## 4 Discussion  
### Uncertainties of the GPP Estimation Based on PRI and SIF  
In this study, we assessed the potential of PRI to improve the relationship between SIF and GPP for corn and soybean. The relationships of GPP to SIF and PRI are influenced by structural and physical-physiological factors. Canopy structure affects the estimation of \(f_{esc}\), which further affects the estimates of the total SIF [8]. The canopy-observed SIF at a solid viewing angle has an angle effect. Therefore, it is necessary to convert the canopy-observed SIF at a solid viewing angle into the total SIF at the hemisphere [4]. Although the ratio of NIRv to fPAR can be as an approximation of the \(f_{esc}\) at the near-infrared band, the influences of complex structure and soil background on the \(f_{esc}\) have not been well explored [7; 11]. In  
Figure 10: Relationship between the ratio of \(GPP_{meas}\) to \(GPP_{meas}\) and Gs based on the validated dataset. (**a,c**) represent the relationship between the ratio to Gs for corn at half-hourly and daily timescales, respectively, while (**b,d**) indicate the relationship between the ratio to Gs for soybean at half-hourly and daily timescales. The color bar indicates the magnitude of PRI. “\(\star\)” is the significance level of 0.05 and “\(\star\)” represents the significance level of 0.01. Figure 9: Validation of the GPP estimation accuracy based on \(SIF_{t}\) and PRI at half-hourly and daily timescales. \(GPP_{meas}\) represents the EC measured GPP. \(GPP_{pre}\) represents the GPP predicted by \(SIF_{t}\) and PRI. The validation findings for corn at half-hourly and daily timescales are shown in (**a,c**), respectively. (**b,d**) illustrate the results for soybean at half-hourly and daily timescales, respectively. The PRI value is depicted by the color bar. The best-fit line is shown by the solid red line, while the short-dashed line is the 1:1 line. addition, a single-wavelength SIF cannot well characterize the broadband SIF covering the 650 nm to 800 nm spectral range [35]. The observed SIF not only contains contributions from PSII but also from PSI, while only SIF emitted from PSII is directly related to light reactions. Hitherto, there are no methods available to distinguish PSI and PSII fluorescence at leaf or canopy levels [6]. In this study, to lessen the impact of the canopy structure, we only explored the GPP-\(SIF_{t}\) relationships using data with NDVI greater than 0.7. This study used PRI as an indicator of NPQ, which has demonstrated that PRI can track the dynamic changes of NPQ in previous studies, especially at short-time timescales [44]. Although this study assessed the role of PRI in regulating the SIF-GPP relationship, it depends on whether PRI is a good proxy for NPQ. Due to the fact that there are three main energy dissipated pathways, it is reasonable to combine the information from SIF and NPQ to improve GPP estimation. The intricate interplay of environmental factors (e.g., air temperature, light intensity, and water availability) have an impact on how SIF and NPQ are linked to GPP. NPQ and SIF tend to increase with PAR [45]. Low temperature may cause NPQ to increase whereas SIF may show a fall trend, provided that it does not cause damage to chlorophyll molecules [19]. According to some studies conducted in hot environments, the NPQ rises as temperature rises but SIF exhibits the opposite pattern [45; 46]. Moreover, water stress made NPQ increase and might decrease SIF [47; 48]. Overall, SIF and NPQ react differently to variable environmental conditions, and they have a comprehensive impact on PQ changes. As a result, the combination of SIF and NPQ has a special ability to indicate PQ dynamics under complex environmental conditions. It is worthy to note that the decoupling of light reactions and dark reactions in response to stress may also alter the relationships of GPP to NPQ and SIF [35]. The stomatal conductance controlling the sink of CO\({}_{2}\) and the loss of H\({}_{2}\)O may be more sensitive to stress conditions than the light reactions.