## 4 Discussion
### Trade-Offs between Model Performance and Applicability at a Regional Scale  
The comparisons conducted in this study are based on site-scale observations. However, the model selection at a regional scale needs to consider both the model performance and the availability and accuracy of the input data [27]. More parameters mean more requirements for data input and more in situ data for model calibration, possibly accompanied by worse model performance [27]. Our results showed that the MVPM and VI are the two best-performing models in the northern China grasslands. The MVPM is a typical LUE model. \(\varepsilon_{\text{max}}\) is a key parameter, which is usually represented by a constant for one vegetation type or even an entire eco-region [3; 86; 38]. [PERSON] et al. [124] suggested that the \(\varepsilon_{\text{max}}\) may vary substantially within a vegetation type due to different species compositions and climate conditions. For example, the \(\varepsilon_{\text{max}}\) at the XL site was 1.9 times that of the NM site, although they are  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
\begin{tabular}{c} MVM \textgreater{} MVPM  
only 2 km apart (0.57 vs. 0.30 g C mol\({}^{-1}\) PPFD, respectively). In contrast, the VI model is a typical statistical model that requires in situ data to calibrate the site-specific scalar \(m\) (Equation (6)). Due to the limited in situ data, the parameter \(m\) was usually indicated by a biome-specific constant [3] or estimated by remote sensing products (e.g., \(LST_{\text{an}}\)) [28; 90], which will lead to poor model performance. For example, we found that the mean \(R^{2}\) of the VI decreased significantly, by 19.0% (0.79 vs. 0.64), if using the same \(m\) (estimated from all the observations) for all four EC sites. Therefore, the choice of the MVPM (LUE model) or VI (statistical model) model depends on the accuracy of \(\varepsilon_{\text{max}}\) and the availability of the EC flux data, respectively.  
Further, the varying performance across vegetation subtypes and models confirmed that a single environmental scalar cannot reflect the different responses of vegetation to environmental stresses [3; 17; 33; 34]. This can be further verified by the much-higher explanation ability of multiple variables (76%) than a single factor such as EVI (62%) or LSWI (50%) of the total variance of the observed GPP in the two grassland subtypes (Table 4). Multiple environmental scalars are recommended for future regional applications of satellite-based GPP models, yet caution should be taken regarding the possibility of more uncertainties associated with input environmental variables.  
It should be noted that both the optimal models (MVPM and VI) performed relatively poorly in the temperate steppe (\(R^{2}<0.68\)) and cannot fully account for the effects of extreme drought, which is predicted to occur more frequently in northern China in the future [63; 64]. Improving water stress variables to address drought effects, such as incorporating the drought index that can monitor drought in both arid and humid regions [125], constitutes a valid topic worthy of future efforts. [PERSON] et al. [45] found that model performances can be largely improved by incorporating an estimation of the effects of soil moisture on LUE, particularly during drought years. Other variables and/or the improvements in model structures may also be required due to the complex and nonlinear effects of drought on GPP [9; 126].