## 3 Results and Discussion
### GPP Estimation of LUE Models, SVM, and RF Based on Forest Types
The SVM and RF decreased the _RMSE_ (gC m\({}^{-2}\) day\({}^{-1}\)) to 1.75 and 1.72, and _RPE_ to \(-\)0.01 and 0, respectively, which further demonstrated that machine learning could significantly improve GPP simulation capabilities. Figure 5 shows the performance of the five single LUE models, MODIS, SVM, and RF across all DBF flux sites. EC-LUE had the highest \(R^{2}\) (0.75), followed by VPM (0.74), GLO-PEM (0.71), MODIS (0.71), C-Fix (0.68), and CASA (0.65), meanwhile, both SVM and RF increased the \(R^{2}\) to 0.90, demonstrating the improved explanation of the GPP variation that machine learning could achieve. VPM gave the smallest _RMSE_ and _RPE_ (2.67 gC m\({}^{-2}\) day\({}^{-1}\), and 0.02) compared to other LUE models, indicating the reliable performance of the GPP simulation in deciduous broadleaf forests. EC-LUE and MODIS also performed well with a lower _RMSE_ (2.79 and 2.92) and _RPE_ (0.03 and 0.12), followed by GLO-PEM, CASA, and C-Fix, as shown in Figure 5. The SVM and RF evidently narrowed the simulation scope, and the RF performed better with a lower _RMSE_ and _RPE_ than SVM (see Figure 5). We put the evaluation of the five LUE models, MODIS product, SVM, and RF across the EBF, ENF, and MF in the supporting information file, and similar results can be seen in Figures S1-S3. Figure 4: The \(R^{2}\) (**a**), _RMSE_ (**b**), and _RPE_ (**c**) of 5 single models, MODIS, SVM, and RF across the DBF, EBF, ENF, and MF. Figure 6 shows the probability distribution of the predictive error in LUE models, MODIS, SVM, and RF compared to FLUXNET2015's GPP product. The VPM, EC-LUE, and GLO-PEM models had maximum value that centered on the \(x\) axis origin with thicker tails on the left hand, which showed that these three LUE models underestimated GPP compared to site observations. CASA and C-Fix had lower peaks compared to EC-LUE, VPM, and GLO-PEM, illustrating that the predictive bias from these two models fluctuated more strongly, which may lead to a higher probability of estimation errors. Compared to individual LUE models and MODIS's GPP product, the GPP error distributions of machine learning estimations were centered on the \(x\) axis origin closely, in a narrow range, with explicitly higher peaks and balanced biases on both sides. Therefore, these histograms indicate that the machine learning fusion strategy--especially the RF--were best at explaining the GPP variance. Figure 5: The scatter plots of \(R^{2}\), _RMSE_, and _RPE_ across the DBF between site-derived GPP and the estimates from the LUE models, MODIS, SVM, and RF. Figure 6: The probability distribution of errors from the LUE models, MODIS, SVM, and RF. The values of the _AIC_ and _BIC_ across all forest types were calculated for each LUE and machine learning model based on Equations (8) and (9) in Section 2.4. Figure 7 shows that machine learning methods gave lower _AIC_/_BIC_ values than individual LUE models, which indicated the SVM and RF were better alternatives than individual LUE models. EC-LUE and VPM outperformed other LUE models, which was consistent with previous results.