## 2 Materials and Methods
### Satellite-Based Products  
We extracted eight-day MODIS version 6 products, including surface reflectance composite data (MOD09A1, 500 m) [60], land surface temperature (_LST_) products (MOD11A2, 1 km) [61], MODIS LAI/FPAR data (MOD15A2, 500 m) [62], and MODIS GPP (GPP_MOD) products (MOD17A2, 500 m) [32] at the position of the flux tower for the years 2009 to 2011 from NASA EOSDIS Land Processes Distributed Active Archive Center (LP DAAC, [[https://lpdaac.usgs.gov/](https://lpdaac.usgs.gov/)]([https://lpdaac.usgs.gov/](https://lpdaac.usgs.gov/))). To compare the agreement between the GPP_MOD and the previous MODIS version 5 GPP products (GPP_MOD5) [31], we also extracted the contemporaneous GPP_MOD5 products (Figure 1). MODIS GPP products, both GPP_MOD5 and GPP_MOD, were calculated from the MOD17A2 algorithm [31; 32] based on light energy use efficiency (LUE) model [2; 63]. \[GPP\_MOD=\epsilon_{\max}\times f(\text{Tmin})\times f(\text{VPD})\times FPAR \times SWrad\times 0.45 \tag{4}\]  
where \(\epsilon_{max}\) (g C M\({}^{-1}\)) is a default parameter obtained from the Biome Properties Look-Up Table (BPLUT), but is not the same for grassland between GPP_MOD5 (0.68 g C M)\({}^{-1}\)) and GPP_MOD (0.86 g C M\({}^{-1}\)) [2; 31; 63; 32]. Two attenuation scalars (_f_(Tmin) and _f_(VPD)) are simple linear ramp functions of the daily minimum air temperature (Tmin) (Equation (5)) and daytime average VPD (Equation (6)) with a range of 0 to 1 [64]. FPAR is the fraction of absorbed PAR by vegetation canopy that is derived from the MOD15A2 product. Incident shortwave radiation (SWard) are obtained from the NASA Data Assimilation Office (DAO) dataset [65]. \[f(Tmin)=\left\{ \begin{array}{cc}0,&T\min\in(-\infty,T\min\_{\min}]\\ \frac{T\min-T\min\_{min}}{T\min\_{max}-T\min\_{min}},&T\min\in(T\min\_{min},T\min \_{max})\\ 1,&T\min\in[T\min\_{max}+\infty)\end{array} \right\} \tag{5}\]  
\[f(VPD)=\left\{ \begin{array}{cc}0,&VPD\in[VPD\max,+\infty)\\ \frac{VPD\max-VPD}{VPD\max-VPD\min},&VPD\in(VPD\min,VPD\max)\\ 1,&VPD\in(-\infty,VPD\min]\end{array} \right\} \tag{6}\]  
In this alpine meadow, a previous study confirmed GPP_MOD strongly underestimated GPP (about \(-40.58\%\) of GPP_EC) because of the 16.05% underestimation of \(\varepsilon_{\max}\) and 14.70% overestimation of ground FPAR (FPARg) from 2005 to 2007 [40]. Thus, in this study, we also use the ground observations to revise these two parameter inputs of MOD17A2 algorithm for discussing the accuracy of MODIS products from 2009 to 2011, especially the new GPP_MOD. Based on the Beer-Lambert law [66], FPARg can be calculated from the LAlg measurements (Equation (7)). \[FPARg=0.95^{*}(1-\mathrm{e}^{(-k^{*}LAIg)}) \tag{7}\]  
where \(k\) is the light extinction coefficient with a value of 0.5 for herbaceous crops in this study [40,67]. The LAlg is a linear regression conversion between ground LAI measurements and MOD15A2 for consecutive measurements on eight-day time step. \(\varepsilon_{max}\) can be estimated by three approaches in the growing season. One is the MOD17A2 algorithm based on LAIg and GPP_EC measurement data on LAIg measurement days. More precisely, it is the linear regression slope between GPP_EC and multiple multiplication of \(f(\mathrm{Tmin}),f(\mathrm{VPD})\), FPARg and PAR on LAlg measurement days [33,40]. The other two approaches are both unit conversion of the apparent quantum yield (\(\alpha\), \(\mathrm{\SIUnitSymbolMicro mol}\) CO\({}_{2}\)\(\mathrm{\SIUnitSymbolMicro mol}\) photons\({}^{-1}\)) (Equation (8)) based on the relationship between NEE and PAR [33]. \[\varepsilon_{\max}=\lambda^{*}Mc^{*}\alpha \tag{8}\]  
where \(\lambda\) is the conversion ratio with a value of 4.43 because 1 J energy of PAR is equivalent to 4.43 \(\mathrm{\SIUnitSymbolMicro mol}\) quantum [68]. _Mc_ (12 g mol\({}^{-1}\)) is the molar quantity of carbon.