## 3 Data and Methods
### Model Calibration and Validation  
We used the subjective optimization [76] to calibrate the most sensitive model parameter, rpleaf (phosphorus resorption coefficients of leaf) by using GPP data from 49 sites of FLUXNET. Available online: [[https://fluxnet.org/data/fluxnet2015-dataset/](https://fluxnet.org/data/fluxnet2015-dataset/)]([https://fluxnet.org/data/fluxnet2015-dataset/](https://fluxnet.org/data/fluxnet2015-dataset/)) (accessed on 21 May 2022) for different biomes. For each site, we controlled other unchanged model parameters, and only increased the parameter value by 5% each time to obtain the GPP model value of model simulation. Since the real range of this parameter was 0.0 to 1, it needs to be tested at least 20 times. When the GPP value of simulation was closest to the observed value, the parameter is regarded as the optimal parameter value of this site. Then the optimal value of the most sensitive parameter for each biome was set as the mean value of all sites optimizations in its biome. The specific information of the rpleaf optimal value setting for each sits and each biome was shown in Table S3. The model validations were based on the three indexes (e.g., formula 18-20), and these indexes were calculated by three variables (GPP, vegetation biomass, SOC) that were selected to verify model performance. In particular, for GPP, observation data was extracted from another 116 global FLUXNET sites. For total biomass, observation data of 933 sites were collected from literatures globally (from Web of Science using the search terms \"biomass\" or \"biomass dataset\") and detail information listed in S6. The observed SOC dataset for model validation was from the Harmonized World Soil Database (HWSD) (version 1.2) of the Food and Agriculture Organization of the United Nations. Available online: [[https://www.foo.org/soils-portal/soil-survey/soil-maps-and-databases/harmonized-world-soil-database-v12/en/](https://www.foo.org/soils-portal/soil-survey/soil-maps-and-databases/harmonized-world-soil-database-v12/en/)]([https://www.foo.org/soils-portal/soil-survey/soil-maps-and-databases/harmonized-world-soil-database-v12/en/](https://www.foo.org/soils-portal/soil-survey/soil-maps-and-databases/harmonized-world-soil-database-v12/en/)) (accessed on 20 April 2022). In the end, data were taken from 75 sites across three biomes: tree, shrubland and grassland. Details about the sites from which data were taken for model validation are provided in Table S3. All simulations for model calibration and validation were at site level. A spin-up run of approximately 100 years using multiyear mean climate data was conducted to achieve an equilibrium state in C pools and then collected climate data were used to make the following simulation for each site. We evaluated model performance using three evaluation indexes. The coefficient of determination (R\({}^{2}\)) was calculated as  
\[\text{R}^{2}=\left[\frac{\sum_{\text{i=1}}^{\text{n}}\left(\text{O}_{\text{i} }-\overline{\text{O}}\right)\left(\text{S}_{\text{i}}-\overline{\text{S}} \right)}{\sqrt{\sum_{\text{i=1}}^{\text{n}}\left(\text{O}_{\text{i}}-\overline {\text{O}}\right)^{2}+\sum_{\text{i=1}}^{\text{n}}\left(\text{S}_{\text{i}}- \overline{\text{S}}\right)^{2}}}\right]^{2} \tag{17}\]  
and the second index of agreement (D) was calculated as  
\[\text{D}=1-\frac{\sum_{\text{i=1}}^{\text{n}}\left(\text{S}_{\text{i}}-\text{ O}_{\text{i}}\right)^{2}}{\sum_{\text{i=1}}^{\text{n}}\left(\left[\text{S}_{ \text{i}}-\overline{\text{O}}\right]+\left|\text{O}_{\text{i}}-\overline{ \text{O}}\right|\right)^{2}} \tag{18}\]where in both cases, n is the number of samples, i means the ordinal numeral of samples, \(\text{S}_{\text{i}}\) represents the simulated results of the model, \(\text{O}_{\text{i}}\) are the observed values of each sites, and \(\overline{\text{O}}\) is the average value of observed values across all sites. D measures the consistency between the model results and observations; it ranges from 0 to 1, and higher values indicate better model performance.