## 4. Study Regions of Interest
### Metropolitan Area of Atlanta  
It is widely acknowledged that for the past 30 years, the city of Atlanta has undergone heavy alterations in its LC: urban growth, sprawl, loss of forest and cropland have modified drastically its territorial features [48]. Such a tendency is confirmed by a visual analysis of the aggregated LC database computed as described in Section 3.2 and shown in Figure 6, where the _Urbanized_, _Forest_/_Shrubland_ and _Cultivated_ LC classes are depicted. Obviously, also the \(I_{v}\) reflects such urban growth: over only 20 years, about 40% of _Cultivated_ and _Forest_/_Shrubland_ pixels became _Urbanized_. Specifically, the developed methodology was applied to an ROI covering an area of about 11,000 km\({}^{2}\), corresponding to the city of Atlanta and its surroundings. The elements of the _Rate Matrices_ (Figure 7a) show the presence of the already mentioned global LST increasing trend, which is independent of the specific LC variation. Nonetheless, it can be observed how the highest increasing rate corresponds precisely to the LC change from the class _Forest_ to _Urbanized_ (0.41 \({}^{\circ}\)C/year), immediately followed by the _Cultivated_ to _Urbanized_ transformation (0.39 \({}^{\circ}\)C/year). Indeed, the substitution of rural and natural areas with dry, impervious surfaces (roofs, asphalplated surfaces, etc.) results in less moisture available to keep the soil cool. On the other hand, even considering the LC stable pixels, it is possible to highlight quite high increasing rates, in the range of 0.29-0.37 \({}^{\circ}\)C/year, which appear unrealistic even in the presence of the well-known global warming phenomenon. Therefore, considering a small portion (about 13.7 km\({}^{2}\), Figure 8) of the urban area located around a permanent weather station for air temperature measurement [49], an extensive comparison was performed between the LST and the air temperature measured at the time (with less than one hour approximation) of each image acquisition (around 10:00, local time) over the period 1992-2011. It is known [9] that in the morning, the difference between LST and air temperature in urban areas can be positive for up to 10 \({}^{\circ}\)C; anyway, the long-term trends of both temperatures should be equal. Actually, the median temperatures difference for 1992 is around 6 \({}^{\circ}\)C, whereas the increasing rates were respectively estimated as equal to 0.22 \({}^{\circ}\)C/year for LST (probably due to the fact that small green areas are included in this urban area) and to 0.08 \({}^{\circ}\)C/year for air temperature, which appears definitely more realistic (Figure 9). A calibration issue in the LST retrieval procedure from Landsat imagery was therefore supposed to explain such a difference. In addition, the LSTs intra-comparison retrieved from Landsat 5 and Landsat 7 in the available common interval  
Figure 6: Atlanta MA: LC situation in 1992 (**a**) and in 2011 (**b**). In red, the _Urbunized_ class, in light green, the _Cultivated_ class, in dark green, the _Forest_ and _Strubland_ classes. Figure 7: Atlanta MA: _Rate_ and _Detrended Rate Matrices._  
(1999-2011) over the same small portion of the urban area evidenced an anomalous increasing rate difference, up to 0.38 \({}^{\circ}\)C/year. Consequently, the results related to the LST increasing rates were judged as unreliable; this is the reason why the _Rate Matrix_ was detrended for the general LST increase, in order to highlight the net effects of the LC changes and the specific role of the urbanization. In detail, the LST trend was separately removed from each row of the _Rate Matrices_, by subtracting the values pertaining to the main diagonal (i.e., the cell representing the permanence in the same LC class during the investigated period) from those related to the other two cells (which represent the changes among the LC classes).