Abstract

Time-series measurements of daylight (skylight plus direct sunlight) spectra beneath overcast skies reveal an unexpectedly wide gamut of pastel colors. Analyses of these spectra indicate that at visible wavelengths, overcasts are far from spectrally neutral transmitters of the daylight incident on their tops. Colorimetric analyses show that overcasts make daylight bluer and that the amount of bluing increases with cloud optical depth. Simulations using the radiative-transfer model MODTRAN4 help explain the observed bluing: multiple scattering within optically thick clouds greatly enhances spectrally selective absorption by water droplets. However, other factors affecting overcast colors seen from below range from minimal (cloud-top heights) to moot (surface colors).

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. A. Kimball, S. B. Idso, J. K. Aase, “A model of thermal radiation from partly cloudy and overcast skies,” Water Resour. Res. 18, 931–936 (1982).
    [CrossRef]
  2. Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
    [CrossRef]
  3. C. Erlick, J. E. Frederick, V. K. Saxena, B. N. Wenny, “Atmospheric transmission in the ultraviolet and visible: aerosols in cloudy atmospheres,” J. Geophys. Res. 103, 31541–31555 (1998).
    [CrossRef]
  4. W. E. K. Middleton, “The color of the overcast sky,” J. Opt. Soc. Am. 44, 793–798 (1954).
    [CrossRef]
  5. V. Hisdal, “Spectral distribution of global and diffuse solar radiation in Ny-Ålesund, Spitsbergen,” Polar Res. 5, 1–27 (1987).
    [CrossRef]
  6. J. Hernández-Andrés, R. L. Lee, J. Romero, J. L. Nieves, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
    [CrossRef]
  7. E. M. Feigelson, Radiation in a Cloudy Atmosphere (Reidel, Dordrecht, 1984), pp. 52–62, 164–169.
  8. S. Nann, C. Riordan, “Solar spectral irradiance under clear and cloudy skies: measurements and a semiempirical model,” J. Appl. Meteorol. 30, 447–462 (1991).
    [CrossRef]
  9. D. A. Siegel, T. K. Westberry, J. C. Ohlmann, “Cloud color and ocean radiant heating,” J. Climate 12, 1101–1116 (1999).
    [CrossRef]
  10. Spatial Distribution of Daylight—CIE Standard Overcast Sky and Clear Sky, CIE Standard S 003/E-1996 (Commission Internationale de l’Eclairage, Vienna, 1996), p. 3.
  11. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 144–145.
  12. Sometimes this spectral assumption is explicit, as in A. J. Preetham, P. Shirley, B. Smits, “A practical analytic model for daylight,” in SIGGRAPH 99 Conference Proceedings, A. Rockwood, ed. (Association for Computing Machinery, New York, 1999), pp. 91–100.
    [CrossRef]
  13. T. S. Glickman, ed., Glossary of Meteorology,2nd ed. (American Meteorological Society, Boston, 2000), p. 550.
  14. Although the CIE 1976 UCS diagram is itself perceptually isotropic, note that in order to show as much detail as possible, we make the ordinate and abscissa scales differ in Fig. 1 and later chromaticity diagrams.
  15. PR-650 spectroradiometer from Photo Research, Inc., 9731 Topanga Canyon Place, Chatsworth, Calif. 91311. According to Photo Research, at specified radiance levels a properly calibrated PR-650 measures luminance and radiance accurate to within ±4%, has a spectral accuracy of ±2 nm, and its CIE 1931 colorimetric errors are x 0.001, y 0.001 for a 2856 K blackbody (CIE standard illuminant A).
  16. R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–4638, 4959 (1994). Gamut ĝ ranges from 0 for constant chromaticity to 1 for the spectrum locus, and thus represents the fraction of the CIE diagram that a given chromaticity curve spans.
    [CrossRef] [PubMed]
  17. R. L. Lee, J. Hernández-Andrés, “Measuring and modeling twilight’s purple light,” Appl. Opt. 42, 445–457 (2003).
    [CrossRef] [PubMed]
  18. Reference 11, pp. 306–310.
  19. Reference 11, pp. 306–310. Here we follow convention and set the JND equal to the semimajor axis length of the MacAdam color-matching ellipse at the given chromaticity.
  20. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [CrossRef]
  21. J. Hernández-Andrés, R. L. Lee, J. Romero, “Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities,” Appl. Opt. 38, 5703–5709 (1999).
    [CrossRef]
  22. Olympus Camedia E-10 User’s Manual (Olympus Optical Co., Ltd., Tokyo, 2000), p. 102.
  23. Reference 11, pp. 224–225.
  24. Our experience is that cloud tops occur approximately where radiosonde relative humidity falls below 96% as altitude z increases. Using this admittedly imperfect criterion, for 24 different overcasts our mean cloud-top z(top) = 1700 m above sea level, median z(top) = 1445 m, and the z(top) standard deviation = 961 m.
  25. R. Sekuler, R. Blake, Perception (Knopf, New York, 1985), pp. 189–192.
  26. B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).
  27. C. F. Bohren, A. B. Fraser, “Green thunderstorms,” Bull. Am. Meteorol. Soc. 74, 2185–2193 (1993).
    [CrossRef]
  28. C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).Our Eq. (2) is derived from Bohren’s Eq. (15) for T as a function of τ, and we use Bohren’s value of g= 0.85 for visible-wavelength scattering by cloud droplets.
    [CrossRef]
  29. MODTRAN uses a plane-parallel atmosphere to calculate multiple-scattering contributions to daylight and skylight, and when h0≤ 0° the model produces nonphysical spectra in the visible.
  30. C. F. Bohren, A. B. Fraser, “Colors of the sky,” Phys. Teach. 23, 267–272 (1985).
    [CrossRef]
  31. Based on radiosonde data from nearby Dulles International Airport (code IAD), we estimated cloud Δz= 0.2 km and 1.0 km on 2-6-03 and 2-17-03, respectively. Perhaps surprisingly, using rλ for green grass in the 2-6-03 wintertime landscape was not unrealistic (this choice aids comparison with Middleton’s results in Fig. 18). Even though we do not know the actual mean Owings rλspectrum on 2-6-03, MODTRAN predicted negligible differences in overcast chromaticities when we tried several different materials (e.g., tree bark, a mixture of dead and living vegetation) for the snow-free surface’s rλ.

2004

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

2003

2001

1999

1998

Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
[CrossRef]

C. Erlick, J. E. Frederick, V. K. Saxena, B. N. Wenny, “Atmospheric transmission in the ultraviolet and visible: aerosols in cloudy atmospheres,” J. Geophys. Res. 103, 31541–31555 (1998).
[CrossRef]

1994

R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–4638, 4959 (1994). Gamut ĝ ranges from 0 for constant chromaticity to 1 for the spectrum locus, and thus represents the fraction of the CIE diagram that a given chromaticity curve spans.
[CrossRef] [PubMed]

1993

C. F. Bohren, A. B. Fraser, “Green thunderstorms,” Bull. Am. Meteorol. Soc. 74, 2185–2193 (1993).
[CrossRef]

1991

S. Nann, C. Riordan, “Solar spectral irradiance under clear and cloudy skies: measurements and a semiempirical model,” J. Appl. Meteorol. 30, 447–462 (1991).
[CrossRef]

1987

V. Hisdal, “Spectral distribution of global and diffuse solar radiation in Ny-Ålesund, Spitsbergen,” Polar Res. 5, 1–27 (1987).
[CrossRef]

C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).Our Eq. (2) is derived from Bohren’s Eq. (15) for T as a function of τ, and we use Bohren’s value of g= 0.85 for visible-wavelength scattering by cloud droplets.
[CrossRef]

1985

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

1982

B. A. Kimball, S. B. Idso, J. K. Aase, “A model of thermal radiation from partly cloudy and overcast skies,” Water Resour. Res. 18, 931–936 (1982).
[CrossRef]

1964

1954

Aase, J. K.

B. A. Kimball, S. B. Idso, J. K. Aase, “A model of thermal radiation from partly cloudy and overcast skies,” Water Resour. Res. 18, 931–936 (1982).
[CrossRef]

Batey, M.

Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
[CrossRef]

Blake, R.

R. Sekuler, R. Blake, Perception (Knopf, New York, 1985), pp. 189–192.

Bohren, C. F.

C. F. Bohren, A. B. Fraser, “Green thunderstorms,” Bull. Am. Meteorol. Soc. 74, 2185–2193 (1993).
[CrossRef]

C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).Our Eq. (2) is derived from Bohren’s Eq. (15) for T as a function of τ, and we use Bohren’s value of g= 0.85 for visible-wavelength scattering by cloud droplets.
[CrossRef]

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

Daniel, J. S.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Dutton, E. G.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Erlick, C.

C. Erlick, J. E. Frederick, V. K. Saxena, B. N. Wenny, “Atmospheric transmission in the ultraviolet and visible: aerosols in cloudy atmospheres,” J. Geophys. Res. 103, 31541–31555 (1998).
[CrossRef]

Eubank, C. S.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Feigelson, E. M.

E. M. Feigelson, Radiation in a Cloudy Atmosphere (Reidel, Dordrecht, 1984), pp. 52–62, 164–169.

Fraser, A. B.

C. F. Bohren, A. B. Fraser, “Green thunderstorms,” Bull. Am. Meteorol. Soc. 74, 2185–2193 (1993).
[CrossRef]

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

Frederick, J. E.

C. Erlick, J. E. Frederick, V. K. Saxena, B. N. Wenny, “Atmospheric transmission in the ultraviolet and visible: aerosols in cloudy atmospheres,” J. Geophys. Res. 103, 31541–31555 (1998).
[CrossRef]

Freidenreich, S. M.

Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
[CrossRef]

Gutman, S. I.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Harshvardhan,

Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
[CrossRef]

Hernández-Andrés, J.

Hisdal, V.

V. Hisdal, “Spectral distribution of global and diffuse solar radiation in Ny-Ålesund, Spitsbergen,” Polar Res. 5, 1–27 (1987).
[CrossRef]

Holub, K. H.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Idso, S. B.

B. A. Kimball, S. B. Idso, J. K. Aase, “A model of thermal radiation from partly cloudy and overcast skies,” Water Resour. Res. 18, 931–936 (1982).
[CrossRef]

Judd, D. B.

Kimball, B. A.

B. A. Kimball, S. B. Idso, J. K. Aase, “A model of thermal radiation from partly cloudy and overcast skies,” Water Resour. Res. 18, 931–936 (1982).
[CrossRef]

Langford, A. O.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Lee, R. L.

MacAdam, D. L.

Middleton, W. E. K.

Nann, S.

S. Nann, C. Riordan, “Solar spectral irradiance under clear and cloudy skies: measurements and a semiempirical model,” J. Appl. Meteorol. 30, 447–462 (1991).
[CrossRef]

Nieves, J. L.

Ohlmann, J. C.

D. A. Siegel, T. K. Westberry, J. C. Ohlmann, “Cloud color and ocean radiant heating,” J. Climate 12, 1101–1116 (1999).
[CrossRef]

Portmann, R. W.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Ramaswamy, V.

Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
[CrossRef]

Ridgway, W.

Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
[CrossRef]

Riordan, C.

S. Nann, C. Riordan, “Solar spectral irradiance under clear and cloudy skies: measurements and a semiempirical model,” J. Appl. Meteorol. 30, 447–462 (1991).
[CrossRef]

Romero, J.

Saxena, V. K.

C. Erlick, J. E. Frederick, V. K. Saxena, B. N. Wenny, “Atmospheric transmission in the ultraviolet and visible: aerosols in cloudy atmospheres,” J. Geophys. Res. 103, 31541–31555 (1998).
[CrossRef]

Sekuler, R.

R. Sekuler, R. Blake, Perception (Knopf, New York, 1985), pp. 189–192.

Siegel, D. A.

D. A. Siegel, T. K. Westberry, J. C. Ohlmann, “Cloud color and ocean radiant heating,” J. Climate 12, 1101–1116 (1999).
[CrossRef]

Sierk, B.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Solomon, S.

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 144–145.

Wenny, B. N.

C. Erlick, J. E. Frederick, V. K. Saxena, B. N. Wenny, “Atmospheric transmission in the ultraviolet and visible: aerosols in cloudy atmospheres,” J. Geophys. Res. 103, 31541–31555 (1998).
[CrossRef]

Westberry, T. K.

D. A. Siegel, T. K. Westberry, J. C. Ohlmann, “Cloud color and ocean radiant heating,” J. Climate 12, 1101–1116 (1999).
[CrossRef]

Wyszecki, G.

D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
[CrossRef]

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 144–145.

Am. J. Phys.

C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).Our Eq. (2) is derived from Bohren’s Eq. (15) for T as a function of τ, and we use Bohren’s value of g= 0.85 for visible-wavelength scattering by cloud droplets.
[CrossRef]

Appl. Opt.

R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–4638, 4959 (1994). Gamut ĝ ranges from 0 for constant chromaticity to 1 for the spectrum locus, and thus represents the fraction of the CIE diagram that a given chromaticity curve spans.
[CrossRef] [PubMed]

J. Hernández-Andrés, R. L. Lee, J. Romero, “Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities,” Appl. Opt. 38, 5703–5709 (1999).
[CrossRef]

R. L. Lee, J. Hernández-Andrés, “Measuring and modeling twilight’s purple light,” Appl. Opt. 42, 445–457 (2003).
[CrossRef] [PubMed]

Bull. Am. Meteorol. Soc.

C. F. Bohren, A. B. Fraser, “Green thunderstorms,” Bull. Am. Meteorol. Soc. 74, 2185–2193 (1993).
[CrossRef]

J. Appl. Meteorol.

S. Nann, C. Riordan, “Solar spectral irradiance under clear and cloudy skies: measurements and a semiempirical model,” J. Appl. Meteorol. 30, 447–462 (1991).
[CrossRef]

J. Climate

D. A. Siegel, T. K. Westberry, J. C. Ohlmann, “Cloud color and ocean radiant heating,” J. Climate 12, 1101–1116 (1999).
[CrossRef]

J. Geophys. Res.

Harshvardhan, W. Ridgway, V. Ramaswamy, S. M. Freidenreich, M. Batey, “Spectral characteristics of solar near-infrared absorption in cloudy atmospheres,” J. Geophys. Res. 103, 28793–28799 (1998).
[CrossRef]

C. Erlick, J. E. Frederick, V. K. Saxena, B. N. Wenny, “Atmospheric transmission in the ultraviolet and visible: aerosols in cloudy atmospheres,” J. Geophys. Res. 103, 31541–31555 (1998).
[CrossRef]

B. Sierk, S. Solomon, J. S. Daniel, R. W. Portmann, S. I. Gutman, A. O. Langford, C. S. Eubank, E. G. Dutton, K. H. Holub, “Field measurements of water vapor continuum absorption in the visible and near-infrared,” J. Geophys. Res. 109 (part 8), D08307 (2004).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Phys. Teach.

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

Polar Res.

V. Hisdal, “Spectral distribution of global and diffuse solar radiation in Ny-Ålesund, Spitsbergen,” Polar Res. 5, 1–27 (1987).
[CrossRef]

Water Resour. Res.

B. A. Kimball, S. B. Idso, J. K. Aase, “A model of thermal radiation from partly cloudy and overcast skies,” Water Resour. Res. 18, 931–936 (1982).
[CrossRef]

Other

E. M. Feigelson, Radiation in a Cloudy Atmosphere (Reidel, Dordrecht, 1984), pp. 52–62, 164–169.

Based on radiosonde data from nearby Dulles International Airport (code IAD), we estimated cloud Δz= 0.2 km and 1.0 km on 2-6-03 and 2-17-03, respectively. Perhaps surprisingly, using rλ for green grass in the 2-6-03 wintertime landscape was not unrealistic (this choice aids comparison with Middleton’s results in Fig. 18). Even though we do not know the actual mean Owings rλspectrum on 2-6-03, MODTRAN predicted negligible differences in overcast chromaticities when we tried several different materials (e.g., tree bark, a mixture of dead and living vegetation) for the snow-free surface’s rλ.

MODTRAN uses a plane-parallel atmosphere to calculate multiple-scattering contributions to daylight and skylight, and when h0≤ 0° the model produces nonphysical spectra in the visible.

Reference 11, pp. 306–310.

Reference 11, pp. 306–310. Here we follow convention and set the JND equal to the semimajor axis length of the MacAdam color-matching ellipse at the given chromaticity.

Olympus Camedia E-10 User’s Manual (Olympus Optical Co., Ltd., Tokyo, 2000), p. 102.

Reference 11, pp. 224–225.

Our experience is that cloud tops occur approximately where radiosonde relative humidity falls below 96% as altitude z increases. Using this admittedly imperfect criterion, for 24 different overcasts our mean cloud-top z(top) = 1700 m above sea level, median z(top) = 1445 m, and the z(top) standard deviation = 961 m.

R. Sekuler, R. Blake, Perception (Knopf, New York, 1985), pp. 189–192.

Spatial Distribution of Daylight—CIE Standard Overcast Sky and Clear Sky, CIE Standard S 003/E-1996 (Commission Internationale de l’Eclairage, Vienna, 1996), p. 3.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 144–145.

Sometimes this spectral assumption is explicit, as in A. J. Preetham, P. Shirley, B. Smits, “A practical analytic model for daylight,” in SIGGRAPH 99 Conference Proceedings, A. Rockwood, ed. (Association for Computing Machinery, New York, 1999), pp. 91–100.
[CrossRef]

T. S. Glickman, ed., Glossary of Meteorology,2nd ed. (American Meteorological Society, Boston, 2000), p. 550.

Although the CIE 1976 UCS diagram is itself perceptually isotropic, note that in order to show as much detail as possible, we make the ordinate and abscissa scales differ in Fig. 1 and later chromaticity diagrams.

PR-650 spectroradiometer from Photo Research, Inc., 9731 Topanga Canyon Place, Chatsworth, Calif. 91311. According to Photo Research, at specified radiance levels a properly calibrated PR-650 measures luminance and radiance accurate to within ±4%, has a spectral accuracy of ±2 nm, and its CIE 1931 colorimetric errors are x 0.001, y 0.001 for a 2856 K blackbody (CIE standard illuminant A).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (20)

Fig. 1
Fig. 1

Portion of the CIE 1976 UCS diagram, showing temporal trends in stratus (St) and stratocumulus (Sc) overcast chromaticities measured at the U.S. Naval Academy in Annapolis, Maryland (USNA) on 4-21-2003 and at the University of Granada in Granada, Spain on 11-8-03. Chromaticities are calculated from horizontal spectral irradiances Eλ. For comparison, we also show chromaticities from two cloudless days at USNA (9-5-02, 9-10-03). On each day, unrefracted Sun elevation h0 ranges from 30.0°–36.3°.

Fig. 2
Fig. 2

Spectrally integrated horizontal irradiances E versus h0 for Fig. 1’s two overcasts. Integrals are calculated from 380–780 nm in 4 nm steps.

Fig. 3
Fig. 3

Scatterplot of overcast u′, v′ chromaticities calculated from zenith spectral radiances Lλ at Owings, Maryland, during stratus overcasts on 4-17-03, 5-22-03, and 6-16-03; h0 ranges from 46.6°–60.3°. The length of the bar labeled “1 JND” equals the local MacAdam just-noticeable difference in chromaticity.

Fig. 4
Fig. 4

Spectrally integrated zenith radiances L versus h0 for Fig. 3’s three stratus overcasts at Owings. The spectroradiometer’s measurement FOV is 1°, and integrals are calculated from 380–780 nm in 4 nm steps.

Fig. 5
Fig. 5

Composite fisheye image of a bright stratus overcast (left half, E = 24.3 W m−2) and a much darker stratocumulus overcast (right half, E ~ 3.6 W m−2) at USNA on 11-18-03 and 11-19-03, respectively. Note that the darker overcast is distinctly bluer. Although exposures differ, in both original photographs the digital camera’s white-balance setting was the same and h0 ~ 18.5°.

Fig. 6
Fig. 6

Correlated color temperature (CCT) in Kelvins versus h0 for all 4278 of our horizontal Eλ spectra for overcasts; individual CCTs are plotted as dots. The right-hand ordinate gives equivalent values of inverse CCT, which is measured in inverse mega-Kelvins (106/CCT; inverse CCT unit is MK−1). The mean CCT curve is calculated using bins that are 2° wide in h0, and each error bar spans 2 standard deviations σ at the given h0.

Fig. 7
Fig. 7

Normalized horizontal irradiances Eλ for the two daytime spectra having the maximum and minimum CCTs in our data (9316 K and 5799 K). These spectra yield our colorimetric extremes in daytime overcasts. Each original spectrum is normalized by its sum; to convert normalized to absolute irradiances, multiply the 11-22-03 Eλ by 0.814 W m−2 nm−1 and the 11-8-03 Eλ by 16.3 W m−2 nm−1.

Fig. 8
Fig. 8

Histogram of inverse CCT for our 4278 overcast Eλ spectra. The modal interval is 154–156 MK−1, and each bin is 2 MK−1 wide.

Fig. 9
Fig. 9

Mean T(λ) transmission spectra for Eλ spectra measured at USNA during stratus overcasts on 4-4, 4-8, and 4-21-03; h0 ranges from 40.1°–57.7°. N = 25 and N = 17 irradiance spectra were used to calculate the mean T(λ, low) and T(λ, high) spectra, respectively. Each error bar spans 2σ at the given wavelength. Best-fit equations are for the interval 400 ≤ λ ≤ 680 nm, with proportionality constants k1 = 4.077 and k2 = 1.946.

Fig. 10
Fig. 10

Mean T(λ) spectra for Eλ spectra measured at USNA during a stratocumulus overcast on 3-19-03; h0 ranges from 41.9°–50.5°. N = 15 and N = 19 irradiance spectra were used to calculate the mean low- and high-transmissivity T(λ) spectra, respectively. Each error bar spans 2σ at the given wavelength, and for clarity we show bars only for the T(λ, high) curve. Best-fit equations are for the interval 400 ≤ λ ≤ 680 nm, with proportionality constants k3 = 4.136 and k4 = 3.943.

Fig. 11
Fig. 11

MODTRAN4 simulated T(λ) spectra for the model’s default stratus overcast when its clouds are 100 m or 670 m thick. In both cases, h0 = 45°, and cloud base is 330 m above the surface. For the thicker overcast, we calculate T(λ) using combined direct-beam and diffuse irradiances at the surface, but we switch to irradiances calculated at cloud top and bottom for the thinner overcast (see Eq. (1)). Best-fit equations are for the interval 380 ≤ λ ≤ 780 nm, with proportionality constants k5 = 1.069 and k6 = 2.544.

Fig. 12
Fig. 12

Comparison of simulated MODTRAN T(λ) for the direct-beam and diffuse components in Fig. 11’s 100 m thick stratus overcast. T(λ, diffuse) > 1 because the diffuse irradiances at cloud bottom (the numerator in Eq. (1)) include energy scattered from the direct solar beam, whereas diffuse irradiances at cloud top exclude direct sunlight.

Fig. 13
Fig. 13

MODTRAN visible-wavelength spectra of absorption cross section Cabs and extinction cross section Cext for stratus droplets of radius a. Cext is normalized by its value at 550 nm and is proportional to 2πa2. Note that Cabs is scaled logarithmically.

Fig. 14
Fig. 14

MODTRAN simulation of horizontal irradiances E at the surface as a function of cloud thickness Δz. For normal optical depth τ, the E(τ) curve is not exactly congruent with the Ez) curve because we calculate the former independent of MODTRAN using Eqs. (1) and (2).

Fig. 15
Fig. 15

MODTRAN simulations of stratus overcast u′, v′ chromaticities calculated from Eλ as functions of Δz and h0. The dashed h0 curve sets Δz = 1 km, and the solid Δz curve sets h0 = 45°. The underlying Lambertian surface has a constant spectral reflectance rλ = 0.2. During the daytime, simulated overcast colors grow steadily bluer as Δz increases and h0 decreases.

Fig. 16
Fig. 16

MODTRAN simulations of stratus overcast u′, v′ chromaticities calculated from Eλ as functions of Δz for the cases of fixed-altitude tops z(top) and fixed-altitude bottoms z(base). Although the Case 2 chromaticities (fixed, high-altitude z(top)) are slightly bluer, in both cases bluing of daylight beneath the overcast depends much more strongly on cloud Δz.

Fig. 17
Fig. 17

Temporal trends in overcast u′, v′ chromaticities calculated from Eλ near Marion Center, Pennsylvania, on 10-12-02 and at Granada on 11-15-03; h0 ranges from 5.0°–12.3°.

Fig. 18
Fig. 18

MODTRAN simulations of stratus overcast u′, v′ chromaticities at the zenith as functions of cloud Δz and the underlying surface’s spectral reflectance rλ. The thick arrow indicates MODTRAN’s prediction of the chromaticity shift caused by changing the surface from grass to snow for Fig. 19’s observed changes in cloud Δz. For historical purposes, we also include overcast chromaticities simulated by Middleton.4

Fig. 19
Fig. 19

Scatterplot of overcast u′, v′ chromaticities calculated from zenith Lλ at Owings during stratus overcasts on 2-6-03 and 2-17-03; h0 ranges from 14.4°–20.5°. Only on 2-17-03 was the ground snow-covered. Compare these measured chromaticities with MODTRAN simulations in Fig. 18.

Fig. 20
Fig. 20

Scatterplot of overcast u′, v′ chromaticities calculated from zenith Lλ at Owings during stratus overcasts on 1-1-03, 1-2-03, and 1-16-03. The ground was snow-free on all days; h0 ranges from 12.3°–20.2°.

Tables (2)

Tables Icon

Table 1 Geographic Details of Our Measurement Sites

Tables Icon

Table 2 Mean Overcast Chromaticities and Chromaticity Gamuts

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

T ( λ ) = E ( λ , OVC ) E ( λ , CLR )
τ = 2 ( T - 1 - 1 ) ( 1 - r ) ( 1 - g ) ,

Metrics