Abstract

The data library of optical properties of hexagonal ice crystals for radiative modeling, Cirrus Optical Properties (COP), is introduced. It includes phase functions, asymmetry parameters, extinction cross sections, and single scattering albedos. Furthermore, lidar ratios and depolarization are given. The dependence of these parameters on wavelength, particle size, and shape is calculated, and different particle orientations are considered. In addition, a simple fortran code is provided to calculate the corresponding properties of size distributions. Thus the data library is a very flexible tool for determining the optical parameters of ice clouds for climatological purposes and remote sensing. The data library and the fortran code are distributed through electronic mail.

© 1994 Optical Society of America

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References

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  1. P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
    [CrossRef] [PubMed]
  2. B. Strauss, “Modellierung der Einfachstreuung an hexagonalen Eiskristallen—mit besonderer Berücksichtigung der horizontalen Ausrichtung der Eiskristalle,” master’s degree thesis (Meteorologisches Institut der Universität, München, Germany, August1989), p. 79.
  3. L. Thomas, J. C. Cartwright, D. P. Wareing, “Lidar observations of the horizontal orientation of ice crystals in cirrus clouds,” Tellus 42B, 211–216 (1990).
  4. Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).
  5. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, Hampton, Va., 1988), pp. 18–24.
  6. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  7. A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
    [CrossRef]
  8. S. G. Warren, “Optical constants of ice from ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]
  9. K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422–429 (1980).
  10. A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
    [CrossRef]
  11. 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]

1990

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

1989

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

1984

S. G. Warren, “Optical constants of ice from ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (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

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

1980

K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422–429 (1980).

1979

1972

A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
[CrossRef]

1970

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

Asano, S.

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

Auer, A. H.

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

Cartwright, J. C.

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

Coulson, K. L.

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, Hampton, Va., 1988), pp. 18–24.

Heymsfield, A.

A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
[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]

Liou, K. N.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[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]

Sassen, K.

K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422–429 (1980).

Strauss, B.

B. Strauss, “Modellierung der Einfachstreuung an hexagonalen Eiskristallen—mit besonderer Berücksichtigung der horizontalen Ausrichtung der Eiskristalle,” master’s degree thesis (Meteorologisches Institut der Universität, München, Germany, August1989), p. 79.

Takano, Y.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

Thomas, L.

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

Veal, D. L.

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

Wareing, D. P.

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

Warren, S. G.

Weickmann, H. K.

Wendling, P.

Wendling, R.

Appl. Opt.

J. Atmos. Sci.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

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

A. Heymsfield, “Ice crystal terminal velocities,” J. Atmos. Sci. 29, 1348–1357 (1972).
[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. Meteorol. Soc. Jpn.

K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422–429 (1980).

Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).

Tellus

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

Other

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, Hampton, Va., 1988), pp. 18–24.

B. Strauss, “Modellierung der Einfachstreuung an hexagonalen Eiskristallen—mit besonderer Berücksichtigung der horizontalen Ausrichtung der Eiskristalle,” master’s degree thesis (Meteorologisches Institut der Universität, München, Germany, August1989), p. 79.

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Figures (7)

Fig. 1
Fig. 1

Phase functions p(ψ) (top curves) and degree of linear polarization P (bottom curves) for six different plates (see Table 1) in random orientation. The wavelength is λ = 830 nm, and the particle sizes are indicated in the legend. 3-D indicates random orientation.

Fig. 2
Fig. 2

Phase functions p(ψ) (top curves) and degree of linear polarization P (bottom curves) for six different wavelengths for plate P4 (see Table 1 in random orientation. The wavelengths are indicated in the legend.

Fig. 3
Fig. 3

Asymmetry parameter for 12 ice crystals in random orientation. Note that calculations were done only for wavelengths marked with symbols. The laser wavelengths given in the text have been omitted. See Table 1 for columns and plates.

Fig. 4
Fig. 4

Same as Fig. 3 but with the single-scattering albedo instead of the asymmetry parameter.

Fig. 5
Fig. 5

Same as Fig. 3 but with the ratio R of unscattered photons instead of the asymmetry parameter.

Fig. 6
Fig. 6

Asymmetry parameter for 12 ice crystals in horizontal orientation at a wavelength of 535 nm. 2-D indicates horizontal orientation.

Fig. 7
Fig. 7

Single-scattering albedo for 12 ice crystals in horizontal orientation at a wavelength of 1615 nm.

Tables (1)

Tables Icon

Table 1 Dimensions (in Micrometers) and Aspect Ratios of Hexagonal Crystals Included in Our Library

Equations (5)

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0 2 π 0 π p ( ψ , φ ) sin ψ d ψ d φ = 1 ,
σ e o = 1 1 - R ω 0 σ e , σ s o = 1 1 - R σ s .
g = 0 2 π 0 π p ( ψ , φ ) cos ψ sin ψ d ψ d φ .
P ( ψ , φ ) = I ( ψ , φ ) - I ( ψ , φ ) I ( ψ , φ ) + I ( ψ , φ ) .
L = 1 ω 0 p ( ψ = 180 ° ) , δ = I ( ψ = 180 º ) I ( ψ = 180 ° ) .

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