## 3 Results
### Improved SIF-Based GPP Estimation by Considering the Influence of Temperature  
From Figure 8, we also see that the responses of photosynthesis and fluorescence to temperature were different during the overwintering period. In addition, from Figures S18 and S19, we also found that the sensitivities of SIF and GPP in response to temperature were different during the entire growing season. Therefore, GPP estimation based on SIF should consider the influence of temperature. In this study, we separately analyzed the correlation of GPP with the total red SIF (\(tSIF_{688}\)) and the total far-red SIF (\(tSIF_{760}\)) and explored the effects of temperature on the \(tSIF\)-GPP relationship during the entire growing season. We compared the relationships between the measured GPP by the EC technique (referred to as \(GPP_{flux}\) hereafter) and the predicted GPP based on \(tSIF\) with or without considering the effects of temperature (Table 1). Based on half-hourly data during the entire growing season, we can see that there was a good relationship between \(GPP_{flux}\) and \(GPP_{F688}\) (R\({}^{2}\) = 0.64, RMSE = 4.90 umol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)), whereas there was a relatively weaker relationship between \(GPP_{flux}\) and \(GPP_{F760}\) (R\({}^{2}\) = 0.42, RMSE = 6.22 umol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\); Figure 9a,c). The \(cSIF_{yield\_688}\) and \(\Phi_{F\_688}\) exhibited significantly positive correlations with \(T_{a}\) (r > 0.7, \(p\)-value \(<\) 0.05), while \(cSIF_{yield\_760}\) and \(\Phi_{F\_760}\) were weakly correlated with \(T_{a}\) (r < 0.3, \(p\)-value > 0.05; Figure 7). The \(tSIF_{688}\) explained large variations in GPP while \(tSIF_{760}\) could explain fewer variations in GPP. Because photosynthesis and fluorescence responded differently to temperature (Figure 8), we further explored the performance of GPP estimation based on \(tSIF\) by considering the influence of temperature using a temperature-corrected function. By using the empirical temperature-corrected equation, the GPP estimation based on \(tSIF_{760}\) was improved (the RMSE dropped from 6.22 to 5.51 umol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\), while R\({}^{2}\) values increased from 0.42 to 0.54; Figure 9d). Similar results can also be seen from the \(tSIF_{688}\)-GPP relationship by considering air temperature (the RMSE decreased from 4.90 to 4.58 umol CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\), while R\({}^{2}\) values increased from 0.64 to 0.69; Figure 9b). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temporal Resolution** & **Band** & **Regression Equation** & **R\({}^{2}\)** & **RMSE** \\ \hline \multirow{3}{*}{half-hourly} & 688 nm & \(GPP_{F688}=0.69\times tSIF_{688}\) & 0.64 & 4.90 \\  & \(GPP_{F688-T_{a}}=0.69\times f(T_{a})\times tSIF_{688}\) & 0.69 & 4.58 \\ \cline{2-5}  & 760 nm & \(GPP_{F760}=9.44\times tSIF_{760}\) & 0.42 & 6.22 \\  & \(GPP_{F760-T_{a}}=9.44\times tSIF_{760}\) & 0.54 & 5.51 \\ \hline \multirow{3}{*}{daily} & 688 nm & \(GPP_{F688}=0.72\times tSIF_{688}\) & 0.65 & 4.41 \\  & \(GPP_{F688-T_{a}}=0.72\times t(T_{a})\times tSI_{688}\) & 0.71 & 4.01 \\ \cline{1-1} \cline{2-5}  & 760 nm & \(GPP_{F760}=10.2\times tSIF_{760}\) & 0.47 & 5.43 \\ \cline{1-1}  & \(GPP_{F760-T_{a}}=10.2\times f(T_{a})\times tSIF_{760}\) & 0.61 & 4.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The \(tSIF\) -based GPP models with and without considering the effects of \(T_{a}\) based on half-hourly and daily mean data. The \(f(T_{a})\) is the temperature-corrected function. Based on daily mean data during the entire growing season, we can also find that there was a good relationship between \(GPP_{flux}\) and \(GPP_{F688}\) (R\({}^{2}\) = 0.645, RMSE = 4.41 umO CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)), but a relatively weaker relationship between \(GPP_{flux}\) and \(GPP_{F760}\) (R\({}^{2}\) = 0.47, RMSE = 5.43 umO CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\); Figure 10a,c).