Abstract

A multiple-scattering Monte Carlo model that can produce near-photographic quality images is developed and used to simulate several dramatic halo displays. The model atmosphere contains an absorbing ozone layer plus two clear, molecular air layers with Rayleigh scattering surrounding a cloud layer and an atmospheric boundary layer with aerosol particles subject to Lorentz–Mie scattering. Halos are produced by right hexagonal or pyramidal crystals that reflect and refract according to geometric optics without diffraction, although “junk” crystals with a pronounced forward-scattering peak but no halo peaks may be included to simulate typical, faint halos. Model parameters include ozone height and content, surface and cloud pressure, cloud optical thickness, crystal shapes, orientations and abundances, atmospheric turbidity, aerosol radius, and albedo. Beams for each wavelength are sorted into small bins as halo beams if they have been scattered once only by a single crystal and otherwise as sky beams, which are smoothed and combined with the halo beams to produce images. Multiple scattering generally vitiates halos, but extremely rare halos, such as Kern’s arc, can be produced if a significant fraction of crystals in optically thick clouds have identical shapes and are highly oriented. Albedo is a model by-product with potential value in climate studies.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (1)

T. Akenine-Möller and H. W. Jensen, “The race for real-time photorealism,” Am. Sci. 98, 132–139 (2010).

2008 (2)

S. D. Gedzelman and M. Vollmer, “Atmospheric optical phenomena and radiative transfer,” Bull. Am. Meteorol. Soc. 89, 471–485 (2008).
[CrossRef]

S. D. Gedzelman, “Simulating halos and coronas in their atmospheric environment,” Appl. Opt. 47, H176–H181 (2008).
[CrossRef]

2007 (1)

C. G. Schmitt and A. J. Heymsfield, “On the occurrence of hollow bullet rosette- and column-shaped ice crystals in midlatitude cirrus,” J. Atmos. Sci. 64, 4514–4519 (2007).
[CrossRef]

2006 (1)

C. G. Schmitt, J. Iaquinta, and A. J. Heymsfield, “The asymmetry parameter of cirrus clouds composed of hollow bullet rosette-shaped ice crystals from ray-tracing calculations,” J. Appl. Meteor. Climatol. 45, 973–981 (2006).
[CrossRef]

2005 (1)

A. J. Baran, V. N. Shcherbakof, B. A. Baker, J. F. Gayet, and R. P. Lawson, “On the scattering phase-function of non-symmetric ice-crystals,” Q. J. R. Meteorol. Soc. 131, 2609–2616 (2005).
[CrossRef]

2003 (1)

1998 (1)

1997 (1)

1995 (1)

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

1994 (1)

1993 (1)

1990 (1)

1987 (1)

1984 (1)

1980 (1)

1974 (1)

A. A. Lacis and J. E. Hansen, “A parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

1971 (1)

E. A. Ripley and B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).

Akenine-Möller, T.

T. Akenine-Möller and H. W. Jensen, “The race for real-time photorealism,” Am. Sci. 98, 132–139 (2010).

Baker, B. A.

A. J. Baran, V. N. Shcherbakof, B. A. Baker, J. F. Gayet, and R. P. Lawson, “On the scattering phase-function of non-symmetric ice-crystals,” Q. J. R. Meteorol. Soc. 131, 2609–2616 (2005).
[CrossRef]

Baran, A. J.

A. J. Baran, V. N. Shcherbakof, B. A. Baker, J. F. Gayet, and R. P. Lawson, “On the scattering phase-function of non-symmetric ice-crystals,” Q. J. R. Meteorol. Soc. 131, 2609–2616 (2005).
[CrossRef]

Cowley, L.

L. Cowley, “Atmospheric optics,” http://www.atoptics.co.uk.

Gayet, J. F.

A. J. Baran, V. N. Shcherbakof, B. A. Baker, J. F. Gayet, and R. P. Lawson, “On the scattering phase-function of non-symmetric ice-crystals,” Q. J. R. Meteorol. Soc. 131, 2609–2616 (2005).
[CrossRef]

Gedzelman, S. D.

Greenler, R.

Hansen, J. E.

A. A. Lacis and J. E. Hansen, “A parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

Heymsfield, A. J.

C. G. Schmitt and A. J. Heymsfield, “On the occurrence of hollow bullet rosette- and column-shaped ice crystals in midlatitude cirrus,” J. Atmos. Sci. 64, 4514–4519 (2007).
[CrossRef]

C. G. Schmitt, J. Iaquinta, and A. J. Heymsfield, “The asymmetry parameter of cirrus clouds composed of hollow bullet rosette-shaped ice crystals from ray-tracing calculations,” J. Appl. Meteor. Climatol. 45, 973–981 (2006).
[CrossRef]

Iaquinta, J.

C. G. Schmitt, J. Iaquinta, and A. J. Heymsfield, “The asymmetry parameter of cirrus clouds composed of hollow bullet rosette-shaped ice crystals from ray-tracing calculations,” J. Appl. Meteor. Climatol. 45, 973–981 (2006).
[CrossRef]

Jensen, H. W.

T. Akenine-Möller and H. W. Jensen, “The race for real-time photorealism,” Am. Sci. 98, 132–139 (2010).

H. W. Jensen, Realistic Image Synthesis Using Photon Mapping (AK Peters, 2001).

Lacis, A. A.

A. A. Lacis and J. E. Hansen, “A parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

Lawson, R. P.

A. J. Baran, V. N. Shcherbakof, B. A. Baker, J. F. Gayet, and R. P. Lawson, “On the scattering phase-function of non-symmetric ice-crystals,” Q. J. R. Meteorol. Soc. 131, 2609–2616 (2005).
[CrossRef]

Lefaudeux, N.

N. Lefaudeux, “Hollow columns halo simulation,” http://www.ursa.fi/blogit/ice_crystal_halos/index.php (2011).

Liou, K. N.

Lock, J.

Macke, A.

Meyer, R.

R. Meyer, Die Haloerscheinungen. Probleme der Kosmischen Physik XII (Henri Grand, 1929), pp. 64–69.

Mikkilä, M.

M. Mikkilä, “Kern arc photographed in Finland,” http://www.ursa.fi/blogit/ice_crystal_halos/index.php?m=20080127(2008).

Moilanen, J.

Pattloch, F.

Pekkola, M.

Riikonen, M.

Ripley, E. A.

E. A. Ripley and B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).

Ruoskanen, J.

Saugier, B.

E. A. Ripley and B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).

Schmitt, C. G.

C. G. Schmitt and A. J. Heymsfield, “On the occurrence of hollow bullet rosette- and column-shaped ice crystals in midlatitude cirrus,” J. Atmos. Sci. 64, 4514–4519 (2007).
[CrossRef]

C. G. Schmitt, J. Iaquinta, and A. J. Heymsfield, “The asymmetry parameter of cirrus clouds composed of hollow bullet rosette-shaped ice crystals from ray-tracing calculations,” J. Appl. Meteor. Climatol. 45, 973–981 (2006).
[CrossRef]

Shcherbakof, V. N.

A. J. Baran, V. N. Shcherbakof, B. A. Baker, J. F. Gayet, and R. P. Lawson, “On the scattering phase-function of non-symmetric ice-crystals,” Q. J. R. Meteorol. Soc. 131, 2609–2616 (2005).
[CrossRef]

Takano, Y.

Tape, W.

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

W. Tape and J. Moilanen, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).
[CrossRef]

Tränkle, E.

Vollmer, M.

S. D. Gedzelman and M. Vollmer, “Atmospheric optical phenomena and radiative transfer,” Bull. Am. Meteorol. Soc. 89, 471–485 (2008).
[CrossRef]

Am. Sci. (1)

T. Akenine-Möller and H. W. Jensen, “The race for real-time photorealism,” Am. Sci. 98, 132–139 (2010).

Appl. Opt. (7)

Bull. Am. Meteorol. Soc. (1)

S. D. Gedzelman and M. Vollmer, “Atmospheric optical phenomena and radiative transfer,” Bull. Am. Meteorol. Soc. 89, 471–485 (2008).
[CrossRef]

J. Appl. Meteor. Climatol. (1)

C. G. Schmitt, J. Iaquinta, and A. J. Heymsfield, “The asymmetry parameter of cirrus clouds composed of hollow bullet rosette-shaped ice crystals from ray-tracing calculations,” J. Appl. Meteor. Climatol. 45, 973–981 (2006).
[CrossRef]

J. Atmos. Sci. (3)

A. A. Lacis and J. E. Hansen, “A parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974).
[CrossRef]

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

C. G. Schmitt and A. J. Heymsfield, “On the occurrence of hollow bullet rosette- and column-shaped ice crystals in midlatitude cirrus,” J. Atmos. Sci. 64, 4514–4519 (2007).
[CrossRef]

J. Opt. Soc. Am. A (3)

Q. J. R. Meteorol. Soc. (1)

A. J. Baran, V. N. Shcherbakof, B. A. Baker, J. F. Gayet, and R. P. Lawson, “On the scattering phase-function of non-symmetric ice-crystals,” Q. J. R. Meteorol. Soc. 131, 2609–2616 (2005).
[CrossRef]

Weather (1)

E. A. Ripley and B. Saugier, “Photometers at Saskatoon on 3 December 1970,” Weather 26, 150–157 (1971).

Other (10)

A reviewer pointed out that these unusual halo arcs may be identified with arcs photographed in a searchlight display by M. Riikonen, “Circular subanthelic halo from 3-5-6-7-(2)-3 raypath,” http://www.ursa.fi/blogit/ice_crystal_halos/index.php?m=20081216 (2008).

H. W. Jensen, Realistic Image Synthesis Using Photon Mapping (AK Peters, 2001).

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

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

L. Cowley, “Atmospheric optics,” http://www.atoptics.co.uk.

N. Lefaudeux, “Hollow columns halo simulation,” http://www.ursa.fi/blogit/ice_crystal_halos/index.php (2011).

J. Ruoskanen, “Halopoint 2.0—software for simulating halo phenomena,” http://www.jukri.net/halopoint2.html (2010).

W. Tape and J. Moilanen, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).
[CrossRef]

M. Mikkilä, “Kern arc photographed in Finland,” http://www.ursa.fi/blogit/ice_crystal_halos/index.php?m=20080127(2008).

R. Meyer, Die Haloerscheinungen. Probleme der Kosmischen Physik XII (Henri Grand, 1929), pp. 64–69.

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Figures (11)

Fig. 1
Fig. 1

Five-layer halo model.

Fig. 2
Fig. 2

Azimuthally symmetric angular scattering phase function, P ( ψ ) characteristic of junk crystals.

Fig. 3
Fig. 3

Fish-eye images of simulated skies with 22 ° and 46 ° halos with c / a = 1.0 , ϕ SUN = 60 ° , β = 1.5 , r aer = 300 nm , p sfc = 1000 hPa , and p cld = 300 hPa for a,  τ cld = 0.05 and b,  τ cld = 0.5 .

Fig. 4
Fig. 4

Graph of relative dot density (radiance) versus zenith angle in the vertical plane of the Sun for the image of Fig. 3 for τ cld = 0.5 : black curve, light only scattered by one crystal; gray (red online) curve, other scattered light.

Fig. 5
Fig. 5

Fish-eye images of simulated sky for the South Pole Halo Display of 4 January 1985 with halos generated by 80% horizontal plates with aspect ratio = 0.27 , crystal tilt mean = 3 ° , standard deviation = 2 ° , and 20% randomly oriented pencils with aspect ratio 3 at ϕ SUN = 67.2 ° , β = 1 , p sfc = 700 hPa , and p cld = 690 hPa for a,  τ cld = 0.04 and b,  τ cld = 0.5 .

Fig. 6
Fig. 6

Fish-eye graphs of dot density maps showing relative number of beams for the conditions of Fig. 5 with a,  τ cld = 0.04 , b,  τ cld = 0.5 , and c,  τ cld = 2.0 .

Fig. 7
Fig. 7

Fish-eye images of simulated skies with halos generated for conditions given in Fig. 5 but with 10% thick plates and 90% junk crystals for τ cld = 0.5 .

Fig. 8
Fig. 8

Fish-eye image of the simulated sky for the South Pole Halo Display of 21 January 1986 with τ cld = 0.04 as the optimal match.

Fig. 9
Fig. 9

Fish-eye image of the simulated display of odd-radius halos at 31,000 feet over British Columbia generated by randomly oriented crystals composed of 50% pencils and 50% pyramidal crystals with dimensions given in the text for ϕ SUN = 40 ° , β = 1.0 , p sfc = 700 hPa and p cld = 300 hPa , and τ cld = 0.05 .

Fig. 10
Fig. 10

Graph of relative dot density (radiance) versus zenith angle in the vertical plane for the simulation of Fig. 9. The black curve gives light only scattered by one crystal, and the gray (red online) curve gives the other scattered light.

Fig. 11
Fig. 11

Wide-angle images of the simulated display of odd-radius halos arcs on 6 January 2004 at Fairbanks, Alaska, with a, 100% crystals with truncated pyramidal endings with c axes vertical and b, 75% junk crystals. ϕ MOON = 35 ° , β = 1.1 , p sfc = 1000 hPa and p cld = 900 hPa , and τ cld = 0.05 .

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