## 4 Discussion on the Initialization of Dynamap and Its Implementation  
In this section, we discuss how Dynamap can be brought to operation from the very beginning. The 24 stations (indexes \(i\) = 1-24) have been chosen so that there are 4 stations (index \(j\) = 1-4) in each one of the six groups, indexed (\(g_{1}\),..., \(g_{6}\)), that the pilot Zone 9 of Milan has been divided into (see Figure 10). We can see, for example, that (\(i\) = 3, 16, 19, 24) belong to group \(g_{1}\). For each group \(g\), we then have the correspondence of (\(g\), \(j\)) with \(i\) using the notation M(\(g\), \(j\)) = \(i\). In this example, correspondence is expressed as follows: M(1, 1) = 3, M(1, 2) = 16, M(1, 3) = 19, and M(1, 4) = 24. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Interval**} & \multirow{2}{*}{**\(\tau\) (min)**} & \multicolumn{3}{c}{**Cluster 1**} & \multicolumn{3}{c}{**Cluster 2**} \\ \cline{2-7}  & & \(n^{\circ}\) **Measurements** & \(\overline{\sigma}_{sample_{1}}\) **(dB)** & \(n^{\circ}\) **Measurements** & \(\overline{\sigma}_{sample_{1}}\) **(dB)** \\ \hline
07:00–21:00 & 5 & 110 & 0.32 & 82 & 0.26 & \\
21:00–01:00 & 15 & 106 & 0.36 & 86 & 0.30 & 192 \\
01:00–07:00 & 60 & 125 & 0.44 & 67 & 0.42 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean expected deviation \(\overline{\sigma}_{sample}\) calculated within the three time intervals used in this work—T\({}_{\rm h}\) = (07:00–21:00), (21:00–01:00), and (01:00–07:00)—for the three discretization times \(\tau\) = (5, 15, 60) min for both clusters. The average daily values are therefore 0.37 dB for C\({}_{1}\) and 0.33 dB for C\({}_{2}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Error/Group** & \(g_{1}\) & \(g_{2}\) & \(g_{3}\) & \(g_{4}\) & \(g_{5}\) & \(g_{6}\) \\ \hline \(\sigma_{pred}\) & 1.47 & 1.44 & 1.40 & 1.37 & 1.36 & 1.31 \\ \(\sigma_{stat}\) & 1.53 & 1.47 & 1.40 & 1.35 & 1.32 & 1.22 \\ \(\sigma_{comp}\) & 0.14 & 0.15 & 0.17 & 0.18 & 0.18 & 0.20 \\ \(\sigma_{sample}\) & 0.35 & 0.35 & 0.35 & 0.35 & 0.35 & 0.35 \\ \(\sigma_{T}\) & 2.16 & 2.09 & 2.02 & 1.96 & 1.94 & 1.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean daily values of the error contributions to \(\sigma_{T}\) (dB) for each group (acoustic map) \(g\). The different symbols correspond to the intrinsic prediction error of the method, \(\sigma_{pred}\), the statistical variance of the equivalent noise levels measured by the monitoring stations, \(\sigma_{stat}\), the different cluster compositions for different time intervals, \(\sigma_{comp}\), and the error due to stratified sampling, \(\sigma_{sample}\). Starting Operations of Dynamap from Four Monitoring Stations in Each Group g: \(\delta_{g,j}^{\tau}(t)\)  
An acoustic map has been associated with each group \(g\), so that all road stretches within a group are represented by the same acoustic map. Operatively, each station \(i\) records a noise signal at a 30 ms resolution, which will be integrated, after filtering the anomalous events, in a 1 s equivalent noise level [44,45]. The signal then needs further integration to obtain \(\mathrm{Le_{q\tau,i}}\) over a predefined temporal interval \(\tau\) (\(\tau\) = 51,560 min). Thus, we get 24 \(\mathrm{Le_{q\tau,i}}\) values every \(\tau\) min, each one corresponding to a recording station \(i\). To update the acoustic maps, we deal with variations \(\delta_{g,j}^{\tau}(t)\), where the time \(t\) is discretized as \(t\) = \(n\tau\) and \(n\) is an integer, defined according to  
\[\delta_{g,j}^{\tau}(t)= \mathrm{Le_{q\tau M(g,j)}(t)_{(\mathrm{measured})}-\mathrm{Le_{q \mathrm{e}pfM(g,j)}(T_{ref})_{(\mathrm{calculated})}}} \tag{13}\]  
where \(\mathrm{Le_{q\mathrm{e}pf,\,M(g,j)\,(\mathrm{calculated})}}\) is a reference value calculated from the acoustic map of group \(g\) (the CADNA model) at the time interval \(\mathrm{T_{ref}}\) = (08:00-09:00) at the point corresponding to the position of the \(M(g,j)\)-th station.