# Modeling Actual Evapotranspirationiration with MSI-Sentinel Images and Machine Learning Algorithms
## 3 Results
### Models
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{N}^{\circ}\) & **Approach 1** & **Approach 2** \\ \hline
1 & B2 & B6 \\
2 & B4 & B8 \\
3 & B8 & B12 \\
4 & (B2 \(-\) B3)/(B2 + B3) & (B2 \(-\) B3)/(B2 + B3) \\
5 & (B2 \(-\) B4)/(B2 + B4) & (B2 \(-\) B4)/(B2 + B4) \\
6 & - & (B2 \(-\) B5)/(B2 + B5) \\
7 & - & (B2 \(-\) B12)/(B2 + B12) \\
8 & - & (B5 \(-\) B11)/(B5 + B11) \\
9 & - & (B5 \(-\) B12)/(B5 + B12) \\
10 & - & (B6 \(-\) B8)/(B6 + B8) \\
11 & - & (B8 \(-\) B12)/(B8 + B12) \\
12 & - & (B11 \(-\) B12)/(B11 + B12) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Selected predictor variables for training models in approaches 1 and 2. Among the four models chosen for this approach, XgbLinear and XgbTree obtained the best statistical results, with R\({}^{2}\) = 0.80 and RMSE = 0.15; followed by the Cubist with R\({}^{2}\) = 0.77 and RMSE = 0.15; lastly, and with the worst result, the multiple linear regression (Lm) with the minimum R\({}^{2}\) = 0.73 and the major RMSE = 0.17. Regardless of the model, the high dispersion shown on the test draws attention, especially in values lower than 0.6 (Figure 6). [PERSON] et al. (2019), when estimating evapotranspiration using machine learning in Landsat-8 data and MODIS for a heterogeneous environment, noted that in areas with crops, there was a higher dispersion between predicted vs. observed values than in areas with forest, grazing, and bushes. Thus, results from these authors agree with the ones found here, as, in crop areas, there is a higher surface movement, being more dynamic both in terms of vegetation cover and in terms of soil moisture. Figure 7 shows the statistical results of the test for approach 2, which used only a 20 m spatial resolution as a source of predictor variables. Figure 6: Statistical results of the test of approach 1. It is observed in Figure 7 that \(\mathrm{Lm}\), as well as in approach 1, obtained the worst result, while Cubist, XgbLinear, and XgbTree were the ones that best explained the response variable, with lower RMSE (0.10) and higher \(\mathrm{R}^{2}\). \(\mathrm{R}^{2}\), as in approach 1, had different values among these last three models, being 0.91 for XgbLinear and 0.90 for Cubist and XgbTree. When comparing Figures 6 and 7, approach 2 obtained more satisfying results than approach 1, with models with  
Notably, Figure 8 maintains the same pattern found in Figures 6 and 7, in which approach 1 presented a result inferior to approach 2 due to the minor concentration of residual points close to the zero value. For Approach 2, a good performance was observed, as less than 10.3% of the values distanced from \(-0.2\) to \(0.2\), which indicates a low prediction error, mainly XbgLinear. In both approaches, the explanatory variable tends to be less precise when ET\({}_{r}F\) is low, especially for values under 0.6, as previously discussed; this is better shown in Figure 9.  
Figure 8: Residual analysis of the estimated ET\({}_{r}F\) through machine learning models. Figure 9 shows the lower precision during the prediction of values lower than 0.6 in greater detail, with particular reference to pivot 9. On this pivot, when METRIC showed values close to 0.6, approaches 1 and 2 obtained predicted values close to zero, which can be seen in Figure 8 with the residual analysis. Nevertheless, Figure 9 also reveals the great assertiveness of the models, which can be seen especially in pivots 7 and 10, where prediction models were able to capture a wealth of details regarding METRIC estimates. On pivot 10, the southeast region shows low ET\({}_{r}F\) values through METRIC and machine learning models. However, for that pivot, this result was more prominent when using Sentinel-2 images, as they showed greater spatial resolution. Additionally, the thermal band on Landsat-8, which has a coarser resolution (100 m), can mask nuances of the surface of the monitored area.