# Modeling Actual Evapotranspirationiration with MSI-Sentinel Images and Machine Learning Algorithms
## 3 Results
### Models Application  
Figure 10 shows the distribution of the crop coefficient (K\({}_{\rm c}\)) during the sugar cane cycle, determined through the XgbLinear, which presented better metrics for approaches 1 and 2 through the METRIC model and also through the FAO-56 report [1]. Figure 9: Spatial variability of ET\({}_{r}F\) for approaches 1, 2, and Metric for 02/12/2020. Figure 10 evidences what was previously discussed; for the initial phases of the crop, with low-density plant coverage, machine learning prediction model values showed uncertainties when compared to METRIC, but, as the culture develops, this error tends to reduce. For phase I (initial), when there is a crop emergency, the K\({}_{\rm c}\) for approaches 1 and 2 were 0.3 and 0.32, respectively, while METRIC estimated a K\({}_{\rm c}\) of 0.20, and the K\({}_{\rm c}\) determined by the 56 FAO's report [1] is 0.40. In phase II (development), the K\({}_{\rm c}\) curves in approaches 1 and 2 become closer to the ones of the METRIC as the phenological state progresses, as well as the K\({}_{\rm c}\)-FAO curve becomes closer to both approaches and distances a little from the METRIC curve. For phase III (mid-season) crop growth, the average K\({}_{\rm c}\) was 0.98 for approach 1 and 1.00 for METRIC, while for approach 2, it was 1.02, and FAO's 56 report recommends using a 1.25 value. Moreover, in phase III, the METRIC curve behaves similarly to approach 2, which corroborates the results found in the models' tests. In phase IV (late-season), maturation, approach 1 was the most distant from both FAO's and METRIC's K\({}_{\rm c}\), with a value equal to 0.69, while approach 2 had a K\({}_{\rm c}\) of 0.76 and METRIC of 0.77. [PERSON] and [PERSON] [35], when quantifying K\({}_{\rm c}\) for sugar cane through the water balance method, found medium values for phases I, III, and IV of 0.36, 1.20, and 0.78, respectively. [PERSON] et al. [36], for the Brazilian semiarid region, obtained a K\({}_{\rm c}\) for ratoon cane in phases I, III, and IV equal to 0.65, 1.10, and 0.85, different from FAO's recommendation. This evinces a divergence in K\({}_{\rm c}\) values shown in the literature from the ones recommended, which can be explained by the specificity of the local weather in which each study was performed, as well as the physiological conditions of the crop at the time of the satellite imaging. Phase III, for this work, reached the maximum value of 1.09; however, it showed variations throughout the whole phase. Regarding Figure 10, it is noticeable that with Sentinel-2, due to its better temporal resolution, it was possible to obtain a larger number of K\({}_{\rm c}\) information throughout the crop cycle than Landsat-8, which is important to obtain a major temporal variability of this coefficient. This can lead to more assertive crop management than if only Landsat-8 data were used. [PERSON] and [PERSON] [37] mention that Sentinel-2 represents a new age for obtaining more precise information about the Earth's surface, as it has a greater spatial and temporal resolution among satellites that provide images for free. Nevertheless, information referring to K\({}_{\rm c}\) can be expanded when joining the two orbital platforms, as more information will be obtained with a larger frequency of images, as highlighted in [PERSON] et al. [9]. Figure 10: Comparison of K\({}_{\rm c}\) values between approaches 1 and 2, METRIC, and the ones recommended by the FAO’s 56 reports. In Figure 11, attention is drawn to DAE 030 with a ray with an ET\({}_{\text{a}}\) larger than for the rest of the pivot. On that day, crops were in the initial emergency phase, and soil was exposed in most of the area, receiving water from irrigation. This ray corresponds to the  
Figure 11: Sugar cane temporal-spatial actual evapotranspiration in three different spatial resolutions evincing, through rectangles, coincident dates between Sentinel-2 and Landsat-8. moisture in the exposed soil, and it is displaced clockwise from the irrigation equipment.