Empirical modeling of hourly direct irradiance by means of hourly global irradiance

A very important factor in the assessment of solar energy resources is the availability of direct irradiance data of high quality. Nevertheless, this quantity is seldom measured and thus must be estimated from measures of global solar irradiance, a quantity that is registered in most radiometric stations. In this work we analyze the results provided by different models in the estimation of hourly direct irradiance values. We have selected several models proposed by Orgill and Hollands, Erbs et al., Reindl et al., Skarveit and Olseth, Maxwell, and Louche et al. With the exception of the model from Louche et al. that estimates direct irradiance values from direct transmittance values, all of the models estimate direct irradiance from the diffuse fraction. The data set used in this study comprises 25 000 hourly values of global and diffuse irradiance. These values were registered in six Spanish locations with different climatic conditions. The results provided by the model depend on the clearness index, kt, and the solar elevation. The best results are obtained for cloudless skies and higher solar elevation. In those conditions we can estimate the direct irradiance with a root square mean error close to 14% of the average measured value. We have estimated the direct irradiance under cloudless sky conditions using a parametric model proposed by Iqbal. In order to analyze the effect of turbidity on the estimation of direct irradiance we have compared the results obtained by the parametric model when using hourly values of the Angstrom turbidity parameter β with those obtained when using monthly means of hourly values of β.