## 2 Methods
### Case 1: High-Latitude Region
#### 3.1.3 Mitigation of Ionospheric Effects on SAR Interferometry  
The SAR interferogram was generated from two L-band full-polarimetric ALOS/PALSAR raw data, which were acquired on 1 April 2007 and 17 May 2007. The ASTER Global Digital Elevation Model (GDEM) with a resolution of 1 arc-seconds (30 m) was used to remove the topographic phase (Figure 6). A complex multi-look operation of two looks in the range direction and 14 looks in the azimuth direction, and an adaptive spectral filtering with a window size of 32 were applied to reduce the interferometric phase noise. Moreover, the interferogram was unwrapped by the minimum cost flow (MCF) method [53].  
Figure 7 shows the Horizontal-Horizontal (HH)-polarized original and corrected interferogram. Figure 7a represents the original interferogram, where the complicated phase patterns are observed. The main contributions of these patterns might result from the ionospheric errors based on the presented observation conditions. Figure 7b derived from (10) demonstrates the severe ionospheric effects. These effects range from \(-\)23.2 to 47.5 rad., which correspond to line-of-sight (LOS) displacements of \(-\)0.43 to 0.89 m. This error can severely degrade the precision of surface deformation monitoring or DEM construction when using the InSAR technique. Figure 7c conveys the interferogram generated by subtracting the ionospheric phase map (Figure 7b) from the original interferogram (Figure 7a). As observed in Figure 7c, most long-wavelength signals in the original interferogram have been successfully removed. This fact indicates that the estimated ionospheric phase successfully mitigates the ionospheric phase distortion. However, the residual long-wavelength signal still remains, which can be attributed to the residual ionospheric phase error. The residual ionospheric phase results from the inaccurate parameters, such as the magnetic field factor and some systematic bias. Figure 7d shows the residual-ionosphere-corrected interferogram, which is generated by subtracting the fitted residual ionospheric phase in (11). However, as observed in Figure 7d, considerable amounts of ionospheric phase error remain, particularly at the top and bottom parts of the interferogram. Finally, Figure 7e shows the interferogram that is jointly corrected by the least square method from (11). The estimated  
Figure 5: VTEC difference map in profile A-A’ of Figure 4d.  
model parameter is shown in Table 2. It can be clearly seen that the complicated fringes in original interferogram have been removed. The remaining major error components of Figure 7e may be attributed to the turbulent tropospheric delay.  
Figure 6: Simulated topographic phase used in this experiment.  
Figure 7: Horizontal- Horizontal (HH)-polarized original and corrected interferogram. (**a**) Original interferogram, (**b**) ionospheric phase map derived from (10), (**c**) ionosphere-corrected interferogram by subtracting Figure 7b from Figure 7a, (**d**) residual-ionosphere-corrected interferogram by subtracting the fitted residual ionospheric phase from Figure 7a, (**e**) integration-corrected interferogram by subtracting the fitted phase in (11) from Figure 7a.