## 2 Materials and Methods
### Research Method
#### 2.3.1. Estimation of NPP Based on the CASA Model  
In this study, the evaluation of NPP based on the CASA model was completed on the GEE platform. The CASA model, which is a satellite-based NPP model, is based on the theory of _LUE_. It uses absorbed photosynthetically active radiation (_APAR_) and _LUE_ to estimate _NPP_ at the time step of a month [31; 68]. The main CASA equation is:  
\[NPP(x,t)=APAR(x,t)\times LUE(x,t) \tag{1}\]  
where \(NPP(x,t)\), \(APAR(x,t)\), and \(LUE(x,t)\) are the _NPP_, \(APAR\), and \(LUE\) at grid position \(x\) in month \(t\), respectively. The units of the first two parameters are gC\(\cdot\)m\({}^{-2}\cdot\)month\({}^{-1}\) and MJ\(\cdot\)m\({}^{-2}\cdot\)month\({}^{-1}\), respectively. _APAR_ is determined jointly by the total solar radiation and the characteristics of the vegetation itself, and can be calculated as:  
\[APAR(x,t)=0.5\times SOL(x,t)\times FPAR(x,t) \tag{2}\]  
where the constant 0.5 is the proportion of solar radiation which can be absorbed by plants (i.e., 0.38-0.71 \(\mu\)m). \(SOL(x,t)\) is the total surface solar radiation, which can be estimated by the relationship between the sunshine duration and solar radiation at grid position \(x\) in month \(t\) (unit: MJ\(\cdot\)m\({}^{-2}\cdot\)month\({}^{-1}\)). For details of the calculation method for SOL, we refer the reader to [PERSON] et al. [69] and [PERSON] et al. [70]. \(FPAR(x,t)\) is the fraction of APAR absorbed by the plant canopy at grid position \(x\) in month \(t\), which has a good linear correlation with NDVI [71; 72]. The formula for FPAR is:  
\[FPAR(x,t)=\frac{NDVI(x,t)-NDVI_{min}}{NDVI_{max}-NDVI_{min}}\times(FPAR_{max}- FPAR_{min})+FPAR_{min} \tag{3}\]  
where \(NDVI(x,t)\) is the NDVI value at grid position \(x\) in month \(t\). \(NDVI_{max}\) and \(NDVI_{min}\) represent the maximum and minimum NDVI values of grassland, respectively. To reduce  
Figure 2. The flowchart of CASA model and NPP analysis methods in this study.  
the influence of extreme values, we used 95% and 5% in the NDVI histogram as the maximum and minimum of each vegetation type. \(FPAR_{max}\) and \(FPAR_{min}\) are constants, with values of 0.001 and 0.95, respectively.  
In real conditions, the LUE is not only determined by the vegetation itself, but also by the influence of environmental factors, such as temperature, moisture, and other factors [68]. The formula for LUE is:  
\[LUE(x,t)=T_{c1}(x,t)\times T_{c2}(x,t)\times W_{\epsilon}(x,t)\times LUE_{ max} \tag{4}\]  
where \(T_{c1}(x,t)\) and \(T_{c2}(x,t)\) are the temperature stress coefficients to depress the LUE, which can be derived by the optimum temperature and the temperature difference between the monthly temperature and the optimum temperature at grid position \(x\) in month \(t\). \(W_{\epsilon}(x,t)\) is the moisture stress coefficient at grid position \(x\) in month \(t\), which can be calculated by the precipitation and temperature data [31; 68]. \(LUE_{max}\) is the maximum LUE of grassland under ideal environmental conditions (unit: gC\(\cdot\)MJ\({}^{-1}\)). According to [PERSON] et al. [72], we set 0.589 as the \(LUE_{max}\) of grassland under a classification accuracy of 85%.