Abstract

The backward cross section of hexagonal ice crystals of arbitrary orientation is calculated for visible light by means of a ray-tracing code. It is shown that backscattering of the tilted crystals is caused by a corner-reflector-like effect. A very large peak of backscattering is found for a tilt of 32.5° between the principal particle axis and the incidence direction. This peak is caused by multiple total internal reflections for part of the rays that are incident upon the skewed rectangular faces. Slant lidar measurements for remote sensing of cirrus clouds are proposed.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. M. R. Platt, J. Appl. Meteorol. 17, 482 (1978).
    [CrossRef]
  2. L. Thomas, J. C. Cartwright, and D. P. Wareing, Tellus B 42, 211 (1990).
    [CrossRef]
  3. K. Sassen, W. P. Arnott, J. B. Barnett, and S. Aulenbach, Appl. Opt. 37, 1427 (1998).
    [CrossRef]
  4. W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
    [CrossRef]
  5. Q. Cai and K. N. Liou, Appl. Opt. 21, 3569 (1982).
    [CrossRef] [PubMed]
  6. Y. Takano and K. N. Liou, J. Atmos. Sci. 46, 3 (1989).
    [CrossRef]
  7. K. Muionen, K. Lumme, J. Peltoniemi, and W. M. Irvine, Appl. Opt. 28, 3051 (1989).
    [CrossRef]
  8. M. Hess and M. Wiegner, Appl. Opt. 33, 7740 (1994).
    [CrossRef] [PubMed]
  9. A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
    [CrossRef]
  10. A. Borovoi, E. Naats, and U. Oppel, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 32–46.
  11. M. Del Guasta, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 48–57.

1998 (1)

1996 (1)

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

1994 (1)

1990 (1)

L. Thomas, J. C. Cartwright, and D. P. Wareing, Tellus B 42, 211 (1990).
[CrossRef]

1989 (2)

1982 (1)

1978 (1)

C. M. R. Platt, J. Appl. Meteorol. 17, 482 (1978).
[CrossRef]

Arnott, W. P.

Aulenbach, S.

Barnett, J. B.

Borovoi, A.

A. Borovoi, E. Naats, and U. Oppel, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 32–46.

Cai, Q.

Cartwright, J. C.

L. Thomas, J. C. Cartwright, and D. P. Wareing, Tellus B 42, 211 (1990).
[CrossRef]

Del Guasta, M.

M. Del Guasta, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 48–57.

Hess, M.

Irvine, W. M.

Liou, K. N.

Y. Takano and K. N. Liou, J. Atmos. Sci. 46, 3 (1989).
[CrossRef]

Q. Cai and K. N. Liou, Appl. Opt. 21, 3569 (1982).
[CrossRef] [PubMed]

Lumme, K.

Macke, A.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Mueller, J.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Muionen, K.

Naats, E.

A. Borovoi, E. Naats, and U. Oppel, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 32–46.

Oppel, U.

A. Borovoi, E. Naats, and U. Oppel, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 32–46.

Peltoniemi, J.

Platt, C. M. R.

C. M. R. Platt, J. Appl. Meteorol. 17, 482 (1978).
[CrossRef]

Raschke, E.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Sassen, K.

Takano, Y.

Y. Takano and K. N. Liou, J. Atmos. Sci. 46, 3 (1989).
[CrossRef]

Tape, W.

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
[CrossRef]

Thomas, L.

L. Thomas, J. C. Cartwright, and D. P. Wareing, Tellus B 42, 211 (1990).
[CrossRef]

Wareing, D. P.

L. Thomas, J. C. Cartwright, and D. P. Wareing, Tellus B 42, 211 (1990).
[CrossRef]

Wiegner, M.

Appl. Opt. (4)

J. Appl. Meteorol. (1)

C. M. R. Platt, J. Appl. Meteorol. 17, 482 (1978).
[CrossRef]

J. Atmos. Sci. (2)

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Y. Takano and K. N. Liou, J. Atmos. Sci. 46, 3 (1989).
[CrossRef]

Tellus B (1)

L. Thomas, J. C. Cartwright, and D. P. Wareing, Tellus B 42, 211 (1990).
[CrossRef]

Other (3)

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
[CrossRef]

A. Borovoi, E. Naats, and U. Oppel, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 32–46.

M. Del Guasta, in 10th International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (University of Florence, Florence, Italy, 1999), pp. 48–57.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Orientation of a hexagonal cylinder.

Fig. 2
Fig. 2

Backscattering efficiencies K1 (solid curve) and K2 (dotted curve) for a hexagonal ice column (aspect ratio, L/2a=3) versus its tilt θ.

Fig. 3
Fig. 3

Decomposition of the backscattering efficiency K2 of Fig. 2 into three terms corresponding to rays that are incident upon (dotted curve) face 1, (solid curve) faces 2 and 6, and (dashed curve) face H.

Fig. 4
Fig. 4

Rays that create backscattering by hexagonal ice columns: (a) rays that are incident upon face 1, and (b) rays that are incident upon skewed faces 2 and 6.

Fig. 5
Fig. 5

Backscattering efficiency Q=K1+K2/2 for both hexagonal ice columns and plates versus their tilt angle θ.

Equations (5)

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

dσ/dΩ=iσiδΩ-Ωi,
σπθ,φ,Ψ=a2Kθ,φ,Ψ.
Kθ,φ,Ψ=Kθ,Ψcos2 φ+Kθ,Ψsin2 φ,
Kθ,Ψ=Kθ,φ=0,Ψ,  Kθ,Ψ=Kθ,φ=π/2,Ψ.
Kθ,Ψ=K1θδΨ,  Kθ,Ψ=K2θδψ for θ0.

Metrics