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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 69, Iss. 8 — Aug. 1, 1979
  • pp: 1119–1122

Frequency analysis of the circumzenithal arc: Evidence for the oscillation of ice-crystal plates in the upper atmosphere

Robin S. McDowell  »View Author Affiliations


JOSA, Vol. 69, Issue 8, pp. 1119-1122 (1979)
http://dx.doi.org/10.1364/JOSA.69.001119


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Abstract

The results of a quantitative treatment of the visibility of the circumzenithal arc as a function of solar elevation are compared with records of the arc’s occurrence in France and the Netherlands, 1894–1931. Both calculated and observed frequency distributions peak at a solar elevation of 22° (minimum deviation), and the width of the observed frequency distribution can be closely matched with the assumption that plate ice crystals in quiet air undergo oscillations of around 1° from equilibrium. This result agrees with other estimates based on studies of the subsun and parhelic circle. The circumzenithal arc is shown to be vertically polarized, with <i>I</i><sub>vert</sub≯<i>I</i><sub>hor</sub>≍ 1.4 in the solar vertical near minimum deviation.

© 1979 Optical Society of America

Citation
Robin S. McDowell, "Frequency analysis of the circumzenithal arc: Evidence for the oscillation of ice-crystal plates in the upper atmosphere," J. Opt. Soc. Am. 69, 1119-1122 (1979)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-69-8-1119


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References

  1. R. S. McDowell, "The Formation of Parhelia at Higher Solar Elevations," J. Atmos. Sci. 31, 1876–1884 (1974).
  2. J. M. Pernter and F. M. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna and Leipzig, 1922), pp. 276f, 410–416.
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  9. Reference 5, pp. 110–112.
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  16. L. Besson, Thesis (Ref. 8), pp. 25–28. The solid triangles in Fig. 2 represent the number of half minutes that the arc was seen, corrected for cloud cover, divided by the number of half minutes that the sun was visible, from his Table A, p. 26; normalized to a maximum of 100.
  17. E. van Everdingen, "Dagelijksche en Jaarlijksche Gang in het Voorkomen van Circumzenithaalbogen," Hemel en Dampkring 14, 113–121 (1916); Onweders Opt. Versch. Neder. 35, 84–98 (1916). The solid circles in Fig. 2 represent his relative frequencies (pp. 117f in the Hemel en Dampkring paper, pp. 92f. in Onweders; also quoted by Wegener, Refs. 2 and 3) divided by the solar frequencies given in Ref. 1 (using 148 hr for h = 30–32.2°), and normalized to a maximum of 100.
  18. C. Visser, "De Frequentie van Halowaarnemingen bij de Zon in Nederland, Voornamelijk van 1914–1931," K. Neder. Meteorol. Inst. Mededeel. Verhandel., No. 37 (1936). The open circles in Fig. 2 are his uncorrected "graadwaarnemingen", p. 60 (equivalent to the "gradzahlen", p. 93), divided by solar frequencies of 362, 369, 399, 489, 399, 340, 300, and 278 hr for h = 0°-4°, 4°-8°, …, 28°-32°, respectively, and normalized to a maximum of 100.
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  22. Reference 15, p. 42.
  23. R. Meyer, "Haloerscheinungen: Theoretische Beiträge zur Meteorologischen Optik," Abhandl. Herder-Inst. Riga 1, No. 5, 1–79 (1925), (especially pp. 43–49).

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