# Numerical Validation of the Radiative Model for the Solar Cadaster Developed for Greater Geneva
## 3 Results
### Mean Irradiance over the Vertical Facades  
The goal of this study is to demonstrate the ability of the solar cadaster to provide accurate results for vertical facades. The results for the homogeneous district are given in Figures 11 and 12, while the results for the heterogeneous district are given in Figures 13 and 14. It appears that the values predicted by the solar cadaster are in good accordance with the values predicted by DIVA-for-Rhino and ENVI-met. Figure 11: Spatial average irradiance received on the facades for the homogeneous district in February. Figure 10: Spatial average of the irradiance received on the unshaded roofs (homogeneous neighborhood or buildings 6 and 7 of the heterogeneous neighborhood). The different orientations of the facades make it possible to evaluate the prediction of the irradiance level for different solar conditions. Indeed, the north facade is mainly irradiated by the diffuse and reflected parts of the solar radiation, while the proportion of direct radiation is higher for the south facade. The east facade is directly irradiated in the morning, while the west facade faces the sun later in the day. Regarding the level of irradiation, it does not have an influence on the concordance of the predicted values. Indeed, the results for the summer day are, in general, as accurate as those for the winter day. The differences between the results of the tools--quantified here with the normalized root mean squared error (NRMSE)--are not significantly impacted by the month of the year considered (see Table 5). The NRMSE values are calculated from differences between the daily profiles of the spatial average irradiance received on the facades and those predicted by the solar cadaster and ENVI-met on the one hand or by the solar cadaster and DIVA-for-Rhino on the other hand. In both cases, the NRMSE remains lower for the roofs (less than 1 % for the roofs versus 4 % to 25 % for the vertical facades; see Table 5). This demonstrates the good accordance between the three tools with respect to the evaluation of the incident radiation on the roof, which are without a mask or reflection here. The observed differences for the vertical facades, which result in an increase in the NRMSE in the last four lines in Table 5, are then due to a difference in the consideration of masks and inter-building reflections. Nevertheless, the time of the year does not influence only the level of irradiance, but also the sun's path. Indeed, regarding the north facade (see Figures 11-14), the results from the solar cadaster are close to the those from DIVA-for-Rhino and ENVI-met (although a bit overestimated). Nonetheless, one peak can be observed in the results at 6:00 a.m. in the month of August (see Figure 12), which is not present for the same facade in February (see Figure 11). This difference in terms of the profile over time for the irradiance level is due to the evolution of the sun's path over the year. Indeed, during the month of August, the sun rises in the north-east and sets in the north-west, while it rises in the east and sets in the west in February. The sun's path has an influence on the level of irradiation as well. Indeed, in the month of February (Figure 11), the south facade shows a slight decrease around noon, which is not present in the GHI (see Figure 9). This decrease is actually due to the shadow cast by building 2 on the central building (see Figures 7 and 8). This does not occur in August because the sun's path is high enough for the shading effect not to occur. The results for the heterogeneous district make it possible to evaluate the ability of the solar cadaster to accurately predict the irradiation level for a more complex city. Indeed, the buildings are randomly located in this case (see Figure 8). The results for the two months considered are given in Figures 13 and 14.