## 3 Results and Discussion
### Correlations among GPP and eWUE with NDVI  
NDVI is an easily accessible vegetation index that typically has significant correlations with GPP [23; 47; 91; 104]. In this study, we found a positive and linear relationship (R\({}^{2}\) = 0.48) between GPP and NDVI (Figure 7A). This correlation depends on several factors. For grassland, [PERSON] et al. [104] found an R\({}^{2}\) from 0.53 to 0.78 depending on the type and spatial distribution. [PERSON] et al. [105] reported an R\({}^{2}\) from 0.2 to 0.4 between NDVI obtained by MODIS and GPP depending on the phenological stage of a temperate deciduous forest. In this sense, NDVI has certain limitations in faithfully representing the evolution and performance of GPP. Environmental factors that cause short-term changes in GPP, such as those reported above, are not always captured by NDVI [104; 106]. In addition, NDVI time series are somewhat limited and must be filtered on days where clouds are present, which also interferes in that NDVI with GPP correlation [91]. Moreover, it is commonly known that NDVI lacks accuracy in areas with low vegetation while it saturates at a certain level of vegetation cover [107], such that the maximum GPP peaks are not always captured by NDVI [105]. Finally, it should also be considered that the GPP calculated by EC works on a different spatial scale than the NDVI obtained by satellite, while the processing of EC data by gap filling also introduces uncertainties that are not determined by NDVI [91].  
All of the above means that, although the NDVI can be an operational and easy-to-obtain index to monitor and estimate GPP, it requires additional data, mainly including environmental factors, to capture the variability in the evolution of the GPP, which is insufficient on its own. To address these environmental factors, we multiplied the average NDVI by the ET, finding an improved and notable correlation with GPP (R\({}^{2}\) = 0.78, Figure 7C). ET has been shown to be a good predictor of plant water use responses to environmental factors [42] and is effective for assessing seasonal GPP responses [82]. Plant evapotranspiration encompasses both plant transpiration and soil water evaporation. These factors are, furthermore, driven by plant physiological performance (plant water use and photosynthesis by stomata) and environmental changes (soil water availability and evaporative demands). Hence, the combination of NDVI, related to photosynthesis potential, with ET reflecting actual plant performance and short-term environmental responses, can improve the estimation of GPP.  
A weaker (R\({}^{2}\) = 0.39) albeit positive and linear correlation was also obtained between eWUE and NDVI. Since the ecosystem WUE is calculated as the ratio GPP/ET, its prediction is affected by the same limitations previously mentioned for GPP. Additionally, since eWUE is calculated as GPP/ET, the combined predictor NDVI \(\times\) ET as a factor to derive eWUE lacks dependability. Nevertheless, we explored this correlation, revealing a poor R\({}^{2}\) = 0.27. As mentioned, water use efficiency greatly depends on a number of environmental factors, especially those related to temperature and evaporative demand [47; 82]. Thus, to unravel eWUE responses, it is important to address other factors besides photosynthesis potential (i.e., NDVI) or consumptive water use/availability (i.e., ET). Hence, a model addressing several environmental factors was explored in this work, which is further discussed in the following sections.