## 1 Introduction  
An accurate estimation of gross primary production (GPP) by terrestrial ecosystems is crucial to understanding the variability of the global carbon (C) cycle [1]. One of the most common ways to estimate GPP relies on the use of light use efficiency (LUE) models (Equation (1)). In the LUE framework [2], estimates of GPP are based on three variables: (i) the fraction of photosynthetically active radiation (fAPAR) absorbed by the vegetation; (ii) the actual light use efficiency of photosynthesis (LUE\({}_{\rm p}\)), i.e., the conversion efficiency of absorbed radiation to fixed carbon; and (iii) incident photosynthetically active radiation (PAR). \[\rm GPP\ =\ fAPAR\ \times PAR\ \times LUE_{\rm p} \tag{1}\]  
The development and retrieval methods in passive sensing of sun-induced chlorophyll fluorescence (SIF), i.e., the radiation emitted by plants upon sun exposure, opens new possibilities to estimate GPP using remotely sensed data [3; 4; 5]. In the last decade, several studies have shown that sun-induced fluorescence at 760 nm retrieved from top-of-canopy (TOC) measurements (F\({}_{760}\)) can track changes in APAR and LUE\({}_{\rm p}\), and therefore can be directly linked to GPP from leaves [6], ecosystem, [7; 8; 9; 10] to regional and global scale [3; 11; 12; 13]. Although the mechanistic link between GPP and F\({}_{760}\) is not completely understood, recent advances in the field have contributed to explain the process under various conditions [14; 15]. The reason F\({}_{760}\) and GPP correlate is that both processes start with the absorption of light by a chlorophyll molecule. Once the photon is captured by the antenna and reaches the reaction center of the photosystem II, the chlorophyll molecule can return to the ground state through photochemical quenching (PQ), through the non-photochemical quenching of the excited state (NPQ), as the photon is dissipated non-radiatively as heat [16], or it can be re-emitted as a photon of fluorescence [17]. Fluorescence emission cannot be physiologically regulated, and its quantum yield depends on the efficiency of PQ and NPQ [17]. The mechanisms regulating the partitioning of absorbed photosynthetically active radiation (APAR) into the different pathways is therefore fundamental to grasping the GPP-F\({}_{760}\) connection [18; 19]. F\({}_{760}\) is usually described with a similar approach to the [PERSON]'s LUE framework, as shown in Equation (2):  
\[\rm F_{760}\ =\ fAPAR\ \times PAR\ \times LUE_{f}\ \times Fesc \tag{2}\]  
where F\({}_{760}\) is equal to the product of fAPAR, PAR, the light use efficiency of fluorescence emission at 760 nm (LUE\({}_{\rm f}\)), and the escape probability of chlorophyll fluorescence at 760 nm (Fesc) [20]. Equations (1) and (2) can be combined into Equation (3), which shows that the only variables that control the relationship between GPP and F\({}_{760}\) are LUE\({}_{\rm p}\), LUE\({}_{\rm f}\) and Fesc:  
\[\rm GPP\ =\ \ F_{760}\times\frac{LUE_{\rm p}}{LUE_{f}\ \times\ Fesc} \tag{3}\]  
Multiple factors can influence the different terms in Equation (3), and eventually GPP-F\({}_{760}\) relationship [5; 8]. Among these, the ones that require more attention because they are not fully understood are: (i) leaf nutrient content, in particular nitrogen (N) and phosphorous (P); and (ii) canopy structural parameters such as leaf area index (LAI) and leaf angle distribution (LAD), which in grasslands are often related to the community structure of the canopy [8; 21]. Quantifying the effect ofnutrients and canopy structure on the partitioning of absorbed radiation and on \(\mathrm{LUE_{P}}\), \(\mathrm{LUE_{f}}\), and Fesc is the first step to shed light on GPP and \(\mathrm{F_{760}}\) changes under different nutrient availability. Canopy N concentration (hereafter N%, N mass per gram of leaves of the whole canopy) is often related to the nutritional condition where the plant grows.