## 3 Results  
### Principal Component Analysis  
The results obtained correspond to the correlation analysis via PCA, which is initially run with eight variables. Only four variables presented KMO values \(>\) 0.7 and were suitable: Elevation, LST, Rainfall, and WUE (medium adequacy, 0.7 \(<\) KMO \(<\) 0.8). The variable WUE (0.8 \(<\) KMO \(<\) 0.9) was classified as good, followed by Elevation, LST, and Rainfall classified as medium (0.7 \(<\) KMO \(<\) 0.8), as shown in Table 1.  
The overall MSA value was 0.79, with a similar classification relative to the KMO test. According to [PERSON]'s criterion (\(\lambda>\) 1), one single component (PC1) explained a good part of the total variance of the relational pattern between the variables and WUE [52; 54]. Table 1 and Figure 2 show the correlation analysis and the percentage of contribution of each variable relative to each PC, indicating a positive correlation (\(\geq\)0.78) between the variables and the WUE of the MATOPIBA region. In addition, the PC1 indicated that the four variables--Elevation, LST, Rainfall, and WUE--explained 65.77% of the total variance. Regarding the degree of contribution of the variables to the PC1, there was a slight difference (\(<\)4%) between the variables with the highest and lowest percentage; the contributions were distributed as follows: Elevation (25.95%), LST (25.64%), Rainfall (25.55%), and WUE (22.86%).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **KMO** & **Correlation PC1** & **Contribution PC1 (\%)** \\ \hline Elevation & 0.79 & 0.82 & 25.95 \\ LST & 0.79 & 0.83 & 25.64 \\ Rainfall & 0.79 & 0.78 & 25.55 \\ WUE & 0.81 & \(-\)0.82 & 22.86 \\ \hline Variance Explained (\%) & - & - & 65.77 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Correlation analysis (CA) and contribution (%) of the variables analyzed for the PC1 and KMO and MSA test results. The results of the KMO and MSA tests vary from 0.50 to 1. The results of the CA vary from \(-\)1 to 1. The explained variance and percentage of contribution vary from 0 to 100.  
Figure 3 shows the factor loadings related to PC1, indicating a different behavior with positive/negative patterns. Negative scores were observed in the western portion of the states of Bahia and Piaui, possibly resulting from agricultural practices in these regions [55; 56]. Proper management in agriculture, necessary for enhancing the development of crops, leads to greater WUE and water demand [57; 58]. In addition, the portions where negative scores were observed were coincidently located in areas with higher elevations, higher LST values, and lower rainfall rates, which corroborates the results of [PERSON] et al. [4].  
Figure 3: Spatial behavior of the Factor Loadings corresponding to the first PC.  
Figure 2: Biplot showing the degree of contribution of the stations (individual) and years (variables), from the first two main components.  
Positive scores were observed in the south of the state of Maranhao and over a large part of the state of Tocantins, possibly related to the variables Rainfall, GPP, and ET, since these areas have a dense vegetation cover (forests in the northern portion of the Maranhao) and watercourses of the main rivers existing in the Brazilian Cerrado. For example, [PERSON] et al. [3] evaluated the behavior of precipitation in the Brazilian Cerrado and identified the highest rainfall rates (>1500 mm\(\cdot\)year\({}^{-1}\)) in the northern part of Maranhao.