Frequency distributions of measured global irradiance for Carpentras (France, 2001) against values generated by different algorithms. For locations with higher yearly global irradiation, the high irradiance peak grows. Mid values are slightly overestimated, and high values are underestimated by the existing models (grey dotted), resulting in RMSE of 0.549% for Aguiar and 0.575% for Skartveit. The modelling quality of the new method (blue) does not overestimate mid irradiance values and shows only little underestimation of high irradiance values. The new RMSE can be reduced to 0.237%.