## 4 Discussion
### The SIF-GPP Relationship  
In our study, a significant correlation between SIF and GPP was observed, as in other studies [16; 19; 20; 22; 23]. We observed large variations in the coefficient of determination (\(r^{2}\)) of the linear regression between SIF and GPP, according to emission wavelength, time scale of observation, sky conditions, or phenological stage. The weakest relationship (\(r^{2}<0.1\)) was observed for SIF687, and the strongest (\(r^{2}>0.9\)) for SIF760. In the regression between SIF687 and GPP, the lowest values of \(r^{2}\) were obtained during the development phase. This supports the view that--unlike SIF760--SIF687 appears to be a poor indicator of crop development, and it is also not suitable to track GPP changes induced by an increase or decrease in photosynthetic biomass. In all cases, \(r^{2}\) values for SIF687 were lower than the corresponding value for SIF760. A low correlation between red SIF and GPP has also been found on maize in another study [23]. On leaves, a positive correlation was observed between fluorescence and carbon assimilation, which has been attributed to increased levels of non-photochemical quenching (NPQ) that dissipates excess energy at the photosystem II level [57]. As NPQ acts on PSII fluorescence, one may expect a better positive correlation between photosynthesis and red fluorescence--where PSII preferentially emits--than with far red fluorescence, which is enriched by a constant PSI fluorescence contribution. This is not the case in our data, which suggests that other mechanisms not linked to fluorescence quenchings control the relationship between SIF and GPP. The highest correlation with GPP was found for SIF760 during canopy structure changes (e.g., during development between DOYs 60-120 or senescence after DOY 150). These time periods are characterized by rapid changes in the amount of photosynthetic biomass and the fraction of APAR. SIF60--unlike SIF687 or reflectance indices like NDVI--has the capability to track these seasonal changes with a high dynamic range, which is supported by data from Figure 6. This parallel change between SIF760 and photosynthetic biomass (and hence between SIF760 and APAR) has been previously suggested by [PERSON] et al. [58], and was further supported by subsequent studies on pine [10], rice [22], and sorghum [9]. In this study, we found that the stationary fluorescence yield as estimated by active measurements at leaf level was not linked to LUE (Figure 10). We also found small variations of ASFY for a given state of the crop, which are much lower than LUE variations. On the other hand, the photochemical yield of PSII (\(\overline{\Phi}_{P}\)) and LUE appear to be strongly linearly correlated (\(r^{2}=0.63,p<0.001\)). Positive correlation between the SIF normalized by APAR (SIF\({}^{yield}\)) and LUE have been found in other studies [23; 29; 59], although no proportional relationship was evidenced. This contradicts theoretical claims that assume that under strong illumination, the ratio of LUE to fluorescence yield remains relatively constant [21; 60; 61]. In any case, the lack of a proportional relationship between SIF\({}^{yield}\) (i.e., ASFY/APAR or SIF/APAR) and LUE will induce a lowering of the \(r^{2}\) coefficient when large variations of LUE occur. In our study, we found a high sensitivity of SIF760 to chlorophyll-driven changes in GPP (Figure 6) and a low sensitivity of fluorescence yield (\(\overline{F}s\)) to changes in LUE (Figure 10). These results suggest that the strong empirical correlation found between FRSIF and GPP in this study and in other previous ones [16; 20; 22] is most likely driven by the close link between FRSIF and APAR rather than by the recognized link between fluorescence yield and photosynthetic efficiency. This indicates that FRSIF has limited capabilities to capture both chlorophyll content and quenching-induced changes in GPP, contrary to what is suggested in [20]. Multiple-variable strategies should be considered instead of a single-variable relationship.