# A Study of Landfast Ice with Sentinel-1 Repeat-Pass Interferometry over the Baltic Sea
## 4 Results and Discussion
### Interferogram Analyses  
Further, we examine the interferogram based on the Equation (6). As expected, the visibility of the interferometric phase fringes is limited by the high coherence polygon area (Figure 9a). Considering the form of the fringes, it is unlikely that they would have been produced by metamorphosis in the surface snow layer or ice growth. Rather, the background must be mechanical displacement. The InSAR displacements are projections in LOS, i.e. the direction between the SAR antenna and the point on the ground. SAR imaging is performed not exactly below the satellite but on the side at a distance determined by the inclination angle (Figure 1). Ascending and descending orbits show observations from west and east respectively. The ground surface is changing in three dimensions. It includes east and west, north and south, up and down but an interferogram can show one-dimensional displacement, and it cannot determine whether the displacement is due to horizontal, vertical or combination of both. The Interferometric phase (Figure 9a) is converted to the displacement map shown in Figure 9b. This conversion includes the steps mentioned in Section 3.2. We applied multi-looking and phase-filtering after interferogram formation, then interferogram was unwrapped and, finally, converted to a displacement map. We chose an island as a grounded control point and calculated displacements based on it. In this case, both image acquisitions are made from the east (descending orbit). One fringe means almost 27.5 mm displacement in LOS. The measured LOS displacement is from -10 cm to 30 cm. Negative signs show the landfast ice is in the direction away from the satellite, which means that the landfast ice sinks or moves to the west. Positive signs show the landfast ice is in the direction close to the satellite, which means that landfast ice uplifts or moves to the east. Figure 8: Interferometric coherence histogram for Sentinel-I image pair on 6 and 18 February 2015 for: (a) VH polarization over the high coherence study area; (b) VV polarization over the high coherence study area; (c) VH polarization over the low coherence area; and (d) VV polarization over the low coherence area. It is seen that the southern part of the high coherence polygon area in Figure 9b moves away while its northern part comes closer. Thus, there is a converging zone between southern and northern parts and the projected strain would be on the order of 40 cm across 20 km (Figure 9b). The 40 cm displacement could have been caused by viscous or plastic deformation during the 12 days. One of the reasons for the vertical displacement can be sea level tilt. Absolute sea level cannot affect interferogram fringes because the landfast ice is afloat, but sea level tilting might affect fringes. Fringes can change by sea level differences according to \(\Delta R=\varphi/2k\), where \(\varphi\) is the interferometric phase, and \(k=\frac{2\pi}{\lambda}\) is the wave number, which is equal to 114.20 m\({}^{-1}\) here [10]. Two sea level stations, Kemi and Oulu, provided sea level data for our area (Figure 10). The plots are based on hourly data. In our period of study, the sea level dropped from 41.4 to 36.0 cm from 6 to 18 February in Oulu, and the corresponding change was from 39.7 to 36.5 cm in Kemi. Thus, the maximum relative change in sea level was 2.2 cm and the distance between sea level stations was 82 km. The absolute sea level ranged within \(\pm\)50 cm in the period of study, but the whole water body moved up and down almost together leaving tilts across the basin below 5 cm over 100 km distance. These tilts can thus cause only minor relative vertical displacements in the landfast ice. Figure 9: (**a**) The interferometric phase over 6 and 18 February 2015. We use the Sentinel-2 image as a background image. Green areas are land and islands, and black areas are water. (**b**) Displacement map from the unwrapped 6 and 18 February interferogram. “Near” means close to the satellite and “Far” means far away from the satellite.