## 2 Materials and Methods
### Materials
#### 2.1.3 Remote Time Series Acquisition  
Remotely sensed datasets include Sentinel-1 SAR and surface temperature time series were derived by processing Landsat 8 TIR images on the Google Earth Engine environment (as discussed later on within the method section). Images acquired from the Sentinel-1 two-satellite constellations were processed to monitor both displacements and water levels; whereas Landsat 8 TIR images allowed the remote determination of the water surface temperature.  
The Sentinel-1 SAR constellation is composed of Sentinel-1A (S1-A) and Sentinel-1B (S1-B) which share the same orbit plane with a 180\({}^{\circ}\) orbital phasing difference (near-polar sun-synchronous orbit). The so-called Interferometric Wide (IW) swath mode allows data acquisition with a 250 km swath with 5 m \(\times\) 20 m ground resolution (single look) over three sub-swaths (IW1, IW2, and IW3 for increasing off-nadir angles, respectively) in the Terrain Observation with Progressive Scans SAR (TOPSAR) mode [47]. However, although S-1B was launched in April 2016, within this research, only S1-A images have been processed; thus, the SAR dataset includes 20 Sentinel TOPSAR S-1A images in Vertical transmit-Vertical receive (VV) polarisation acquired in Single Look Complex (SLC) mode in ascending, right-looking overpasses (relative orbit number 117, sub-swath IW2) (Figure 2, black box), and 17 in descending right-looking overpasses (relative orbit number 22, sub-swath IW1) (Figure 2, white box). The acquisition incidence angles were \(\approx\) 39\({}^{\circ}\) and 34\({}^{\circ}\) for the ascending and descending images, respectively. The dataset is freely provided by the Copernicus Open Access Hub [51] (previously known as the Sentinel Scientific Data Hub). Although the dataset size is limited, the interferometric outcomes remain reliable according to [PERSON] et al. [38]. Even if the use of X-band is more appropriate for datasets with limited image numerousness [52].  
Images acquired in both ascending and descending relative orbits span over a year (January 2015-January 2016) (Table 1). Most of the images were collected during the annual emptying phase of the reservoir (period 3; 17 images); during the st  
Figure 2: The Terrain Observation with Progressive Scans SAR (TOPSAR) S-1A track over Google Earth: ascending orbit (relative orbit number 117, sub-swath IW2, thick black box) and descending orbit (relative orbit number 22, sub-swath IW1, thick white box). Other sub-swaths are represented with thin black and white lines (ascending and descending orbits, respectively). The position of the Castello dam is indicated (red dot).  
10 images were available, whereas the smaller number of images were acquired during the filling phases (periods 1 and 4; three and seven images, respectively). The image acquired on 12 January 2016 was used only for the full-graph MBC method.  
The Land Surface Temperature (\(LST\)) time series was derived by averaging a number of points randomly distributed within the Magazzolo reservoir by processing several Landsat 8 Thermal Infrared Sensor (TIRS) images. In particular, 23 and 14 images were processed over the scene 189034 and 190034, respectively, spanning from 8 January 2015 to 26 December 2015. Just two images per month were available during the winter-spring periods from February to May 2015; three clean acquisitions per month were available in the winter period, specifically in January, November, and December; finally, four images per month were available over the Summer-Autumn periods, from June to October.