## 5 Conclusions  
In this study, we collected discrete FLUXNET eddy-covariance and meteorological data and spatially continuous MODIS, GLASS and ERA-Interim data to estimate the global LUE and GPP. The SCE-UA optimization method had a high efficiency of solving the global optimal solution under nonlinear constraints and never depended on the initial value of the mode, and the Cubist regression tree approach provided a powerful tool with which to upscale site-observed fluxes to a larger scale with satellite-derived parameters and other explanatory variables. We established three LUE-based GPP  
Figure 14: LUE and GPP curves in US-Los and US-Tw4.  
Figure 13: Left: LUE and GPP curves and land surface images in homogeneous sites. US-WCr, US-Me2 and AU-Gin); right: LUE and GPP curves and land surface images in heterogeneous sites (DE-Kli and CH-Oe2) (red rectangles cover 500 m \(\times\) 500 m land, yellow rectangles cover 5000 m \(\times\) 5000 m land.  
approaches to assess the different performances at both the site and the global scales. The method of obtaining the LUE was based on (1) a parameterization approach without the CI, (2) a parameterization approach with the CI, and (3) a Cubist regression tree approach.  
By validating with FLUXNET measurements at the site scale, we obtained the following:  
(1) The Cubist regression approach performed better than the parameterization approaches in estimating LUE and GPP.  
(2) The three approaches all underestimated the LUE, especially when the FLUXNET LUE exceeded 2.0 gC/MJ. However, the underestimation problem was alleviated for GPP.  
However, when applying these models to the global LUE and GPP in 2014, we found the following:  
(1) The LUE and GPP estimated by the three approaches were reliable, of which the parameterization approach with the CI produced the most satisfactory result then closely followed by the parameterization approach without the CI, while the Cubist regression approach produced the least satisfactory result.  
(2) The accuracy of GPP was higher than that of LUE for all types of vegetation.  
(3) The LUE distributions showed some variations in different seasons, but vegetation had the highest LUE at approximately 1.5 gC/MJ for the entire year in equatorial regions (South America, middle Africa and Southeast Asia).  
(4) The three approaches produced roughly consistent global annual GPP values, ranging from 109.23 to 120.65 Pg/yr.  
In conclusion, our results suggest the parameterization approaches are robust when extrapolating to the global scale, of which the parameterization approach with CI performs slightly better than that without CI. By contrast, the Cubist regression tree produced LUE and GPP with lower accuracy even though it performed the best for model validation at the site scale.  
[PERSON] and [PERSON] conceived and designed the work; [PERSON] analyzed the data and wrote the manuscript, [PERSON] provided ideas and modified the manuscript; [PERSON] processed some experimental data. [PERSON] provided data and suggestions. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Key R&D Program of China (2017 YFA0603002, 2016 YFB0501502) and the National Natural Science Foundation of China (41531174).  
The data used in this paper include Fluxnet2015 dataset, MODIS GPP/NPP products (MOD17A3 and MOD17A2). We sincerely thank all contributors of the data. We thank all the reviewers for their careful reading of the manuscript and their constructive remarks.  
The authors declare no conflict of interest.