Clear sky luminance and illuminance Lvcl, Evclh--Algorithm 1.32

The relative luminance of the clear sky is given by a standard formula published by the CIE (1) which gives the luminance of a sky point as a fraction of the zenith luminance. Empirical equations give the zenith luminance and the corresponding illuminance on the ground.

a. Luminance distribution

This version of the CIE distribution uses illuminance turbidity as a parameter. The original CIE formulation gives 2 separate equations which correspond to Til =2.45 and Til =5.5, for clean and industrial atmospheres respectively.

Input
Solar altitude, gs radians
Altitude of sky point, g radians
Angular distance of sky point from sun, q radians
(algorithm 5.13 or using cosq = sing sings + cosg cosgs cos(a-as) )
Illuminance turbidity factor ,Til (algorithm1.21)
Relative optical air mass, m (algorithm1.22)
Extraterrestrial solar illuminance, Evo klx (algorithm1.23)
Mean extinction coefficient, (algorithm 1.24)

Equation
The relative luminance of a sky point at altitude g and angular distance q from the sun is

Source
Kittler(2)

b. Zenith luminance

An alternative luminance distribution formula was developed by Nagata(3,4,5) from luminance measurements made in Japan. This formula gives absolute luminance values with a distribution similar to the CIE equation. It may be used to predict zenith luminance with atmospheres of given turbidity.

Input
Solar altitude, gs radians
Illuminance turbidity,Til (algorithm1.21)
Relative optical air mass, m (algorithm1.22)
Extraterrestrial solar illuminance, Evo klx (algorithm1.23)
Mean extinction coefficient, (algorithm 1.24)

Equation

Source
Kittler(2) , Nagata(5)

c. Horizontal illuminance

With moderate turbidity (approximately Til=3) the illuminance on the ground from the clear sky may be estimated from the following empirical equation (illuminance from direct sun is, of course excluded):

Input
Solar altitude, gs
Equation

Source
IES(6)
References
  1. Commission Internationale de lĠEclairage Standardisation of luminance distribution on clear skies (Paris: Commission Internationale de lĠEclairage) (1973)
  2. Kittler R Luminance distribution characteristics of homogeneous skies: a measurement and prediction strategy Lighting Research and Technology 17 (4) 183-188 (1985)
  3. Nagata T Luminance distribution of clear skies, part 1: measurements of the luminance distribution Transactions of the Architectural Institute of Japan (185) 65-70 (1971)
  4. Nagata T Luminance distribution of clear skies, part 2: theoretical considerations Transactions of the Architectural Institute of Japan (186) 41-48 (1971)
  5. Nagata T Luminance distribution of clear sky and the resulting horizontal illuminance Journal of Light and Visual Environment 7 (1) 23-27 (1983)
  6. IES Calculation Procedures Committee Recommended practice for the calculation of daylight availability Journal of the Illuminating Engineering Society of North America 13 (4) 381-392 (1984)

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