## 2 Materials and Methods
### The Satellite-Based Vegetation Photosynthesis Model  
Based on the conceptual partitioning of chlorophyll and non-photosynthetically active vegetation (NPV) within a canopy, [PERSON] _et al._ developed the vegetation photosynthesis model (VPM) for estimation of GPP using the following function ([PERSON] _et al._, 2017):\[GPP=\epsilon_{\rm g}\times FPAR_{\rm chl}\times PAR \tag{4}\]  
where \(FPAR_{\rm chl}\) is the fraction of PAR absorbed by chlorophyll in the canopy, \(\epsilon_{\rm g}\) is the light use efficiency (\(\rm\upmu mol\ CO_{2}/\upmu mol\) photosynthetic photon flux density, PPFD), and PAR is the photosynthetically active radiation (\(\rm\upmu mol\ PPFD\)). \(FPAR_{\rm chl}\) and \(\epsilon_{\rm g}\) are estimated as follows [25; 26; 29]:  
\[FPAR_{\rm chl}=\alpha\times EVI \tag{5}\]  
\[\epsilon_{\rm g}=\epsilon_{0}\times T_{\rm scalar}\times W_{\rm scalar}\times P _{\rm scalar} \tag{6}\]  
\[T_{scalar}=\frac{(T-T_{\rm min})(T-T_{\rm max})}{\left[(T-T_{\rm min})(T-T_{ \rm max})\right]-\left(T-T_{opt}\right)^{2}} \tag{7}\]  
\[W_{scalar}=\frac{1+LSWI}{1+LSWI_{\rm max}} \tag{8}\]  
\[P_{scalar}=\frac{1+LSWI}{2} \tag{9}\]  
where \(\epsilon_{0}\) is the maximum light use efficiency (LUE) (\(\rm\upmu mol\ CO_{2}/\upmu mol\ PPFD\)), and \(T_{\rm scalar}\), \(W_{\rm scalar}\), and \(P_{\rm scalar}\) are the downregulation scalars for the effects of temperature, water, and leaf phenology on LUE, respectively. \(T_{\rm min}\), \(T_{\rm max}\), and \(T_{\rm opt}\) are the minimum, maximum, and optimal temperature for photosynthetic activities, respectively. \(LSWI_{\rm max}\) is the maximum LSWI (land surface water index) over the study period.  
In the VPM model, \(\epsilon_{0}\) is estimated for each type of ecosystem individually. In order to obtain the \(\epsilon_{0}\) values for the alpine wetland, we estimated the nonlinear model between observed NEE and PAR by using the Michaelis-Menten function (Equation (10)), based on data collected during the peak period of vegetation growth in 2008 and 2009. Here, we used 0.53 \(\upmu mol\ CO_{2}/\upmu mol\ PPFD\) as \(\epsilon_{0}\) for 2008 and 2009:  
\[NEE=\frac{\epsilon_{0}\times PAR\times GPP_{\rm max}}{\epsilon_{0}\times PAR+ GPP_{\rm max}}-R_{eco} \tag{10}\]  
where the \(GPP_{\rm max}\) (mg \(\rm CO_{2}\ m^{-2}\cdot s^{-1}\)) is the ecosystem maximum photosynthetic capacity and \(R_{eco}\) is ecosystem respiration. The estimated \(\epsilon_{0}\) value is used as an estimate of the maximum light use efficiency parameter in the VPM model.  
In the calculation of \(T_{\rm scalar}\)[27], \(T_{\rm min}\), \(T_{\rm opt}\), and \(T_{\rm max}\) values vary among vegetation types. For the alpine wetland ecosystem in our study, when air temperature falls below \(T_{\rm min}\), \(T_{\rm scalar}\) is set to zero. We used \(T_{\rm min}\) of 0 \({}^{\circ}\)C, \(T_{\rm opt}\) of 16 \({}^{\circ}\)C, and \(T_{\rm max}\) of 32 \({}^{\circ}\)C, based on the relationship between temperature and photosynthesis over 2008-2009.  
Estimation of site-specific \(LSWI_{\rm max}\) is dependent on the time series of remote sensing data. As a parameter describing water status, \(LSWI_{\rm max}\) varies across years. The maximum LSWI value within the plant-growing season was selected as an estimate of \(LSWI_{\rm max}\)[25; 27; 31]. Based on the analysis of LSWI seasonal dynamics derived from MODIS image data from 2008 to 2009, the \(LSWI_{\rm max}\) value was 0.26 and 0.36 for 2008 and 2009, respectively.  
More details on parameters and functions of the validated VPM model are described in [PERSON] _et al._[29]. By running the VPM model at an eight-day time scale with the validated parameters, vegetation indices derived from the eight-day MODIS surface reflectance product, and site-specific data of air temperature and PAR during 2000-2011, we obtained the GPP data for each year.