## 3 Results  
### Comparison of Model Performance at the Site Scale  
Globally among all the 10 models evaluated, the LUE-EF model had the highest correlation coefficient of r = 0.86, followed by the LUE-NDWI model with r = 0.82 (Figure 1a). The LUE-EF model had the smallest normalized RMSE (0.50), indicating that the difference between the LUE-EF model and EC-tower GPP was the smallest among all models. The LUE-NDWI model had the second smallest normalized RMSE (0.52). The normalized RMSE for the other models was larger than the two new models. Model LUE-EF simulatedthe amplitude of the variations close to the data amplitude of EC-towers (SD ratio = 0.93). When grouped by latitudinal zone (Figure 1b-e) the improvements of the new models were more apparent for tropical and northern temperate zones. In the temperate zones, the distribution of models in the Taylor diagram was relatively concentrated, whereas in the tropical and boreal areas there were larger differences among models. When grouped by biome (Figure A1), the new LUE-EF model showed advantages of fit in simulating daily GPP for most biomes, both in terms of correlation coefficients and RMSE. For example, correlation coefficients were highest for LUE-EF in deciduous broadleaved and evergreen needleleaf forests, wetlands, and grasslands (DBF, ENF, WET, and GRA), with LUE-NDWI being the second highest in the latter three of those. It is important to note that these biomes also have the largest number of EC-towers. It is relevant to note that many biomes are underrepresented in the current EC-tower network, such as closed shrublands or deciduous needle-leaved forests (CSH and DNF), each represented by only one and two EC-towers. The Taylor diagram shows that the models in CSH, DNF, and SAV are more dispersed, which means that model performances in these biomes vary greatly.  
The distribution of double mass curves (Figure 2) show that those of the LUE-EF were the most concentrated around the 1:1 correspondence line among the 10 models compared, which indicates its greater ability to simulate the patterns in temporal variability of GPP. Figure 2 also shows the distributions of relative bias in ratio (PB-percentage biases), which ranged \(\pm\) 0.4 for all models, indicating that the models had a large heterogeneity (i.e., the PB of each EC-tower is quite different) in simulating the temporal change of GPP across sites. The biases were however narrower for the LUE-EF and LUE-NDWI models, respectively, containing 120 and 110 of the EC-towers within \(\pm\) 0.2 in their PB, the largest number of EC-towers amongst all models. In contrast, the number of sites with PB \(\pm\) 0.2 did not exceed 100 sites for each of the other models. This indicates that the two new models had a stronger ability to capture the spatial (smaller dispersion of the double mass curves) and temporal (smaller deviation of the double mass curve from the 1:1 reference line) changes of GPP.  
Figure 1: The Taylor diagram showing (**a**) the performance of all models, data from eddy covariance (EC) towers were used.; (**b–e**) the performance of all models in different latitudinal geographical zones (tropics:\(-23.5^{\circ}\)\(-23.5^{\circ}\), temperate:\(-23.5^{\circ}\)\(-\)\(-\)\(-66.5^{\circ}\)) and (\(23.5^{\circ}\)\(-\)\(66.5^{\circ}\)), boreal and tundra: \(66.5^{\circ}\)–\(90^{\circ}\)), where N and S represent the Northern and Southern hemispheres, respectively. The upper right corner of subplot ”n” is number of EC-towers.