Abstract

A model (SKYCOLOR) is developed that simulates the light and color of the sky and open cloud decks in the vertical plane including the Sun and the observer and animates the changes as the Sun goes down. Model skylight consists of sunbeams that are scattered toward the observer, but depleted by scattering and absorption in the Chappuis bands of ozone. SKYCOLOR includes the Earth’s curvature, atmospheric refraction, cloud shadows, and solar eclipses. Scattering is given a wavelength (λ) dependence of λ−4 for air molecules (Rayleigh scattering), λ−1 for tropospheric aerosols, and λ+1 for volcanic aerosol particles. Multiple scattering is calculated directly in clouds but is parameterized in clear air by decreasing the scattering rates of sunlight and of skylight in the Earth’s shadow by 30%.

© 2005 Optical Society of America

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References

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  1. The Sky Color model is available from the author at sgedzelman@ccny.cuny.edu. Internet Sites for sky color simulations include http://www.vterrain.org/Atmosphere/ and http://ucsu.colorado.edu/~kuestern/Rtweb/startRT/html and http://www.ati.com/developer/SIGGRAPH03/PreethamSig2003CourseNotes.pdf and http://webexhibits.org/causesof-color/14B.html .
  2. A. Meinel, M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge Univ., London, 1983).
  3. D. K. Lynch, W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge Univ., London, 2001).
  4. P. Candy, Le Meraviglie del Cielo (II Castello, Milano, 1997).
  5. F. W. Gallagher, W. H. Beasley, C. F. Bohren, “Green thunderstorms observed,” Bull. Am. Meteorol. Soc. 77, 2889–2897 (1996).
    [CrossRef]
  6. S. D. Gedzelman, “Atmospheric optics in art,” Appl. Opt. 30, 3514–3522, 3550–3551 (1991).
    [CrossRef] [PubMed]
  7. W. J. Humphreys, Physics of the Air (Dover, New York, 1964, reprint of 1940 edition), pp. 557–570.
  8. M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954, reprint of 1938 edition), pp. 235–308.
  9. J. Tyndall, Philos. Mag. 37, 384 (1869).
  10. Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120274–279 (1871).
  11. G. V. Rozenberg, Twilight: A Study in Atmospheric Optics (Plenum, New York, 1966), pp. 10, 89.
  12. R. L. Lee, “Horizon brightness revisited: measurements and a model of clear-sky radiances,” Appl. Opt. 33, 4620–4628 (1994).
    [CrossRef] [PubMed]
  13. R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–4638 (1994).
    [CrossRef] [PubMed]
  14. A. Meinel, M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, London, 1983), p. 36.
  15. R. L. Lee, J. Hernández-Andrés, “Measuring and modeling twilight’s purple light,” Appl. Opt. 42, 445–457 (2003).
    [CrossRef] [PubMed]
  16. The model is available by e-mail at sgedzelman@ccny.cuny.edu.
  17. S. D. Gedzelman, J. Lock, “Simulating coronas in color,” Appl. Opt. 42, 497–504 (2003).
    [CrossRef] [PubMed]
  18. S. D. Gedzelman, “Simulating glories and cloudbows in color,” Appl. Opt. 42, 429–335 (2003).
    [CrossRef] [PubMed]
  19. S. D. Gedzelman, “Sky color near the horizon during a total solar eclipse,” Appl. Opt. 14, 2831–2837 (1975).
    [CrossRef] [PubMed]
  20. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  21. S. D. Gedzelman, “Simulating rainbows and halos in color,” Appl. Opt. 33, 4607–4614, 4958 (1994).
    [CrossRef] [PubMed]
  22. C. N. Adams, G. N. Plass, G. W. Kattawar, “The influence of ozone and aerosols on the brightness and color of the twilight sky,” J. Atmos. Sci. 31, 1662–1674 (1974). Raymond Lee pointed this out to me.
    [CrossRef]
  23. K.-N. Liou, An Introduction to Atmospheric Radiation, Vol. 26 of International Geophysics Series, (Academic, New York, 1980), p. 55.
  24. S. T. Henderson, Daylight and its Spectrum (Elsevier, New York, 1970), pp. 34–43.
  25. R. W. Bergstrom, P. B. Russell, P. Hignett, “Wavelength dependence of the absorption of black carbon particles: predictions and results from the TARFOX experiment and implications for the aerosol single scattering albedo,” J. Atmos. Sci. 59, 567–577 (2002).
    [CrossRef]
  26. C. F. Bohren, A. B. Fraser, “Colors of the sky,” Phys. Teacher 23, 267–272 (1985).
    [CrossRef]
  27. Ref. 3, pp. 33–45.
  28. D. L. Chandler, “The mystifying shuttle shadows,” Weatherwise 54(4), 14–15 (2001).
    [CrossRef]
  29. R. Greenler, “The NASA, Shuttle-launch dark-moon-ray mystery,” presented at the Topical Meeting in Meteorological Optics, Boulder, Colo., 6–8 June 2001.
  30. Many photographs of the sky near the horizon during total solar eclipses that show twilight colors are available at http://www.comet-track.com/eclipse . Courtesy of Bob Yen.

2003

2002

R. W. Bergstrom, P. B. Russell, P. Hignett, “Wavelength dependence of the absorption of black carbon particles: predictions and results from the TARFOX experiment and implications for the aerosol single scattering albedo,” J. Atmos. Sci. 59, 567–577 (2002).
[CrossRef]

2001

D. L. Chandler, “The mystifying shuttle shadows,” Weatherwise 54(4), 14–15 (2001).
[CrossRef]

1996

F. W. Gallagher, W. H. Beasley, C. F. Bohren, “Green thunderstorms observed,” Bull. Am. Meteorol. Soc. 77, 2889–2897 (1996).
[CrossRef]

1994

1991

1985

C. F. Bohren, A. B. Fraser, “Colors of the sky,” Phys. Teacher 23, 267–272 (1985).
[CrossRef]

1975

1974

C. N. Adams, G. N. Plass, G. W. Kattawar, “The influence of ozone and aerosols on the brightness and color of the twilight sky,” J. Atmos. Sci. 31, 1662–1674 (1974). Raymond Lee pointed this out to me.
[CrossRef]

1871

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120274–279 (1871).

1869

J. Tyndall, Philos. Mag. 37, 384 (1869).

Adams, C. N.

C. N. Adams, G. N. Plass, G. W. Kattawar, “The influence of ozone and aerosols on the brightness and color of the twilight sky,” J. Atmos. Sci. 31, 1662–1674 (1974). Raymond Lee pointed this out to me.
[CrossRef]

Beasley, W. H.

F. W. Gallagher, W. H. Beasley, C. F. Bohren, “Green thunderstorms observed,” Bull. Am. Meteorol. Soc. 77, 2889–2897 (1996).
[CrossRef]

Bergstrom, R. W.

R. W. Bergstrom, P. B. Russell, P. Hignett, “Wavelength dependence of the absorption of black carbon particles: predictions and results from the TARFOX experiment and implications for the aerosol single scattering albedo,” J. Atmos. Sci. 59, 567–577 (2002).
[CrossRef]

Bohren, C. F.

F. W. Gallagher, W. H. Beasley, C. F. Bohren, “Green thunderstorms observed,” Bull. Am. Meteorol. Soc. 77, 2889–2897 (1996).
[CrossRef]

C. F. Bohren, A. B. Fraser, “Colors of the sky,” Phys. Teacher 23, 267–272 (1985).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Candy, P.

P. Candy, Le Meraviglie del Cielo (II Castello, Milano, 1997).

Chandler, D. L.

D. L. Chandler, “The mystifying shuttle shadows,” Weatherwise 54(4), 14–15 (2001).
[CrossRef]

Fraser, A. B.

C. F. Bohren, A. B. Fraser, “Colors of the sky,” Phys. Teacher 23, 267–272 (1985).
[CrossRef]

Gallagher, F. W.

F. W. Gallagher, W. H. Beasley, C. F. Bohren, “Green thunderstorms observed,” Bull. Am. Meteorol. Soc. 77, 2889–2897 (1996).
[CrossRef]

Gedzelman, S. D.

Greenler, R.

R. Greenler, “The NASA, Shuttle-launch dark-moon-ray mystery,” presented at the Topical Meeting in Meteorological Optics, Boulder, Colo., 6–8 June 2001.

Henderson, S. T.

S. T. Henderson, Daylight and its Spectrum (Elsevier, New York, 1970), pp. 34–43.

Hernández-Andrés, J.

Hignett, P.

R. W. Bergstrom, P. B. Russell, P. Hignett, “Wavelength dependence of the absorption of black carbon particles: predictions and results from the TARFOX experiment and implications for the aerosol single scattering albedo,” J. Atmos. Sci. 59, 567–577 (2002).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964, reprint of 1940 edition), pp. 557–570.

Kattawar, G. W.

C. N. Adams, G. N. Plass, G. W. Kattawar, “The influence of ozone and aerosols on the brightness and color of the twilight sky,” J. Atmos. Sci. 31, 1662–1674 (1974). Raymond Lee pointed this out to me.
[CrossRef]

Lee, R. L.

Liou, K.-N.

K.-N. Liou, An Introduction to Atmospheric Radiation, Vol. 26 of International Geophysics Series, (Academic, New York, 1980), p. 55.

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge Univ., London, 2001).

Lock, J.

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge Univ., London, 2001).

Meinel, A.

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

A. Meinel, M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, London, 1983), p. 36.

Meinel, M.

A. Meinel, M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, London, 1983), p. 36.

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

Minnaert, M.

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954, reprint of 1938 edition), pp. 235–308.

Plass, G. N.

C. N. Adams, G. N. Plass, G. W. Kattawar, “The influence of ozone and aerosols on the brightness and color of the twilight sky,” J. Atmos. Sci. 31, 1662–1674 (1974). Raymond Lee pointed this out to me.
[CrossRef]

Rayleigh,

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120274–279 (1871).

Rozenberg, G. V.

G. V. Rozenberg, Twilight: A Study in Atmospheric Optics (Plenum, New York, 1966), pp. 10, 89.

Russell, P. B.

R. W. Bergstrom, P. B. Russell, P. Hignett, “Wavelength dependence of the absorption of black carbon particles: predictions and results from the TARFOX experiment and implications for the aerosol single scattering albedo,” J. Atmos. Sci. 59, 567–577 (2002).
[CrossRef]

Strutt, J. W.

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120274–279 (1871).

Tyndall, J.

J. Tyndall, Philos. Mag. 37, 384 (1869).

Appl. Opt.

Bull. Am. Meteorol. Soc.

F. W. Gallagher, W. H. Beasley, C. F. Bohren, “Green thunderstorms observed,” Bull. Am. Meteorol. Soc. 77, 2889–2897 (1996).
[CrossRef]

J. Atmos. Sci.

C. N. Adams, G. N. Plass, G. W. Kattawar, “The influence of ozone and aerosols on the brightness and color of the twilight sky,” J. Atmos. Sci. 31, 1662–1674 (1974). Raymond Lee pointed this out to me.
[CrossRef]

R. W. Bergstrom, P. B. Russell, P. Hignett, “Wavelength dependence of the absorption of black carbon particles: predictions and results from the TARFOX experiment and implications for the aerosol single scattering albedo,” J. Atmos. Sci. 59, 567–577 (2002).
[CrossRef]

Philos. Mag.

J. Tyndall, Philos. Mag. 37, 384 (1869).

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120274–279 (1871).

Phys. Teacher

C. F. Bohren, A. B. Fraser, “Colors of the sky,” Phys. Teacher 23, 267–272 (1985).
[CrossRef]

Weatherwise

D. L. Chandler, “The mystifying shuttle shadows,” Weatherwise 54(4), 14–15 (2001).
[CrossRef]

Other

R. Greenler, “The NASA, Shuttle-launch dark-moon-ray mystery,” presented at the Topical Meeting in Meteorological Optics, Boulder, Colo., 6–8 June 2001.

Many photographs of the sky near the horizon during total solar eclipses that show twilight colors are available at http://www.comet-track.com/eclipse . Courtesy of Bob Yen.

Ref. 3, pp. 33–45.

K.-N. Liou, An Introduction to Atmospheric Radiation, Vol. 26 of International Geophysics Series, (Academic, New York, 1980), p. 55.

S. T. Henderson, Daylight and its Spectrum (Elsevier, New York, 1970), pp. 34–43.

G. V. Rozenberg, Twilight: A Study in Atmospheric Optics (Plenum, New York, 1966), pp. 10, 89.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964, reprint of 1940 edition), pp. 557–570.

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, New York, 1954, reprint of 1938 edition), pp. 235–308.

The Sky Color model is available from the author at sgedzelman@ccny.cuny.edu. Internet Sites for sky color simulations include http://www.vterrain.org/Atmosphere/ and http://ucsu.colorado.edu/~kuestern/Rtweb/startRT/html and http://www.ati.com/developer/SIGGRAPH03/PreethamSig2003CourseNotes.pdf and http://webexhibits.org/causesof-color/14B.html .

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

D. K. Lynch, W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge Univ., London, 2001).

P. Candy, Le Meraviglie del Cielo (II Castello, Milano, 1997).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

The model is available by e-mail at sgedzelman@ccny.cuny.edu.

A. Meinel, M. Meinel, Sunsets, Twilights and Evening Skies (Cambridge University, London, 1983), p. 36.

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Figures (23)

Fig. 1
Fig. 1

Geometry of the sky color model. Light reaching an observer looking up at angle ϕv on a spherical Earth consists of sunlight at true elevation angle, θ0, scattered by air molecules, aerosol particles near the ground, volcanic particles in the stratosphere, and clouds at height hcld and apparent elevation angle ϕcld. Sunbeams are refracted downward by an amount Δz. Shading due to a total solar eclipse or a broken or opaque cloud deck is included if desired.

Fig. 2
Fig. 2

The ratio of optical path length of a refracted sunbeam to that of a straight sunbeam reaching point (xp, zp) when T = 273. Dashed curves are based on a refraction model, solid curves, from Eq. (2).

Fig. 3
Fig. 3

Mie-scattering efficiency (ratio of scattering cross section to geometric cross section) and color of scattered sunlight as a function of particle-size parameter (ratio of circumference to wavelength at λ = 0.55 μm) for spherical water droplets.

Fig. 4
Fig. 4

Comparison of angular-scattering phase function using a = 3.3 in Eq. (3) (thick curve) with Mie-scattering solution for spheres of radius 0.4 μm, at wavelength λ = 0.5 μm and index of refraction n = 1.33 (thin curve).

Fig. 5
Fig. 5

Absorption coefficient in the Chappuis bands of ozone as a function of wavelength, λ, used in SKYCOLOR.

Fig. 6
Fig. 6

Vertical distribution of ozone number density used in SKYCOLOR when the total ozone in the atmospheric column is 300 Dobson units.

Fig. 7
Fig. 7

Photographs of the sky for clean air in Sydney Australia (left), highly polluted air in New York City (center), and turbid stratosphere after Pinatubo producing a blue Sun (right).

Fig. 8
Fig. 8

SKYCOLOR simulations of the appearance of the sky from horizon facing the Sun at the bottom through the zenith to the opposite horizon at top when the Sun’s elevation angle, θ0 = 40°, for an atmosphere with no aerosols (left), turbidity β = 5 and aerosol scale height 2.5 km (center), and sulfuric acid droplets of optical depth τvul = 0.1 centered in the stratosphere at 25 km with e-folding height 2.0 km (right).

Fig. 9
Fig. 9

Simulated color purity as a function of observer elevation angle, ϕv, for the cases modeled in Fig. 8.

Fig. 10
Fig. 10

Integrated sky brightness for values of turbidity, β, from 1 to 8 as a function of viewer elevation angle for solar elevation angles θ0 = 5° (top) and θ0 = 40° (bottom).

Fig. 11
Fig. 11

Sequence of sky colors in pure air for θs = θ0 = 15° to −6° at 3° intervals from the horizon to ϕv = 45° for four different pairs of β and τvul.

Fig. 12
Fig. 12

Maximum green sky color purity defined as fraction of distance from the achromatic point (x = 0.3333, y = 0.3333) to the “green” point (x = 0.1547, y = 0.8049) as a function of solar elevation angle, θ0, for β = 1 and 2, and for an eclipse sky with β = 1.

Fig. 13
Fig. 13

Skylight spectra for the Blue of clean air at ϕv = 44°, θ0 = 60° (heavy solid curve), Green sky at ϕv = 2.4°, θ0 = 2° in clean air (thin solid curve), Red horizon sky at twilight, ϕv = 0.06°, θ0 = 2° in clean air (thin dotted curve), and Purple sky at ϕv = 29.4°, θ0 = −6°, with β = 1.2 and τvul = 0.01.

Fig. 14
Fig. 14

Photographs of sky and cloud color when the Sun is near the horizon: (a) Color of the horizon sky when the Sun is above the horizon and an opaque cloud layer shades the observer; (b) yellow and orange clouds when the Sun is 2° above the horizon.

Fig. 15
Fig. 15

Photograph showing color gradation on a thunderstorm (15 August 1988) facing the setting Sun over New York City. SKYCOLOR can only show one cloud height and viewer elevation angle per run.

Fig. 16
Fig. 16

Simulated appearances of the sky from horizon facing the Sun to viewer elevation angle, ϕv = 45°, with pure air (β = 1) and an open altocumulus deck with base, hcld = 8 km, at ϕcld = 3° without shadows for θ0 = 30° (left), 2° (center), and −3° (right). Each cloud consists of a core on bottom and a fringe on top.

Fig. 17
Fig. 17

Chromaticity diagrams with dotted contours of color purity illustrating the impact of shading. Top: Sky and cloud color for a cloud deck with base, hcld = 6 km and ϕcld = 2°, when the Sun is at θ0 = 20°. Thin lines represent sky color below cloud base, heavy lines represent cloud color. Sky and clouds with shadows are yellower and redder. Bottom: Sky color during a total solar eclipse when the Sun’s altitude is θ0 = 53° and distance to the penumbra =100 km for β = 1 (thick line) and β = 2.5, haer = 5 km (thin line).

Fig. 18
Fig. 18

Fisheye photograph of the sky during the 11 August 1999 total solar eclipse in Bagdere, Turkey showing spectral colors near the horizon. Reproduced with permission of Bob Yen, photographer. E-mail: http://www.comet-track.com/eclipse/.

Fig. 19
Fig. 19

Postvolcanic twilights: (a) Predawn sky over New York City in October 1991 after Mt. Pinatubo. (b) Postsunset sky over Sarasota, Fla., in January, 1984, after El Chichon.

Fig. 20
Fig. 20

Chromaticity diagram showing the impact of turbidity on volcanic twilight skies for θ0 = −6° and τvul = 0.01 when β = 1 (thick line) and β = 1.2 (thin line). Only a small amount of aerosols in stratosphere and troposphere turn the feeble light aloft from orange-red to purple.

Fig. 21
Fig. 21

SKYCOLOR simulated appearances of the sky for an observer at hobs = 10 km, for θs = θ0 = 15° to −6° (3° below the horizon) in clean air.

Fig. 22
Fig. 22

Photograph of a clear twilight sky seen from the air.

Fig. 23
Fig. 23

SKYCOLOR simulated appearances of the volcanic sky with τvul = 0.1 for θ0 = −6° showing the impact of turbidity and observer height. β = 1.5 at ho = 0 km (left panel) with purple sky near ϕv = 45°, β = 1.0 at ho = 0 km (center panel), and β = 1.0 at hobs = 10 km (right panel). The golden strip of sky seen by an observer at sea level changes to blue for an airborne observer, whose horizon appears at ϕv = −3°.

Tables (2)

Tables Icon

Table 1 Parameter Choices Available to a User of SKYCOLOR

Tables Icon

Table 2 Comparison of Simulated (fSKYCOLOR) and Measured (fv) Elevation Angles of Brightest Elevation Angle of Sky for Cases Measured by Lee12

Equations (3)

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RGB = 255 ( I ( ϕ , θ 0 ) I max ( ϕ , θ 00 ) ) 0.15 ,
τ rat = 0.5 [ 1 + tanh ( z p - 10500 + 100 T e x p 2650 T q ) ] , q = 66 T - 0.0004 x p ,             H scl = R d T g , q = 19000 e x p 1800000 ,             H scl = 2500 ,
P ( Ψ ) = 2 ( 1 + a 2 ) 1 + e - a π [ ( 1 - e - a π 2 ) e - a Ψ + e - a π 2 e - a ( π - Ψ ) ] .

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