## 2 Materials and Methods
### Performance of the GPP Prediction Model  
Figure 5 shows the scatter matrix of the distribution and correlation between GPP and VI indices, including GPP, NDVI, EVI, NIRv, SIF, and PAR. The correlation between GPP and SIF is the highest (r = 0.75), indicating a significant positive correlation, followed by EVI (0.65) and NDVI (0.49). The weakest correlations are noted for NIRv (0.31) and PAR (0.20). Among different vegetation indices, the correlation between SIF and EVI is the highest at 0.84, indicating EVI's strong ability to reflect vegetation photosynthetic capacity. NDVI and EVI are highly correlated (r = 0.81), indicating that they capture similar vegetation characteristics; similarly, NDVI and SIF are also highly correlated (r = 0.66), suggesting that NDVI is less effective than EVI in reflecting photosynthetic capacity. The correlations of  
Figure 4: Monthly distribution of daily GPP values at four flux sites. Figure 3: Annual GPP values from flux observations at four sites. NIRv and PAR with other indices are relatively weak, around r = 0.2. The correlations of SIF, EVI, NDVI, NIRv, and PAR with GPP all passed the significance test. The above indicates that GPP has the strongest correlations with EVI and SIF, highlighting their potential as GPP indicators. The moderate correlations of NIRv and PAR with GPP suggest that they are useful supplements. The results of the geographical detector interaction analysis showed whether NDVI, EVI, NIRv, SIF, and PAR individually or in combination enhance or weaken the prediction of GPP (Table 2). Individually, SIF is the most effective predictor of GPP, with a q value of 0.56. EVI also has a strong predictive ability for GPP, with a q value of 0.45. NDVI and NIRv have weaker predictive effects on GPP, with q values of 0.24 and 0.12, respectively. PAR has the poorest predictive ability for GPP, with a q value of only 0.05. In combination, the effect of SIF improves when combined with other factors, and the q values are relatively stable, ranging from 0.60 to 0.62. EVI also shows good predictive ability for GPP when combined with other factors, with q values of EVI combined with PAR, NIRv, and NDVI ranging from 0.50 to 0.52. PAR is a very intriguing factor. Its q value for predicting GPP is  
Figure 5: Scatter matrix plot of the distribution and correlation between GPP and VI indices. Significant correlations are indicated with \({}^{\star}\) (\(p<0.05\)). In the upper-right plots, the colors of the ellipses represent the strength of the correlations. In the lower-left plots, the red line indicates the regression line, and the shaded area represents the 95% confidence intervals. only 0.05 individually. However, when combined with any other factor, the q value exceeds the sum of the individual q values. This indicates that PAR has a nonlinear enhancement ability for predicting GPP. Similarly, the combined effect of NIRv and NDVI also shows a significant nonlinear enhancement. Overall, the combination of SIF with other factors consistently shows high predictive ability for GPP, and PAR and NIRv are very beneficial supplements for predicting GPP. Understanding these interactions helps to improve models for predicting GPP under different environmental conditions. Figure 6 depict the performance of the GPP prediction model using training and validation datasets. For the training dataset, the model shows a high degree of accuracy with an rRMSE of 0.22. The scatter plot for the training dataset indicates a strong correlation between observed and predicted GPP values. Similarly, the validation dataset demonstrates the model's robustness with an rRMSE of 0.23. The validation scatter plot confirms the consistency of the model's predictions against the observed GPP values. Both datasets indicate that the model can reliably predict GPP under different conditions. The close alignment of rRMSE values between training and validation datasets suggests minimal overfitting.