## 3 Methodology  
### NPP Estimation  
#### 3.1.1 Model Description  
This study proposed an alpine vegetation photosynthetic model (AVPM) to estimate the net primary productivity. This model improved the water stressor part of the MOD17 model [11; 69]. The AVPM NPP was calculated using the following equation:  
\[\mathrm{NPP}=\mathrm{GPP}-\mathrm{R_{a}} \tag{13}\]  
where NPP is the net primary productivity (gCm\({}^{-2}\)month\({}^{-1}\)), GPP is the gross primary productivity (gCm\({}^{-2}\)month\({}^{-1}\)), and \(\mathrm{R_{a}}\) is the automatic respiration (gCm\({}^{-2}\)month\({}^{-1}\)). Then, the GPP was estimated based on the LUE theory, suggested by [PERSON] [70], as follows:  
\[\mathrm{GPP}=\mathrm{PAR}\times\mathrm{FPAR}\times 0.45\times\varepsilon \tag{14}\]  
where PAR is the total incident solar radiation (MJ m\({}^{-2}\)month\({}^{-1}\)) and FPAR accounts for the fraction intercepted by PAR (0-1). The constant 0.45 represents that approximately half of the PAR was useful for photosynthesis and \(\varepsilon\) is the radiation efficiency coefficient (gC/MJ). PAR is calculated as being equal to the solar shortwave radiation from the sun. FPAR measures the available radiation in the photosynthetically active wavelengths that are absorbed by the plant canopy. FPAR is calculated using the following equation [71]:  
\[\mathrm{FPAR}=\mathrm{APAR}/\mathrm{PAR}\approx\mathrm{NDVI} \tag{15}\]  
where PAR is the total incident solar radiation, APAR is the activated PAR, and NDVI is the normalized difference vegetation index, which directly quantifies absorbed FPAR (ranging from 0 to 1). Temperature and water are two indicators that attenuate \(\varepsilon_{\mathrm{max}}\) to \(\varepsilon\) using the following equation:  
\[\varepsilon=\varepsilon_{\mathrm{max}}\times\mathrm{f(T)}\times\mathrm{f(W)} \tag{16}\]  
where \(\mathrm{f(T)}\) and \(\mathrm{f(W)}\) represent the ecophysiological constraints of temperature and soil moisture on \(\varepsilon_{\mathrm{max}}\). The equation of \(\mathrm{f(W)}\) refers to Section 3.1.2. The \(\mathrm{f(T)}\) is a simple linear function with the temperature [71] as follows:  
\[\mathrm{f(T)}=\left\{ \begin{array}{ll}0,&\quad\mathrm{if\ T_{min}\leq T_{ min}}\\ \frac{\mathrm{T_{min}}-\mathrm{T_{min}}}{T_{\mathrm{max}}-\mathrm{T_{min}}},& \quad\mathrm{if\ T_{max}>T_{min}>T_{min}}\\ 1,&\quad\mathrm{if\ T_{min}\geq T_{min}}\end{array} \right. \tag{17}\]  
where \(\mathrm{T_{min}}\) is the minimum temperature, \(\mathrm{T_{mmax}}\) is the maximum temperature, at which \(\varepsilon=0.0\), and \(\mathrm{T_{min}}\) is the minimum temperature, at which \(\varepsilon=\varepsilon_{\mathrm{max}}\). The light use efficiency (LUE) is the ratio of the latent chemical energy contained in the dry matter produced to the photosynthetic active radiant energy per unit area within the same period [72]. MOD17 considers 11 different vegetation types and defines their LUE as a range of 0.604-1.259 gC/MJ. For more detailed parameters, refer to MOD17 [71]. Automatic respiration includes maintenance respiration and growth respiration. The former relates to the maintenance respiration coefficient of each tissue and organ [73; 74], and the latter depends on the amount and tissue type of plant tissue [73; 74; 75]. The equation is as follows [71]:  
\[\mathrm{R_{a}}=\sum_{i=1}^{N}R_{m,\ i}+R_{g} \tag{18}\]  
where \(\mathrm{R_{a}}\) represents the auto respiration, \(\mathrm{R_{m,\ i}}\) is the maintenance respiration, \(\mathrm{i}\) is an index for the different plant components, and \(\mathrm{R_{g}}\) is the growth respiration. The different allocation patterns between the ecosystems are likely to modify the maintenance respiration coefficient of the whole plant; therefore, it seems better to consider a different maintenance coefficient for each organ [73; 74].