## 5 Conclusions  
This study analyzed and explained the underlying mechanism responsible for the changes in gross primary productivity (GPP) and sun-induced fluorescence at 760 nm (F\({}_{760}\)), and their relationship, due to a nutrient fertilization with nitrogen (N), phosphorous (P), and the combination of the two nutrients (NP). The nitrogen additions (N and NP) had an effect mainly through changes in absorbed photosynthetically active radiation (APAR) and escape probability of fluorescence (Fescfw). Changes in APAR are directly related to changes in GPP and F\({}_{760}\) and are due to the combination of changes in canopy chlorophyll content and in species composition that modifies the canopy structure. Changes in Fescfw are mainly due to the changes in the abundance of erectophile vegetation with N addition. In the treatment with the addition of N, forbs (non-erectophile) increased while graminoids (erectophile) decreased, which ultimately led to changes in leaf angle distribution and modified the F\({}_{760}\) observed in particular in 2015. This has an effect on GPP-F\({}_{760}\) relationship both across treatments and from year to year. Phosphorous addition had a significant effect on the light use efficiency of fluorescence, in particular when combined with high nitrogen availability. This result points toward the need of better understanding the thus far neglected role of phosphorous on modulating sun-induced fluorescence. With a path analysis, we also revealed that N% not only affects F\({}_{760}\) indirectly through APAR and Fescfw, but also is tightly related with surface temperature (Ts). The negative relationship between N% and Ts is biophysically mediated by higher albedo observed after the fertilization, and only marginally physiological mediated by increase in transpiration. We also found a trade-off between F\({}_{760}\) and Ts (likely mediated by the non-photochemical quenching mechanisms), indicating the importance of measuring simultaneously these two quantities. We finally found that Ts is also the main predictor of the light use efficiency of photosynthesis, which is a fundamental parameter to improve the predictability of GPP. In conclusion, our results show that both nutrient availability and their indirect effect on biodiversity are fundamental drivers of sun-induced fluorescence, and its relationship with gross primary productivity. Our results also reveal the interlink among fluorescence, surface temperature and GPP, and support the importance of tandem missions such as the FLUorescence EXplorer (FLEX) and Sentinel-3, providing concomitant estimates of sun-induced fluorescence, vegetation related spectral indices, and land surface temperature. The following are available online at [[http://www.mdpi.com/2072-4292/11/21/2562/s1](http://www.mdpi.com/2072-4292/11/21/2562/s1)]([http://www.mdpi.com/2072-4292/11/21/2562/s1](http://www.mdpi.com/2072-4292/11/21/2562/s1)), Figure S1: Aerial photograph of the experimental site (SMANIE). Figure S2: Group differences among treatment of carbon isotopic signature (\(\delta^{13}\)C). Figure S3: The two transpiration estimates and the albedo\({}_{400-900}\) across treatments. Figure S4: Schematic of the radiometric and chamber footprint. Figure S5: Scatterplot of the two APAR estimations. Figure S6: Scatterplot of modeled vs. observed GPP and F\({}_{760}\). Figure S6: Relationship between F\({}_{760\text{leaf}}\) from forward runs of SCOPE, inverse runs and empirical estimates. Figure S7: Scatterplot of GPP-F\({}_{760}\) at leaf and canopy scales across treatments. Figure S8: Relative importance analysis of GPP, F\({}_{760\text{leaf,fw}}\), F\({}_{760\text{leaf,inv}}\), LUE\({}_{\text{P}}\), LUE\({}_{\text{f}}\), and Fesc\({}_{\text{fw}}\) with Ts -Ta instead of Ts. Figure S9: Set of equations that represent the model structure for the path analysis. Figure S10: Path analysis without the nitrogen treatment. Figure S11: Path analysis without the nitrogen and phosphorus treatment. Figure S12: Path analysis without the nitrogen treatment.