## 3 Results
### Improving the Estimation of GPP Using a Combination of SIF and CI  
To further analyze the relationships between both \(\text{SIF}_{760}\) and GPP and relevant environmental variables across the growing period, we applied linear correlation analysis to investigate the effect of CI, AT, and VPD on \(\text{SIF}_{760}\) and GPP at different time scales (Table 1). Compared to other environmental variables, it was found that CI had a more significant effect on the variations in GPP and \(\text{SIF}_{760}\) at different time scales in 2017 and 2018. Therefore, it may be that CI is the dominant environmental variable in terms of the variations in the \(\text{SIF}_{760}\)-GPP relationship. Furthermore, over the whole growing season, we found that GPP will saturate or increase more slowly when the CI is high (Figure 6). Maize \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Independent Variables**} & \multirow{2}{*}{**Explanatory Variables**} & \multicolumn{3}{c}{**Pearson’s Correlation Coefficient**} \\ \cline{3-5}  & & **2017** & \multicolumn{2}{c}{**2018**} \\  & & **30 min** & **Day** & **30 min** & **Day** \\ \hline CI & & 0.32 & 0.67 & 0.41 & 0.71 \\ VPD & GPP/\(\text{SIF}_{760}\) & 0.17 & 0.53 & 0.07 & 0.47 \\ AT & & 0.13 & 0.40 & 0.02 & 0.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlation between CI, AT, and VPD with the ratio of GPP to \(\text{SIF}_{760}\) over the whole growing season in the DM maize field in 2017 and 2018. Figure 6: Relationships between canopy GPP and SIF based on half-hourly (**a,c**) and daily (**b,d**) mean data observed over the whole growing season in the DM maize field in 2017 (**a,b**) and 2018 (**c,d**). The color scale represents the value of the clearness index (CI). Hyperbolic regression lines are shown in black and the coefficient of determination (R\({}^{2}\)) for each best-fitting line is given. canopy GPP exhibited a greater tendency to saturate under high levels of direct light but the saturation was less likely to occur when the amount of scattered light was extremely high. Therefore, it was decided that CI should be included in the SIF\({}_{760}\)-based GPP estimation model. Next, we investigated the influence of CI on the relationship between GPP and SIF\({}_{760}\) based on half-hourly and daily measurements of the training dataset made in the DM maize field. Figure 7 illustrates the variation in the ratio of canopy GPP to SIF\({}_{760}\) with changes in CI based on the training data. The ratio of GPP to SIF\({}_{760}\) exhibits an obvious decreasing trend as CI increases (Figure 7a,b). For the half-hourly data, the correlation between CI and the ratio of GPP to SIF\({}_{760}\) exhibits a weak relationship, with an R\({}^{2}\) value of 0.17 (Figure 7c). However, the relationship between the ratio of GPP to SIF\({}_{760}\) and CI shows a stronger correlation for the daily data, giving an R\({}^{2}\) value of 0.51 (Figure 7d). Overall, these results show that the ratio of GPP to SIF\({}_{760}\) decreases as CI increases, reflecting the differences in the response of GPP and SIF\({}_{760}\) to the weather conditions. From Figure 6, we found that under the same SIF value, when the CI value was small (indicated by a yellow circle), the corresponding GPP was large. Moreover, we can see from Figure 7 that the ratio of GPP to SIF\({}_{760}\) exhibits an obvious decreasing trend as CI increases, reflecting the difference in the response of GPP and SIF\({}_{760}\) to weather conditions. These results indicated that the CI was a key factor that affected the slope of GPP against SIF\({}_{760}\) and the influence of CI should be introduced in the SIF760-based GPP estimation model. Therefore, we added CI to the SIF\({}_{760}\)-based GPP estimation models (both linear and non-linear), which can be seen in the Equations (10) and (11).