## 3 Results
### Improvement of GPP Estimation Using a Combination of SIF and PRI for Corn and Soybean  
At half-hourly and daily timescales, the impact of PRI on the \(SIF_{t}\)-GPP relationship was evaluated for corn and soybean. The measured data was randomly divided into two parts: 70% of the measured data is utilized for modeling and the remaining 30% of the measured data is performed for validation. The multi-variable regression results are displayed in Table 3. After combining \(SIF_{t}\) and PRI, the slopes between GPP and \(SIF_{t}\) for corn (4.89-6.32) were also higher than those for soybean (0.95-2.87), and there is a good GPP estimation accuracy with higher R\({}^{2}\) values (0.78) and lower RMSE (6.60 \(\upmu\)mol CO\({}_{2}\cdot\)m\({}^{-2}\)s\({}^{-1}\)) at half-hourly timescales as well as with higher R\({}^{2}\) values (0.82-0.84) and lower RMSE (3.56-4.3 \(\upmu\)mol CO\({}_{2}\cdot\)m\({}^{-2}\)s\({}^{-1}\)) at daily timescales. These results suggest that fluorescence and PRI should be considered in the GPP estimation model. It is worthy to note that the slope of the \(SIF_{t}\)-GPP relationship differs between corn (a C4 crop) and soybean (a C3 crop), with a higher slope for corn than that for soybean. In comparison to the GPP estimation model based solely on \(SIF_{t}\), the GPP estimation model based on both \(SIF_{t}\) and PRI has a lower value of fitted coefficients between \(SIF_{t}\) and GPP (Tables 1 and 3). The remaining 30% of the data was used for validating the above equations. Figure 9 shows the relationships between true GPP obtained from EC measurements (\(GPP_{meas}\)) and the modeled GPP (\(GPP_{pre}\)). At half-hourly and daily timescales, the slopes of the regression lines for both corn and soybean were approximately equal to 1. There are higher R\({}^{2}\) values for corn (0.79-0.92) and soybean (0.75-0.80). Therefore, PRI can be used to improve the \(SIF_{t}\)-based GPP estimation. In addition, we investigate the effects of Gs on the GPP estimation. From Figure 10, we can see that the ratio of \(GPP_{meas}\) to \(GPP_{pre}\) correlated to Gs for corn (r = 0.25, \(p<0.01\)) and soybean (r = 0.13, \(p<0.05\)) at half-hourly timescales. The effects of soil water content (SWC) on the GPP estimation can be found in Figure S4. At daily timescales, the ratio of \(GPP_{meas}\) to \(GPP_{pre}\) was not correlated with Gs for corn (r = 0.14, \(p=0.52\)), while it was relatively significantly related to Gs for soybean (r = 0.45, \(p<0.05\)). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{3}{*}{**Crops**} & \multirow{3}{*}{**Timescales**} & \multirow{3}{*}{**Pearson’s Coefficient**} & \multicolumn{6}{c}{**Partial Correlation Coefficient**} \\ \cline{3-10}  & & & **Physiology** & & **Structure** & & **Environment** & \\ \cline{3-10}  & & & **(Gs)** & **(NIRv)** & **(NDVI)** & **(PAR)** & **(Ta)** & **(VPD)** & **(CWSD)** \\ \hline \multirow{3}{*}{Corn} & Half-hourly & 0.31 ** & 0.33 ** & 0.02 & 0.28 ** & 0.45 ** & 0.30 ** & 0.26 ** & 0.27 ** \\  & Daily & 0.45 ** & 0.51 ** & 0.23 * & 0.56 ** & 0.56 ** & 0.41 ** & 0.47 ** & 0.45 ** \\ \cline{1-1} \cline{2-10}  & Half-hourly & 0.33 ** & 0.31 ** & 0.13 ** & 0.06 * & 0.45 ** & 0.45 ** & 0.33 ** & 0.25 ** \\ \cline{1-1}  & Daily & 0.22 * & 0.19 * & 0.24 * & 0.02 & 0.45 ** & 0.34 ** & 0.18 & 0.23 * \\ \hline \end{tabular}  
* * is the significance level of 0.05 and *** represents the significance level of 0.01.  
\end{table} 
Table 2: Correlation coefficients for the links between PRI and the ratio of GPP to \(SIF_{t}\) for corn and soybean at half-hourly timescales. The control variables are included in parenthesis, and the Pearson and Partial correlation coefficients are provided.