Abstract

It has been hypothesized that the frequent lack of halos in observations of cirrus and contrails and laboratory measurements is caused by small ice crystal sizes that put the particles outside the geometrical optics domain of size parameters. We test this hypothesis by exploiting a strong similarity of ray tracing phase functions for finite hexagonal and circular ice cylinders and using T-matrix computations of electromagnetic scattering by circular cylinders with size parameters up to 180 in the visible. We conclude that well-defined halos should be observable for ice crystal size parameters of the order of 100 and larger and discuss remote-sensing implications of this result.

© 1999 Optical Society of America

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  1. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
    [CrossRef]
  2. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
    [CrossRef] [PubMed]
  3. J. Iaquinta, H. Isaka, P. Personne, “Scattering phase function of bullet rosette ice crystals,” J. Atmos. Sci. 52, 1401–1413 (1995).
    [CrossRef]
  4. Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III: Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
    [CrossRef]
  5. P. Minnis, P. W. Heck, D. F. Young, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part II: Verification of theoretical cirrus radiative properties,” J. Atmos. Sci. 50, 1305–1322 (1993).
    [CrossRef]
  6. K. Sassen, N. C. Knight, Y. Takano, A. J. Heymsfield, “Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies,” Appl. Opt. 33, 4590–4601 (1994).
    [CrossRef] [PubMed]
  7. P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
    [CrossRef]
  8. P. J. Huffman, W. R. Thursby, “Light scattering by ice crystals,” J. Atmos. Sci. 26, 1073–1077 (1969).
    [CrossRef]
  9. K. Sassen, K.-N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part I: Angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
    [CrossRef]
  10. O. A. Volkovitskiy, L. N. Pavlova, A. G. Petrushin, “Scattering of light by ice crystals,” Izvestiya. Atmos. Ocean. Phys. 16, 98–102 (1980).
  11. J. S. Foot, “Some observations of the optical properties of clouds. Part II: Cirrus,” Q. J. R. Meteorol. Soc. 114, 145–164 (1988).
    [CrossRef]
  12. P. N. Francis, “Some aircraft observations of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
    [CrossRef]
  13. P. Posse, W. von Hoyningen-Huene, “Information about scattering properties and particle characteristics of a stratiform cloud at Helgoland by remote optical measurements,” Contr. Atmos. Phys. 68, 359–366 (1995).
  14. O. Crépel, J. F. Gayet, J. F. Fournol, S. Oschepkov, “A new airborne polar nephelometer for the measurements of optical and microphysical cloud properties. Part II: Preliminary tests,” Ann. Geophys. 15, 460–470 (1997).
  15. R. P. Lawson, A. J. Heymsfield, S. M. Aulenbach, T. L. Jensen, “Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS,” Geophys. Res. Lett. 25, 1331–1334 (1998).
    [CrossRef]
  16. P. Minnis, K.-N. Liou, Y. Takano, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part I: Parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
    [CrossRef]
  17. M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
    [CrossRef]
  18. C. M. R. Platt, N. L. Abshire, G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
    [CrossRef]
  19. H. Chepfer, G. Brogniez, Y. Fouquart, “Cirrus clouds’ microphysical properties deduced from POLDER observations,” J. Quant. Spectrosc. Radiat. Transfer 60, 375–390 (1998).
    [CrossRef]
  20. W. L. Eberhard, “Cirrus properties deduced from CO2 lidar observations of zenith-enhanced backscatter from oriented crystals,” NASA Conf. Publ. 3238, 9–12 (1993).
  21. K.-D. Rockwitz, “Scattering properties of horizontally oriented ice crystal columns in cirrus clouds. Part 1,” Appl. Opt. 28, 4103–4110 (1989).
    [CrossRef] [PubMed]
  22. R. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1990).
  23. J. D. Spinhirne, “Cirrus infrared parameters and shortwave reflectance relations from observations,” J. Atmos. Sci. 53, 1438–1458 (1996).
    [CrossRef]
  24. J. Descloitres, J. C. Buriez, F. Parol, Y. Fouquart, “POLDER observations of cloud bidirectional reflectances compared to a plane-parallel model using the International Cloud Climatology Project cloud phase functions,” J. Geophys. Res. 103, 11,411–11,418 (1998).
    [CrossRef]
  25. K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422–429 (1980).
  26. J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276–2285 (1995).
    [CrossRef]
  27. C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
    [CrossRef]
  28. W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
    [CrossRef]
  29. K. Sassen, “Contrail-cirrus and their potential for regional climate change,” Bull. Am. Meteorol. Soc. 78, 1885–1903 (1997).
    [CrossRef]
  30. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  31. A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
    [CrossRef] [PubMed]
  32. S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
    [CrossRef] [PubMed]
  33. A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
    [CrossRef]
  34. P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contr. Atmos. Phys. 71, 223–248 (1998).
  35. M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
    [CrossRef]
  36. P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A. D. Pierce, R. N. Thurston, eds. (Academic, San Diego, Calif., 1992), Vol. 21, pp. 1–234.
  37. J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [CrossRef]

1998 (5)

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

R. P. Lawson, A. J. Heymsfield, S. M. Aulenbach, T. L. Jensen, “Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS,” Geophys. Res. Lett. 25, 1331–1334 (1998).
[CrossRef]

H. Chepfer, G. Brogniez, Y. Fouquart, “Cirrus clouds’ microphysical properties deduced from POLDER observations,” J. Quant. Spectrosc. Radiat. Transfer 60, 375–390 (1998).
[CrossRef]

J. Descloitres, J. C. Buriez, F. Parol, Y. Fouquart, “POLDER observations of cloud bidirectional reflectances compared to a plane-parallel model using the International Cloud Climatology Project cloud phase functions,” J. Geophys. Res. 103, 11,411–11,418 (1998).
[CrossRef]

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contr. Atmos. Phys. 71, 223–248 (1998).

1997 (3)

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

K. Sassen, “Contrail-cirrus and their potential for regional climate change,” Bull. Am. Meteorol. Soc. 78, 1885–1903 (1997).
[CrossRef]

O. Crépel, J. F. Gayet, J. F. Fournol, S. Oschepkov, “A new airborne polar nephelometer for the measurements of optical and microphysical cloud properties. Part II: Preliminary tests,” Ann. Geophys. 15, 460–470 (1997).

1996 (5)

J. D. Spinhirne, “Cirrus infrared parameters and shortwave reflectance relations from observations,” J. Atmos. Sci. 53, 1438–1458 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

1995 (5)

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

P. Posse, W. von Hoyningen-Huene, “Information about scattering properties and particle characteristics of a stratiform cloud at Helgoland by remote optical measurements,” Contr. Atmos. Phys. 68, 359–366 (1995).

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

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

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276–2285 (1995).
[CrossRef]

1994 (2)

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

K. Sassen, N. C. Knight, Y. Takano, A. J. Heymsfield, “Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies,” Appl. Opt. 33, 4590–4601 (1994).
[CrossRef] [PubMed]

1993 (4)

P. Minnis, P. W. Heck, D. F. Young, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part II: Verification of theoretical cirrus radiative properties,” J. Atmos. Sci. 50, 1305–1322 (1993).
[CrossRef]

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

P. Minnis, K.-N. Liou, Y. Takano, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part I: Parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

W. L. Eberhard, “Cirrus properties deduced from CO2 lidar observations of zenith-enhanced backscatter from oriented crystals,” NASA Conf. Publ. 3238, 9–12 (1993).

1989 (3)

K.-D. Rockwitz, “Scattering properties of horizontally oriented ice crystal columns in cirrus clouds. Part 1,” Appl. Opt. 28, 4103–4110 (1989).
[CrossRef] [PubMed]

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

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

1988 (1)

J. S. Foot, “Some observations of the optical properties of clouds. Part II: Cirrus,” Q. J. R. Meteorol. Soc. 114, 145–164 (1988).
[CrossRef]

1984 (1)

1980 (2)

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

O. A. Volkovitskiy, L. N. Pavlova, A. G. Petrushin, “Scattering of light by ice crystals,” Izvestiya. Atmos. Ocean. Phys. 16, 98–102 (1980).

1979 (1)

K. Sassen, K.-N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part I: Angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

1978 (1)

C. M. R. Platt, N. L. Abshire, G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

1974 (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

1969 (1)

P. J. Huffman, W. R. Thursby, “Light scattering by ice crystals,” J. Atmos. Sci. 26, 1073–1077 (1969).
[CrossRef]

Abshire, N. L.

C. M. R. Platt, N. L. Abshire, G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

Arnott, W. P.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Aulenbach, S. M.

R. P. Lawson, A. J. Heymsfield, S. M. Aulenbach, T. L. Jensen, “Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS,” Geophys. Res. Lett. 25, 1331–1334 (1998).
[CrossRef]

Brogniez, G.

H. Chepfer, G. Brogniez, Y. Fouquart, “Cirrus clouds’ microphysical properties deduced from POLDER observations,” J. Quant. Spectrosc. Radiat. Transfer 60, 375–390 (1998).
[CrossRef]

Buriez, J. C.

J. Descloitres, J. C. Buriez, F. Parol, Y. Fouquart, “POLDER observations of cloud bidirectional reflectances compared to a plane-parallel model using the International Cloud Climatology Project cloud phase functions,” J. Geophys. Res. 103, 11,411–11,418 (1998).
[CrossRef]

Chepfer, H.

H. Chepfer, G. Brogniez, Y. Fouquart, “Cirrus clouds’ microphysical properties deduced from POLDER observations,” J. Quant. Spectrosc. Radiat. Transfer 60, 375–390 (1998).
[CrossRef]

Crépel, O.

O. Crépel, J. F. Gayet, J. F. Fournol, S. Oschepkov, “A new airborne polar nephelometer for the measurements of optical and microphysical cloud properties. Part II: Preliminary tests,” Ann. Geophys. 15, 460–470 (1997).

Descloitres, J.

J. Descloitres, J. C. Buriez, F. Parol, Y. Fouquart, “POLDER observations of cloud bidirectional reflectances compared to a plane-parallel model using the International Cloud Climatology Project cloud phase functions,” J. Geophys. Res. 103, 11,411–11,418 (1998).
[CrossRef]

Dong, Y. Y.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Eberhard, W. L.

W. L. Eberhard, “Cirrus properties deduced from CO2 lidar observations of zenith-enhanced backscatter from oriented crystals,” NASA Conf. Publ. 3238, 9–12 (1993).

Foot, J. S.

J. S. Foot, “Some observations of the optical properties of clouds. Part II: Cirrus,” Q. J. R. Meteorol. Soc. 114, 145–164 (1988).
[CrossRef]

Fouquart, Y.

J. Descloitres, J. C. Buriez, F. Parol, Y. Fouquart, “POLDER observations of cloud bidirectional reflectances compared to a plane-parallel model using the International Cloud Climatology Project cloud phase functions,” J. Geophys. Res. 103, 11,411–11,418 (1998).
[CrossRef]

H. Chepfer, G. Brogniez, Y. Fouquart, “Cirrus clouds’ microphysical properties deduced from POLDER observations,” J. Quant. Spectrosc. Radiat. Transfer 60, 375–390 (1998).
[CrossRef]

Fournol, J. F.

O. Crépel, J. F. Gayet, J. F. Fournol, S. Oschepkov, “A new airborne polar nephelometer for the measurements of optical and microphysical cloud properties. Part II: Preliminary tests,” Ann. Geophys. 15, 460–470 (1997).

Francis, P. N.

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

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

Gayet, J. F.

O. Crépel, J. F. Gayet, J. F. Fournol, S. Oschepkov, “A new airborne polar nephelometer for the measurements of optical and microphysical cloud properties. Part II: Preliminary tests,” Ann. Geophys. 15, 460–470 (1997).

Greenler, R.

R. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1990).

Hallett, J.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Hansen, J. E.

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Hart, W. D.

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

Heck, P. W.

P. Minnis, P. W. Heck, D. F. Young, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part II: Verification of theoretical cirrus radiative properties,” J. Atmos. Sci. 50, 1305–1322 (1993).
[CrossRef]

Heymsfield, A. J.

R. P. Lawson, A. J. Heymsfield, S. M. Aulenbach, T. L. Jensen, “Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS,” Geophys. Res. Lett. 25, 1331–1334 (1998).
[CrossRef]

K. Sassen, N. C. Knight, Y. Takano, A. J. Heymsfield, “Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies,” Appl. Opt. 33, 4590–4601 (1994).
[CrossRef] [PubMed]

Hignett, P.

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Huffman, P. J.

P. J. Huffman, W. R. Thursby, “Light scattering by ice crystals,” J. Atmos. Sci. 26, 1073–1077 (1969).
[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]

Isaka, H.

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

Jensen, T. L.

R. P. Lawson, A. J. Heymsfield, S. M. Aulenbach, T. L. Jensen, “Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS,” Geophys. Res. Lett. 25, 1331–1334 (1998).
[CrossRef]

Kahn, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

Klett, J. D.

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276–2285 (1995).
[CrossRef]

Knight, N. C.

Lacis, A. A.

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

Lawson, R. P.

R. P. Lawson, A. J. Heymsfield, S. M. Aulenbach, T. L. Jensen, “Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS,” Geophys. Res. Lett. 25, 1331–1334 (1998).
[CrossRef]

Liou, K. N.

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contr. Atmos. Phys. 71, 223–248 (1998).

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

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

Liou, K.-N.

P. Minnis, K.-N. Liou, Y. Takano, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part I: Parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

K. Sassen, K.-N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part I: Angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

Macke, A.

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

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

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Marston, P. L.

P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A. D. Pierce, R. N. Thurston, eds. (Academic, San Diego, Calif., 1992), Vol. 21, pp. 1–234.

McNice, G. T.

C. M. R. Platt, N. L. Abshire, G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

Minnis, P.

P. Minnis, K.-N. Liou, Y. Takano, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part I: Parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

P. Minnis, P. W. Heck, D. F. Young, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part II: Verification of theoretical cirrus radiative properties,” J. Atmos. Sci. 50, 1305–1322 (1993).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

A. Macke, M. I. Mishchenko, “Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles,” Appl. Opt. 35, 4291–4296 (1996).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

Mueller, J.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Oschepkov, S.

O. Crépel, J. F. Gayet, J. F. Fournol, S. Oschepkov, “A new airborne polar nephelometer for the measurements of optical and microphysical cloud properties. Part II: Preliminary tests,” Ann. Geophys. 15, 460–470 (1997).

Parol, F.

J. Descloitres, J. C. Buriez, F. Parol, Y. Fouquart, “POLDER observations of cloud bidirectional reflectances compared to a plane-parallel model using the International Cloud Climatology Project cloud phase functions,” J. Geophys. Res. 103, 11,411–11,418 (1998).
[CrossRef]

Pavlova, L. N.

O. A. Volkovitskiy, L. N. Pavlova, A. G. Petrushin, “Scattering of light by ice crystals,” Izvestiya. Atmos. Ocean. Phys. 16, 98–102 (1980).

Personne, P.

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

Petrushin, A. G.

O. A. Volkovitskiy, L. N. Pavlova, A. G. Petrushin, “Scattering of light by ice crystals,” Izvestiya. Atmos. Ocean. Phys. 16, 98–102 (1980).

Platt, C. M. R.

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

C. M. R. Platt, N. L. Abshire, G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

Poelott, M. R.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Posse, P.

P. Posse, W. von Hoyningen-Huene, “Information about scattering properties and particle characteristics of a stratiform cloud at Helgoland by remote optical measurements,” Contr. Atmos. Phys. 68, 359–366 (1995).

Raschke, E.

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

Rockwitz, K.-D.

Rossow, W. B.

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

Sassen, K.

K. Sassen, “Contrail-cirrus and their potential for regional climate change,” Bull. Am. Meteorol. Soc. 78, 1885–1903 (1997).
[CrossRef]

K. Sassen, N. C. Knight, Y. Takano, A. J. Heymsfield, “Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies,” Appl. Opt. 33, 4590–4601 (1994).
[CrossRef] [PubMed]

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

K. Sassen, K.-N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part I: Angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

Spinhirne, J. D.

J. D. Spinhirne, “Cirrus infrared parameters and shortwave reflectance relations from observations,” J. Atmos. Sci. 53, 1438–1458 (1996).
[CrossRef]

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

Takano, Y.

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

K. Sassen, N. C. Knight, Y. Takano, A. J. Heymsfield, “Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies,” Appl. Opt. 33, 4590–4601 (1994).
[CrossRef] [PubMed]

P. Minnis, K.-N. Liou, Y. Takano, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part I: Parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

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

Thursby, W. R.

P. J. Huffman, W. R. Thursby, “Light scattering by ice crystals,” J. Atmos. Sci. 26, 1073–1077 (1969).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Volkovitskiy, O. A.

O. A. Volkovitskiy, L. N. Pavlova, A. G. Petrushin, “Scattering of light by ice crystals,” Izvestiya. Atmos. Ocean. Phys. 16, 98–102 (1980).

von Hoyningen-Huene, W.

P. Posse, W. von Hoyningen-Huene, “Information about scattering properties and particle characteristics of a stratiform cloud at Helgoland by remote optical measurements,” Contr. Atmos. Phys. 68, 359–366 (1995).

Warren, S. G.

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

Yang, P.

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contr. Atmos. Phys. 71, 223–248 (1998).

Young, D. F.

P. Minnis, P. W. Heck, D. F. Young, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part II: Verification of theoretical cirrus radiative properties,” J. Atmos. Sci. 50, 1305–1322 (1993).
[CrossRef]

Ann. Geophys. (1)

O. Crépel, J. F. Gayet, J. F. Fournol, S. Oschepkov, “A new airborne polar nephelometer for the measurements of optical and microphysical cloud properties. Part II: Preliminary tests,” Ann. Geophys. 15, 460–470 (1997).

Appl. Opt. (5)

Bull. Am. Meteorol. Soc. (1)

K. Sassen, “Contrail-cirrus and their potential for regional climate change,” Bull. Am. Meteorol. Soc. 78, 1885–1903 (1997).
[CrossRef]

Contr. Atmos. Phys. (2)

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contr. Atmos. Phys. 71, 223–248 (1998).

P. Posse, W. von Hoyningen-Huene, “Information about scattering properties and particle characteristics of a stratiform cloud at Helgoland by remote optical measurements,” Contr. Atmos. Phys. 68, 359–366 (1995).

Geophys. Res. Lett. (1)

R. P. Lawson, A. J. Heymsfield, S. M. Aulenbach, T. L. Jensen, “Shapes, sizes and light scattering properties of ice crystals in cirrus and a persistent contrail during SUCCESS,” Geophys. Res. Lett. 25, 1331–1334 (1998).
[CrossRef]

Izvestiya. Atmos. Ocean. Phys. (1)

O. A. Volkovitskiy, L. N. Pavlova, A. G. Petrushin, “Scattering of light by ice crystals,” Izvestiya. Atmos. Ocean. Phys. 16, 98–102 (1980).

J. Appl. Meteorol. (1)

C. M. R. Platt, N. L. Abshire, G. T. McNice, “Some microphysical properties of an ice cloud from lidar observation of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220–1224 (1978).
[CrossRef]

J. Atmos. Sci. (11)

J. D. Spinhirne, “Cirrus infrared parameters and shortwave reflectance relations from observations,” J. Atmos. Sci. 53, 1438–1458 (1996).
[CrossRef]

J. D. Klett, “Orientation model for particles in turbulence,” J. Atmos. Sci. 52, 2276–2285 (1995).
[CrossRef]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

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

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

P. Minnis, K.-N. Liou, Y. Takano, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part I: Parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

P. J. Huffman, W. R. Thursby, “Light scattering by ice crystals,” J. Atmos. Sci. 26, 1073–1077 (1969).
[CrossRef]

K. Sassen, K.-N. Liou, “Scattering of polarized laser light by water droplet, mixed-phase and ice crystal clouds. Part I: Angular scattering patterns,” J. Atmos. Sci. 36, 838–851 (1979).
[CrossRef]

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

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

P. Minnis, P. W. Heck, D. F. Young, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. Part II: Verification of theoretical cirrus radiative properties,” J. Atmos. Sci. 50, 1305–1322 (1993).
[CrossRef]

J. Geophys. Res. (5)

M. I. Mishchenko, W. B. Rossow, A. Macke, A. A. Lacis, “Sensitivity of cirrus cloud albedo, bidirectional reflectance and optical thickness retrieval accuracy to ice particle shape,” J. Geophys. Res. 101, 16,973–16,985 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, R. A. Kahn, R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16,831–16,847 (1997).
[CrossRef]

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

J. Descloitres, J. C. Buriez, F. Parol, Y. Fouquart, “POLDER observations of cloud bidirectional reflectances compared to a plane-parallel model using the International Cloud Climatology Project cloud phase functions,” J. Geophys. Res. 103, 11,411–11,418 (1998).
[CrossRef]

J. Meteorol. Soc. Jpn. (1)

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

J. Quant. Spectrosc. Radiat. Transfer (2)

H. Chepfer, G. Brogniez, Y. Fouquart, “Cirrus clouds’ microphysical properties deduced from POLDER observations,” J. Quant. Spectrosc. Radiat. Transfer 60, 375–390 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

NASA Conf. Publ. (1)

W. L. Eberhard, “Cirrus properties deduced from CO2 lidar observations of zenith-enhanced backscatter from oriented crystals,” NASA Conf. Publ. 3238, 9–12 (1993).

Q. J. R. Meteorol. Soc. (2)

J. S. Foot, “Some observations of the optical properties of clouds. Part II: Cirrus,” Q. J. R. Meteorol. Soc. 114, 145–164 (1988).
[CrossRef]

P. N. Francis, P. Hignett, A. Macke, “The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93,” Q. J. R. Meteorol. Soc. 124, 1273–1291 (1998).
[CrossRef]

Space Sci. Rev. (1)

J. E. Hansen, L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[CrossRef]

Other (2)

P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A. D. Pierce, R. N. Thurston, eds. (Academic, San Diego, Calif., 1992), Vol. 21, pp. 1–234.

R. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1990).

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Figures (2)

Fig. 1
Fig. 1

Ray tracing phase functions (with diffraction not included) for randomly oriented hexagonal and circular cylinders with a length-to-diameter ratio of 1. The refractive index is 1.311 + i0.311 × 10-8 and corresponds to water ice at a visible wavelength.32

Fig. 2
Fig. 2

Comparison of GO and T-matrix phase functions for monodisperse, randomly oriented, circular ice cylinders with varying size parameters.

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