# Monitoring of Ground Movement and Groundwater Changes in London Using InSAR and GRACE
## 5 Discussions  
### Validation of InSAR Subsidence with GNSS Data  
To validate the reliability of results obtained from PSInSAR, we studied the PSInSAR results in comparison to GNSS data obtained from The British Isles continuous GNSS Facility (BIGF). The BIGF Level 2 products are a time series of the station-specific daily coordinate estimates obtained from the processing of continuous GNSS data, which have been subject to time series analysis to represent them as Cartesian differences or north, east, up differences (from an assumed reference coordinate at the central epoch) such that the \"up\" differences can be compared with PSInSAR-derived subsidence results. To verify PSInSAR subsidence results with the GNSS data, several steps were performed:  
* The average monthly data sets were obtained by averaging the daily data for a particular month. * The overlapping period for GNSS and InSAR image data were selected for each GNSS station. * To get the subsidence at the location of the GNSS station, the average of all the persistent scatterers that are present within 300 m of the GNSS station was used. This was done as getting PS point and GNSS station at the exact same location may not always be possible, and also GNSS up values will be affected by its nearby areas, and hence it is suitable to take the contribution of nearby points for a particular GNSS station. * Two-sample paired \(t\)-test (at 95% confidence limit) was done on each station to test the null hypothesis that the mean difference between the two sets is zero. The location of GNSS stations is shown in Figures 1 and 3. We discussed subsidence patterns for three GNSS stations, namely Bark, Stra and Tedd, because data available from these stations overlap with our InSAR data both spatially and temporally. Figure 7a-c highlights that both the InSAR-derived subsidence and GNSS up values exhibit a non-linear pattern. In Figure 3, the region surrounding Bark station has a red-yellow patch and exhibits average subsidence of approximately 5 mm/year. The time variation of InSAR subsidence and GNSS up values from December 2002 to September 2010 at Bark station are shown in Figure 7a. Both the series exhibit similar patterns with negative subsidence, which means that the bark station is subsiding with some seasonal variations. To check whether the differences between the two series are within the acceptable range, we carried out the two-sample \(t\)-test. Table 5 shows the results of two-sample \(t\)-test for Bark, Tedd and Stra stations. For each of the stations, the mean difference is not the same, but it is important to check if this difference is statistically significant to conclude whether our PSInSAR results are in agreement with observed GNSS results or not. For two-sample paired \(t\)-test, we took the null hypothesis and alternate hypothesis as: Null Hypothesis (H\({}_{0}\)): \(\mu=0\), the mean difference is zero and alternate Hypothesis (H\({}_{\text{A}}\)): \(\mu\
eq 0\), the mean difference is not zero. From the observed results, we are mainly interested in the \(t\)-value that we calculated, and at Bark it is 0.221. This signifies that these results are occurring about 0.22 standard deviations away from the mean. To accept the null hypothesis, \(t\)-value less than critical \(t\)-value (2.011 for Bark) is required. The \(t\)-value for Bark is less than the critical \(t\)-value, signifying acceptance of null hypothesis, showing no significant difference between the average monthly up and InSAR subsidence. Another way is to look  
Figure 7: Time series comparison for InSAR subsidence and GNSS up values at **(a)** Bark **(b)** Tedd and **(c)** Stra stations.