## 4 Discussion  
### Error Sources in Estimation of \(cSIF_{yield}\) and \(\Phi_{F}\)  
In this study, \(cSIF_{yield}\) and \(\Phi_{F}\) were calculated based on some assumptions. The \(fPAR\) was not measured directly and was generally estimated by spectral indices, such as WDRVI. Although WDRVI is a good proxy of \(fPAR\) for different soil backgrounds (Figures S1, S3 and S4), it should be noted that WDRVI cannot represent the impact of direct and diffuse radiation components on \(fPAR\). This will bring some uncertainties to the estimation of \(cSIF_{yield}\). It is very challenging to accurately retrieve \(\Phi_{F}\) using remote sensing approaches [40]. By investigating the radiative transfer process within the canopy, [PERSON] and [PERSON] [51] showed that \(f_{esc\_760}\) could be mostly explained by the canopy reflectance, canopy interception probability (\(i_{0}\)) and leaf albedo (\(\omega_{1}\)). [PERSON] et al. [54] used the near-infrared reflectance of vegetation (\(NIR_{v}\)) and the \(fPAR\) to estimate the \(f_{esc\_760}\), but this method is not applicable to the red band SIF. Using the random-forest regression method, [PERSON] et al. [41] introduced a practical approach (Random Forest, abbreviated as RF) to estimate the SIF escape probability and further explored a simple NDVI\({}^{2}\)-corrected method to compensate for the effects of the soil background [21]. It should also be noted that the \(Red_{v}\) is not strictly derived  
Figure 10: The relationships of GPP with \(tSIF_{688}\) (**a**), \(tSIF_{688}*f(T_{a})\) (**b**), \(tSIF_{60}\) (**c**), and \(tSIF_{60}*f(Ta)\) (**d**) based on daily mean data. The blue dotted line is the 1:1 line. The red line is the fitted line. because the mixing of vegetation and soil reflectance at the red band is much more complex than at the NIR band and is influenced by the brightness of the soil and the vegetation's structural and component parameters. [PERSON] et al. [51] found that the scattered portion of soil does not affect the relationship due to the fact that the scattering of the soil is indifferent to the emitted SIF or scattered incident. However, the part of the soil receiving solar or sky light directly can contribute to the observed reflected flux but not to the observed SIF because it does not produce SIF. The direct contribution of sunlit soil to TOC reflectance may affect the relationship and change with canopy coverage. Based on the SCOPE simulations (Figures S8 and S9), we can see that \(f_{esc,688}\) estimated by \(Red_{v}/fPAR\) agreed moderately well with that estimated by RF. However, the fact that the \(Red_{v}/fPAR\) approach shows a nonlinear, saturating relationship with \(f_{esc,688}\) suggests this approach could introduce misleading trends in \(f_{esc,688}\). These modeling results are yet to be validated with rigorous field measurements. From Figure 5, we can see that \(Red_{v}/fPAR\) and \(NIR_{v}/fPAR\) had the same temporal variations, except for April-June. This indicates that different study periods might have an influence on the SIF-GPP relationship (Figures 9 and 10). Therefore, this might indicate that the changes in pigment pool and canopy structure did have some potential influence on the estimation of \(f_{esc}\) and \(\Phi_{F}\) and cause some uncertainty regarding the results. Until now, the accurate estimation of \(\Phi_{F}\) has relied on the accurate estimation of \(f_{esc}\), while \(f_{esc}\) has largely been influenced by canopy structure, \(\omega_{L}\) and the soil background effects. Firstly, the canopy structure in winter wheat changes dramatically during the entire growing period. Due to the effects of low-temperature stress, the canopy structure in winter wheat can also change [31; 65]. There might be some uncertainties in the estimation of \(f_{esc}\) due to the fact that the soil background would be exposed for too much time during the overwintering period in winter wheat.