Luminous efficacy of direct solar radiation for clear skies

In the present work we have modelled mean hourly values of the luminous efficacy of direct solar radiation for clear skies in Madrid using solar elevation as the only independent variable. Models of the polynomial type, similar to those given by different authors, and a model for the direct luminous efficacy mathematically coherent with the corresponding models of direct illuminance and irradiance, are developed. This last luminous efficacy model can be obtained from the corresponding illuminance and irradiance models in an apparently new approach to the subject, and shows a statistical performance as good as the polynomial models. We have taken the opportunity to show how arbitrary polynomial luminous efficacy models can be, and tested the dependence of coefficients in these models on local climatic conditions.