## 2 Materials
### Sentinel-1 SAR Data
Each study site underwent the acquisition of 10 SAR images per month, comprising 5 ascending and 5 descending images. The descending SAR image (morning) for the Montpellier site (Figure 3a) was acquired 36 h before the ascending evening image, exhibiting incidence angles of 38.1\({}^{\circ}\) and 39.3\({}^{\circ}\), respectively. Similarly, in Tarbes (Figure 3b), the morning acquisition preceded the evening acquisition by 36 h, and the incidence angles were 36.2\({}^{\circ}\) and 40.3\({}^{\circ}\), respectively. ESA's S1 toolbox was employed to calibrate a total of 288 S1 images. This calibration process encompassed radiometric and geometric adjustments, which transformed the digital numbers into backscattering coefficients (\(o^{0}\)) in linear units (radiometric calibration) and ortho-rectified the images (geometric calibration) using a 30 m digital elevation model derived from the Shuttle Radar Topography Mission (SRTM). Finally, two distinct sets of \(o^{0}\) temporal series were derived for each study site. These series represent the repeated images obtained through the same acquisition mode (ascending and descending) every six days. The first set corresponded to the morning acquisition and was labeled as DM1 for the Montpellier site in 2017, and DM2, DM3, and DM4 for Tarbes in 2018, 2019, and 2020, respectively. Moreover, the temporal series acquired in the afternoon were denoted as MA1 for the Montpellier site in 2017, while for the Tarbes site, they were labeled as MA2, MA3, and MA4 for the years 2018, 2019, and 2020, respectively. For each acquired S1 SAR image of the temporal series (DM1, DM2, DM3, DM4, MA1, MA2, MA3, and MA4), the SAR \(o^{0}\) at plot scale (\(o^{0}_{\rm P}\)) was calculated by averaging the pixel values within each plot (P1, P2, P3, and P4) in both the VV and VH polarizations. The SAR incidence angle (\(\theta_{\rm P}\)) was determined for each SAR image at every plot. The increase in SSM values can be attributed not only to irrigation events but also to rainfall events, which are the primary contributors to SSM variations. Therefore, it is necessary to distinguish between rainfall events and irrigation events. Both rainfall and irrigation events are considered water supplements and can have a similar effect on the value of \(o^{0}_{\rm P}\) and SAR backscattering coefficient at the grid scale (\(o^{0}_{\rm G}\)). Thus, resolving the ambiguity between  
Figure 3: Sequences of Sentinel-1 images in both the ascending “A” (afternoon, represented by blue) and descending “D” (morning, represented by yellow) modes over a month, namely, in April 2017 for the P1 plot in Montpellier (**a**) and in April 2018 for the P2 plot in Tarbes (**b**). Also indicated are the incidence angles associated with each acquisition. rainfall and irrigation is crucial for accurately detecting irrigation events. To achieve better detection of irrigation events, information about rainfall is essential. In this study, information about rainfall occurrence was determined through the SSM value obtained at the grid scale (Section 2.4). It was assumed that if the bare soil plots with low vegetation cover within the 10 km \(\times\) 10 km spatial extent exhibited an increase in SSM values between two consecutive SAR acquisitions, a rainfall event likely occurred. This correlation between rainfall and \(\sigma_{\text{G}}^{0}\) was demonstrated by [PERSON] et al. [88], where they compared SSM estimations at bare soil plots in a 10 km grid scale with rainfall events at the same scale, revealing a strong consistency between rainfall events and SSM values at the 10 km grid scale. The backscattering coefficient at grid scale (10 km \(\times\) 10 km), namely, \(\sigma_{\text{G}}^{0}\), was obtained for each SAR acquisition of each temporal series by averaging the SAR backscattering coefficient of all pixels within each grid cell that corresponded to either bare soil or areas with small vegetation cover.