Abstract

Many halo arcs are caused by pyramidal crystals that have {1 0 -1 1} crystal faces. We treat halo arcs arising from pyramidal crystals that fall in the air with their c axes vertically oriented. To our knowledge only 6 of the 12 possible halo phenomena that belong to this category have been dealt with in the literature. Surprisingly the yet undiscussed halos are predicted to be of comparable intensity with those already treated. They are produced by reflections from pyramidal crystal basal faces. A theoretical summary and computer simulations are presented of the mentioned 12 halo phenomena and of the individual arcs into which they break in the sky. We give an overview to the current level of documentation of these phenomena by listing the first published photographs of each phenomenon known to the authors.

© 1998 Optical Society of America

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References

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  1. H. Steinmetz, H. Weickmann, “Zusammenhänge zwischen einer seltenen Haloerscheinung und der gestalt der Eiskristalle,” Heidelb. Beitr. Mineral. 1, 31–36 (1947).
  2. H. Weickmann, “The ice phase in the atmosphere,” Royal Aircraft Establishment Library translation 273 (Ministry of Supply, London, 1948).
  3. E. C. W. Goldie, G. T. Meaden, R. White, “The concentric halo display of 14 April 1974,” Weather 31, 304–311 (1976).
    [CrossRef]
  4. R. A. R. Tricker, “Arcs associated with halos of unusual radii,” J. Opt. Soc. Am. 69, 1093–1100 (1979).
    [CrossRef]
  5. E. Barkow, “Eine seltene Haloerscheinung,” Meteorol. Z. 33, 476 with plate (1916).
  6. P. J. Neiman, “The Boulder, Colorado, concentric halo display of 21 July 1986,” Bull. Am. Meteorol. Soc. 70, 258–264 (1989).
    [CrossRef]
  7. W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).
  8. V. Mäkelä, ed., Ursa Minor, Bulletin of the Ursa Astronomical Association (Helsinki, Finland, 1986–1997).
  9. M. Riikonen, “Hämäränsäteitä ja haloja Filippiineillä,” Tähdet ja Avaruus 24, 45–47 (1994).
  10. W. Tape, “Pyramidal ice crystals and odd radius halos,” in Light and Color in the Open Air, Vol. 12 of 1990 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1990), pp. 64–66.
  11. The extension of the word parhelia to ascribe arcs associated with odd radius halos was introduced by Tape in 1994 (Ref. 7). For convenience we apply the same term in this paper.
  12. P. Parviainen, C. F. Bohren, V. Mäkelä, “Vertical elliptical coronas caused by pollen,” Appl. Opt. 33, 4548–4551 (1994).
    [CrossRef] [PubMed]
  13. J. Hakumäki, M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
    [CrossRef]
  14. M. Pekkola, “Finnish halo observing network: search for rare halo phenomena,” Appl. Opt. 30, 3542–3544 (1991).
    [CrossRef] [PubMed]
  15. M. Riikonen, J. Ruoskanen, “Observations of vertically elliptical halos,” Appl. Opt. 33, 4537–4538 (1994).
    [CrossRef] [PubMed]
  16. T. Ohtake, “Unusual crystal in ice fog,” J. Atmos. Sci. 27, 509–511 (1970).
    [CrossRef]
  17. C. Magono, S. Fujita, T. Taniguchi, “Unusual type of single ice crystals originating from frozen cloud droplets,” J. Atmos. Sci. 36, 2495–2501 (1979).
    [CrossRef]
  18. A. B. Fraser, “What size of ice crystals causes the halos?,” J. Opt. Soc. Am. 69, 1112–1118 (1979).
    [CrossRef]
  19. K. Sassen, “Remote sensing of planar ice crystal fall attitudes,” J. Meteorol. Soc. Jpn. 58, 422–429 (1980).
  20. W. Tape, Department of Mathematical Sciences, University of Alaska Fairbanks, Fairbanks, Alaska 99775 (personal communication, 1997).
  21. 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]
  22. M. Pekkola, “Kolme komeaa halonäytelmää,” Tähdet ja Avaruus 6, 40–41 (1993).
  23. R. G. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, 1980).
  24. P.-P. Hattinga Verschure, “Bijzondere halo’s waarnemingen in 1973 and 1974,” Zenit 2, 364–365 (1975).

1994 (4)

1993 (1)

M. Pekkola, “Kolme komeaa halonäytelmää,” Tähdet ja Avaruus 6, 40–41 (1993).

1991 (1)

1989 (2)

P. J. Neiman, “The Boulder, Colorado, concentric halo display of 21 July 1986,” Bull. Am. Meteorol. Soc. 70, 258–264 (1989).
[CrossRef]

J. Hakumäki, M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
[CrossRef]

1980 (1)

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

1979 (3)

1976 (1)

E. C. W. Goldie, G. T. Meaden, R. White, “The concentric halo display of 14 April 1974,” Weather 31, 304–311 (1976).
[CrossRef]

1975 (1)

P.-P. Hattinga Verschure, “Bijzondere halo’s waarnemingen in 1973 and 1974,” Zenit 2, 364–365 (1975).

1970 (1)

T. Ohtake, “Unusual crystal in ice fog,” J. Atmos. Sci. 27, 509–511 (1970).
[CrossRef]

1947 (1)

H. Steinmetz, H. Weickmann, “Zusammenhänge zwischen einer seltenen Haloerscheinung und der gestalt der Eiskristalle,” Heidelb. Beitr. Mineral. 1, 31–36 (1947).

1916 (1)

E. Barkow, “Eine seltene Haloerscheinung,” Meteorol. Z. 33, 476 with plate (1916).

Barkow, E.

E. Barkow, “Eine seltene Haloerscheinung,” Meteorol. Z. 33, 476 with plate (1916).

Bohren, C. F.

Fraser, A. B.

Fujita, S.

C. Magono, S. Fujita, T. Taniguchi, “Unusual type of single ice crystals originating from frozen cloud droplets,” J. Atmos. Sci. 36, 2495–2501 (1979).
[CrossRef]

Goldie, E. C. W.

E. C. W. Goldie, G. T. Meaden, R. White, “The concentric halo display of 14 April 1974,” Weather 31, 304–311 (1976).
[CrossRef]

Greenler, R. G.

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

Hakumäki, J.

J. Hakumäki, M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
[CrossRef]

Hattinga Verschure, P.-P.

P.-P. Hattinga Verschure, “Bijzondere halo’s waarnemingen in 1973 and 1974,” Zenit 2, 364–365 (1975).

Heymsfield, A. J.

Knight, N. C.

Magono, C.

C. Magono, S. Fujita, T. Taniguchi, “Unusual type of single ice crystals originating from frozen cloud droplets,” J. Atmos. Sci. 36, 2495–2501 (1979).
[CrossRef]

Mäkelä, V.

Meaden, G. T.

E. C. W. Goldie, G. T. Meaden, R. White, “The concentric halo display of 14 April 1974,” Weather 31, 304–311 (1976).
[CrossRef]

Neiman, P. J.

P. J. Neiman, “The Boulder, Colorado, concentric halo display of 21 July 1986,” Bull. Am. Meteorol. Soc. 70, 258–264 (1989).
[CrossRef]

Ohtake, T.

T. Ohtake, “Unusual crystal in ice fog,” J. Atmos. Sci. 27, 509–511 (1970).
[CrossRef]

Parviainen, P.

Pekkola, M.

M. Pekkola, “Kolme komeaa halonäytelmää,” Tähdet ja Avaruus 6, 40–41 (1993).

M. Pekkola, “Finnish halo observing network: search for rare halo phenomena,” Appl. Opt. 30, 3542–3544 (1991).
[CrossRef] [PubMed]

J. Hakumäki, M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
[CrossRef]

Riikonen, M.

M. Riikonen, J. Ruoskanen, “Observations of vertically elliptical halos,” Appl. Opt. 33, 4537–4538 (1994).
[CrossRef] [PubMed]

M. Riikonen, “Hämäränsäteitä ja haloja Filippiineillä,” Tähdet ja Avaruus 24, 45–47 (1994).

Ruoskanen, J.

Sassen, K.

Steinmetz, H.

H. Steinmetz, H. Weickmann, “Zusammenhänge zwischen einer seltenen Haloerscheinung und der gestalt der Eiskristalle,” Heidelb. Beitr. Mineral. 1, 31–36 (1947).

Takano, Y.

Taniguchi, T.

C. Magono, S. Fujita, T. Taniguchi, “Unusual type of single ice crystals originating from frozen cloud droplets,” J. Atmos. Sci. 36, 2495–2501 (1979).
[CrossRef]

Tape, W.

W. Tape, Department of Mathematical Sciences, University of Alaska Fairbanks, Fairbanks, Alaska 99775 (personal communication, 1997).

W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

W. Tape, “Pyramidal ice crystals and odd radius halos,” in Light and Color in the Open Air, Vol. 12 of 1990 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1990), pp. 64–66.

Tricker, R. A. R.

Weickmann, H.

H. Steinmetz, H. Weickmann, “Zusammenhänge zwischen einer seltenen Haloerscheinung und der gestalt der Eiskristalle,” Heidelb. Beitr. Mineral. 1, 31–36 (1947).

H. Weickmann, “The ice phase in the atmosphere,” Royal Aircraft Establishment Library translation 273 (Ministry of Supply, London, 1948).

White, R.

E. C. W. Goldie, G. T. Meaden, R. White, “The concentric halo display of 14 April 1974,” Weather 31, 304–311 (1976).
[CrossRef]

Appl. Opt. (4)

Bull. Am. Meteorol. Soc. (1)

P. J. Neiman, “The Boulder, Colorado, concentric halo display of 21 July 1986,” Bull. Am. Meteorol. Soc. 70, 258–264 (1989).
[CrossRef]

Heidelb. Beitr. Mineral. (1)

H. Steinmetz, H. Weickmann, “Zusammenhänge zwischen einer seltenen Haloerscheinung und der gestalt der Eiskristalle,” Heidelb. Beitr. Mineral. 1, 31–36 (1947).

J. Atmos. Sci. (2)

T. Ohtake, “Unusual crystal in ice fog,” J. Atmos. Sci. 27, 509–511 (1970).
[CrossRef]

C. Magono, S. Fujita, T. Taniguchi, “Unusual type of single ice crystals originating from frozen cloud droplets,” J. Atmos. Sci. 36, 2495–2501 (1979).
[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. Opt. Soc. Am. (2)

Meteorol. Z. (1)

E. Barkow, “Eine seltene Haloerscheinung,” Meteorol. Z. 33, 476 with plate (1916).

Tähdet ja Avaruus (2)

M. Pekkola, “Kolme komeaa halonäytelmää,” Tähdet ja Avaruus 6, 40–41 (1993).

M. Riikonen, “Hämäränsäteitä ja haloja Filippiineillä,” Tähdet ja Avaruus 24, 45–47 (1994).

Weather (2)

E. C. W. Goldie, G. T. Meaden, R. White, “The concentric halo display of 14 April 1974,” Weather 31, 304–311 (1976).
[CrossRef]

J. Hakumäki, M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
[CrossRef]

Zenit (1)

P.-P. Hattinga Verschure, “Bijzondere halo’s waarnemingen in 1973 and 1974,” Zenit 2, 364–365 (1975).

Other (7)

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

W. Tape, Department of Mathematical Sciences, University of Alaska Fairbanks, Fairbanks, Alaska 99775 (personal communication, 1997).

H. Weickmann, “The ice phase in the atmosphere,” Royal Aircraft Establishment Library translation 273 (Ministry of Supply, London, 1948).

W. Tape, “Pyramidal ice crystals and odd radius halos,” in Light and Color in the Open Air, Vol. 12 of 1990 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1990), pp. 64–66.

The extension of the word parhelia to ascribe arcs associated with odd radius halos was introduced by Tape in 1994 (Ref. 7). For convenience we apply the same term in this paper.

W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

V. Mäkelä, ed., Ursa Minor, Bulletin of the Ursa Astronomical Association (Helsinki, Finland, 1986–1997).

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Figures (3)

Fig. 1
Fig. 1

Numbering of the pyramidal crystal faces (adapted from Ref. 7).

Fig. 2
Fig. 2

Effect of the crystal aspect ratio and crystal tilting for the halo arcs for Sun elevations of 2° and 20°. Thin crystals [(a), (c), (e), (g)] are effective in forming halo arcs that require basal face reflections; thick crystals [(b), (d), (f), (h)] form only arcs that require no basal face reflections. Tilting of the crystals weakens the basal reflection arcs [(c), (g)] more markedly than the arcs requiring no basal face reflections [(d), (h)]. Tilts of 10° were used on simulations (c), (d), (g), (h) and 0° for (a), (b), (e), and (f) (refer to Table 1 for the identification of the numbered halo arcs). Parhelia are marked with P, subparhelia with SP, Sun with S, and subsun with SS. For simulations (a), (c), (e), and (g), the number of rays considered is 70,000 and two populations of pyramid crystals with aspect ratios of 0.05/0.05/0.05 and 0.03/0.03/0.03 were used. For simulations (b), (d), (f), and (h), the number of rays is 50,000 and the aspect ratios are 0.25/0.25/0.25 and 0.20/0.20/0.20. The aspect ratio of the pyramid crystal is given in the form pyramid prism/middle prism/pyramid prism. The simulations were made with a program developed by Frank Pattloch and Eberhard Tränkle.

Fig. 3
Fig. 3

Distances of the arcs from the Sun and subsun found from the solar vertical as a function of solar elevation. The numbers next to each curve indicate the halo arcs that the curve represents. Refer to Table 1 for the halo arc identification. For readability, two curves are dashed.

Tables (1)

Tables Icon

Table 1 Different Pyramidal Crystal Halo Forms and Arcs into which They Divide

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