## 2 Materials and Methods
### Modeling GPP Based on SIF and PRI  
In order to assess the performance of GPP estimation based on canopy and ecosystem-level SIF using a linear model, we compared the GPP results estimated with \(\text{SIF}_{\text{TOC}}\) (\(\text{GPP}_{\text{TOC}}\)) and the GPP results estimated with \(\text{SIF}_{\text{TOT},\text{FULL},\text{PSII}}\) (\(\text{GPP}_{\text{TOT}}\)).  
Since obtaining the necessary parameters for the physical modeling of the GPP is challenging (e.g., FvCB and MLR), a statistical model was trained on the dataset to estimate GPP. According to [PERSON] et al. [31] and [PERSON] et al. [27], the inclusion of the PRI with SIF-based GPP estimation models enhances the GPP estimation accuracy, but they neglected to account for the seasonal effects of SIF and PRI in the canopy. In this study, we also used a multi-linear regression model to investigate GPP estimation using \(\text{SIF}_{\text{TOT},\text{FULL},\text{PSII}}\) and \(\Delta\text{PRI}\):  
\[\text{GPP}_{\text{TOT},\text{APRI}}=\text{f}(\text{SIF}_{\text{TOT},\text{ FULL},\text{PSII}},\Delta\text{PRI})=\text{a}\text{SIF}_{\text{TOT},\text{FULL},\text{PSII}}+\text{b} \Delta\text{PRI}+\text{c} \tag{11}\]  
where a, b, and c are parameters fitted using regression analysis. We used the observed canopy SIF and PRI to model GPP for comparison:  
\[\text{GPP}_{\text{TOC},\text{PRI}}=\text{f}(\text{SIF}_{\text{TOC},\text{ 760}},\text{PRI})=\text{a}^{\prime}\text{SIF}_{\text{TOC},\text{760}}+\text{b} ^{\prime}\text{PRI}+\text{c}^{\prime} \tag{12}\]  
where a\({}^{\prime}\), b\({}^{\prime}\), and c\({}^{\prime}\) are parameters fitted using regression analysis. To better determine whether the CI has a great impact on the model, partial correlation analysis was carried out to examine the influence of environmental conditions (CI, PAR, Ta, and VPD) on the ratio of \(\text{GPP}_{\text{EC}}\) to \(\text{GPP}_{\text{TOT\_APRI}}\).  
In addition, since environmental conditions have complex effects on GPP estimation using \(\text{SIF}_{\text{TOT\_FULL\_PSII}}\) and \(\Delta\text{PRI}\), we used Random Forest (RF) regression--one of the best machine learning models for predictive analytical approaches--to model the ratio of \(\text{GPP}_{\text{EC}}\) to \(\text{GPP}_{\text{TOT\_APRI}}\):  
\[\text{GPP}_{\text{RF}}=\text{f}(\text{Ta},\text{VPD})\times\text{GPP}_{\text {TOT\_APRI}} \tag{13}\]  
\[\text{GPP}_{\text{RF\_CI}}=\text{f}(\text{CI},\text{Ta},\text{VPD})\times \text{GPP}_{\text{TOT\_APRI}} \tag{14}\]  
where \(\text{f}(\text{Ta},\text{VPD})\) represents the RF regression result, which describes the effects of Ta and VPD on the ratio of \(\text{GPP}_{\text{EC}}\) to \(\text{GPP}_{\text{TOT\_APRI}}\); (\(\text{CI},\text{Ta},\text{VPD}\)) denotes the RF regression result, which describes the effects of CI, Ta, and VPD on the ratio of \(\text{GPP}_{\text{EC}}\) to \(\text{GPP}_{\text{TOT\_APRI}}\). Finally, we obtained the \(\text{GPP}_{\text{RF}}\) and \(\text{GPP}_{\text{RF\_CI}}\) by combining Equation (10) and the RF results. The overall research framework is shown in Figure 3. The different relationships of \(\text{GPP}_{\text{EC}}\) to \(\text{GPP}_{\text{RF}}\) and \(\text{GPP}_{\text{RF\_CI}}\) reveal the influences of the CI on GPP estimation using \(\text{SIF}_{\text{TOT\_FULL\_PSII}}\) and \(\Delta\text{PRI}\) and emphasize the importance of including the CI in GPP models based on SIF and the PRI.