Abstract

A model for calculation of the depolarization of a laser beam propagating through a water cloud is described, in which multiple scattering up to sixth order is included using a Monte Carlo technique. The influence of beam geometry, drop size distribution, and cloud extinction coefficient on the depolarization is discussed. Good agreement between calculated and measured profiles of the depolarization observed in water clouds has been obtained.

© 1989 Optical Society of America

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References

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  1. R. L. T. Chung, A. Ishimaru, “Transmission, Backscattering, and Depolarization of Waves in Randomly Distributed Spheri-cle Particles,” Appl. Opt. 21, 3792–3798 (1982).
    [CrossRef]
  2. C. M. R. Platt, “Lidar Observation of a Mixed-Phase Altostratus Cloud,” J. Appl. Meteorol. 16, 339–345 (1977).
    [CrossRef]
  3. R. J. Allen, C. M. R. Platt, “Lidar for Multiple Backscattering and Depolarization Observations,” Appl. Opt. 16, 3193–3199 (1977).
    [CrossRef] [PubMed]
  4. W. R. McNeil, A. I. Carswell, “Lidar Polarization Studies of the Troposphere,” Appl. Opt. 14, 2158–2168 (1975).
    [CrossRef] [PubMed]
  5. J. D. Houston, A. I. Carswell, “Four-Component Polarization Measurement of Lidar Atmospheric Scattering,” Appl. Opt. 17, 614–620 (1978).
    [CrossRef] [PubMed]
  6. S. R. Pal, A. I. Carswell, “Polarization Anisotropy in Lidar Multiple Scattering from Atmospheric Clouds,” Appl. Opt. 24, 3464–3471 (1985).
    [CrossRef] [PubMed]
  7. K. Sassen, R. L. Petrilla, “Lidar Depolarization from Multiple Scattering in Marine Stratus Clouds,” Appl. Opt. 25, 1450–1454 (1986).
    [CrossRef] [PubMed]
  8. A. I. Carswell, S. R. Pal, “Polarization Anisotropy in Lidar Multiple Scattering from Clouds,” Appl. Opt. 19, 4123–4126 (1980).
    [CrossRef] [PubMed]
  9. K. N. Liou, “On Depolarization of Visible Light from Water Clouds for a Monostatic Lidar,” J. Atmos. Scie. 29, 1000–1003 (1972).
    [CrossRef]
  10. S. R. Pal, A. I. Carswell, “Polarization Properties of Lidar Backscattering from Clouds,” Appl. Opt. 12, 1530–1535 (1973).
    [CrossRef] [PubMed]
  11. K. E. Kunkel, J. A. Weinman, “Monte Carlo Analysis of Multiply Scattered Lidar Returns,” J. Atmos. Scie. 33, 1772–1781 (1976).
    [CrossRef]
  12. D. Deirmendijan, Electromagnetic Scattering on Spherical Polydispersions (American Elsvier, New York, 1969).
  13. F. G. Fernald, “Analysis of Atmospheric Lidar Observations: Some Comments.” Appl. Opt., 23, 652–653 (1984).
    [CrossRef] [PubMed]
  14. K. N. Liou, R. M. Schotland, “Multiple Backscattering and Depolarization from Water Clouds for a Pulsed Lidar System,” J. Atmos. Scie. 28, 772–784 (1971).
    [CrossRef]
  15. E. W. Eloranta, “Calculation of Doubly Scattered Lidar Returns,” Ph.D. Thesis, U. Wisconsin (1972).

1986

1985

1984

1982

1980

1978

1977

R. J. Allen, C. M. R. Platt, “Lidar for Multiple Backscattering and Depolarization Observations,” Appl. Opt. 16, 3193–3199 (1977).
[CrossRef] [PubMed]

C. M. R. Platt, “Lidar Observation of a Mixed-Phase Altostratus Cloud,” J. Appl. Meteorol. 16, 339–345 (1977).
[CrossRef]

1976

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

1975

1973

1972

K. N. Liou, “On Depolarization of Visible Light from Water Clouds for a Monostatic Lidar,” J. Atmos. Scie. 29, 1000–1003 (1972).
[CrossRef]

1971

K. N. Liou, R. M. Schotland, “Multiple Backscattering and Depolarization from Water Clouds for a Pulsed Lidar System,” J. Atmos. Scie. 28, 772–784 (1971).
[CrossRef]

Allen, R. J.

Carswell, A. I.

Chung, R. L. T.

Deirmendijan, D.

D. Deirmendijan, Electromagnetic Scattering on Spherical Polydispersions (American Elsvier, New York, 1969).

Eloranta, E. W.

E. W. Eloranta, “Calculation of Doubly Scattered Lidar Returns,” Ph.D. Thesis, U. Wisconsin (1972).

Fernald, F. G.

Houston, J. D.

Ishimaru, A.

Kunkel, K. E.

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

Liou, K. N.

K. N. Liou, “On Depolarization of Visible Light from Water Clouds for a Monostatic Lidar,” J. Atmos. Scie. 29, 1000–1003 (1972).
[CrossRef]

K. N. Liou, R. M. Schotland, “Multiple Backscattering and Depolarization from Water Clouds for a Pulsed Lidar System,” J. Atmos. Scie. 28, 772–784 (1971).
[CrossRef]

McNeil, W. R.

Pal, S. R.

Petrilla, R. L.

Platt, C. M. R.

R. J. Allen, C. M. R. Platt, “Lidar for Multiple Backscattering and Depolarization Observations,” Appl. Opt. 16, 3193–3199 (1977).
[CrossRef] [PubMed]

C. M. R. Platt, “Lidar Observation of a Mixed-Phase Altostratus Cloud,” J. Appl. Meteorol. 16, 339–345 (1977).
[CrossRef]

Sassen, K.

Schotland, R. M.

K. N. Liou, R. M. Schotland, “Multiple Backscattering and Depolarization from Water Clouds for a Pulsed Lidar System,” J. Atmos. Scie. 28, 772–784 (1971).
[CrossRef]

Weinman, J. A.

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

Appl. Opt.

J. Appl. Meteorol.

C. M. R. Platt, “Lidar Observation of a Mixed-Phase Altostratus Cloud,” J. Appl. Meteorol. 16, 339–345 (1977).
[CrossRef]

J. Atmos. Scie.

K. N. Liou, “On Depolarization of Visible Light from Water Clouds for a Monostatic Lidar,” J. Atmos. Scie. 29, 1000–1003 (1972).
[CrossRef]

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

K. N. Liou, R. M. Schotland, “Multiple Backscattering and Depolarization from Water Clouds for a Pulsed Lidar System,” J. Atmos. Scie. 28, 772–784 (1971).
[CrossRef]

Other

E. W. Eloranta, “Calculation of Doubly Scattered Lidar Returns,” Ph.D. Thesis, U. Wisconsin (1972).

D. Deirmendijan, Electromagnetic Scattering on Spherical Polydispersions (American Elsvier, New York, 1969).

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Figures (9)

Fig. 1
Fig. 1

Profiles of the depolarization ratio δ for two drop size distributions: FOV = 1 mrad, γs = .5 mrad, σ = 30 km−1.

Fig. 2
Fig. 2

Effect of extinction coefficient on the δ profile: FOV = 1 rnrad, γS = 0.5 mrad.

Fig. 3
Fig. 3

Effect of receiver field of view on δ: cloud base = 6360 m, γs = 0.5 mrad.

Fig. 4
Fig. 4

Effect of the distance to cloud on δ. FOV = 1 mrad, γS = 0.5 mrad, σ = 30 km−1.

Fig. 5
Fig. 5

Effect of cloud layer thickness on δ averaged over the total cloud return. Cloud base = 6360 m, FOV = 1 mrad, γS = 0.5 mrad.

Fig. 6
Fig. 6

Two examples of backscattered returns of clouds measured by lidar.

Fig. 7
Fig. 7

Profiles of δ: solid lines, measured profiles; dashed lines, calculated profiles.

Fig. 8
Fig. 8

Profiles of extinction coefficients for an altocumulus inverted from Fig. 6 by Klett’s method.

Fig. 9
Fig. 9

Comparison of calculations model with measurements published by Pal and Carswell (four different profiles a–d). Calculated curves included after Liou and Schotland (1), Eloranta (2), and our model (3).

Equations (4)

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P = [ P 2 ( θ ) 4 π cos θ cos 2 ϕ + P 1 ( θ ) 4 π sin 2 ϕ ] 2 P 0 π r 2 Q R 2 ,
P = [ P 2 ( θ ) 4 π cos θ cos ϕ sin ϕ P 1 ( θ ) 4 π sin ϕ cos ϕ ] 2 P 0 π r 2 Q R 2 ,
δ ( ϕ ) = P P = [ ( P 2 ( θ ) cos θ P 1 ( θ ) ) sin ϕ cos ϕ ] 2 [ P 1 ( θ ) sin 2 ϕ + P 2 ( θ ) cos θ cos 2 ϕ ] 2 ,
δ = P P

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