Abstract

The formation mechanism of elliptical halos and Bottlinger’s rings has long remained uncertain. The current model for elliptical halos requires multiple scattering from two different populations of ice crystals in a complex mode of motion. New evidence indicates that elliptical halos, and possibly Bottlinger’s rings, are due to refraction through ice crystals shaped like obtuse pyramids. This unusual ice crystal may not have been documented previously.

© 1999 Optical Society of America

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References

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  1. W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
    [CrossRef]
  2. R. G. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, New York, 1980).
  3. D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995).
  4. M. Pekkola, “Arvoituksellinen Hissinkin halo,” Tähdet ja Avaruus 18, 60–63 (1988).
  5. J. Hakumäki, M. Pekkola, “Rare vertically elliptical halos,” Weather 44, 466–473 (1989).
    [CrossRef]
  6. C. M. Broomall, “Lunar halo,” Science 13, 327 (1901).
    [CrossRef]
  7. E. Tränkle, M. Riikonen, “Elliptical halos, Bottlinger’s rings, and the ice-plate snow-star transition,” Appl. Opt. 35, 4871–4878 (1996).
    [CrossRef] [PubMed]
  8. C. F. Bottlinger, “Über eine interessante optische Erscheinung bei einer Ballonfahrt,” Meteorol. Z. 27, 74–75 (1910).
  9. D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 21, 4580–4589 (1994).
    [CrossRef]
  10. S. W. Visser, Optische verschijnselen aan de hemel (Koninklijk Nederlands Meteorologisch Institut s’Gravenhage, The Netherlands, 1957).
  11. M. Pekkola, “Finnish Halo Observing Network: search for rare halo phenomena,” Appl. Opt. 30, 3542–3544 (1991).
    [CrossRef] [PubMed]
  12. M. Riikonen, J. Ruoskanen, “Observations of vertically elliptical halos,” Appl. Opt. 33, 4537–4538 (1994).
    [CrossRef] [PubMed]
  13. M. Sillanpää, M. Pekkola, “Ellipsihalojen selitys näköpiirissä,” Tähdet ja Avaruus 27, 40–41 (1997).
  14. W. Tape, “Some ice crystals that made halos,” J. Opt. Soc. Am. 73, 1641–1644 (1983).
    [CrossRef]
  15. F. Pattloch, E. Tränkle, “Monte Carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. A 1, 520–526 (1984).
    [CrossRef]
  16. E. Tränkle, R. G. Greenler, “Multiple scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
    [CrossRef]
  17. R. A. R. Tricker, “Arcs associated with halos of unusual radii,” J. Opt. Soc. Am. 69, 1093–1100 (1979).
    [CrossRef]

1997 (1)

M. Sillanpää, M. Pekkola, “Ellipsihalojen selitys näköpiirissä,” Tähdet ja Avaruus 27, 40–41 (1997).

1996 (1)

1994 (2)

D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 21, 4580–4589 (1994).
[CrossRef]

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

1991 (1)

1989 (1)

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

1988 (1)

M. Pekkola, “Arvoituksellinen Hissinkin halo,” Tähdet ja Avaruus 18, 60–63 (1988).

1987 (1)

1984 (1)

1983 (1)

1979 (1)

1910 (1)

C. F. Bottlinger, “Über eine interessante optische Erscheinung bei einer Ballonfahrt,” Meteorol. Z. 27, 74–75 (1910).

1901 (1)

C. M. Broomall, “Lunar halo,” Science 13, 327 (1901).
[CrossRef]

Bottlinger, C. F.

C. F. Bottlinger, “Über eine interessante optische Erscheinung bei einer Ballonfahrt,” Meteorol. Z. 27, 74–75 (1910).

Broomall, C. M.

C. M. Broomall, “Lunar halo,” Science 13, 327 (1901).
[CrossRef]

Fraser, A. B.

D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 21, 4580–4589 (1994).
[CrossRef]

Gedzelman, S. D.

D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 21, 4580–4589 (1994).
[CrossRef]

Greenler, R. G.

Hakumäki, J.

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

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995).

Lynch, D. K.

D. K. Lynch, S. D. Gedzelman, A. B. Fraser, “Subsuns, Bottlinger’s rings, and elliptical halos,” Appl. Opt. 21, 4580–4589 (1994).
[CrossRef]

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995).

Pattloch, F.

Pekkola, M.

M. Sillanpää, M. Pekkola, “Ellipsihalojen selitys näköpiirissä,” Tähdet ja Avaruus 27, 40–41 (1997).

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]

M. Pekkola, “Arvoituksellinen Hissinkin halo,” Tähdet ja Avaruus 18, 60–63 (1988).

Riikonen, M.

Ruoskanen, J.

Sillanpää, M.

M. Sillanpää, M. Pekkola, “Ellipsihalojen selitys näköpiirissä,” Tähdet ja Avaruus 27, 40–41 (1997).

Tape, W.

W. Tape, “Some ice crystals that made halos,” J. Opt. Soc. Am. 73, 1641–1644 (1983).
[CrossRef]

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
[CrossRef]

Tränkle, E.

Tricker, R. A. R.

Visser, S. W.

S. W. Visser, Optische verschijnselen aan de hemel (Koninklijk Nederlands Meteorologisch Institut s’Gravenhage, The Netherlands, 1957).

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

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

Meteorol. Z. (1)

C. F. Bottlinger, “Über eine interessante optische Erscheinung bei einer Ballonfahrt,” Meteorol. Z. 27, 74–75 (1910).

Science (1)

C. M. Broomall, “Lunar halo,” Science 13, 327 (1901).
[CrossRef]

Tähdet ja Avaruus (2)

M. Sillanpää, M. Pekkola, “Ellipsihalojen selitys näköpiirissä,” Tähdet ja Avaruus 27, 40–41 (1997).

M. Pekkola, “Arvoituksellinen Hissinkin halo,” Tähdet ja Avaruus 18, 60–63 (1988).

Weather (1)

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

Other (4)

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
[CrossRef]

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

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995).

S. W. Visser, Optische verschijnselen aan de hemel (Koninklijk Nederlands Meteorologisch Institut s’Gravenhage, The Netherlands, 1957).

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Figures (7)

Fig. 1
Fig. 1

Peak of the display of two elliptical halos in Kokkola, Finland, on 13 February 1997 at a solar elevation of 8.9°. Martti Penttinen took the photograph with a 50-mm lens. Horizontal and upper vertical radii of the ellipses are 2.3° × 9° and 5.7° × 13.5°. There is a slight violation of the left–right symmetry in the larger ellipse: the left-hand side is slightly more rounded than the right-hand side. This can be explained by inhomogeneities in the cloud composition. Although ring dimensions change as a function of solar elevation, the larger ring is the largest elliptical halo ever documented.

Fig. 2
Fig. 2

Images and surface profiles of the plastic replicas of a few typical obtuse pyramidal crystals. A complete description of crystal types is listed as a footnote in Table 1. (a) Type 1B with an angle of 6.45°. This crystal is clearly eccentric, with curved ridges. (b) Type 1C with angles for the pyramid and cavity of 3.83° and 2.95°. The crystal has gaps on two sides and is slightly eccentric. (c) Type 1E with angles of 1.26° and 3.40°. The center of the cavity is irregular. (d) Type 1A with visible rime growth has an angle of 5.93°. Crystals (a) to (c) are from the Kokkola display and (d) is from the Juva display. In (a) the profile is scanned along the narrower symmetry axis; for other crystals the profile was scanned along the horizontal line of the image. Boundaries of the crystals are marked in the profile data by dashed vertical lines.

Fig. 3
Fig. 3

Attempt to simulate the Kokkola display of 13 February 1997 with multiple scattering from three crystal populations. Note the obvious discrepancy between this and the photograph in Fig. 1. In this simulation we used three plate crystal populations. The first population was perfectly horizontal, the second population gyrated at a mean inclination angle of 7° with a 0.05° tilting angle, and the third gyrated with 5° inclination angles having a 0.05° tilting angle. Relative weights of the populations were 3, 1, and 0.5, respectively. The population with the largest inclination angle contributes to the largest ellipse and the second gyrating population creates the smaller ring. The tickmarks are at 1° intervals.

Fig. 4
Fig. 4

Schematic of the obtuse pyramidal ice crystal and the numbering of crystal faces (according to Tape): upper and lower basal faces are 1 and 2, lateral faces are 3 through 8, upper pyramidal faces are 13 through 18 (3 and 13 touch each other), and lower pyramidal faces 23 through 28, with 23 and 3 touching each other. For clarity, only a few numbers and one ray path (1–23) are presented. The ellipses originated by paths 1–23 and 13–23 are the brightest and largest and lie relatively close to each other. The three fainter and smaller ones appear as 13–24, 13–2 and 13–25, with approximately the same dimensions. In the simulation of the Kokkola display, the outermost ring is a combination of 1–23 from the 7.6° population and 13–23 from the 3.6° population, which happen to be very close (approximately 1°) to each other. The inner ring is caused by 1–23 from the 3.6° population. Note that the dimensions of the rings strongly depend on the solar elevation.

Fig. 5
Fig. 5

Simulation of the Kokkola display with two populations of obtuse pyramidal crystals having base angles of 3.6° and 7.6°. This simulation seems to be in excellent agreement with the photograph in Fig. 1. We used two pyramid populations with no middle prism part. The first population was a single pyramid that fell apex downward, having a 0.7 truncation, but the second population also had the upper pyramidal part (hence it was a double pyramid) with 0.4 and 0.7 upper and lower truncations. The interfacial base angles were 7.6° and 3.6°, tilting angles of 2.5° and 6.0°, and relative population weights of 2.5 and 1, respectively. The tickmarks are at 1° intervals.

Fig. 6
Fig. 6

Simulation of the 12 April 1993 display with three pyramid populations with base angles of 3.3°, 4.2°, and 5.0°; upper and lower truncations of 0.95 and 0.95, 0 and 0.95, 0.9 and 0.9; tilting angles of 5°, 6°, and 8°; and relative population weights of 5, 1, and 2. The simulation seems to be in excellent agreement with the photographs.12

Fig. 7
Fig. 7

Simulation illustrating the Bottlinger’s rings (subhorizontal elliptical halos centered around the subsun) generated by the 3.6° base angle population of Fig. 4 for a solar elevation of 12°. The horizon is represented by the horizontal line. The tickmarks are at 1° intervals.

Tables (1)

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Table 1 Crystal Classifications and Measured Values of Pyramidal Anglesa

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