The three sky types

Statistics on sky types are useful to characterize the climatic trends of a site. For this purpose, three sky types are used in Satel-Light: cloudy, intermediate and sunny. Each sky type corresponds to a range of cloud index values. A cloudy sky corresponds to a cloud index larger than 0.6. An intermediate sky corresponds to a cloud index larger than 0.15 and smaller than 0.6. A sunny sky corresponds to a cloud index smaller than 0.15. This classification was based on the analysis of the frequency distribution of clearness indices in 5 measurements sites (Olseth, 1997) and on the relationship between the cloud index and the clearness index.

The sky luminance distribution

Sky luminance information is essential to assess the performance of daylighting systems. Most apertures of buildings tend to be vertical, at least for residential and office buildings. Vertical windows collect light from the non-zenithal areas of the sky. This leads to a high sensitivity to the specific luminance of the section of the sky seen from the interior of the building. This luminance may change quickly depending on sky type and solar elevation. The ideal information is obtained from hourly or even half hourly sky luminances. This can be generated with Satel-Light.

To produce the sky luminance distribution, we first thought we could use the light reflected by the various pixels above a site. Ineichen (Ineichen, 1996) compared sky scans taken from the ground in Geneva, Switzerland, (145 luminance measurements, every 15 minutes, each of them with an aperture of 10°) and luminances computed from the pixels, assuming clouds to behave as perfect diffusers. The results were disappointing: (1) because of the size of the pixels, the satellite data can only generate a maximum of 9 luminances, (2) these luminances do not take into account the influence of the circumsolar zone, (3) their position in the sky vault change with the altitude of the cloud layer, (4) the altitude of the cloud layer is difficult to determine. We concluded that the satellite information was insufficient to help in finding out the directionality of the light.

Therefore, in Satel-Light, the sky luminance distribution is estimated with models using global and diffuse horizontal irradiances and illuminances as input. Based on earlier studies (Perez, 1993) and (Ineichen, 1994), we have selected the ASRC-CIE Perez sky luminance distribution model (Perez, 1990). This model is a combination of four sky luminance models: (1) the standard CIE cloudless sky (CIE, 1996), (2) a high turbidity formulation of the latter (CIE, 1996), (3) a realistic formulation for intermediate skies proposed by Nakamura (Nakamura, 1985) and (4) the standard CIE overcast sky (CIE, 1996). The linear interpolation between the four models is a function of sky conditions. The figure below gives an idea of the sky luminance distribution predicted by each of the four models (solar elevation: 30°, solar azimuth: 180°).

The Satel-Light server produces every half hour, the average sky luminances of 13 zones in the sky. This sky division in 13 zones (see the figure below) is the minimum needed to take into account the directionality of light (Dumortier, 1995). The sky vault is first divided in 835 cells of identical solid angle (0.0075 sr). The luminance at the center of each cell is computed using the ASRC-CIE Perez model. Then the luminance of each cell covered by a zone is used to compute the average luminance of the zone.