# Modeling Actual Evapotranspirationiration with MSI-Sentinel Images and Machine Learning Algorithms
###### Abstract  
The modernization of computational resources and application of artificial intelligence algorithms have led to advancements in studies regarding the evapotranspiration of crops by remote sensing. Therefore, this research proposed the application of machine learning algorithms to estimate the ET\({}_{\mathrm{F}}\)F (Evapotranspiration Fraction) of sugar can crop using the METRIC (Mapping Evapotranspiration at High Resolution with Internalized Calibration) model with data from the Sentinel-2 satellites constellation. In order to achieve this goal, images from the MSI sensor (MultiSpectral Instrument) from the Sentinel-2 and the OLI (Operational Land Imager) and TIRS (Thermal Infrared Sensor) sensors from the Landsat-8 were acquired nearly at the same time between the years 2018 and 2020 for sugar can crops. Images from OLI and TIR sensors were intended to calculate ET\({}_{\mathrm{F}}\)F through METRIC (target variable), while for the MSI sensor images, the explanatory variables were extracted in two approaches, using 10 m (approach 1) and 20 m (approach 2) spatial resolution. The results showed that the algorithms were able to identify patterns in the MSI sensor data to predict the ET\({}_{\mathrm{F}}\)F of the METRIC model. For approach 1, the best predictions were XgbLinear (R\({}^{2}\) = 0.80; RMSE = 0.15) and XgbTree (R\({}^{2}\) = 0.80; RMSE = 0.15). For approach 2, the algorithm that demonstrated superiority was the XgbLinear (R\({}^{2}\) = 0.91; RMSE = 0.10), respectively. Thus, it became evident that machine learning algorithms, when applied to the MSI sensor, were able to estimate the ET\({}_{\mathrm{F}}\)F in a simpler way than the one that involves energy balance with the thermal band used in the METRIC model. ir 2022 2022 2022 2022 20222 20222 20222 2022  
empirical relationships, fuzzy, genetic [3] and machine learning algorithms. Remote sensing can be included in the physical models because it uses the radiation reflected and emitted by the Earth's surface to estimate the properties of the Earth's surface when subjected to radiation interaction models. Vegetation cover biomass, and indexes for each image can also be spatially and temporally modeled [4; 5]. Several models for estimating evapotranspiration based on remote sensing were developed and have been widely used, especially in scientific research focused on the water planning field. Some examples are the Surface Energy Balance Algorithm for Land (SEBAL) [6], Mapping Evapotranspiration at High Resolution with Internalized Calibration (METRIC) [7], and Simple Algorithm for Evapotranspiration Retrieving (SAFER) [8]. However, these models estimate a fraction of the evapotranspiration, which corresponds to a coefficient that must be multiplied by the reference evapotranspiration to obtain the actual daily evapotranspiration. The METRIC model [7] estimates the evapotranspiration fraction (ET\({}_{\text{r}}\)F) through the instantaneous evapotranspiration (ET\({}_{\text{ints}}\)) and the reference potential evapotranspiration of the alfalfa (ET\({}_{\text{r}}\)) or grass (ET\({}_{\text{o}}\)) on a daily scale. This model is very complex, as it demands, a priori, the estimation of parameters for the energy balance calculations, which can be prone to errors since this model presents an interactive method of selecting \"hot\" and \"cold\" pixels to calculate aerodynamic resistance to heat transport and exchange derived from the SEBAL model [6]. The aforementioned models were developed using data from the Landsat satellite constellation sensors with dependence on visible, near, mid and thermal infrared wavelengths. Satellites from the Landsat series provide information about the Earth's surface with a temporal resolution of 16 days and a spatial resolution of 30 m. Temporal resolution limits the model's application, as it presents a limited number of images available by the sensors on these satellites. In contrast, the Sentinel-2 satellites constellation arises as an alternative to this limitation.