Abstract

Halo phenomena produced by horizontally oriented plate and column ice crystals are computed. Owing to the effect of multiple scattering, a number of optical features, in addition to the well-known halos and arcs caused by single scattering, can be produced in the sky. These include the 44° parhelion, the 66° parhelion, the anthelion, the uniform and white parhelic circle, and the uniform and white circumzenithal circle in the case of horizontally oriented plates. The anthelion is a result of double scattering that involves horizontally oriented columns that produce the Parry arc. The optical phenomena identified in the present study are compared with those of previous research and discussed.

© 1990 Optical Society of America

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References

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  1. R. A. R. Tricker, Ice Crystal Haloes (Optical Society of America, Washington, D.C., 1979).
  2. R. G. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1980).
  3. F. Pattloch, E. Tränkle, “Monte Carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. A 1, 520–526 (1984).
    [CrossRef]
  4. R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
    [CrossRef]
  5. E. Tränkle, R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
    [CrossRef]
  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. Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).There is a typographical error in this reference. L/2a 4 μm/40 μm in the caption of Fig. 11 should be replaced with L/2a= 8 μm/80 μm.
    [CrossRef]
  8. E. A. Ripley, B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).
    [CrossRef]
  9. Y. Takano, K. Jayaweera, “Scattering phase matrix for hexagonal ice crystals computed from ray optics,” Appl. Opt. 24, 3254–3263 (1985).
    [CrossRef] [PubMed]
  10. D. K. Lynch, Pt. Schwartz, “Origin of the anthelion,” J. Opt. Soc. Am. 69, 383–386 (1979).
    [CrossRef]
  11. G. H. Liljequist, “Halo phenomena and ice crystals,” in Norwegian-British-Swedish Antarctic Expedition, 1949–1952, Scientific Results (Norsk Polarinstitutt, Oslo, 1956), Vol. 2, Part 2, p. 52.
  12. W. J. Humphreys, Physics of the Air (Dover, New York, 1964).
  13. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  14. Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,” J. Meteorol. Soc. Jpn. 61, 289–300 (1983).
  15. W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
    [CrossRef]

1989 (2)

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, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).There is a typographical error in this reference. L/2a 4 μm/40 μm in the caption of Fig. 11 should be replaced with L/2a= 8 μm/80 μm.
[CrossRef]

1987 (1)

1985 (1)

1984 (2)

F. Pattloch, E. Tränkle, “Monte Carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. A 1, 520–526 (1984).
[CrossRef]

R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
[CrossRef]

1983 (1)

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

1979 (1)

1972 (1)

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

1971 (1)

E. A. Ripley, B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).
[CrossRef]

Asano, S.

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

Evans, W. F. J.

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

Greenler, R. G.

E. Tränkle, R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
[CrossRef]

R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
[CrossRef]

R. G. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1980).

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964).

Jayaweera, K.

Liljequist, G. H.

G. H. Liljequist, “Halo phenomena and ice crystals,” in Norwegian-British-Swedish Antarctic Expedition, 1949–1952, Scientific Results (Norsk Polarinstitutt, Oslo, 1956), Vol. 2, Part 2, p. 52.

Liou, K. N.

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).There is a typographical error in this reference. L/2a 4 μm/40 μm in the caption of Fig. 11 should be replaced with L/2a= 8 μm/80 μm.
[CrossRef]

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]

Lynch, D. K.

Pattloch, F.

Ripley, E. A.

E. A. Ripley, B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).
[CrossRef]

Saugier, B.

E. A. Ripley, B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).
[CrossRef]

Schwartz, Pt.

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, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).There is a typographical error in this reference. L/2a 4 μm/40 μm in the caption of Fig. 11 should be replaced with L/2a= 8 μm/80 μm.
[CrossRef]

Y. Takano, K. Jayaweera, “Scattering phase matrix for hexagonal ice crystals computed from ray optics,” Appl. Opt. 24, 3254–3263 (1985).
[CrossRef] [PubMed]

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

Tränkle, E.

Tricker, R. A. R.

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

R. A. R. Tricker, Ice Crystal Haloes (Optical Society of America, Washington, D.C., 1979).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Appl. Opt. (1)

J. Atmos. Sci. (2)

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, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).There is a typographical error in this reference. L/2a 4 μm/40 μm in the caption of Fig. 11 should be replaced with L/2a= 8 μm/80 μm.
[CrossRef]

J. Meteorol. Soc. Jpn. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nature (London) (1)

R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
[CrossRef]

Weather (2)

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

E. A. Ripley, B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).
[CrossRef]

Other (5)

G. H. Liljequist, “Halo phenomena and ice crystals,” in Norwegian-British-Swedish Antarctic Expedition, 1949–1952, Scientific Results (Norsk Polarinstitutt, Oslo, 1956), Vol. 2, Part 2, p. 52.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

R. A. R. Tricker, Ice Crystal Haloes (Optical Society of America, Washington, D.C., 1979).

R. G. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1980).

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Figures (6)

Fig. 1
Fig. 1

Scattering geometry for 2-D plates. IO and SO denote the incident and scattered directions, respectively. All the scattered light is confined to the latitude belts II’ and JJ’ and their mirror images with respect to the horizontal plane XOY.

Fig. 2
Fig. 2

Intensity of the sunlight transmitted by 2-D plates with L/2a = 0.4 along the latitude belt of (a) θ = 77° and (b) 0 = 29° at a wavelength of 0.55 μm. The solar zenith angle θ0 = 77°. In (a) the intensity due to single scattering is also shown on a different scale. When the optical depth becomes 32 in (a), the intensity takes a constant value of 6.7 × 10−4, which is not in the figure.

Fig. 3
Fig. 3

Intensity distribution for Parry columns with L/2a = 2.5 at λ = 0.55 μm (a) above the horizon and (b) below the horizon. The solar zenith angle θ0 is 73°. ·,+,*, and ■ denote 0,1,2, and 3, respectively, in units of [log10P11], where P11 is the relative intensity and [ ] denotes the integral part. SID, the solar incident direction.

Fig. 4
Fig. 4

Intensity of the sunlight transmitted by Parry columns with L/2a = 2.5 as a function of the azimuth angle ϕϕ0 for (a) θ0 = θ = 73° and (b) θ0 = θ = 30°. The intensity due to single scattering is also shown in the lower part of the figure on a different scale.

Fig. 5
Fig. 5

Same as Fig. 3 but for 2-D columns. Since SID, ATP, SS, and ASP cannot be pinpointed exactly, arrows are used to indicate these positions.

Fig. 6
Fig. 6

(a) Intensity pattern for 2-D columns with L/2a = 2.5 at λ = 0.55 μm. above the horizon. The solar zenith angle θ0 is 73°. ·, +, *, and ■ denote 0,1,2, and 3, respectively, in units of [2 log10P11] − 2 in order to enhance the pattern around the Sun. (b) Same as in (a) but for L/2a = 1.5 and θ0 = 60° and in units of [2 log10P11] − 3.

Equations (2)

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θ * = { π / 2 sin 1 ( m r 2 sin 2 θ 0 ) 1 / 2 for θ 0 > sin 1 ( m r 2 1 ) 1 / 2 58 ° sin 1 ( m r 2 cos 2 θ 0 ) 1 / 2 for θ 0 < cos 1 ( m r 2 1 ) 1 / 2 32 ° .
( ϕ ϕ 0 ) c = 2 sin 1 [ ( m r 2 1 ) 1 / 2 / sin θ 0 ] .

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