrossRef]
  9. A. G. Borovoi and I. A. Grishin, “Scattering matrices for large ice crystal particles,” J. Opt. Soc. Am. A20(11), 2071–2080 (2003).
    [CrossRef] [PubMed]
  10. L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1492–1508 (2011).
    [CrossRef]
  11. P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
    [CrossRef]
  12. G. Chen, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Scattering phase functions of horizontally oriented hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf.100(1-3), 91–102 (2006).
    [CrossRef]
  13. M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett.20(12), 1356–1358 (1995).
    [CrossRef] [PubMed]
  14. G. G. Gimmestad, “Re-examination of depolarization in lidar measurements,” Appl. Opt.47(21), 3795–3802 (2008).
    [CrossRef] [PubMed]
  15. D. L. Mitchell, “Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities,” J. Atmos. Sci.53(12), 1710–1723 (1996).
    [CrossRef]
  16. K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res.111(D22), D22213 (2006), doi:.
    [CrossRef]
  17. K. Sassen, “Remote sensing of planar ice crystals fall attitude,” J. Meteorol. Soc. Jpn.58, 422–429 (1980).
  18. J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci.52(12), 2276–2285 (1995).
    [CrossRef]
  19. H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res.115(D22), D22209 (2010), doi:.
    [CrossRef]
  20. K. Sato and H. Okamoto, “Refinement of global ice microphysics using spaceborne active sensors,” J. Geophys. Res.116(D20), D20202 (2011), doi:.
    [CrossRef]
  21. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge University, 1999).
  22. S. Iwasaki and H. Okamoto, “Analysis of the enhancement of backscattering by nonspherical particles with flat surfaces,” Appl. Opt.40(33), 6121–6129 (2001).
    [CrossRef] [PubMed]
  23. Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express15(9), 5327–5332 (2007).
    [CrossRef] [PubMed]
  24. R. Yoshida, H. Okamoto, Y. Hagihara, and H. Ishimoto, “Global analysis of cloud phase and ice crystal orientation from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data using attenuated backscattering and depolarization ratio,” J. Geophys. Res.115, D00H32 (2010), doi:.
    [CrossRef]
  25. K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett.39(20), L20805 (2012), doi:.
    [CrossRef]

2012 (1)

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett.39(20), L20805 (2012), doi:.
[CrossRef]

2011 (2)

K. Sato and H. Okamoto, “Refinement of global ice microphysics using spaceborne active sensors,” J. Geophys. Res.116(D20), D20202 (2011), doi:.
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1492–1508 (2011).
[CrossRef]

2010 (2)

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res.115(D22), D22209 (2010), doi:.
[CrossRef]

R. Yoshida, H. Okamoto, Y. Hagihara, and H. Ishimoto, “Global analysis of cloud phase and ice crystal orientation from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data using attenuated backscattering and depolarization ratio,” J. Geophys. Res.115, D00H32 (2010), doi:.
[CrossRef]

2009 (1)

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (3)

M. Del Guasta, E. Vallar, O. Riviere, F. Castagnoli, V. Venturi, and M. Morandi, “Use of polarimetric lidar for the study of oriented ice plates in clouds,” Appl. Opt.45(20), 4878–4887 (2006).
[CrossRef] [PubMed]

G. Chen, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Scattering phase functions of horizontally oriented hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf.100(1-3), 91–102 (2006).
[CrossRef]

K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res.111(D22), D22213 (2006), doi:.
[CrossRef]

2005 (2)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng.44(7), 071208 (2005).
[CrossRef]

V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
[CrossRef]

2003 (2)

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

A. G. Borovoi and I. A. Grishin, “Scattering matrices for large ice crystal particles,” J. Opt. Soc. Am. A20(11), 2071–2080 (2003).
[CrossRef] [PubMed]

2001 (2)

S. Iwasaki and H. Okamoto, “Analysis of the enhancement of backscattering by nonspherical particles with flat surfaces,” Appl. Opt.40(33), 6121–6129 (2001).
[CrossRef] [PubMed]

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci.58(15), 2103–2112 (2001).
[CrossRef]

1996 (1)

D. L. Mitchell, “Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities,” J. Atmos. Sci.53(12), 1710–1723 (1996).
[CrossRef]

1995 (2)

1980 (1)

K. Sassen, “Remote sensing of planar ice crystals fall attitude,” 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(8), 1220–1224 (1978).
[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(8), 1220–1224 (1978).
[CrossRef]

Baum, B. A.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1492–1508 (2011).
[CrossRef]

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Benson, S.

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci.58(15), 2103–2112 (2001).
[CrossRef]

Bi, L.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1492–1508 (2011).
[CrossRef]

Borovoi, A. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng.44(7), 071208 (2005).
[CrossRef]

A. G. Borovoi and I. A. Grishin, “Scattering matrices for large ice crystal particles,” J. Opt. Soc. Am. A20(11), 2071–2080 (2003).
[CrossRef] [PubMed]

Castagnoli, F.

Chen, G.

G. Chen, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Scattering phase functions of horizontally oriented hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf.100(1-3), 91–102 (2006).
[CrossRef]

Del Guasta, M.

Flittner, D.

Gimmestad, G. G.

Grishin, I. A.

Hagihara, Y.

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res.115(D22), D22209 (2010), doi:.
[CrossRef]

R. Yoshida, H. Okamoto, Y. Hagihara, and H. Ishimoto, “Global analysis of cloud phase and ice crystal orientation from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data using attenuated backscattering and depolarization ratio,” J. Geophys. Res.115, D00H32 (2010), doi:.
[CrossRef]

Hostetler, C. A.

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Hovenier, J. W.

Hu, Y.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1492–1508 (2011).
[CrossRef]

Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express15(9), 5327–5332 (2007).
[CrossRef] [PubMed]

Hu, Y. X.

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Huang, J.

Hunt, B.

Hunt, W. H.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Ishimoto, H.

R. Yoshida, H. Okamoto, Y. Hagihara, and H. Ishimoto, “Global analysis of cloud phase and ice crystal orientation from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data using attenuated backscattering and depolarization ratio,” J. Geophys. Res.115, D00H32 (2010), doi:.
[CrossRef]

Iwasaki, S.

Kattawar, G. W.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1492–1508 (2011).
[CrossRef]

G. Chen, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Scattering phase functions of horizontally oriented hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf.100(1-3), 91–102 (2006).
[CrossRef]

Kayetha, V. K.

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett.39(20), L20805 (2012), doi:.
[CrossRef]

Klett, J. D.

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci.52(12), 2276–2285 (1995).
[CrossRef]

Kuehn, R.

Kustova, N. V.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng.44(7), 071208 (2005).
[CrossRef]

Lin, B.

Liu, Z.

Lucker, P. L.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[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(8), 1220–1224 (1978).
[CrossRef]

Mishchenko, M. I.

G. Chen, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Scattering phase functions of horizontally oriented hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf.100(1-3), 91–102 (2006).
[CrossRef]

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

M. I. Mishchenko and J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett.20(12), 1356–1358 (1995).
[CrossRef] [PubMed]

Mitchell, D. L.

D. L. Mitchell, “Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities,” J. Atmos. Sci.53(12), 1710–1723 (1996).
[CrossRef]

Morandi, M.

Noel, V.

V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
[CrossRef]

Okamoto, H.

K. Sato and H. Okamoto, “Refinement of global ice microphysics using spaceborne active sensors,” J. Geophys. Res.116(D20), D20202 (2011), doi:.
[CrossRef]

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res.115(D22), D22209 (2010), doi:.
[CrossRef]

R. Yoshida, H. Okamoto, Y. Hagihara, and H. Ishimoto, “Global analysis of cloud phase and ice crystal orientation from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data using attenuated backscattering and depolarization ratio,” J. Geophys. Res.115, D00H32 (2010), doi:.
[CrossRef]

K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res.111(D22), D22213 (2006), doi:.
[CrossRef]

S. Iwasaki and H. Okamoto, “Analysis of the enhancement of backscattering by nonspherical particles with flat surfaces,” Appl. Opt.40(33), 6121–6129 (2001).
[CrossRef] [PubMed]

Oppel, U. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng.44(7), 071208 (2005).
[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(8), 1220–1224 (1978).
[CrossRef]

Poole, L.

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Powell, K.

Powell, K. A.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Reichardt, J.

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Riviere, O.

Rodier, S.

Sassen, K.

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett.39(20), L20805 (2012), doi:.
[CrossRef]

V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol.44(5), 653–664 (2005).
[CrossRef]

K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing. Part II: Microphysical properties derived from lidar depolarization,” J. Atmos. Sci.58(15), 2103–2112 (2001).
[CrossRef]

K. Sassen, “Remote sensing of planar ice crystals fall attitude,” J. Meteorol. Soc. Jpn.58, 422–429 (1980).

Sato, K.

K. Sato and H. Okamoto, “Refinement of global ice microphysics using spaceborne active sensors,” J. Geophys. Res.116(D20), D20202 (2011), doi:.
[CrossRef]

H. Okamoto, K. Sato, and Y. Hagihara, “Global analysis of ice microphysics from CloudSat and CALIPSO: Incorporation of specular reflection in lidar signals,” J. Geophys. Res.115(D22), D22209 (2010), doi:.
[CrossRef]

K. Sato and H. Okamoto, “Characterization of Ze and LDR of nonspherical and inhomogeneous ice particles for 45-GHz cloud lidar: Its implication to microphysical retrievals,” J. Geophys. Res.111(D22), D22213 (2006), doi:.
[CrossRef]

Trepte, C.

Vallar, E.

Vaughan, M.

Vaughan, M. A.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Venturi, V.

Weimer, C.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Winker, D.

Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express15(9), 5327–5332 (2007).
[CrossRef] [PubMed]

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Winker, D. M.

W. H. Hunt, D. M. Winker, M. A. Vaughan, K. A. Powell, P. L. Lucker, and C. Weimer, “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Technol.26(7), 1214–1228 (2009).
[CrossRef]

Wu, D.

Yang, P.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transf.112(9), 1492–1508 (2011).
[CrossRef]

Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization - attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express15(9), 5327–5332 (2007).
[CrossRef] [PubMed]

G. Chen, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Scattering phase functions of horizontally oriented hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf.100(1-3), 91–102 (2006).
[CrossRef]

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Yoshida, R.

R. Yoshida, H. Okamoto, Y. Hagihara, and H. Ishimoto, “Global analysis of cloud phase and ice crystal orientation from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data using attenuated backscattering and depolarization ratio,” J. Geophys. Res.115, D00H32 (2010), doi:.
[CrossRef]

Zhao, J.

P. Yang, Y. X. Hu, D. Winker, J. Zhao, C. A. Hostetler, L. Poole, B. A. Baum, M. I. Mishchenko, and J. Reichardt, “Enhanced lidar backscattering by quasi-horizontally oriented ice crystal plates in cirrus clouds,” J. Quant. Spectrosc. Radiat. Transf.79–80, 1139–1157 (2003).
[CrossRef]

Zhu, J.

K. Sassen, V. K. Kayetha, and J. Zhu, “Ice cloud depolarization for nadir and off-nadir CALIPSO measurements,” Geophys. Res. Lett.39(20), L20805 (2012), doi:.
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Appl. Opt. (3)

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Figures (7)

Fig. 1
Fig. 1

Geometry of a tilted lidar.

Fig. 2
Fig. 2

The specular and corner-reflection components in the backscatter.

Fig. 3
Fig. 3

The backscattering cross section for the specular (light solid curve) and corner-reflection (dashed curve) components. The black curve is their sum.

Fig. 4
Fig. 4

The backscattering Mueller matrix partially averaged over crystal orientations M t (Θ,D) as a function of crystal tilts Θ and diameters D at λ=0.532μm and t=3°.

Fig. 5
Fig. 5

The totally averaged backscattering cross section (a) and the depolarization ratio (b) versus the parameters Θ s and D m of the optical model of Eq. (6) for λ=0.532μm and t=3°.

Fig. 6
Fig. 6

Color ratio for fixed plate diameters D with an averaging over particle tilts.

Fig. 7
Fig. 7

Color ratio at the lidar tilts of 3° (a, b) and 0.3° (c, d) as functions of the parameters Θ s and D m . The right column shows selective profiles.

Equations (11)

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E(n,i)= E 1 (n,i) e θ + E 2 (n,i) e φ ,
M= M 11 ( 1 d 12 0 0 d 12 1 d 22 0 0 0 0 1+ d 33 d 34 0 0 d 34 1+ d 22 + d 33 ),
M 0 = M 11 ( 1 0 0 0 0 1d 0 0 0 0 1+d 0 0 0 0 1+2d ).
δ= d 22 cos 2 2χ+ d 33 sin 2 2χ 2+2 d 12 cos2χ d 22 cos 2 2χ d 33 sin 2 2χ .
h2.02 D 0.449 (in microns).
p(Θ,D| Θ s , D m )= D e D/ D m e Θ 2 /2 Θ s 2 10μm 1000μm D e D/ D m dD 0 20° e Θ 2 /2 Θ s 2 sinΘdΘ .
M 0 (Θ)= 0 2π L(Φ)Q(Θ)L(Φ) dΦ/2π,
L(Φ)=( 1 0 0 0 0 cos2Φ sin2Φ 0 0 sin2Φ cos2Φ 0 0 0 0 1 ).
σ(0)= M 0°11 (0)=[r+r (1r) 2 +O( r 2 )] S 2 / λ 2 ,
M= D min D max dD 0 π M(Θ,D)p(Θ,D)sinΘdΘ .
M t (Θ,D)= 0 2π L( ξ(Φ) )Q( η(Φ),D ) L( ξ(Φ) )dΦ/2π,

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