## 3 Results and Discussion
### Combined Analysis of HD/HW Occurrence and Pollutants Concentrations  
In the groups SS2, SS3, and SS5, highlighted by cluster procedure, the frequency of Hot Days is higher than in the other SSs. In 2015, 53% of summer days are classified as \(HD_{L1}\), while the other SSs show an average of 43% of \(HD_{L1}\), while in 2017, these two percentages are 50% and 40%, respectively (Table 2). Regarding Heat Waves' occurrence (Table 3), the difference is more marked. In the first group of SSs, in 2015, an average of four \(HW_{\text{L1}}\) for the sampling site is recorded; on the contrary, in the other group of SSs, this mean frequency is 2.5. In 2017, the \(HW_{\text{L1}}\) frequencies were 4.3 and 3.4, respectively. Moreover, also the Heat Waves intensity (or length of HWs) was significantly different: in 2015, for the first group of SSs, 73% of sampling days classified as \(HD_{L1}\), which includes Heat Waves; on the contrary, in the other group of SSs, this percentage is 53%; in 2017, analogous behavior was observed, and the two percentage were 62% and 55%, respectively. In the following, we present and discuss the results for the sampling site SS3 Badia (Parma, West Plain Area); this choice is based on the results previously discussed. SS3 shows a certain number of HW and HD that is statistically significant, allowing a detailed discussion of the correlation structure. Using the HD and HW identification procedure [3], we introduce, as explained in Section 2.3, two external variables with double modalities (HD/noHD) and (HW/noHW) determining the submatrices:  
\[(M_{HD})_{SS3}^{y}=[m_{HD}\ x\ n]\text{ and }(M_{noHD})_{SS3}^{y}=[m_{noHD} \ x\ n\ ]\]  
\[(M_{HW})_{SS3}^{y}=[m_{HW}\ x\ n]\text{ and }(M_{noHW})_{SS3}^{y}=[m_{noHW} \ x\ 6\ DS].\]  
in which \(n\) is the number of DS (\(n=6\)); \(m_{HD}\) is the number of Hot Days; and \(m_{HW}\) is the number of Hot Days included in HW (reported in Table 5 as N number of sampling days). In Table 5, for each year and for each pollutant, we report the mean value calculated in summer and the percentage difference of mean values calculated only on sampling days classified as HD or HW. Levels of gaseous pollutants NOx and O3 show limited variations; on the contrary, the levels of particulate (PM\({}_{10}\) and PM\({}_{2.5}\)) show a significant increase in the HD and in the HW sampling day subsets. The concentration percentage increase is in the range 15-31%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(N\) & \(m_{\text{tot}}\)(**PM1o**) & \(m_{\text{tot}}\)(PM2s) & \(m_{\text{tot}}\)(NO3) & \(m_{\text{tot}}\)(O3) \\ \hline \(M_{\text{SS33}}^{2015}\) & 92 & 21 & 12.9 & 6.6 & 104.4 \\  & & \(\Delta\)m\% & \(\Delta\)m\% & \(\Delta\)m\% & \(\Delta\)m\% \\ \((M_{\text{HD}})_{\text{SS3}}^{2015}\) & 59 & 17\% & 16\% & \(-3\)\% & 12\% \\ \((M_{\text{HW}})_{\text{SS3}}^{2015}\) & 43 & 22\% & 22\% & \(-4\)\% & 14\% \\ \hline  & \(N\) & \(m_{\text{tot}}\)(PM1o) & \(m_{\text{tot}}\)(PM2s) & \(m_{\text{tot}}\)(NO3) & \(m_{\text{tot}}\)(O3) \\ \hline \(M_{\text{SS3}}^{2016}\) & 92 & 16.1 & 9.3 & 7.2 & 90.8 \\  & & \(\Delta\)m\% & \(\Delta\)m\% & \(\Delta\)m\% & \(\Delta\)m\% \\ \((M_{\text{HD}})_{\text{SS3}}^{2016}\) & 36 & 21\% & 18\% & 1\% & 18\% \\ \((M_{\text{HW}})_{\text{SS3}}^{2016}\) & 13 & 31\% & 30\% & \(-11\)\% & 14\% \\ \hline  & \(N\) & \(m_{\text{tot}}\)(PM1o) & \(m_{\text{tot}}\)(PM2s) & \(m_{\text{tot}}\)(NO3) & \(m_{\text{tot}}\)(O3) \\ \hline \(M_{\text{SS3}}^{2017}\) & 92 & 18.1 & 9.6 & 6.6 & 106.5 \\  & & \(\Delta\)m\% & \(\Delta\)m\% & \(\Delta\)m\% & \(\Delta\)m\% \\ \((M_{\text{HD}})_{\text{SS3}}^{2017}\) & 53 & 17\% & 15\% & 6\% & 6\% \\ \((M_{\text{HW}})_{\text{SS3}}^{2017}\) & 38 & 20\% & 17\% & 7\% & 8\% \\ \hline \hline \end{tabular}
\end{table}