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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6209–6214
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Observations of specular reflective particles and layers in crystal clouds

Yurii S. Balin, Bruno V. Kaul, Grigorii P. Kokhanenko, and Ioganes E. Penner  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 6209-6214 (2011)
http://dx.doi.org/10.1364/OE.19.006209


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Abstract

In the present article, results of observations of high crystal clouds with high spatial and temporal resolution using the ground-based polarization LOSA-S lidar are described. Cases of occurrence of specularly reflective layers formed by particles oriented predominantly in the horizontal plane are demonstrated. Results of measuring echo-signal depolarization are compared for linear and circular polarization states of the initial laser beam.

© 2011 OSA

1. Introduction

Cirrus clouds cover a significant part of the Earth’s surface and hence influence significantly the radiation balance and climate, primarily because of radiation extinction and reflection effects [1

1. K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” J. Geophys. Res. 103, 1799–1805 (1986).

]. Especially strong influence on radiation transmission and scattering has predominant orientation of particles in the horizontal plane [2

2. C. Lavigne, A. Roblin, and P. Chervet, “Solar glint from oriented crystals in cirrus clouds,” Appl. Opt. 47(33), 6266–6276 (2008). [CrossRef] [PubMed]

]. This orientation can be caused by aerodynamic forces of particles falling free in the atmosphere [3

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

]. Lidar observations provide the most complete information on the properties of crystal particles [4

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]

6

6. W. N. Chen, C. W. Chiang, and J. B. Nee, “Lidar ratio and depolarization ratio for cirrus clouds,” Appl. Opt. 41(30), 6470–6476 (2002). [CrossRef] [PubMed]

]. The presence of crystal particles in these observations is primarily manifested through the depolarization of backscattered radiation. Situations with randomly oriented particles having the depolarization ratio δ = 0.3–0.6 depending on the particle shape are most frequently observed [7

7. 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]

,8

8. Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 470–482 (2006). [CrossRef]

]. The particles whose long axes are predominantly oriented in the horizontal plane cause specular light reflection; they have δ close to zero and enhanced backscattering [9

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

]. The CALIPSO experiments with a space-based polarization lidar [10

10. H. M. Cho, P. Yang, G. W. Kattawar, S. L. Nasiri, Y. Hu, P. Minnis, C. Trepte, and D. Winker, “Depolarization ratio and attenuated backscatter for nine cloud types: analyses based on collocated CALIPSO lidar and MODIS measurements,” Opt. Express 16(6), 3931–3948 (2008). [CrossRef] [PubMed]

] demonstrate a significant relative fraction of these particles at temperatures from –5 to –35°С.

This paper presents results of ground-based lidar observations of the polarization structure of cirrus cloudiness with high spatial and temporal resolution and reveals the spatial structure of formations in which particles with pronounced horizontal orientation are dominant.

2. Depolarization parameters

Generally, the experimentally measured backscattering phase matrices (BSPM) have nonzero nondiagonal elements a12,a14, and a34 [11

11. 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(36), 6620–6628 (2004). [CrossRef]

]. With allowance for the well-known symmetry relations [12

12. H. C. van de Hulst, Light scattering by small particles (Wiley, 1957).

,13

13. C. R. Hu, G. W. Kattawar, M. E. Parkin, and P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26(19), 4159–4173 (1987). [CrossRef] [PubMed]

] for purely random (chaotic) orientation of crystal particles in the cloud, the BSPM assumes the simple diagonal form [14

14. 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]

,15

15. C. J. Flynn, A. Mendoza, Y. Zheng, and S. Mathur, “Novel polarization-sensitive micropulse lidar measurement technique,” Opt. Express 15(6), 2785–2790 (2007). [CrossRef] [PubMed]

]
A=βπdiag[1,1d,d1,2d1].
(1)
For this case, only the depolarization parameter d which unambiguously determines the degree of backscattered radiation polarization remains in the matrix [15

15. C. J. Flynn, A. Mendoza, Y. Zheng, and S. Mathur, “Novel polarization-sensitive micropulse lidar measurement technique,” Opt. Express 15(6), 2785–2790 (2007). [CrossRef] [PubMed]

,16

16. G. G. Gimmestad, “Reexamination of depolarization in lidar measurements,” Appl. Opt. 47(21), 3795–3802 (2008). [CrossRef] [PubMed]

].

Let us assume that laser radiation is linearly polarized (the initial vector is S0L=[1,1,0,0]T). Then the 2nd (normalized by the intensity) Stokes parameter Q is expressed through the measured signal components as follows: Q=(II)/(I+I)=(a12+a22)/(1+a12). The 4th Stokes parameter is measured analogously; in this case, the circularly polarized beam (S0C=[1,0,0,1]T) was used, and the λ/4 plate in front of the receiver was rotated through an angle of 45°: V=(II)/(I+I)=(a14a44)/(1a14). For the diagonal matrix, expressions are simplified: Q=a22=1d and V=a44=12d. The assumption about the chaotic orientation of particles is very convenient for interpretation of experimental observations. Measurements [11

11. 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(36), 6620–6628 (2004). [CrossRef]

] confirm that the zero value of a14 is the most probable one (a14=0±0.05). At the same time, significant number of cases with pronounced predominant azimuth orientation of particles was observed: the average value of the element was a12=0.22±0.2.

For chaotic particle orientation, the well-known relationship between the depolarization ratios for linearly and circularly polarized radiation δC=2δL/(1δL) [14

14. 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]

,17

17. G. Roy and N. Roy, “Relation between circular and linear depolarization ratios under multiple-scattering conditions,” Appl. Opt. 47(35), 6563–6579 (2008). [CrossRef] [PubMed]

] is transformed into
dC=dL=(1Q)=(1V)/2.
(2)
The superscripts L and C in formula (2) indicate that the corresponding values are calculated from measurements with linear or circular polarization using formulas corresponding to the diagonal BSPM. For chaotic particle orientation (diagonal matrix), dL and dC are in fact one and the same parameter, but for actually observed ensembles of particles with partial orientation, it is very probable that elements a14 and, in particular, a12 are nonzero and relation (2) is not valid. In general, a relationship between dL and dC determined for linear and circular initial polarization states can be expressed in the form
(1Q)=(1V)/K4,dL=2dC/K4,
(3)
where K4<2. Cases in which circular depolarization was close to linear one were previously observed experimentally in [18

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(20), 4878–4887 (2006). [CrossRef] [PubMed]

] for sensing at an angle of 30° to the vertical when particles had pronounced azimuth (relative to the lidar axis) orientation. It then follows that the proximity of the parameter K4 to K4=2 demonstrates that the BSPM is close to the diagonal form.

3. Experimental results

The optical scheme of the polarization LOSA-S lidar channel was presented in [19

19. Yu. 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]

]. An LS2137U laser (532 nm, 300 mJ) with pulse repetition frequency of 10 Hz was used. A lens 0.15 m in diameter with a focal distance of 0.75 m was used for a receiving antenna. A quarter-wavelength λ/4 quartz plate was inserted into the beam to change the polarization state of transmitted radiation from linear to circular one. The Wollaston prism was inserted into the scattered beam to form two beams with mutually orthogonal polarization states. A λ/4 plate was also placed in front of the prism. The fast axis of the λ/4 plates could be oriented at an angle of 0 or 45° to the reference plane. Two FÉU-84 photomultipliers simultaneously registered the parallel (I) and orthogonal (I) signal components in the measuring channels. Rotating simultaneously the plates in front of the source and receiver, we could measure either the second (Q) or fourth (V) component of the Stokes vector of backscattered radiation. The error in calibration of the relative photodetector sensitivity did not exceed 4%. As a rule, echo-signals were accumulated during 3.2 s (32 laser pulses). Taking into account the ADC digitization frequency (25 MHz), we can consider that the spatial resolution of the data on the cloudiness structure was about 20 m.

Experimental data presented in this work were obtained since April, 2009 till May, 2010. A total of 30 records of sensing of high clouds not screened by underlying cloudiness were obtained. Figure 1
Fig. 1 Observations of crystal clouds at successively changed (from linear to circular) state of initial laser beam polarization. May 28, 2009, 16:35 – 17:19.
shows an example of lidar signals from cirrus cloudiness. From the data of balloon sensing at the station Novosibirsk (250 km to the south-west of the observation point), the temperature at an altitude of 8 km and 12:00 UCT was –34.5°С, and the tropopause height was 12.1 km (–59°С) [20]. Each signal was accumulated during 3.2 s (32 laser pulses). The component I corrected for the squared distance is shown at the upper figure in artificial colors, and the depolarization parameter d is shown at the lower figure. Grey color illustrates regions with the scattering ratio R < 4.

The polarization state of the transmitter and receiver radiation was periodically changed by simultaneous rotation of both quarter-wavelength plates through an angle of 45° (circular) or 0° (linear). The corresponding polarization states are indicated at the top of the figure.

In calculations of d in the case of circular polarization, the parameter K 4 was adjusted so that to minimize visible changes of the depolarization pattern at the interface between regions with different initial polarization states. In this case, we succeeded in obtaining this for K4=1.52, which corresponds to the Stokes parameters Q = 0.1 and V = –0.37 at points with maximum depolarization. Cloud regions with the most pronounced specular backscattering are indicated by white ellipses. They are characterized by the maximum backscattering and low depolarization (d < 0.1). At the same time, regions with pronounced vertical flows (indicated by green ellipses), including the entire lower cloud boundary, had high depolarization close to d = 0.9.

The data shown in Fig. 1 represent a rather rare case in which the choice of one value K 4 made it possible to achieve exact joining of the depolarization pattern at interfaces between regions for the entire cloud thickness. As a rule, different spatial formations inside of the cloud can call for the application of different K 4 values. In our measurements, these values changed from 1.4 to 1.8. Undoubtedly, the K 4 value was influenced by the azimuth orientation of particles causing the occurrence of the nondiagonal BSPM elements.

Figure 2
Fig. 2 Observations of crystal clouds using circularly polarized laser radiation. May 19, 2009, 10:25 – 11:12.
shows an analogous example of sensing with circularly polarized laser radiation. The tropopause height at 00:00, UCT was 10.5 km (–55°C). In this case, K4=1.6 was chosen to calculate the d value. As in the majority of other cases of cirrus cloudiness sensing, specularly scattering objects are shaped as thin horizontal layers. Probably, ascending flows that make a steady-state levitation of crystal particles and their orientation in the horizontal plane possible prevail in these layers.

Figure 3
Fig. 3 Observations of crystal clouds using circularly polarized laser radiation. April 24, 2009, 18:38 – 18:54.
shows the record of a specularly reflecting layer at an altitude of 6400 m. To the right of the figure, the vertical signal profile (crosses) and values of the a 44 element (the blue curve) are shown for the brightest point of the layer indicated by the arrow at the upper left of the figure. The tropopause height was 11.1 km (–61.6°С), and T = –29°С at an altitude of 6200 m. The thickness of the layer with the pronounced horizontal orientation of particles (a 44 < –0.6) was about 200 m, whereas the specularly reflective layer (distinguished from the I component) was much thinner. The field-of-view angle of the receiver for a 6-km range was about 50 μrad. Obviously, when the particle deviates at a greater angle, specular reflection disappears, but the a 44 value changes weakly and still remains in the range (−1…-0.6) typical of the horizontally oriented particles.

In some scattering events, signals from individual specularly reflective particles are clearly pronounced. An example of such record is shown in Fig. 1, where separate bright spots are clearly pronounced against the total background to the left of the layer at 6500 m. In records of single lidar pulses, specular particles are manifested through sharp peaks of the I component, but as a rule, are absolutely unnoticed for the I component. In the case of the strongest reflections, the depolarization ratio was in the limits δ210%. In Fig. 4
Fig. 4 Observations of individual specularly reflective particles with recording of each lidar signal. Circular polarization. The component I is shown at the left of the figure, and the depolarization parameter d (K4=1.6) is shown in the centre. The record of single pulse number 103 is shown at the right of the figure. May 28, 2009, 16:30 – 16:41.
(records of each lidar signal), individual particles are manifested against the background of layers with high depolarization at 6500 and 7000 m. It seems likely that particles in these layers were chaotically oriented, but some of them acquired horizontal orientation when they fall down. These free-falling particles were concentrated at a level of 6200 m, passed into the steady-state levitation state, and formed a layer with specular reflection below which no specular particles were present.

4. Summary

Lidar observations of the cirrus cloud structure using linearly and circularly polarized radiation revealed the presence of thin (several tens of meters) specularly reflective horizontal layers with low depolarization degree and high backscattering coefficient. In the structures shaped as vertical stripes (free-falling particles or pronounced turbulent flows), radiation was strongly depolarized, which indicated that chaotic orientation of particles dominated in these cloud regions. It seems likely that the anomalous zones with pronounced horizontal orientation of crystal particles are caused by homogeneous ascending flows promoting the steady-state levitation of crystals and their orientation in the horizontal plane.

The double excess of the depolarization degree typical of the diagonal BSPM and sensing with circularly polarized laser beam in comparison with linearly polarized beam was not observed in our experiment in which values of the parameter K4 were within the limits 1.4–1.8. This testified to the presence of pronounced azimuth orientation of particles for which the nondiagonal a 12 element was nonzero.

Acknowledgements

This work was supported in part by the Russian Foundation for Basic Research (grant No. 10-08-00347-a) and the Ministry of Education and Science (State Contracts Nos. 14.740.11.0204 and 02.740.11.0674).

References and links

1.

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” J. Geophys. Res. 103, 1799–1805 (1986).

2.

C. Lavigne, A. Roblin, and P. Chervet, “Solar glint from oriented crystals in cirrus clouds,” Appl. Opt. 47(33), 6266–6276 (2008). [CrossRef] [PubMed]

3.

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

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 ice crystal orientation in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol. 44(5), 653–664 (2005). [CrossRef]

6.

W. N. Chen, C. W. Chiang, and J. B. Nee, “Lidar ratio and depolarization ratio for cirrus clouds,” Appl. Opt. 41(30), 6470–6476 (2002). [CrossRef] [PubMed]

7.

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]

8.

Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 470–482 (2006). [CrossRef]

9.

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

10.

H. M. Cho, P. Yang, G. W. Kattawar, S. L. Nasiri, Y. Hu, P. Minnis, C. Trepte, and D. Winker, “Depolarization ratio and attenuated backscatter for nine cloud types: analyses based on collocated CALIPSO lidar and MODIS measurements,” Opt. Express 16(6), 3931–3948 (2008). [CrossRef] [PubMed]

11.

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(36), 6620–6628 (2004). [CrossRef]

12.

H. C. van de Hulst, Light scattering by small particles (Wiley, 1957).

13.

C. R. Hu, G. W. Kattawar, M. E. Parkin, and P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26(19), 4159–4173 (1987). [CrossRef] [PubMed]

14.

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]

15.

C. J. Flynn, A. Mendoza, Y. Zheng, and S. Mathur, “Novel polarization-sensitive micropulse lidar measurement technique,” Opt. Express 15(6), 2785–2790 (2007). [CrossRef] [PubMed]

16.

G. G. Gimmestad, “Reexamination of depolarization in lidar measurements,” Appl. Opt. 47(21), 3795–3802 (2008). [CrossRef] [PubMed]

17.

G. Roy and N. Roy, “Relation between circular and linear depolarization ratios under multiple-scattering conditions,” Appl. Opt. 47(35), 6563–6579 (2008). [CrossRef] [PubMed]

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(20), 4878–4887 (2006). [CrossRef] [PubMed]

19.

Yu. 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]

20.

http://weather.uwyo.edu/upperair/sounding.html.

OCIS Codes
(280.3640) Remote sensing and sensors : Lidar
(290.1090) Scattering : Aerosol and cloud effects
(290.1350) Scattering : Backscattering
(290.5855) Scattering : Scattering, polarization

ToC Category:
Remote Sensing

History
Original Manuscript: December 9, 2010
Revised Manuscript: February 7, 2011
Manuscript Accepted: February 7, 2011
Published: March 18, 2011

Citation
Yurii S. Balin, Bruno V. Kaul, Grigorii P. Kokhanenko, and Ioganes E. Penner, "Observations of specular reflective particles and layers in crystal clouds," Opt. Express 19, 6209-6214 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6209


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References

  1. K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” J. Geophys. Res. 103, 1799–1805 (1986).
  2. C. Lavigne, A. Roblin, and P. Chervet, “Solar glint from oriented crystals in cirrus clouds,” Appl. Opt. 47(33), 6266–6276 (2008). [CrossRef] [PubMed]
  3. B. V. Kaul and I. V. Samokhvalov, “Orientation of particles in Ci crystal clouds. Part 1. Orientation at gravitational sedimentation,” Atmos. Oceanic Opt. 18, 866–870 (2005).
  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 ice crystal orientation in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol. 44(5), 653–664 (2005). [CrossRef]
  6. W. N. Chen, C. W. Chiang, and J. B. Nee, “Lidar ratio and depolarization ratio for cirrus clouds,” Appl. Opt. 41(30), 6470–6476 (2002). [CrossRef] [PubMed]
  7. 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]
  8. Y. You, G. W. Kattawar, P. Yang, Y. X. Hu, and B. A. Baum, “Sensitivity of depolarized lidar signals to cloud and aerosol particle properties,” J. Quant. Spectrosc. Radiat. Transf. 100(1-3), 470–482 (2006). [CrossRef]
  9. K. Sassen and S. Benson, “A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing: II. Microphysical properties derived from lidar depolarization,” J. Atmos. Sci. 58(15), 2103–2112 (2001). [CrossRef]
  10. H. M. Cho, P. Yang, G. W. Kattawar, S. L. Nasiri, Y. Hu, P. Minnis, C. Trepte, and D. Winker, “Depolarization ratio and attenuated backscatter for nine cloud types: analyses based on collocated CALIPSO lidar and MODIS measurements,” Opt. Express 16(6), 3931–3948 (2008). [CrossRef] [PubMed]
  11. 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(36), 6620–6628 (2004). [CrossRef]
  12. H. C. van de Hulst, Light scattering by small particles (Wiley, 1957).
  13. C. R. Hu, G. W. Kattawar, M. E. Parkin, and P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26(19), 4159–4173 (1987). [CrossRef] [PubMed]
  14. 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]
  15. C. J. Flynn, A. Mendoza, Y. Zheng, and S. Mathur, “Novel polarization-sensitive micropulse lidar measurement technique,” Opt. Express 15(6), 2785–2790 (2007). [CrossRef] [PubMed]
  16. G. G. Gimmestad, “Reexamination of depolarization in lidar measurements,” Appl. Opt. 47(21), 3795–3802 (2008). [CrossRef] [PubMed]
  17. G. Roy and N. Roy, “Relation between circular and linear depolarization ratios under multiple-scattering conditions,” Appl. Opt. 47(35), 6563–6579 (2008). [CrossRef] [PubMed]
  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(20), 4878–4887 (2006). [CrossRef] [PubMed]
  19. Yu. 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]
  20. http://weather.uwyo.edu/upperair/sounding.html .

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