## 3 Method  
In this study, we used measurements from InSAR to determine land displacement rates in Yunlin, which were then calibrated and assessed by the displacement rates from GPS and leveling. Figure 4 shows the workflow for computing and calibrating the InSAR displacement rates. First, the Sentinel-1A data were processed by an open source InSAR processing tool GMTSAR [15], which also provided a two-dimensional phase unwrapping tool SNAPHU [16]. We determined the LOS displacement rates from April 2016 to April 2017 and cumulative displacements in the wet and dry seasons by the SBAS method. SBAS used differential interferograms acquired at satellite positions with a small distance and a short-time interval, resulting in the so-called small baselines [17]. To reduce noises in the InSAR results, the spatial resolution of the final set of LOS displacement measurements was re-sampled to \(10.5^{\prime\prime}\times 3^{\prime\prime}\) along the longitude and latitude, which corresponded to a resolution of \(297.5\)m \(\times\)\(85\)m in Yunlin. The re-sampling reduced the noise, but preserved the signals of land subsidence. Then, the GPS data (Figures 2 and 3) were used to determine velocities from April 2016 to April 2017 (the Sentinel-A time span). The three-dimensional velocity components (\(V_{N}\), \(V_{E}\), and \(V_{h}\)) from GPS were converted into the LOS velocity (\(V_{LOS}\)) using [18]:  
\[V_{LOS}=\left[ \begin{array}{cc}\sin\theta\sin\alpha&-\sin\theta\cos\alpha& \cos\theta\\ \end{array} \right] \tag{1}\]  
where \(\theta\) and \(\alpha\) are the Sentinel-1A incidence angle and the satellite heading angle (azimuth), respectively. Next, all the GPS measurements were used to calibrate the initial InSAR result (see Section 4.1), which contained phase ramps in interferograms that were likely caused by orbit error and long-wavelength atmospheric effects [19; 20]. The orbit error of InSAR could be decomposed into along-track (azimuth), across-track (range), and radial components [21]. The along-track orbit errors  
Figure 4: The workflow of the Sentinel-1A SAR determination of line of sight (LOS) and vertical velocities. could be regarded as timing errors, which are usually corrected during the coregistration of the two images in the InSAR processing. The across-track and the radial orbit errors can cause time-dependent baseline errors between the master and slave images and induce systematic phase ramps along the range and azimuth directions [18; 21; 22; 23; 24]. In addition, baseline errors can introduce errors in the across-track direction and cause phase ramps [21; 25]. Such error-induced phase ramps can be modeled by a trend surface [22; 24; 26]; see Equation (2) below. A justification for using a trend surface was given by [PERSON] [16], who showed that the ratio between the coefficients of a trend surface term and those of the quadratic surface was approximately \(10^{6}\), suggesting that only the linear term was needed. In addition to orbit errors, the effect of the reference frame on InSAR results has been discussed [20]. As this effect results in a linear trend in the range direction, it is reduced when estimating a trend surface in the calibration step. We used the GPS displacement rates along the LOS direction to estimate the required parameters in a trend surface that accounts for the systematic errors in the initial InSAR result. First, we calculated the mean LOS displacement rate from InSAR within a circular area around each GPS station and then calculated its difference with the GPS displacement rate (called the observed difference).