## 4 Results  
### Synthetic Experiments and Sensitivity Analysis  
#### 4.1.1 Flood Irrigation  
Figure 2 summarizes the results of the synthetic experiments for the flood irrigation technique for the three window lengths. Figure 2a-c represent, respectively, the Pbias, the TruPosRat and the IrrigEvntRat when there is no constraint on the timing of irrigation. Figure 2d-f and g-i are the same as Figure 2a-c but applying a constraint of 5 days and 10 days between two irrigation events, respectively. For a 3-day revisit time, the Pbias ranges between \(-25\%\) and \(33\%\). An overestimation is only observed when no timing constraint is applied between two irrigation events. This overestimation is attributed to the false detection of two irrigation events during rainy period also illustrated by the IrrigEvntRat values of \(1.28\).. The Pbias is significantly lower with the application of a 5-day constraint with a value of \(25\%\); the IrrigEvntRat also improved going from \(1.28\) to \(1.00\) while a 10-day constraint improved only slightly the metrics. The number of irrigations detected around the actual irrigation day within a 4-day interval is more than \(80\%\) (TruPosRat = 0.8) for all cases and errors. With 5- and 10-day constraints, close performance is always obtained. The best TruPosRat values is 0.88 corresponding to a \(2\%\) error on SSM but close values are obtained for error from \(0\%\) to \(4\%\) (TruPosRat = 0.86). By contrast, the lowest TruPosRat equal to 0.80 is observed when the observation error is \(10\%\) and the constraint is 5 days. By contrast with the 3-day window, an underestimation of the amounts is observed whatever the error or the timing constraint for a 6-day window (IrrigEvntRat values of 0.88). This is due to an undetected event rather than an underestimation of the events  
Figure 2: Statistical metrics of the synthetic experiment for the flood irrigation technique at different window length: 3-, 6- and 12-day and for different error on the surface soil moisture (SSM error). (**a–c**) are the Pbias, TruPosRat and IrrigEvntRat when there is no constraint on the irrigation timing (No Constraint), (**d–f**) when a constraint of 5 days is applied and (**g–i**) when a constraint of 10 days is applied. amounts (not shown). A further analysis of the time series pointed out that one event was not detected because two rainfalls for a total of 35 mm were recorded at the time of the irrigation event. A low difference between the two SSM observations around the event in addition to the presence of an important rainfall prevented the approach from identifying a need for additional water in this period. Regarding the error on SSM, \(\mathrm{Pbias}\) is less than \(-12\%\) up to an error of 4% and it drops to \(-20\%\) for higher errors due to an underestimation of both irrigation amounts and of the number of events (as clearly shown by the IrrigEvntRat). Likewise, IrrigEvntRat is almost stable up to an error of 4%, around 0.93 meaning that almost all the irrigation events are detected on time when no timing constraint is applied and above 4% it drops to 0.8 (for errors of 6 and 10%). In terms of timing, TruPosRat decreases from 0.85 when there is no error on the SSM to 0.63 when considering a 10% error. Between 2 and 4% of error, a likely error range for existing products derived from SMOS [81, 82] or Si [17, 39], the TruPosRat is between 0.8 and 0.75 meaning that 75-80% of the irrigation events are detected on time. Finally, the worst metrics are obtained for the 12-day revisit time. This was expected considering the rapid dynamic of SSM that can dry out in a couple of days and well before the next available observation with a revisit time of 12-day. For instance, a loss of 17% and 5% in terms of TruPosRat is observed with regards to a revisit time of 3 and 6 days, respectively for an error of 4%. As for the 6-day window, adding a timing constraint has almost no impact on the metrics.