## 1 Introduction  
The need for areas with agricultural potential in the world has been growing over the years due to population growth [1]. The Brazilian Cerrado has been essential in this search for agricultural areas and has undergone significant transformations over decades due to large-scale food production, whether for export or domestic supply [2, 3, 4]. Such transformations associated with human activities influence the climate, causing changes in land use and land cover (LULC) and, consequently, affecting the carbon (C) and water (H\({}_{2}\)O) cycles of the local vegetation [5]. [PERSON] et al. [4] showed a brief approach to influences in an exploratory way, spatially describing the behavior of vegetation associated with these changes and those influenced by some environmental variables that altered the WUE in MATOPIBA. However, it was not clear what the contribution rate of each environmental variable in the WUE changes, which will be described and detailed in this study by using multivariate analyses in order to identify the contributions in the C-H\({}_{2}\)O balance of the vegetation. One method for identifying the C-H\({}_{2}\)O balance of the vegetation is to analyze the water use efficiency (WUE), a method based on the relationship between the gross primary productivity (GPP) of the crop or vegetation and evapotranspiration (ET) [6; 7; 8]. Gross primary productivity represents the primary carbon inputs to the terrestrial system [9], and ET is a measure of water loss from the ecosystem [10]. Therefore, water-use efficiency provides fundamental information in assessing impacts related to climate change, irrigation deficiency, and the management of ecosystem productivity [11]. Previous studies have shown that internal and external factors affect WUE [12; 13]. For example, regarding internal factors, each species has singularities regarding stomatal conductance and photosynthetic rates, which influence the assimilation of C and the efficiency of using H\({}_{2}\)O and, thus, the C-H\({}_{2}\)O balance [14]. Furthermore, vegetation is one of the basic components of terrestrial ecosystems and is responsible for the equilibrium of the C-H\({}_{2}\)O balance [5; 15]. In turn, external factors are related to climatic variables such as air temperature, rainfall [16; 17], and elevation [13], due to the fact that the distribution of vegetation is determined by water availability and temperature [18; 19]. Changes in the vegetation directly cause changes in the ecosystem. Plants play an important role in greenhouse gas (GHG) absorption and contribute to climate stability [20]. The interaction between plants and their associated soil biota can lead to complex feedback, regulating plant community dynamics and ecosystem processes [21]. In areas where agricultural expansion occurs, land use for agricultural purposes on the vegetation and the environment includes reducing carbon storage and the degradation of natural habitats with a consequent loss of biodiversity [22; 23]. However, the most significant impact is probably the reduction in climate services provided by carbon storage in frontier soils, particularly in extensive high-latitude agricultural frontiers [24]. In Brazil, the new agricultural frontier is known as MATOPIBA. This region is located in the Cerrado biome and is favorable for the development of agriculture, especially for the production of grains [25]. Furthermore, the area within this delimitation is characterized by expanding an agricultural frontier equipped with high-productivity technologies [26]. The MATOPIBA was officially recognized as an agricultural frontier through Decree number 8447 of 6 May 2015, which deals with the Agricultural Development Plan for the region to promote and coordinate public policies aimed at sustainable economic development based on agricultural activities and livestock [27].