## 4 Comparative Study of the Different Approaches to Obtain the VSC  
Three different procedures to calculate the VSC have been described. In this section, the results of the different approaches to calculate the VSC in Burgos during the experimental campaign will be compared, taking the VSC calculated by Equation (6) as a reference. The comparison was conducted on a half-hourly basis. The two widely used statistical parameters, root mean square deviation, RMSD, and mean bias deviation, MBD, calculated in Equations (13) and (14), respectively, were chosen as indices to assess any differences between the procedures:  
\[\text{RMSD}=100\cdot\sqrt{\frac{1}{\text{n}}\sum_{\text{i}}\biggl{(}\frac{( \text{X}_{\text{estimation}}-\text{X}_{\text{measured}})}{\text{X}_{\text{measured}}} \biggr{)}^{2}} \tag{13}\]  
\[\text{MBD}=100\cdot\frac{1}{\text{n}}\ \sum_{\text{i}}\frac{(\text{X}_{\text{ estimation}}-\text{X}_{\text{measured}})}{\text{X}_{\text{measured}}} \tag{14}\]  
Information on the long-term performances of the estimation is given by the MBD. The RMSD indicates the data scattering around the estimation and gives information on the short-term performance. The calculation of the diffuse illuminance on surfaces of any inclination and orientation is carried out by means of Equations (7)-(10), from the measurements of the sky scanner. An estimation of the error in the calculation of the diffuse illuminance can be obtained comparing the experimental data of horizontal diffuse illuminance, L\({}_{\text{dh}}\), and the one that is calculated from the projection on the horizontal surface of the sky luminance pattern obtained with the sky scanner data. The RMSD and the MBD, both for the city of Burgos and for all experimental results of L\({}_{\text{dh}}\) recorded during the experimental campaign, were 27.14% and \(-\)3.8%, respectively. Hence, the use of the sky scanner data from the device used in this study (EKO, model MS-321 LR) to determine illuminance on inclined surfaces facing any orientation had an implicit error higher than 25% in the city of Burgos. This error was caused by three main factors. First, the field of view (FOV) of the sky scanner (11\({}^{\circ}\) as indicated in Table 1). Secondly, the main assumption of the measurement with the sky scanner: As shown in Figure 2, it was assumed that the luminance of a sky patch was the value measured in the circumference inscribed within that patch. Thirdly, every scanning time was about 4 min and the measurements were taken every 15 min. Therefore, important variations in sky illuminance may occur between records. The experimental data of L\({}_{\text{dv}}\) were obtained from Equation (5). Those values, calculated on the four cardinal facing surfaces, were compared to those calculated as projections on the same surface using the sky-scanner luminance pattern. Both the RMSD and the MBD values are recorded in Table 5 and, as can be appreciated, are comparable to those obtained for horizontal diffuse illuminance. It can, therefore, be concluded from this study that the use of the sky-scanner measurements, to determine the diffuse illuminance on any horizontal or tilted surface, had an intrinsic RMSD due, mainly, to the technical specifications of the experimental device, near 30%, agreeing with other works [11]. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Orientation** & **RMSD (\%)** & **MBD (\%)** \\ \hline \multirow{4}{*}{**Vertical**} & South surface & 27.31 & \(-\)3.55 \\ \cline{2-4}  & North surface & 21.46 & \(-\)0.31 \\ \cline{2-4}  & East Surface & 31.19 & \(-\)11.87 \\ \cline{2-4}  & West Surface & 27.69 & 4.63 \\ \hline
**Horizontal** & & 27.14 & \(-\)3.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: RMSD and MBD calculated for the vertical diffuse illuminance, L\({}_{\text{dv}}\), and the horizontal diffuse illuminance, L\({}_{\text{dh}}\). The reference values of L\({}_{\text{dv}}\) were calculated from Equation (5). The reference values of L\({}_{\text{dh}}\) were measured in the experimental facility, described in Section 2.