# Interpretation of Bridge Health Monitoring Data from Satellite InSAR Technology
## 4 Results and Discussion
### Correlation between Displacements and Water Level Variations  
We proceed with the correlation analysis by studying the correlation between PS displacements and water level variations of the Po River. First, we decimate the water level dataset to one measurement per day for the days corresponding to the satellite passage over the case study area. Figure 17(a) illustrates the map of the identified PS on the bridge, represented in a colour scale corresponding to the Pearson correlation coefficient resulting from comparing displacements and water level for each PS. Figure 17(b) shows a zoom on the riverbed portion of the bridge. As in Figure 17(a), we can observe in Figure 17(a) a clear difference in the correlation values between the floodplain and the riverbed portions. Specifically, we notice that the Pearson coefficient of most PSs in the floodplain portion of the bridge is almost zero, while it is negative and between \(-0.5\) and \(-1\) for the PSs over the riverbed portion. This difference in correlation along the bridge is also clearly visible in Figure 19, where this parameter is reported for the three lines of PSs highlighted in the figure plotted against the length of the bridge. Figure 17: (**a**) Scheme explaining the negative and positive sign of the horizontal longitudinal displacements of the cantilevers obtained from satellite measurements as temperature increases; (**b**) application to the A22 Po River Bridge, highlighting the portions with a positive and a negative correlation between displacements time series and temperature variation. The displacement periodicity of the PSs in the floodplain does not seem correlated with the seasonal water level changes. In contrast, the displacement periodicity of the PSs in the riverbed does, with downward-westward displacements occurring when the water level rises--the Po River flows from West to East. Since the soil is highly heterogeneous, these displacements may be related to ground deformations associated with seepage through soils of different permeabilities. However, further geotechnical investigations should be carried out to evaluate the pore water pressure distribution and the physical properties of the soil both below the river and in the surrounding area. Note that the displacements of the PSs located over Pier 11 show a lower correlation with water level variation than those of PSs on other peers in the riverbed. That is probably due to the peculiar characteristics of Pier 11: greater height above the ground level, scour effects and relative maintenance works, and higher long-term displacement trend. Figure 19: Linear correlation between PS displacement time series and water level variation plotted against the length of the bridge. PSs are divided into three lines. Figure 18: Linear correlation between water level variation of the Po River and displacement time series of PSs identified on (a) the A22 Po River Bridge and (b) the portion of the bridge in the riverbed. Similar results on the negative correlation between the PS displacements of a bridge crossing the Po River and the Po River water level were obtained and discussed by [32], who monitored through satellite InSAR three bridges not far away from our case-study area: the San Benedetto Po Road Bridge, and both the road bridge and railway bridge connecting the villages of Ostiglia and Revere. These authors observed an inverse correlation between the displacements of the PSs identified on the bridges and the water level of the Po River. They analysed SAR images acquired in C-band by the satellite constellation Sentinel 1 from 2018 to 2020 in ascending and descending geometries. They performed the MT-InSAR analysis through the open-access software SNAP&StaMPS to extract PS displacement time series. The authors concluded that the displacements were mainly vertical and seemed correlated with the seasonal changes in the water level of the Po River, with downward displacements occurring when the river rises.