An approximate formula for sky luminance under overcast conditions taking into account different pollution content of the atmosphere is determined. The homogeneous cloud layer is considered to be a constant source of light, while the undercloud atmosphere is taken as a single scattering medium. The final mathematical expressions depend on turbidity and scattering ability of the undercloud atmosphere as well as on the altitude of the clouds. Such a parameterised model is therefore easily scalable and well adjusted to the actual meteorological situation (contrary to empirical models in current use). The derived analytical formula is suitable for engineering practice to perform rapid simulations of sky luminance.
Get full access to this article
View all access options for this article.
References
1.
Kittler R., Valko P.Radiance distribution on densely overcast skies: Comparison with CIE luminance standard. Solar Energy1993; 51: 349-355.
2.
Commission Internationale de IEclairage. Natural Daylight, Official Recommendation. Compte Rendu CIE 13 Session 1955, 2, part 3.2, 2-4.
3.
Lenoble J.Radiative transfer in scattering and absorbing atmospheres: standard computational procedures. Hampton: A. Deepak Publishing , 1985.
4.
Minin INTheory of radiative transfer in planetary atmospheres. Moscow: Nauka, 1988, (in Russian).
5.
Lehar MA, Glicksman LRRapid algorithm for modeling daylight distributions in office buildings . Building and Environment2007; 42: 2908-2919.
6.
Li DHW , Tsang EKW.An analysis of daylight performance for office buildings in Hong Kong. Building and Environment2008; 43: 1446-1458.
7.
Carter DJThe measured and predicted performance of passive solar light pipe system . Lighting Research and Technology2002; 34: 39-52.
8.
Kocifaj M., Darula S., Kittler R.HOLIGILM: Hollow light guide interior illumination method - An analytic calculation approach for cylindrical light-tubes. Solar Energy2008; 82: 247-259.
9.
Born M., Wolf E.Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 7th Edition. Cambridge: Cambridge University Press, 1999.
10.
Zuev VE, Krekov GMOptical models of the atmosphere. Leningrad: Gidrometeoizdat, 1986, (in Russian).
11.
Davis JMAn evaluation of the delta-Eddington contrast transmission model. Atmospheric Environment1991; 25A: 1679-1687.
12.
Kocifaj M.Optical air mass and refraction in a Rayleigh atmosphere. Contributions of the Astronomical Observatory Skalnaté Pleso1996; 26: 23-30.
13.
Thomas GE, Stamnes K.Radiative transfer in the atmosphere and ocean. Cambridge : Cambridge University Press, 2002 .
14.
Gibson FWIn situ photometric observations of angular scattering from atmospheric aerosols . Applied Optics1976; 15: 2520-2533.
15.
Yang S., Cotton WR, Jensen TLFeasibility of retrieving aerosol concentration in the atmospheric boundary layer using multiangle lidar returns and visual range. Journal of Atmospheric and Oceanic Technology1997; 14: 1064-1078.
16.
Horvath H., Alados Arboledas L., Olmo FJ, Jovanović O., Gangl M., Kaller W., Sanchez C., Sauerzopf H., Seidl S.Optical characteristics of the aerosol in Spain and Austria and its effect on radiative forcing. Journal of Geophysical Research2002; 107(D19): AAC9.1-AAC9.18.
17.
van de Hulst HCMultiple light scattering. tables, formulas and applications. New York, London , Toronto, Sydney, San Francisco: Academic Press, 1980 .
18.
Braak JC, de Haan JF, Van der Mee CVM, Hovenier JW, Travis LDParameterized scattering matrices for small particles in planetary atmospheres . Journal of Quantitative Spectroscopy and Radiative Transfer2001; 69: 585-604.
19.
Toublanc D.Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations. Applied Optics1996; 35: 3270-3274.
20.
Box MA, Deepak A.Retrieval of aerosol size distributions by inversion of simulated aureole data in the presence of multiple scattering. Applied Optics1979; 18: 1376-1382.
21.
Stramski D. , Sedlák M.Application of dynamic light scattering to study of small marine particles . Applied Optics1994; 33: 4825-4834.
22.
Moon P., Spencer DEIllumination from a nonuniform sky. Illuminating Engineering1942; 37: 707-726.
23.
Muneer T.Evaluation of the CIE overcast sky model against Japanese data. Energy and Buildings1998; 27: 175-177.
24.
Brunger A., Hooper F.Anisotropic sky radiance model based on narrow field of view measurements of shortwave radiance. Solar Energy1993; 51: 53-64.
25.
Kokhanovsky AALight scattering media optics. Berlin, Heidelberg, New York : Springer-Verlag, 2004 .
26.
BenZvi SY, Connolly BM, Matthews JAJ, Prouza M., Visbal EF, Westerhoff S.Measurements of the aerosol phase function at the Pierre Auger Observatory. Astroparticle Physics2007; 28: 312-320.
27.
Pesic P.Estimating Avogadro’s number from skylight and airlight. European Journal of Physics2005; 26: 183-187.
28.
Tiwari YK, Devara PCS, Raj PE, Maheskumar RS, Pandithurai G., Dani KKTropical urban aerosol distributions during pre-sunrise and post-sunset as observed with lidar and solar radiometer at Pune, India. Journal of Aerosol Science2003; 34: 449-458.
29.
Guyon P., Boucher O., Graham B., Beck J., Mayol-Bracero OL, Roberts GC, Maenhaut W., Artaxo P., Andreae MORefractive index of aerosol particles over the Amazon tropical forest during LBA-EUSTACH1999. Journal of Aerosol Science2003; 34: 883-907.
30.
Liu L., Mishchenko MI, Menon S., Macke A., Lacis AAThe effect of black carbon on scattering and absorption of solar radiation by cloud droplets. Journal of Quantitative Spectroscopy and Radiative Transfer2002; 74: 195-204.
31.
Li DHW , Lau CCS , Lam JCOvercast sky conditions and luminance distribution in Hong Kong. Building and Environment2004 ; 39: 101-108.
32.
Soler A., Robledo L.Investigation of the overcast skies luminance distribution using 35 sensors fixed on a dome. Energy Conversion and Management2005; 46: 2739-2747.
33.
Commission Internationale de I’Eclairage.Spatial distribution of daylight - CIE standard general sky. CIE Publication S011/E:2003, Vienna: CIE, 2003.
34.
International Organization for Standardization (ISO).Spatial distribution of daylight - CIE standard general sky. ISO Standard 15469:2004, Geneva: ISO, 2004.
35.
Tregenza PRA simple mathematical model of illumination from a cloudy sky. Lighting Research and Technology1980; 12: 121-128.
