## 2 Study Region and Methodology
### Methodology
#### 2.2.2 NPP Estimated by the CASA Model  
The CASA model was a process-based remote sensing model driven by the global climate, radiation, soil, and vegetation index datasets. The model was not only suitable for simulating potential vegetation distribution and estimating NPP change but also appropriate for analyzing the relationship between them [17]. In this research, the CASA model proposed by [PERSON] et al. [28] was adopted. The vegetation NPP was mainly determined by the absorbed photosynthetically active radiation (APAR, MJ/m\({}^{2}\)) and the light energy utilization efficiency (E, gC/MJ), which were as follows:  
\[NPP(x,t)=APAR(x,t)\cdot E(x,\ t) \tag{1}\]  
\[APAR(x,t)=0.5\cdot SOL(x,t)\cdot FPAR(x,\ t) \tag{2}\]  
\[E(x,t)=T_{E1}(x,t)\cdot T_{E2}(x,t)\cdot W_{E}(x,t)\cdot E_{max} \tag{3}\]  
\[FPAR(x,\ t)=min\{[SR(x,t)-SR_{min}]/(SR_{max}-SR_{min}),0.95\} \tag{4}\]  
\[SR(x,t)=[1+NDVI(x,t)]/[1-NDVI(x,t)] \tag{5}\]  
\[T_{E1}(x,t)=0.8+0.02\cdot T_{opt}(x)-0.0005\cdot\left[T_{opt}(x)\right]^{2} \tag{6}\]  
\[T_{E2}(x,t)=\frac{1.184}{1+\text{e}^{0.2\cdot[T_{opt}(x)-10-T(x,t)]}}\cdot \frac{1}{1+\text{e}^{0.3\cdot[-T_{opt}(x)-10+T(x,t)]}} \tag{7}\]  
\[W_{E}(x,t)=0.5+0.5\cdot ET(x,t)/ET_{p}(x,t) \tag{8}\]  
where \(x\), \(t\) represent the pixel and month, respectively; \(SOL(x,t)\) represents the total solar radiation of pixel \(x\) in \(t\) month obtained from meteorological data; \(FPAR\) represents the fraction of photosynthetically active radiation, defining a linear function of \(NDVI\); \(SR\), transformation of \(NDVI\), represents the simple ratio, and the value of \(SR_{max}\) is determined by vegetation type and is related to \(SR\) when all downwelling solar radiation is intercepted [15], while \(SR_{min}\) represents the \(SR\) of unvegetated land areas remaining at 1.08 [26]; \(T_{opt}(x,t)\) (\({}^{\circ}\)C) represents the optimum temperature for vegetation growth during the month of \(NDVI_{max}\) at a certain extent; \(T_{E1}(x,t)\) (\({}^{\circ}\)C) and \(T_{E2}(x,t)\) (\({}^{\circ}\)C) denote the stress function of low temperature and high temperature to light energy utilization, respectively, among which \(T_{E1}(x,t)\) means the limitation of photosynthesis caused by plants' biochemical effects at high and low temperatures, while \(T_{E2}(x,t)\) shows the decreasing trend of vegetation light energy utilization efficiency from \(T_{opt}\) to critical temperature; \(T(x,t)\) is the mean temperature of pixel \(x\) in \(t\) month; \(W_{E}(x,t)\) denotes the water stress coefficient varying from 0.5 to 1 that reflects the effect of available water conditions on light energy utilization efficiency (\(E\)); \(ET\) (mm) and \(ET_{p}\) (mm) represent estimated evapotranspiration and potential evapotranspiration obtained from MYD16A2 that are resampled into 1 km spatial resolution; \(E_{max}\) (gC/MJ) means the largest light energy utilization efficiency under ideal conditions proposed by [PERSON] et al. [29]. As Southwest China is in the high cold-altitude zone, the relatively recognized data (Table 1) obtained by [PERSON] et al. [26] were selected to better reflect the environmental conditions in the study region.