# Monitoring of Ground Movement and Groundwater Changes in London Using InSAR and GRACE
## 3 Materials and Methods
### Groundwater from GRACE  
GRACE (Gravity Recovery And Climate Experiment) is a combined venture of the National Aeronautics and Space Administration (NASA), USA and the German Aerospace Center (DLR) [42]. It was launched on a rocket launch vehicle from the Plesetsk cosmodrome in Russia on 17 March 2002. The mission was operated by the German Space Operations Center (GSOC) and it consisted of two identical satellites named GRACE-A and GRACE-B. With over 15 years of operation, the predicted mission lifetime of 5 years was exceeded by more than 3 times and ended on October 2017. The GRACE Follow-On (GRACE-FO) is a sequel of the mission on almost similar hardware and was launched in May 2018.  
A change in the mass of the Earth surface causes a change in gravity. This mass change can be assumed to be mainly concentrated near the earth surface in a shallow layer of a thickness of water. The monthly gravity changes mainly result from changes in water content in hydrologic reservoirs, atmospheric and land ice masses and by mass exchanges between the Earth system's compartments [43]. Thus, after postprocessing and applying corrections for non-water mass changes, GRACE gravity anomalies can provide the Terrestrial Water Storage (TWS) variation.  
TWS was obtained using COST-G, RL01, level-3 data [44] filtered with VDK5 and VDK3 anisotropic filters [45]. The deterministic components from VDK5 were combined with residual monthly variations from VDK3, to account for noise level of seasonal components. To calculate TWS, stokes coefficients were used to invert mass anomalies by applying thin layer approximation [43]. To reduce the effect of atmospheric mass variability, the non-tidal de-aliasing product AOD1B RL06 [46] was used for processing of level 2 monthly gravity fields. The signal estimates were accompanied by TWS standard deviations, which represents associated uncertainties that take into account the varying noise level from month-to-month. The uncertainty was simulated using the empirical covariance model, which considers non-stationarity, non-homogenous and anisotropic structures of spatial correlations.  
The final Groundwater Storage Change (\(\Delta\)GWS) could then be calculated by subtracting surface water storage, soil moisture and snow and ice water storage from TWS.  
\[\Delta\text{GWS}=\ \Delta\text{TWS}-(\Delta\text{SWS}+\Delta\text{SMS}+\ \Delta\text{SIS}) \tag{1}\]  
where \(\Delta\)TWS is the change in terrestrial water storage, \(\Delta\)SWS is the change in surface water storage, \(\Delta\)SMS is the change in soil moisture storage, and \(\Delta\)SIS is the change in snow and ice water storage.  
The surface water and soil moisture were used from a monthly GLDAS Land Surface Model (LSM). GLDAS drives four LSMs, namely NOAH [47], Community Land Model (CLM) [48], MOSAIC [49], and Variable Infiltration Capacity (VIC) [50]. To minimize any inherent deficiency in any model, an average of four LSM hydrological outputs from NOAH, CLM, MOSAIC and VIC were adopted for our study time period. The change in snow and ice cover was considered negligible given the climatic scenario of London city. To ascertain that spatial resolution of TWS provided by GRACE is consistent with SWS and SMS provided by GLDAS, the kriging interpolation was adopted to resample the GLDAS data with the same resolution as the GRACE data.