Abstract

Coronas are simulated in color by use of the Mie scattering theory of light by small droplets through clouds of finite optical thickness embedded in a Rayleigh scattering atmosphere. The primary factors that affect color, visibility, and number of rings of coronas are droplet size, width of the size distribution, and cloud optical thickness. The color sequence of coronas and iridescence varies when the droplet radius is smaller than ∼6-μm. As radius increases to approximately 3.5 μm, new color bands appear at the center of the corona and fade as they move outward. As the radius continues to increase to ∼6 μm, successively more inner rings become fixed in the manner described by classical diffraction theory, while outer rings continue their outward migration. Wave clouds or rippled cloud segments produce the brightest and most vivid multiple ringed coronas and iridescence because their integrated drop size distributions along sunbeams are much narrower than in convective or stratiform clouds. The visibility of coronas and the appearance of the background sky vary with cloud optical depth τ. First the corona becomes visible as a white aureole in a blue sky when τ ∼ 0.001. Color purity then rapidly increases to an almost flat maximum in the range 0.05 ≤ τ ≤ 0.5 and then decreases, so coronas are almost completely washed out by a bright gray background when τ ≥ 4.

© 2003 Optical Society of America

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References

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2003

1998

1994

1992

R. J. Kubesh, “Computer display of chromaticity coordinates with the rainbow as an example,” Am. J. Phys. 60, 919–923 (1992).
[CrossRef]

1991

1988

S. D. Gedzelman, “In praise of altocumulus,” Weatherwise 41, 143–149 (1988).
[CrossRef]

1987

1980

1959

W. Mordy, “Computations of the growth by condensation of a population of cloud droplets,” Tellus 11, 17–43 (1959).

Bohren, C. F.

Gedzelman, S. D.

Greenler, R. G.

Hallett, J.

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964), Chap. 6.

Kubesh, R. J.

R. J. Kubesh, “Computer display of chromaticity coordinates with the rainbow as an example,” Am. J. Phys. 60, 919–923 (1992).
[CrossRef]

Laven, P.

Livingston, W.

D. K. Lynch, W. Livingston, Light and Color in Nature (Cambridge U. Press, New York1995), p. 124.

Lock, J.

Lynch, D. K.

D. K. Lynch, W. Livingston, Light and Color in Nature (Cambridge U. Press, New York1995), p. 124.

Mace, G. G.

Makelä, V.

Mielke, B.

Mims, F.

Minnaert, M.

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954), Chap. 10.

Mordy, W.

W. Mordy, “Computations of the growth by condensation of a population of cloud droplets,” Tellus 11, 17–43 (1959).

Nakajima, T.

Neiman, P. J.

J. A. Shaw, P. J. Neiman, “Iridescence and coronas related to cloud particle-size distributions and meteorology,” presented at the Seventh Topical Meeting on Meteorological Optics, Boulder, Colo., 5–8 June 2001; preprint available at http://www.asp.ucar.edu/MetOptics/Preprints.pdf .

Parviainen, P.

Piellot, M. R.

Sassen, K.

Shaw, J. A.

J. A. Shaw, P. J. Neiman, “Iridescence and coronas related to cloud particle-size distributions and meteorology,” presented at the Seventh Topical Meeting on Meteorological Optics, Boulder, Colo., 5–8 June 2001; preprint available at http://www.asp.ucar.edu/MetOptics/Preprints.pdf .

Spinhirne, J. D.

Tränkle, E.

Tricker, R. A. R.

R. A. R. Tricker, An Introduction to Atmospheric Optics (American Elsevier, New York, 1970), Chaps 5 and 7.

Yang, L.

Am. J. Phys.

R. J. Kubesh, “Computer display of chromaticity coordinates with the rainbow as an example,” Am. J. Phys. 60, 919–923 (1992).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Tellus

W. Mordy, “Computations of the growth by condensation of a population of cloud droplets,” Tellus 11, 17–43 (1959).

Weatherwise

S. D. Gedzelman, “In praise of altocumulus,” Weatherwise 41, 143–149 (1988).
[CrossRef]

Other

J. A. Shaw, P. J. Neiman, “Iridescence and coronas related to cloud particle-size distributions and meteorology,” presented at the Seventh Topical Meeting on Meteorological Optics, Boulder, Colo., 5–8 June 2001; preprint available at http://www.asp.ucar.edu/MetOptics/Preprints.pdf .

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954), Chap. 10.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964), Chap. 6.

R. A. R. Tricker, An Introduction to Atmospheric Optics (American Elsevier, New York, 1970), Chaps 5 and 7.

D. K. Lynch, W. Livingston, Light and Color in Nature (Cambridge U. Press, New York1995), p. 124.

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Figures (12)

Fig. 1
Fig. 1

The three-layer corona cloud model. The corona beam consists of light that reaches the ground after being scattered once in the cloud. The glory beam consists of light that reaches an observer above cloud level after being scattered once in the cloud.

Fig. 2
Fig. 2

Photographs of coronas and iridescence in (a) a thin patch of cirrocumulus in July 1984 over Manhattan, New York; (b) wavy cirrocumulus on 26 December 1993 over Sarasota, Florida, with a hint of a dark blue band; and (c) iridescence in wavy altocumulus on 1 January 2000 over Boynton Beach, Florida.

Fig. 3
Fig. 3

Schematic diagram showing ranges of droplet sizes encountered by sunbeams passing through a convective cloud and through a wave cloud with a top-hat relative humidity profile.

Fig. 4
Fig. 4

Droplet size distributions for a convective cloud and for wave clouds with Gaussian and top-hat humidity profiles.

Fig. 5
Fig. 5

Relationship between droplet radius and the optical thickness τ of a wave cloud 10 hPa thick. Coalescence begins once optical thickness approaches 2.

Fig. 6
Fig. 6

Mie scattering phase functions for λ = 0.5 μm and droplets with radii 2.75 and 3.0 μm, showing rapid changes in the shape of the curve.

Fig. 7
Fig. 7

Deflection angles of the first peak of the Mie scattering phase function for λ = 0.4, 0.5, 0.6, 0.7 μm as a function of droplet radius. Overlapping of these peaks at small droplet radii illustrates why corona colors vary with droplet radius.

Fig. 8
Fig. 8

Color map showing corona colors as a function of droplet radius and scattering angle for a perfect Mie scattering model. The sequence of corona colors changes rapidly for small droplets but becomes fixed once droplet radius exceeds ∼6 μm.

Fig. 9
Fig. 9

Chromaticity diagrams for a cloud of optical thickness 0.1 when a = 3.0, 8.0 μm. Scattering angles (deg) given for circled points.

Fig. 10
Fig. 10

Maximum color purity of the inner ring of the corona as a function of cloud optical thickness τ for solar zenith angle Z = 35° and droplet radius a = 3.0 μm (solid curve, top) compared with maximum color purity given by the perfect Mie scattering model (dashed-dotted curve). Circles indicate maximum color purity for convective cloud, wave cloud, and monodisperse droplet size distributions when the largest droplet has a radius of 8.0 μm at optical thickness 0.1.

Fig. 11
Fig. 11

Color map of coronas as a function of cloud optical thickness and scattering angle for solar zenith angle Z = 35° and droplet radius a = 3.0 μm.

Fig. 12
Fig. 12

Color-intensity maps showing the effects of cloud optical thickness and the sharpness of droplet size distribution on the appearance of the corona. The most vibrant, multiringed coronas are produced by optically thin clouds with narrow droplet size distributions. Interference that results from flat and wide droplet size distributions washes out the outer rings, whereas multiple scattering from optically thick clouds blurs the entire corona. A dark blue ring just outside the red ring is present only in optically thin clouds with sharply peaked droplet size distributions.

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