The present study evaluates the performance of thirty-eight (38) parametric solar radiation models under a large range of conditions. The models are used to predict the clear-sky DNI at a 1-min time resolution. High quality radiometric databases, recorded at PSDA station, located in the Atacama Desert, Chile, are used for this analysis. The models have been arranged into seven sets according to their crucial inputs to identify the impact of each parameter on models' performance. The results show that turbidity-independent models (sets A, B and C) are not suitable for the modeling of solar direct irradiance. Besides, turbidity-dependent models (sets D, E, F, and G) perform so much better than turbidity-independent models. However, few models perform well under all conditions. Among 11 AOD-dependent models, only six models are considered "good". The performance of the models of set F decreases with the increase of beta (aerosols' turbidity), while those belonging set G perform adequately even at high turbidity. Overall, the accuracy of most models is sensitive to solar elevation and atmospheric turbidity. Besides, some models are accurate only under limited conditions. As a result of this detailed investigation, six high-performance models can be recommended: ESRA, Ineichen, Yang, MLWT1, REST and MWLT2. (C) 2019 Published by Elsevier Ltd.