Abstract

The backscattering Mueller matrix has been calculated for the first time for the hexagonal ice columns and plates with both zenith and azimuth preferential orientations. The possibility of a vertically pointing polarization lidar measuring the full Mueller matrix for retrieving the orientation distributions of the crystals is considered. It is shown that the element m44 or, equivalently, the circular depolarization ratio distinguishes between the low and high zenith tilts of the crystals. Then, at their low or high zenith tilts, either the element m22 or m34, respectively, should be measured to retrieve the azimuth tilts.

© 2016 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. V. Noel, H. Chepfer, G. Ledanois, A. Delaval, and P. H. Flamant, “Classification of particle effective shape ratios in cirrus clouds based on the lidar depolarization ratio,” Appl. Opt. 41(21), 4245–4257 (2002).
    [Crossref] [PubMed]
  4. 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]
  5. 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]
  6. 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]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  18. W. W. Willmarth, N. E. Hawk, and R. L. Harvey, “Steady and unsteady motions and wakes of freely falling disks,” Phys. Fluids 7(2), 197–208 (1964).
    [Crossref]
  19. C. D. Westbrook, A. J. Illingworth, E. J. O’Connor, and R. J. Hogan, “Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds,” Q. J. R. Meteorol. Soc. 136(646), 260–276 (2010).
    [Crossref]
  20. A. J. Heymsfield and L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIREII,” J. Atmos. Sci. 52(23), 4302–4326 (1995).
    [Crossref]
  21. D. L. Mitchell and W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51(6), 817–832 (1994).
    [Crossref]
  22. https://github.com/sasha-tvo/Beam-Splitting . Branch: physical-optics.
  23. A. Borovoi, A. Konoshonkin, and N. Kustova, “The physical-optics approximation and its application to light backscattering by hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf. 146, 181–189 (2014).
    [Crossref]

2016 (1)

2015 (1)

2014 (3)

2013 (1)

2010 (1)

C. D. Westbrook, A. J. Illingworth, E. J. O’Connor, and R. J. Hogan, “Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds,” Q. J. R. Meteorol. Soc. 136(646), 260–276 (2010).
[Crossref]

2009 (2)

Y. Balin, B. Kaul, G. Kokhanenko, and D. Winker, “Application of circularly polarized laser radiation for sensing of crystal clouds,” Opt. Express 17(8), 6849–6859 (2009).
[Crossref] [PubMed]

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 (1)

2005 (1)

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]

2004 (1)

2002 (1)

2001 (1)

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]

1995 (2)

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

A. J. Heymsfield and L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIREII,” J. Atmos. Sci. 52(23), 4302–4326 (1995).
[Crossref]

1994 (1)

D. L. Mitchell and W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51(6), 817–832 (1994).
[Crossref]

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]

1964 (1)

W. W. Willmarth, N. E. Hawk, and R. L. Harvey, “Steady and unsteady motions and wakes of freely falling disks,” Phys. Fluids 7(2), 197–208 (1964).
[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]

Arnott, W. P.

D. L. Mitchell and W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51(6), 817–832 (1994).
[Crossref]

Balin, Y.

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]

Borovoi, A.

Castagnoli, F.

Cheong, H. D.

Chepfer, H.

Del Guasta, M.

Delaval, A.

Ding, J.

Flamant, P. H.

Flynn, C. J.

Gimmestad, G. G.

Harvey, R. L.

W. W. Willmarth, N. E. Hawk, and R. L. Harvey, “Steady and unsteady motions and wakes of freely falling disks,” Phys. Fluids 7(2), 197–208 (1964).
[Crossref]

Hawk, N. E.

W. W. Willmarth, N. E. Hawk, and R. L. Harvey, “Steady and unsteady motions and wakes of freely falling disks,” Phys. Fluids 7(2), 197–208 (1964).
[Crossref]

Hayman, M.

Heymsfield, A. J.

A. J. Heymsfield and L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIREII,” J. Atmos. Sci. 52(23), 4302–4326 (1995).
[Crossref]

Hogan, R. J.

C. D. Westbrook, A. J. Illingworth, E. J. O’Connor, and R. J. Hogan, “Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds,” Q. J. R. Meteorol. Soc. 136(646), 260–276 (2010).
[Crossref]

Holz, R. E.

Hu, Y.

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]

Illingworth, A. J.

C. D. Westbrook, A. J. Illingworth, E. J. O’Connor, and R. J. Hogan, “Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds,” Q. J. R. Meteorol. Soc. 136(646), 260–276 (2010).
[Crossref]

Kaul, B.

Kaul, B. V.

Kim, D.

King, M. D.

Klett, J. D.

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

Kokhanenko, G.

Konoshonkin, A.

Kustova, N.

Ledanois, G.

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]

Mathur, S.

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]

Mendoza, A.

Meyer, K. G.

Miloshevich, L. M.

A. J. Heymsfield and L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIREII,” J. Atmos. Sci. 52(23), 4302–4326 (1995).
[Crossref]

Mitchell, D. L.

D. L. Mitchell and W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51(6), 817–832 (1994).
[Crossref]

Morandi, M.

Morley, B.

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]

V. Noel, H. Chepfer, G. Ledanois, A. Delaval, and P. H. Flamant, “Classification of particle effective shape ratios in cirrus clouds based on the lidar depolarization ratio,” Appl. Opt. 41(21), 4245–4257 (2002).
[Crossref] [PubMed]

O’Connor, E. J.

C. D. Westbrook, A. J. Illingworth, E. J. O’Connor, and R. J. Hogan, “Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds,” Q. J. R. Meteorol. Soc. 136(646), 260–276 (2010).
[Crossref]

Platnick, S.

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]

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]

Riviere, O.

Samokhvalov, I. V.

Sassen, K.

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]

Spuler, S.

Vallar, E.

Vaughan, M. A.

J. Ding, P. Yang, R. E. Holz, S. Platnick, K. G. Meyer, M. A. Vaughan, Y. Hu, and M. D. King, “Ice cloud backscatter study and comparison with CALIPSO and MODIS satellite data,” Opt. Express 24(1), 620–636 (2016).
[Crossref] [PubMed]

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.

Volkov, S. N.

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]

Westbrook, C. D.

C. D. Westbrook, A. J. Illingworth, E. J. O’Connor, and R. J. Hogan, “Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds,” Q. J. R. Meteorol. Soc. 136(646), 260–276 (2010).
[Crossref]

Willmarth, W. W.

W. W. Willmarth, N. E. Hawk, and R. L. Harvey, “Steady and unsteady motions and wakes of freely falling disks,” Phys. Fluids 7(2), 197–208 (1964).
[Crossref]

Winker, D.

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]

Yang, P.

Zheng, Y.

Appl. Opt. (5)

J. Appl. Meteorol. (2)

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]

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]

J. Atmos. Ocean. Technol. (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]

J. Atmos. Sci. (4)

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]

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

A. J. Heymsfield and L. M. Miloshevich, “Relative humidity and temperature influences on cirrus formation and evolution: observations from wave clouds and FIREII,” J. Atmos. Sci. 52(23), 4302–4326 (1995).
[Crossref]

D. L. Mitchell and W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51(6), 817–832 (1994).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (1)

A. Borovoi, A. Konoshonkin, and N. Kustova, “The physical-optics approximation and its application to light backscattering by hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transf. 146, 181–189 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Fluids (1)

W. W. Willmarth, N. E. Hawk, and R. L. Harvey, “Steady and unsteady motions and wakes of freely falling disks,” Phys. Fluids 7(2), 197–208 (1964).
[Crossref]

Q. J. R. Meteorol. Soc. (1)

C. D. Westbrook, A. J. Illingworth, E. J. O’Connor, and R. J. Hogan, “Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds,” Q. J. R. Meteorol. Soc. 136(646), 260–276 (2010).
[Crossref]

Other (2)

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000).

https://github.com/sasha-tvo/Beam-Splitting . Branch: physical-optics.

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Figures (8)

Fig. 1
Fig. 1 The model of crystal orientations.
Fig. 2
Fig. 2 The element m 44 versus the zenith tilts for the hexagonal ice plates (solid) and columns (dashed).
Fig. 3
Fig. 3 Typical ray trajectories: specular reflection (a), grazing-ray trajectory (b), and corner reflection (c).
Fig. 4
Fig. 4 The backscattering cross section for the hexagonal ice plates (solid) and columns (dashed). The crystal size is marked by the same color as in Fig. 2.
Fig. 5
Fig. 5 The element m 12 versus the azimuth A and zenith B tilts: (a) plate, D = 31.6 µm, h = 9.53 µm; (b) plate, D = 100 µm, h = 16 µm; (c) column, D = 22.1 µm, h = 31.6 µm; (d) column, D = 123.8 µm, h = 316 µm.
Fig. 6
Fig. 6 The same as in Fig. 5 for the element m 34 .
Fig. 7
Fig. 7 The same as in Fig. 5 for the element m 22 .
Fig. 8
Fig. 8 The same as in Fig. 5 for the element m 33 .

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

M 0 = σ π ( 1 0 0 0 0 1 d 0 0 0 0 1 + d 0 0 0 0 1 + 2 d ) .
δ l = d / ( 2 d ) ; δ c = d / ( 1 d ) .
M 1 = σ π ( 1 m 12 0 0 m 12 m 22 0 0 0 0 m 33 m 34 0 0 m 34 m 44 ) .
m 22 m 33 + m 44 = 1.
M 2 = R ( φ ) M 1 R ( φ ) ,
R ( φ ) = ( 1 0 0 0 0 cos 2 φ sin 2 φ 0 0 sin 2 φ cos 2 φ 0 0 0 0 1 ) .
M 2 = σ π ( 1 m 12 cos 2 φ m 12 sin 2 φ 0 m 12 cos 2 φ m 22 ( m 22 + m 33 ) sin 2 φ ( m 22 + m 33 ) cos 2 φ sin 2 φ m 34 sin 2 φ m 12 sin 2 φ ( m 22 + m 33 ) cos 2 φ 2 sin φ m 33 ( m 22 + m 33 ) sin 2 2 φ m 34 cos φ 0 m 34 sin 2 φ m 34 cos 2 φ m 34 ) .
δ c = ( 1 + m 44 ) / ( 1 m 44 ) .
m 12 = m 34 = 0 ; m 22 = m 33 .
p ( α , β ) = { 1 / S p , c within the shaded domains, 0 otherwise,
m 22 ( A , B ) m 33 ( A , B ) + m 44 ( B ) = 1

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