A fast and simple model to estimate the contribution of the circumsolar irradiance to measured broadband beam irradiance under cloud-free conditions in desert environment

Routine measurements of the broadband beam irradiance at normal incidence by means of pyrheliometers or equivalent pyranometric systems include unknown contributions from the irradiance originating from within the extent of the solar disc Bnsun, and that from a larger circumsolar region defined by its solid angle aperture, called the circumsolar normal irradiance CSn. This article describes a fast and simple parametric model that estimates the beam and circumsolar radiation, for opening half-angles in the interval [0.4°, 5°], under cloud-free conditions in a desert environment. 1 min measurements of the beam normal Bn, global G and diffuse D horizontal irradiances at Solar Village, Saudi Arabia, and Tamanrasset, Algeria, were used for calibration and validation. Using AERONET measurements as inputs to the radiative transfer code libRadtran, it has been checked-through an 'indirect' validation with the ground measured Bn-that the modelled Bnsun and CSn are accurate. Accordingly, a library of Bnsun and CSn modelled by libRadtran for varying solid angle apertures was generated. Building on this library, a fast parametric model was developed to estimate Bnsun and CSn using G, D and Bn as inputs. The coefficients of the model were fitted to a training set of measurements and then validated twice: once at their respective site, and once at the other site. When using the coefficients for their own site for both Solar Village and Tamanrasset for CSn, the relative bias is respectively −2.7% and −1.5%, the relative root mean square error (RMSE) is 19.9% and 19.6%, and the correlation coefficient is 0.871 and 0.935. As for Bnsun, the relative bias is −2.0% and −2.2%, the RMSE is 2.7% and 3.6%, and the correlation coefficient is 0.999 and 0.998. Applying the coefficients of one site to the other site yields satisfactory results. It is recommended to use the coefficients of Tamanrasset for desert sites exhibiting frequent clear skies, and those of Solar Village for sites exhibiting frequent turbid skies. The coefficients have also been fitted using data from both sites, for a combined model.