Abstract

We ascertain the usefulness of simple ice particle geometries for modeling the intensity distribution of light scattering by atmospheric ice particles. To this end, similarities and differences in light scattering by axis-equivalent, regular and distorted hexagonal cylindric, ellipsoidal, and circular cylindric ice particles are reported. All the results pertain to particles with sizes much larger than a wavelength and are based on a geometrical optics approximation. At a nonabsorbing wavelength of 0.55 μm, ellipsoids (circular cylinders) have a much (slightly) larger asymmetry parameter g than regular hexagonal cylinders. However, our computations show that only random distortion of the crystal shape leads to a closer agreement with g values as small as 0.7 as derived from some remote-sensing data analysis. This may suggest that scattering by regular particle shapes is not necessarily representative of real atmospheric ice crystals at nonabsorbing wavelengths. On the other hand, if real ice particles happen to be hexagonal, they may be approximated by circular cylinders at absorbing wavelengths.

© 1996 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Scattering by irregular shaped ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
    [CrossRef]
  4. J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
    [CrossRef]
  5. A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. (1996), in press.
    [CrossRef]
  6. 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]
  7. J. Hallet, “Faceted snow crystals,” J. Opt. Soc. Am. A 4, 581–588 (1987).
    [CrossRef]
  8. B. J. Mason, “Snow crystals, natural and man-made,” Contemp. Phys. 33, 227–243 (1992).
    [CrossRef]
  9. P. N. Francis, “Some aircraft observations of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
    [CrossRef]
  10. J.-F. Gayet, O. Crepel, J.-F. Fournol, “A new polar nephelometer for in situ measurements of microphysical and optical properties of clouds,” in Proceedings of the American Meteorological Society Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1995), pp. 26–30.
  11. G. L. Stephens, S-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
    [CrossRef]
  12. S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
    [CrossRef]
  13. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  14. M. I. Mishchenko, “Light scattering by size-shape distribution of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
    [CrossRef] [PubMed]
  15. M. I. Mishchenko, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
    [CrossRef]
  16. J. E. Hansen, “Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial water clouds,” J. Atmos. Sci. 28, 1400–1426 (1971).
    [CrossRef]
  17. M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
    [CrossRef]
  18. P. Beckmann, The Depolarization of Electromagnetic Waves (Golem Press, Boulder, Colo., 1968).
  19. A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray optics approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
    [CrossRef] [PubMed]
  20. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]
  21. A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
    [CrossRef]
  22. D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
    [CrossRef]

1995

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Scattering by irregular shaped ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

P. N. Francis, “Some aircraft observations of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
[CrossRef]

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray optics approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

1994

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

M. I. Mishchenko, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

1993

1992

B. J. Mason, “Snow crystals, natural and man-made,” Contemp. Phys. 33, 227–243 (1992).
[CrossRef]

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

1990

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

1989

1987

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]

1971

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

J. E. Hansen, “Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial water clouds,” J. Atmos. Sci. 28, 1400–1426 (1971).
[CrossRef]

1970

A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Ackermann, T. A.

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Arnott, W. P.

D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

Auer, A. H.

A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Beckmann, P.

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem Press, Boulder, Colo., 1968).

Carlson, B. E.

Crepel, O.

J.-F. Gayet, O. Crepel, J.-F. Fournol, “A new polar nephelometer for in situ measurements of microphysical and optical properties of clouds,” in Proceedings of the American Meteorological Society Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1995), pp. 26–30.

Flatau, P. J.

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

Fournol, J.-F.

J.-F. Gayet, O. Crepel, J.-F. Fournol, “A new polar nephelometer for in situ measurements of microphysical and optical properties of clouds,” in Proceedings of the American Meteorological Society Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1995), pp. 26–30.

Francis, P. N.

P. N. Francis, “Some aircraft observations of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
[CrossRef]

Gayet, J.-F.

J.-F. Gayet, O. Crepel, J.-F. Fournol, “A new polar nephelometer for in situ measurements of microphysical and optical properties of clouds,” in Proceedings of the American Meteorological Society Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1995), pp. 26–30.

Hallet, J.

Hansen, J. E.

J. E. Hansen, “Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial water clouds,” J. Atmos. Sci. 28, 1400–1426 (1971).
[CrossRef]

Heymsfield, A. J.

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[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]

Iaquinta, J.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

Irvine, W. M.

Isaka, H.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

Kinne, S.

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Liou, K. N.

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Scattering by irregular shaped ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

Lumme, K.

Macke, A.

Mason, B. J.

B. J. Mason, “Snow crystals, natural and man-made,” Contemp. Phys. 33, 227–243 (1992).
[CrossRef]

Mishchenko, M. I.

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray optics approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

M. I. Mishchenko, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

M. I. Mishchenko, “Light scattering by size-shape distribution of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4666 (1993).
[CrossRef] [PubMed]

Mitchell, D. L.

D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

Mueller, J.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. (1996), in press.
[CrossRef]

Muinonen, K.

Peltoniemi, J. I.

Personne, P.

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[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]

Raschke, E.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. (1996), in press.
[CrossRef]

Sassen, K.

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Spinhirne, J.

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Stackhouse, P. W.

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

Takano, Y.

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Scattering by irregular shaped ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

Tsay, S-C.

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

Valero, F. P. J.

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Veal, D. L.

A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Warren, S. G.

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Appl. Opt.

Contemp. Phys.

B. J. Mason, “Snow crystals, natural and man-made,” Contemp. Phys. 33, 227–243 (1992).
[CrossRef]

J. Atmos. Sci.

P. N. Francis, “Some aircraft observations of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Scattering by irregular shaped ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
[CrossRef]

G. L. Stephens, S-C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[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. E. Hansen, “Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial water clouds,” J. Atmos. Sci. 28, 1400–1426 (1971).
[CrossRef]

A. H. Auer, D. L. Veal, “The dimensions of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

D. L. Mitchell, W. P. Arnott, “A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part II: Dependence of absorption and extinction on ice crystal morphology,” J. Atmos. Sci. 51, 817–832 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

M. I. Mishchenko, L. D. Travis, “Light scattering by polydisperse, rotationally symmetric nonspherical particles: linear polarization,” J. Quant. Spectrosc. Radiat. Transfer 51, 759–778 (1994).
[CrossRef]

Mon. Weather Rev.

S. Kinne, T. A. Ackermann, A. J. Heymsfield, F. P. J. Valero, K. Sassen, J. Spinhirne, “Cirrus microphysics and radiative transfer: cloud field study on 28 October 1986,” Mon. Weather Rev. 120, 661–684 (1992).
[CrossRef]

Opt. Commun.

M. I. Mishchenko, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. D

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Other

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. (1996), in press.
[CrossRef]

J.-F. Gayet, O. Crepel, J.-F. Fournol, “A new polar nephelometer for in situ measurements of microphysical and optical properties of clouds,” in Proceedings of the American Meteorological Society Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1995), pp. 26–30.

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem Press, Boulder, Colo., 1968).

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Figures (5)

Fig. 1
Fig. 1

Particle shapes for axis-equivalent hexagonal crystals, ellipsoids, and circular cylinders with aspect ratios ar = 0.2, 1, and 5.

Fig. 2
Fig. 2

Ray-tracing phase functions P ref(θ) for hexagonal cylinder and axis-equivalent ellipsoids with aspect ratios ar = 0.2, 1, and 5. Results for ar = 0.2 and ar = 1 are multiplied by 10,000 and 100, respectively.

Fig. 3
Fig. 3

Asymmetry parameter g for hexagonal and axis-equivalent ellipsoidal particles as a function of particle eccentricity ∊.

Fig. 4
Fig. 4

Scattering phase function P ref(θ) (excluding diffraction) for axis-equivalent hexagonal particles—with different degrees of crystal distortion—, ellipsoids, and circular cylinders. Aspect ratio is 0.2 and 5 for prolate and oblate particles, respectively.

Fig. 5
Fig. 5

Single scattering albedo and asymmetry parameter as a function of effective distance for axis/d eff equivalent hexagonal cylinder, ellipsoids, and circular cylinders. Results are shown for λ1 = 1.6 μm (thick curves) and λ1 = 3.7 μm (thin curves).

Tables (1)

Tables Icon

Table 1 Dimensions (in micrometers) of the Particles used in Section 4 a

Equations (2)

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

P ( θ ) = 1 2 ω 0 [ ( 2 ω 0 1 ) P ref ( θ ) + P dif ( θ ) ] ,
g = cos θ = 0 π P ( θ ) cos θ sin θdθ .

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