Analytical expressions for estimating sky diffuse irradiance and illuminance on tilted planes for the CIE Standard General Skies

Abstract This work proposes a set of analytical expressions for the calculation of the relationship between sky diffuse illuminance on a tilted plane and horizontal plane corresponding to the 15 ISO/CIE standard sky types. Given the parallelism in the angular distribution of sky diffuse radiance and luminance, these expressions can also be used to calculate the diffuse sky irradiance on an inclined plane. The proposed analytical expressions are obtained by adjusting the results of a numerical calculation whose methodology is described in detail in the paper. The use of these analytical expressions significantly reduces the calculation time. It is verified that the relative root-mean-square errors obtained with the analytical expressions are small compared with the use of numerical calculation, ranging from 0.03% to 4.09%, and with a tendency to increase with clear skies and high solar zenith angles.