Abstract

As part of our ongoing research into the clear daytime sky’s visible structure, we analyze over 1500 skylight spectra measured during a seven-month period in Granada, Spain. We use spectral radiances measured within 3° fields of view (FOV’s) to define colorimetric characteristics along four sky meridians: the solar meridian and three meridians at azimuths of 45°, 90°, and 315° relative to it. The resulting clear-sky chromaticities in 44 different view directions (1) are close to but do not coincide with the CIE daylight locus, (2) form V-shaped meridional chromaticity curves along it (as expected from theory), and (3) have correlated color temperatures (CCT’s) ranging from 3800 K to ∞ K. We also routinely observe that sky color and luminance are asymmetric about the solar meridian, usually perceptibly so. A principal-components analysis shows that three vectors are required for accurate clear-sky colorimetry, whereas six are needed for spectral analyses.

© 2001 Optical Society of America

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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 (1)

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 (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).
[CrossRef]

D. H. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
[CrossRef] [PubMed]

1991 (2)

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

S. Nann, C. Riordan, “Solar spectra irradiance under clear and cloudy skies: measurements and semiempirical model,” J. Appl. Meteorol. 30, 447–462 (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 (4)

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]

C. Riordan, D. R. Myers, R. Hulstrom, W. Marion, C. Jennings, C. Whitaker, “Spectral solar radiation data base at SERI,” Sol. Energy 20, 67–79 (1989).
[CrossRef]

D. R. Myers, “Estimates of uncertainty for measured spectra in the SERI spectral solar radiation database,” Sol. Energy 43, 347–353 (1989).
[CrossRef]

J. P. S. Parkinnen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
[CrossRef]

1988 (2)

A. W. Harrison, C. A. Coombes, “Angular distribution ofclear 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]

1986 (1)

1985 (1)

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

1978 (1)

1973 (1)

M. P. Thekaekara, “Solar energy outside the earth’s atmosphere,” Sol. Energy 14, 109–127 (1973).
[CrossRef]

1971 (1)

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

1968 (2)

V. D. P. Sastri, S. R. Das, “Typical spectral distributions and color for tropical daylight,” J. Opt. Soc. Am. 58, 391–398 (1968).
[CrossRef]

A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).

1967 (1)

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull Electrotech. Lab. 31, 1127–1135 (1967).

1966 (1)

1965 (2)

S. R. Das, V. D. P. Sastri, “Spectral distribution and color of tropical daylight,” J. Opt. Soc. Am. 55, 319–323 (1965).
[CrossRef]

J. F. Collins, “The color temperature of daylight,” Br. J. Appl. Phys. 16, 527–532 (1965).
[CrossRef]

1964 (2)

1963 (3)

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

G. J. Chamberlin, A. Lawrence, A. A. Belbin, “Observations on the related colour temperature of north daylight in southern England,” Light Light. 56, 70–72 (1963).

Y. Nayatani, G. Wyszecki, “Color of daylight from north sky,” J. Opt. Soc. Am. 53, 626–629 (1963).
[CrossRef]

Belbin, A. A.

G. J. Chamberlin, A. Lawrence, A. A. Belbin, “Observations on the related colour temperature of north daylight in southern England,” Light Light. 56, 70–72 (1963).

Bohren, C. F.

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

Boshoff, M. C.

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]

Chamberlin, G. J.

G. J. Chamberlin, A. Lawrence, A. A. Belbin, “Observations on the related colour temperature of north daylight in southern England,” Light Light. 56, 70–72 (1963).

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]

Collins, J. F.

J. F. Collins, “The color temperature of daylight,” Br. J. Appl. Phys. 16, 527–532 (1965).
[CrossRef]

Condit, H. R.

Coombes, C. A.

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

Curcio, J. A.

G. L. Knestrick, J. A. Curcio, “Measurements of the spectral radiance of the horizon sky,” (U.S. Naval Research Laboratory, Washington, D.C., 1967).

Das, S. R.

Dixon, E. R.

du Toit, A. G.

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]

Fraser, A. B.

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

Garci´a-Beltrán, A.

Grum, F.

Hallikainen, J.

Harrison, A. W.

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

Henderson, S. T.

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

S. T. Henderson, Daylight and Its Spectrum (American Elsevier, New York, 1970), pp. 173–184.

Hernández-Andrés, J.

Hitani, M.

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull Electrotech. Lab. 31, 1127–1135 (1967).

Hodgkiss, D.

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

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]

Hulstrom, R.

C. Riordan, D. R. Myers, R. Hulstrom, W. Marion, C. Jennings, C. Whitaker, “Spectral solar radiation data base at SERI,” Sol. Energy 20, 67–79 (1989).
[CrossRef]

Inamdar, A. K.

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

Jaaskelainen, T.

Jennings, C.

C. Riordan, D. R. Myers, R. Hulstrom, W. Marion, C. Jennings, C. Whitaker, “Spectral solar radiation data base at SERI,” Sol. Energy 20, 67–79 (1989).
[CrossRef]

Judd, D. B.

Knestrick, G. L.

G. L. Knestrick, J. A. Curcio, “Measurements of the spectral radiance of the horizon sky,” (U.S. Naval Research Laboratory, Washington, D.C., 1967).

Kok, C. J.

Lawrence, A.

G. J. Chamberlin, A. Lawrence, A. A. Belbin, “Observations on the related colour temperature of north daylight in southern England,” Light Light. 56, 70–72 (1963).

Lee, R. L.

MacAdam, D. L.

Maloney, L. T.

Manamohanan, S. B.

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

Marimont, D. H.

Marion, W.

C. Riordan, D. R. Myers, R. Hulstrom, W. Marion, C. Jennings, C. Whitaker, “Spectral solar radiation data base at SERI,” Sol. Energy 20, 67–79 (1989).
[CrossRef]

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).
[CrossRef]

Minato, H.

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull Electrotech. Lab. 31, 1127–1135 (1967).

Myers, D. R.

D. R. Myers, “Estimates of uncertainty for measured spectra in the SERI spectral solar radiation database,” Sol. Energy 43, 347–353 (1989).
[CrossRef]

C. Riordan, D. R. Myers, R. Hulstrom, W. Marion, C. Jennings, C. Whitaker, “Spectral solar radiation data base at SERI,” Sol. Energy 20, 67–79 (1989).
[CrossRef]

Nann, S.

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

Nayatani, Y.

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull Electrotech. Lab. 31, 1127–1135 (1967).

Y. Nayatani, G. Wyszecki, “Color of daylight from north sky,” J. Opt. Soc. Am. 53, 626–629 (1963).
[CrossRef]

Nieves, J. L.

Parkinnen, J. P. S.

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).
[CrossRef]

Prasad, C. R.

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

Riordan, C.

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

C. Riordan, D. R. Myers, R. Hulstrom, W. Marion, C. Jennings, C. Whitaker, “Spectral solar radiation data base at SERI,” Sol. Energy 20, 67–79 (1989).
[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]

Sastri, V. D. P.

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).
[CrossRef]

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), p. 11.

Stotts, L. B.

Tarrant, A. W. S.

A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).

Thekaekara, M. P.

M. P. Thekaekara, “Solar energy outside the earth’s atmosphere,” Sol. Energy 14, 109–127 (1973).
[CrossRef]

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]

Wandell, B. A.

Whitaker, C.

C. Riordan, D. R. Myers, R. Hulstrom, W. Marion, C. Jennings, C. Whitaker, “Spectral solar radiation data base at SERI,” Sol. Energy 20, 67–79 (1989).
[CrossRef]

Winch, G. T.

Winter, E. M.

Wyszecki, G.

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. (5)

Br. J. Appl. Phys. (2)

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

J. F. Collins, “The color temperature of daylight,” Br. J. Appl. Phys. 16, 527–532 (1965).
[CrossRef]

Bull Electrotech. Lab. (1)

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull Electrotech. Lab. 31, 1127–1135 (1967).

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. Appl. Meteorol. (1)

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

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. (7)

J. Opt. Soc. Am. A (4)

J. Phys. D (1)

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

J. Sol. Energy Eng. (2)

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]

Light Light. (1)

G. J. Chamberlin, A. Lawrence, A. A. Belbin, “Observations on the related colour temperature of north daylight in southern England,” Light Light. 56, 70–72 (1963).

Phys. Teach. (1)

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

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 (7)

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Figures (15)

Fig. 1
Fig. 1

Azimuths relative to the sun ϕrel and view elevations h above the astronomical horizon at which we measured Granada skylight spectra.

Fig. 2
Fig. 2

CIE 1931 chromaticities of our 1567 Granada clear skylight spectra (open circles), overlaid with the CIE daylight locus (dashed curve), the Planckian locus (curve with open squares), and the Granada clear skylight locus [curve with open triangles; Eq. (1)]. The inset shows the entire CIE 1931 diagram and Planckian locus.

Fig. 3
Fig. 3

Histogram of inverse CCT (in reciprocal megaKelvins) corresponding to our Granada skylight chromaticities. Some low-frequency outliers are excluded.

Fig. 4
Fig. 4

(a) Chromaticity curve for Granada clear skylight along ϕrel=0° (the clear-sky principal plane) when solar elevation h0=60° on August 19, 1998. Note that view elevations beyond the zenith are indicated by h>90°. The dotted line is the CIE daylight locus, while the inset shows the entire CIE 1931 diagram and Planckian locus. Figures 57 reuse Fig. 4’s notation. (b) Chromaticity curve for clear skylight along ϕrel=90° when h0=60° (August 19, 1998).

Fig. 5
Fig. 5

(a) Chromaticity curve for clear skylight along ϕrel=0° when h0=19° (August 6, 1998). (b) Chromaticity curve for clear skylight along ϕrel=90° when h0=19° (August 6, 1998).

Fig. 6
Fig. 6

(a) Chromaticity curve for clear skylight along ϕrel=0° when h0=11° (August 19, 1998). (b) Chromaticity curve for clear skylight along ϕrel=90° when h0=11° (August 19, 1998).

Fig. 7
Fig. 7

(a) Chromaticity curve for clear skylight along ϕrel=0° when h0=1.6° (August 5, 1998). (b) Chromaticity curve for clear skylight along ϕrel=90° when h0=1.6° (August 5, 1998).

Fig. 8
Fig. 8

Relative luminance differences (solid symbols) and chromaticity differences in JND units (open symbols) as a function of h along ϕrel=90° for the four h0 shown in Figs. 4(b), 5(b), 6(b), and 7(b). Solar elevation symbols are squares for h0=60°, circles for h0=18.5°, upright triangles for h0=10°, and inverted triangles for h0=0.4°.

Fig. 9
Fig. 9

Chromaticity curves for Granada clear skylight along ϕrel=45°, 315° when solar elevation h0=58° on August 19, 1998. Chromaticities along ϕrel=45° are denoted with filled squares; those along ϕrel=315°, with open circles. As in Figs. 47, view elevations beyond the zenith at each ϕrel are indicated by h>90°. The dotted line is the CIE daylight locus, while the inset shows the entire CIE 1931 diagram and Planckian locus. Figures 1012 reuse Fig. 9’s notation.

Fig. 10
Fig. 10

Chromaticity curves for Granada clear skylight along ϕrel=45°, 315° when h0=52° (August 20, 1998).

Fig. 11
Fig. 11

Chromaticity curves for Granada clear skylight along ϕrel=45°, 315° when h0=42° (August 25, 1998).

Fig. 12
Fig. 12

Chromaticity curves for Granada clear skylight along ϕrel=45°, 315° when h0=6° (August 6, 1998).  

Fig. 13
Fig. 13

Inverse CCT as a function of scattering angle Ψ for all Granada skylight chromaticities. Solid squares mark the mean inverse CCT for each 5°-wide bin, and error bars are 2 standard deviations wide.

Fig. 14
Fig. 14

Spectral distribution of the first five eigenvectors for the Granada skylight basis set from 380–780 nm. Solid curve, p=1 eigenvector (mean vector); dashed curve, p=2 eigenvector; dotted curve, p=3 eigenvector; solid curve with open squares, p=4 eigenvector; dashed curve with solid circles, p=5 eigenvector.

Fig. 15
Fig. 15

Mean CIELUV color difference ΔE*uv as a function of mean GFC. Numbers next to each point indicate the number of eigenvectors p necessary in Eq. (2) to yield the given GFC. Error bars are 2 standard deviations wide.

Equations (3)

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y=-0.24770 + 2.72203x-2.77935x2.
ER(λ)=i=1pEE(λ)|Vi(λ)Vi(λ),
GFC=jEE(λj)ER(λj)j[EE(λj)]21/2j[ER(λj)]21/2.

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