A clear-sky solar irradiance model is certainly a basic tool in the estimation of solar resources. With all the abundance of such models, there is plenty of room for searching a clear-sky solar irradiance model with general applicability, i.e. to be able to provide high-accurate estimates in most places around the world. This paper reports an upgraded version (further referred to as SIMv.2) of our parametric clear-sky solar irradiance model SIMv.1, aiming to improve the accuracy of estimates in arid environment. The new elements of SIMv.2, such as new equations for aerosol absorption and downward fraction, have been introduced targeting a better capture of the peculiarities of the solar radiation extinction by aerosols. Overall, the results of testing SIMv.2 at twelve stations located in regions with temperate, arid and tropical climate show that SIMv.2 performs much better than SIMv.1, an improvement in nRMSE of 37.1% for global solar irradiance and of 24.7% for the diffuse component being noticed. The comparison with other fourteen clear-sky solar irradiance models at five stations located in arid climate places SIMv.2 in the class of the best performing models. The limitation of the SIMv.2 performance in extreme weather conditions is discussed in two cases.