## 2 Materials and Methods
### Model Overview
#### 2.1.1 The Vegetation Photosynthesis Model (VPM)
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **Type** & **fPAR** & **PAR** & **LUEteg** & **Calibrated** & & & \\  & & & & & & & & **Parameters** & **Input Data** \\ \hline Vegetation photosynthesis model (VPM) [25] & LUE & EVI & PAR & \(\varepsilon_{max}\)-\(\gamma\)-\(\gamma\)-\(\varepsilon_{max}\), \(T_{min}\), \(T_{opt}\), \(T_{max}\) & EVI, PAR, Ta, LSWI \\ Modified VPM (MVPM) [9] & LUE & EVI & PAR & \(\varepsilon_{max}\)-\(\gamma\)-\(\gamma\)-\(\varepsilon_{min}\), \(T_{opt}\), \(T_{max}\) & EVI, PAR, Ta, VTD, \\  & & & & & & & & \(\varepsilon_{max}\)-\(\gamma\)-\(\varepsilon_{min}\), \\ MODIS-GPP algorithm (MODES-GPP) [66] & LUE & MODIS-GPP & PAR & \(\varepsilon_{max}\)-\(\gamma\)-\(\gamma\)-\(\varepsilon_{min}\) & \(T_{min}\)-\(\gamma\)-\(\varepsilon_{min}\), VPD\({}_{max}\), & & & \\  & & & & & & & & \\ Temperature and premes model (TG) [28] & Statistical & /EVI & — & /(1) & \(m\) & EVI, TST \\  & Greemnes and radiation model (GK) [29] & Statistical & EVI & PAR & — & & & EVI, PAR \\ Vegetation index model (VVI) [30] & Statistical & EVI & PAR & EVI & \(m\) & EVI, PAR \\ Alpine vegetation model (AVM) [30] & Statistical & /EVI & — & /(1) & \(m\), \(T_{min}\)-\(T_{max}\) & EVI, Ta \\ Photosynthetic capacity model (PCM) [30] & Statistical & /EVI & — & /(1)-\(\gamma\)-\(\gamma\)-\(\varepsilon_{min}\)-\(\gamma\)-\(\varepsilon_{min}\) & EVI, Ta, LSWI \\ \hline \hline \end{tabular}  
* PAR, incident photosynthetically active radiation; fPAR, the fraction of PAR absorbed by vegetation canopy; EVI, enhanced vegetation index; \(\varepsilon_{\max}\), potential LUE without environmental stress; \(ft\), effects of air temperature on \(\varepsilon_{\max}\); _fv_, effects of water availability on \(\varepsilon_{\max}\); \(T_{\min}\), \(T_{\text{opt}}\), and \(T_{\max}\) represent minimum, optimum, and maximum air temperatures for photosynthetic activities, respectively. Ta, air temperature; LSWI, satellite-derived land surface water index; VPD, vapor pressure deficit; \(T_{min}\), the daily minimum temperature at which \(\varepsilon_{g}=\varepsilon_{\max}\); \(T_{min}\), the daily minimum temperature at which \(\varepsilon_{g}=0\); \(VPD_{max}\), the daylight average VPD at which \(\varepsilon_{g}=\varepsilon_{\max}\); \(VPD_{min}\), the daylight average VPD at which \(\varepsilon_{g}=0\); \(m\) is a scalar determined by the model calibration; \(SW_{\text{rad}}\), the incident shortwave radiation; LST, land surface temperature; \(\text{LST}_{\text{nn}}\), mean annual nighttime LST.  
\end{table} 
Table 1: Model structures and parameters of the eight satellite-based gross primary production (GPP) models. LUE, light use efficiency. the growing season [25; 26], and \(P_{s}\) indicates the phenology effect on \(\varepsilon_{\text{max}}\)[69]. In this study, \(P_{s}\) is set to 1.0 because the grassland canopies have new leaves emerging throughout the growing season [4]. LSWI is calculated via near-infrared (NIR, 841-875 nm) and shortwave infrared (SWIR, 1628-1652 nm) bands of MODIS images as follows:  
\[LSWI\ =\ \frac{\rho_{NIR}-\rho_{SWIR}}{\rho_{NIR}+\rho_{SWIR}} \tag{1g}\]