## 4 Conclusions  
In this study, we present a statistical procedure investigating the behavior of air pollutants concentrations during Hot Day and Heat Waves. Our procedure was based on the following steps: definition of HD and HW from the comparison with the 30-year reference periods of each sampling site; identification of homogenous subgroups of sampling sites by means of Cluster analysis; and characterization of the correlation patterns among air pollutants during Hot Days and Heat Waves by means of Principal Component Analysis. For the examined test case, by analyzing extreme events of maximum temperature through the identification of the number of occurrences of the Hot Days and their persistence (Heat Waves), it is possible to state that: summer 2016 presented a lower frequency of extreme event occurrence than summers 2015 and 2017; during the investigated and in examined area, no Heat Wave of the third level was identified. The last step of our procedure shows that there is a different behavior of pollutants during Heat Waves; particularly, Particulate Matter concentrations are higher independent from humidity, whereas NO\({}_{2}\) and O\({}_{3}\) concentrations seem to be not influenced by Heat Waves. We want to emphasize that our procedure is easily applicable also in different geographical areas and with different pollutants. This method works well even if the pollutants' concentrations are low and if there are no large differences in the level of pollutants between Hot Days and no Hot Days. The discussed procedure can be used in other contexts at local scale; it is useful for understanding the influence of extreme events on air pollutant concentrations and may be used by decision makers that have the responsibility of taking additional measures to prevent health effects on the population. \begin{table}
\begin{tabular}{c c c c} \hline
**2015** & **PC1** & **PC2** & **PC3** \\ \hline \(P\%\) & 50.7 & 28.5 & 10.6 \\ \(P_{cum}\%\) & & 79.2 & 89.9 \\ \(w(PM_{10})\%\) & 28.8 & 3.4 & 0.2 \\ \(w(PM_{2.5})\%\) & 21.2 & 10.9 & 8.1 \\ \(w(NO_{x})\%\) & 9.6 & 21.0 & 45.8 \\ \(w(O_{3})\%\) & 18.7 & 9.3 & 22.8 \\ \(w(T_{max})\%\) & 19.6 & 13.8 & 3.5 \\ \(w(RI_{min})\%\) & 2.2 & 41.5 & 19.6 \\ \(2016\) & _PC1_ & _PC2_ & _PC3_ \\ \(P_{\omega}\) & 48.6 & 26.2 & 12.3 \\ \(P_{cum}\%\) & & 74.8 & 87.1 \\ \(w(PM_{10})\%\) & 21.0 & 18.6 & 2.1 \\ \(w(PM_{2.5})\%\) & 18.0 & 15.9 & 11.0 \\ \(w(NO_{x})\%\) & 12.6 & 0.8 & 82.6 \\ \(w(O_{3})\%\) & 20.7 & 11.1 & 3.9 \\ \(w(T_{max})\%\) & 24.8 & 6.6 & 0.1 \\ \(w(RI_{min})\%\) & 3.0 & 47.0 & 0.3 \\ \(2017\) & _PC1_ & _PC2_ & _PC3_ \\ \(P_{\omega}\) & 48.4 & 27.1 & 11.5 \\ \(P_{cum}\%\) & & 75.5 & 87.0 \\ \(w(PM_{10})\%\) & 26.3 & 6.5 & 1.7 \\ \(w(PM_{2.5})\%\) & 25.7 & 3.9 & 1.3 \\ \(w(NO_{x})\%\) & 11.9 & 5.9 & 79.2 \\ \(w(O_{3})\%\) & 12.4 & 24.6 & 16.0 \\ \(w(T_{max})\%\) & 9.2 & 31.8 & 1.8 \\ \(w(RI_{min})\%\) & 14.4 & 27.2 & 0.1 \\ \hline \end{tabular}
\end{table} 
Table 7: PCA results for noHDs detected in SS3 sampling site. In the upper part of the table, the percentage of explained variance (\(P\%\)) and the cumulative percentage (\(P_{cum}\%\)) for the first three Principal Components (PC); in the lower part, the percentage weights (\(w\%\)) of the original descriptors in the new factors. **Author Contributions:** Conceptualization, M.R., M.D., and V.T. ; data curation, M.R. and L.C. ; formal analysis, M.R. ; investigation, M.R., M.D., L.C., and V.T. ; methodology, M.R., M.D., and V.T. ; resources, M.R., M.D., L.C., and V.T. ; validation, M.R. and L.C. ; writing--original draft, M.R. and M.D. ; writing--review and editing, M.R. and M.D. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded in the framework of the project 'OT4 CLIMA', which was funded by the Italian Ministry of Education, University, and Research (D.D. 2261 del 6.9.2018, PON R&I 2014-2020 and FSC. **Data Availability Statement:** All analyzed data are freely downloaded from www.arpae.it.