## 5 Conclusions  
The multivariate analysis of the environmental variables and WUE in the MATOPIBA region showed that only four variables were suitable for analysis, namely, Elevation, LST, Rainfall, and WUE, with KMO and MSA values > 0.75, and 0.79, respectively. In the PCA, it was found that one PC was sufficient for the evaluation, as the PC1 corresponded to 65.77% of the explained variance. Elevation was the highest contribution in the PC1(25.95%) variable and influenced the other variables due to the altitude gradient existing in MATOPIBA. This behavior alters the carbon-water cycle of the vegetation and consequently affects the WUE.  
In the spatial aspect, positive (negative) scores were observed in regions of the states of Maranhao and Tocantins (west of the states of Bahia and Piaui). Negative scores were related to higher WUE values, prompted by the expansion of agricultural practices in the region. When associated with higher LST values, these practices increase the water demand in croplands existing in MATOPIBA. On the other hand, positive scores were related to greater water availability associated with areas of dense vegetation and ecoregions of the Cerrado biome existing in the MATOPIBA region, contributing to the increase in GPP and ET.  
The results obtained indicate that agricultural expansion in the MATOPIBA region is directly affected by changes in environmental factors (Elevation, LST, Rainfall, GPP, and ET). Such factors are directly linked to the way the vegetation, whether in natural or agricultural lands, behaves with the carbon-water cycle and its spatio-temporal distribution, which impacts the efficiency of water use in MATOPIBA.  
D.d.B.S.: Conceptualization; formal analysis; investigation; methodology; writing--original draft. H.A.B.: Writing--review and editing. W.L.F.C.F.: Writing--review and editing. J.F.d.O.-J.: Writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico-(CNPq/MCTI/FNDCT N\({}^{*}\) 18/2021), Brazil, through Universal--Programa de Monitoramento da Desertificacao por Snelite no Semiarido Brasileiro--under the grant/award number (403223/2021-0 to H.A.B).  
The ethical review is not applicable for this study due tonot involving of humans or animals.  
Not Applicable.  
We are thankful to MODIS ([[https://lpdaac.usgs.gov/products/](https://lpdaac.usgs.gov/products/)]([https://lpdaac.usgs.gov/products/](https://lpdaac.usgs.gov/products/)), accessed on 10 May 2022) for GPP (MOD17A2), ET (MOD16A2), and LST (MOD11A2) data. Elevation, roughness, and slope data referring to the MATOPIBA region were obtained from the EarthEnv website ([[https://www.earthenv.org/topography/](https://www.earthenv.org/topography/)]([https://www.earthenv.org/topography/](https://www.earthenv.org/topography/)), accessed on 11 May 2022). Land Use and Land Cover data were obtained from the MAPBIOMAS website ([[https://mapbiomas.org/](https://mapbiomas.org/)]([https://mapbiomas.org/](https://mapbiomas.org/)), accessed on 15 May 2022). The rainfall data is obtained from Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS) product ([[http://chg.geog.ucsb.edu/data/chirps/index.html](http://chg.geog.ucsb.edu/data/chirps/index.html)]([http://chg.geog.ucsb.edu/data/chirps/index.html](http://chg.geog.ucsb.edu/data/chirps/index.html)), accessed on 20 January 2019).  
The first author thanks the Coordination for the Improvement of Higher Education Personnel (CAPES) for granting the doctoral scholarship. The second author thanks CNPq for granting the Research Productivity Fellowship level 1-D (317633/2021-0). The fourth author thanks CNPq for granting the Research Productivity Fellowship level 2 (309681/2019-7).  
The authors declare no conflict of interest.