## 3 Results
### Sample Dates
#### 3.1.2 Cluster Analysis  
Figure 8 shows the configuration of clusters 1-4 on the three selected dates. Even though pixels represented by the lowest portion of the scale are found in each of the clusters their number generally decreased in favor of hotter pixels as the cluster order increased. Figure 9 shows the silhouette diagrams for these case studies. In general, each pixel was well matched to their own cluster. The information entropy for these dates was 0.96 (01/08/2011), 1.10 (04/01/2014) and 1.14 (12/10/2016; results not shown). These results mean that between the palettes of clouds present in these three days (cf. Figure 7) a better representation by means of a four-cluster set was achieved for the first of the dates. Another interpretation is that in terms of cloudiness the last date is the one that is more disordered. According to the number of pixels in Figure 8a-c, cluster 1 accounts for approximately 8%, 4% and 7%, respectively, of the corresponding original T\({}_{\rm b}\) images (not shown). Unlike with the rest of the clusters, pixels in cluster 1 on the selected dates did not extend beyond approximately 60 \({}^{\circ}\)S. Table 2 shows the mean values and the SDs for both T\({}_{\rm b}\) and CTH for all the clusters in Figure 8. The mean T\({}_{\rm b}\) value for Figure 8a-c was 232 K, 230 K and 228 K, respectively; SD equaled 11 K, 12 K and 11 K, respectively. In terms of CTH, the mean values were 10.71 km, 11.56 km and 10.26 km, respectively, and the SDs were 1.79 km, 2.01 km and 2.75 km, respectively. The distributions of T\({}_{\rm b}\) and CTH for the clusters in Figure 8 are shown in Figure 10. Regarding cluster 1, Figure 10a shows that the T\({}_{\rm b}\) pixels spanned the support's lower half, with values below approximately 260 K. The distributions in Figure 10b were more scattered than those in Figure 10a, highlighting the fact that the same temperature may be related to distinct heights at different regions. The Cis associated to the UTJ's curvature and the upper-level trough in Figure 7b or the convective cells over Bolivia, Brazil and Paraguay in Figure 7d were just examples of the CC represented by this cluster. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{\(\mathbf{T_{b}}\) (K)} & \multicolumn{4}{c}{CTH (km)} \\ \cline{2-9}
**Date** & \multicolumn{4}{c}{Mean} & \multicolumn{4}{c}{Mean} & \multicolumn{4}{c}{Mean} \\  & \multicolumn{4}{c}{(SD)} & \multicolumn{4}{c}{(SD)} \\ \cline{2-9}  & **\#1** & **\#2** & **\#3** & **\#4** & **\#1** & **\#2** & **\#3** & **\#4** \\ \hline \hline
01/08/2011 & 232 & 256 & 278 & 278 & 10.71 & 6.04 & 2.16 & 1.22 \\  & (**11**) & (**15**) & (**13**) & (**12**) & (**1.79**) & (**1.91**) & (**1.15**) & (**0.92**) \\ \hline
04/01/2014 & 230 & 253 & 280 & 285 & 11.56 & 7.34 & 2.94 & 1.61 \\  & (12) & (10) & (10) & (9) & (2.01) & (1.63) & (1.39) & (1.00) \\ \hline
12/10/2016 & 228 & 253 & 279 & 284 & 10.26 & 6.06 & 2.98 & 1.44 \\  & (11) & (13) & (11) & (11) & (2.75) & (2.67) & (1.28) & (0.84) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Brightness temperature \((\mathrm{T_{b}})\) and cloud top height (CTH) mean values and standard deviations (SDs) for clusters (#) 1–4 on the sample dates. Figure 8: Pixel patterns for 1 August 2011 (left), 4 January 2014 (centre) and 12 October 2016 (right). Clusters 1, 2, 3 and 4 are shown in plates (**a–c**), (**d–f**), (**g–i**) and (**j–l**), respectively. The color scale is the same for all the panels. Cluster 2's number of pixels in Figure 8d-f represents 14%, 11% and 12% of the original T\({}_{\rm b}\) images, respectively (not shown). The mean T\({}_{\rm b}\) values for Figure 8d-f were 256 K, 253 K and 253 K, respectively, while the SDs were 15 K, 10 K and 13 K, respectively (Table 2). As to CTH, the mean values were 6.04 km, 7.34 km and 6.06 km, respectively, and the SD values were 1.91 km, 1.63 km and 2.67 km, respectively.