## 3 Results
### Principal Component Analysis (PCA) Outcome  
As explained in Section 2.2, PCA was performed in order to reduce the number of clustering variables. The scree plot, reported in Figure 5a for the first 12 components, shows that 10 components have eigenvalues \(\geq\)1, a value commonly used as a cutoff point at which principal components are retained. The cumulative percentage of variance explained by these 10 principal components is 86.7% (Figure 5b).  
Thus, a matrix of 90 observations (the sites) and 10 variables, that is, the retained principal components (90/10 = 9), was the input for the k-means cluster analysis, setting the number of clusters to two. The obtained classification was completely in accordance with that already determined by k-means applied to the 48 variables. This result confirms the robustness of the partition obtained by k-means accounting for the 48 variables.  
Comparison between Clustering Patterns of \(\delta\) and IR Median Hourly Values and Measured Data  
The rationale of determining the 24 h patterns of \(\delta\) and IR for each cluster, shown in Figure 4, is to assign these patterns to the sites according to their cluster membership. This assignment, of course, introduces an uncertainty that should be evaluated (Figure 3). For this purpose, at each ith hour, the difference \(\varepsilon_{\mathrm{i}}\) between the pattern cluster value (PCi) and the measured value (Mi) was determined:  
\[\varepsilon_{\mathrm{Si}}=\delta_{\mathrm{PCI}}-\delta_{\mathrm{Mi}}\quad[ \mathrm{dB}], \tag{3}\]  
\[\varepsilon_{\mathrm{IRi}}=\mathrm{IR}_{\mathrm{PCI}}-\mathrm{IR}_{\mathrm{Mi}} \quad[\%], \tag{4}\]  
This error \(\varepsilon\) can be expressed in different ways, either as relative error \(\varepsilon_{\mathrm{r}}\),  
\[\varepsilon_{\mathrm{r\delta}}=10\mathrm{log}\Big{[}10^{(\delta_{\mathrm{PI}} -\delta_{\mathrm{Mi}})/10}/10^{\delta_{\mathrm{Mi}}/10}\Big{]}, \tag{5}\]  
\[\varepsilon_{\mathrm{r\mathrm{R}}}=(\mathrm{IR}_{\mathrm{PI}}-\mathrm{IR}_{ \mathrm{Mi}})/\mathrm{IR}_{\mathrm{Mi}}, \tag{6}\]  
or as the root mean square of the error \(\varepsilon\) (RMSE),  
\[\mathrm{RMSE}=\sqrt{\frac{\sum_{k=1}^{n}\left(\varepsilon_{\mathrm{RK}}\right) ^{2}}{n}}\quad[\mathrm{dB}],\quad\mathrm{RMSE}=\sqrt{\frac{\sum_{k=1}^{n} \left(\varepsilon_{\mathrm{IRK}}\right)^{2}}{n}}\quad[\%], \tag{7}\]  
where n is the number of observations (sites) in each cluster. Indeed, the patterns have their own uncertainties (grey areas in Figure 3), but, for sake of simplicity, only their median values are considered in the following.  
For practical application, the RMSE error in dB was considered for the \(\delta\) parameter because it is more representative (Figure 6a), whereas for IR, measured in %, the relative error \(\varepsilon_{\mathrm{r}}\) was chosen and is reported in Figure 6b. For all the sites belonging to the same cluster, the \(\varepsilon_{\mathrm{i}}\) absolute values for  
Figure 5: Eigenvalues (**a**) and percentage of explained variance (**b**) for the first 12 principal components.  
each ith hour were determined and grouped (in %) in an interval bin width from 0.5 to 3 dB with steps of 0.5 dB. The median values of these percentages for each interval width were determined for the day (06:00-22:00) and night (22:00-06:00) periods and are plotted in Figure 6c,d, together with fitting curves. No large differences between clusters are observed for the error \(\varepsilon_{\delta}\) determined for \(\delta\); the largest values of RMSE error (Figure 6a) and the lowest values of the percentage of \(\varepsilon_{\delta}\) (Figure 6c) are observed for the period 00:00-05:00 (median error \(\varepsilon_{\delta}>2.0\) dB), which, on the other hand, is the most suitable to discriminate between the two clusters. The relative error \(\varepsilon_{\text{FIR}}\) for IR is greater for cluster 1 during the day-time (06:00-22:00) (Figure 6b, median error \(\varepsilon_{\text{HR}}=0.63\)).