## 4 Energy Balance
#### CO\({}_{2}\) Balance
The values of this peak were \(-8.14\) umol m\({}^{-2}\) s\({}^{-1}\) in 2009 and \(-4.09\) umol m\({}^{-2}\) s\({}^{-1}\) in 2012, showing a remarkable variability between the two years. This finding is consistent with the expected pattern of lower NEE variability at night and higher variability during the daytime. Figure 7 shows the mean monthly values of GPP and NEE in 2009 and 2012, respectively, evidencing the existence of distinct seasonal variability. The annual mean GPP varied from 7.52 umol m\({}^{-2}\) s\({}^{-1}\) in 2009 to 4.62 umol m\({}^{-2}\) s\({}^{-1}\) in 2012, showing an increase at the onset of the wet season, especially in April. The annual average NEE was \(-1.86\) umol m\({}^{-2}\) s\({}^{-1}\) in 2009 and \(-0.81\) umol m\({}^{-2}\) s\({}^{-1}\) in 2012. With the onset of the dry season in May, the GPP reduced in magnitude. In 2009, GPP values were higher compared to 2012. The monthly variation of GPP in the study area was influenced by the seasonality of rainfall. This behavior of GPP has been reported by [56], who explains that it is attributed to the response of Caatinga plants' phenological dynamics to the increased availability of water for leaf development. Thus, a more robust leaf area enhances the capacity for light absorption and the photosynthetic uptake of CO\({}_{2}\), leading to higher vegetation productivity, as previously shown by [66]. Figure 8 shows the relationships between the monthly values of the CO\({}_{2}\) balance components (GPP, NEE and NEP) and rainfall. According to [67], NEP is the net production of the ecosystem, which accounts for the net primary production minus carbon losses due to heterotrophic respiration. NEP is essentially the diurnal NEE, reflecting carbon uptake during the day. It is calculated from 08:00 h to 16:00 h, resulting in negative values. Figure 7: Monthly average of GPP (**A**) and NEE (**B**) simulated during the years 2009 and 2012. It is possible to observe that during the wettest year (2009), the saturation of GPP, NEE, and NEP occurred at approximately 300 mm of monthly rainfall, followed by a subsequent stabilization of the fitted curve. On the other hand, the fitted curve in 2012 was almost linear, without reaching saturation for GPP, NEE, or NEP due to the low rainfall rates. The variation in CO\({}_{2}\) flux was significantly adjusted with rainfall during the wet season (R\({}^{2}\) = 0.488) for GPP, NEE (R\({}^{2}\) = 0.761), and NEP (R\({}^{2}\) = 0.701). In extreme drought conditions, the coefficients of determination were also significant for GPP (R\({}^{2}\) = 0.750), NEE (R\({}^{2}\) = 0.912), and NEP (R\({}^{2}\) = 0.722). Therefore, rainfall has exerted a significant influence on the behavior of the CO\({}_{2}\) flux components. Figure 8: Regression analysis of simulated CO\({}_{2}\) flux components with monthly accumulated rainfall during the years 2009 (blue) and 2012 (red). Equations: (**A**) GPP 2009 = 6.102 + 0.025x \(-\) 4 \(\times\) 10\({}^{-5}\)x\({}^{2}\) R\({}^{2}\) = 0.488, GPP 2012 = 3.305 + 0.065 R\({}^{2}\) = 0.750, (**B**) NEE 2009 = \(-\)0.900 \(-\) 0.019x + 4 \(\times\) 10\({}^{-5}\)x\({}^{2}\) R\({}^{2}\) = 0.761, NEE 2012 = \(-\)0.264 \(-\) 0.033x R\({}^{2}\) = 0.912, (**C**) NEP 2009 = \(-\)3.545 \(-\) 0.038x + 8 \(\times\) 10\({}^{-5}\)x\({}^{2}\) R\({}^{2}\) = 0.701, NEP 2012 = \(-\)2.864 \(-\) 0.045x R\({}^{2}\) = 0.722.