## 3 Results
### Validation of LUE-Based and SIF-Based Models  
The estimation performances of the LUE models and the linear SIF model were finally evaluated using the testing dataset from the year 2016 at the CN-YuC site. Maize photosynthesis started around mid-June with a rapid rise in GPP and ended in mid-October with GPP approaching zero, while wheat photosynthesis started around late February after the overwintering period and ended in mid-June. In general, GPPSL-LUE, GPPTL-LUE, and GPPSIF captured the seasonal variations and magnitude of tower GPP well, except for some underestimation for the growth stage of maize on the mid-day timescale (Figure 6a). By contrast, the SIF model and the TL-LUE model could better describe the trajectory of the whole growing period of summer maize and winter wheat, and especially better described the fluctuation details for the early (\"green-up\") and late (senescence) phases compared with SL-LUE (Figure 6a-c). As a result, the SIF model and TL-LUE model had higher values of R\({}^{2}\) and lower values of RMSE than the SL-LUE model across all temporal aggregation levels (Figure 6; Table 4), which is consistent with the fitted coefficient of determination using the training dataset in Table 2. The averaged changing trajectory of GPP explained by the SIF model and TL-LUE model was 77% and 83%, respectively. The averaged R\({}^{2}\) values were better than that of the SL-LUE model by 15.5% and 23.9%, and the corresponding average RRMSE values decreased by 2.9% and 2.9%, respectively (Table 4). Although the averaged biases of the SL-LUE model were lower than the biases of the SIF and TL-LUE models, its fluctuations in bias values were much greater. The small biases of the SL-LUE model might be due to bias items with opposite signs that cancel each other. Overall, the model performance in predicting GPP was ranked in three tiers as: TL-LUE > SIF model > SL-LUE. Moreover, the cross-validation and prediction results show that the SIF model and the TL-LUE model both have good stability and powerful prediction ability. These results indicate that the performance of the SIF models was comparable to the LUE models and actually better than the SL-LUE model, even though the SIF models were completely based on SIF and did not contain any ancillary data (e.g., temperature, radiation, VPD). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time Scales** & **Parameters** & **ECI < 0.8** & **ECI > 0.8** & **CV (\%)** \\ \hline \multirow{4}{*}{**mid-day**} & \(\varepsilon/SIF_{\text{yield}}\) & 23.09 (\(\pm\)4.67) & 29.28 (\(\pm\)7.6) & **16.7** \\  & \(\varepsilon_{\text{max}}\) & 1.89 (\(\pm\)0.57) & 3.30 (\(\pm\)0.74) & 38.4 \\  & \(\varepsilon_{\text{msu}}\) & 1.05 (\(\pm\)1.04) & 3.79 (\(\pm\)2.08) & 80.0 \\  & \(\varepsilon_{\text{msh}}\) & 7.75 (\(\pm\)3.46) & 1.23 (\(\pm\)10.60) & 102.8 \\ \hline \multirow{4}{*}{**daily**} & \(\varepsilon/SIF_{\text{yield}}\) & 28.18 (\(\pm\)2.99) & 30.56 (\(\pm\)3.92) & **5.7** \\  & \(\varepsilon_{\text{max}}\) & 2.11 (\(\pm\)0.34) & 2.48 (\(\pm\)0.30) & **11.5** \\  & \(\varepsilon_{\text{msu}}\) & 1.64 (\(\pm\)0.95) & 2.28 (\(\pm\)0.73) & **23.0** \\  & \(\varepsilon_{\text{msh}}\) & 5.70 (\(\pm\)3.22) & 4.63 (\(\pm\)2.91) & **14.7** \\ \hline \multirow{4}{*}{**monthly**} & \(\varepsilon/SIF_{\text{yield}}\) & 22.61 (\(\pm\)10.69) & 31.16 (\(\pm\)5.04) & **22.5** \\  & \(\varepsilon_{\text{max}}\) & 1.26 (\(\pm\)0.49) & 1.97 (\(\pm\)0.84) & 31.0 \\ \cline{1-1}  & \(\varepsilon_{\text{msu}}\) & 1.09 (\(\pm\)2.33) & 0.75 (\(\pm\)0.88) & 26.6 \\ \cline{1-1}  & \(\varepsilon_{\text{msh}}\) & 5.11 (\(\pm\)10.68) & 9.39 (\(\pm\)4.20) & 41.8 \\ \hline \hline \end{tabular}
\end{table}