## 3 Results
### Biases in Remote Sensing Data Products and Consequences on Global GPP Estimation  
First, various biases were found when the spatial datasets that feed the models for global GPP simulations were evaluated at the site scale (Figures 3 and A2). For example, the spatial PAR dataset only explained 57% of the observed PAR variation at the EC-towers, and the slope and intercept were 1.2 and 0.57, respectively, indicating that the PAR data fields overestimated PAR as a whole and slightly underestimated PAR at the low value. The determination coefficients of the global datasets of CO\({}_{2}\), LE, and H at the EC-towers were less than 20% (R\({}^{2}\) < 0.2), and only temperature data was efficient in representing site-scale variation (R\({}^{2}\) = 0.89). Second, the biases in the spatial datasets had a significant impact on GPP simulations was found through orthogonal regression. Before correcting these biases, the simulated GPP by the LUE-EF and LUE-NDWI models explained only 49% and 61% of the EC-tower GPP variation, and the slopes of the linear regression between simulated and tower-estimated GPP were 1.54 and 1.31, respectively, and the corresponding intercepts were \(-\)2.09 and \(-\)1.23. These results indicate that both models overestimated GPP as a whole, but underestimated low GPP values (Figure 3b,f). After correcting the biases in the spatial datasets, the R\({}^{2}\) of LUE-EF and LUE-NDWI models improved to 0.80 and 0.79, with the slopes closer to 1 (1.20 and 1.18 values, respectively) and the intercepts closer to 0 (\(-\)0.59 and \(-\)0.91, respectively) (Figure 3c,g). The results also indicated that the LUE-NDWI model was less sensitive to the biases in the spatial data fields than the LUE-EF model, as shown by the smaller differences in R\({}^{2}\) before and after data correction. This can probably be attributed to the fact that the LUE-NDWI relies on NDWI, a factor that can be derived directly from remote sensing data and thereby less prone to error propagation than the LUE-EF model. Figure 2: Comparison of cumulative gross primary production (GPP) estimates from the flux towers and the models. The color lines represent the GPP value of cumulative comparison between the EC-tower and model for each site. The red dashed line is the 1:1 reference to the differences of modeled GPP and EC-tower. Inset histogram shows the frequency distribution of the percentage biases (PB) at the flux towers. The two shaded plots (panels i and j) are two new models devel-oped in this study. (**a**) EC-LUE (eddy covariance-light use efficiency model), (**b**) VPM (vegetation photosynthesis model), (**c**) CFIX (carbon fixation model), (**d**) MODIS (moderate resolution imaging spectroradiometer model), (**e**) GR (green-ness-radiation model), (**f**) VI (vegetation-indices model), (**g**) TG (temperature-greenness model), (**h**) AVM (alpine vegetation model), (**i**) LUE-EF (light use efficiency-evaporative fraction model), (**j**) LUE-NDWI (light use efficiency-normalized difference water index model). At a global scale, the biases in spatial data inputs had a great impact on the simulated GPP even for the less sensitive model LUE-NDWI. Figure 4a shows the global average annual GPP distribution from 2000 to 2018, simulated by the LUE-NDWI model using corrected input data layers. The spatial pattern of GPP agrees well with previous studies. However, the impact of data biases on the spatial pattern of simulated GPP was obvious and not uniform across space (Figure 4b). The area overestimated is much larger than the underestimated area when the data biases were not attended, and the area fractions with GPP biases at \((-50\%)\)-\((-30\%)\), \((-30\%)\)-\((-10\%)\), \(10\)-\(30\%\), and \(30\)-\(50\%\), were \(8\%\), \(19\%\), \(27\%\), \(31\%\), and \(15\%\), respectively. After data correction, the area of GPP serious reduction occurs in the mountain systems of the Tibetan plateau in Asia, northern Africa, and South America region. Growth trends of GPP were observed in Australia, northwest North America, and Siberia.