# Modeling Actual Evapotranspirationiration with MSI-Sentinel Images and Machine Learning Algorithms
###### Abstract
Formed by two satellites, Sentinel-2A and Sentinel-2B, with sensors with similar waveband characteristics, this constellation supplies images every 5 days, with spatial resolution fluctuating between 10, 20, and 60 m, hence, producing a larger number of images of the Earth's surface than the Landsat constellation. The sensor from the Sentinel-2 satellites constellation is the MultiSpectral Instrument (MSI). It acquires information from the Earth's surface in the visible, red edge, near, and mid-infrared wavelengths. However, it does not have a sensor in the thermal infrared portion of the spectrum. By considering the differences between the satellites mentioned above, the development of models with a prediction capacity of the crop's actual evapotranspiration (ET\({}_{\text{a}}\)) using the MSI sensor will be of great value for the scientific community and field professionals, enabling determining ET\({}_{\text{a}}\) with a better spatial and temporal resolution during crop cycles, and can even be integrated with sensors on other satellite platforms forming a multi-sensor suite, which, in the absence of information from one sensor, allows it to be complemented by the other, in concordance with the approach described by [PERSON] et al. [9]. Another important aspect is that, even though the MSI does not include the thermal infrared band, ET\({}_{\text{a}}\) can be estimated without the surface temperature information, which can reduce the introduction of additional errors as models involving thermal information have, in their structure, the complex energy balance to quantify the latent energy of the system. Furthermore, thermal bands have a coarser spatial resolution, so interpolation is often necessary to align pixel sizes with those of the other bands, such as Landsat 5.7 and 8. Alternatively, modeling evapotranspiration in the absence of data from the thermal band can generate unsatisfactory results due to the intrinsic relationship between vegetation canopy temperature derived from the thermal band with stomatal conductance [10; 11]. By aiming to develop models with higher prediction capacity and reliability, this work, through the application of machine learning (ML) algorithms, sought to model variables of interest. Such algorithms, based on artificial intelligence, have a robust structure that allows the identification of relationship patterns between the variables to be modeled and the so-called predictor variables (independent). According to [PERSON] et al. [12], ML is an interdisciplinary area based on computer science, statistics, mathematics, and optimization,among several other areas. Many ML algorithms, each with different characteristics, are used for prediction and classification, being, in recent years, applied in research focused on agricultural sciences and remote sensing to develop models with greater ability to represent phenomena [13; 14; 15; 16; 17]. In evapotranspiration prediction, these models used remote sensing data and climate data to estimate actual evapotranspiration [18; 19], as well as only climate data to estimate reference evapotranspiration [20; 21; 22; 23]. The various available studies applied the algorithms in predicting reference evapotranspiration or actual evapotranspiration using remote sensing with thermal data. Thus, this work sought to train machine learning algorithms to estimate the evapotranspiration fraction (ET\({}_{\mathrm{r}}F\)) used in the METRIC model from the data of the Sentinel-2 satellites constellation that does not use thermal data on the sugar cane crop used in this case study.