Abstract

A long-standing assumption about the clear sky is that its colors and luminances are distributed symmetrically about the principal plane. As useful as this approximation is, our digital-image analyses show that clear-sky color and luminance routinely depart perceptibly from exact symmetry. These analyses reconfirm our earlier measurements with narrow field-of-view spectroradiometers [J. Opt. Soc. Am. A 18, 1325 (2001)], and they do so with much higher temporal and angular resolution across the entire sky dome.

© 2003 Optical Society of America

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References

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  1. F. C. Hooper, A. P. Brunger, C. S. Chan, “A clear sky model of diffuse sky radiance,” J. Sol. Energy Eng. 109, 9–14 (1987).
    [CrossRef]
  2. R. Perez, J. Michalsky, R. Seals, “Modelling sky luminance angular distribution for real sky conditions: experimental evaluation of existing algorithms,” J. Illum. Eng. Soc. 21, 84–92 (1992).
  3. F. M. F. Siala, M. A. Rosen, F. C. Hooper, “Models for the directional distribution of the diffuse sky radiance,” J. Sol. Energy Eng. 112, 102–109 (1990).
    [CrossRef]
  4. C. R. Prasad, A. K. Inamdar, H. P. Venkatesh, “Computation of diffuse radiation,” Sol. Energy 39, 521–532 (1987).
    [CrossRef]
  5. R. Perez, R. Seals, J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).
    [CrossRef]
  6. A. W. Harrison, C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy 40, 57–63 (1988).
    [CrossRef]
  7. E. M. Winter, T. W. Metcalf, L. B. Stotts, “Sky-radiance gradient measurements at narrow bands in the visible,” Appl. Opt. 34, 3681–3685 (1995).
    [CrossRef] [PubMed]
  8. G. Zibordi, K. J. Voss, “Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
    [CrossRef]
  9. C. Chain, D. Dumortier, M. Fontoynont, “A comprehensive model of luminance, correlated colour temperature and spectral distribution of skylight: comparison with experimental data,” Sol. Energy 65, 285–295 (1999).
    [CrossRef]
  10. S. Sekine, “Spectral distributions of clear sky light and their chromaticities,” J. Light Visual Environ. 15, 23–32 (1991).
    [CrossRef]
  11. R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–4638, 4959 (1994).
    [CrossRef] [PubMed]
  12. R. L. Lee, “Colorimetric calibration of a video digitizing system: algorithm and applications,” Color Res. Appl. 13, 180–186 (1988).
    [CrossRef]
  13. J. Hernández-Andrés, J. Romero, R. L. Lee, “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412–420 (2001).
    [CrossRef]
  14. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 306–310, 828–829.
  15. LI-1800 spectroradiometer from LI-COR. Incorporated, 4421 Superior Street, Lincoln, Neb. 68504-1327.
  16. PR-650 spectroradiometer from Photo Research, Incorporated, 9731 Topanga Canyon Place, Chatsworth, Calif. 91311.
  17. Nikkor fish-eye lens from Nikon USA, 1300 Walt Whitman Road, Melville, New York 11747.
  18. This particular lens is described in R. Kingslake, A History of the Photographic Lens (Academic, Boston, 1989), pp. 146–147. Although near-horizon skylight passes through a much greater thickness of its optical glass than does zenith skylight entering along its optical axis, this difference likely has negligible effects on our asymmetry results because spectral transmissivity in this lens is independent of rotation angle about its optical axis.
  19. ASTM Committee E-12, “Standard practice for computing the colors of objects by using the CIE system (E 308-95), in ASTM standards on color and appearance measurements” (American Society for Testing and Materials, Philadelphia, Pa., 1996), pp. 262–263.
  20. Photo Research, Incorporated, PR-650 SpectraScan SpectraColorimeter Operating Manual, Software Version 1.10 (Photo Research, Incorporated, Chatsworth, Calif., 1996), Sec. 3, p. 4.
  21. R. Gerharz, “Self polarization in refractive systems,” Optik 43, 471–485 (1975).
  22. R. L. Lee, “Digital imaging of clear-sky polarization,” Appl. Opt. 37, 1465–1476 (1998).
    [CrossRef]
  23. R. L. Lee, “Horizon brightness revisited: measurements and a model of clear-sky radiances,” Appl. Opt. 33, 4620–4628, 4959 (1994).
    [CrossRef] [PubMed]
  24. J. Romero, A. García-Beltrán, J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
    [CrossRef]
  25. J. Hernández-Andrés, J. Romero, A. García-Beltrán, J. L. Nieves, “Testing linear models on spectral daylight measurements,” Appl. Opt. 37, 971–977 (1998).
    [CrossRef]
  26. 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]
  27. J. Hernández-Andrés, J. Romero, J. L. Nieves, R. L. Lee, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
    [CrossRef]

2001 (2)

1999 (2)

C. Chain, D. Dumortier, M. Fontoynont, “A comprehensive model of luminance, correlated colour temperature and spectral distribution of skylight: comparison with experimental data,” Sol. Energy 65, 285–295 (1999).
[CrossRef]

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]

1998 (2)

1997 (1)

1995 (1)

1994 (2)

1993 (1)

R. Perez, R. Seals, J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).
[CrossRef]

1992 (1)

R. Perez, J. Michalsky, R. Seals, “Modelling sky luminance angular distribution for real sky conditions: experimental evaluation of existing algorithms,” J. Illum. Eng. Soc. 21, 84–92 (1992).

1991 (1)

S. Sekine, “Spectral distributions of clear sky light and their chromaticities,” J. Light Visual Environ. 15, 23–32 (1991).
[CrossRef]

1990 (1)

F. M. F. Siala, M. A. Rosen, F. C. Hooper, “Models for the directional distribution of the diffuse sky radiance,” J. Sol. Energy Eng. 112, 102–109 (1990).
[CrossRef]

1989 (1)

G. Zibordi, K. J. Voss, “Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
[CrossRef]

1988 (2)

A. W. Harrison, C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy 40, 57–63 (1988).
[CrossRef]

R. L. Lee, “Colorimetric calibration of a video digitizing system: algorithm and applications,” Color Res. Appl. 13, 180–186 (1988).
[CrossRef]

1987 (2)

C. R. Prasad, A. K. Inamdar, H. P. Venkatesh, “Computation of diffuse radiation,” Sol. Energy 39, 521–532 (1987).
[CrossRef]

F. C. Hooper, A. P. Brunger, C. S. Chan, “A clear sky model of diffuse sky radiance,” J. Sol. Energy Eng. 109, 9–14 (1987).
[CrossRef]

1975 (1)

R. Gerharz, “Self polarization in refractive systems,” Optik 43, 471–485 (1975).

Brunger, A. P.

F. C. Hooper, A. P. Brunger, C. S. Chan, “A clear sky model of diffuse sky radiance,” J. Sol. Energy Eng. 109, 9–14 (1987).
[CrossRef]

Chain, C.

C. Chain, D. Dumortier, M. Fontoynont, “A comprehensive model of luminance, correlated colour temperature and spectral distribution of skylight: comparison with experimental data,” Sol. Energy 65, 285–295 (1999).
[CrossRef]

Chan, C. S.

F. C. Hooper, A. P. Brunger, C. S. Chan, “A clear sky model of diffuse sky radiance,” J. Sol. Energy Eng. 109, 9–14 (1987).
[CrossRef]

Coombes, C. A.

A. W. Harrison, C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy 40, 57–63 (1988).
[CrossRef]

Dumortier, D.

C. Chain, D. Dumortier, M. Fontoynont, “A comprehensive model of luminance, correlated colour temperature and spectral distribution of skylight: comparison with experimental data,” Sol. Energy 65, 285–295 (1999).
[CrossRef]

Fontoynont, M.

C. Chain, D. Dumortier, M. Fontoynont, “A comprehensive model of luminance, correlated colour temperature and spectral distribution of skylight: comparison with experimental data,” Sol. Energy 65, 285–295 (1999).
[CrossRef]

García-Beltrán, A.

Gerharz, R.

R. Gerharz, “Self polarization in refractive systems,” Optik 43, 471–485 (1975).

Harrison, A. W.

A. W. Harrison, C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy 40, 57–63 (1988).
[CrossRef]

Hernández-Andrés, J.

Hooper, F. C.

F. M. F. Siala, M. A. Rosen, F. C. Hooper, “Models for the directional distribution of the diffuse sky radiance,” J. Sol. Energy Eng. 112, 102–109 (1990).
[CrossRef]

F. C. Hooper, A. P. Brunger, C. S. Chan, “A clear sky model of diffuse sky radiance,” J. Sol. Energy Eng. 109, 9–14 (1987).
[CrossRef]

Inamdar, A. K.

C. R. Prasad, A. K. Inamdar, H. P. Venkatesh, “Computation of diffuse radiation,” Sol. Energy 39, 521–532 (1987).
[CrossRef]

Kingslake, R.

This particular lens is described in R. Kingslake, A History of the Photographic Lens (Academic, Boston, 1989), pp. 146–147. Although near-horizon skylight passes through a much greater thickness of its optical glass than does zenith skylight entering along its optical axis, this difference likely has negligible effects on our asymmetry results because spectral transmissivity in this lens is independent of rotation angle about its optical axis.

Lee, R. L.

Metcalf, T. W.

Michalsky, J.

R. Perez, R. Seals, J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).
[CrossRef]

R. Perez, J. Michalsky, R. Seals, “Modelling sky luminance angular distribution for real sky conditions: experimental evaluation of existing algorithms,” J. Illum. Eng. Soc. 21, 84–92 (1992).

Nieves, J. L.

Perez, R.

R. Perez, R. Seals, J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).
[CrossRef]

R. Perez, J. Michalsky, R. Seals, “Modelling sky luminance angular distribution for real sky conditions: experimental evaluation of existing algorithms,” J. Illum. Eng. Soc. 21, 84–92 (1992).

Prasad, C. R.

C. R. Prasad, A. K. Inamdar, H. P. Venkatesh, “Computation of diffuse radiation,” Sol. Energy 39, 521–532 (1987).
[CrossRef]

Romero, J.

Rosen, M. A.

F. M. F. Siala, M. A. Rosen, F. C. Hooper, “Models for the directional distribution of the diffuse sky radiance,” J. Sol. Energy Eng. 112, 102–109 (1990).
[CrossRef]

Seals, R.

R. Perez, R. Seals, J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).
[CrossRef]

R. Perez, J. Michalsky, R. Seals, “Modelling sky luminance angular distribution for real sky conditions: experimental evaluation of existing algorithms,” J. Illum. Eng. Soc. 21, 84–92 (1992).

Sekine, S.

S. Sekine, “Spectral distributions of clear sky light and their chromaticities,” J. Light Visual Environ. 15, 23–32 (1991).
[CrossRef]

Siala, F. M. F.

F. M. F. Siala, M. A. Rosen, F. C. Hooper, “Models for the directional distribution of the diffuse sky radiance,” J. Sol. Energy Eng. 112, 102–109 (1990).
[CrossRef]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 306–310, 828–829.

Stotts, L. B.

Venkatesh, H. P.

C. R. Prasad, A. K. Inamdar, H. P. Venkatesh, “Computation of diffuse radiation,” Sol. Energy 39, 521–532 (1987).
[CrossRef]

Voss, K. J.

G. Zibordi, K. J. Voss, “Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
[CrossRef]

Winter, E. M.

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 306–310, 828–829.

Zibordi, G.

G. Zibordi, K. J. Voss, “Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
[CrossRef]

Appl. Opt. (6)

Color Res. Appl. (1)

R. L. Lee, “Colorimetric calibration of a video digitizing system: algorithm and applications,” Color Res. Appl. 13, 180–186 (1988).
[CrossRef]

J. Illum. Eng. Soc. (1)

R. Perez, J. Michalsky, R. Seals, “Modelling sky luminance angular distribution for real sky conditions: experimental evaluation of existing algorithms,” J. Illum. Eng. Soc. 21, 84–92 (1992).

J. Light Visual Environ. (1)

S. Sekine, “Spectral distributions of clear sky light and their chromaticities,” J. Light Visual Environ. 15, 23–32 (1991).
[CrossRef]

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

J. Sol. Energy Eng. (2)

F. C. Hooper, A. P. Brunger, C. S. Chan, “A clear sky model of diffuse sky radiance,” J. Sol. Energy Eng. 109, 9–14 (1987).
[CrossRef]

F. M. F. Siala, M. A. Rosen, F. C. Hooper, “Models for the directional distribution of the diffuse sky radiance,” J. Sol. Energy Eng. 112, 102–109 (1990).
[CrossRef]

Optik (1)

R. Gerharz, “Self polarization in refractive systems,” Optik 43, 471–485 (1975).

Remote Sens. Environ. (1)

G. Zibordi, K. J. Voss, “Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements,” Remote Sens. Environ. 27, 343–358 (1989).
[CrossRef]

Sol. Energy (4)

C. Chain, D. Dumortier, M. Fontoynont, “A comprehensive model of luminance, correlated colour temperature and spectral distribution of skylight: comparison with experimental data,” Sol. Energy 65, 285–295 (1999).
[CrossRef]

C. R. Prasad, A. K. Inamdar, H. P. Venkatesh, “Computation of diffuse radiation,” Sol. Energy 39, 521–532 (1987).
[CrossRef]

R. Perez, R. Seals, J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).
[CrossRef]

A. W. Harrison, C. A. Coombes, “Angular distribution of clear sky short wavelength radiance,” Sol. Energy 40, 57–63 (1988).
[CrossRef]

Other (7)

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 306–310, 828–829.

LI-1800 spectroradiometer from LI-COR. Incorporated, 4421 Superior Street, Lincoln, Neb. 68504-1327.

PR-650 spectroradiometer from Photo Research, Incorporated, 9731 Topanga Canyon Place, Chatsworth, Calif. 91311.

Nikkor fish-eye lens from Nikon USA, 1300 Walt Whitman Road, Melville, New York 11747.

This particular lens is described in R. Kingslake, A History of the Photographic Lens (Academic, Boston, 1989), pp. 146–147. Although near-horizon skylight passes through a much greater thickness of its optical glass than does zenith skylight entering along its optical axis, this difference likely has negligible effects on our asymmetry results because spectral transmissivity in this lens is independent of rotation angle about its optical axis.

ASTM Committee E-12, “Standard practice for computing the colors of objects by using the CIE system (E 308-95), in ASTM standards on color and appearance measurements” (American Society for Testing and Materials, Philadelphia, Pa., 1996), pp. 262–263.

Photo Research, Incorporated, PR-650 SpectraScan SpectraColorimeter Operating Manual, Software Version 1.10 (Photo Research, Incorporated, Chatsworth, Calif., 1996), Sec. 3, p. 4.

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Figures (9)

Fig. 1
Fig. 1

Fish-eye photograph of a clear sky in Granada, Spain, on 21 May 2000 at 10:24 UTC. Unrefracted solar elevation h 0 = 60.0° above the astronomical horizon, and the photograph is centered on the zenith.

Fig. 2
Fig. 2

Clear-sky color-difference map derived from Fig. 1. Overlaid on this map are the solar meridian (or clear-sky principal plane) with ϕrel = 0° and three meridians corresponding to ϕrel = 45°, 90°, and 315°. Because we are looking up at the zenith rather than down at the nadir, ϕrel increases counterclockwise in this figure. Each map contour spans 5 units of the CIELUV color difference ΔEuv*. The most chromatic skylight colors are plotted in red (ΔEuv* = 160) near h = 45°, ϕrel = 180°; the least-chromatic skylight colors (ΔEuv* = 0) are near the Sun.

Fig. 3
Fig. 3

Clear-sky luminance map derived from Fig. 1. Each map contour spans a range of luminances ΔL v = 2%. The darkest skylight colors (ΔL v = 0%) are plotted in red near h = 45°, ϕrel = 180°; the brightest skylight colors (ΔL v = 60%) are near the Sun.

Fig. 4
Fig. 4

Fish-eye photograph of a clear sky in Granada, Spain, on 9 April 2001 at 18:50 UTC. Solar elevation h 0 = -2.1° (i.e., during civil twilight), and the photograph is centered on the zenith.

Fig. 5
Fig. 5

Clear-sky color-difference map derived from Fig. 4, with each map contour spanning ΔEuv* = 6.

Fig. 6
Fig. 6

Clear-sky luminance map derived from Fig. 4, with each map contour spanning ΔL v = 2%.

Fig. 7
Fig. 7

Fish-eye photograph of a clear sky in Granada, Spain, on 10 April 2001 at 15:36 UTC. Solar elevation h 0 = 36.1°, and the photograph is centered on the zenith.

Fig. 8
Fig. 8

Clear-sky color-difference map derived from Fig. 7, with each map contour spanning ΔEuv* = 6.

Fig. 9
Fig. 9

Clear-sky luminance map derived from Fig. 7, with each map contour spanning ΔL v = 2%.

Tables (1)

Tables Icon

Table 1 Summary Statistics for ΔLv(%), Δu* v*, and ΔEuv* in Figs. 1, 4, and 7 a

Equations (1)

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

ΔEuv*= ΔL*2+ Δu*2+ Δv*1/2.

Metrics