Abstract

Beneath most overcasts, clouds’ motions and rapidly changing optical depths complicate mapping their angular distributions of luminance Lv and visible-wavelength radiance L. Fisheye images of overcast skies taken with a radiometer-calibrated digital camera provide a useful new approach to solving this problem. Maps calculated from time-averaged images of individual overcasts not only show their brightness distributions in unprecedented detail, but they also help solve a long-standing puzzle about where brightness maxima of overcasts are actually located. When combined with simulated radiance distributions from MODTRAN4, our measured radiances also let us estimate the gradients of cloud thickness observed in some overcasts.

© 2008 Optical Society of America

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  1. M. Minnaert, Light and Color in the Outdoors, translated and revised by L.Seymour (Springer-Verlag, 1993), pp. 154-155.
  2. P. Moon and D. E. Spencer, “Illumination from a non-uniform sky,” Illum. Eng. 37, 707-726 (1942).
  3. Commission Internationale de l'Eclairage (CIE), Spatial Distribution of Daylight--CIE Standard Overcast Sky and Clear Sky, CIE Standard no. S 003/E-1996 (CIE, 1996).
  4. R. L. Lee, Jr. and J. Hernández-Andrés, “Short-term variability of overcast brightness,” Appl. Opt. 44, 5704-5711 (2005).
    [CrossRef] [PubMed]
  5. We use “brightness” to connote either luminance or visible-wavelength radiance if no qualitative visual difference likely exists between the two. That said, we are well aware of the quantitative differences between these two photometric and radiometric measures of skylight energy; e.g., see G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 259-260.
  6. S. Fritz, “Illuminance and luminance under overcast skies,” J. Opt. Soc. Am. 45, 820-825 (1955).
    [CrossRef]
  7. F. C. Hooper and A. P. Brunger, “A model for the angular distribution of sky radiance,” J. Sol. Energy Eng. 102, 196-202 (1980).
    [CrossRef]
  8. M. A. Rosen and F. C. Hooper, “A comparison of two models for the angular distribution of diffuse sky radiance for overcast skies,” Sol. Energy 42, 477-482 (1989).
    [CrossRef]
  9. N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137-157 (2004).
    [CrossRef]
  10. M. D. Steven and M. H. Unsworth, “The angular distribution and interception of diffuse solar radiation below overcast skies,” Q. J. R. Meteorol. Soc. 106, 57-61 (1980).
    [CrossRef]
  11. D. Enarun and P. Littlefair, “Luminance models for overcast skies: assessment using measured data,” Int. J. Lighting Res. Technol. 27, 53-58 (1995).
    [CrossRef]
  12. A. Bartzokas, S. Darula, H. D. Kambezidis, and R. Kittler, “Sky luminance distribution in central Europe and the Mediterranean area during the winter period,” J. Atmos. Sol.-Terr. Phys. 65, 113-119 (2003).
    [CrossRef]
  13. D. H. Li, C. C. Lau, and J. C. Lam, “Overcast sky conditions and luminance distribution in Hong Kong,” Build. Environ. 39, 101-108 (2004).
    [CrossRef]
  14. T. Muneer, “Evaluation of the CIE overcast sky model against Japanese data,” Energy Build. 27, 175-177 (1998).
    [CrossRef]
  15. J. I. Gordon and P. V. Church, “Overcast sky luminances and directional luminous reflectances of objects and backgrounds under overcast skies,” Appl. Opt. 5, 919-923 (1966).
    [CrossRef] [PubMed]
  16. R. Kittler and P. Valko, “Radiance distribution on densely overcast skies: comparison with CIE luminance standard,” Sol. Energy 51, 349-355 (1993).
    [CrossRef]
  17. R. H. Grant and G. M. Heisler, “Obscured overcast sky radiance distributions for ultraviolet and photosynthetically active radiation,” J. Appl. Meteorol. 36, 1336-1345 (1997).
    [CrossRef]
  18. R. Perez, R. Seals, and J. Michalsky, “All-weather model for sky luminance distribution--preliminary configuration and validation,” Sol. Energy 50, 235-245 (1993)
    [CrossRef]
  19. R. Perez, R. Seals, and J. Michalsky, “Erratum to all-weather model for sky luminance distribution--preliminary configuration and validation,” Sol. Energy 51, 423 (1993).
    [CrossRef]
  20. Commission Internationale de l'Eclairage, Spatial Distribution of Daylight--CIE Standard General Sky CIE Standard no. S 011/E:2003 (CIE, 2003).
  21. C. A. Coombes and A. W. Harrison, “Angular distribution of overcast sky short wavelength radiance,” Sol. Energy 40, 161-166 (1988).
    [CrossRef]
  22. A. W. Harrison, “Directional sky luminance versus cloud cover and solar position,” Sol. Energy 46, 13-19 (1991).
    [CrossRef]
  23. R. H. Grant, G. M. Heisler, and W. Gao, “Ultraviolet sky radiance distributions of translucent overcast skies,” Theor. Appl. Climatol. 58, 129-139 (1997).
    [CrossRef]
  24. A. Soler and L. Robledo, “Investigation of the overcast skies luminance distribution using 35 sensors fixed on a dome,” Energy Convers. Manage. 46, 2739-2747 (2005).
    [CrossRef]
  25. S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131-148 (2006).
    [CrossRef]
  26. R. L. Lee, Jr., and J. Hernández-Andrés, “Colors of the daytime overcast sky,” Appl. Opt. 44, 5712-5722 (2005).
    [CrossRef] [PubMed]
  27. R. L. Lee, Jr., “Measuring overcast colors with all-sky imaging,” Appl. Opt. 47, H106-H115 (2008).
  28. For examples of overcast L distributions from individual photographs, see Figs. 3-4 in E. G. Rossini and A. Krenzinger, “Maps of sky relative radiance and luminance distributions acquired with a monochromatic CCD camera,” Sol. Energy 81, 1323-1332 (2007).
    [CrossRef]
  29. J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
    [CrossRef] [PubMed]
  30. Photo Research, Inc., 9731 Topanga Canyon Place, Chatsworth, Calif. 91311. The PR-650's spectral range is 380-780 nm, its step size is 4 nm, and its telescopic lens permits radiance measurements across a 1° diameter FOV.
  31. D. Wüller and H. Gabele, “The usage of digital cameras as luminance meters,” Proc. SPIE 6502, 65020U (2007).
    [CrossRef]
  32. Clearly sin⁡(θi)=rn cannot describe exactly the projection of a nominally orthographic lens that forms images at θi>90° where rn>1.
  33. K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic 'fisheye' camera radiance distribution system,” J. Atmos. Ocean. Technol. 6, 652-662(1989).
    [CrossRef]
  34. Although the FC-E8 FOV actually exceeds 180° by a few degrees, we ignore all pixels below the astronomical horizon as irrelevant to our interests here. In actual practice, topography seen from our USNA rooftop site obstructs the lowest 1° or so of the sky.
  35. T.S.Glickman, ed., Glossary of Meteorology, 2nd ed. (American Meteorological Society, 2000), pp. 390, 694.
  36. C. F. Bohren and A. B. Fraser, “Colors of the sky,” Phys. Teach. 23, 267-272 (1985).
    [CrossRef]
  37. R. L. Lee, Jr., “Horizon brightness revisited: measurements and a model of clear-sky radiances,” Appl. Opt. 33, 4620-4628, 4959 (1994).
    [CrossRef] [PubMed]
  38. J. Li, J. W. Geldart, and P. Chylek, “Solar radiative transfer in clouds with vertical internal inhomogeneity,” J. Atmos. Sci. 51, 2542-2552 (1994).
    [CrossRef]
  39. A. Los and P. G. Duynkerke, “Microphysical and radiative properties of inhomogeneous stratocumulus: observations and model simulations,” Q. J. R. Meteorol. Soc. 126, 3287-3307 (2000).
    [CrossRef]
  40. A. A. Kokhanovsky, “The influence of horizontal inhomogeneity on radiative characteristics of clouds: an asymptotic case study,” IEEE Trans. Geosci. Remote Sens. 41, 817-825 (2003).
    [CrossRef]
  41. Y. Chen, K. N. Liou, and Y. Gu, “An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 92, 189-200 (2005).
    [CrossRef]
  42. A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
    [CrossRef]
  43. G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
    [CrossRef]
  44. Our MODTRAN4 simulations use (1) the model's default single-scattering properties for each cloud type and for boundary-layer aerosols, (2) a 23 km surface visual range, (3) a spectral interval of 400-700 nm, (4) a locally measured surface air temperature, and (5) a surface Lambertian albedo of 0.2. Although a nearby ceilometer measured zbase, we could find no comparable data on cloud top heights that met our temporal and spatial requirements (i.e., samples at intervals of 30 s and 50-100 m).

2007 (2)

For examples of overcast L distributions from individual photographs, see Figs. 3-4 in E. G. Rossini and A. Krenzinger, “Maps of sky relative radiance and luminance distributions acquired with a monochromatic CCD camera,” Sol. Energy 81, 1323-1332 (2007).
[CrossRef]

D. Wüller and H. Gabele, “The usage of digital cameras as luminance meters,” Proc. SPIE 6502, 65020U (2007).
[CrossRef]

2006 (1)

S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131-148 (2006).
[CrossRef]

2005 (6)

A. Soler and L. Robledo, “Investigation of the overcast skies luminance distribution using 35 sensors fixed on a dome,” Energy Convers. Manage. 46, 2739-2747 (2005).
[CrossRef]

Y. Chen, K. N. Liou, and Y. Gu, “An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 92, 189-200 (2005).
[CrossRef]

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
[CrossRef] [PubMed]

R. L. Lee, Jr. and J. Hernández-Andrés, “Short-term variability of overcast brightness,” Appl. Opt. 44, 5704-5711 (2005).
[CrossRef] [PubMed]

R. L. Lee, Jr., and J. Hernández-Andrés, “Colors of the daytime overcast sky,” Appl. Opt. 44, 5712-5722 (2005).
[CrossRef] [PubMed]

2004 (2)

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137-157 (2004).
[CrossRef]

D. H. Li, C. C. Lau, and J. C. Lam, “Overcast sky conditions and luminance distribution in Hong Kong,” Build. Environ. 39, 101-108 (2004).
[CrossRef]

2003 (2)

A. Bartzokas, S. Darula, H. D. Kambezidis, and R. Kittler, “Sky luminance distribution in central Europe and the Mediterranean area during the winter period,” J. Atmos. Sol.-Terr. Phys. 65, 113-119 (2003).
[CrossRef]

A. A. Kokhanovsky, “The influence of horizontal inhomogeneity on radiative characteristics of clouds: an asymptotic case study,” IEEE Trans. Geosci. Remote Sens. 41, 817-825 (2003).
[CrossRef]

2000 (2)

A. Los and P. G. Duynkerke, “Microphysical and radiative properties of inhomogeneous stratocumulus: observations and model simulations,” Q. J. R. Meteorol. Soc. 126, 3287-3307 (2000).
[CrossRef]

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

1998 (1)

T. Muneer, “Evaluation of the CIE overcast sky model against Japanese data,” Energy Build. 27, 175-177 (1998).
[CrossRef]

1997 (2)

R. H. Grant, G. M. Heisler, and W. Gao, “Ultraviolet sky radiance distributions of translucent overcast skies,” Theor. Appl. Climatol. 58, 129-139 (1997).
[CrossRef]

R. H. Grant and G. M. Heisler, “Obscured overcast sky radiance distributions for ultraviolet and photosynthetically active radiation,” J. Appl. Meteorol. 36, 1336-1345 (1997).
[CrossRef]

1995 (1)

D. Enarun and P. Littlefair, “Luminance models for overcast skies: assessment using measured data,” Int. J. Lighting Res. Technol. 27, 53-58 (1995).
[CrossRef]

1994 (2)

R. L. Lee, Jr., “Horizon brightness revisited: measurements and a model of clear-sky radiances,” Appl. Opt. 33, 4620-4628, 4959 (1994).
[CrossRef] [PubMed]

J. Li, J. W. Geldart, and P. Chylek, “Solar radiative transfer in clouds with vertical internal inhomogeneity,” J. Atmos. Sci. 51, 2542-2552 (1994).
[CrossRef]

1993 (3)

R. Kittler and P. Valko, “Radiance distribution on densely overcast skies: comparison with CIE luminance standard,” Sol. Energy 51, 349-355 (1993).
[CrossRef]

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

R. Perez, R. Seals, and J. Michalsky, “Erratum to all-weather model for sky luminance distribution--preliminary configuration and validation,” Sol. Energy 51, 423 (1993).
[CrossRef]

1991 (1)

A. W. Harrison, “Directional sky luminance versus cloud cover and solar position,” Sol. Energy 46, 13-19 (1991).
[CrossRef]

1989 (2)

M. A. Rosen and F. C. Hooper, “A comparison of two models for the angular distribution of diffuse sky radiance for overcast skies,” Sol. Energy 42, 477-482 (1989).
[CrossRef]

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic 'fisheye' camera radiance distribution system,” J. Atmos. Ocean. Technol. 6, 652-662(1989).
[CrossRef]

1988 (1)

C. A. Coombes and A. W. Harrison, “Angular distribution of overcast sky short wavelength radiance,” Sol. Energy 40, 161-166 (1988).
[CrossRef]

1985 (1)

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

1980 (2)

F. C. Hooper and A. P. Brunger, “A model for the angular distribution of sky radiance,” J. Sol. Energy Eng. 102, 196-202 (1980).
[CrossRef]

M. D. Steven and M. H. Unsworth, “The angular distribution and interception of diffuse solar radiation below overcast skies,” Q. J. R. Meteorol. Soc. 106, 57-61 (1980).
[CrossRef]

1966 (1)

1955 (1)

1942 (1)

P. Moon and D. E. Spencer, “Illumination from a non-uniform sky,” Illum. Eng. 37, 707-726 (1942).

Acharya, P. K.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Adler-Golden, S. M.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Ammannato, L.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Anderson, G. P.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Bais, A.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Barnaba, F.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Bartzokas, A.

A. Bartzokas, S. Darula, H. D. Kambezidis, and R. Kittler, “Sky luminance distribution in central Europe and the Mediterranean area during the winter period,” J. Atmos. Sol.-Terr. Phys. 65, 113-119 (2003).
[CrossRef]

Berk, A.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Bernstein, L. S.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Blumthaler, M.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Bohren, C. F.

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

Brunger, A. P.

F. C. Hooper and A. P. Brunger, “A model for the angular distribution of sky radiance,” J. Sol. Energy Eng. 102, 196-202 (1980).
[CrossRef]

Chen, Y.

Y. Chen, K. N. Liou, and Y. Gu, “An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 92, 189-200 (2005).
[CrossRef]

Chetwynd, J. H.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Church, P. V.

Chylek, P.

J. Li, J. W. Geldart, and P. Chylek, “Solar radiative transfer in clouds with vertical internal inhomogeneity,” J. Atmos. Sci. 51, 2542-2552 (1994).
[CrossRef]

Coombes, C. A.

C. A. Coombes and A. W. Harrison, “Angular distribution of overcast sky short wavelength radiance,” Sol. Energy 40, 161-166 (1988).
[CrossRef]

Darula, S.

A. Bartzokas, S. Darula, H. D. Kambezidis, and R. Kittler, “Sky luminance distribution in central Europe and the Mediterranean area during the winter period,” J. Atmos. Sol.-Terr. Phys. 65, 113-119 (2003).
[CrossRef]

Dothe, H.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Duynkerke, P. G.

A. Los and P. G. Duynkerke, “Microphysical and radiative properties of inhomogeneous stratocumulus: observations and model simulations,” Q. J. R. Meteorol. Soc. 126, 3287-3307 (2000).
[CrossRef]

Enarun, D.

D. Enarun and P. Littlefair, “Luminance models for overcast skies: assessment using measured data,” Int. J. Lighting Res. Technol. 27, 53-58 (1995).
[CrossRef]

Felde, G. W.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Fraser, A. B.

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

Fritz, S.

Gabele, H.

D. Wüller and H. Gabele, “The usage of digital cameras as luminance meters,” Proc. SPIE 6502, 65020U (2007).
[CrossRef]

Gao, W.

R. H. Grant, G. M. Heisler, and W. Gao, “Ultraviolet sky radiance distributions of translucent overcast skies,” Theor. Appl. Climatol. 58, 129-139 (1997).
[CrossRef]

Gardner, J. A.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Geldart, J. W.

J. Li, J. W. Geldart, and P. Chylek, “Solar radiative transfer in clouds with vertical internal inhomogeneity,” J. Atmos. Sci. 51, 2542-2552 (1994).
[CrossRef]

Gobbi, G. P.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Gordon, J. I.

Grant, R. H.

R. H. Grant and G. M. Heisler, “Obscured overcast sky radiance distributions for ultraviolet and photosynthetically active radiation,” J. Appl. Meteorol. 36, 1336-1345 (1997).
[CrossRef]

R. H. Grant, G. M. Heisler, and W. Gao, “Ultraviolet sky radiance distributions of translucent overcast skies,” Theor. Appl. Climatol. 58, 129-139 (1997).
[CrossRef]

Gu, Y.

Y. Chen, K. N. Liou, and Y. Gu, “An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 92, 189-200 (2005).
[CrossRef]

Harrison, A. W.

A. W. Harrison, “Directional sky luminance versus cloud cover and solar position,” Sol. Energy 46, 13-19 (1991).
[CrossRef]

C. A. Coombes and A. W. Harrison, “Angular distribution of overcast sky short wavelength radiance,” Sol. Energy 40, 161-166 (1988).
[CrossRef]

Heisler, G. M.

R. H. Grant and G. M. Heisler, “Obscured overcast sky radiance distributions for ultraviolet and photosynthetically active radiation,” J. Appl. Meteorol. 36, 1336-1345 (1997).
[CrossRef]

R. H. Grant, G. M. Heisler, and W. Gao, “Ultraviolet sky radiance distributions of translucent overcast skies,” Theor. Appl. Climatol. 58, 129-139 (1997).
[CrossRef]

Hernández-Andrés, J.

Hoke, M. L.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Hooper, F. C.

M. A. Rosen and F. C. Hooper, “A comparison of two models for the angular distribution of diffuse sky radiance for overcast skies,” Sol. Energy 42, 477-482 (1989).
[CrossRef]

F. C. Hooper and A. P. Brunger, “A model for the angular distribution of sky radiance,” J. Sol. Energy Eng. 102, 196-202 (1980).
[CrossRef]

Igawa, N.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137-157 (2004).
[CrossRef]

Jäkel, E.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Jeong, L. S.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Junkermann, W.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Kambezidis, H. D.

A. Bartzokas, S. Darula, H. D. Kambezidis, and R. Kittler, “Sky luminance distribution in central Europe and the Mediterranean area during the winter period,” J. Atmos. Sol.-Terr. Phys. 65, 113-119 (2003).
[CrossRef]

Kazadzis, S.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Kift, R.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Kittler, R.

A. Bartzokas, S. Darula, H. D. Kambezidis, and R. Kittler, “Sky luminance distribution in central Europe and the Mediterranean area during the winter period,” J. Atmos. Sol.-Terr. Phys. 65, 113-119 (2003).
[CrossRef]

R. Kittler and P. Valko, “Radiance distribution on densely overcast skies: comparison with CIE luminance standard,” Sol. Energy 51, 349-355 (1993).
[CrossRef]

Kjeldstad, B.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Kniffka, A.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Koga, Y.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137-157 (2004).
[CrossRef]

Kokhanovsky, A. A.

A. A. Kokhanovsky, “The influence of horizontal inhomogeneity on radiative characteristics of clouds: an asymptotic case study,” IEEE Trans. Geosci. Remote Sens. 41, 817-825 (2003).
[CrossRef]

Krenzinger, A.

For examples of overcast L distributions from individual photographs, see Figs. 3-4 in E. G. Rossini and A. Krenzinger, “Maps of sky relative radiance and luminance distributions acquired with a monochromatic CCD camera,” Sol. Energy 81, 1323-1332 (2007).
[CrossRef]

Kylling, A.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Lam, J. C.

D. H. Li, C. C. Lau, and J. C. Lam, “Overcast sky conditions and luminance distribution in Hong Kong,” Build. Environ. 39, 101-108 (2004).
[CrossRef]

Lau, C. C.

D. H. Li, C. C. Lau, and J. C. Lam, “Overcast sky conditions and luminance distribution in Hong Kong,” Build. Environ. 39, 101-108 (2004).
[CrossRef]

Lee, R. L.

Li, D. H.

D. H. Li, C. C. Lau, and J. C. Lam, “Overcast sky conditions and luminance distribution in Hong Kong,” Build. Environ. 39, 101-108 (2004).
[CrossRef]

Li, J.

J. Li, J. W. Geldart, and P. Chylek, “Solar radiative transfer in clouds with vertical internal inhomogeneity,” J. Atmos. Sci. 51, 2542-2552 (1994).
[CrossRef]

Liou, K. N.

Y. Chen, K. N. Liou, and Y. Gu, “An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 92, 189-200 (2005).
[CrossRef]

Littlefair, P.

D. Enarun and P. Littlefair, “Luminance models for overcast skies: assessment using measured data,” Int. J. Lighting Res. Technol. 27, 53-58 (1995).
[CrossRef]

Los, A.

A. Los and P. G. Duynkerke, “Microphysical and radiative properties of inhomogeneous stratocumulus: observations and model simulations,” Q. J. R. Meteorol. Soc. 126, 3287-3307 (2000).
[CrossRef]

Matsuzawa, T.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137-157 (2004).
[CrossRef]

Matthew, M. W.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Mayer, B.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Mello, J.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Michalsky, J.

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

R. Perez, R. Seals, and J. Michalsky, “Erratum to all-weather model for sky luminance distribution--preliminary configuration and validation,” Sol. Energy 51, 423 (1993).
[CrossRef]

Minnaert, M.

M. Minnaert, Light and Color in the Outdoors, translated and revised by L.Seymour (Springer-Verlag, 1993), pp. 154-155.

Moon, P.

P. Moon and D. E. Spencer, “Illumination from a non-uniform sky,” Illum. Eng. 37, 707-726 (1942).

Muneer, T.

T. Muneer, “Evaluation of the CIE overcast sky model against Japanese data,” Energy Build. 27, 175-177 (1998).
[CrossRef]

Nakamura, H.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137-157 (2004).
[CrossRef]

Nascimento, S. M. C.

Nieves, J. L.

Perez, R.

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

R. Perez, R. Seals, and J. Michalsky, “Erratum to all-weather model for sky luminance distribution--preliminary configuration and validation,” Sol. Energy 51, 423 (1993).
[CrossRef]

Pukall, B.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Ratkowski, A. J.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Richtsmeier, S. C.

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

Robledo, L.

A. Soler and L. Robledo, “Investigation of the overcast skies luminance distribution using 35 sensors fixed on a dome,” Energy Convers. Manage. 46, 2739-2747 (2005).
[CrossRef]

Romero, J.

Rosen, M. A.

M. A. Rosen and F. C. Hooper, “A comparison of two models for the angular distribution of diffuse sky radiance for overcast skies,” Sol. Energy 42, 477-482 (1989).
[CrossRef]

Rossini, E. G.

For examples of overcast L distributions from individual photographs, see Figs. 3-4 in E. G. Rossini and A. Krenzinger, “Maps of sky relative radiance and luminance distributions acquired with a monochromatic CCD camera,” Sol. Energy 81, 1323-1332 (2007).
[CrossRef]

Schallhart, B.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Scheirer, R.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Schmidt, S.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Schmitt, R.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Seals, R.

R. Perez, R. Seals, and J. Michalsky, “Erratum to all-weather model for sky luminance distribution--preliminary configuration and validation,” Sol. Energy 51, 423 (1993).
[CrossRef]

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

Seckmeyer, G.

S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131-148 (2006).
[CrossRef]

Silbernagl, R.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Soler, A.

A. Soler and L. Robledo, “Investigation of the overcast skies luminance distribution using 35 sensors fixed on a dome,” Energy Convers. Manage. 46, 2739-2747 (2005).
[CrossRef]

Spencer, D. E.

P. Moon and D. E. Spencer, “Illumination from a non-uniform sky,” Illum. Eng. 37, 707-726 (1942).

Steven, M. D.

M. D. Steven and M. H. Unsworth, “The angular distribution and interception of diffuse solar radiation below overcast skies,” Q. J. R. Meteorol. Soc. 106, 57-61 (1980).
[CrossRef]

Stiles, W. S.

We use “brightness” to connote either luminance or visible-wavelength radiance if no qualitative visual difference likely exists between the two. That said, we are well aware of the quantitative differences between these two photometric and radiometric measures of skylight energy; e.g., see G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 259-260.

Thiel, S.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Thorseth, T. M.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Unsworth, M. H.

M. D. Steven and M. H. Unsworth, “The angular distribution and interception of diffuse solar radiation below overcast skies,” Q. J. R. Meteorol. Soc. 106, 57-61 (1980).
[CrossRef]

Valero, E. M.

Valko, P.

R. Kittler and P. Valko, “Radiance distribution on densely overcast skies: comparison with CIE luminance standard,” Sol. Energy 51, 349-355 (1993).
[CrossRef]

Voss, K. J.

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic 'fisheye' camera radiance distribution system,” J. Atmos. Ocean. Technol. 6, 652-662(1989).
[CrossRef]

Webb, A. R.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Wendisch, M.

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Wüller, D.

D. Wüller and H. Gabele, “The usage of digital cameras as luminance meters,” Proc. SPIE 6502, 65020U (2007).
[CrossRef]

Wuttke, S.

S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131-148 (2006).
[CrossRef]

Wyszecki, G.

We use “brightness” to connote either luminance or visible-wavelength radiance if no qualitative visual difference likely exists between the two. That said, we are well aware of the quantitative differences between these two photometric and radiometric measures of skylight energy; e.g., see G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 259-260.

Zibordi, G.

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic 'fisheye' camera radiance distribution system,” J. Atmos. Ocean. Technol. 6, 652-662(1989).
[CrossRef]

Appl. Opt. (5)

Atmos. Chem. Phys. (1)

A. Kylling, A. R. Webb, R. Kift, G. P. Gobbi, L. Ammannato, F. Barnaba, A. Bais, S. Kazadzis, M. Wendisch, E. Jäkel, S. Schmidt, A. Kniffka, S. Thiel, W. Junkermann, M. Blumthaler, R. Silbernagl, B. Schallhart, R. Schmitt, B. Kjeldstad, T. M. Thorseth, R. Scheirer, and B. Mayer, “Spectral actinic flux in the lower troposphere: measurement and 1-D simulations for cloudless, broken cloud and overcast situations,” Atmos. Chem. Phys. 5, 1975-1997 (2005).
[CrossRef]

Build. Environ. (1)

D. H. Li, C. C. Lau, and J. C. Lam, “Overcast sky conditions and luminance distribution in Hong Kong,” Build. Environ. 39, 101-108 (2004).
[CrossRef]

Energy Build. (1)

T. Muneer, “Evaluation of the CIE overcast sky model against Japanese data,” Energy Build. 27, 175-177 (1998).
[CrossRef]

Energy Convers. Manage. (1)

A. Soler and L. Robledo, “Investigation of the overcast skies luminance distribution using 35 sensors fixed on a dome,” Energy Convers. Manage. 46, 2739-2747 (2005).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

A. A. Kokhanovsky, “The influence of horizontal inhomogeneity on radiative characteristics of clouds: an asymptotic case study,” IEEE Trans. Geosci. Remote Sens. 41, 817-825 (2003).
[CrossRef]

Illum. Eng. (1)

P. Moon and D. E. Spencer, “Illumination from a non-uniform sky,” Illum. Eng. 37, 707-726 (1942).

Int. J. Lighting Res. Technol. (1)

D. Enarun and P. Littlefair, “Luminance models for overcast skies: assessment using measured data,” Int. J. Lighting Res. Technol. 27, 53-58 (1995).
[CrossRef]

J. Appl. Meteorol. (1)

R. H. Grant and G. M. Heisler, “Obscured overcast sky radiance distributions for ultraviolet and photosynthetically active radiation,” J. Appl. Meteorol. 36, 1336-1345 (1997).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic 'fisheye' camera radiance distribution system,” J. Atmos. Ocean. Technol. 6, 652-662(1989).
[CrossRef]

J. Atmos. Sci. (1)

J. Li, J. W. Geldart, and P. Chylek, “Solar radiative transfer in clouds with vertical internal inhomogeneity,” J. Atmos. Sci. 51, 2542-2552 (1994).
[CrossRef]

J. Atmos. Sol.-Terr. Phys. (1)

A. Bartzokas, S. Darula, H. D. Kambezidis, and R. Kittler, “Sky luminance distribution in central Europe and the Mediterranean area during the winter period,” J. Atmos. Sol.-Terr. Phys. 65, 113-119 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transf. (1)

Y. Chen, K. N. Liou, and Y. Gu, “An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 92, 189-200 (2005).
[CrossRef]

J. Sol. Energy Eng. (1)

F. C. Hooper and A. P. Brunger, “A model for the angular distribution of sky radiance,” J. Sol. Energy Eng. 102, 196-202 (1980).
[CrossRef]

Phys. Teach. (1)

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

Proc. SPIE (2)

G. P. Anderson, A. Berk, P. K. Acharya, M. W. Matthew, L. S. Bernstein, J. H. Chetwynd, H. Dothe, S. M. Adler-Golden, A. J. Ratkowski, G. W. Felde, J. A. Gardner, M. L. Hoke, S. C. Richtsmeier, B. Pukall, J. Mello, and L. S. Jeong, “MODTRAN4: radiative transfer modeling for remote sensing,” Proc. SPIE 4049, 176-183 (2000).
[CrossRef]

D. Wüller and H. Gabele, “The usage of digital cameras as luminance meters,” Proc. SPIE 6502, 65020U (2007).
[CrossRef]

Q. J. R. Meteorol. Soc. (2)

M. D. Steven and M. H. Unsworth, “The angular distribution and interception of diffuse solar radiation below overcast skies,” Q. J. R. Meteorol. Soc. 106, 57-61 (1980).
[CrossRef]

A. Los and P. G. Duynkerke, “Microphysical and radiative properties of inhomogeneous stratocumulus: observations and model simulations,” Q. J. R. Meteorol. Soc. 126, 3287-3307 (2000).
[CrossRef]

Sol. Energy (8)

For examples of overcast L distributions from individual photographs, see Figs. 3-4 in E. G. Rossini and A. Krenzinger, “Maps of sky relative radiance and luminance distributions acquired with a monochromatic CCD camera,” Sol. Energy 81, 1323-1332 (2007).
[CrossRef]

R. Kittler and P. Valko, “Radiance distribution on densely overcast skies: comparison with CIE luminance standard,” Sol. Energy 51, 349-355 (1993).
[CrossRef]

M. A. Rosen and F. C. Hooper, “A comparison of two models for the angular distribution of diffuse sky radiance for overcast skies,” Sol. Energy 42, 477-482 (1989).
[CrossRef]

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137-157 (2004).
[CrossRef]

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

R. Perez, R. Seals, and J. Michalsky, “Erratum to all-weather model for sky luminance distribution--preliminary configuration and validation,” Sol. Energy 51, 423 (1993).
[CrossRef]

C. A. Coombes and A. W. Harrison, “Angular distribution of overcast sky short wavelength radiance,” Sol. Energy 40, 161-166 (1988).
[CrossRef]

A. W. Harrison, “Directional sky luminance versus cloud cover and solar position,” Sol. Energy 46, 13-19 (1991).
[CrossRef]

Theor. Appl. Climatol. (2)

R. H. Grant, G. M. Heisler, and W. Gao, “Ultraviolet sky radiance distributions of translucent overcast skies,” Theor. Appl. Climatol. 58, 129-139 (1997).
[CrossRef]

S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131-148 (2006).
[CrossRef]

Other (10)

Commission Internationale de l'Eclairage, Spatial Distribution of Daylight--CIE Standard General Sky CIE Standard no. S 011/E:2003 (CIE, 2003).

Clearly sin⁡(θi)=rn cannot describe exactly the projection of a nominally orthographic lens that forms images at θi>90° where rn>1.

Although the FC-E8 FOV actually exceeds 180° by a few degrees, we ignore all pixels below the astronomical horizon as irrelevant to our interests here. In actual practice, topography seen from our USNA rooftop site obstructs the lowest 1° or so of the sky.

T.S.Glickman, ed., Glossary of Meteorology, 2nd ed. (American Meteorological Society, 2000), pp. 390, 694.

Photo Research, Inc., 9731 Topanga Canyon Place, Chatsworth, Calif. 91311. The PR-650's spectral range is 380-780 nm, its step size is 4 nm, and its telescopic lens permits radiance measurements across a 1° diameter FOV.

R. L. Lee, Jr., “Measuring overcast colors with all-sky imaging,” Appl. Opt. 47, H106-H115 (2008).

Commission Internationale de l'Eclairage (CIE), Spatial Distribution of Daylight--CIE Standard Overcast Sky and Clear Sky, CIE Standard no. S 003/E-1996 (CIE, 1996).

We use “brightness” to connote either luminance or visible-wavelength radiance if no qualitative visual difference likely exists between the two. That said, we are well aware of the quantitative differences between these two photometric and radiometric measures of skylight energy; e.g., see G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 259-260.

M. Minnaert, Light and Color in the Outdoors, translated and revised by L.Seymour (Springer-Verlag, 1993), pp. 154-155.

Our MODTRAN4 simulations use (1) the model's default single-scattering properties for each cloud type and for boundary-layer aerosols, (2) a 23 km surface visual range, (3) a spectral interval of 400-700 nm, (4) a locally measured surface air temperature, and (5) a surface Lambertian albedo of 0.2. Although a nearby ceilometer measured zbase, we could find no comparable data on cloud top heights that met our temporal and spatial requirements (i.e., samples at intervals of 30 s and 50-100 m).

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Figures (21)

Fig. 1
Fig. 1

Angular mappings for various fisheye lens projections, where θ i is the angle between a lens’ optical axis and an incident light ray, and r n is the normalized radius from the image’s center to the pixel illuminated by that ray. The FC-E8 curve is the measured mapping for our particular model of Nikon fisheye lens.

Fig. 2
Fig. 2

Normalized effective transmissivity T eff as a function of θ i measured for our FC-E8 fisheye lens. T eff accounts for all radiance losses at the image sensor due to the camera optics, including illumination factors, external and internal reflections, and absorption within the lens.

Fig. 3
Fig. 3

Gray-scale version of a time-averaged color image of a stratocumulus (Sc) overcast photographed at USNA in Annapolis, Maryland on 4 April 2007. Averaging of small-scale details in the 83 individual photographs that comprise Fig. 3 makes this Sc overcast resemble stratus (St).

Fig. 4
Fig. 4

Map of binned relative radiances L rel calculated from Fig. 3 by using Eqs. (1, 2) and corrected for brightness rolloff in the original image. L rel is Fig. 3’s absolute L in W / ( m 2 sr ) normalized by its maximum radiance L max . A black + marks the zenith, and two small black squares near the 6 o’clock position show the limits of the Sun’s position during photography. This and subsequent maps of L rel include details about the underlying mean image and its corresponding range of unrefracted Sun elevations h 0 .

Fig. 5
Fig. 5

Map of binned L rel calculated from the time-averaged color image [Fig. 4(a) in [27]] of a Sc overcast photographed at USNA on 30 August 2006.

Fig. 6
Fig. 6

Map of binned L rel calculated from the time-averaged color image of a Sc overcast photographed at USNA on 5 October 2006.

Fig. 7
Fig. 7

Map of binned L rel calculated from the time-averaged color image of a Sc overcast photographed at USNA on 7 March 2007. Unlike other days at our site, snow was falling then and covered the surrounding terrain.

Fig. 8
Fig. 8

Map of binned L rel calculated from the time-averaged color image of a Sc overcast photographed at USNA on 20 February 2007.

Fig. 9
Fig. 9

Map of binned L rel calculated from the time-averaged color image of a Sc overcast photographed at USNA on 12 February 2008.

Fig. 10
Fig. 10

Map of binned L rel calculated from the time-averaged color image of a Sc overcast photographed at USNA on 13 November 2006.

Fig. 11
Fig. 11

Gray-scale version of the time-averaged color image of a Sc overcast photographed at USNA on 29 November 2006.

Fig. 12
Fig. 12

Map of binned L rel calculated from Fig. 11’s color original. Note that the brightest area of this occasionally thin overcast lies between the zenith and Sun, which is just visible in 14 % of the individual photographs that comprise Fig. 11.

Fig. 13
Fig. 13

Meridional profiles of skylight luminance L v as a function of sky zenith angle θ at USNA for one clear sky (labeled CLR) and two overcasts (labeled OVC). L v ( θ ) in each profile are averaged over all relative azimuths ϕ rel at fixed θ. Although the near-horizon brightness maximum in the clear sky is fairly well understood [37], similar extrema in overcasts are not.

Fig. 14
Fig. 14

Gray-scale version of the time-averaged color image of a Sc overcast photographed at USNA on 20 August 2007. The alternating bright and dark bands are caused by persistent minima and maxima in overcast optical depth that parallel the mean low-level flow.

Fig. 15
Fig. 15

Meridional profiles of radiance L ( θ ) and luminance L v ( θ ) averaged across all ϕ rel for the same St overcast. In most daytime overcasts, the ratio L v ( θ ) L ( θ ) is nearly constant.

Fig. 16
Fig. 16

Meridional profiles of L ( θ ) averaged across all ϕ rel for two overcasts at USNA on 30 August 2006 and 7 March 2007. Compare these profiles with the corresponding all-sky maps of L rel (Figs. 5, 7, respectively).

Fig. 17
Fig. 17

Meridional profiles of L ( θ ) averaged across all ϕ rel for two overcasts at USNA on 13 November and 29 November 2006. Compare these profiles with the corresponding all-sky maps of L rel (Figs. 10, 12, respectively).

Fig. 18
Fig. 18

Schematic cross section of an overcast with vertical geometric thickness h that increases nearly linearly in the direction x. In our calculations, we make this gradient Δ h / Δ x constant in magnitude and direction. Overcast thickness and curvature are exaggerated here; θ is the sky zenith angle for a surface-based observer.

Fig. 19
Fig. 19

MODTRAN4 simulations of L rel in a Sc overcast with (a) constant h = 0.894 km and (b) constant, unidirectional Δ h / Δ x = 0.00155 ( 0.089 ° ) at an angle of 34 ° from the principal plane. The L rel scale here is the same as in Fig. 9, and h increases from 0.687 to 1.101 km over a horizontal distance that is twice the tangent-line distance from our site to Fig. 9’s observed z base = 1.4 km .

Fig. 20
Fig. 20

Map of binned overcast thickness h calculated from Fig. 9’s measured L ( θ , ϕ rel ) and MODTRAN simulated L ( θ , h ) , with model parameters set to match the conditions observed at USNA on 12 February 2008. The mean h = 0.858 km and its standard deviation s ( h ) = 0.0598 km .

Fig. 21
Fig. 21

Map of binned overcast h calculated from Fig. 4’s measured L ( θ , ϕ rel ) and MODTRAN simulated L ( θ , h ) , with model parameters set to match the conditions observed at USNA on 4 April 2007. The mean h = 0.80 km and s ( h ) = 0.0742 km .

Tables (1)

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Table 1 Sun Elevations for and Positions of Overcast Radiance Maxima

Equations (2)

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G = B ρ T ( ρ ρ T ) 1 ,
B r = G ρ r ,

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