## 4 Result and Discussion
Thus, an _a priori_ assumption or an empirical relation must be introduced to solve the system [26]. On this basis, several temperature/emissivity separation methods were developed to be used with both multispectral and hyperspectral infrared sensors [21, 27]: among the most popular, the reference channel method, the emissivity normalization, the alpha residual, the temperature/emissivity separation (TES) and the day/night method. The last one, adopted for MODIS products, uses two images to increase the number of equations, avoiding the ill-posed problem. All of these separation methods usually assume that the contribution of the atmosphere to the recorded radiance has been already removed [13, 26, 27]. Equation 3, however, shows that separating atmospheric and emissivity corrections in two steps would require further simplifications (e.g., neglecting the downwelling radiance). In the present study, the aerial camera acquires only a single infrared band; thus, an alternative approach was adopted: the emissivity values of surfaces were assigned on the basis of a classification of roofing materials from a high resolution satellite image (as described in Section 3.3). The emissivity values were estimated, for each class, by means of direct measurements or other data sources. The main  
Figure 8: Statistics on the temperature differences for each class, resulting from a decrease by 1% of the emissivity values listed in Table 2.  
disadvantage of this approach is related to the number of direct measurements on roofs, which are often limited because of logistic problems. As a first attempt of validation, the temperature values obtained from the corrected images were compared with the surface temperatures measured in the field. Temperature differences between the measured and computed values at the five locations are shown in Table 4. In the first column, the differences obtained by considering temperatures from uncorrected images are shown and prove the relevance of the calibration process. As can be seen, all of the parameterizations of the radiative transfer model produced an average underestimation of the surface temperature. Surprisingly, the worst results were obtained using the radio sounding profile, but this fact can be explained considering that the profile was measured 30 km away from Bologna in the countryside, so it is probably not representative of the spatial variations of atmospheric transmissivity over urban areas [5]. Furthermore, [PERSON] _et al._[28], performing a sensitivity study on thermal data acquired over a rural area in France, inferred a sensible bias in the retrieved temperature when the profile was measured about 30 km from the scene, even if they were not able to quantify its amount precisely. They explain this fact in terms of the effects of the topography and spatial variability of the atmosphere. The use of MODIS for the parameterization of the atmospheric correction models is discussed in several works dealing with images acquired in the reflective part of the electromagnetic spectrum. Conversely, the use of MODIS atmosphere data for thermal images is still poorly investigated. For instance, [PERSON] _et al._[18] published the results of some tests in rural areas in Spain using medium-resolution satellite images. They found that average differences between surface temperatures derived using MODIS data and local radio sounding profiles do not exceed 1 \({}^{\circ}\)C. However, they do not compare these temperature values with field measurements. The results obtained in the experimentations presented here show a slightly worse performance with respect to the use of the general MLW model. This fact may be due to the loose description of the strata close to the surface, which provide the highest contribution, especially in the case of airborne sensors. Clearly, further investigations and a wider collection of test sites are required to reach more reliable conclusions.