## 2 Methods
### Case 1: High-Latitude Region  
#### 3.1.1 Experimental Region and Data  
The experimental region with high latitude is located in Alaska, which is the largest state in the United States by area and situated in the northwest extremity of the Americas (Figure 2a). Two L-band full-polarimetric ALOS/PALSAR images acquired on 1 April 2007 and 17 May 2007 were collected in this experiment. As shown in Table 1, the temporal baseline is 46 days and perpendicular baseline is 6 m.  
For generating reference information about ionospheric variation at the SAR acquisition time, the dual-frequency GPS data at a permanent station near Fairbanks is processed (the red star in Figure 2a). This procedure is carried out by calculating the GPS carrier phase difference between frequency L1 and L2. This difference can remove the tropospheric delays errors and GPS receiver clock errors because they have the same effects on the observation for both frequency L1 and L2 [16]. Moreover, the inter-frequency difference in satellite clock offsets are so small that they can be neglected. As for the receiver and satellite's instrumental biases, they can be cancelled since they remain constant over a short observation session. Finally, the cycle slips are detected and corrected using the algorithm proposed by [PERSON] [49]. After these operations, the residual phase components are mainly from the ionospheric contribution. Figure 2b,c shows the time rate of changes of total electronic content (ROT), an index to reflect the ionospheric variation) on 1 April 2007 and 17 May 2007, respectively, where SAR acquisition time is marked with a dotted line. Figure 2b presents the clear ionospheric fluctuation from 5:00 to 18:00 UT and a peak value at about 7:00 UT. This suggests the strong ionospheric irregularities over experimental area on 1 April 2007. Unlike Figure 2b,c shows the weak ionospheric irregularities, indicating the background ionospheric condition on 17 May 2007. Additionally, the Auroral Electrojet (AE) index, a quantitative measure of auroral zone magnetic activity, was obtained from the Super Dual Auroral Radar Network (SuperDARN) ([[http://vt.superdarn.org/tiki-index.php?](http://vt.superdarn.org/tiki-index.php?)]([http://vt.superdarn.org/tiki-index.php?](http://vt.superdarn.org/tiki-index.php?))), as shown in Figure 2d-e. It is found that the geomagnetic activity is relatively strong on 1 April, when the AE value at the SAR-acquired time is about 600 nT. The geomagnetic activity is quiet on 17 May, when the AE value at the SAR-acquired time is about 80 nT. This result provides another piece of evidence for ionospheric irregularities on 1 April 2007 and the background ionospheric condition on 17 May 2007.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No.** & **Master** & **Slave** & **Center** & **Incident** & **Center** & **Center** & **\(B_{T}\)** & **\(B_{P}\)** \\  & & & **Frequency** & **Angle** & **Latitude** & **Longitude** & **(Days)** & **(m)** \\ \hline
1 & 01/04/2007 & 17/05/2007 & 1270 MHz & 23.93\({}^{\circ}\) & 62.47\({}^{\circ}\) & \(-\)144.77\({}^{\circ}\) & 46 & 6 \\
2 & 26/03/2010 & 29/03/2011 & 1270 MHz & 24.01\({}^{\circ}\) & 100.56\({}^{\circ}\) & 14.87\({}^{\circ}\) & 368 & 1091 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Interferometric parameters used in the experiment, where \(B_{T}\) stands for temporal baseline and \(B_{P}\) stands for perpendicular baseline.