Model represents overcast sky with ideal unity sky luminance, i.e. each sky element has the same luminance value. This model is also so called „Lambertian model“
▼Lambert, J.H. Merkwűrdigste Eigenschaften der Bahn des Lichts durch die Luft und űberhaupt durch verschiedene sphärische und concentrische Mittel, 1773. (Notable qualities of the light path through the air and mainly through various spherical and concentric particles). German translation from the French origin. Haude – Spener, Berlin.
Model represents a sky luminance distribution pattern of homogeneous sky considering average cloud influence. The sky luminance distribution is calculated in physical unit cd/m2.
▼Littlefair, P.J. The luminance distribution of an average sky. Lighting Research and Technology, 1981, 13, 4, p. 192-198.
(LITTLEFAIR_LRT_1981_4-192_The luminance distribution of an average sky .pdf)
▼Roy, G.G., Ruck, N., Reid, G., Winkelmann, F.C., Julian, W. The Development of Modelling Strategies for Whole Sky Spectrums under Real Conditions for International Use. ARC Project A89131897, Final Report, University of Sydney, Murdoch University, September 1995.
https://simulationresearch.lbl.gov/dirpubs/skymap_report.pdf
The luminance at the sky element La is express by the formula:
▼Nakamura, H. and Oki, M. and Iwata, T. Mathematical Description of the Intermediate Sky, Proceedings 21st CIE Session, Venice, La Scientifica, 1987, p. 230-31.
▼Roy, G.G., Ruck, N., Reid, G., Winkelmann, F.C., Julian, W. The Development of Modelling Strategies for Whole Sky Spectrums under Real Conditions for International Use. ARC Project A89131897, Final Report, University of Sydney, Murdoch University, September 1995.
https://simulationresearch.lbl.gov/dirpubs/skymap_report.pdf
Perradeau proposed Nebulosity Index N and classified 5 categories of sky luminance distributions for: – Overcast sky, – Intermediate Overcast Sky. – Intermediate Mean Sky, – Intermediate Blue Sky, – Blue Sky
Table. Values of coefficients
▼Perraudeau, M. Luminance models. Proc. CIBSE National Lighting Conf., Cambridge, UK, 1988, p. 291-292.
▼Perraudeau, M. “Distribution de la Luminance du Ciel”, Cathiers du Centre Scientifique et Technique du Batiment – CSTB 2305, December 1988.
Perez at al. proposed Clearness Index and Sky Brightness Index to select sky luminance patterns in the range of overcast skies to clear skies. Model is based on the measured diffuse and direct irradiance and calculated air mass. The relative luminance lv is defined as the ratio between the luminance of the considered sky element La, and the luminance of an arbitrary sky element as
▼Perez, R., Seals, R., Michalsky, J.: All-weather model for sky luminance distribution – Preliminary configuration and validation. Solar Energy, 1993, 50, 3, p. 235-245.
(Perez_All-weather model for sky luminance_SE_1993-50-3-235-245.pdf)
▼Roy, G.G., Ruck, N., Reid, G., Winkelmann, F.C., Julian, W. The Development of Modelling Strategies for Whole Sky Spectrums under Real Conditions for International Use. ARC Project A89131897, Final Report, University of Sydney, Murdoch University, September 1995.
https://simulationresearch.lbl.gov/dirpubs/skymap_report.pdf
Model describes sky luminance pattern similar to clear sky but with higher atmospheric turbidity
▼Matsuura K. Luminance distributions of various reference skies. CIE Technical report, T.C.3-09 (Draft), 1988.
▼Matsuura K. and Iwata T. A model of daylight source for the daylight illuminance calculations on the all weather conditions. Proc. Daylight Conf., Moscow, 1990, A2, pp.1-6.
▼Matsuura, K. (1994). Spatial distribution of daylight – Luminous distribution of various reference skies. Publ. CIE 110-1994, CIE Central Bureau, Vienna.
The All Sky Model- R and the All Sky Model-L developed by Igawa et al. classifies sky conditions from the solar radiation data and formulate sky radiance distribution and sky luminance distribution for all sky conditions. Models are based on the stattistical evaluation of meteorological data global, direct and diffuse irradiances and luminous efficacy model. The sky radiance and luminance distribution are expressed in absolute values
▼Igawa, N., Koga, Y., Matsuzawa, T., Nakamura, H. Models of sky radiance distribution and sky luminance distribution. Solar Energy, 2004, 77, 2, p. 137-157.
(IGAWA_SE_2004_2-137_Models of sky radiance distribution.pdf)