## 4 Discussion  
### Possible Reasons for the Influence of CI on the SIF-GPP Relationship  
In this study, we analyzed how CI affected the SIF\({}_{760}\)-GPP relationship for a C4 crop of maize. Our results showed that CI was an important environmental factor influencing the SIF\({}_{760}\)-GPP relationship, as found in previous studies [26; 32; 64; 65; 66; 67]. In addition, we found that the inclusion of CI played a key role in correcting the non-linear relationship between SIF\({}_{760}\) and GPP. It was observed that GPP would either saturate, or increase more slowly than SIF\({}_{760}\), at high values of CI (see Figures 5 and 6). There are several possible reasons for this. First, the responses of LUE and the quantum yield of SIF (SIF\({}_{\text{yield}}\)) to illumination conditions are different, and CI is a sensitive indicator of illumination. In our research, we found that, for a maize field, the responses to variations in the light conditions differed between SIF\({}_{760}\) and GPP. The SIF-PAR relationship showed no significant saturation phenomenon, whereas, as also observed by [PERSON] et al. [61], for the GPP-PAR relationship, there was slight saturation at the diurnal scale (Figure 5). The light-use efficiency (LUE) is mainly influenced by the fraction of diffuse radiation. Some studies have concluded that carbon uptake is enhanced under cloudy conditions (the so-called \"diffuse light fertilization effect\") [45; 46], whereas the quantum yield of SIF remains relatively constant [67]. Nichol  
Figure 9: Validation of the SIF\({}_{760}\)-based GPP models that did and did not include the clear-sky index (CI) using the daily tower-based daily observations of the validated dataset. \(GPP_{rms}\) represents the GPP measured by EC technique. \(GPP_{L}\) and \(GPP_{NL}\) represent the GPP predicted by the linear and non-linear model, respectively. (**a**) and (**b**) illustrate the validation results for the linear regression models, and (**c**) and (**d**) illustrate the results for the non-linear regression models. The color scale represents the CI value. The short-dashed line is the 1:1 line and the solid line represents the best-fit line. et al. [64] confirmed that the linear regression of SIF and GPP was mainly affected by the shadowed canopy fractions. [PERSON] et al. [68] also found that diurnal LUE did not recover to the same level after solar soon compared to before solar soon, and that SIF\({}_{\text{yield}}\) increased much more strongly than LUE. Therefore, we concluded that, CI, as a proxy for the illumination conditions, was an important factor affecting the non-linear relationships between GPP and SIF at half-hourly and daily time scales (Figure 6). Second, CI is usually related to other environmental parameters, such as the temperature, humidity, and precipitation, which also have different influences on the LUE and SIF\({}_{\text{yield}}\). [PERSON] et al. [45] concluded that the enhanced carbon uptake under cloudy conditions might result from the interaction between various environmental factors related to the presence of clouds. Previous studies have reported that the GPP-SIF relationship is influenced by the relative humidity (RH) and air temperature. For example, [PERSON] et al. [69] reported that the quantum yield for CO\({}_{2}\) uptake under normal atmospheric conditions was temperature-dependent in C3 plants but apparently not in C4 plants. [PERSON] et al. [31] found that the ratio of GPP to SIF generally increased along with the relative humidity (RH) and confirmed that incorporating the relative humidity, the diffuse PAR fraction, and the growth stage into multiple regression analyses led to improvements in estimates of GPP for a rice paddy. In this study, although we found the VPD and AT exhibited a certain relationship with the GPP/SIF\({}_{760}\), the introduction of more parameters will also accumulate, increasing the uncertainties of the model. Therefore, we only considered the influence of the CI on the relationship between SIF\({}_{760}\) and GPP.