## 4 Results
In the case of two clusters, the maximum ratio BSS/TSS is 17.75, indicating a low separation between clusters, and the AJ values are 0.867 and 0.878, showing their high stability. By comparison, selecting six clusters gave BSS/TSS = 64.4%, so there was a better separation between clusters. The AJ values computed after 20 bootstrapping are between 0.600 and 0.780, indicating that two clusters are unstable and four stable. In conclusion, \(k=2\) is kept as the best choice. Moreover, the excessive fragmentation of the data series is avoided. Figure 9 shows the cluster plots for the series in Zone 1, for \(k=2\) and \(k=6\). For the series in Zone 2, the best number of clusters were 2 (10 algorithms), 3 (5 algorithms), and 6 (7 methods). The highest BSS/TSS was 82.7% for \(k=6\). The Connectivity and Silhouette indicate that the highest internal clustering connectivity is obtained for \(k=2\), whereas [PERSON] provided \(k=3\). The highest clusters' stability was determined for \(k=6\) by AD and FOM, \(k=2\) by APM, and \(k=3\) by ADM (Table 4--rows 7--10). The AJ values indicated one highly unstable cluster when \(k=6\). When \(k=2\) and \(k=3\), the clusters are stable. The cluster plots are presented in Figure 10.  
For the series in Zone 3, the best number of clusters was found to be 1 (5) by one (one) algorithm, 2 by 8 procedures, 3 (and 6) by 5 (5) methods, and 4 by 3 methods. The rows 11-13 in Table 4 contain the optimal internal connectivity and stabilities (computed by varying the number of clusters between 2 and (6). It indicates the highest internal connectivity for \(k=2\). The highest clusters' stability was found when \(k=2\) or \(k=6\), but AJ indicated two unstable clusters when \(k=6\). Therefore, we selected \(k=2\) as the best number of clusters. The groups obtained when \(k=2\) and \(k=6\) are presented in Figure 11.  
The clustering in Figure 11a shows the highest variation in the series values from Z3M5, leading to a clear separation of this series from the others. Z3M5 presents a significantly high peak, which can be associated with the beginning of the revision period, followed by lower values of concentrations. The lowest variability is in the series Z3M11, situated at a significant distance from the other elements in the first cluster in Figure 11a. The values of other statistical characteristics--mean, standard deviation, normality, and homoscedasticity-balance the decision to cluster the data series in various groups. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Internal Clustering Connectivity**} & \multicolumn{3}{c}{**Clusters’ Stability**} \\ \hline Zone & Index & Score & \(k\) & Index & Score & \(k\) \\ \hline \multirow{4}{*}{1} & Connectivity & 3.1401 & 2 & APN & 0.0371 & 2 \\  & Dunn & 0.7462 & 2 & ADM & 0.2720 & 3 \\  & Silhouette & 0.2156 & 2 & AD & 3.1895 & 6 \\  & & & & FOM & 0.9115 & 6 \\ \hline \multirow{4}{*}{2} & Connectivity & 9.4143 & 2 & APN & 0.0000 & 2 \\  & Dunn & 0.6032 & 3 & ADM & 0.0000 & 3 \\  & Silhouette & 0.3583 & 2 & AD & 1.8039 & 6 \\  & & & & FOM & 0.5100 & 6 \\ \hline \multirow{4}{*}{3} & Connectivity & 2.9290 & 2 & APN & 0.0000 & 2 \\  & Dunn & 0.9335 & 4 & ADM & 0.0000 & 2 \\  & Silhouette & 0.3555 & 2 & AD & 1.9479 & 6 \\  & & & & FOM & 0.6360 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Highest internal connectivity and stability scores and the number of clusters. Figure 11: Cluster plots for the series in Zone 3 for (**a**) \(k=2\) and (**b**) \(k=6\). Figure 9: The cluster plots of the series in Zone 1 for (**a**) \(k=2\) and (**b**) \(k=6\). In the second stage, the sites in each zone were clustered, considering the features' series determined in I and II. Specifically, the list of the features used is: F1--minimum, F2--maximum, F3--mean, F4--standard deviation, F5--Skewness, F6--kurtosis, F7--normality, F8--homoskedasticity, F9--ACF, F10--PACF, F11-- outliers.