A model yielding hourly global irradiance from cloud observations is presented. Tested against independent observations of hourly irradiance, the model yields a correlation coefficient 0.92. The corresponding correlation coefficients for daily and monthly values are 0.975 and 0.998, respectively. The mean bias and root-mean-square errors for hourly data are less than, respectively, 3% and 30% of the average. Moreover, the frequency distributions and the lag one autocorrelations of modelled hourly averages are close to those of the observed data.