## 3 Results and Discussion
### Performance of Individual LUE Models  
The selected LUE models exhibited significant differences in the simulation of daily GPP at forest-type and flux-site scales (Figures 3 and 4, Table S3 in the Supporting Information File). Considering \(R^{2}\), \(RMSE\), and \(RPE\), EC-LUE outperformed other models as Figure 4 and Table S3 show. Carbon fixation and evapotranspiration are two closely related processes occurring simultaneously in the same place, the stomata of leaves, during the growth of a forest. On the one hand, the sensible heat and latent heat were taken as parameters of water stress function in the EC-LUE model, which caught the key aspect in photosynthesis and evapotranspiration. Therefore, the evaporative fraction, EF, as shown in Table 1, could serve as a good representative index of soil surface moisture that was the main water limitation for forest growth [19]. On the other hand, latent heat and sensible heat were taken from FLUXNET2015 products, which means EC-LUE had the best spatial and temporal matching of input water stress parameters, while other LUE models' water stress parameters were derived from ground energy and CO\({}_{2}\) exchange measurements or remote sensing observations. Therefore, EC-LUE was the best model compared with other LUE models in extracting the key information in the carbon sequestration process.  
As a popular LUE model, VPM gave quite good performance, especially in mixed forest terrain types. Leaf phenology and chlorophyll content in the growth period play vital roles in light harvesting reactions during forest photosynthesis [56], so the leaf phenology factor in VPM's environmental constraints could help to capture seasonal variance in photosynthetic processes, bringing an advantage in GPP simulation over other LUE models. As for the water stress function, the soil water index (LSWI) that is computed by the combination of NIR and SWIR bands from remote sensing data, is sensitive to soil moisture, which could represent the water limitation in forest growth. The ease of obtaining remote sensing data enables VPM to simulate GPP at large temporal and spatial scales across different terrestrial ecosystems [34].  
Figure 9: Boxplot of performance of \(R^{2}\) (**a**), \(RMSE\) (**b**), and \(AIC\) (**c**) of LUE and machine learning methods across 45 FLUXNET2015 sites.  
GLO-PEM and CASA were proposed in the 1990s and applied to model net or gross primary production using the production efficiency approach at global or regional scales [8; 12]. Although GLO-PEM and CASA yielded slightly lower accuracy compared to EC-LUE and VPM, they still performed quite well in forest GPP simulation. C-Fix was proposed to estimate net biomass in Europe using ground-site measurements and remote sensing data and has seldom been applied in other areas [15; 41]. C-Fix is the only one that accounts for the effect of CO\({}_{2}\) fertilization in the photosynthesis process; however, the water stress is ignored, which may be the reason for a relatively poor performance compared with other LUE models in this study.  
MODIS's GPP is a composite product on an 8-day timescale with a spatial resolution of 500 m based on the definition of radiation use efficiency, providing long time series data from 2000 to present on a global scale [13; 18]. As a dataset used worldwide, MODIS's GPP product offered good performance in the validation using FLUXNET2015's GPP across four forest types at 45 ground sites as Figures 3, 4 and 6 show.