## 3 Results and Discussion
### Mass Closure Analysis  
Results on mass closure analysis (or mass reconstruction) are here reported to quantitatively identify the contribution of various emission sources on PM\({}_{2.5}\) samples, respectively, on the two prevailing directions identified and then confirmed by LDA. Mass reconstruction is defined by seven main classes (sources): sea-spray, crustal matter, secondary inorganic aerosol (SIA), secondary organic aerosol (SOA), combustion, anthropogenic metals, and the undefined mass (UM). The different calculations and hypotheses used for the aerosol mass reconstruction are reported below. Sea-spray mass concentrations were calculated by adding to sodium, chloride, and the sea-salt (ss) contributions of calcium, potassium, and sulphate as follows:  
\[\text{Sea-spray}=\text{Na}^{+}+\text{Cl}^{-}+\text{ss-Mg}^{2+}+\text{ss-K}^{+}+ \text{ss-Ca}^{2+}+\text{ss-SO}_{4}{}^{2-} \tag{1}\]  
where ss-K\({}^{+}\), ss-Ca\({}^{2+}\), ss-Mg\({}^{2+}\), and ss-SO\({}_{4}{}^{2-}\) have been estimated as measured Na\({}^{+}\) times 0.036, 0.038, 0.129, and 0.2516, respectively [57]. Crustal matter mass concentration estimate is based on Al, Si, Fe, and insoluble fraction (M\({}_{\text{ins}}\)) of Na, K, Mg, and Ca. Due to the high correlation between Ca and WSIC, the presence of carbonates was assumed (0.72, \(p<0.05\)) and the WSIC concentration was added to crustal matter. Then the crustal matter was calculated by the following equation assuming that Al and Fe are of crustal origin [58; 59]:  
\[\text{Crustal matter}=21.67\,\text{Mg}_{\text{ins}}+1.4\,\text{*}\,\text{Ca}_{ \text{ins}}+1.35\,\text{*}\,\text{Na}_{\text{ins}}+1.43\,\text{-Fe}+1.89\, \text{*}\,\text{Al}+2.14\,\text{*}\,(\text{Si/Al})_{\text{crust}}\,\text{*}\, \text{Al}+1.2\,\text{*}\,\text{K}_{\text{ins}}+\text{WSIC} \tag{2}\]  
where (Si/Al)crust is the ratios determined by Wedephol [60], and the insoluble fraction of Ca, Mg, K, and Na were calculated as follows:  
\[\text{M}_{\text{ins}}=\text{M}_{\text{tot}}\text{-}\,\text{M}^{\text{n+}} \tag{3}\]  
Secondary inorganic aerosol (SIA) mass concentrations were calculated as:  
\[\text{SIA}=(\text{nss-SO}_{4}{}^{2-}+\text{NO}_{3}{}^{-}+\text{NH}_{4}{}^{+}) \cdot 1.29 \tag{4}\]  
where 1.29 is the factor to convert the inorganic species into hydrated species. Secondary organic aerosol (SOA) mass concentrations were calculated from OCsec mass concentrations as:  
\[\text{SOA}=\text{f}_{\text{OM/OC}}\text{OC}_{\text{sec}} \tag{5}\]  
where \(\text{f}_{\text{OM/OC}}=2.1\) for samples collected with prevalent wind from port direction and \(\text{f}_{\text{OM/OC}}=1.8\) when winds blew from urban-industrial area [61]. Moreover, the EC-tracer method was employed to derive OCsec from the EC [62]. Combustion mass concentration was calculated as follows:  
\[\text{Combustion}=\text{nss-K}^{+}+\text{EC}+\text{OC}_{\text{prim}}\cdot \text{f}_{\text{OM/OC}} \tag{6}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Urban-Industrial** & **Port** &
\begin{tabular}{c} **Correct Prediction** \\ **(\%)** \\ \end{tabular} \\ \hline Urban-Industrial & 20 & 13 & 61 \\ Port & 10 & 48 & 83 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Confusion matrix in cross validation and percentage of correct predictions. where nss-K\({}^{+}\) has been calculated as:  
\[\text{nss-K}^{+}=\text{K}^{+}\text{-ssK}^{+} \tag{7}\]  
Table 4 shows the mean mass concentrations of the six main sources considered for the mean mass reconstruction of the PM\({}_{2.5}\) fraction. For both prevailing wind directions, the unexplained mass was low, that is 1.8% and 1.6% for urban-industrial direction and port direction, respectively. Moreover, considering that the particulate mass (PM\({}_{2.5}\) mass) was higher for samples of urban-industrial area direction, the SIA, SOA, combustion, and crustal fractions were present in larger amounts when winds blew from this area, while the sea salt contribution was not statistically different between the two directions.