## 3 Results
### The Critical Factors for the Machine Learning Algorithms-Based GPP Estimation Model  
We further investigated the factors that are the best candidates for developing the GPP estimation models with different VIs. The GPP models developed based only on VIs suggest that SIF is the best proxy for the estimation of global GPP using the RF algorithm (R\({}^{2}\) = 0.67, RMSE = 2.24 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)), followed by NIR\({}_{\rm v}\) (R\({}^{2}\) = 0.61, RMSE = 2.45 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)) and LAI (R\({}^{2}\) = 0.50, RMSE = 2.79 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\)). Likewise, the models developed based on the BPNN algorithm also suggest that SIF is the best VI for global GPP estimation if other variables, i.e., CO\({}_{2}\), PFT, plant traits, and climate factors, were not included (R\({}^{2}\) = 0.70, RMSE = 2.13 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\), Figure S10). Nevertheless, VIs are the most critical input when compared to other variables, confirming the usefulness of these VIs in estimating global GPP. Figure 4: Comparisons of annual mean GPP among different GPP products. Global land is divided into the northern hemisphere (NH: 30\({}^{\circ}\)N–90\({}^{\circ}\)N) and tropical and southern hemisphere (SH+Trop: 90\({}^{\circ}\)S–30\({}^{\circ}\)N). The SIF-based, NIR\({}_{\rm v}\)-based, and LAI-based labels represent the GPP estimates based on each vegetation index with optimal configurations. The dashed lines represent the maximum and minimum values of the ten processed models in the TRENDY group (‘S3’ scenarios). TRENDY MMEM represents the average of the multi-model ensemble mean. Incorporating atmospheric CO\({}_{2}\) concentration helps the estimation of GPP based on VIs and machine learning algorithms (Figure 5). However, the benefits of incorporating CO\({}_{2}\) are different for different VIs. We found that improvement in model performance was more evident for LAI-based models, with the R\({}^{2}\) value increasing from 0.50 to 0.58 and RMSE decreasing from 2.79 to 2.52 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\). The improvements for NIR\({}_{v}\)-based and SIF-based models were not that significant, with the R\({}^{2}\) value increasing from 0.61 to 0.66 and from 0.67 to 0.70 for NIR\({}_{v}\) and SIF, respectively, while the RMSE values respectively decreased from 2.45 to 2.30 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) and from 2.24 to 2.13 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) (Figure 5). We also found that explicitly including PFT in the RF model achieved similar improvements to including CO\({}_{2}\). Nevertheless, incorporating both CO\({}_{2}\) and PFT did not achieve an evident improvement in model performance compared to the models that incorporated CO\({}_{2}\) or PFT. Including plant traits and/or climate factors led to a further notable improvement in model performance (Figure 5). For the SIF models, plant traits significantly improved model performance (R\({}^{2}\) increased by 0.13 and RMSE decreased by 0.51 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) from the SC models to the SCT models) while climate factors did not (R\({}^{2}\) and RMSE were 0.70 and 2.13 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) for the SC models and 0.73 and 2.05 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) for the SCF models). For the NIR\({}_{v}\) and LAI models (VC models), considering plant traits (VCT models) or climate factors (VCF models) significantly contributed to model performance. Furthermore, models that incorporated both plant traits and climatic factors (VCPT models) achieved the best performance (R\({}^{2}\) = 0.87 and RMSE = 1.40 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) for NIR\({}_{v}\); R\({}^{2}\) = 0.86 and RMSE = 1.45 g C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) for LAI). We found that results did not change for the machine learning algorithms because the combination test of VIs, PFT, plant traits, and climate factors based on the BPNN algorithm showed similar results to tests based on the RF algorithm (Figure S10).