## 2 Materials and Methods
### InSAR Dataset  
The interferometric phase (\(\Delta\phi\)) is a combination of several components given by  
\[\Delta\phi=\Delta\phi_{suf}+\Delta\phi_{iono}+\Delta\phi_{hyd}+\Delta\phi_{ wet}+\Delta\phi_{liq}+\Delta\phi_{orb}+\Delta\phi_{topo}+\Delta\phi_{noise} \tag{4}\]  
where \(\Delta\phi_{suf}\) is the surface displacement contribution (due to tectonic activity or even anthropogenic effects), \(\Delta\phi_{iono}\) is the phase component related to the ionosphere, \(\Delta\phi_{hyd}\), \(\Delta\phi_{wet}\), and \(\Delta\phi_{liq}\) are the hydrostatic, non-hydrostatic (wet), and liquid contributions, respectively, \(\Delta\phi_{orb}\) and \(\Delta\phi_{topo}\) are the phase contributions related to inaccuracies in orbits and topographic distortions, respectively, and \(\Delta\phi_{noise}\) is the phase noise (decorrelation effects). The \(\Delta\) symbol refers to a temporal variation [42]. In the absence of surface displacements, orbital and topographic effects (compensated by using precise orbits and a digital elevation model), and ionospheric contribution (can be neglected in the C-band SAR missions) and after removing the hydrostatic temporal variations (more stable in space and time, can be removed using NWP data), the remaining phase is related to the wet and liquid contribution. The liquid phase contribution is due to the liquid water mass in clouds and falling droplets (hydrometeors). Separating the wet (vapor) from the liquid part is challenging, requiring external measurements at the time of SAR acquisitions, e.g., by a meteorological weather radar. Under normal atmospheric conditions, this contribution can be disregarded; however, this may not hold when acquiring SAR images during a convective cell associated with extreme rainfall events [43; 44]. In this study, 85 interferograms were generated using 112 Single-Look Complex (SLC) images acquired in 2017 by the C-band Sentinel-1 A&B Synthetic Aperture Radar (SAR) mission. Fifty SLC images were taken along the ascending orbit (path 34) and 62 along the descending orbit (path 143) between 12:00 and 12:30 UTC. Figure 1 shows both footprints. These images were processed using the SAR interferometry technique applied using the Sentinel Application Platform (SNAP) toolbox, available at [[https://step.esa.int/main/download/snap-download/](https://step.esa.int/main/download/snap-download/)]([https://step.esa.int/main/download/snap-download/](https://step.esa.int/main/download/snap-download/)) (accessed on 20 January 2024). The interferograms were processed based on the short temporal baseline method. This method consists of processing a time series of N SLC images to generate (N \(-\) 1) interferograms by selecting couples of subsequent SLC images with the shortest temporal baseline. Consequently, the phase contribution due to temporal decorrelation, especially in vegetated areas, and the Earth's surface deformation, is diminished. Precise orbit ephemeris and a high-resolution digital elevation model (\(\sim\)30 m) were used to mitigate orbital and topographic phase contributions, respectively. A visual analysis of the interferometric fringes revealed no significant Earth surface deformation, indicating that the resulting interferometric phase primarily comprises contributions from ionospheric, tropospheric (hydrostatic, wet, and liquid phase components), and noise from other sources. The complex interferogram values are known only modulo-2\(\pi\) and must be unwrapped to achieve a quantitative interpretation. Phase unwrapping involves restoring the correct multiple of 2\(\pi\) to each point in the interferometric phase image [42]. In fact, successfully applying an unwrapping algorithm is one of the most challenging aspects of InSAR. In this way, to improve the success rate of the phase unwrapping, a Goldstein filter was applied to enhance the signal-to-noise ratio of the image [45]. We also used a spatial filter (multilook) to reduce the intensity of residues due to phase noise.