# Spatial Distribution and Monitoring of Land Subsidence Using Sentinel-1 SAR Data in Java, Indonesia
## 2 Data and Methodology
### Data Coverage and Processing
Orbital error, \(\phi_{orbit}\), due to the inaccuracy of satellite position data may lead to a parallel fringe on the interferogram, called \"orbit phase ramp\". One of the efficient methods to reduce the effect of orbital error is to fit and model the orbit phase ramp using an n-order polynomial [30; 31]. The polynomial can also model the phase contribution from ionospheric error since both patterns are similar [32]. The orbital error can also be reduced by using the satellite precise orbit, which is applied in this study. Close inspection of most generated interferograms does not show any significant orbital phase ramp. It is found that corrections using polynomial fitting led to overfitting. Moreover, we select the descending route that observes the area of study early in the day in local time, resulting in ionospheric contribution, which is also considered small. The phase contribution due to the inaccuracy of the Elevation Model, \(\phi_{DEM}\) can be expressed as the following equation [33]:  
\[\Delta\phi_{DEM}(t_{A},t_{B})=\frac{4\pi}{\lambda}\cdot\frac{B\bot(t_{A},t_{B })}{r\sin{(\theta)}}\cdot z_{e} \tag{2}\]  
where \(\Delta\phi_{DEM}(t_{A},t_{B})\) is the phase error due to the DEM error between two SAR acquisitions at time \(t_{A}\) and \(t_{B}\), \(\lambda\) is the radar wavelength, \(B\bot(t_{A},t_{B})\) is the perpendicular baseline between the two acquisitions, \(r\) is the slant range (distance between the satellite and the target), \(\theta\) is the look angle, and \(z_{e}\) is the DEM error. It is clear that the DEM error can be considered as a function of the perpendicular baseline. As mentioned, in this study, the perpendicular baseline length has been limited to 180 m to minimize the error contribution. Further correction has been performed by estimating the contribution of the DEM error phase using the baseline history, following [33]. For tropospheric phase contribution correction, Generic Atmospheric Correction Online Service for InSAR [27; 28] has been used. It provides atmospheric delay correction maps using high-resolution numerical weather model data from the European Centre for Medium-Range Weather Forecasts (ECMWF). These maps are spatially interpolated to the Synthetic Aperture Radar (SAR) image resolution and provide corrections for large-scale atmospheric effects, particularly long-wavelength delays correlated with topography. The Generic Atmospheric Correction Online Service for InSAR (GACOS) corrections have been applied to the unwrapped phase of each interferogram and reduce the height-dependent delays and spatially correlated tropospheric delays. Due to the large decorrelation area caused by heavy vegetation and wet area, the coherence value in several locations are below the determined threshold. In many cases, this situation may lead to an island-like area, which contributes to phase unwrapping error. In this study, the error is corrected by benefiting the SBAS network generated using the TIN method. Each face of the TIN represents a linearly dependent interferogram, for which the vector resultant is zero. The correction in the time-series domain following [34] has also been applied. The deformation obtained from InSAR processing is typically in the line of sight (LOS). To find the true vertical displacement, the LOS displacement must be decomposed into vertical and horizontal components. There are several ways to accomplish this task, but essentially, multiple observations from different look angles are required [35]. However, since the focus is exclusively on the vertical displacement, and the horizontal displacement can be discarded, the conversion of LOS displacement (\(d_{LOS}\)) into vertical displacement (\(d_{LOS}\))can be carried out using the following equation: \(d_{v}=d_{LOS}/cos\theta\), where \(\theta\) is the look angle (e.g., refs. [8; 36]).