## 3 Determination of VSC  
The Vertical Sky Component (VSC) is defined as the ratio of the vertical diffuse illuminance, \(L_{\rm dv}\), over the unobstructed horizontal diffuse illuminance, \(L_{\rm dh}\), simultaneously measured at the same point, as shown in Equation (1). \[VSC=\frac{L_{\rm dv}}{L_{\rm dh}}. \tag{1}\]  
In this study, the measured global, beam, and diffuse illuminance on a horizontal surface and vertical global illuminance on vertical surfaces facing the four cardinal orientations (north, east, south and west) were used to compute the VSC for subsequent analysis. As \(\rm L_{\rm dv}\)  data were not available at the experimental facility described in the Section 2, these data will be obtained, considering the similar characteristics of both solar irradiance and illuminance. The models developed for solar irradiance prediction on a vertical surface can, therefore, also be employed for daylight calculations [12]. The illuminance incident on a vertical surface, \(\rm L_{\rm gv}\), was evaluated as the sum of beam, \(\rm L_{\rm bv}\), sky-diffuse, \(\rm L_{\rm dv}\), and ground-reflected, \(\rm L_{\rm rv}\), components. It can be written as:  
\[\rm L_{\rm gv}=L_{\rm bv}+L_{\rm dv}+L_{\rm rv}. \tag{2}\] \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **MS-321 LR Sky Scanner** \\ \hline Dimensions (W \(\times\) D \(\times\) H) & 430 mm \(\times\) 380 mm \(\times\) 440 mm \\ Mass & 12.5 kg \\ FOV & \(11^{\circ}\) \\ Luminance & 0 to 50 kcd/m\({}^{2}\) \\ Radiance & 0 to 300 W/m\({}^{2}\) \\ A/D Convertor & 16 bits \\ Calibration Error & 2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sky scanner specifications. \begin{table}
\begin{tabular}{l c} \hline \hline
**Model** & **ML-020S-O** \\ \hline Irradiance Range & 0 to 150,000 lux \\ Output & 0 to 30,000 μV \\ Impedance & 280 \(\Omega\) \\ Operating temperature range & \(\sim\)10 \({}^{\circ}\)C to 50 \({}^{\circ}\)C \\ Temperature response & 0.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Luxmeter technical specifications. \begin{table}
\begin{tabular}{l c} \hline \hline (a) \(\rm L_{\rm gh}>1.2\)-\(\rm L_{0}\) & (e) \(\rm L_{\rm gh}\), \(\rm L_{\rm dh}\), \(\rm L_{\rm hh}\)  if \(\alpha_{\rm s}<5^{\circ}\) \\ (b) \(\rm L_{\rm dh}>0.8\)\(\rm L_{0}\) & (f) \(\rm L_{\rm dh}>1.15\)-\(\rm L_{\rm gh}\) \\ (c) \(\rm L_{\rm hh}>L_{0}\) & (g) \(\rm L_{\rm gh}=(L_{\rm gh}\cdot\cos Z_{\rm s}+\ L_{\rm dh})\pm 15\%\) \\ (d) \(\rm L_{\rm ghv},L_{\rm dh},L_{\rm thh}<20\) Lux & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quality criteria for experimental illuminance measurements. The experimental data were discarded if any of the following conditions were met. \(\rm L_{0}\) is the luminous solar constant (133.8 kLx). Calculation of beam illuminance is quite straightforward, given the position of the sun and the orientation of the surface, as shown in Equation (3):  
\[\mathrm{L_{bv}}=\left(\frac{\mathrm{L_{bh}}}{\sin\alpha_{\mathrm{s}}}\right)\cos \alpha_{\mathrm{s}}\cdot\cos(\phi_{\mathrm{s}}-\phi_{\mathrm{Nr}}), \tag{3}\]  
where \(\alpha_{\mathrm{s}}\) is the solar elevation, \(\phi_{\mathrm{s}}\) is the azimuth angle of the sun, and, \(\phi_{\mathrm{Nr}}\) is the azimuth vertical surface angle (which is 0 for the south-facing surfaces, \(-\frac{\pi}{2}\) for the vertical east surface, \(+\frac{\pi}{2}\) for the vertical west surface, and \(\pi\) for the north surface). It was assumed when estimating the ground-reflected illuminance, \(\mathrm{L_{rv}}\), that vertical surfaces will receive half of the total illuminance reflected isotropically from the ground, ignoring the inter-reflection between the vertical and the ground surfaces. \(\mathrm{L_{rv}}\) depends on the albedo, \(\rho\), and the global horizontal illuminance, \(L_{gh}\), as it is shown in Equation (4). In this work, the value of \(\rho=0.1519\) was experimentally obtained [40]. \[\mathrm{L_{rv}}=\frac{\rho}{2}\mathrm{L_{gh}}. \tag{4}\]  
\(\mathrm{L_{dv}}\) can then be calculated with Equation (5).