# Interpretation of Bridge Health Monitoring Data from Satellite InSAR Technology
## 4 Results and Discussion
### Correlation between Displacements and Temperature Variations  
We start the correlation analysis by studying the linear correlation between PS displacements and temperature variations. First, we decimate the temperature dataset to one measurement per day for the days corresponding to the satellite passage over the case study area. Figure 14 illustrates the map of identified PSs on the bridge, represented in a colour scale corresponding to the Pearson correlation coefficient resulting from comparing displacements time series of each PS and temperatures. In Figure 14a, we can immediately observe a clear difference in correlation values between the floodplain and the riverbed portions. Specifically, a positive correlation ranging from \(1\) to \(0.7\) is observed in the riverbed portion between Pier 8 and 11, while a positive but lower correlation--below \(0.5\)--is seen between Pier 11 and the southern bank of the river. In contrast, in the floodplain portion, there is a periodic variation in the colours of the PSs, ranging from transverse groups of yellow-orange-red PSs (with a negative correlation between \(-1\) and \(-0.3\)) to transverse groups of green PSs (with a correlation between \(-0.3\) and \(0.1\)), and finally to transverse groups of blue PSs (with a correlation between \(0.1\) and \(0.5\)), followed by another yellow-red PS groups (where the correlation drops down to \(-1\) again). Figure 14b shows a zoom on the floodplain portion of the bridge where magenta arrows highlight the yellow-red coloured PS groups. These differences in the linear correlation are also clearly visible in Figure 15, which shows the scatterplot of the variables _Displacements_ (\(d_{\text{LOS}}\)) and _Temperature_ with the least-squares reference line--the slope of which is equal to the displayed correlation coefficient \(\rho\)--for some PSs whose displacement time series have been reported in Figure 13. In the riverbed, the displacements of the PSs located over the Pier 9 exhibit a positive correlation ranging from \(0.7\) to \(0.9\). In the floodplain, the displacements of the PSs located over the north cantilever of Pier 4 exhibit a negative correlation, while those located over its south cantilever exhibit a positive correlation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{PS} & \multirow{2}{*}{**Pier**} & \multicolumn{2}{c}{\(\epsilon_{0}\) [\(\mu\varepsilon\)]} & \multicolumn{2}{c}{\(\
u\) [\(\mu\varepsilon\)/Year]} & \multicolumn{2}{c}{\(\
u\) [mm/Year]} & \multicolumn{2}{c}{\(\alpha\) [\(\mu\varepsilon^{\prime}\)C]} \\  & & \(\mu\) & \(\sigma\) & \(\mu\) & \(\sigma\) & \(M\) & \(\sigma\) & \(\mu\) & \(\sigma\) \\ \hline
6228 & \(10\) & \(23.32\) & \(15.60\) & \(-25.56\) & \(3.236\) & \(-0.3840\) & \(0.0485\) & \(19.22\) & \(0.790\) \\
6160 & \(10\) & \(156.3\) & \(20.70\) & \(-48.76\) & \(4.293\) & \(-0.7315\) & \(0.0644\) & \(18.93\) & \(1.050\) \\
6705 & \(11\) & \(78.06\) & \(22.91\) & \(-182.2\) & \(4.751\) & \(-2.7334\) & \(0.0713\) & \(22.54\) & \(1.162\) \\
6831 & \(11\) & \(65.14\) & \(23.58\) & \(-150.5\) & \(4.891\) & \(-2.2583\) & \(0.0734\) & \(13.09\) & \(1.196\) \\ \hline \end{tabular}
\end{table} 
Table 1: Mean value (\(\mu\)) and standard deviation (\(\sigma\)) of the model parameters fitting PS deformation time series estimated through LSA, including deformation trend \(\upsilon\)—both in \(\mu\varepsilon\) /year and mm/year—and the thermal deformation coefficient \(\alpha\). \(1\mu\varepsilon=\mu\)m/m. This periodic variation of the linear correlation along the bridge is clearly visible in Figure 16, where this parameter is reported for the three lines of PSs highlighted in the figure plotted against the length of the bridge. Figure 16 also shows the longitudinal section of the bridge on the same scale as the PS map and the graph.