## 4 Results and Discussion
### Gaussian Fitting of SUHI Maps  
As discussed in Section 3.2, the 2D Gaussian surface can be a useful representation of the SUHI pattern when an urban area shows a clear and clustered heat island decreasing towards the rural area. Some situations (anomalous spotted rural heating or negligible temperature differences between LST\({}_{\text{URB}}\) and LST\({}_{\text{RUR}}\)) can lead to a low correlation coefficient r between the SUHI maps from MODIS data and the fitted Gaussian surface. Table 1 describes the capability of the fitting surface to follow the actual SUHI pattern, reporting the r mean value for the years 2003-2016. We have considered the fitting reliable when is greater than 0.6 and the Gaussian footprint covers the urban area. Figure 4: Surface urban heat island (SUHI) during summer 2013 for the six cities at 22:00. Table 1 shows that some combinations of city-season-hour do not have a robust fit. An explanation will be provided in the successive Figures 5 and 6 by examining the correspondent SUHI patterns. The correlation is always better for the summer nighttime fitting with respect to the summer daytime, whereas the same is not confirmed for the winter. Considering the whole daily cycle, Chiang May has the best performance in terms of correlation. Figures 5 and 6 show the SUHI maps and the correspondent Gaussian fitting for the six cities during 2014 both in summer and winter, reporting also the diurnal variation at 10:00, 14:00, 22:00, and 02:00. Each SUHI(x, y) pattern from MODIS data--with x and y representing the latitude and longitude--were fitted with a Gaussian surface and the descriptive parameters collected. In Figures 5 and 6, the black continuous ellipse superimposed on the maps represents the footprint area Ar61%, while the black dashed ellipse represents Ar1C. The red and green straight lines correspond to the directions of the ellipse's major and minor axes, the former also defining the orientation angle \(\varphi\). The intersection point of the two lines (i.e., the footprint center) is the central location (x\({}_{0}\), y\({}_{0}\)), expressed as shift from the center of the map (0, 0). For example, with reference to the first panel of Figure 5 (BG Summer 10:00), Ar61% = 755.6 km\({}^{2}\), Ar1C = 1815.7 km\({}^{2}\), \(\varphi\) = 72.3\({}^{\circ}\) (i.e., along the north-east and south-west (NE-SW) quarters) and (x\({}_{0}\), y\({}_{0}\)) = (7.3, \(-\)5.5) km; the estimated magnitude a0 is 3.4 \({}^{\circ}\)C. The Gaussian fitting procedure is not generally conditioned by localized surface temperature peaks within the pattern, being prone to smooth such isolated thermal discontinuities. As a general overview of Figures 5 and 6, the daytime SUHI is a more evident phenomenon with respect to the nighttime one, while summer and winter SUHIs at the same hour are quite similar. At nighttime periods, due to the absence of solar forcing and the reduced working activities and traffic, the urban heat island intensity decreases, since rural and urban temperatures tend to get closer. The exceptions are NR and KK, since their daytime SUHI intensities are similar to those at night in the urban area. Particularly, KK, one of the six cities with the smallest urban size, always exhibits a very weak urban heating with respect to rural surroundings. Ar61% and Ar1C, clearly distinct during daytime, are almost the same at night. In some cases, Ar1C is inside Ar61% for NR and KK, indicating a weaker SUHI with respect to the other cities. The biggest city, BG, shows the highest SUHI intensities. In the next Sections 4.2 and 4.3, these aspects will be analyzed in depth for each city across the years. Figures 5 and 6 also provide an explanation of the lack of Gaussian fitting in some cases, as reported in Table 1. Concerning the daytime NR SUHI pattern (Figure 5), the urban fitting is not possible due to anomalous spotted rural heating in the south part of the map. Specifically, in the southeast zone, paddy rice areas are present, while in southwest areas, there are corn, sugarcane,