Abstract

From an aircraft, a short distinct vertical structure is sometimes seen above the setting sun. Such a feature can be understood as a halo, which is the counterpart of the well-known subsun. Whereas the latter arises from reflections off basal faces of plate-oriented ice crystals illuminated from above, what we call the supersun emerges when these crystals are illuminated from below. The supersun occurs when the sun is below the true horizon and is only visible from elevated positions. The curvature of the Earth causes the ensemble of reflecting crystal faces to act as a hollow mirror and the supersun appears as a vertical band of uniform width, extending from the sun upwards to its supersolar point. We discuss the geometrical properties of the phenomenon and simulate its shape and radiance distribution with an extended version of an atmospheric ray-tracing program.

© 2011 Optical Society of America

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References

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  1. L. Cowley and M. Schroeder, HaloSim3 Software, http://www.atoptics.co.uk/halo/halfeat.htm.
  2. W. Tape and G. P. Können, “A general setting for halo theory,” Appl. Opt. 38, 1552–1625 (1999).
    [CrossRef]
  3. G. P. Können, “Symmetry in halo displays and symmetry in halo-making crystals,” Appl. Opt. 42, 318–331(2003).
    [CrossRef] [PubMed]
  4. In German the subsun is known as the “Untersonne,” and “Übersonne” would be the appropriate translation for supersun. In French, the “sub-soleil” or “soleil inferieur” would find their logical counterparts in “super-soleil” and “soleil superieur.” In Dutch the subsun is called “onderzon” and the supersun will be the “bovenzon.”
  5. S. Y. van der Werf, “Ray tracing and refraction in the modified US1976 atmosphere,” Appl. Opt. 42, 354–366 (2003).
    [CrossRef] [PubMed]
  6. S. Y. van der Werf, G. P. Können, and W. H. Lehn, “Novaya Zemlya effect and sunsets,” Appl. Opt. 42, 367–378 (2003).
    [CrossRef] [PubMed]
  7. S. Y. van der Werf, “Comment on ‘Improved ray tracing air mass numbers model,’” Appl. Opt. 47, 153–156 (2008).
    [CrossRef] [PubMed]
  8. D. R. Lide, Handbook of Chemistry and Physics, 81st ed. (CRC, 2000).
  9. W. Tape, Atmospheric Halos, Antarctic Research Series(American Geophysical Union, 1994), Vol.  64.
    [CrossRef]
  10. Astronomical observatories often document values of k per amount of air mass relative to their own unit air mass above the site of the observatory, Xobs, instead of the unit air mass at sea level, X0. This must be kept in mind when comparing extinction parameters for different observatories.
  11. A. Meinel and M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, 1983).
  12. H. Tüg, “Measurements of the energy distributions of southern standard stars from 3200 Å to 8800 Å,” Astron. Astrophys. 82, 195–202 (1980).
  13. M. Golay, Introduction to Astronomical Photometry (Reidel, 1974).
    [CrossRef]
  14. V. B. Nikonov, “Methods of Investigating Variable Stars,” (NASA Technical Translation TT-F-797, Washington, 1973).
  15. P. Wang, W. H. Knap, P. Kuipers Munneke, and P. Stammes, “Clear-sky shortwave radiative closure for the Cabauw Baseline Surface Radiation Network site, the Netherlands,” J. Geophys. Res. 114, D14206 (2009).
    [CrossRef]
  16. G. T. Fechner, Elemente der Psychophysik (Breidkopf und Härtel, 1860), Vol.  II, Chap. 16, English translation from the 1912 edition, http://psychclassics.yorku.ca/Fechner/.
  17. K. Hariti, “Parhelic circle over the Dead Sea,” Atmospheric Optics (2007), http://www.atoptics.co.uk/halo/parcirc.htm.
  18. C. Hinz, “Upper parhelia over the Alps,” Ice Crystal Holos (2010), http://www.ursa.fi/blogit/ice_crystal_halos/index.php?title=upper_parhelia_over_the_alps.

2009

P. Wang, W. H. Knap, P. Kuipers Munneke, and P. Stammes, “Clear-sky shortwave radiative closure for the Cabauw Baseline Surface Radiation Network site, the Netherlands,” J. Geophys. Res. 114, D14206 (2009).
[CrossRef]

2008

2003

1999

1980

H. Tüg, “Measurements of the energy distributions of southern standard stars from 3200 Å to 8800 Å,” Astron. Astrophys. 82, 195–202 (1980).

Cowley, L.

L. Cowley and M. Schroeder, HaloSim3 Software, http://www.atoptics.co.uk/halo/halfeat.htm.

Fechner, G. T.

G. T. Fechner, Elemente der Psychophysik (Breidkopf und Härtel, 1860), Vol.  II, Chap. 16, English translation from the 1912 edition, http://psychclassics.yorku.ca/Fechner/.

Golay, M.

M. Golay, Introduction to Astronomical Photometry (Reidel, 1974).
[CrossRef]

Hariti, K.

K. Hariti, “Parhelic circle over the Dead Sea,” Atmospheric Optics (2007), http://www.atoptics.co.uk/halo/parcirc.htm.

Hinz, C.

C. Hinz, “Upper parhelia over the Alps,” Ice Crystal Holos (2010), http://www.ursa.fi/blogit/ice_crystal_halos/index.php?title=upper_parhelia_over_the_alps.

Knap, W. H.

P. Wang, W. H. Knap, P. Kuipers Munneke, and P. Stammes, “Clear-sky shortwave radiative closure for the Cabauw Baseline Surface Radiation Network site, the Netherlands,” J. Geophys. Res. 114, D14206 (2009).
[CrossRef]

Können, G. P.

Kuipers Munneke, P.

P. Wang, W. H. Knap, P. Kuipers Munneke, and P. Stammes, “Clear-sky shortwave radiative closure for the Cabauw Baseline Surface Radiation Network site, the Netherlands,” J. Geophys. Res. 114, D14206 (2009).
[CrossRef]

Lehn, W. H.

Lide, D. R.

D. R. Lide, Handbook of Chemistry and Physics, 81st ed. (CRC, 2000).

Meinel, A.

A. Meinel and M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, 1983).

Meinel, M.

A. Meinel and M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, 1983).

Nikonov, V. B.

V. B. Nikonov, “Methods of Investigating Variable Stars,” (NASA Technical Translation TT-F-797, Washington, 1973).

Schroeder, M.

L. Cowley and M. Schroeder, HaloSim3 Software, http://www.atoptics.co.uk/halo/halfeat.htm.

Stammes, P.

P. Wang, W. H. Knap, P. Kuipers Munneke, and P. Stammes, “Clear-sky shortwave radiative closure for the Cabauw Baseline Surface Radiation Network site, the Netherlands,” J. Geophys. Res. 114, D14206 (2009).
[CrossRef]

Tape, W.

W. Tape and G. P. Können, “A general setting for halo theory,” Appl. Opt. 38, 1552–1625 (1999).
[CrossRef]

W. Tape, Atmospheric Halos, Antarctic Research Series(American Geophysical Union, 1994), Vol.  64.
[CrossRef]

Tüg, H.

H. Tüg, “Measurements of the energy distributions of southern standard stars from 3200 Å to 8800 Å,” Astron. Astrophys. 82, 195–202 (1980).

van der Werf, S. Y.

Wang, P.

P. Wang, W. H. Knap, P. Kuipers Munneke, and P. Stammes, “Clear-sky shortwave radiative closure for the Cabauw Baseline Surface Radiation Network site, the Netherlands,” J. Geophys. Res. 114, D14206 (2009).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

H. Tüg, “Measurements of the energy distributions of southern standard stars from 3200 Å to 8800 Å,” Astron. Astrophys. 82, 195–202 (1980).

J. Geophys. Res.

P. Wang, W. H. Knap, P. Kuipers Munneke, and P. Stammes, “Clear-sky shortwave radiative closure for the Cabauw Baseline Surface Radiation Network site, the Netherlands,” J. Geophys. Res. 114, D14206 (2009).
[CrossRef]

Other

G. T. Fechner, Elemente der Psychophysik (Breidkopf und Härtel, 1860), Vol.  II, Chap. 16, English translation from the 1912 edition, http://psychclassics.yorku.ca/Fechner/.

K. Hariti, “Parhelic circle over the Dead Sea,” Atmospheric Optics (2007), http://www.atoptics.co.uk/halo/parcirc.htm.

C. Hinz, “Upper parhelia over the Alps,” Ice Crystal Holos (2010), http://www.ursa.fi/blogit/ice_crystal_halos/index.php?title=upper_parhelia_over_the_alps.

L. Cowley and M. Schroeder, HaloSim3 Software, http://www.atoptics.co.uk/halo/halfeat.htm.

M. Golay, Introduction to Astronomical Photometry (Reidel, 1974).
[CrossRef]

V. B. Nikonov, “Methods of Investigating Variable Stars,” (NASA Technical Translation TT-F-797, Washington, 1973).

In German the subsun is known as the “Untersonne,” and “Übersonne” would be the appropriate translation for supersun. In French, the “sub-soleil” or “soleil inferieur” would find their logical counterparts in “super-soleil” and “soleil superieur.” In Dutch the subsun is called “onderzon” and the supersun will be the “bovenzon.”

D. R. Lide, Handbook of Chemistry and Physics, 81st ed. (CRC, 2000).

W. Tape, Atmospheric Halos, Antarctic Research Series(American Geophysical Union, 1994), Vol.  64.
[CrossRef]

Astronomical observatories often document values of k per amount of air mass relative to their own unit air mass above the site of the observatory, Xobs, instead of the unit air mass at sea level, X0. This must be kept in mind when comparing extinction parameters for different observatories.

A. Meinel and M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, 1983).

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Figures (9)

Fig. 1
Fig. 1

Vertically elongated structure above the sun. It extends upwards to 2 ° .6 above the sun and has a width of 0 ° .5 . The sun is setting behind the apparent horizon, which is 3 ° .3 below the true horizon. The horizontal field of view of the picture is 13 ° . Photograph taken on 10 September 2008 at 17:46 UTC by G.P. Können on a flight from Oslo to Kirkenes (Norway) from a height of 12 km .

Fig. 2
Fig. 2

Parhelion, photographed during the passage through the frontal clouds. The appearance of this halo proves that horizontally oriented crystal faces were present in the frontal clouds in which the vertical feature of Fig. 1 appeared 14 min later. The horizontal field of view of the picture is 21 ° . Photograph taken on 10 September 2008 at 17:32 UTC by G.P. Können.

Fig. 3
Fig. 3

Geometry of supersun formation by reflection of crystals at a negative sun altitude.

Fig. 4
Fig. 4

Locus of the positions of reflecting horizontal faces creating the subsun/supersun. The figure is for a sun below the true horizon, but above the apparent horizon. Blue (solid) rays reflect from bottom faces, red (dashed) rays from top faces. In the former case, the distance of the locus above the Earth shows a local maximum. To the right, the surface of the Earth puts a lower bound on the subsun.

Fig. 5
Fig. 5

Ray tracing for subsun/supersun simulation. The rays are traced backward from the observer until they reach the upper mesosphere. Because the Earth’s surface is drawn as a straight line, all light rays bend upward. A kink indicates the place where a ray is reflected by a horizontally oriented crystal face.

Fig. 6
Fig. 6

Scatter plot and limits on the subsun and supersun for a single reflection off horizontally oriented faces of ice crystals, assumed present between 1.5 and 14 km above the Earth’s surface. Atmospheric refraction is neglected; the sun is taken as a point source. Points above the diagonal contribute to the supersun, those below it to the subsun. The dashed vertical line indicates a sun altitude of 3 ° .2 . The aircraft is at 12 km above the Earth, and, in the absence of refraction, horizon dip = 3 ° .5 .

Fig. 7
Fig. 7

Relative air mass X / X 0 for the calculated single-reflection ensemble of ray tracings, which contribute to the formation of the subsun or the supersun. Halo points of the subsun or supersun have been calculated between altitude 15 ° and + 15 ° , but the mirror horizon imposes a cutoff at 3 ° 19 .

Fig. 8
Fig. 8

Radiance distribution of the supersun as a function of altitude, as seen from a flight level of 12 km , with the sun just above the 3 ° .3 dipped apparent horizon. The dashed line neglects atmospheric extinction, while for the 15 × scaled-up solid line it is included.

Fig. 9
Fig. 9

Transition of the subsun into the supersun, as seen from a flight level of 12 km , in the presence of ice crystals between 1.5 and 14 km above the Earth. The brightness of the subsun/supersun in the drawing is represented on a logarithmic scale, spanning a difference of 10 stellar magnitudes between white and black. An extinction coefficient k = 0.15 has been adopted.

Tables (1)

Tables Icon

Table 1 Special Points on the Reflection Locus for Sun Depression α = 3 ° .2 a

Equations (11)

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β = α γ
δ = α 2 β = α + 2 γ
R xtl = R aircraft cos ( δ ) cos ( β ) = R aircraft cos ( α 2 γ ) cos ( α γ ) .
h xtl ( γ ) = h 0 2 R aircraft cos ( 1 2 γ ) sin [ 1 2 ( 2 α 3 γ ) ] cos ( α γ ) .
R min = R aircraft cos ( δ ) ,
γ ( 2 α 3 γ ) = ( δ + α 2 ) ( α 3 δ 2 ) 2 ( h xtl h 0 ) R Earth ,
α = δ ± δ 2 + 2 ( h xtl h 0 ) / R Earth .
rnd ( 1 ) | sin ( β ) | < ds / λ 0 reflection, rnd ( 1 ) | sin ( β ) | ds / λ 0 no reflection ,
ln ( I ) ln ( I 0 ) = b X / X 0 ,
m m 0 2.5 [ log 10 ( I 0 ) log 10 ( I ) ] = k X / X 0 ,
k 2.5 log 10 ( e ) b = 1.08574 b

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