Abstract

The computation of the scattering properties of cirrus cloud ice crystals by the ray-tracing approach is described. A light beam is represented by its Stokes quadrivector I, which describes intensity as well as polarization, and the scattering properties of particles (molecules, droplets, or ice crystals) are introduced by means of a 4 × 4 transformation matrix M known as the Mueller matrix, or M matrix. Obtaining such a matrix for each kind of particle gives access to a complete description of the scattering medium. Most computations of the M matrices of cirrus ice crystals have introduced several simplifying hypotheses, by using basic shapes, by assuming a random orientation of the particles, or both. The present study focuses on the calculation of the complete M matrix for a specific shape of particles (i.e., hexagonally based crystals) either with optional oscillation about the horizontal plane or with random orientation. The validity of the computation code is checked against specific well-known cases for randomly oriented particles. For horizontally oscillating particles the computation of this matrix is a new result. Sensitivity of the M matrix to the following variables is studied: refractive index, amplitude of oscillation, particle shape and size, and angle of incidence.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flateau, “The relevance of the microphysical and radiative properties of cirrus clouds to the climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
    [CrossRef]
  2. K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” J. Geophys. Res. 103, 1799–1805 (1986).
  3. D. P. Wylie, W. P. Menzel, H. M. Woolf, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 315–335 (1994).
    [CrossRef]
  4. P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
    [CrossRef] [PubMed]
  5. Q. Cai, K. N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982).
    [CrossRef] [PubMed]
  6. G. Brogniez, “Light scattering by finite hexagonal crystals arbitrarily oriented in space,” in Proceedings of the 1998 International Radiation Symposium, (Deepak, Hampton, Va., 1989), pp. 64–67.
  7. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice clouds,” J. Atmos. Sci. 49, 3–19 (1989).
    [CrossRef]
  8. A. Macke, “Scattering of light by polydrehal ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
    [CrossRef] [PubMed]
  9. H. Mueller, “Foundations of optics,” J. Opt. Soc. Am. 38, 661(A) 1948).
  10. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1952).
  11. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).
  12. G. Bruhat, Cours de Physique Générale—Optique (Masson, Paris1954).
  13. M. I. Mishchenko, L. D. Travis, A. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium 1996 Proceedings, (Deepak, Hampton, Va., 1996), pp. 801–807.
  14. 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]
  15. D. D. Downling, L. F. Radke, “A summary of the physical properties of cirrus clouds,” J. Appl. Meteorol. 29, 970–978 (1990).
    [CrossRef]
  16. L. M. Miloshevich, A. J. Heymsfield, “A balloon-borne cloud particle replicator for measuring vertical profiles of clouds microphysics: instrument design and performance,” presented at the International Conference on Clouds and Precipitation, Zurich, Switzerland, 19–23 August 1996.
  17. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]
  18. L. Thomas, J. C. Cartwright, D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus Ser. B 42, 211–216 (1990).
    [CrossRef]
  19. H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
    [CrossRef]
  20. D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 33, 4580–4589 (1994).
    [CrossRef] [PubMed]
  21. D. K. Lynch, J. G. Shanks, S. D. Gedzelman, “Specular scattering and crystal dynamics in cirrus clouds,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere II, D. K. Lynch, ed., Proc. SPIE2309, 375–382 (1994).
  22. J. G. Shanks, D. K. Lynch, “Specular scattering in cirrus clouds,” in Infrared Remote Sensing of Clouds and Atmosphere III, D. K. Lynch, E. P. Shettle, eds., Proc. SPIE2578, 227–238 (1995).
    [CrossRef]
  23. P. Bratley, L. F. Benett, “Implementing Sobol’s quasirandom sequence generator,” ACM Trans. Math. Software 14, 88–100 (1988).
    [CrossRef]
  24. K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 11.
    [CrossRef]
  25. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1959).
  26. M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing scattering functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
    [CrossRef]
  27. M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
    [CrossRef] [PubMed]
  28. M. Hess, “Modellierung und Messung optischer Eigenschaften von Cirren,” Ph.D. dissertation (Universität München, Meteorologisches Institut, Munich, Germany, 1996).
  29. T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Rad. Transfer 63, 643–666 (1999).
    [CrossRef]
  30. K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
    [CrossRef]
  31. P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
    [CrossRef]

1999

H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
[CrossRef]

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Rad. Transfer 63, 643–666 (1999).
[CrossRef]

1998

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing scattering functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

1994

M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
[CrossRef] [PubMed]

D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 33, 4580–4589 (1994).
[CrossRef] [PubMed]

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 315–335 (1994).
[CrossRef]

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

1993

1991

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

1990

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flateau, “The relevance of the microphysical and radiative properties of cirrus clouds to the climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

D. D. Downling, L. F. Radke, “A summary of the physical properties of cirrus clouds,” J. Appl. Meteorol. 29, 970–978 (1990).
[CrossRef]

L. Thomas, J. C. Cartwright, D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus Ser. B 42, 211–216 (1990).
[CrossRef]

1989

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice clouds,” J. Atmos. Sci. 49, 3–19 (1989).
[CrossRef]

1988

P. Bratley, L. F. Benett, “Implementing Sobol’s quasirandom sequence generator,” ACM Trans. Math. Software 14, 88–100 (1988).
[CrossRef]

1986

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

1984

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]

S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

1982

1979

1948

H. Mueller, “Foundations of optics,” J. Opt. Soc. Am. 38, 661(A) 1948).

Benett, L. F.

P. Bratley, L. F. Benett, “Implementing Sobol’s quasirandom sequence generator,” ACM Trans. Math. Software 14, 88–100 (1988).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1959).

Bratley, P.

P. Bratley, L. F. Benett, “Implementing Sobol’s quasirandom sequence generator,” ACM Trans. Math. Software 14, 88–100 (1988).
[CrossRef]

Breon, F. M.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

Bréon, F. M.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
[CrossRef]

Brickaud, A.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

Brogniez, G.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
[CrossRef]

G. Brogniez, “Light scattering by finite hexagonal crystals arbitrarily oriented in space,” in Proceedings of the 1998 International Radiation Symposium, (Deepak, Hampton, Va., 1989), pp. 64–67.

Bruhat, G.

G. Bruhat, Cours de Physique Générale—Optique (Masson, Paris1954).

Buriez, J. C.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

Cai, Q.

Cartwright, J. C.

L. Thomas, J. C. Cartwright, D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus Ser. B 42, 211–216 (1990).
[CrossRef]

Chepfer, H.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
[CrossRef]

Deschamps, P. Y.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

Downling, D. D.

D. D. Downling, L. F. Radke, “A summary of the physical properties of cirrus clouds,” J. Appl. Meteorol. 29, 970–978 (1990).
[CrossRef]

Flamant, P. H.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
[CrossRef]

Flateau, P. J.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flateau, “The relevance of the microphysical and radiative properties of cirrus clouds to the climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Fraser, A. B.

Gedzelman, S. D.

D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 33, 4580–4589 (1994).
[CrossRef] [PubMed]

D. K. Lynch, J. G. Shanks, S. D. Gedzelman, “Specular scattering and crystal dynamics in cirrus clouds,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere II, D. K. Lynch, ed., Proc. SPIE2309, 375–382 (1994).

Goloub, P.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
[CrossRef]

Hess, M.

M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
[CrossRef] [PubMed]

M. Hess, “Modellierung und Messung optischer Eigenschaften von Cirren,” Ph.D. dissertation (Universität München, Meteorologisches Institut, Munich, Germany, 1996).

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]

L. M. Miloshevich, A. J. Heymsfield, “A balloon-borne cloud particle replicator for measuring vertical profiles of clouds microphysics: instrument design and performance,” presented at the International Conference on Clouds and Precipitation, Zurich, Switzerland, 19–23 August 1996.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Leroy, M.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

Liou, K. N.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice clouds,” J. Atmos. Sci. 49, 3–19 (1989).
[CrossRef]

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

Q. Cai, K. N. Liou, “Polarized light scattering by hexagonal ice crystals: theory,” Appl. Opt. 21, 3569–3580 (1982).
[CrossRef] [PubMed]

Lynch, D. K.

D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 33, 4580–4589 (1994).
[CrossRef] [PubMed]

J. G. Shanks, D. K. Lynch, “Specular scattering in cirrus clouds,” in Infrared Remote Sensing of Clouds and Atmosphere III, D. K. Lynch, E. P. Shettle, eds., Proc. SPIE2578, 227–238 (1995).
[CrossRef]

D. K. Lynch, J. G. Shanks, S. D. Gedzelman, “Specular scattering and crystal dynamics in cirrus clouds,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere II, D. K. Lynch, ed., Proc. SPIE2309, 375–382 (1994).

Macke, A.

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing scattering functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

A. Macke, “Scattering of light by polydrehal ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium 1996 Proceedings, (Deepak, Hampton, Va., 1996), pp. 801–807.

Menzel, W. P.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 315–335 (1994).
[CrossRef]

Miloshevich, L. M.

L. M. Miloshevich, A. J. Heymsfield, “A balloon-borne cloud particle replicator for measuring vertical profiles of clouds microphysics: instrument design and performance,” presented at the International Conference on Clouds and Precipitation, Zurich, Switzerland, 19–23 August 1996.

Mishchenko, M. I.

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing scattering functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium 1996 Proceedings, (Deepak, Hampton, Va., 1996), pp. 801–807.

Mueller, H.

H. Mueller, “Foundations of optics,” J. Opt. Soc. Am. 38, 661(A) 1948).

Muinonen, K.

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Rad. Transfer 63, 643–666 (1999).
[CrossRef]

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 11.
[CrossRef]

Nousiainen, T.

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Rad. Transfer 63, 643–666 (1999).
[CrossRef]

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]

Podaire, A.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

Radke, L. F.

D. D. Downling, L. F. Radke, “A summary of the physical properties of cirrus clouds,” J. Appl. Meteorol. 29, 970–978 (1990).
[CrossRef]

Sassen, K.

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

Sèze, G.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

Shanks, J. G.

D. K. Lynch, J. G. Shanks, S. D. Gedzelman, “Specular scattering and crystal dynamics in cirrus clouds,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere II, D. K. Lynch, ed., Proc. SPIE2309, 375–382 (1994).

J. G. Shanks, D. K. Lynch, “Specular scattering in cirrus clouds,” in Infrared Remote Sensing of Clouds and Atmosphere III, D. K. Lynch, E. P. Shettle, eds., Proc. SPIE2578, 227–238 (1995).
[CrossRef]

Stackhouse, P. W.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flateau, “The relevance of the microphysical and radiative properties of cirrus clouds to the climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Stephens, G. L.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flateau, “The relevance of the microphysical and radiative properties of cirrus clouds to the climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Strabal, K. L.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 315–335 (1994).
[CrossRef]

Takano, Y.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice clouds,” J. Atmos. Sci. 49, 3–19 (1989).
[CrossRef]

Thomas, L.

L. Thomas, J. C. Cartwright, D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus Ser. B 42, 211–216 (1990).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, A. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium 1996 Proceedings, (Deepak, Hampton, Va., 1996), pp. 801–807.

Tsay, S. C.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flateau, “The relevance of the microphysical and radiative properties of cirrus clouds to the climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1952).

Wareing, D. P.

L. Thomas, J. C. Cartwright, D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus Ser. B 42, 211–216 (1990).
[CrossRef]

Warren, S. G.

Weickmann, H. K.

Wendling, P.

Wendling, R.

Wiegner, M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1959).

Woolf, H. M.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 315–335 (1994).
[CrossRef]

Wylie, D. P.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 315–335 (1994).
[CrossRef]

ACM Trans. Math. Software

P. Bratley, L. F. Benett, “Implementing Sobol’s quasirandom sequence generator,” ACM Trans. Math. Software 14, 88–100 (1988).
[CrossRef]

Appl. Opt.

Bull. Am. Meteorol. Soc.

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

IEEE Trans. Geosci. Rem. Sens.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Brickaud, J. C. Buriez, G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32, 598–615 (1994).
[CrossRef]

J. Appl. Meteorol.

D. D. Downling, L. F. Radke, “A summary of the physical properties of cirrus clouds,” J. Appl. Meteorol. 29, 970–978 (1990).
[CrossRef]

J. Atmos. Sci.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flateau, “The relevance of the microphysical and radiative properties of cirrus clouds to the climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. 1. Single-scattering and optical properties of hexagonal ice clouds,” J. Atmos. Sci. 49, 3–19 (1989).
[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]

J. Clim.

D. P. Wylie, W. P. Menzel, H. M. Woolf, K. L. Strabal, “Four years of global cirrus clouds statistics using HIRS,” J. Clim. 7, 315–335 (1994).
[CrossRef]

J. Geophys. Res.

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

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing scattering functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

J. Opt. Soc. Am. 38

H. Mueller, “Foundations of optics,” J. Opt. Soc. Am. 38, 661(A) 1948).

J. Quant. Spectrosc. Rad. Transfer

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Rad. Transfer 63, 643–666 (1999).
[CrossRef]

J. Quantum Spectrosc.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Bréon, P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quantum Spectrosc. 63, 521–543 (1999).
[CrossRef]

Tellus Ser. B

L. Thomas, J. C. Cartwright, D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus Ser. B 42, 211–216 (1990).
[CrossRef]

Other

G. Brogniez, “Light scattering by finite hexagonal crystals arbitrarily oriented in space,” in Proceedings of the 1998 International Radiation Symposium, (Deepak, Hampton, Va., 1989), pp. 64–67.

D. K. Lynch, J. G. Shanks, S. D. Gedzelman, “Specular scattering and crystal dynamics in cirrus clouds,” in Passive Infrared Remote Sensing of Clouds and the Atmosphere II, D. K. Lynch, ed., Proc. SPIE2309, 375–382 (1994).

J. G. Shanks, D. K. Lynch, “Specular scattering in cirrus clouds,” in Infrared Remote Sensing of Clouds and Atmosphere III, D. K. Lynch, E. P. Shettle, eds., Proc. SPIE2578, 227–238 (1995).
[CrossRef]

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 11.
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1959).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1952).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

G. Bruhat, Cours de Physique Générale—Optique (Masson, Paris1954).

M. I. Mishchenko, L. D. Travis, A. Macke, “Light scattering by nonspherical particles in the atmosphere: an overview,” in International Radiation Symposium 1996 Proceedings, (Deepak, Hampton, Va., 1996), pp. 801–807.

L. M. Miloshevich, A. J. Heymsfield, “A balloon-borne cloud particle replicator for measuring vertical profiles of clouds microphysics: instrument design and performance,” presented at the International Conference on Clouds and Precipitation, Zurich, Switzerland, 19–23 August 1996.

M. Hess, “Modellierung und Messung optischer Eigenschaften von Cirren,” Ph.D. dissertation (Universität München, Meteorologisches Institut, Munich, Germany, 1996).

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 (7)

Fig. 1
Fig. 1

Hexagonal ice crystal laboratory coordinate system R L (i L , j L , k L ): L, length; R, radius.

Fig. 2
Fig. 2

M matrix nonzero values for crystals randomly oriented, with three values of shape ratio Q, as a function of scattering angle Θ.

Fig. 3
Fig. 3

Sixteen values of the M matrix for horizontally oriented particles, as a function of θ and φ, for a size factor of 0.05, an incidence angle of 40°, an oscillation angle of 5°, and a refractive index of 1.311.

Fig. 4
Fig. 4

Same as Fig. 3 but for an oscillation angle of 15°.

Fig. 5
Fig. 5

Same as Fig. 4 but for an incidence angle of 20°.

Fig. 6
Fig. 6

Same as Fig. 4 but for a size factor of 0.2.

Fig. 7
Fig. 7

Same as Fig. 4 but for a refractive index of 1.02.

Tables (1)

Tables Icon

Table 1 Asymmetry Parameters and Reflection/Transmission Ratios (R/T) as a Function of Shape Ratio, Oscillation Angle, and Incidence Angle

Equations (3)

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

Mtotalθv, φv=1Ni=1N Miθv,i, φv,i.
M=M11M1200M12M220000M33M3400-M34M44.
M  SSAASSAAAASSAASS,

Metrics