CIE standard sky model with reduced number of scaling parameters

The calculation of diffuse horizonthal illuminance DV outdoors is generalized and interrelated to parameters that characterize the sky luminance distribution function. The derived analytical formula for DV,rel which is DV normalized using luminance in the zenith can be commonly applicable to all 15 ISO-standardized sky types. This makes the modelling of all 15 skies more uniform than ever before. The presented analytical solution is simplified enough because the set of 60 parameters B1, C1, D1, E1 – B15, C15, D15, E15 scaling the diffuse illuminance is no more necessary in the new solution. In addition, the analytical formulae substituting the empirical ones are valid for all solar altitudes γS (including the situations with sun in zenith). On the contrary, the empirical formulae may become inapplicable for γS > 75° and fail when γS approaches 90°. Compared with detail numerical integration the analytical formula guarantees more rapid calculation of DV,rel.