Measurements of the global surface solar irradiation and its direct and diffuse components performed at three Egyptian sites (Aswan, Cairo, and Port Said) are used to test the ability of two published decomposition models to estimate the hourly direct normal irradiance from the measured global horizontal one in cloud-free conditions. The tested models failed to reproduce the temporal variability of the measurements, which we show to be partly induced by the large variability of the atmospheric content in aerosols. We propose a revised formulation of the decomposition models that takes into account the aerosol optical depth (AOD) at 1000 nm derived from onsite measurements. It leads to a significant reduction of the bias and root mean square deviation of the original models and this at the three Egyptian sites. However, because the AOD is rarely measured at the meteorological stations, we also quantify the performance of the revised models when the AOD is either derived from the MODIS observations or obtained by the products from Copernicus Atmospheric Monitoring Service (CAMS). Probably because of their finer temporal resolution that makes them more apt to reproduce the rapid variations of the AOD, the best results are obtained with the CAMS products. Therefore, we recommend using a combination of the revised decomposition models and these CAMS products to estimate the hourly direct normal irradiance in areas such as Egypt where aerosols are ubiquitous. Note that the improved decomposition models are generally applicable in all-sky conditions, although their benefit has been demonstrated to be significant, and probably limited to, cloud-free conditions.