## 4 Discussion
### Temporal Scaling Effect on the SIF-Based and LUE-Based Models  
There was no evidence of obvious nonlinearity or changes in the slope (\(\varepsilon/SIF_{\text{yield}}\)) direction of the SIF-based model across the mid-day to monthly timescales (Figure 3; Table 2), which is consistent with previous results [13; 37; 66]. [PERSON] et al. [13] points out that the responses of GPP to light at the ecosystem-scale display low saturation levels when considering the mid-day (half-hourly) data and become further linearized with increasing spatial or temporal aggregation. Similar results were demonstrated in [37], and the GPP-SIF relationship remained consistent from mid-day to monthly timescales for both the maize and landscape ecosystem (Table 5). The linear correlation between GPP and SIF tends to converge across different timescales and may primarily depend on the fact that SIF is only emitted from photosystems and is closely linked to the fraction of PAR absorbed by the chlorophyll in all leaves of the canopy (\(fPAR_{\text{chl}}\)) [38; 67]. [PERSON] et al. [38] derived an estimation of the \(fPAR_{\text{chl}}\), which defined by \(SIF/\cos(SZA)\) from 127 flux tower sites, and found that the light use efficiency (\(\varepsilon\)) showed a spatial-temporal convergence using chlorophyll-absorbed light (\(PAR_{\text{chl}}\)) to fix carbon dioxide. Moreover, both theoretical and experimental investigations have suggested that the two terms (\(\varepsilon\) and \(SIF_{\text{yield}}\)) in the SIF model covary and the ratio of one to the other tends to be constant under high light intensities [67; 68]. In this case, it is possible to conserve the GPP-SIF relationship across space and time. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Ecosystem** & **Time Scale** & **Slope** & **R\({}^{2}\)** & **CV of the Slope** \\ \hline This study & maize–wheat rotation & Mid-day & 26.31 (\(\pm\)3.89) & 0.67 & 6.1 \\  & & Daily & 29.70 (\(\pm\)2.70) & 0.83 & \\  & & monthly & 28.43 (\(\pm\)2.60) & 0.89 & \\ [PERSON] et al. [37] & Corn & Mid-day & 23.2 (\(\pm\)2.8) & 0.81 & 9.0 \\  & & Daily & 19.9 (\(\pm\)0.88) & 0.97 & \\  & & monthly & 23.5 (\(\pm\)1.15) & 0.98 & \\  & & Mid-day & 15.6 (\(\pm\)2.1) & 0.79 & 5.8 \\  & & Daily & 14.8 (\(\pm\)1.81) & 0.82 & \\  & & monthly & 13.9 (\(\pm\)1.3) & 0.92 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The slope, R\({}^{2}\), and the coefficients of variation (CV = standard deviations/mean \(\times\) 100%) of the linear GPP–SIF model in this study, from [PERSON] et al. [37]. By comparison, the values of the \(\epsilon_{\text{max}}\) in the SL-LUE model were similarly robust as \(\varepsilon/SIF_{yield}\) and considerably more stable than \(\varepsilon_{\text{msu}}\) and \(\varepsilon_{\text{msh}}\) in the TL-LUE for all temporal aggregation levels. As for the SL-LUE model, at the site scale, the photoresponse of an unstressed canopy is generally more linear for the variation in light absorption, along with canopy depth [69], and the slope of this photosynthesis-APAR relationship is the \(\varepsilon_{\text{max}}\). The \(\varepsilon_{\text{max}}\) value at the satellite overpass time (e.g., mid-day) is close to that of the daily average [70; 71], and the relative similarity between the mid-day and daily \(\varepsilon_{\text{max}}\) values also appears on the annual scale. As for the TL-LUE model, two possibilities exist for the large fluctuations of \(\varepsilon_{\text{msu}}\) and \(\varepsilon_{\text{msh}}\). First, the diffuse and direct radiation were partitioned using the exponential model with default parameters [72], which would result in uncertainty in the estimates of sunlit and shaded GPP. Additionally, it should be noted that any deviation of the parameter may also be related to biases in the GPP simulations [11]. The second possibility to consider is that no unique solution for \(\varepsilon_{\text{msu}}\) and \(\varepsilon_{\text{msh}}\) occurs at different spatial or temporal scales.