## 2 Materials and Methods
### SIF Retrial  
Chlorophyll fluorescence is the re-emission of solar radiation absorbed by leaf chlorophyll at longer wavelengths, and it has a distinct spectral shape with one peak at 685-690 nm (red fluorescence) that is mainly attributed to the fluorescence emission of photosystem II (PSII) and another at 730-740 nm (far-red fluorescence) that is attributed to both PSI and PSII [34]. The solar-induced fluorescence (SIF) adds a weak signal to the reflected solar radiation. Depending on the wavelength, the amount of SIF that is emitted by the canopy is approximately 8.7-21.9% and 2-5.2% of the total reflected light at 685 nm and 740 nm, respectively [25; 55; 56].  
The SIF signal is usually discriminated using the Fraunhofer lines in which irradiance is strongly reduced [57; 58]. Three Fraunhofer lines are generally used in the visible and near-infrared region: H\(\alpha\) line (centered at 656.4 nm) due to hydrogen absorption in the solar atmosphere, O\({}_{2}\)-A (centered at 760.4 nm) and O\({}_{2}\)-B (centered at 687 nm) due to telluric oxygen absorption in the atmosphere [59; 60; 61]. As PSI emits fluorescence only in the near-infrared part of the fluorescence spectrum and PSII emits over a wide spectrum and peaks in the red part, the two oxygen absorption lines that corresponded with the two fluorescence emission peaks can be used to obtain SIF signal emitted mainly by PSI and PSII, respectively [34]. Previous studies have demonstrated that red SIF is affected by the reabsorption of leaf chlorophyll and LAI variations, which causes a lower correlation between red SIF and GPP when compared with the far-red SIF [62; 36]. Thus, we mainly consider the far-red SIF in this study.  
Almost all SIF retrieval algorithms are based on the Fraunhofer line depth (FLD) principle that was originally proposed by [PERSON] [57] and [PERSON] [58]. The principle assumes that the reflectance signal and the SIF signal within and outside the dark line remain constant (see the review written by [PERSON] et al. [59]).  
In this study, we used the O\({}_{2}\)-A line to obtain the far-red SIF (SIF\({}_{760}\)) according to the modified FLD method proposed by [PERSON] et al. [63]. This approach, which is referred to as 3 FLD, assumes that the variations in the SIF and reflectance signals are linear. The signals at three bands, including one within the absorption valley and two outside the valley, are used to derive the SIF. The weights of the two outside channels are defined as  
\[w_{\text{left}}=\frac{\lambda_{\text{right}}-\lambda_{\text{in}}}{\lambda_{ \text{right}}-\lambda_{\text{left}}} \tag{1}\]  
and  
\[w_{\text{right}}=\frac{\lambda_{\text{in}}-\lambda_{\text{left}}}{\lambda_{ \text{right}}-\lambda_{\text{left}}} \tag{2}\]  
where \(\lambda_{\text{left}}\) and \(\lambda_{\text{right}}\) indicate the shorter and longer wavelengths adjacent to the absorption valley, respectively. The SIF can be generated using  
\[SIF=\frac{\Big{(}E_{\text{left}}w_{\text{left}}+E_{\text{right}}w_{\text{ right}}\Big{)}L_{\text{in}}-E_{\text{in}}\Big{(}L_{\text{left}}w_{\text{left}}+L_{ \text{right}}w_{\text{right}}\Big{)}}{\Big{(}E_{\text{left}}w_{\text{left}}+E _{\text{right}}w_{\text{right}}\Big{)}-E_{\text{in}}} \tag{3}\]  
where \(E\) and \(L\) represent the ground irradiance and the canopy radiance, respectively.  
Former studies have indicated that the 3 FLD algorithm can generate reliable SIF signals when used on datasets obtained using the aforementioned HR4000 (SR = 0.13 nm, SNR \(>\) 300) [64; 65]. Therefore, we considered the derived SIF to be suitable for our research.