# Evaluation of Water and Carbon Estimation Models in the Caatinga Biome Based on Remote Sensing
## 3 Results and Discussion
### ET Validation
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**DC**} \\ \hline \hline  & \multicolumn{3}{c}{**Average \(\pm\) SD**} & \\ \hline  & **Observed** & **Estimated** & **R\({}^{2}\)** & **MAE** & **MPE** & **RMSE** \\ \hline ET MOD16A2 & \multirow{2}{*}{\(2.16\pm 1.49\)} & \(1.91\pm 1.3\) & 0.67 & 0.73 & 1.19 & 0.87 \\ \cline{2-6} ET SEBAL & & \(2.61\pm 0.42\) & 0.30 & 2.01 & 3.67 & 2.19 \\ \hline GPP MOD17A2H & \multirow{2}{*}{\(8.58\pm 5.0\)} & \(3.68\pm 1.54\) & 0.76 & 4.04 & 0.50 & 4.9 \\ \cline{2-6} GPP Modeled & & \(6.69\pm 2.02\) & 0.28 & 3.19 & 0.28 & 4.84 \\ \hline  & \multicolumn{6}{c}{**SC**} \\ \hline  & \multicolumn{3}{c}{**Average \(\pm\) SD**} & \\ \hline  & **Observed** & **Estimated** & **R\({}^{2}\)** & **MAE** & **MPE** & **RMSE** \\ \hline ET MOD16A2 & \multirow{2}{*}{\(2.39\pm 1.12\)} & \(1.22\pm 0.67\) & 0.66 & 0.60 & 0.52 & 0.74 \\ \cline{2-6} ET SEBAL & & \(1.81\pm 0.51\) & 0.48 & 1.26 & 1.17 & 1.50 \\ \hline GPP MOD17A2H & \multirow{2}{*}{\(3.42\pm 1.64\)} & \(2.56\pm 1.25\) & 0.65 & 2.32 & 0.47 & 2.60 \\ \cline{2-6} GPP Modeled & & \(2.63\pm 1.96\) & 0.12 & 2.01 & 0.50 & 2.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical analyzes for ET (MOD16A2 and SEBAL), in mm-d\({}^{-1}\), and GPP (MOD17A2H and Modeled), in g-C-m\({}^{-2}\)-d\({}^{-1}\), for the year 2013 in the DC and SC areas. These results agree with those observed in [58], who found that the actual daily evapotranspiration (ET) values for the DC region ranged from 5.0 to 6.7 mm\(\cdot\)day\({}^{-1}\) decrease in the ET values when the native vegetation becomes sparser. In areas with open or semi-open savannah, ET values were between 4.0- and 5.0-mm\(\cdot\)day\({}^{-1}\), and observed values ranged from 3.0 to 4.0 mm\(\cdot\)day\({}^{-1}\). In Table 2, the mean values of the ET observed in DC were 2.2 mm\(\cdot\)day\({}^{-1}\) (ranging from 0.11 to 4.8 mm\(\cdot\)day\({}^{-1}\)), from 2.6 mm\(\cdot\)day\({}^{-1}\) for the ET SEBAL (ranging from 2.3 to 3.5 mm\(\cdot\)day\({}^{-1}\)) and 1.9 mm\(\cdot\)day\({}^{-1}\) for MOD16A2 ET (ranging from 0.4 to 5.8 mm\(\cdot\)day\({}^{-1}\)). For SC, the mean value was 2.4 mm\(\cdot\)day\({}^{-1}\) for the measured ET (ranging from 0.3 to 4.1 mm\(\cdot\)day\({}^{-1}\)), 1.8 mm\(\cdot\)day\({}^{-1}\) for the ET SEBAL (ranging from 1.6 to 3.6 mm\(\cdot\)day\({}^{-1}\)), and 1.2 mm\(\cdot\)day\({}^{-1}\) for the ET of MOD16A2 (ranging from 0.4 to 3.3 mm\(\cdot\)day\({}^{-1}\)). It is observed that, considering the average values, the results of MOD16A2 showed very good agreement with the field measurements. This evidence shows that our methodology is a reliable alternative and simple to perform for estimating ET in the Caatinga biome, both for the dry and rainy seasons, corroborating previous results [25]. The authors of [6], in a study carried out in the Caatinga area in the municipality of Petrolina using two Landsat 8 images, found maximum Eta values of 8.0 mm\(\cdot\)day\({}^{-1}\) using the SEBAL method (SEBAL manual). In the same study, the authors used, for comparison purposes, the Geographic Resources Analysis Support System (GRASS) Python surface energy balance algorithm for land (GP-SEBAL), a new Python-based methodology for applying fully automated versions of SEBAL to Landsat images, obtaining a maximum value of 7.6 mm\(\cdot\)day\({}^{-1}\). The results differ from this study; however, in addition to the specificities of each study area and the differences inherent to the sensors used, it is necessary to highlight that our study calculated the latent heat of vaporization based on the air temperature product from MODIS (MOD0_L2). In contrast, the study above used a constant value for this same variable.