## 3 Results
### Improving the Estimation of GPP Using a Combination of SIF and CI
The relationship between the measured GPP (true values of GPP measured by the EC technique, referred to as \(GPP_{meas}\) hereafter) and the predicted GPP based on SIF was used to establish a relationship with CI for both linear and non-linear SIF-based GPP estimation models. The ratio of \(GPP_{meas}\) to the predicted GPP (\(GPP_{L}\) or \(GPP_{NL}\)) represents the difference between the real GPP and GPP predicted by SIF for a linear or non-linear model. We found that this difference is related to CI for the linear SIF-based GPP estimation model and the \(GPP_{meas}\)/\(GPP_{L}\) had a strong relationship with CI, as we can see in Figure 7, and we used this ratio to fit the relationship with CI and integrated it into the SIF\({}_{760}\)-based  
Figure 7: Dependence of canopy GPP/SIF\({}_{760}\) on the clearness index (CI) averaged at 0.1 intervals (**a**,**b**) in the DM maize field for the training dataset. Half-hourly data with CI \(<\) 0.3 and daily data with CI \(<\) 0.2 were excluded from the analysis. The linear correlations between CI and GPP/SIF\({}_{760}\) are based on the half-hourly mean data (**c**) and daily mean data (**d**), respectively. Error bars indicate \(\pm SD\) from the mean. GPP model to improve the estimation accuracy of GPP. By comparing the results of the linear model with and without CI, it was shown that CI is indeed an important factor that affects the slope of GPP against \(\text{SIF}_{760}\) (Table 2). In addition, compared to the linear model, we found the \(GPP_{meas}/GPP_{NL}\) was not so strongly correlated with CI (Figure 8) for the non-linear \(\text{SIF}_{760}\)-based GPP estimation model. Meanwhile, \(GPP_{NL}\) was better related to \(GPP_{meas}\) than \(\text{GPP}_{\text{PL}}\), which we can see in Table 2 & Figure 9a,c. These results indicated that the non-linear \(\text{SIF}_{760}\)-based GPP estimation model may partially correct the influence of CI on the \(\text{SIF}_{760}\)-GPP relationship. As described in Figure 8, the correlation of \(GPP_{meas}/GPP_{NL}\) and CI was relatively weak. However, the non-linear model could not fully correct the impact of CI, as the accuracy of GPP estimation could be further improved by integrating CI into the non-linear model (which we can see from Table 2). In conclusion, the accuracy of GPP estimation can be improved by considering the influence of CI, especially for the linear model. Finally, we investigated the performance of the combinations of \(\text{SIF}_{760}\) with CI in terms of GPP estimation. The \(\text{SIF}_{760}\)-based GPP models with and without the inclusion of CI were trained using the 70% tower-based daily observations from 2017 and 2018, as summarized in Table 2, and the models were validated using the remaining 30% dataset. The \(g(CI)\) functions were determined using the empirical statistical equations shown in Figures 7 and 8, which were used to represent the impact of CI on the GPP estimation. It can be seen that, for both the linear and non-linear \(\text{SIF}_{760}\)-based models, including the CI, improved the GPP estimation: the R\({}^{2}\) value increased from 0.71 to 0.82 for the linear model, and from 0.82 to 0.87 for the non-linear model. These \(\text{SIF}_{760}\)-based models (summarized in Table 2) were validated using the remaining 30% daily tower-based dataset, as illustrated in Figure 9. The validation results also confirmed that the \(\text{SIF}_{760}\)-based GPP estimation was greatly improved