## 4 Discussion
Such relationships have been mainly found when comparing instantaneous _PRI_-based indices with daily or midday light use efficiency [56; 72; 73; 74; 75], or when simultaneously observing similar canopies under contrasting stress levels [60; 76; 77]. However, estimation of instantaneous \(\varepsilon\) is complex and has been tackled using continuous multi-angular observations [78; 79]. Nonetheless, empirical and theoretical works question to what extent the facultative component of _PRI_ rather than structural, directional and pigment-pool effects can induce these relationships [76; 80; 81; 82]. In our case, none of the _PRI_ formulations added significant information about light use efficiency, whereas [PERSON] et al. [83] found that a _PRI_-based index was a good predictor of grass _GPP_ in the same ecosystem. The combination of grass and sparse trees could hamper any _PRI_-based modeling of \(\varepsilon\) in our case. Trees _PRI_ showed large variability which suggests that crown geometry and self-shadowing could operate as a strong confounding factor. Overall, results suggest that in a heterogeneous ecosystem as a TGE, _PRI_ snapshots might be rarely linked to instantaneous \(\varepsilon\), and that more advanced approaches should be used to account for structural and pigment-related effects of trees and grasses. MOD4 slightly raised \(R^{2}\) but also was the least efficient model. Large equifinality between \(f_{PAR}\) and \(\varepsilon_{\text{max}}\) led to senseless coefficients (not shown) and had to be constrained using prior knowledge of the _NDVI-LAI_ relationship. Some authors already reported the sensitivity of this parameter, and suggested modifying \(\varepsilon_{\text{max}}\) to improve _GPP_ prediction [84; 85]. Retrieved parameters are quite close to those estimated for MOD17A2 in Savanna ecosystems. Large confidence intervals found in _VPD_ and \(T_{\text{air}}\) limits could be explained by covariance of these variables [65]; in fact MODIS, _VPD_ limits were independently parameterized from the BIOME-BGC model [86]. In addition, [PERSON] et al. [85] used soil water content to stabilize solutions. Retrieved \(VPD_{\text{max}}\) doubled the MODIS value, which could mean that, in this site, photosynthesis does not stop under high _VPD_. This hypothesis should be handled carefully since the assumption of linear relationships between \(\varepsilon_{\text{stress}}\) and \(T_{\text{air}}\) and _VPD_ might be unrealistic, and others could be more suitable [87; 88]. Nonetheless, larger tolerance to VPD could be explained in this site by the fact that trees have access to deep water reservoirs. In fact, a significant reduction of leaf water content in these trees was only observed during an extremely dry summer [89]. Finally, despite including meteorological variables, MOD4 performance was comparable to other models. This suggests that \(\varepsilon\) and \(f_{PAR}\) should be separately modeled at least for the main vegetation types of the ecosystem (stress and grasses). In addition, other variables better describing their respective resources availability such as soil water content could improve modeling [85; 90] and contribute to separate the different physiologies. The authors recognize the limitations of the semi-empirical approaches and the relatively small dataset size (11 images). However, in the case of MOD4, the similarity to MODIS parameters suggests high robustness. The description of \(f_{\mathit{PAR}}\) provided by the different models might also result inadequate in TGE and structurally complex ecosystems. The SVI-based [4] or the Beer-Lambert law-based (Equation (11)) approaches might require that the assumption of homogeneity and random distribution of leaves helds [91]. However, dispersed trees add a geometric component to scattering [92; 93] that modifies radiation distribution over vegetation. In fact, \(\mathit{NDVI}\)-\(f_{\mathit{PAR}}\) relationships of different nature have been found in grass savannas [94; 95].