## 2 Materials and Methods
### Data Processing and Analysis  
A script running in \"R\" environment, version 3.5.1 [10], was written to import each of the 24 h time series as input in terms of text file (four columns with date, time, SPL dB(A) at 1 s intervals, and a code to indicate whether the source was road traffic or something different). In order to provide indicators for the classification, a time window of duration T = 1 hour was chosen to compute L\({}_{\text{Aeq}}\) and IR values This time period was established by the Italian legislation for road traffic noise measurement. Besides this requirement, the chosen measurement time T was considered a reasonable compromise between longer time (i.e., 24 hours, day and night periods, and so on) and shorter ones (i.e., 30 min or even shorter). For the sites where the noise monitoring lasted more days, the median value of IR and L\({}_{\text{Aeq}}\) for each hour was determined, as this parameter is less influenced than the mean by the presence of outliers. From the input data, the script was computed for each hour:  
* The IR value, according to the definition given in [7] and determined by the following: \[IR=\frac{10^{0.1L_{\text{eq},T,Events}}}{10^{0.1L_{\text{eq},T,lat}}}\cdot 1 00\ [\%]\] (1) where \(L_{\text{eq},T,Events}\) accounts for all sound energy contributions that exceed a given threshold K, that is, clearly standing out from background noise; \(L_{\text{eq},T,lat}\) is the overall continuous equivalent level referred to the measurement time T; and the threshold K is given by the following: \[K=L_{\text{eq},T,lat}+C\ [\text{dB}]\] (2) where C, as stated in [7], can be assumed equal to 3 as a result of the numerical simulations for different traffic situations; \begin{table}
\begin{tabular}{c c c} \hline \hline
**Road Type** & **N. of Sites** & **N. of 24 h Time Series** \\ \hline A (motorway) & 2 & 15 \\ \hline D (thoroughflare roads) & 7 & 18 \\ \hline E (urban district roads) & 29 & 83 \\ \hline F (urban local roads) & 52 & 135 \\ \hline Total & 90 & 251 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distribution of the 90 sites considered in the study according to the Italian legislative classification of roads. Figure 1: The spatial distribution of road types in the urban area of Milan. * The L\({}_{\text{Aeqd}}\) referred to the corresponding day-time L\({}_{\text{Aeqd}}\) (06:00-22:00), taken as a reference level, that is, the difference \(\delta=\text{L}_{\text{Aeqh}}-\text{L}_{\text{Aeqd}}\); this computation was necessary because of the different monitoring set-up at the sites, such as different distances from the road and the characteristics of the road itself (its geometry, the presence of reflecting surfaces and obstacles in sound propagation, and types of paving) [11]. As explained in Section 2.1, the microphone was placed close to the road to reduce the influence of noise from other sources and, therefore, the source-receiver distance was not always the same. This factor influences the IR values (Figure 4 in [12]). Thus, a matrix formed by 48 variables, (IR and \(\delta\) for each hour) \(\times\) 90 observations (sites) = 4320 values, was the input of the subsequent cluster analysis, an unsupervised machine-learning technique, performed to find out similarities in the time patterns. Because the data are measured by different scales, namely \(\delta\) is in dB and IR in percentage, they needed to be scaled (mean = 0 and standard deviation = 1) before clustering; in addition, the Euclidean distance, one of the most used distance metrics, was considered to represent the similarity between pairs of sites. To select the optimal solution for clustering, that is, the agglomeration algorithm and number of clusters, the \"cIValid\" R package, version 0.6-6 [13] was applied.