## 4 Discussion
### Varying Performances of the Eight Satellite-Based GPP Models in the Temperate Steppe  
We found large disparities in performance across models in the temperate steppe, agreeing well with previous findings [9; 17; 18; 37; 38]. The mean soil water content (0.12 m\({}^{3}\) m\({}^{-3}\)) was close to the wilting point (0.05-0.07 m\({}^{3}\) m\({}^{-3}\)) during the growing season, confirming the dominant role of water stress on photosynthesis in the temperate steppe [58; 59]. The relatively better performance of the MVPM and VI can be attributed to their better representation of moisture conditions than the other models [9]. The water stress in the MVPM was represented by both VPD and LSWI, reflecting atmospheric water content [9; 97; 98] and leaf water content [25], respectively. The model performance of the MVPM should therefore be better than that of the LUE models using only LSWI (VPM) or VPD  
Figure 8: The \(R^{2}\) of (**a**) GPP\({}_{\_}\)tower vs. fPAR, (**b**) GPP\({}_{\_}\)tower vs. LUE for the three LUE models and (**c**) GPP\({}_{\_}\)tower vs. multiplication of environmental factors for the five statistical models in the temperate steppe, alpine shrub meadow, and alpine swamp meadow (\(p<0.01\)). The \(R^{2}\) value between the GPP\({}_{\_}\)tower and LUE for MODIS-GPP was not calculated due to the unavailability of the LUE data used by the model. The multiplication of environmental factors for the TG, GR, VI, AVM, and PCM are EVI \(\times\) Scaled\({}_{\_}\)LST, EVI \(\times\) PAR, EVI \(\times\) EVI \(\times\) PAR, EVI \(\times\) Ta, and EVI \(\times\) LSWI, respectively. (MODIS-GPP). For example, the mean value of the water stress scalar in the VPM was 29.4% higher than in the MVPM (0.82 vs. 0.58, respectively), contributing to the overestimation of the modeled GPP by the VPM from 2004 to 2011 (Table 3 and Figure 7a). The water stress in the VI model was represented by the EVI, which was widely documented as the most comprehensive indicator of photosynthetic capacity [(39; 111)]. It thus performed better than the other statistical models using LST (TG), air temperature (AVM), or LSWI (PCM). For instance, the correlation between the observed GPP and the multiplication of environmental factors was also higher in the VI model than in the other four statistical models by 7.8%-22.1% (Figure 8). Similar to previous studies in grassland and agriculture ecosystems [(88; 18; 94); 18), our results indicated that these satellite-based GPP models do not capture all the effects of frequent extreme drought events on vegetation growth in the temperate steppe. The poor model performances in drought years may be due to their failure to address water stress (as discussed above) and the exacerbated effects of severe water stress (62; 112). The interannual variability of grassland carbon flux may be generally caused by both abiotic factors (climate) and biotic factors (ecosystem responses) [(113; 114)]. Severe drought events can amplify ecosystem responses to climate [(114)]. However, without considering the interrelated physiological and ecological processes, these parametric satellite-based GPP models tend to neglect the effects of ecosystem responses on GPP during drought years [(35; 36)], which can be partially proven by the lower reduction rates of the fPAR (i.e., EVI) and water stress indicators (i.e., LSWI, VPD, and EVI) than the GPP_tower for the two best-performing models (MVPM and VI) during drought years (Figure 4a,b and Figure 5a,b). Worse still, the late response of the vegetation indices to drought-related changes in photosynthesis [(100)] may lead to an overestimation of the modeled GPP during the periods after the drought events (Figure 5). Consequently, the GPP was clearly overestimated even by these two better models during drought years (Table 3 and Figure 7a). The overestimation would be further exaggerated if the models were calibrated using the normal-year data only, as in previous efforts [(25; 8; 29)].