## 4 Case Study: Clipped Area
### Ojiya City  
Ojiya city is located on a terrace of the Shinano River (Figures 10 and 12). The Quaternary layer is composed of alluvium (thickness of 10-20 m), Holocene terrace deposits (5-20 m), lower terrace deposits (10-25 m), and Uonuma formation (\(>450\) m) from the top [66]. The deposits are mainly composed of gravel, sand, silt, and clay. The largest volumes of yearly groundwater usage in this area are devoted to snow-melting (38%) and industrial purposes (27%) [66]. The snow-melting system using the groundwater is laid along roads throughout the city (Figure 12a). The groundwater usage  
Figure 11: (a) Vertical velocities derived from InSAR (background colors) and leveling surveys (circles) in Niigata Ccity. (b) Correlation diagram of the vertical velocity between InSAR and leveling. The grey line denotes a 1:1. (c) Time series of the vertical displacement at benchmark A just east of the mouth of the Agano River. for snow-melting is concentrated in winter, which results in a sudden drop of the groundwater level every winter (Figure 12d and Figure S9). Figure 12: **(a)** Map of Ojiya City. Background color denotes the LOS velocity. Gray lines denote the distribution of the snow-melting system. **(b)** LOS displacement on 13 February 2018. **(c)** Cumulative LOS displacements with reference to the first acquisition of 25 November 2014. The acquisition dates (yyyymmdd) are shown on the top of each figure. The color range is the same as Figure 12b. All the acquisitions are shown in Figure S11. **(d)** Time series of the LOS displacement derived from InSAR and GNSS at 950240, and the groundwater level at Well I. A continuous GNSS station (950240) has recorded large seasonal vertical displacements since 1996 (Figure 12d and Figure S9) with subsidence starting around December, when winter snowfall begins [67]. When the accumulated snow melts away around March, recovery of the subsidence begins, exponentially decays, and then converges in autumn. This temporal evolution of vertical displacements is consistent with the groundwater level in Well I, which is located 300 m northeast of the GNSS station (Figure 12d, Figures S9 and S10) [67]. The periodic subsidence is almost completely recovered every year, and interannual subsidence hardly remains. The depth of Well I is 200 m, and the screens are located at the depth of 134-189 m, corresponding to the Unouma formation. These facts suggest the predominant mechanism of this vertical fluctuation is elastic compaction and expansion of the aquifer in the Unouma formation, rather than inelastic [67; 68]. Here, we reveal the spatial extent of the vertical fluctuations, as well as the detailed temporal evolution. We computed the InSAR-derived LOS time series and velocity with reference to the GNSS station 960566 (\(\sim\)26 km north-northeast from 950240). Although the velocity shows no significant long-term subsidence (Figure 12a), the time series clearly captures the periodic subsidence and retrieval temporally and spatially in detail (Figure 12c,d and Figure S11). The distribution of the fluctuating areas is almost the same every year. The InSAR-derived time series at 950240 closely agrees with the time series measured by GNSS (Figure 12d). The STD of the difference between the two datasets is 9.5 mm, which is consistent with the result for the entire frame (Section 3.2), even with the large nonlinear periodic displacement. In February 2018, the subsidence was larger than the other years, presumably because the amount of snowfall was the largest that winter of 2018, and this is also clearly captured in the InSAR results (Figure 12c,d and Figure S11; see also Section 4.4). In terms of the spatial distribution, there are two peaks of the subsidence either side of the river (Figure 12b,c). The eastern one has a smaller amount of the subsidence than the western one, which is consistent with the fact that the groundwater level change at the eastern Well II is smaller than that at the western Well I (Figure S9).