. Relation between cloud index and clear sky index
The clear sky index is an appropriate and thus an established quantity for the description of the transmission properties of the Earth's atmosphere.
It is defined by
k* = Ig / Idear (3)
where the current global radiation Ig is related to the expected clear sky radiation Idear. In addition a model is needed, which describes the atmospheric conditions, a so called clear sky model, see sec. 2.2.
[Beyer et al. 96] introduced the relation
k* = 1 - n (4)
into the Heliosat method. This relation can be used without a previous calibration with ground data, but it is necessary that the clear sky model is optimally adapted to the regarded area. By Fontoynont et al.  relation (4) was improved in order to detail the case of complete cloudiness and to limit the clear sky index to meaningful values.