## 3 Results  
### The Performance of the Optimal VI-Based GPP Estimation Models  
We found that all optimal VI-based GPP estimation models show reasonable accuracy in predicting GPP at a global scale (R\({}^{2}\) ranges from 0.79 to 0.87, RMSE ranges from 1.40 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) to 1.65 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)), but the NIR\({}_{v}\)-based PFT-specific RF models performed the best (R\({}^{2}\) = 0.87, RMSE = 1.40 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)). Our results also suggest that the RF models generally performed better than the BPNN models, and the PFT-specific models performed better than the universal models, although their differences were minor (Table 2). For the three VIs, both RF and BPNN methods show that NIR\({}_{v}\)-based models outperformed SIF-based models, followed by LAI-based ones.  
Figure 2 shows the latitudinal distribution of universal models' performance using the RF method. Prediction accuracy discrepancies are mostly present among various latitudinal zones and different PFTs, rather than different models. The GPP estimation models derived from the different combinations of BPNN or RF methods and universal or PFT-specific configurations show similar performance (Figures 2 and S5-S7), indicating that rather than the machine learning algorithms, the uncertainties and sample size of the training data seem to be the main factors that affect the performance of the GPP estimation models when estimating regional GPP.  
The R\({}^{2}\) values of the models appear to be greater than or near to 70% in all latitudinal zones except 70\({}^{\circ}\)N-80\({}^{\circ}\)N (R\({}^{2}\) = 0.27-0.34), with minor differences between the models based on different VIs and machine learning algorithms (Figures 2 and S2-S4). Overall, the regional and PFT-specific performance of the GPP models, which is also closely related to the sample size, is much better in the northern latitudes (the median of R\({}^{2}\) is 0.85; the median of RMSE is 1.12 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)) than latitudes near the equator (the median of R\({}^{2}\) is 0.74; the median of RMSE is 1.19 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)). With a dense distribution of flux tower sites (Figure 1) in the northern mid-high latitudes (30\({}^{\circ}\)N-70\({}^{\circ}\)N), diverse PFTs, and a large amount of data available, the models performed well on all types of vegetation (forests, shrublands, grasslands, croplands, and wetlands) in this region (R\({}^{2}\) ranges from 0.48 to 0.97, and RMSE ranges from 0.51 to 3.13 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)). However, the poor performance in the northern high latitudes (70\({}^{\circ}\)N-80\({}^{\circ}\)N) is likely because only one flux tower was available (the open shrublands site, Ru-Cok). Similarly, the poor model performance for EBF near the equator (R\({}^{2}\) = 0.10-0.22) is also due to the limited flux tower observations (Figure 1).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Vegetation** **Index**} & \multirow{2}{*}{**RF**} & \multirow{2}{*}{**RPNN**} & \multirow{2}{*}{**RMSE**} \\  & & & & & **(g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\))** \\ \hline \multirow{3}{*}{PFT-Specific} & SIF & 0.86 & 1.46 & 0.84 & 1.43 \\  & NIR\({}_{v}\) & 0.87 & 1.40 & 0.85 & 1.43 \\  & LAI & 0.86 & 1.45 & 0.83 & 1.50 \\ \hline \multirow{3}{*}{Universal} & SIF & 0.85 & 1.54 & 0.81 & 1.60 \\  & NIR\({}_{v}\) & 0.85 & 1.51 & 0.83 & 1.54 \\ \cline{1-1}  & LAI & 0.84 & 1.54 & 0.79 & 1.65 \\ \hline \end{tabular}
\end{table}
Table 2: Performance of optimal models for each vegetation index. Note that PFT was used as a predictor in the PFT-specific models, while it was not included in the universal models.