Abstract

A scattering model is described for the investigation of depolarization of polarized light caused by ice clouds. The scattering by a single particle is described by refraction, reflection, and diffraction. The ice cloud is assumed to be a random mixture of hexagonal columns and plates of random orientation and size. Multiple scattering effects are included by means of a Monte Carlo method, where single photon histories are constructed from random samples of the distributions governing the basic scattering parameters. The dependence of depolarization on cloud extinction coefficient, receiver field of view, and mixing ratio of columns to plates are studied. Lidar measurements of depolarization by a high altitude cirrus cloud are presented and discussed within the frame of the present model. Good agreement can be obtained assuming a variation of crystal shape distribution with height.

© 1989 Optical Society of America

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References

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  1. K. Sassen, K. N. Liou, “Scattering of Polarized Laser Light by Water Droplet, Mixed-Phase and Ice Crystal Clouds. Part 2: Angular Depolarizing and Multiple-Scattering Behavier,” J. Atmos. Sci. 36, 852–861 (1979).
    [CrossRef]
  2. C. M. R. Platt, N. L. Abshire, 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]
  3. S. R. Pal, A. I. Carswell, “Polarization Anisotropy in Lidar Multiple Scattering from Atmospheric Clouds,” Appl. Opt. 24, 3464–3741 (1985).
    [CrossRef] [PubMed]
  4. R. H. Dubinsky, A. I. Carswell, S. R. Pal, “Determination of Cloud Microphysical Properties by Laser Backscattering and Extinction Measurements,” Appl. Opt. 24, 1614–1622 (1985).
    [CrossRef] [PubMed]
  5. J. D. Spinhirne, M. Z. Hansen, J. Simpson, “The Structure and Phase of Cloud Tops as Observed by Polarization Lidar,” J. Appl. Meteorol. 22, 1319–1331 (1983).
    [CrossRef]
  6. Q. Cai, K. N. Liou, “Polarized Light Scattering by Hexagonal Ice Crystals: Theory,” Appl. Opt. 21, 3569–3580 (1982).
    [CrossRef] [PubMed]
  7. S. Asano, M. Sato, “Light Scattering by Randomly Oriented Spheroidal Particles,” Appl. Opt. 19, 962–974 (1980).
    [CrossRef] [PubMed]
  8. C. M. R. Platt, “Remote Sounding of High Clouds. 3: Monte Carlo Calculations of Multiple-Scattering Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
    [CrossRef]
  9. K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
    [CrossRef]
  10. P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of Solar Radiation by Hexagonal Ice Crystals,” Appl. Opt. 18, 2663–2671 (1979).
    [CrossRef] [PubMed]
  11. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  12. A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
    [CrossRef]
  13. F. G. Fernald, “Analysis of Atmospheric Lidar Observations: Some Comments,” Appl. Opt. 23, 652–653 (1984).
    [CrossRef] [PubMed]
  14. J. D. Klett, “Lidar Inversion with Variable Backscatter/Extinction Ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef] [PubMed]
  15. W. Carnuth, R. Reiter, “Cloud Extinction Profile Measurements by Lidar using Klett’s Inversion Method,” Appl. Opt. 25, 2899–2907 (1986).
    [CrossRef] [PubMed]
  16. A. I. Carswell, “Laser measurements in clouds,” in CloudsP. V. Hobbs, A. Deepak, Eds. (Academic, New York, 1981) p. 381.
  17. S. R. Pal, A. I. Carswell, “The Polarization Characteristics of Lidar Scattering from Snow and Ice Crystals in the Atmosphere,” J. Appl. Meteorol. 16, 70–80 (1977).
    [CrossRef]
  18. C. M. R. Platt, A. C. Dilley, “Remote Sounding of High Clouds. 4: Observed Temperature Variations in Cirrus Optical Properties,” J. Atmos. Sci. 38, 1062–1082 (1981).
    [CrossRef]
  19. M. Kumai, “Formation of Ice Crystals and Dissipation of Suppercooled Fog by Artificial Nucleation, and Variations of Crystal Habit at Early Growth Stages,” J. Appl. Meteorol. 21, 579–587 (1982).
    [CrossRef]
  20. B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, “Ground-Based and Airborne Holography of Ice and Water Clouds,” Atmos. Environ. 16, 1193–1207 (1982).
    [CrossRef]

1986 (1)

1985 (3)

1984 (2)

F. G. Fernald, “Analysis of Atmospheric Lidar Observations: Some Comments,” Appl. Opt. 23, 652–653 (1984).
[CrossRef] [PubMed]

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

1983 (1)

J. D. Spinhirne, M. Z. Hansen, J. Simpson, “The Structure and Phase of Cloud Tops as Observed by Polarization Lidar,” J. Appl. Meteorol. 22, 1319–1331 (1983).
[CrossRef]

1982 (3)

M. Kumai, “Formation of Ice Crystals and Dissipation of Suppercooled Fog by Artificial Nucleation, and Variations of Crystal Habit at Early Growth Stages,” J. Appl. Meteorol. 21, 579–587 (1982).
[CrossRef]

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, “Ground-Based and Airborne Holography of Ice and Water Clouds,” Atmos. Environ. 16, 1193–1207 (1982).
[CrossRef]

Q. Cai, K. N. Liou, “Polarized Light Scattering by Hexagonal Ice Crystals: Theory,” Appl. Opt. 21, 3569–3580 (1982).
[CrossRef] [PubMed]

1981 (2)

C. M. R. Platt, A. C. Dilley, “Remote Sounding of High Clouds. 4: Observed Temperature Variations in Cirrus Optical Properties,” J. Atmos. Sci. 38, 1062–1082 (1981).
[CrossRef]

C. M. R. Platt, “Remote Sounding of High Clouds. 3: Monte Carlo Calculations of Multiple-Scattering Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

1980 (1)

1979 (2)

K. Sassen, K. N. Liou, “Scattering of Polarized Laser Light by Water Droplet, Mixed-Phase and Ice Crystal Clouds. Part 2: Angular Depolarizing and Multiple-Scattering Behavier,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of Solar Radiation by Hexagonal Ice Crystals,” Appl. Opt. 18, 2663–2671 (1979).
[CrossRef] [PubMed]

1978 (1)

C. M. R. Platt, N. L. Abshire, 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]

1977 (1)

S. R. Pal, A. I. Carswell, “The Polarization Characteristics of Lidar Scattering from Snow and Ice Crystals in the Atmosphere,” J. Appl. Meteorol. 16, 70–80 (1977).
[CrossRef]

1976 (1)

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Abshire, N. L.

C. M. R. Platt, N. L. Abshire, 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]

Asano, S.

Bentley, A. N.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, “Ground-Based and Airborne Holography of Ice and Water Clouds,” Atmos. Environ. 16, 1193–1207 (1982).
[CrossRef]

Cai, Q.

Carnuth, W.

Carswell, A. I.

R. H. Dubinsky, A. I. Carswell, S. R. Pal, “Determination of Cloud Microphysical Properties by Laser Backscattering and Extinction Measurements,” Appl. Opt. 24, 1614–1622 (1985).
[CrossRef] [PubMed]

S. R. Pal, A. I. Carswell, “Polarization Anisotropy in Lidar Multiple Scattering from Atmospheric Clouds,” Appl. Opt. 24, 3464–3741 (1985).
[CrossRef] [PubMed]

S. R. Pal, A. I. Carswell, “The Polarization Characteristics of Lidar Scattering from Snow and Ice Crystals in the Atmosphere,” J. Appl. Meteorol. 16, 70–80 (1977).
[CrossRef]

A. I. Carswell, “Laser measurements in clouds,” in CloudsP. V. Hobbs, A. Deepak, Eds. (Academic, New York, 1981) p. 381.

Caughey, S. J.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, “Ground-Based and Airborne Holography of Ice and Water Clouds,” Atmos. Environ. 16, 1193–1207 (1982).
[CrossRef]

Conway, B. J.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, “Ground-Based and Airborne Holography of Ice and Water Clouds,” Atmos. Environ. 16, 1193–1207 (1982).
[CrossRef]

Dilley, A. C.

C. M. R. Platt, A. C. Dilley, “Remote Sounding of High Clouds. 4: Observed Temperature Variations in Cirrus Optical Properties,” J. Atmos. Sci. 38, 1062–1082 (1981).
[CrossRef]

Dubinsky, R. H.

Fernald, F. G.

Hansen, M. Z.

J. D. Spinhirne, M. Z. Hansen, J. Simpson, “The Structure and Phase of Cloud Tops as Observed by Polarization Lidar,” J. Appl. Meteorol. 22, 1319–1331 (1983).
[CrossRef]

Heymsfield, A. J.

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

Klett, J. D.

Kumai, M.

M. Kumai, “Formation of Ice Crystals and Dissipation of Suppercooled Fog by Artificial Nucleation, and Variations of Crystal Habit at Early Growth Stages,” J. Appl. Meteorol. 21, 579–587 (1982).
[CrossRef]

Kunkel, K. E.

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Liou, K. N.

Q. Cai, K. N. Liou, “Polarized Light Scattering by Hexagonal Ice Crystals: Theory,” Appl. Opt. 21, 3569–3580 (1982).
[CrossRef] [PubMed]

K. Sassen, K. N. Liou, “Scattering of Polarized Laser Light by Water Droplet, Mixed-Phase and Ice Crystal Clouds. Part 2: Angular Depolarizing and Multiple-Scattering Behavier,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

McNice, G. T.

C. M. R. Platt, N. L. Abshire, 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]

Pal, S. R.

Platt, C. M. R.

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

C. M. R. Platt, “Remote Sounding of High Clouds. 3: Monte Carlo Calculations of Multiple-Scattering Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

C. M. R. Platt, A. C. Dilley, “Remote Sounding of High Clouds. 4: Observed Temperature Variations in Cirrus Optical Properties,” J. Atmos. Sci. 38, 1062–1082 (1981).
[CrossRef]

C. M. R. Platt, N. L. Abshire, 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]

Reiter, R.

Sassen, K.

K. Sassen, K. N. Liou, “Scattering of Polarized Laser Light by Water Droplet, Mixed-Phase and Ice Crystal Clouds. Part 2: Angular Depolarizing and Multiple-Scattering Behavier,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

Sato, M.

Simpson, J.

J. D. Spinhirne, M. Z. Hansen, J. Simpson, “The Structure and Phase of Cloud Tops as Observed by Polarization Lidar,” J. Appl. Meteorol. 22, 1319–1331 (1983).
[CrossRef]

Spinhirne, J. D.

J. D. Spinhirne, M. Z. Hansen, J. Simpson, “The Structure and Phase of Cloud Tops as Observed by Polarization Lidar,” J. Appl. Meteorol. 22, 1319–1331 (1983).
[CrossRef]

Turton, J. D.

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, “Ground-Based and Airborne Holography of Ice and Water Clouds,” Atmos. Environ. 16, 1193–1207 (1982).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Weickmann, H. K.

Weinman, J. A.

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Wendling, P.

Wendling, R.

Appl. Opt. (8)

Atmos. Environ. (1)

B. J. Conway, S. J. Caughey, A. N. Bentley, J. D. Turton, “Ground-Based and Airborne Holography of Ice and Water Clouds,” Atmos. Environ. 16, 1193–1207 (1982).
[CrossRef]

J. Appl. Meteorol. (4)

M. Kumai, “Formation of Ice Crystals and Dissipation of Suppercooled Fog by Artificial Nucleation, and Variations of Crystal Habit at Early Growth Stages,” J. Appl. Meteorol. 21, 579–587 (1982).
[CrossRef]

C. M. R. Platt, N. L. Abshire, 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. D. Spinhirne, M. Z. Hansen, J. Simpson, “The Structure and Phase of Cloud Tops as Observed by Polarization Lidar,” J. Appl. Meteorol. 22, 1319–1331 (1983).
[CrossRef]

S. R. Pal, A. I. Carswell, “The Polarization Characteristics of Lidar Scattering from Snow and Ice Crystals in the Atmosphere,” J. Appl. Meteorol. 16, 70–80 (1977).
[CrossRef]

J. Atmos. Sci. (5)

C. M. R. Platt, A. C. Dilley, “Remote Sounding of High Clouds. 4: Observed Temperature Variations in Cirrus Optical Properties,” J. Atmos. Sci. 38, 1062–1082 (1981).
[CrossRef]

A. J. Heymsfield, C. M. R. Platt, “A Parameterization of the Particle Size Spectrum of Ice Clouds in Terms of the Ambient Temperature and the Ice Water Content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

C. M. R. Platt, “Remote Sounding of High Clouds. 3: Monte Carlo Calculations of Multiple-Scattering Lidar Returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

K. Sassen, K. N. Liou, “Scattering of Polarized Laser Light by Water Droplet, Mixed-Phase and Ice Crystal Clouds. Part 2: Angular Depolarizing and Multiple-Scattering Behavier,” J. Atmos. Sci. 36, 852–861 (1979).
[CrossRef]

Other (2)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

A. I. Carswell, “Laser measurements in clouds,” in CloudsP. V. Hobbs, A. Deepak, Eds. (Academic, New York, 1981) p. 381.

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Figures (6)

Fig. 1
Fig. 1

Calculated profiles of depolarization ratio δ for ice plates and columns for σ = 1 km−1, FOV = 1 mrad, γs = 0.5 mrad.

Fig. 2
Fig. 2

Calculated dependence of the depolarization ratio on cloud extinction coefficient and receiver field of view (FOV). Transmitter divergence γs = 0.5 mrad.

Fig. 3
Fig. 3

Measured profiles of backscatter intensities in one plane of polarization from transmitted laser pulse pairs with orthogonal planes of polarization.

Fig. 4
Fig. 4

Profiles of extinction coefficients for cirrus clouds inverted from Fig. 3 by means of Klett’s inversion method.

Fig. 5
Fig. 5

Measured profiles of depolarization ratio for cirrus clouds.

Fig. 6
Fig. 6

Calculated profiles of depolarization ratio for cirrus clouds (left), corresponding profiles of percentage of ice plates fp (right) are assumed. Extinction profiles according to measurements: top, 10/10/87 19:59:4, bottom, 10/10/87 19:59:30.

Equations (11)

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[ I Q U V ] = 1 k 2 R 2 F ( Ө , Φ ) [ I 0 Q 0 U 0 V 0 ] ,
I = E l E * l + E r E * r Q = E l E * l E r E * r U = E l E * r + E r E * l V = i ( E r E * l E l E * r ) ,
F = [ 1 / 2 ( M 2 + M 3 + M 4 + M 1 ) 1 / 2 ( M 2 M 3 + M 4 M 1 ) S 23 + S 41 D 23 D 41 1 / 2 ( M 2 + M 3 M 4 M 1 ) 1 / 2 ( M 2 M 3 M 4 + M 1 ) S 23 S 41 D 23 + D 41 S 24 + S 31 S 24 S 31 S 21 + S 34 D 21 + D 34 D 24 + D 31 D 24 D 31 D 21 + D 34 S 21 S 34 ] ,
M k = A k A * k = ( A k ) 2 S k l = S l k = ( 1 / 2 ) ( A l A * k + A k A * l ) D k l = D l k = ( i / 2 ) ( A l A * k A k A * l ) ,
P = c F ,
P ( Ө ) = [ P 11 P 12 0 0 P 12 P 22 0 0 0 0 P 33 P 43 0 0 P 43 P 44 ] .
4 π P 11 ( Ω ) d Ω / 4 π = 1 .
[ I Q U V ] = c 4 π R 2 [ P 11 P 12 0 0 P 12 P 22 0 0 0 0 P 33 P 43 0 0 P 43 P 44 ] [ I 0 Q 0 U 0 V 0 ] .
cos θ = cos ( R N * γ s ) ,
L = ( 1 / β ext ) ln ( 1 R N ) .
L R = ( 1 / β ext ) ln { 1 R N [ 1 exp ( τ R ) ] } ,

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