# Numerical Validation of the Radiative Model for the Solar Cadaster Developed for Greater Geneva
## 2 Materials and Methods
### Weather Conditions for the Study  
The present study focused on two different days: 15 February, which had a short daylight period, and 16 August, which had a longer one. These two days are representative of a winter and a summer day for a location such as Geneva (cold and not very sunny for the first, hot and more sunny for the second). Furthermore, the sun's path corresponding to these two days was halfway between the solstices and the equinoxes.  
The two days were actually those for which the sun's path was closest to the mean paths for the months. Indeed, in order to reduce the number of simulated days (two days to be simulated for the months of February and August instead of 59) while avoiding the specific conditions of a given day, this study considered two representative average days for the two considered months [10]. A representative average day (RAD) is defined, according to Equation (6), as a day for which the meteorological conditions (including irradiation level, temperature, and wind velocity and direction) for each hour are equal to the average of these conditions over all days of the month (\(N_{day}\)). Carrying out the study for two different months allowed us to evaluate the influence of the irradiation level on the accuracy of the predicted results.  
\[X_{RAD}(t)=<X_{i}(t)>_{N_{day}} \tag{6}\]  
where \(<\cdots>\) stands for the time-average operator.  
The two considered months had a double advantage. First, they allowed the validation of the values predicted by the solar cadaster under low and high irradiation levels (February and August, respectively). Second, they made it possible to evaluate the influence of the evolution of the sun's path over the year on the irradiance profiles.  
Since the solar cadaster was developed for Greater Geneva, the fictitious districts studied were located at this place. The data used as input for the simulations came from the METEONORM(r) version 7.3 database for this city. The hourly averaged values issued from the METEONORM database were then averaged by month according to Equation (6) in order to reduce the computation time. Since the values used as input for the simulations were averaged by hour, the level of irradiation was considered constant between two consecutive hours for both the input and output data.  
In this study, only the shortwave radiation (SW) was considered, as it is the most important energy content in the solar spectrum. Thus, the waveband considered was 2500 nm. The daily profiles of the different components of the solar radiation over Geneva for the representative days of the months of February and August are given in Figure 9. The direct shortwave radiation represents the amount of energy that comes straight from the sun, while the diffuse part is the amount of solar radiation reflected by the atmosphere prior to hitting the ground. The total shortwave radiation is the sum of the direct and the diffuse parts.  
Although the overall evolution of the shortwave radiation is similar between February and August, differences are noticeable. Indeed, the maximum in terms of GHI is two times higher in August. This is mainly due to the direct part of the solar radiation, which exceeds 350 W m\({}^{-2}\) in August, in comparison with 150 W m\({}^{-2}\) in February.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Indicator** & **Definition** & **Value** \\ \hline Building Height & & 18 m to 42 m \\ Street Width & & 5 m to 25 m \\ Height-to-Width Ratio & Ratio between the building height and the width of the distance between buildings & 0.72 to 8.4 \\ Number of meshes per facade & & 360 to 840 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Urban morphology indicators specific to the heterogeneous district.