## 3 Materials and Methods
### Thermal Images  
An aerial thermal infrared survey over the city of Bologna was performed on 7 March 2011. The survey was carried out by the National Institute of Oceanography and Experimental Geophysics (OGS), in the framework of the Central Europe European Project \"EnergyCity\" [10]. The thermal infrared frames were acquired using a thermal camera, NEC TS9260, characterized by an un-cooled microbolometer sensor operating in the 6-17 \(\upmu\)m spectral range, with a spatial resolution of \(640\times 480\) pixels (with a corresponding field of view of \(21.7^{\circ}\times 16.4^{\circ}\)). The infrared camera was installed with a rigid mounting device on a \"Piper Seneca II\" aircraft, in combination with an inertial measuring unit (IMU), a video encoder-decoder (VED) and a GNSS receiver. The relative position between the GNSS antenna reference point and the optical center of the thermal camera was accurately measured in order to compute with high precision the coordinates of the principal point for each photogram. In order to have optimal coverage, a forward overlapping factor of 60% and a transversal overlapping factor of 20% were chosen. In addition, to obtain an average ground sampling distance of 50 cm and considering a time span between two adjacent shots of 2 s, an average height of the flight of 840 m and an average speed of the aerial platform of 110 knots were planned. The area of the city of Bologna was surveyed following parallel strips in the W-E direction. The entire thermal survey is formed by 1417 infrared frames.  
To carry out the thermal survey, some recommendations about the optimal meteorological conditions, derived from previous studies on the thermal mapping of buildings [9], were followed. The flight was carried out over a few hours after sunset, minimizing the effect of solar irradiation on the surfaces. Furthermore, it was performed in the winter season, during a cold night, with light winds and clear skies, in order to both maximize the differences between the temperatures of the roofs of the buildings and the outside air temperature and to minimize the effects of turbulence at the flight altitude on the stability of the aerial platform.  
Simultaneously with the aerial survey, some ground measurements of surface temperature and emissivity were collected, as described in Section 3.4.  
The entire processing workflow described in this paper was performed only on a small test area of about 1.06 km\({}^{2}\), covered by 30 thermal frames, in order to define the methodology and to evaluate the sensitivity of the model at each step of the processing chain.  
The aerial thermal orthophoto-mosaic of Bologna was generated using the Socet Set\({}^{\text{TM}}\) 5.6 digital photogrammetric workstation. The whole process includes several phases: after the project creation, with the indication of the chosen datum and reference system, the images were imported into the project, associating the corresponding camera calibration file (in this case, the only information available about the camera is the focal length and the principal point coordinates). After these steps, the image exterior orientation can be solved by means of a photogrammetric triangulation procedure, using tie and control points. The municipality technical cartography of Bologna at 1:2000 scale was used as the cartographic base for the individuation of the control points, which usually are the edges of buildings' roofs; a large number of points was used, achieving an RMS of 1.5 pixels and residuals of some centimeters for the control points.  
After the image orientation, the orthophoto-mosaic, characterized by a ground sampling distance of 0.5 m, was generated (Figure 2) by using a digital surface model (DSM), derived from an aerial LiDAR survey carried out in 2009 and provided by the Municipality of Bologna, with a post spacing of 1 m.