## 3 Results
### Identification of Cirrus and Cumulonimbus in Cluster 1  
Cirrocumulus (Ccs), cirrostratus (Css), Cbs and Cis populate the upper troposphere [77]. Given that cluster 1 had the lowest T\({}_{\rm b}\) values all these types of clouds might coexist on particular dates. These clouds have different properties concerning precipitation so it is desirable to separate Cbs from the rest of them in order to have them isolated given the potential effects these particular clouds have on weather (e.g., flash floods). In a first attempt to do this using the information extracted from the cluster analysis we made use of the area-perimeter fractal dimension as follows. For each individual cluster 1 image different objects, each one of them with clear boundaries that enabled its distinction from the rest of the objects in the image, were identified. The perimeter P of each object was calculated by counting the outermost pixels. Similarly, the area A of each object was estimated by summing up the number of pixels encompassing it. Following [95] objects with A \(<\) 200 km\({}^{2}\) were excluded from the analysis. Objects with hollow regions were excluded as well. For each object that fulfills the condition A \(>200\) km\({}^{2}\) a quantity R that measures its raggedness was constructed by taking into account the area-perimeter ratio in the following way  
\[\mathrm{R}=\frac{\ln(\mathrm{P})}{\ln(\mathrm{A})} \tag{8}\]  
Expression (8) exploits the notion of fractal dimension as the object's raggedness increases as R increases. A vector including the R parameters was built. The same k-means/k-means++ clustering algorithm described in Section 2.2 was implemented with K = 2 to break this new vector down into two vectors with quite different properties regarding the geometry, one of them capturing the features of Cis (Ci-vector) and the other of Cbs (Cb-vector). For each object in these two vectors the perimeter fractal dimension \(\mathrm{D}(\mathrm{P})\) can be estimated through the relation ([95] and references therein)  
\[\mathrm{P}=\mathrm{CA}^{\frac{\mathrm{D}(\mathrm{P})}{2}} \tag{9}\]  
In the above equation C is a constant. The linearization of (9) leads to  
\[\ln\mathrm{P}=\ln\mathrm{C}+\frac{\mathrm{D}(\mathrm{P})}{2}\ln\mathrm{A} \tag{10}\]  
from which both the intercept \(\ln\mathrm{C}\) and the slope \(\mathrm{D}(\mathrm{P})/2\) can be easily obtained from a linear fit considering all the individual objects in each Ci- and Cb-vector. By averaging over the 2036 realizations we get \(\mathrm{D}_{\mathrm{Ci}}(\mathrm{P})=1.178\pm 0.014\). The second term is the SD across the 2036 Ci-vectors. In a similar fashion, \(\mathrm{D}_{\mathrm{Cb}}(\mathrm{P})=1.364\pm 0.022\). These values, which are in very good agreement with the ones in [95], were used to classify the pixels in cluster 1. Figure 13a shows the breakdown of Figure 8a into groups of pixels of Cis and Cbs. In this particular case Cis and Cbs represent approximately 89% and 9% of cluster 1's total number of pixels, respectively. The remaining 2% of the pixels correspond to the clouds that were unaccounted for by the condition A \(>200\) km\({}^{2}\). The largest cluster seen in Figure 13a was the one associated to Cis that outline the anticyclonic curvature of the UTJ discussed in Section 3.1.1. The quarterly time series of mean seasonal percentages of Cis and Cbs across the study period are shown in Figure 13b. Cluster 1's population of Ci and Cb pixels across all seasons is, on average, around 83% and 6%, respectively. In agreement with the existing literature [96] the percentages of Ci pixels reached a maximum (minimum) in winter (summer). These results are in accordance with a boreal lower temperature in the troposphere that favored both the formation and the maintenance of ice crystals, which are the constituents of this type of clouds [97]. A concomitance in the increase or decrease in the number of Ci and Cb pixels is expected seasonally.