Abstract

The application of circularly polarized laser radiation and measurement of the fourth Stokes parameter of scattered radiation considerably reduce the probability of obtaining ambiguous results for radiation depolarization in laser sensing of crystal clouds. The uncertainty arises when cloud particles appear partially oriented by their large diameters along a certain azimuth direction. Approximately in 30% of all cases, the measured depolarization depends noticeably on the orientation of the lidar reference plane with respect to the particle orientation direction. In this case, the corridor of the most probable depolarization values is about 0.1–0.15, but in individual cases, it can be noticeably wider. The present article considers theoretical aspects of this phenomenon and configuration of a lidar capable of measuring the fourth Stokes parameter together with an algorithm of lidar signal processing in the presence of optically thin cloudiness when molecular scattering cannot be neglected. It is demonstrated that the element a 44 of the normalized backscattering phase matrix (BSPM) can be measured. Results of measurements are independent of the presence or absence of azimuthal particle orientation. For sensing in the zenith or nadir, this element characterizes the degree of horizontal orientation of long particle diameters under the action of aerodynamic forces arising during free fall of particles.

© 2009 Optical Society of America

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References

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  1. K. Sassen and D. K.  Lynch, "What are cirrus clouds?" in Cirrus, OSA Technical Digest (Opt. Soc. Am., Washington DC, 1998), pp. 2-3.
  2. Yu. F.  Arshinov, B. V. Kaul, and I. V.  Samokhvalov, "Study of crystal clouds by measuring the backscattering phase matrices with polarization lidar: Particle orientation in cirrus," in Cirrus, OSA Technical Digest (Opt. Soc. Am., Washington DC, 1998), pp. 131-134.
  3. C. M. R. Platt, Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals," J. Appl. Meteorol. 17, 1220-1224 (1978).
    [CrossRef]
  4. H.-R.  Cho, J. V. Iribarne, and W. G. Richards, "On the orientation of ice crystals in a cumulo-nimbus cloud," J. Atmos. Sci. 38, 1111 - 1114 (1981).
    [CrossRef]
  5. J. D.  Klett, "Orientation model for particles in turbulence," J. Atmos. Sci. 52, 2276-2285 (1995).
    [CrossRef]
  6. B. V. Kaul and I. V. Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation," J. Atmos. Oceanic Opt. 18, 866- 870 (2005).
  7. B. V.  Kaul, I. V.  Samokhvalov, and S. N.  Volkov, "Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar," Appl. Opt. 43, 6620 -6628 (2004).
    [CrossRef]
  8. V. Noel and K. Sassen, "Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations," J. Appl. Meteor. 44, 653-664 (2005).
    [CrossRef]
  9. D. M. Winker, W. H. Hunt, and M. J. McGill, "Initial performance assessment of CALIOP," Geophys. Res. Lett. 34, L19803, doi:10.1029/2007GL030135 (2007).
    [CrossRef]
  10. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley and Sons, Inc. New York; Chapman and Hall, Ltd. London, 1957).
  11. B. V. Kaul, "Symmetry of light backscattering matrices of nonspherical aerosol particles," J. Atmos. Oceanic Opt. 13, 829-833 (2000).
  12. M. I. Mishchenko and J. W. Hovenier, "Depolarization of light backscattered by randomly oriented nonspherical particles," Opt. Lett. 20, 1356-1358 (1995).
    [CrossRef] [PubMed]
  13. G. G.  Gimmestad, "Reexamination of depolarization in lidar measurements," Appl. Opt. 47, 3795-3802 (2008).
    [CrossRef] [PubMed]
  14. C. J.  Flynn, A.  Mendoza, Yu.  Zheng, and S.  Mathur, "Novel polarization-sensitive micropulse lidar measurement technique," Opt. Express 15, 2785-2790 (2007).
    [CrossRef] [PubMed]
  15. B. V. Kaul and I. V.  Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation," J. Atmos. Oceanic Opt. 19, 38- 42 (2006).
  16. B. V. Kaul, "Influence of electric field on ice cloud orientation," J. Atmos. Oceanic Opt. 19, 835- 840 (2006).
  17. D. N.  Romashov, "Backscattering matrix for monodisperse ensembles of hexagonal ice crystals," J. Atmos. Oceanic Opt. 12, 376-384 (1999).
  18. 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, 4878-4887 (2006).
    [CrossRef] [PubMed]
  19. P. B.  Russell, J. Y.  Swissler, and P. M.  McCormick, "Methodology of error analysis and simulation of lidar aerosol measurements," Appl. Opt. 18, 3783-3790 (1979).
    [PubMed]

2008

2007

C. J.  Flynn, A.  Mendoza, Yu.  Zheng, and S.  Mathur, "Novel polarization-sensitive micropulse lidar measurement technique," Opt. Express 15, 2785-2790 (2007).
[CrossRef] [PubMed]

D. M. Winker, W. H. Hunt, and M. J. McGill, "Initial performance assessment of CALIOP," Geophys. Res. Lett. 34, L19803, doi:10.1029/2007GL030135 (2007).
[CrossRef]

2006

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, 4878-4887 (2006).
[CrossRef] [PubMed]

B. V. Kaul and I. V.  Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation," J. Atmos. Oceanic Opt. 19, 38- 42 (2006).

B. V. Kaul, "Influence of electric field on ice cloud orientation," J. Atmos. Oceanic Opt. 19, 835- 840 (2006).

2005

B. V. Kaul and I. V. Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation," J. Atmos. Oceanic Opt. 18, 866- 870 (2005).

V. Noel and K. Sassen, "Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations," J. Appl. Meteor. 44, 653-664 (2005).
[CrossRef]

2004

2000

B. V. Kaul, "Symmetry of light backscattering matrices of nonspherical aerosol particles," J. Atmos. Oceanic Opt. 13, 829-833 (2000).

1999

D. N.  Romashov, "Backscattering matrix for monodisperse ensembles of hexagonal ice crystals," J. Atmos. Oceanic Opt. 12, 376-384 (1999).

1995

1981

H.-R.  Cho, J. V. Iribarne, and W. G. Richards, "On the orientation of ice crystals in a cumulo-nimbus cloud," J. Atmos. Sci. 38, 1111 - 1114 (1981).
[CrossRef]

1979

1978

C. M. R. Platt, Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals," J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Castagnoli, Francesco

Cho, H.-R.

H.-R.  Cho, J. V. Iribarne, and W. G. Richards, "On the orientation of ice crystals in a cumulo-nimbus cloud," J. Atmos. Sci. 38, 1111 - 1114 (1981).
[CrossRef]

Del Guasta, Massimo

Flynn, C. J.

Gimmestad, G. G.

Hovenier, J. W.

Hunt, W. H.

D. M. Winker, W. H. Hunt, and M. J. McGill, "Initial performance assessment of CALIOP," Geophys. Res. Lett. 34, L19803, doi:10.1029/2007GL030135 (2007).
[CrossRef]

Iribarne, J. V.

H.-R.  Cho, J. V. Iribarne, and W. G. Richards, "On the orientation of ice crystals in a cumulo-nimbus cloud," J. Atmos. Sci. 38, 1111 - 1114 (1981).
[CrossRef]

Kaul, B. V.

B. V. Kaul and I. V.  Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation," J. Atmos. Oceanic Opt. 19, 38- 42 (2006).

B. V. Kaul, "Influence of electric field on ice cloud orientation," J. Atmos. Oceanic Opt. 19, 835- 840 (2006).

B. V. Kaul and I. V. Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation," J. Atmos. Oceanic Opt. 18, 866- 870 (2005).

B. V.  Kaul, I. V.  Samokhvalov, and S. N.  Volkov, "Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar," Appl. Opt. 43, 6620 -6628 (2004).
[CrossRef]

B. V. Kaul, "Symmetry of light backscattering matrices of nonspherical aerosol particles," J. Atmos. Oceanic Opt. 13, 829-833 (2000).

Klett, J. D.

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

Mathur, S.

McCormick, P. M.

McGill, M. J.

D. M. Winker, W. H. Hunt, and M. J. McGill, "Initial performance assessment of CALIOP," Geophys. Res. Lett. 34, L19803, doi:10.1029/2007GL030135 (2007).
[CrossRef]

Mendoza, A.

Mishchenko, M. I.

Morandi, Marco

Noel, V.

V. Noel and K. Sassen, "Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations," J. Appl. Meteor. 44, 653-664 (2005).
[CrossRef]

Platt, C. M. R.

C. M. R. Platt, Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals," J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Richards, W. G.

H.-R.  Cho, J. V. Iribarne, and W. G. Richards, "On the orientation of ice crystals in a cumulo-nimbus cloud," J. Atmos. Sci. 38, 1111 - 1114 (1981).
[CrossRef]

Riviere, Olivier

Romashov, D. N.

D. N.  Romashov, "Backscattering matrix for monodisperse ensembles of hexagonal ice crystals," J. Atmos. Oceanic Opt. 12, 376-384 (1999).

Russell, P. B.

Samokhvalov, I. V.

B. V. Kaul and I. V.  Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation," J. Atmos. Oceanic Opt. 19, 38- 42 (2006).

B. V. Kaul and I. V. Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation," J. Atmos. Oceanic Opt. 18, 866- 870 (2005).

B. V.  Kaul, I. V.  Samokhvalov, and S. N.  Volkov, "Investigating particle orientation in cirrus clouds by measuring backscattering phase matrices with lidar," Appl. Opt. 43, 6620 -6628 (2004).
[CrossRef]

Sassen, K.

V. Noel and K. Sassen, "Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations," J. Appl. Meteor. 44, 653-664 (2005).
[CrossRef]

Swissler, J. Y.

Vallar, Edgar

Venturi, Valerio

Volkov, S. N.

Winker, D. M.

D. M. Winker, W. H. Hunt, and M. J. McGill, "Initial performance assessment of CALIOP," Geophys. Res. Lett. 34, L19803, doi:10.1029/2007GL030135 (2007).
[CrossRef]

Zheng, Yu.

Appl. Opt.

Geophys. Res. Lett.

D. M. Winker, W. H. Hunt, and M. J. McGill, "Initial performance assessment of CALIOP," Geophys. Res. Lett. 34, L19803, doi:10.1029/2007GL030135 (2007).
[CrossRef]

J. Appl. Meteor.

V. Noel and K. Sassen, "Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations," J. Appl. Meteor. 44, 653-664 (2005).
[CrossRef]

J. Appl. Meteorol.

C. M. R. Platt, Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals," J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

J. Atmos. Oceanic Opt.

B. V. Kaul and I. V. Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation," J. Atmos. Oceanic Opt. 18, 866- 870 (2005).

B. V. Kaul, "Symmetry of light backscattering matrices of nonspherical aerosol particles," J. Atmos. Oceanic Opt. 13, 829-833 (2000).

B. V. Kaul and I. V.  Samokhvalov, "Orientation of particles in Ci crystal clouds. Part 2. Azimuth orientation," J. Atmos. Oceanic Opt. 19, 38- 42 (2006).

B. V. Kaul, "Influence of electric field on ice cloud orientation," J. Atmos. Oceanic Opt. 19, 835- 840 (2006).

D. N.  Romashov, "Backscattering matrix for monodisperse ensembles of hexagonal ice crystals," J. Atmos. Oceanic Opt. 12, 376-384 (1999).

J. Atmos. Sci.

H.-R.  Cho, J. V. Iribarne, and W. G. Richards, "On the orientation of ice crystals in a cumulo-nimbus cloud," J. Atmos. Sci. 38, 1111 - 1114 (1981).
[CrossRef]

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

Opt. Express

Opt. Lett.

Other

K. Sassen and D. K.  Lynch, "What are cirrus clouds?" in Cirrus, OSA Technical Digest (Opt. Soc. Am., Washington DC, 1998), pp. 2-3.

Yu. F.  Arshinov, B. V. Kaul, and I. V.  Samokhvalov, "Study of crystal clouds by measuring the backscattering phase matrices with polarization lidar: Particle orientation in cirrus," in Cirrus, OSA Technical Digest (Opt. Soc. Am., Washington DC, 1998), pp. 131-134.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley and Sons, Inc. New York; Chapman and Hall, Ltd. London, 1957).

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Figures (3)

Fig. 1.
Fig. 1.

Relative recurrence frequencies f for values of the indicated elements of the reduced normalized backscattering phase matrices for crystal clouds obtained by processing of 450 signal realizations.

Fig. 2.
Fig. 2.

Optical scheme of the LOSA-S lidar.

Fig. 3.
Fig. 3.

Structure of a layer of crystal clouds recorded on April 10, 2008 with a circular polarization lidar. The signal from the photodetector oriented in the reference plane is shown at the top, and the a 44 element is shown at the bottom of the figure. Scales in artificial colors for the corresponding signals are shown to the right of the figure.

Equations (29)

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S = 1 r 2 M S 0 Δ V .
M = A + ,
A 11 A 22 + A 33 A 44 = 0
A ij = A ij , when i or j 3 and A ij = A ij , when i or j = 3
A ' = ( A 11 ' A 12 ' 0 A 14 ' A 21 ' A 22 ' 0 0 0 0 A 33 ' A 34 ' A 41 ' 0 A 43 ' A 44 ' )
A ' = R ( Φ ) AR ( 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 ) .
A = ( A 11 0 0 A 14 0 A 22 0 0 0 0 A 33 0 A 41 0 0 A 44 ) ,
A = A 11 ( 1 0 0 a 14 0 1 d 0 0 0 0 d 1 0 a 14 0 0 2 d 1 ) .
a ij = A ij / A 11 , a ' ij = A ' ij / A 11 ' .
a 11 = a 11 ' 1 , a 14 = a 14 ' = a 41 = a 41 ' , a 44 = a 44 '
χ = ( a 22 ' + a 33 ' ) / ( 1 + a 44 ' ) .
a 12 = a 12 ' cos 2 φ ,
D = 1 P = 1 Q 2 + U 2 + V 2 / I = 1 q 2 + u 2 + ν 2 ,
L = 1 2 ( 1 1 0 0 ) , L = 1 2 ( 1 1 0 0 )
G = 1 2 ( 1 0 0 1 ) , G = 1 2 ( 1 0 0 1 ) .
I = k L a S 0 L = k ( a 11 + a 12 + a 21 + a 22 ) , I = k L a S 0 L = k ( a 11 + a 12 a 21 a 22 ) ,
( I I ) / ( I + I ) = q
D L = 1 q = ( 1 a 22 ) / ( 1 + a 12 ) = 2 I / ( I + I ) .
I = k G a S 0 c = k ( a 11 a 14 a 41 + a 44 ) , I = k G a S 0 c = k ( a 11 a 14 + a 41 a 44 ) ,
( I I ) / ( I + I ) = ν = ( a 44 a 41 ) / ( 1 a 14 ) ,
D C = 1 ν = ( 1 a 44 ) / ( 1 a 14 ) = 2 I / ( I + I ) .
P ( h ) s ( h ) = 1 2 c W 0 D h 2 T 2 M ( h ) S 0 c ,
F ( h ) = 1 2 c W 0 D h 2 T 2 κ G M ( h ) S 0 c ,
F ( h ) = 1 2 c W 0 D h 2 T 2 κ G M ( h ) S 0 c .
C ( h ) = F ( h ) F ( h ) F ( h ) + F ( h ) = ( G α G ) M ( h ) S 0 c ( G + α G ) M ( h ) S 0 c ,
M ( h ) = A 11 ( h ) [ a ( h ) + γ ( h ) a 1 ( h ) S 0 c σ ] ,
γ ( h ) = 1 / ( R ( h ) 1 ) , where R ( h ) = ( β a ( h ) + 11 ( h ) ) / 11 ( h ) ,
a 44 ( h ) = ( K ( h ) + 1 ) + γ ( h ) ( 1 + a 14 ( h ) ) [ K ( h ) ( 1 + σ 44 ) + ( 1 σ 44 ) ] 2 K ( h ) a 14 ( h ) 1 K ( h ) ,

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