# Numerical Validation of the Radiative Model for the Solar Cadaster Developed for Greater Geneva
## 3 Results
### Irradiance Maps  
Although the results presented so far show a good accordance between the three tools, a consideration of the spatial mean value alone is not sufficient. Indeed, as shown in Figures 15 and 16, the range of the level of irradiance received over the facade can be very important. The range of the predicted values may be due to the method of modeling radiative phenomena (ray-tracing or radiosity) or the shading effect. The latter may have an important impact on the level of irradiance. Thus, the study of the mean irradiance over the facades needs to be complemented with the study of irradiance maps. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**February**} & \multicolumn{2}{c}{**August**} \\
**Facade** & **ENVI-Met** & **DIVA** & **ENVI-Met** & **DIVA** \\ \hline North Facade & 32.46 & 28.00 & 36.30 & 32.98 \\ South Facade & 12.11 & 10.09 & 12.45 & 7.76 \\ East Facade & 22.46 & 18.72 & 18.66 & 21.54 \\ West Facade & 26.69 & 25.30 & 21.22 & 21.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Normalized root mean squared error of the predicted level of irradiance (%) in the heterogeneous district. Figure 14: Spatial average irradiance received on the facades in the heterogeneous district in August. The level of irradiance on unshaded roofs appears to be perfectly homogeneous and equal for the three tools considered, and it corresponds to the sum of the BHI and the DHI when given as the input of the simulation. Figure 16: Distribution of the irradiance over the vertical facades for the homogeneous district in August. Figure 15: Distribution of the irradiance over the vertical facades for the homogeneous district in February. Nevertheless, the level of irradiance on the vertical facades depends on the orientation of the facade, the time of the day, and the time of the year. The levels of irradiance for the south facade of the central building of the homogeneous district are given in Figure 17. Figure 17a-c show the results for the month of February, while Figure 17d-f show the results for the month of August. Regarding the data, not all are used for comparisons. All of the facades of the buildings are 20 m wide. However, the data at the edges of facades were not analyzed. Indeed, these data are difficult to compare because of the difference in terms of the calculation method for the three tools considered (depending on the tool, irradiance is considered as that at the center of the mesh or as the average over it); see Figure 4. This source of difference, due to the schemes specific to the tools, does not lead to a significant difference in the results, except at the edges of the facades. The irradiance levels appear to be more homogeneous on the south facade for the month of August than for the month of February. This can be explained by the sun's higher path at this time of year. The greater range in terms of value (see Figures 15 and 16) is then due to the shading effect, which is more intense in February and leads to a range of irradiance of 50 W m\({}^{-2}\) over the south facade in August in comparison with 350 W m\({}^{-2}\) in February. Regarding the level of irradiance predicted by the solar cadaster, which is shown in Figure 17a,d, the values are similar to those predicted by ENVI-met and DIVA-for-Rhino. Figure 17: Irradiance map of the homogeneous district for the south facade over 12 h.  
Nevertheless, although the predicted irradiance levels are close to each other, there are two particular points. First, the shape induced by the shading is not exactly the same for the solar cadaster and ENVI-met on the one hand and for DIVA-for-Rhino on the other hand. The latter predicts a smoother evolution of the predicted irradiance level. This smoothness is due to the method used for the evaluation of the radiative phenomena; DIVA-for-Rhino uses ray-tracing while ENVI-met and the solar cadaster use the radiosity method. The second point is how the irradiance is evaluated.