# Evaluation of the Urban Weather Generator on the City of Toulouse (France)
## 2 Materials and Methods
### UWG Evaluation  
For this study, we select 2 periods of 2 consecutive days where the meteorological conditions are favorable for UHI. They correspond to 5 th-6 th and 19 th-20 th of August 2020. On these days, the sky was clear (no decrease in radiation fluxes due to the presence of clouds), atmospheric pressure, humidity, and wind speed were low and therefore air temperatures reached high levels [54] (above 30 \({}^{\circ}\)C). The main meteorological variables for these pairs of days are shown in Figure 3.  
Formally, from atmospheric, surface parameters and measurements from the rural station, UWG estimates a series of temperatures \(\hat{T}(t)=UWG(\Theta_{a},\Theta_{r},\Theta_{u},t)\) with:  
* \(UWG\) the UWG model's function;
* \(t\in[t_{min},t_{max}]\) the discrete-time;
* \(\Theta_{a}\) the set of \(N_{a}\) input atmospheric parameters: \(\Theta_{a}:\{\theta_{ni}\},i\in[1,N_{a}]\);
* \(\Theta_{r}\) the set of \(N_{r}\) input parameters associated with the rural station: \(\Theta_{r}=\{\theta_{ri}\}\), \(i\in[1,N_{r}]\);
* \(\Theta_{u}\) the set of \(N_{u}\) input internal parameters associated with the urban surface: \(\Theta_{u}=\{\theta_{ui}\},i\in[1,N_{u}]\).  
Note that for notation purposes, we also denote \(\hat{T}(t)=UWG(\Theta,t)\) with \(\Theta\) the set of input parameters: \(\Theta=\{\Theta_{a},\Theta_{r},\Theta_{u}\}\). As mentioned in Section 2, we evaluate UWG under the view of estimated temperature accuracy in Carmes station. Given that the model depends on a large number of parameters of different natures, to understand into details, its behavior, we analyze its accuracy under the view of:  
1. The impact of the rural station;
2. The sensitivity concerning atmospheric and urban parameters;
3. The UWG performances that simulate urban temperatures under real conditions.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Group** & **Parameter** & **Description** & **Carmes** \\  & & & **Values** \\ \hline \multirow{4}{*}{City Information} & \multirow{4}{*}{bldtype} & Building Type from U.S. Department of & \\  & & Energy (DOE) classification. Fifteen & \\  & & commercial building types and one & \\  & & multifamily residential building were & \\  & & determined by consensus between & \\  & & DOE [53]. & \\ \hline \multirow{4}{*}{City Information} & \multirow{4}{*}{bldtera} & Building Built Era must be one of the & \\  & & following: “pre80” (pre-1980s), “pst80” & \\  & & (post-1980s), or “new” (new & \\  & & construction). & \\ \hline \multirow{4}{*}{City Information} & \multirow{4}{*}{bld} & Building Array. For each combination & LargeOffice, \\  & & building type-building built era, its & \\ \cline{1-1}  & & fraction of the total built stock the & \\ \cline{1-1}  & & building occupies is given. & \\ \cline{1-1} \cline{2-4}  & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._Figure 3: Meteorological conditions for 5–6 August 2020 and 19–20 August 2020 at Centre équestre rural station. For these sunny pairs of days, we illustrate the meteorological situation **favourable to UHI** through wind speed, humidity, atmospheric pressure, downwelling shortwave (SWD) and longwave (LWD) radiative fluxes. (**a**) Wind speed on 5 and 6 August 2020. (**b**) Wind speed on 19 and 20 August 2020. (**c**) Humidity on 5 and 6 August 2020. (**d**) Humidity on 19 and 20 August 2020. (**e**) Pressure fluxes on 5 and 6 August 2020. (**f**) Pressure fluxes on 19 and 20 August 2020. (**g**) SWD fluxes on 5 and 6 August 2020. (**h**) SWD fluxes on 19 and 20 August 2020. (**i**) LWD fluxes on 5 and 6 August 2020. (**j**) LWD fluxes on 19 and 20 August 2020.  
The methodology associated with these three steps is described in the following three paragraphs.