## 2 Data and Methods
### Dataset Descriptions and Validation  
The primary data are derived from the database of the Program for Climate Model Diagnosis and Intercomparison (PCMDI) ([[https://pcmdi.llnl.gov/CMIP6/](https://pcmdi.llnl.gov/CMIP6/)]([https://pcmdi.llnl.gov/CMIP6/](https://pcmdi.llnl.gov/CMIP6/))). PCMDI data were distributed by the IPCC Data Statistics Center. After all simulation results and other results were counted, the PCMDI database was established and shared free of charge. The model results of CMIP6 has been verified in the global scale, and it is a common practice to use these models to analyze the results [31; 32; 33; 34; 35; 36; 37; 38]. Here we used model-averaging to increase the reliability of the forecasts and interpretation of factors that impact the model-averaged forecast. Considering the data integrity of relevant statistics, such as research purposes and scenarios, we selected CESM2, CESM2 WACM, EC-EARTH3-VEG, MPI-ESM1-2-HR, and BCC-CSM2-MR of scenario MIP, one of the subplans of CMIP6 [39; 40] (Table 1), based on three radiative forcing levels, SSP1-2.6, SSP3-7.0, and SSP5-8.5 varying the radiative forcing to \(\sim\)2.6 W/m\({}^{2}\), \(\sim\)7.0 W/m\({}^{2}\), and \(\sim\)8.5 W/m\({}^{2}\), respectively; we chose monthly GPP, NPP, precipitation and temperature predicted by corresponding models for analysis. The data are in NetCDF format with a nominal resolution of 100 km that covers the globe. Due to the lack of CO\({}_{2}\) concentration data in the corresponding model, the future long-term series CO\({}_{2}\) prediction data come from the CO\({}_{2}\) concentration data in the 21 st century scenario designed by [PERSON] et al. [41].  
For model validation, except comparing the results of other publish model, we also chose Moderate Resolution Imaging Spectroradiometer (MODIS) data (GPP from MYD17A2H and NPP from MYD17A3H, [[https://lpdaascvc.cr.usgs.gov/appeears/products](https://lpdaascvc.cr.usgs.gov/appeears/products)]([https://lpdaascvc.cr.usgs.gov/appeears/products](https://lpdaascvc.cr.usgs.gov/appeears/products))) as one of the bases to discuss and verify the results of multi model calculation. The data of annual NPP and GPP accumulated 8 day of data from 2000 to 2010 were obtained by MODIS. We converted the 8-day GPP data into annual GPP data. We added up to all 8-day GPP data to obtain the annual GPP data. For each year, we calculate the spatial average value to obtain the average level of this index after eliminating the outliers in the Qinghai-Tibet  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Models** & **Research Institutes** \\ \hline CESM2 & National Center for Atmospheric Research \\ CESM2-WACM & National Center for Atmospheric Research \\ EC-Earth3-Veg & EC-Earth-Consortium \\ MPI-ESM1-2-HR & Deutsches Klimarechenzentrum \\ BCC-CSM2-MR & Beijing Climate Center \\ \hline \hline \end{tabular}
\end{table}
Table 1: Introduction of models with the same spatial resolution of 100 km.  
plateau. Finally, the spatial value of each year's CUE is obtained by calculating the ratio of annual NPP and GPP of each year from MODIS from 2000 to 2010 for the validation with model-averaging of the same period each Year).