## 3 Materials and Methods
### Emissivity Map  
To produce an emissivity map suitable for the radiometric correction of the thermal image, the major roofing materials in the investigated area were identified, and for each material, a different emissivity value was assigned [19]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Radiosonde** & **MODIS Terra** & **MLW Model** \\ \hline Central wavelength (\(\mu\)n) & 10.58 & 10.58 & 10.58 \\ Spectral range (\(\mu\)n) & 6–17 & 6–17 & 6–17 \\ Transmittance \(T\) & 0.7957 & 0.8052 & 0.8046 \\ Upwelling radiance \(L_{\alpha}\) (W/m\({}^{2}\)/sr/\(\mu\)m) & 1.2868 & 1.0969 & 1.0401 \\ Downwelling radiance \(L_{\alpha}\) (W/m\({}^{2}\)/sr/\(\mu\)m) & 2.0037 & 1.8243 & 2.0068 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Broadband atmospheric parameters computed by Modtran 5 simulations, using the atmospheric profiles of the radiosonde data, of the MODIS Terra image and of the mid-latitude winter (MLW) predefined model. Figure 3: Comparison between the vertical profiles of air temperature derived respectively by radiosonde data (black), by the MODIS Terra second level product (orange) at the same location of the meteorological station and by the mid-latitude winter pre-defined profile (grey). To distinguish among the major roofing material types, an object-oriented supervised classification was applied on a WorldView-2 multispectral image acquired in 2011 (see Figure 4), which provides 8 spectral bands at a resolution of 2 m, together with the raster DSM, resampled at a resolution of 0.5 m, and a DTM (digital terrain model), at a resolution of 5 m. The object-oriented image analysis was performed with the software eCognition 8. Before the classification procedure, the satellite image had been radiometrically calibrated and orthorectified. The object-oriented classification consists of two steps: firstly the segmentation, which divides the image into continuous and homogeneous segments, called image objects; and secondly, the classification of the objects generated, using not only the radiometry, but also information, such as texture, shape and context. In this work, at first, the objects corresponding to the buildings were identified; then, they were distinguished depending on their roofing material. A specific feature of buildings is the sudden change in elevation at their borders; in addition, buildings usually have a different elevation than the surrounding environment; therefore, a surface calculation algorithm, which works out slopes, was applied to the DSM. The slope layer has high contrast, and the steep and flat areas are easily recognizable. Thus, the segmentation was applied on this layer using the \"contrast split segmentation\" algorithm. In particular, two segmentation steps were necessary: the first to get the steep slope objects; the second to separate those with a medium slope from those with very steep ones. This segmentation based on slope information allowed the extraction of objects whose shape is very close to the real footprint of the buildings (see Figure 5). This would have been difficult if a more common multi-resolution segmentation, based on multispectral data only, had been applied. In fact, because of unavoidable artefacts introduced by the orthorectification, the extension of some roofs is greater than the real one. After obtaining the image objects, a masking classification approach was followed, in order to identify the objects that certainly do not belong to the general class \"building\". Firstly, vegetated areas have been excluded by means of the NDVI index. Secondly, due to the availability of a DTM of the study area, for each image object, the actual height was calculated by a subtraction operation between DSM and DTM. Then, a threshold was applied to distinguish buildings from other cover types.