In this paper, a procedure for generating a family of parametrical broadband clear-sky models is described. The key element is the conversion of one or more model input variables into tunable mathematical parameters. The approach is tested on the PS model [Paulescu, M. and Schlett, Z., Theor. Appl. Climatol. 75, 203 (2003)], with the free parameter being the Ångström exponent (α). This allows us to fine-tune for conditions dominated by desert dust, urban-industrial, and mixed aerosols. We find that for an arbitrary set of data, the optimal value of the free parameter is not the same as its actual measured value (inserting the measured value in the model would result in a lower performance). We attribute this fact to the inaccurate nature of the base model. The optimal α value varies with the considered solar irradiance component, aerosol type and loading, and the error measure(s) used for assessing model accuracy. A set of recommended models for each aerosol type and loading class is given. The tabled values for the aerosol transmittance coefficients are also listed. A preliminary validation shows that the newly developed models are very reliable. The optimal version generally falls within a few percent of the results of REST2v5, a benchmark model in clear-sky solar irradiance estimation. While some established models outperform REST2v5 for certain aerosol types and for only one solar irradiance component, the new models prove competitive under most scenarios. Beyond showing the performance of the developed model family, these results hint at great potential of our approach.
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