# Modeling Actual Evapotranspirationiration with MSI-Sentinel Images and Machine Learning Algorithms
## 2 Materials and Methods
### Landsat-8 and Sentinel-2 Data  
The data from the sensors onboard the Landsat-8 and Sentinel-2 satellites were acquired to generate the observed variable through the METRIC model, and the explanatory variables used for training and testing the machine learning algorithms can be seen in a simplified way in the flowchart in Figure 3.  
Figure 3: Acquisition of data from sensors onboard Landsat-8 and Sentinel-2 for training and testing in machine learning algorithms.  
Figure 2: Climatological normal of the study region extracted from station 83,386 of INMET (Instituto Nacional de Meteorologia).  
A total of 56 satellite images were acquired, of which 22 were from OLI (Operational Land Imager) sensor and TIRS (Thermal Infrared Sensor) from the Landsat-8 satellite, and 34 came from the MSI (Multispectral Instrument) sensor of the Sentinel-2A and 2B satellites. Images from OLI and TIRS sensors were necessary to estimate the evapotranspiration fraction (ET\({}_{\mathrm{r}}\)_F_) using the METRIC model, this being the response variable, whereas data from the MSI sensor were used as predictor variables in the machine learning models. The spectral and spatial characteristics of the sensors used are available in Tables 1 and 2.  
Images were obtained between the years 2018 and 2020. During this period, eight images from the Landsat-8 satellite and eight from the MSI sensor covered the study area on the same day. Images of those dates were used to train and test the models and the application of residual analysis. The choice for images with coinciding dates between the two satellites was made to avoid different reflectance of the same study area since vegetation, especially crops, change quickly. Thus, obtaining images on different days to perform the modeling could have introduced bias and not a faithful representation of the modeled product. In Table 3, images with date, time (GMT-3), and path/row used to train the models are available.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Spectral Band** & **Wavelength (\(\upmu\)m)** & **Spatial Resolution (m)** \\ \hline  & OLI & & \\ \hline B1 & Coastal aerosol (Ca) & 0.43–0.45 & \\ B2 & Blue (B) & 0.45–0.51 & \\ B3 & Green (G) & 0.53–0.59 & \\ B4 & Red (R) & 0.64–0.67 & \\ B5 & Near-infrared (NIR) & 0.85–0.88 & 30 \\ B6 & Shortwave infrared 1 (SWIR1) & 1.57–1.65 & \\ B7 & Shortwave infrared 2 (SWIR2) & 2.11–2.29 & \\ B8 & Panchromatic (PCh) & 0.50–0.68 & \\ B9 & Cirrus (C) & 1.36–1.38 & \\ \hline  & & & \\ \hline  & & & \\ \hline B10 & Thermal infrared 1 (TIRS1) & 10.60–11.19 & \\ B11 & Thermal infrared 2 (TIRS2) & 11.50–12.51 & 100 * \\ \hline \hline \end{tabular}  
* The sensor’s resolution is 100 m, but images are resampled and made available in 30 m.  
\end{table}
Table 1: Spectral and spatial characteristics of the OLI and TIRS sensor.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Spectral Band** & **Wavelength (\(\upmu\)m)** & **Spatial Resolution (m)** \\ \hline  & & MSI & \\ \hline B2 & Blue (B) & 0.459–0.525 & \\ B3 & Green (G) & 0.542–0.578 & \\ B4 & Red (R) & 0.650–0.680 & 10 \\ B8 & Near-infrared (NIR) & 0.781–0.887 & \\ \hline B5 & red edge 1 (Re1) & 0.697–0.712 & \\ B6 & red edge 2 (Re2) & 0.733–0.748 & \\ B7 & red edge 3 (Re2) & 0.773–0.793 & \\ B8A & Near-infrared narrow (NIRn) & 0.856–0.876 & 20 \\ B11 & Shortwave infrared 1 (SWIR1) & 1.569–1.660 & \\ B12 & Shortwave infrared 2 (SWIR2) & 2.115–2.290 & \\ \hline B1 & Coastal aerosol & 0.433–0.453 & \\ B9 & Water vapor & 0.935–0.955 & 60 \\ B10 & Cirrus & 1.359–1.390 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Spectral and spatial characteristics of the MSI sensor.  
From 11/23/2019 to 09/04/2020, 17 images were obtained from OLI and TIRS sensors (including 4 images in Table 3) and 30 from MSI sensors (including 4 images in Table 3). Those images were used to determine crop coefficient (K\({}_{\rm c}\)) and actual evapotranspiration (ET\({}_{\rm a}\)) during the sugar cane cycle. The estimation was performed by both the METRIC model and the suggested model.