*2.1. Studied Area*

Our investigation site, an urban area located at Chaingy (France) with a semi-oceanic (i.e., slightly continental) climate, is characterized by a high level of shrink/swell hazard (Figure 1). Since 2016, two in situ extensometers (EXT1 and EXT2), spaced about 12 m apart, and a battery of soil moisture sensors at 1.2 m depth are deployed (Figure 1).

#### *2.2. Synthetic Aperture Radar (SAR) Data and Interferometic Processing*

Copernicus Sentinel-1 SAR data was utilized for the investigation of induced ground displacements in the vicinity of the extensometers EXT1 and EXT2 (see Table 1). Interferometric SAR (InSAR) processing was performed on the Geohazards Exploitation Platform (GEP) (https://geohazards-tep.eu, accessed on 23 September 2021). GEP is a platform originated by ESA as part of the Thematic Exploitation Platforms (TEP) initiative, aiming to support the exploitation of Earth Observation (EO) satellites to assess geohazards and their impact [10].

For the InSAR processing the Parallel Small Baseline Subset (P-SBAS) algorithm [11–13], as implemented on the GEP, was exploited. P-SBAS method is based on the processing of temporal series of co-registered SAR images acquired over the same target area for the generation of Line-of-Sight (LoS) ground displacement time series and average velocity maps. The technique allows for the extraction of both linear and non-linear motion components without a priori assumption on the displacement model. The service is provided at 90 m spacing distributed on a regular grid covering the user defined area of interest.

Between September 2016 and December 2019, the entire Sentinel-1A/1B archive data from both ascending and descending orbit geometries, 183 and 178 scenes, respectively, were processed. Supposing a 1D vertical displacement, the LOS motions are projected to vertical, whereas combination of different viewing geometries provide us the actual vertical motion component (the equation below was adapted from Hanssen (2001) [14]):

$$\text{VERT\\_ASC\\_DES} = (\text{LOS}\_{\text{AS\mathcal{C}}} + \text{LOS}\_{\text{DES}}) / (\cos \theta\_{\text{AS\mathcal{C}}} + \cos \theta\_{\text{DES}}) \tag{1}$$

VERT is the vertical displacement, LOS the motion in the Line-Of-Sight direction, θ the incidence angle, and the subscript ASC and DES for the ascending (θASC = 34.4◦) and descending (θDES = 42.8◦) tracks, respectively.

**Figure 1.** Map of the Chaingy experimental site. (**a**) Regional setting in France (Map data: Google, Landsat/Copernicus, SIO, NOAA, US Navy, NGA, and GEBCO) that contains modified Copernicus Sentinel data (2016) and a ~25 km cell of the EASE equal-area grid used by the SMOS satellite (black rectangle). (**b**) Simplified superficial geology of the studied zone modified from the BRGM geological map of France at the 1:50,000 scale showing the P-SBAS grid (black circles) and the location of the studied zone (red filled polygon). (**c**) Local setting (Map data: Google, Landsat/Copernicus, SIO, NOAA, US Navy, NGA, and GEBCO) of the studied zone (red polygon) showing two extensometers (EXT1 and EXT2) (red placemarks), three soil moistures sensors at E1, E5, and W5 (blue placemarks), three electric profiles (green lines), two core sampling SC1 and SC2 (white polygons), and two P-SBAS grid cells (white and black rectangle) around two grid points West Point WP and East Point EP (white circle). Maps (**a**–**c**) were created using Google Earth Pro and map b by QGIS (Version 3.4.14, Bern and Chur, Switzerland, http://qgis.org, accessed on 23 September 2021).

**Table 1.** Sentinel-1A/1B GEP InSAR processing parameters.


**Table 1.** *Cont.*


### *2.3. SMOS Level 3 Surface Soil Moisture (SSM) Products*

SMOS satellite was successfully launched on 2 November 2009 by ESA. We use here the term Surface Soil moisture (SSM) to refer to the volumetric soil moisture in the first few centimeters (0–5 cm) of the soil. L-band radiometry is achieved resulting in a ground resolution of 50 km. SMOS Level 0 (L0) to Level 2 (L2) data products are designed by ESA for scientific and operational use. The products are divided in half orbits, from pole to pole, ascending or descending, spanning about 50 min of acquisition 3. Level 3 products are geophysical variables with improved characteristics through temporal resampling or processing. In order to prevent any inconsistency resulting from interpolation over highly heterogeneous surfaces, no spatial averaging is operated in the algorithms [15–17]. It must also be noted that ascending and descending overpasses are bound to show different values of the retrieved parameters that may not be always comparable, and they are, thus, retrieved separately. The performance of each satellite SSM product depends on many factors such as, but not limited to, soil type, climate, presence of noise (Radio Frequency Interference), and land cover. It is therefore difficult to predict the performance of SSM products over a region, without performing a quality assessment using in situ measurements. The SMOS Level 3 SSM products were accessed through the CATDS Data Processing Center [16] (https://www.catds.fr, accessed on 23 September 2021). The data are presented over the Equal-Area Scalable Earth (EASE grid 2) [18] with a sampling of about 25 km × 25 km and the studied area is included in one grid cell (Figure 1). We used these 3-day aggregated SMOS-CATDS SSM products for ascending and descending overpasses between September 2016 and December 2019 for each Sentinel-1 acquisition (6 day-repeat cycle).

#### *2.4. Signal Processing Using Fourier Analysis*

Fourier analysis is well suited for the quantification of constant periodic components in time series. To perform filtering of satellite and in situ signals, time series of measurements are smoothed using a one-dimensional convolution approach with a HANNING window [19]. To carry out the spectral analysis, the filtered time series is first padded with trailing zeros to a length of 100 yr before computing the Discrete Fourier Transform (DFT) using the Fast Fourier Transform (FFT) Matlab (Matrix Laboratory, the MathWorks, Natick MA, USA) function [20]. The frequency maxima of Fourier power spectrum are therefore computed with a precision of 1/100 yr<sup>−</sup>1. The magnitude and the phase angles of complex FFT values are calculated by Matlab ABS and ANGLE operators, respectively. Whenever the jump between consecutive angles is greater than or equal to π radians, UNWRAP function shifts the angles by adding multiples of ±2π until the jump is less than π.
