Abstract

Using a hit-and-miss Monte Carlo method, we followed many paths of Sun rays through a layer of hexagonal ice crystals. The angle of scattering by a single crystal is determined by tracing the path of the Sun rays through the crystal with its particular orientation. In this way we produced point plots of the intensity of the scattered sunlight for a specified population of crystals. By comparing the intensity patterns from single and multiple scattering, we looked for additional effects caused by multiple scattering. Several new secondary structures appear; however, their intensities are significant only when they result from spotlike primary structures. It appears that secondary structures from two combinations should be observable: from thick-plate crystals, the sun dogs of the sun dogs; and for long-column crystals in the Parry-arc orientation, the subsun of the lower tangent arc for Sun elevations around 15°. We show that multiple scattering is essential to explain the Saskatoon display.

© 1987 Optical Society of America

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References

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  1. R. G. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1980).
  2. F. Pattloch, E. Tränkle, “Monte Carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. A 1, 520–526 (1984).
    [CrossRef]
  3. R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
    [CrossRef]
  4. Y. Takano, S. Asano, “Fraunhofer diffraction by ice crystals suspended in the atmosphere,”J. Met. Soc. Jpn. 61, 289–300 (1983).
  5. W. Tape, Department of Mathematics, University of Alaska, Fairbanks, Alaska 99701 (personal communication, 1986).
  6. E. A. Ripley, B. Saugier, “Photometeors at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).
    [CrossRef]
  7. W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–236 (1972).
    [CrossRef]

1984 (2)

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

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

1983 (1)

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

1972 (1)

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–236 (1972).
[CrossRef]

1971 (1)

E. A. Ripley, B. Saugier, “Photometeors 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. Met. 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, 234–236 (1972).
[CrossRef]

Greenler, R. G.

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).

Pattloch, F.

Ripley, E. A.

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

Saugier, B.

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

Takano, Y.

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

Tape, W.

W. Tape, Department of Mathematics, University of Alaska, Fairbanks, Alaska 99701 (personal communication, 1986).

Tränkle, E.

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

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

Tricker, R. A. R.

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–236 (1972).
[CrossRef]

J. Met. Soc. Jpn. (1)

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

J. Opt. Soc. Am. A (1)

Nature (London) (1)

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

Weather (2)

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

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–236 (1972).
[CrossRef]

Other (2)

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

W. Tape, Department of Mathematics, University of Alaska, Fairbanks, Alaska 99701 (personal communication, 1986).

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Figures (7)

Fig. 1
Fig. 1

Model of ray tracing through the ice crystal layer.

Fig. 2
Fig. 2

Intensity plots for randomly oriented crystals: (a) single scattering, (b) multiple scattering.

Fig. 3
Fig. 3

Intensity plots for thick, oriented plates: (a) single scattering, (b) multiple scattering.

Fig. 4
Fig. 4

Intensity plots for long, singly oriented columns: (a) single scattering, (b) multiple scattering.

Fig. 5
Fig. 5

Intensity plots for long, Parry-arc-oriented columns: (a) single scattering, (b) multiple scattering.

Fig. 6
Fig. 6

(a) Contribution from thick plates (a = 1.2) to the Saskatoon display, (b) contribution from thin plates (a = 10) to the Saskatoon display.

Plate XIV
Plate XIV

(E. Trankle and Robert G. Greenler, p. 591.) Sun with 22° parhelion. The diamond-shaped structure on the Sun in this photo probably results from diffraction rather than from double scattering. Photographed in Wisconsin by Robert G. Greenler.

Tables (2)

Tables Icon

Table 1 Parameter Values for Four Orientations

Tables Icon

Table 2 Parameter Values for the Saskatoon Display

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