Statistical properties of the sunshine number illustrated with measurements from Timisoara (Romania)

The sunshine number is a Boolean random parameter stating whether the sun is covered or not by clouds. The first four statistical moments of the sunshine number are theoretically derived as a function of a single parameter, the cloud shade. Alternately, this single parameter may be the total cloud cover amount. These parameters are very often measured by the meteorological stations. Time series of global and diffuse solar irradiance recorded at 15-second time intervals between sunrise and sunset during all the days in 2009 in the Romanian town of Timisoara are used to validate the theory. In case of cloud shade representation, there is very good agreement between theory and measurements for all statistical indicators, for all summer and winter days analyzed here, which belong to various classes of cloud shade. In case of cloud cover amount representation, there is a good concordance between theory and measurements when the skewness is considered. In case of the variance and the kurtosis, the concordance is still reasonable. Three types of probability distributions for the sunshine number values have been defined. They were evaluated by using the existing sunshine number database and best fit analytical relationships have been obtained.

Research Highlights
► Sunshine number stating whether the sun is covered or not by clouds.
► The first four statistical moments are theoretically derived.
► Data recorded 2009 in the Romanian town of Timisoara are used to validate the theory.
► Three types of probability distributions have been defined.
► Best fit analytical relationships have been obtained.