## 3 Results
### GPP Models Performance  
Table 4 shows the median model coefficients and the corresponding 95% confidence intervals estimated by Bootstrap. In models MOD1-MOD3, coefficient \(\text{a}_{1}\) is almost always positive, suggesting a direct relationship between \(NDVI\) and \(f_{\text{PAR}}\). However, in MOD3-\(PRI_{515}\) the coefficient is negative and the confidence interval overlaps negative values suggesting a slope close to 0. In MOD3, the median value of coefficient \(\text{a}_{3}\) is always positive, suggesting a positive relationship with \(\varepsilon\). However, confidence intervals overlap 0 in all the cases. For MOD4 inversion, a linear model predicting \(LAI\) from \(NDVI\) was fit (\(r^{2}=0.72\), \(RMSE=0.28\) m\({}^{2}\)/m\({}^{2}\)); prior estimates of \(a_{6}\) and \(a_{7}\) coefficients were (\(2.826\), \(-0.430\)) with respective uncertainties (\(0.544\), \(0.359\)). Estimated coefficients were close to the priors with narrow confidence intervals. The remaining coefficients in MOD4 can be compared to values used by MODIS \(GPP\) algorithm for Savannas (2007). Estimated coefficient \(a_{1}\) (representing \(\varepsilon_{\text{max}}\)) median is \(1.644\) gC/MJ similar to the MODIS \(\varepsilon_{\text{max}}\) (\(1.206\) gC/MJ). Coefficients \(a_{2}\) and \(a_{3}\) represent \(VPD_{\text{max}}\) and \(VPD_{\text{min}}\) respectively, the first is larger than the value used in MODIS (\(31.0\) hPa) and the second is lower than the MODIS parameter (\(6.5\) hPa). Coefficients \(\text{a}_{4}\) and \(\text{a}_{5}\) representing \(T_{\text{MINmin}}\) and \(T_{\text{MINmax}}\) respectively are quite close to MODIS parameters (\(-8\)\({}^{\circ}\)C and \(11.39\)\({}^{\circ}\)C, respectively). In addition, \(VPD_{\text{max}}\) and \(T_{\text{MINmax}}\) present wide confidence intervals. Table 5 shows the statistics \(R^{2}\), \(RRMSE\) and \(AIC\) for the different model fits using the \"vegetation\" and \"all\" covers from the \"Flight\" dataset. Footprint and pixel-based approaches are compared for synthetic pixels of different size. Model fits using footprint climatology and \"vegetation\" pixels (\(S_{\text{fp,veg}}\)) show similar performances in terms of \(R^{2}\) and \(RRMSE\). MOD1 achieves the lowest \(R^{2}\) (\(0.65\)) and \(RRMSE\) (\(35.89\%\)), but also the largest efficiency. MOD2-MOD3 present similar errors and fits (\(R^{2}\in(0.67\)-\(0.68)\); \(RRMSE\in(36.71\)-\(37.66)\)), and thus the most efficient model is the simplest one (MOD2). MOD3-\(PRI_{515}\) achieves best performance in all the statistics. MOD4 presents the largest \(R^{2}\) (\(0.72\)) and an intermediate \(RRMSE\) (\(37.19\%\)), as well as the lowest efficiency. The combination of footprint climatology without discrimination of non-vegetated pixels (subindex \"all\") (\(S_{\text{fp,all}}\)) reduces the performance of all models, where MOD3-\(PRI_{515}\) and MOD4 are the least sensible. In the table, the statistics of model fits using all the pixels within synthetic squared pixels centered on each tower of different sizes--\(S_{\text{P250,all}}\), \(S_{\text{P500,all}}\), \(S_{\text{P1000,all}}\)--present similar performances than \(S_{\text{fp,all}}\). In most cases \(R^{2}\) increases; \(RRMSE\) either increases or decreases and in all cases \(AIC\) increases. Figure 5a-h shows \(R^{2}\) and \(RRMSE\) of the different models using the \(S_{\text{fp,veg}}\) dataset. In each subplot, the statistics of the \"Flight\" and \"Daily\" models are compared. For simplicity, only results of