## 2 Materials and Methods
### Data Analysis Procedure  
Using historical series of maximum temperature and following the methodology proposed in [3], Hot Days (HD) and Heat Waves (HW) for each sampling site and for each summer were determined. For each station, we defined the degree of severity of these extreme events, comparing the 2015-2017 data with the respective historical time series from 1971-2000. The current daily value of temperature was compared with its mean historical value, including standard deviation (\(\sigma\)). We define Hot Days of the first degree \(HD_{L1}\) if the current value is higher than historical values \(\pm\sigma\); Hot Days of the second degree \(HD_{L2}\) with \(n\{HD_{L2}\}\ \leq\ n\{HD_{L1}\}\), if the current value is higher than historical values \(\pm\ 2\sigma\); and Hot Days of the third degree \(HD_{L3}\) with \(n(HD_{L3})\leq n\{HD_{L2}\}\leq n\{HD_{L1}\}\), if the current value is higher than historical values \(\pm\ 3\sigma\). Furthermore, to measure the persistence of these events, the occurrence of Heat Waves is defined with the following criteria: occurrence of at least six consecutive days classified as \(HD_{L1}=\) occurrence of Heat Wave of the first degree \(H\mathrm{W}_{\mathrm{L1}}\); occurrence of at least six consecutive days classified as \(HD_{L2}=\) occurrence \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Label** & **Geographical Zone** & **Municipality** & **AQ cl.** & **Q** \\  & & & & **(m.a.s.l.)** \\ \hline SS1 & Montecucco & West plain area & Piacenza & Urban & 61 \\ SS2 & Cittdella & West plain area & Parma & Urban & 60 \\ SS3 & Badia & Westplain area & Parma & Rural & 202 \\ SS4 & San Lazzaro & West plain area & Reggio Emilia & Urban & 55 \\ SS5 & Castellano & West plain area & Reggio Emilia & Suburban & 150 \\ SS6 & Parco Ferrari & West plain area & Modena & Urban & 30 \\ SS7 & G. Margherita & Bologna area & Bologna & Urban & 43 \\ SS8 & S.Pietro Capofiume & Eastplain area & Bologna & Rural & 11 \\ SS9 & Villa Fulvia & East plainarea & Ferrara & Urban & 8 \\ SS10 & J. di Savoia & East plain area & Ferrara & Rural & \(-2\) \\ SS11 & Parco Bertozzi & Eastplain area & Ravenna & Urban & 35 \\ SS12 & Parco Resistenza & Eastplain area & Forl-Cesena & Urban & 29 \\ SS13 & Mareschia & East plain area & Rimini & Urban & 5 \\ SS14 & Porretta Terme & Apennine mountains & Bologna & Rural & 970 \\  & & and hill area & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sampling sites: in the last two columns, the classification according to Air Quality Monitoring Network of Emilia-Romagna region (AQ cl.) and the altitude (Q). of Heat Wave of the second degree \(HW_{L2}\); and occurrence of at least six consecutive days classified as \(HD_{L3}\) = occurrence of Heat Wave of the third degree \(HW_{L3}\). In a second step, multivariate statistical procedures were applied [34; 35]. For each sampling site, all data related to summer 2015-2017 were organized in data matrices at daily scale. Cluster Analysis (CA) and Principal Component Analysis (PCA) were applied to highlight the underlying correlation structure between pollutants concentrations and meteorological parameters [36]. CA is a classification technique used for determining homogeneous subgroups of sampling sites. For each data matrix, we calculated the association matrix using the Euclidean distance, and we applied the clustering algorithm at complete linkage. For results validation, each cluster has to be characterized by means of endogenous indices (centroids are the mean values of descriptors measured in SS included in the cluster) and by means of exogenous indices (mean values of variables external to the clustering procedure). The correspondence among endogenous and exogenous indices allowed us to explain the clustering structure. If the data matrix is correctly constructed, the results must not depend on the selected parameters  
PCA is the most common factorial technique for reducing the space dimensionality and for highlighting the underlying correlation structure among measured variables.