## 2 Materials and Methods
### GPP Model Based on VIs and GCC  
The LUE model was used in study to estimate GPP, as follows:  
\[\mathrm{GPP_{model}}=\varepsilon\times\mathrm{FPAR}\times\mathrm{PAR} \tag{7}\]  
\[\varepsilon=\varepsilon_{\mathrm{max}}\times\mathrm{f(Tmin)}\times\mathrm{f( VPD)} \tag{8}\]  
\[\mathrm{FPAR}=\alpha\times\mathrm{NDVI} \tag{9}\]  
\[\mathrm{FPAR}=\alpha\times\mathrm{EVI} \tag{10}\]  
\[\mathrm{FPAR}=\alpha\times\mathrm{CI_{norm}} \tag{11}\]  
where \(\varepsilon\) is light use efficiency in photosynthesis (g C/MJ) and PAR (MJ/d/m\({}^{2}\)) is photosynthetically active radiation. PAR = n \(\times\) RG. n is the proportion of PAR in the global total solar radiation and was not a fixed value. For calculations, n = 0.45 was used. FPAR is the fraction of absorbed photosynthetically active radiation by vegetation. In this study, FPAR was estimated from the normalized color index (CInorm) of GCC, NDVI and EVI by Equations (9)-(11). \(\alpha\) is the coefficient constant and is assumed to be 1.0 [14]. The value of \(\varepsilon_{\mathrm{max}}\) was set to 1.6 g C\(\cdot\)m\({}^{-2}\cdot\)day\({}^{-1}\cdot\)MJ\({}^{-1}\) according to literature for alpine meadow [39].  
Figure 5: Changes of ROI_GCC1 (**a**,**b**) and ROI_GCC2 (**c**,**d**) with GPP from eddy covariance, time from (**a**) 15 April to 16 December, 2017, (**b**) from 5 January to 31 December 2018, (**c**) from 15 April to 16 December 2017, and (**d**) from 5 Januaryto 31 December 2018.  
f(T\({}_{\text{min}}\)) and f(VPD) are simple linear piecewise slope functions of daily minimum temperature (T\({}_{\text{min}}\)) and daily average VPD [42]. f(T\({}_{\text{min}}\)) and f(VPD) reflect the environmental stress on vegetation photosynthesis and are expressed as:  
\[\text{f(Tmin)}=\left\{\begin{array}{ll}0,&\text{Tmin}<\text{Tmin}_{\text{min} }\\ \frac{\text{Tmin-Tmin}_{\text{min}}}{\text{Tmin}_{\text{max}}-\text{Tmin}_{\text {min}}},&\text{Tmin}_{\text{min}}<\text{Tmin}<\text{Tmin}_{\text{max}}\\ 1,&\text{Tmin}>\text{Tmin}_{\text{max}}\end{array}\right. \tag{12}\]  
\[\text{f(VPD)}=\left\{\begin{array}{ll}0,&\text{VPD}>\text{VPD}_{\text{max}} \\ \frac{\text{VPD}_{\text{max}}-\text{VPD}}{\text{VPD}_{\text{max}}-\text{VPD}_{ \text{min}}},&\text{VPD}_{\text{min}}<\text{VPD}<\text{VPD}_{\text{max}}\\ 1,&\text{VPD}<\text{VPD}_{\text{min}}\end{array}\right. \tag{13}\]  
where VPD\({}_{\text{max}}\), VPD\({}_{\text{min}}\), Tmin\({}_{\text{max}}\), and Tmin\({}_{\text{min}}\) are model parameters and the values were from the default parameters for grass in the BPLUT table [43].  
The GCC values of RGB color photos of the AR station from 2017 to 2018 were calculated in Python 3.5, and the CI\({}_{\text{norm}}\) index was calculated with the GCC values (Equation (14)). The CI\({}_{\text{max}}\) and CI\({}_{\text{min}}\) were the maximum and minimum value of GCC in each year, respectively. The GPPs based on CI\({}_{\text{norm}}\) and the remote sensing VIs was conducted by Equations (15)-(17), and the equations are given by:  
\[\text{CI}_{\text{norm}}=\frac{\text{CI}-\text{CI}_{\text{min}}}{\text{CI}_{ \text{max}}-\text{CI}_{\text{min}}} \tag{14}\]  
\[\text{GPP}_{\text{model}}=\varepsilon\times\text{CI}_{\text{norm}}\times \text{PAR} \tag{15}\]  
\[\text{GPP}_{\text{model}}=\varepsilon\times\text{NDVI}\times\text{PAR} \tag{16}\]  
\[\text{GPP}_{\text{model}}=\varepsilon\times\text{EVI}\times\text{PAR} \tag{17}\]