## 5 Discussion  
### Model Sensitivity Analysis  
Parameterization of C-N-P process models remains a challenge [53; 54; 57], so we made the task more tractable by conducting sensitivity analysis to identify the most influential parameters and we used hypothetical values from previous studies (Figure 6a) [53; 54]. In this way, we were able to identify rpleaf as more influential than other model parameters listed in Table 1, which is consistent with a meta-analysis describing direct feedback of P on photosynthesis [71]. Then, for the model calibration, we divided all 49 sites into 5 different biomes. For each biome, the optimal rpleaf value was further determined (detailed values are in Table S3). The rpleaf parameter values of each biome were found to be spatially heterogeneous. For example, average rpleaf in forest was 0.61 which was larger than the average value (0.49) of grasslands and shrublands. GPP simulated by TRILEX-CNP was most sensitive to precipitation and temperature (Figure 6b, Table S2), and pleaf was sensitive to temperature (Figures 2 and 6b). In general, both responses of GPP and pleaf to precipitation show a great positive correlation. The increase in GPP with increasing precipitation at most sites is consistent with results of in six larch forest sites in East Asia, based on the process-based terrestrial biosphere model BIOME-BGC [77]. A positive relationship is consistent with previous modeling studies based on TRIPLEX [64] and TRIPLEX-GHG [78]. The relationship between GPP simulated with P cycle and mean annual temperature was negative for most tropical forest sites, but positive at most boreal forest and temperate forest sites, in which the positive relationship is consistent with TRIPLEX-GHG [78]. Warming eliminates the control of P availability on GPP in the typical alpine dry meadow [79]. As with GPP, pleaf as a variable of plant phosphorus increased with precipitation in most biomes examined, except the two variables correlated negatively in evergreen needleleaf forest and grassland, as reported for desert ecosystems in northwest China [80]. It is also consistent with other models: temperature explained as much as 37.7% of the variation in annual GPP across northern Eurasia, based on the light-use-efficiency-based model [81; 82]. In our study, pleaf decreased with increasing temperature across various biomes, consistent with previous work [83]. Similarly, senesced-leaf P concentration was found  
Figure 6: Taylor diagram assessing the sensitivity of (**a**) GPP to variations in model parameters, (**b**) GPP to meteorological factors and (**c**) amount of leaf phosphorus to meteorological factors. In Figure 6a showed the quality of observed GPP and the simulated GPP by all model parameters that were listed in Table 1. 1.5* parameter = +50% and 0.5* parameter = \(-\)50% in (**a**), while in (**b**), 0.8* factor represents meteorological factor decreased 20% to simulate GPP and 1.2* factor represents meteorological factor increased 20%; and the same meanings of legend in Figure 6c but for pleaf simulations, near-surface temperature was varied by \(\pm\)2 \({}^{\circ}\)C, indicated respectively as tmp \(-\)2 and tmp +2 \({}^{\circ}\)C.  
to decrease with increasing cumulative temperature in a larch forest in northeast China across an entire growing season [84]. leaf P decreased with increasing temperature as one approached the equator [80; 85; 86]. Changes in cloudiness of \(\pm\)20% did not significantly affect GPP in most biomes in our study. Studies have given divergent results about the potential relationship between cloud cover and GPP. Some studies have reported that increases in cloud cover and the corresponding change in radiation fraction can enhance ecosystem productivity in temperate broadleaf forests in North America [87] and northwestern China [88]. In some tropical savannas, GPP has been shown to peak when cloud cover was minimal or absent [89]. Tropical forests show strong responses to cloudiness [90].