Abstract

Glories and cloudbows are simulated in color by use of the Mie scattering theory of light upwelling from small-droplet clouds of finite optical thickness embedded in a Rayleigh scattering atmosphere. Glories are generally more distinct for clouds of droplets of as much as ∼10 μm in radius. As droplet radius increases, the glory shrinks and becomes less prominent, whereas the cloudbow becomes more distinct and eventually colorful. Cloudbows typically consist of a broad, almost white band with a slightly orange outer edge and a dark inner band. Multiple light and dark bands that are related to supernumerary rainbows first appear inside the cloudbow as droplet radius increases above ∼10 μm and gradually become more prominent when all droplets are the same size. Bright glories with multiple rings and high color purity are simulated when all droplets are the same size and every light beam is scattered just once. Color purity decreases and outer rings fade as the range of droplet sizes widens and when skylight, reflected light from the ground or background, and multiply scattered light from the cloud are included. Consequently, the brightest and most colorful glories and bows are seen when the observer is near a cloud or a rain swath with optical thickness of ∼0.25 that consists of uniform-sized drops and when a dark or shaded background lies a short distance behind the cloud.

© 2003 Optical Society of America

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References

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2003 (2)

2001 (2)

J. A. Adam, “Mathematical physics of rainbows and glories,” Phys. Rep. 356, 229–365 (2001).
[CrossRef]

S. Kato, G. G. Mace, E. E. Clothiaux, J. C. Liljegren, R. T. Austin, “Doppler cloud radar derived drop size distributions in liquid water stratus clouds,” J. Atmos. Sci. 58, 2895–2916 (2001).
[CrossRef]

2000 (1)

M. Kuji, T. Hayasaka, N. Kikuchi, T. J. Nakajima, M. Tanaka, “The retrieval of effective particle radius and liquid water path of low-level marine clouds from NOAA AVHRR data,” J Appl. Meteorol. 39, 999–1016 (2000).
[CrossRef]

1998 (2)

Q. Han, W. B. Rossow, J. Chou, R. M. Welch, “Global survey of the relationships of cloud albedo and liquid water path with droplet size using ISCCP,” J. Clim. 11, 1516–1528 (1998).
[CrossRef]

R. L. Lee, “Mie theory, Airy theory, and the natural rainbow,” Appl. Opt. 37, 1506–1519 (1998).
[CrossRef]

1994 (3)

1992 (1)

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

1991 (3)

1989 (1)

1987 (1)

1982 (1)

1980 (1)

1977 (1)

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

1974 (1)

H. C. Bryant, N. Jarmie, “The glory,” Sci. Am. 231, 60–71 (1974).
[CrossRef]

1970 (1)

J. E. Hansen, J. B. Pollack, “Near infrared light scattering by terrestrial clouds,” J. Atmos. Sci. 27, 265–281 (1970).
[CrossRef]

1967 (1)

S. Twomey, H. Jacobowitz, H. Howell, “Light scattering by cloud layers,” J. Atmos. Sci. 24, 70–79 (1967).
[CrossRef]

1947 (1)

Adam, J. A.

J. A. Adam, “Mathematical physics of rainbows and glories,” Phys. Rep. 356, 229–365 (2001).
[CrossRef]

Austin, R. T.

S. Kato, G. G. Mace, E. E. Clothiaux, J. C. Liljegren, R. T. Austin, “Doppler cloud radar derived drop size distributions in liquid water stratus clouds,” J. Atmos. Sci. 58, 2895–2916 (2001).
[CrossRef]

Bryant, H. C.

H. C. Bryant, N. Jarmie, “The glory,” Sci. Am. 231, 60–71 (1974).
[CrossRef]

Chou, J.

Q. Han, W. B. Rossow, J. Chou, R. M. Welch, “Global survey of the relationships of cloud albedo and liquid water path with droplet size using ISCCP,” J. Clim. 11, 1516–1528 (1998).
[CrossRef]

Clothiaux, E. E.

S. Kato, G. G. Mace, E. E. Clothiaux, J. C. Liljegren, R. T. Austin, “Doppler cloud radar derived drop size distributions in liquid water stratus clouds,” J. Atmos. Sci. 58, 2895–2916 (2001).
[CrossRef]

Futterman, S. N.

Gedzelman, S. D.

Greenler, R.

R. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, Cambridge, 1980), Chap. 1 and 6.

Greenler, R. G.

Han, Q.

Q. Han, W. B. Rossow, J. Chou, R. M. Welch, “Global survey of the relationships of cloud albedo and liquid water path with droplet size using ISCCP,” J. Clim. 11, 1516–1528 (1998).
[CrossRef]

Hansen, J. E.

J. E. Hansen, J. B. Pollack, “Near infrared light scattering by terrestrial clouds,” J. Atmos. Sci. 27, 265–281 (1970).
[CrossRef]

Hayasaka, T.

M. Kuji, T. Hayasaka, N. Kikuchi, T. J. Nakajima, M. Tanaka, “The retrieval of effective particle radius and liquid water path of low-level marine clouds from NOAA AVHRR data,” J Appl. Meteorol. 39, 999–1016 (2000).
[CrossRef]

Howell, H.

S. Twomey, H. Jacobowitz, H. Howell, “Light scattering by cloud layers,” J. Atmos. Sci. 24, 70–79 (1967).
[CrossRef]

Humphreys, W. J.

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

Jacobowitz, H.

S. Twomey, H. Jacobowitz, H. Howell, “Light scattering by cloud layers,” J. Atmos. Sci. 24, 70–79 (1967).
[CrossRef]

Jarmie, N.

H. C. Bryant, N. Jarmie, “The glory,” Sci. Am. 231, 60–71 (1974).
[CrossRef]

Kato, S.

S. Kato, G. G. Mace, E. E. Clothiaux, J. C. Liljegren, R. T. Austin, “Doppler cloud radar derived drop size distributions in liquid water stratus clouds,” J. Atmos. Sci. 58, 2895–2916 (2001).
[CrossRef]

Khare, V.

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

Kikuchi, N.

M. Kuji, T. Hayasaka, N. Kikuchi, T. J. Nakajima, M. Tanaka, “The retrieval of effective particle radius and liquid water path of low-level marine clouds from NOAA AVHRR data,” J Appl. Meteorol. 39, 999–1016 (2000).
[CrossRef]

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]

Kuji, M.

M. Kuji, T. Hayasaka, N. Kikuchi, T. J. Nakajima, M. Tanaka, “The retrieval of effective particle radius and liquid water path of low-level marine clouds from NOAA AVHRR data,” J Appl. Meteorol. 39, 999–1016 (2000).
[CrossRef]

Laven, P.

P. Laven, “Simulation of rainbows, coronas, and glories by use of Mie theory,” Appl. Opt. 42, 436–444 (2003).
[CrossRef] [PubMed]

P. Laven, European Broadcasting Union Geneva, Switzerland (personal communication, 2002).

Lee, R. L.

Liljegren, J. C.

S. Kato, G. G. Mace, E. E. Clothiaux, J. C. Liljegren, R. T. Austin, “Doppler cloud radar derived drop size distributions in liquid water stratus clouds,” J. Atmos. Sci. 58, 2895–2916 (2001).
[CrossRef]

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U. Press, Cambridge, 2001), Chap. 4.

Lock, J.

Lock, J. A.

Lynch, D. K.

Mace, G. G.

S. Kato, G. G. Mace, E. E. Clothiaux, J. C. Liljegren, R. T. Austin, “Doppler cloud radar derived drop size distributions in liquid water stratus clouds,” J. Atmos. Sci. 58, 2895–2916 (2001).
[CrossRef]

Minnaert, M.

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

Nakajima, T.

Nakajima, T. J.

M. Kuji, T. Hayasaka, N. Kikuchi, T. J. Nakajima, M. Tanaka, “The retrieval of effective particle radius and liquid water path of low-level marine clouds from NOAA AVHRR data,” J Appl. Meteorol. 39, 999–1016 (2000).
[CrossRef]

Nussenzveig, H. M.

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

Pollack, J. B.

J. E. Hansen, J. B. Pollack, “Near infrared light scattering by terrestrial clouds,” J. Atmos. Sci. 27, 265–281 (1970).
[CrossRef]

Rossow, W. B.

Q. Han, W. B. Rossow, J. Chou, R. M. Welch, “Global survey of the relationships of cloud albedo and liquid water path with droplet size using ISCCP,” J. Clim. 11, 1516–1528 (1998).
[CrossRef]

Schwartz, P.

Spinhirne, J. D.

Tanaka, M.

M. Kuji, T. Hayasaka, N. Kikuchi, T. J. Nakajima, M. Tanaka, “The retrieval of effective particle radius and liquid water path of low-level marine clouds from NOAA AVHRR data,” J Appl. Meteorol. 39, 999–1016 (2000).
[CrossRef]

Tape, W.

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

Tränkle, E.

Tricker, R. A. R.

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

Twomey, S.

S. Twomey, H. Jacobowitz, H. Howell, “Light scattering by cloud layers,” J. Atmos. Sci. 24, 70–79 (1967).
[CrossRef]

van de Hulst, H. C.

Welch, R. M.

Q. Han, W. B. Rossow, J. Chou, R. M. Welch, “Global survey of the relationships of cloud albedo and liquid water path with droplet size using ISCCP,” J. Clim. 11, 1516–1528 (1998).
[CrossRef]

Yang, L.

Am. J. Phys. (1)

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

Appl. Opt. (10)

J Appl. Meteorol. (1)

M. Kuji, T. Hayasaka, N. Kikuchi, T. J. Nakajima, M. Tanaka, “The retrieval of effective particle radius and liquid water path of low-level marine clouds from NOAA AVHRR data,” J Appl. Meteorol. 39, 999–1016 (2000).
[CrossRef]

J. Atmos. Sci. (3)

S. Kato, G. G. Mace, E. E. Clothiaux, J. C. Liljegren, R. T. Austin, “Doppler cloud radar derived drop size distributions in liquid water stratus clouds,” J. Atmos. Sci. 58, 2895–2916 (2001).
[CrossRef]

S. Twomey, H. Jacobowitz, H. Howell, “Light scattering by cloud layers,” J. Atmos. Sci. 24, 70–79 (1967).
[CrossRef]

J. E. Hansen, J. B. Pollack, “Near infrared light scattering by terrestrial clouds,” J. Atmos. Sci. 27, 265–281 (1970).
[CrossRef]

J. Clim. (1)

Q. Han, W. B. Rossow, J. Chou, R. M. Welch, “Global survey of the relationships of cloud albedo and liquid water path with droplet size using ISCCP,” J. Clim. 11, 1516–1528 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Phys. Rep. (1)

J. A. Adam, “Mathematical physics of rainbows and glories,” Phys. Rep. 356, 229–365 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

V. Khare, H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
[CrossRef]

Sci. Am. (1)

H. C. Bryant, N. Jarmie, “The glory,” Sci. Am. 231, 60–71 (1974).
[CrossRef]

Sky Telescope (1)

“Observer’s notebook: the magic of fog,” Sky Telescope 87(5), 110–111 (1994).

Other (8)

P. Laven, European Broadcasting Union Geneva, Switzerland (personal communication, 2002).

R. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, Cambridge, 1980), Chap. 1 and 6.

D. K. Lynch, W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge U. Press, Cambridge, 2001), Chap. 4.

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.

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

D. Bruton, “Color science” (1996), http://www.physics.sfasu.edu/astro/color.html .

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Figures (7)

Fig. 1
Fig. 1

Mie scattering phase functions for a point Sun for droplet radii 3, 12, and 50 μm at λ = 0.5 μm, showing decreasing angular size of glory and increasing prominence of cloudbow as droplet radius increases.

Fig. 2
Fig. 2

Comparison of Mie scattering phase functions about the antisolar point at λ = 0.5 μm for a = 9.0 μm and for an average over 21 equally spaced radii from 8.9 and 9.1 μm. Amplitudes of scattering peaks and troughs change rapidly with radius, but angles do not.

Fig. 3
Fig. 3

Smoothed color maps of simulated glories and cloudbows produced by a perfect Mie scattering model (MIE), clouds of optical thickness τ = 0.5 and τ = 3.0, and drop size distributions (DSD) centered at a = 4 μm (see text). For cloud simulations the observer stands at cloud edge (800 hPa) with background of albedo 0.03 immediately behind the cloud.

Fig. 4
Fig. 4

Five-layer glory model. Light can be scattered multiple times in any layer. All scattered beams that well up to the observer at the top of layer 2 are counted, but only those that are scattered once in the cloud, but nowhere else, contribute to the glory.

Fig. 5
Fig. 5

Chromaticity diagrams from 0° to 15° from the antisolar point for the same situations as in Figs. 3a, 3b, and 3d. (a) Perfect Mie scattering for droplets with 4-μm radii, (b) a cloud of droplets with 4-μm radii and an optical thickness of 0.5, and (c) perfect Mie scattering for a drop size distribution. Red, Green, and Blue work the tristimulus points. Small numbers accompanying open circles represent scattering angle (in degrees) from the antisolar point.

Fig. 6
Fig. 6

Brightness of the glory compared to various sources of background illumination as a function of cloud optical thickness. The curve marked Foreground Skylight at Jet Level is for an observer at pressure 300 hPa when cloud-top pressure is 800 hPa and surface pressure is 1013.25 hPa. All other curves are for an observer at cloud edge with the surface immediately behind the cloud.

Fig. 7
Fig. 7

Maximum color purity of the two innermost red rings Ring #1 and Ring #2, of the simulated glory for the same situations as in Fig. 6 as a function of cloud optical thickness. The maximum color purity of the inner red ring for the perfect Mie scattering model is shown for comparison. DSDs, drop size distributions.

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