## 4 Result and Discussion  
All of the data described in the previous section were processed by the ENVI-IDL procedure, and the results of the different parameterizations were compared, to quantify the impacts of each element of the processing chain. As can be seen in Figure 7, the statistics on the corrected temperatures derived by computing the atmospheric parameters using the different vertical profiles presented in Section 3.2 were compared firstly. In order to compare the temperature maps derived from the different atmosphericprofiles, pixels with a surface temperature below \(-10\)\({}^{\circ}\)C or above \(+10\)\({}^{\circ}\)C, corresponding in each image to about 5% of the total number of pixels, were masked out. The mean roof temperature obtained using the sounding profiles is \(-0.7\)\({}^{\circ}\)C, while the mean value using the MODIS data is \(+1.0\)\({}^{\circ}\)C, and it rises to \(+1.6\)\({}^{\circ}\)C when the standard MLW model is applied. The standard deviation is more stable and ranges from \(2.5\)\({}^{\circ}\)C with the MLW model to \(2.7\)\({}^{\circ}\)C with the sounding profiles. The main difference in the results derived from the sounding profiles with respect to the one obtained using MODIS data is related to a thin layer of thermal inversion in the measured vertical profile of the temperature, located between the ground and a height of 200 m, which is not detectable in the MODIS one (see Figure 3). It must be noted here that lateral variations and micro-scale patterns of the air temperature in the urban environment were neglected in all of the computations performed. These patterns include temperature differences between urban canyons and open spaces (as large squares or parks) [23] and also horizontal and vertical variations inside urban canyons [24]. Such a simplification is often necessary because of the huge amount of ground measurements that would be required to model all of these complex effects. To evaluate the sensitivity to emissivity variation, a test was performed by decreasing the emissivity values reported in Table 2 by about 1%. Clearly, the effect is an overall increase of the retrieved temperatures, by about 0.3 \({}^{\circ}\)C on average. The effects on each class are shown in Figure 8. The larger variance of the metal class (0.017) corresponds to a larger variance of its surface temperature, and it may be explained by a greater variability of the roofing material types belonging to this class. In a pioneer study about aerial thermography in urban areas, [PERSON] and [PERSON] [25] concluded that the emissivity variations over the most common roofing materials have a minimal effect on the retrieved temperatures. However, they came to this conclusion because of the substantial homogeneity of roofing materials in  
Figure 7: Temperature differences among the corrected images obtained using the atmospheric parameters derived from sounding and MODIS data with respect to the standard MLW profile. the investigated area. Nowadays, on the other hand, the variety of roofing materials in modern towns is expanding, as the number of design solutions has been increasing since the 1970s. The results presented here indeed demonstrate that the impact of emissivity variation cannot be ignored any longer. Retrieval of LST from IR data requires, indeed, an accurate knowledge of the emissivity of the surfaces [13], which is controlled by several factors, such as chemical composition, structure and roughness. Furthermore, it can be altered by the possible presence of dew. As described in Section 2, the thermal infrared radiation acquired by a sensor is a function of, among others, the temperature and emissivity of the surface. Their simultaneous estimation is an ill-posed inversion problem, because the unknowns always exceed the equations. Even with a multispectral infrared sensor with N thermal bands, in fact, any separation method has to solve N + 1 parameters (N emissivity values + 1 LST) with N equations.