## 3 Methods
### Metrics Associated with Detection Issues  
This section presents the results of assessing the performance of the irrigation detection approach discussed earlier by examining its capability to accurately retrieve irrigation dates and amounts over the four reference plots. Three metrics were calculated based on the concepts of true positive, false positive, and false negative, which are defined as follows. A \"probably detected irrigation\" I\({}_{\{\mathrm{j,k}\}}\) was classified as a true positive (TP) if it was detected within three days of a real irrigation date (d\({}_{\mathrm{Re}}\)) collected during the field trials. On the other hand, any probably detected irrigation I\({}_{\{\mathrm{j,k}\}}\) that deviated significantly from these dates was classified as a false positive (FP). Conversely, if an irrigation event was not detected, it was considered a false negative (FN). The methodology was applied to SSM temporal series from the ascending (evening overpass) and descending (morning overpass) SAR acquisitions separately due to diurnal variations caused by differences in vegetation water content between morning and evening. Studies consistently showed that the radar backscattering coefficient (\(\sigma^{0}\)) is generally higher in the morning overpass compared with the evening overpass [95,96]. As a result, it is recommended to investigate each SAR temporal series separately, with one acquired in the morning and the other in the evening for each of the four reference plots (Section 2.4). In other words, the method of irrigation retrieval was employed by examining the variation in SSM between consecutive SAR images, which were denoted as t\({}_{\{\mathrm{i}\}}\) and the previous image t\({}_{\{\mathrm{i}\}}\), acquired within the same SAR time series acquisition. It is important to note that this approach was applied, independently, to both the ascending and descending SAR time series. Therefore, the time interval between two SSM observations was fixed at 6 days (t\({}_{\{\mathrm{i}\}}\) - t\({}_{\{\mathrm{i}\}}\) = 6 days, revisit time of S1). Moreover, there was an overlap in the time span between t\({}_{\{\mathrm{i}\}}\) and t\({}_{\{\mathrm{i}\}}\) in both ascending and descending temporal series, as the morning acquisition was only 36 h prior to the evening acquisition. For example, the evaluation of irrigation retrieval was conducted between the t\({}_{\{\mathrm{i}\}}\) = 6 August 2017 SAR image acquired in the ascending mode and the date of the previous image t\({}_{\{\mathrm{i}\}}\) = 31 July 2017. Similarly, in the descending mode, another SAR image was acquired at t\({}_{\{\mathrm{i}\}}\) = 5 August 2017 (36 h before the evening image), with t\({}_{\{\mathrm{i}\}}\) = 30 July 2017. Consequently, a real irrigation event that occurred on 3 August 2017 could potentially be detected using either the descending SAR image (t\({}_{\{\mathrm{i}\}}\) = 5 August 2017) or the ascending SAR image (t\({}_{\{\mathrm{i}\}}\) = 6 August 2017). As a result, two dates of irrigation detection could be recorded for the same actual irrigation date. The retrieved irrigation date that exhibited the shortest time lapse between the real irrigation event and the retrieved irrigation date was considered a true positive (TP). The \"Recall\" (Re) was the first metric, representing the overall accuracy and sensitivity in detecting irrigation dates (Equation (15)). It is calculated as TP divided by TP + FN (all irrigation events). A low FN count favors a higher Re value, indicating better irrigation