# Evaluation of the Urban Weather Generator on the City of Toulouse (France)
## 3 Experimental Results
### Sensitivity Analysis  
The sensitivity analysis of a model such as UWG is an essential step given the large number of input parameters used. As introduced in Section 2.3.2, we rely on the Morris technique whose goal is to identify, with a specific selection of input parameters, how a variation of one input influences the temperature by computing the normalized elementary effects (see Equation (4)) and their standard deviation (see Equation (5)).  
We have depicted in Figure 8a,b the normalized elementary effects of each variable shown in Table 5 along the two chosen pairs of days for the evaluation. The complete description of each input parameter can be seen in Table 5. The objective of this analysis is to order the inputs according to their importance in the model so the quantitative (non-relative) impact of each parameter can not be known. As can be seen in these figures, atmospheric variables (nighttime urban boundary layer height and reference height) seem to have the most impact on the sensitivity of the results. This point will be developed further in Section 4.  
Figure 8a,b shows the impact of each variable on the accuracy of the result. To go more into detail on the interaction of the variables between them, we have plotted in Figure 9, for each variable, the standard deviation of the elementary effect (see Equation (5)) against the elementary effect itself (see Equation (5)). These values have been averaged during all time steps in order to have a global evaluation of the influence of each variable. The interest of such a representation is to highlight three situations:  
1. Input parameters that have a low influence on UWG's output temperatures. The corresponding points are close to the origin since their averaged elementary effects as well as their standard deviations are small;
2. Input parameters that have a linear influence on UWG's output temperatures. The corresponding points follow a line: their standard deviations are proportional to their elementary effects;
3. Input parameters that have a nonlinear influence on UWG's output temperatures or that are in interactions together. Associated points are those that differ from the line mentioned above.  
As can be seen in Figure 9, all albedo variables, grass cover, and daytime boundary layer have almost no effects on the output (first situation listed above). Tree cover and other surface parameters (building height, facade length, and building density) have a linear influence on the temperature, noting however that building density (from 0.1 to 0.8) has a stronger impact on air temperatures of up to 5.6 \({}^{\circ}\)C (second situation listed above, see Figure 10c). Reference height \(href\) has also an important linear impact on air temperature. Nighttime urban boundary layer height \(ubl\_night\) is in the third situation, i.e., has a non-linear influence or is in interaction with other variables. Since it is the only variable in this situation, it is likely that it has a non-linear influence on UWG's output air temperature rather than an interaction effect with other inputs.  
Figure 8: **Hourly normalized elementary effects of the input UWG parameters**. Simulations were performed on Carmes station on sunny and hot days in August 2020, the 5 th–6 th **(a)** and 19 th–20 th **(b)** using Centre equestre as a rural station. **(a)** 5 and 6 August 2020. **(b)** 19 and 20 August 2020.  
To quantitatively assess the influence of the input parameters, we have plotted the simulated air temperatures at Carmes station for the eight most influential parameters in Figure 10. As can be seen, the atmospheric parameters in Figure 10a-d and the building density in Figure 10e,f show the greatest variability in the simulated air temperatures (up to 0.87 \({}^{\circ}\)C on average). In contrast, surface parameters such as facade length in Figure 10g,h have a small influence on the variability of the output (up to 0.16 \({}^{\circ}\)C on average).