Abstract

With the aid of computer-simulated halo patterns, we show that Kern’s arc, as seen on the latitude of the circumzenithal arc and on the other side of the zenith, is produced by double-plate ice crystals with a vertical principal axis. Light rays that contribute to Kern’s arc are demonstrated by geometric ray tracing. We also discuss the condition under which an arc that is opposite a circumhorizontal arc can appear.

© 1997 Optical Society of America

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References

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  1. C. S. Ling, “Complex solar halo observed at Ellendale, N. Dak.,” Mon. Weather Rev. 50, 132–133 (1922).
    [CrossRef]
  2. E. A. Ripley, B. Saugier, “Photometeors at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).
    [CrossRef]
  3. , “Halos of March 1–4 1906,” Mon. Weather Rev. 34, 123–124 (1906).
    [CrossRef]
  4. L. Besson, “The halos of November 1 and 2, 1913,” Mon. Weather Rev. 42, 431–446 (1914).
    [CrossRef]
  5. R. A. R. Tricker, Ice Crystal Haloes (Optical Society of America, Washington, D.C., 1979), Chaps. 1 and 7.
  6. E. Tränkle, R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
    [CrossRef]
  7. Y. Takano, K. N. Liou, “Halo phenomena modified by multiple scattering,” J. Opt. Soc. Am. A 7, 885–889 (1990).
    [CrossRef]
  8. R. G. Greenler, Rainbow, Halos, and Glories (Cambridge U. Press, New York, 1980), Chap. 3, p. 96.
  9. W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994), Chap. 11, pp. 101–104.
  10. D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995), Chap. 5, p. 166.
  11. Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
    [CrossRef]
  12. R. T. Bruintjes, A. J. Heymsfield, T. W. Krauss, “An examination of double-plate ice crystal and the initiation of precipitation in continental cumulus clouds,” J. Atmos. Sci. 44, 1331–1349 (1987).
    [CrossRef]
  13. A. J. Heymsfield, “Laboratory and field observations of the growth of columnar and plate crystals from frozen droplets,” J. Atmos. Sci. 30, 1650–1656 (1973).
    [CrossRef]
  14. W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1940), Chap. 4, pp. 513–514.
  15. 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]
  16. K. Iwai, “Three-dimensional structure of plate-like snow crystals,” J. Meteorol. Soc. Jpn. 61, 746–755 (1983).
  17. N. Fukuta, M. W. Kowa, N. H. Gong, “Determination of ice crystal growth parameters in a new supercooled cloud tunnel,” in Proceedings of the Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1982), pp. 325–328.

1995 (1)

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

1990 (1)

1989 (1)

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]

1987 (2)

R. T. Bruintjes, A. J. Heymsfield, T. W. Krauss, “An examination of double-plate ice crystal and the initiation of precipitation in continental cumulus clouds,” J. Atmos. Sci. 44, 1331–1349 (1987).
[CrossRef]

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

1983 (1)

K. Iwai, “Three-dimensional structure of plate-like snow crystals,” J. Meteorol. Soc. Jpn. 61, 746–755 (1983).

1973 (1)

A. J. Heymsfield, “Laboratory and field observations of the growth of columnar and plate crystals from frozen droplets,” J. Atmos. Sci. 30, 1650–1656 (1973).
[CrossRef]

1971 (1)

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

1922 (1)

C. S. Ling, “Complex solar halo observed at Ellendale, N. Dak.,” Mon. Weather Rev. 50, 132–133 (1922).
[CrossRef]

1914 (1)

L. Besson, “The halos of November 1 and 2, 1913,” Mon. Weather Rev. 42, 431–446 (1914).
[CrossRef]

1906 (1)

, “Halos of March 1–4 1906,” Mon. Weather Rev. 34, 123–124 (1906).
[CrossRef]

Besson, L.

L. Besson, “The halos of November 1 and 2, 1913,” Mon. Weather Rev. 42, 431–446 (1914).
[CrossRef]

Bruintjes, R. T.

R. T. Bruintjes, A. J. Heymsfield, T. W. Krauss, “An examination of double-plate ice crystal and the initiation of precipitation in continental cumulus clouds,” J. Atmos. Sci. 44, 1331–1349 (1987).
[CrossRef]

Fukuta, N.

N. Fukuta, M. W. Kowa, N. H. Gong, “Determination of ice crystal growth parameters in a new supercooled cloud tunnel,” in Proceedings of the Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1982), pp. 325–328.

Gong, N. H.

N. Fukuta, M. W. Kowa, N. H. Gong, “Determination of ice crystal growth parameters in a new supercooled cloud tunnel,” in Proceedings of the Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1982), pp. 325–328.

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, Rainbow, Halos, and Glories (Cambridge U. Press, New York, 1980), Chap. 3, p. 96.

Heymsfield, A. J.

R. T. Bruintjes, A. J. Heymsfield, T. W. Krauss, “An examination of double-plate ice crystal and the initiation of precipitation in continental cumulus clouds,” J. Atmos. Sci. 44, 1331–1349 (1987).
[CrossRef]

A. J. Heymsfield, “Laboratory and field observations of the growth of columnar and plate crystals from frozen droplets,” J. Atmos. Sci. 30, 1650–1656 (1973).
[CrossRef]

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1940), Chap. 4, pp. 513–514.

Iwai, K.

K. Iwai, “Three-dimensional structure of plate-like snow crystals,” J. Meteorol. Soc. Jpn. 61, 746–755 (1983).

Kowa, M. W.

N. Fukuta, M. W. Kowa, N. H. Gong, “Determination of ice crystal growth parameters in a new supercooled cloud tunnel,” in Proceedings of the Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1982), pp. 325–328.

Krauss, T. W.

R. T. Bruintjes, A. J. Heymsfield, T. W. Krauss, “An examination of double-plate ice crystal and the initiation of precipitation in continental cumulus clouds,” J. Atmos. Sci. 44, 1331–1349 (1987).
[CrossRef]

Ling, C. S.

C. S. Ling, “Complex solar halo observed at Ellendale, N. Dak.,” Mon. Weather Rev. 50, 132–133 (1922).
[CrossRef]

Liou, K. N.

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

Y. Takano, K. N. Liou, “Halo phenomena modified by multiple scattering,” J. Opt. Soc. Am. A 7, 885–889 (1990).
[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]

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995), Chap. 5, p. 166.

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995), Chap. 5, p. 166.

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

Y. Takano, K. N. Liou, “Halo phenomena modified by multiple scattering,” J. Opt. Soc. Am. A 7, 885–889 (1990).
[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]

Tape, W.

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994), Chap. 11, pp. 101–104.

Tränkle, E.

Tricker, R. A. R.

R. A. R. Tricker, Ice Crystal Haloes (Optical Society of America, Washington, D.C., 1979), Chaps. 1 and 7.

J. Atmos. Sci. (4)

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

R. T. Bruintjes, A. J. Heymsfield, T. W. Krauss, “An examination of double-plate ice crystal and the initiation of precipitation in continental cumulus clouds,” J. Atmos. Sci. 44, 1331–1349 (1987).
[CrossRef]

A. J. Heymsfield, “Laboratory and field observations of the growth of columnar and plate crystals from frozen droplets,” J. Atmos. Sci. 30, 1650–1656 (1973).
[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]

J. Meteorol. Soc. Jpn. (1)

K. Iwai, “Three-dimensional structure of plate-like snow crystals,” J. Meteorol. Soc. Jpn. 61, 746–755 (1983).

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

Mon. Weather Rev. (3)

C. S. Ling, “Complex solar halo observed at Ellendale, N. Dak.,” Mon. Weather Rev. 50, 132–133 (1922).
[CrossRef]

, “Halos of March 1–4 1906,” Mon. Weather Rev. 34, 123–124 (1906).
[CrossRef]

L. Besson, “The halos of November 1 and 2, 1913,” Mon. Weather Rev. 42, 431–446 (1914).
[CrossRef]

Weather (1)

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

Other (6)

R. A. R. Tricker, Ice Crystal Haloes (Optical Society of America, Washington, D.C., 1979), Chaps. 1 and 7.

N. Fukuta, M. W. Kowa, N. H. Gong, “Determination of ice crystal growth parameters in a new supercooled cloud tunnel,” in Proceedings of the Conference on Cloud Physics (American Meteorological Society, Dallas, Tex., 1982), pp. 325–328.

R. G. Greenler, Rainbow, Halos, and Glories (Cambridge U. Press, New York, 1980), Chap. 3, p. 96.

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994), Chap. 11, pp. 101–104.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, New York, 1995), Chap. 5, p. 166.

W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1940), Chap. 4, pp. 513–514.

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Figures (6)

Fig. 1
Fig. 1

Crystal geometry for a double plate.

Fig. 2
Fig. 2

Intensity distribution for the horizontally oriented (a) double plates and (b) single plates at 0.55-µm wavelength. The solar zenith angle θ0 is 72°. The ★, +, and · are, respectively, 2, 1, and 0 in units of the integral part of a common logarithm of the phase function.

Fig. 3
Fig. 3

(a) Geometric ray path that contributes to Kern’s arc. T denotes the total reflection. (b) The ray path suggested by Humphreys that contributes to Kern’s arc.

Fig. 4
Fig. 4

Scattered intensity for the horizontally oriented double plates of the crystal geometry shown in Fig. 3(a) along the circumzenithal latitude for θ0 = 72° and 82° at 0.55-µm wavelength.

Fig. 5
Fig. 5

Intensity distribution for the horizontally oriented (a) double plates and (b) single plates at 0.55-µm wavelength. The solar zenith angle θ0 is 27°. The symbols + and · are the same as those in Fig. 2.

Fig. 6
Fig. 6

Ray path that contributes to the anticircumhorizontal arc defined in this paper.

Tables (1)

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Table 1 Crystal Geometry in Arbitrary Units

Equations (1)

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θ*=π/2-sin-1mr2-sin2 θ01/2,

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