## 3 Results and Discussion  
### GPP Estimation of LUE Models, SVM, and RF Based on Forest Types  
Figure 3 shows Taylor diagrams for the site-derived GPP and estimated GPP using different LUE models at the 45 EC sites. The Taylor diagram is a graph in polar coordinate which includes the metric of standard deviation (_SD_), the correlation coefficient (\(R\)) and the root-mean-square difference (_RMSD_) between the estimations and the reference values [53]. In Figure 3, _SD_ is the distance from the original coordinate point; R is the cosine of the azimuth angle; and _RMSD_ denotes the distance from the reference value (i.e., FLUXNET2015's GPP products). Figure 3 indicates that the performance of different LUE models varied across forest types. In the deciduous broadleaf forest (DBF), the VPM estimation was the closest one to site-derived GPP compared to other LUE models including MODIS's GPP in the dimensions of _SD_, R, and _RMSD_. EC-LUE and MODIS held similar R and _RMSD_ but higher and lower _SD_ values compared to VPM. The _RMSD_ of GLO-PEM was higher than that of VPM, EC, and MODIS, while CASA and C-Fix stayed further away from the referenced point (site-derived GPP), which means that CASA and C-Fix ranked lower compared to other LUE models. In the evergreen broadleaf forest (EBF), EC-LUE and MODIS outperformed other LUE models with a lower _RMSD_, higher R, and closer _SD_ distance to site-derived GPP. In the ENF and MF types, EC-LUE, VPM, and MODIS performed better than GLO-PEM, CASA, and C-Fix. In Figure 3, the machine learning methods, SVM and RF, showed significant advantages in estimating forest GPP over individual LUE models. The _RMSD_ of the SVM and RF were within 2 gC m\({}^{-2}\)day\({}^{-1}\) while that of individual LUE models ranged from 2 to 6 gC m\({}^{-2}\)day\({}^{-1}\). The correlation coefficient (R) of the SVM and RF were obviously higher than that of individual LUE models in all four forest types. Most correlation coefficients of the SVM and RF across the DBF, EBF, ENF, and MF were higher than 0.9, while LUE models held lower R values below 0.9. The lowest R value of C-Fix was even below 0.5 with the highest _RMSD_ in the EBF. Figure 4 shows that the single LUE models, SVM, and RF exhibited substantial differences for each forest type using \(R^{2}\), _RPE_, and _RMSE_ compared to ground site-derived GPP. EC-LUE, VPM, and GLO-PEM explained major GPP variations across each forest type, indicated by \(R^{2}\) of 0.62, 0.57 and 0.56, and C-Fix and CASA explained less variations with an average \(R^{2}\) of 0.51 and 0.47. The \(R^{2}\) of MODIS's GPP was 0.61, only less than EC-LUE, which indicated a good performance compared to other LUE models. The SVM and RF  
Figure 3: The Taylor diagrams for site-derived GPP and LUE models/machine learning estimates at the 45 FLUXNET2015 sites. The dotted circular lines which connect the X and Y axes denote _SD_. The dotted radial lines represent R. The brown curves are _RMSD_ compared to the referenced site’s GPP. significantly improved the ability to explain variations for each forest type with \(R^{2}\) of 0.79 and 0.80, respectively. The _RMSE_ and _RPE_ describe the errors from estimation, so lower values indicate better performance. In the five LUE models, EC-LUE had the smallest _RMSE_ of 2.77 gC m\({}^{-2}\) day\({}^{-1}\), while VPM had the least absolute _RPE_ of \(-\)0.04, which means EC-LUE and VPM outperformed other LUE models in terms of simulation errors. The _RMSE_ (gC m\({}^{-2}\) day\({}^{-1}\)) and _RPE_ of C-Fix (5.79 and 0.53) and CASA (4.96 and 0.23) were much higher than those of EC-LUE and VPM. MODIS performed well with a 2.55 gC m\({}^{-2}\) day\({}^{-1}\)_RMSE_ and _RPE_ of \(-\)0.11, indicating that it was justifiably trustworthy as a popular worldwide research product. VPM, EC-LUE, and MODIS, as the better performance models, underestimated GPP compared to site observations.