###### Abstract
Previous studies have suggested that SIF in the far-red band primarily responds to changes in canopy structure changes represented by the product of the photosynthetic active radiation (PAR) and the near-infrared reflectance (\(NIR_{p}P\)) rather than actual physiological changes in the fluorescence quantum yield for crop species [16]. In addition, some studies explored the dynamic changes between SIF and GPP in evergreen forests and found that SIF responded sensitively to PQ and NPQ [15; 17]. It should be emphasized that the important abilities of SIF to track GPP are attributed to the potential physiological link between \(LUE_{p}\) and \(\Phi_{F}\), which remains unclear, especially under environmental stresses [18]. To better underly the GPP-SIF relationship, it is necessary to investigate \(LUE_{p}\), \(\Phi_{F}\) and the canopy escape probability of SIF (\(f_{esc}\)) separately [19]. _GPP_ is generally calculated as the light use efficiency (\(LUE_{p}\)) multiplied by the absorbed photosynthetic active radiation (\(APAR\)) using a semiempirical LUE framework [20]:  
\[GPP=APAR\times LUE_{p} \tag{1}\]  
Similarly, canopy directional SIF (\(cSIF\)) can be expressed as the product of \(cSIF_{yield}\) and \(APAR\), which contains information on canopy escape efficiency (\(f_{esc}\)) and the photosystem fluorescence yield (\(\Phi_{F}\)):  
\[cSIF=APAR\times cSIF_{yield} \tag{2}\]  
\[cSIF_{yield}=\Phi_{F}\times f_{esc} \tag{3}\]  
In addition, photosynthesis has two photosystems, named PSI and PSII. Both PSI and PSII are engaged in the emission spectrum for fluorescence in chloroplasts, which covers a wavelength range of 640-850 nm (Figure 1). However, the spectral characteristics between SIF emitted from PSI and PSII differ at the photosystem level and canopy level [4]. The fluorescence spectrum shape emitted from PSII has two peaks, with the magnitude of the left peak at 685 nm (red band) being substantially larger than the right peak at 740 nm (far-red band), but the fluorescence spectrum released from PSI only has one peak at 740 nm [21; 22]. Due to the fact that the relative contribution of PSI fluorescence is generally modest and constant under changeable illumination, the fluorescence from PSI is frequently assumed to be stable, which is also the assumption of the SCOPE model (Soil Canopy Observation, Photochemistry and Energy fluxes) [23]. It should be noted that SCOPE is a 1D model and cannot accurately account for horizontal heterogeneity in the canopy. In addition, some studies have reported that the PSI activity is enhanced in overwintering plants [24]. Therefore, it is important to separate the portion of PSII and PSI in far-red SIF and red SIF to better understand the link mechanism between SIF and GPP under environmental stress conditions [25]. SIF emitted from PSII is susceptible to the PSII photochemistry, which is closely connected to carbon reactions [26]. Nevertheless, many studies only explored the physiological link between far-red SIF and GPP [27; 28; 29; 30]. [PERSON] et al. [27] explored the physiological mechanism of far-red SIF and its unique potential for physiological stress detection based on a high-temperature experiment in a soybean field. They found that far-red SIF yield at the photosystem level (\(\Phi_{F\_760}\)) outperformed far-red SIF yield at the leaf level (\(cSIF_{yield\_760}\)) and \(\Phi_{F\_760}\) sensitively responded to the physiological downregulation of soybean gross primary productivity under high temperatures. [PERSON] et al. [28] evaluated the performance of the satellite SIF for winter wheat in response to heat stress and found that the \(cSIF_{yield\_760}\) could provide a larger physiology-related stress response than \(APAR\) and vegetation indices. [PERSON] et al.