## 4 Discussion  
### The Differences in the Magnitude and Trend of GPP Estimates  
Gross primary productivity (GPP) is the largest component flux of the global carbon cycle, and the accuracy of GPP estimates strongly determines terrestrial carbon fluxes and carbon budget [44]. A recent study shows that LUE models perform as well as the best process-based models evaluated by observations from 36 North American flux towers [45]. One of the major reasons is that LUE models are always calibrated and evaluated based on flux tower eddy covariance measurements across various geographic and climate areas [12, 19, 20, 21, 35, 38]. The seven LUE models used in this study have utilized parameters calibrated using eddy covariance measurements [26]. The global GPP estimates of these models is \(119.07\pm 15.29\) Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\), which is comparable to the flux-tower-based simulations of \(119.4\pm 5.9\) Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\) and \(123\pm 8\) Pg\(\cdot\)C\(\cdot\)yr\({}^{-1}\) using model tree ensemble approach and data-driven method, respectively [1, 46]. However, large uncertainties still exist in GPP simulations by LUE models, one of which is associated with uncertainty of model input data. For instance, it is difficult to characterize water available for plants and its effect on photosynthesis over large areas from modeling, and this limits the accuracy of any spatial GPP models [26]. The estimated ET of the revised RS-PM model driven by the global MERRA meteorological data can explain 67% of the variations of annual mean ET across 54 flux sites [39], which indicates that ET model errors will further reduce the performance of LUE models [47].  
Therefore, though site-scale model parameterization and evaluation can improve the performance of LUE models, large differences still exist over the global scale. These large differences are unexpected because all models have been calibrated. Difference in model formulations is probably a major cause. Previous studies have shown that different GPP estimates among models are caused by model structural differences [48, 49, 50]. For example, changes in the formulations of LUE models result in large differences in the spatial pattern of the simulated GPP [49]. Changes in the model structures will change the model outputs, as suggested by inter-comparison of 26 models, including 6 LUE models [50]. Our study showed that GPP simulations of shrubland, grassland, and savanna differed most pronounced among models (Tables 1 and 2). These ecosystems are vulnerable to water limitation. Previous study has revealed water stress algorithms generate the largest variation among models compared to temperature factors [26]. Hence, the GPP difference of these ecosystems may be attributed to the model discrepancy in quantifying water stress. GPP of evergreen broadleaf forest and cropland also showed large differences among models (Tables 1 and 2). Plant photosynthesis of evergreen broadleaf forest is jointly determined by various environmental variables, increasing the difficulty in modeling [26, 51]. Cropland is heavily influenced by complex anthropogenic activities, which is not formulated into models [52, 53]. Therefore, it is necessary to conduct model inter-comparison to understand the impacts of algorithms of LUE models on GPP estimates [48, 54].  
The interannual variability of GPP estimates also differed among the seven models from the spatial perspective. Several site-based studies have revealed the same conclusion [26, 33, 45]. For example, a model comparison, which assessed the performance of 16 terrestrial biosphere models and 3 remote sensing products at 11 forested sites in North America, has found that none of the models consistentlyreproduce the observed interannual variability [33]. Large difference in environmental regulations and vegetation indices is one of the major causes (see Sections 4.2 and 4.3).