Using a large dataset of 135 stations encompassing very diverse geographic locations (82.5 degrees N to 67.6 degrees S) and climates, two new models are presented to predict the monthly-average hourly global irradiation distribution from its dairy counterpart. It is found that a quadratic in the sine of solar elevation fits the data very well at all locations. Other parameters include the mean monthly clearness index, K-t, the average day length, and the daily average solar elevation. Based on this dataset, a detailed performance assessment is conducted for these new models, as well as for six models of the literature. Their respective performance is discussed, particularly with respect to the latitudinal effect. The proposed models appear to correctly predict irradiations even for a very low sun typical of near-polar night conditions. The accurate predictions of the newly proposed ＇daily integration model＇ translate into the lowest yearly-average and site-average Root Mean Square Difference, a statistic obtained by comparison with 21 722 measured hourly irradiations. However, it is stressed that the performance of this kind of model is seriously limited by artefacts due to shading (e.g., from mountains), and, more importantly, by strong morning/afternoon radiative asymmetries due to local or climatological influences, which cannot be predicted from just daily irradiation data. (C) 2000 Elsevier Science Ltd. All rights reserved.