## 4 Discussion  
### Uncertainties in the GPP Estimates Made with SIF and PRI  
In this study, we determined the performance of GPP estimation by using only SIF or using both SIF and the PRI. Compared to \(\text{SIF}_{\text{TOC}}\), \(\text{SIF}_{\text{TOT\_FULL\_PSII}}\) could quantify canopy photosynthesis more accurately for both the half-hourly and daily data (Figure 4). This indicates that broadband photosystem-level PSII Sir can better track the dynamics of GPP. In addition, GPP was estimated better using both SIF and the PRI than when using only SIF (Figure 4). These results agree with the previous studies based on leaf and satellite observations [27; 51]. This study used the PRI as an indicator of NPQ to track dynamic changes, as per previous studies, especially at short timescales [47]. Although this study assessed the role of the PRI in SIF-based GPP estimation, the PRI is a good proxy for NPQ. Regulated NPQ is affected by the xanthophyll cycle, which can be detected by a canopy reflectance of 531 nm at short timescales [33; 52]. However, the seasonal variations in the PRI were largely influenced by changes in the pigment pools (e.g., chlorophyll content), and the reliability of using the PRI to indicate NPQ needs to be further investigated. [PERSON] et al. [12] reported \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Crops** & **Timescale** & \multicolumn{2}{c}{**Linear Model**} & **RMSE** & \(\mathbf{p}\) \\ \hline \multirow{4}{*}{Soybean} & \multirow{2}{*}{Half-hourly} & \(\text{GPP}_{\text{TOT\_APRI}}=12.81\times\text{SIF}_{\text{TOT\_FULL\_PSII}}+238. 93\times\Delta\text{PRI}+10.75\) & 0.64 & 8.28 & \textless{}0.01 \\  & & \(\text{GPP}_{\text{TOT\_APRI}}=9(\text{CI})\times\text{GPP}_{\text{TOT\_APRI}}\) & 0.71 & 7.42 & \textless{}0.01 \\  & & \(\text{g}(\text{CI})=-4.74\,\ast\,\text{CI}^{2}+3.87\,\ast\,\text{CI}+0.45\) & & & \\ \cline{2-6}  & \multirow{2}{*}{Daily} & \(\text{GPP}_{\text{TOT\_APRI}}=14.08\times\text{SIF}_{\text{TOT\_FULL\_PSII}}+191.80 \times\Delta\text{PRI}+9.33\) & 0.71 & 6.69 & \textless{}0.01 \\  & & \(\text{GPP}_{\text{TOT\_APRI}}=9(\text{CI})\times\text{GPP}_{\text{TOT\_APRI}}\) & 0.81 & 5.34 & \textless{}0.01 \\  & & \(\text{g}(\text{CI})=-4.01\,\ast\,\text{CI}^{2}+2.83\,\ast\,\text{CI}+0.71\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The multi-variable linear GPP models based on the training dataset when considering the influences of CI or not. The impact of CI on the GPP models is represented by the function g(CI). Figure 8: Validation of the GPP estimates using the half-hourly observations (**a**) and daily data (**b**). \(\text{GPP}_{\text{EC}}\) represents the GPP measured by the EC technique. \(\text{GPP}_{\text{TOT\_APRI\_CI}}\) represents the GPP predicted by \(\text{SIF}_{\text{TOT\_FULL\_PSII}}\) and \(\Delta\text{PRI}\), considering the CI. The CI value is represented by the color scale. The best-fit line is shown by the solid red line, while the short, dashed, black line is the 1:1 line. that plant adaptation to winter not only corresponds to changes in the xanthophyll cycle but also to a variation in a variety of carotenoids (e.g., lutein and beta-carotene), which may play a photoprotective role for plants in response to low temperatures. In addition, canopy reflectance was influenced by the solar viewing geometry, the canopy structure, and the soil background, which further affected the calculation of the PRI and the linkage of PRI to NPQ. Due to this, the change in heat dissipation (NPQ) can be described using the PRI; therefore, it is reasonable to combine the information from PRI and SIF to enhance GPP estimation. Numerous studies have shown that improvement in GPP estimation for various ecosystems can be achieved by combining SIF and the PRI [27; 30; 31; 47]. Several studies have employed PRI measurements to monitor the diurnal variations in photosynthesis [28; 30; 34]. However, due to chlorophyll and carotenoid absorption, it is challenging to measure photosynthesis using the PRI across a season [53; 54].