## 2 Materials and Methods
### Methods
#### 2.3.2 Descriptions of GPP Models  
The CASA model is a widely recognized LUE model for its capability to downregulate photosynthetic efficiency in response to different vegetation, soil and climate conditions, and intercept solar radiation [7; 40; 41]. The CASA model was proposed by [PERSON] [41]. CASA model-based GPP was estimated monthly and annually under the following equation (Equation (1)):  
\[GPP=NPP/\sigma \tag{1}\]  
\[NPP_{(x,t)}=APAR_{(x,t)}\times\varepsilon_{(x,t)} \tag{2}\]  
where \(GPP\) is gross primary productivity (gC\(\cdot\)m\({}^{-2}\cdot\)timescale\({}^{-1}\)), \(t\) is timescale (monthly and yearly), and \(x\) is grid position [42]. \(NPP\) is net primary productivity (gC\(\cdot\)m\({}^{-2}\cdot\)timescale\({}^{-1}\)); \(\sigma\) is the ratio associated with different dominated biomes (Table 2). Figure 2: Spatial and patterns distribution of different biomes and other land covers and their related coverage extents in percentages and square kilometre unities along the GLR-SSA. \(APAR_{(x,t)}\) is absorbed photosynthetically active radiation measured in MJ\(\cdot\)m\({}^{-2}\) and \(\varepsilon_{(x,t)}\) is light-use efficient (gC\(\cdot\)M)\({}^{-1}\)) [7]. \(APAR_{(x,t)}\) is determined in function with both solar radiation and the characteristics of the plant canopy and is calculated by this equation (Equation (3)). \[APAR_{(x,t)}=0.5\times SoR_{(x,t)}\times fAPAR_{(x,t)} \tag{3}\]  
\(SoR_{(x,t)}\) stands for solar radiation (in MJ\(\cdot\)m\({}^{-2}\)-timescale\({}^{-1}\)); \(fAPAR_{(x,t)}\) is the fraction of APAR absorbed from plant canopy; and 0.5 indicates the proportion of radiation that can be absorbed by plants in range of 0.38-0.71 \(\upmu\)m electromagnetic spectrum [7]. Therefore, \(fAPAR_{(x,t)}\) was estimated based on the variations of NDVI [47] as the following equation (Equation (4)):  
\[fAPAR_{(x,t)}=\frac{\left(NDVI_{(x,t)}-NDVI_{i,\;min}\right)\times\left(fAPAR _{max}-fAPAR_{min}\right)}{NDVI_{i,max}-NDVI_{i,\;min}}+fAPAR_{min} \tag{4}\]  
where \(NDVI_{(i,\;min)}\) and \(NDVI_{(i,\;max)}\) stand for minimum and maximum of vegetation type assigned 5% and 95% in the NDVI histogram; and \(fAPAR_{max}-fAPAR_{min}\) are constant, with values 0.95 and 0.001, respectively [7]. \(\varepsilon\) is a function of climate factors such as temperature and vapor pressure deficit [48] and was calculated based on the following equation (Equation (5)). \[\varepsilon_{(x,t)}=T_{\tau 1(x,t)}\times T_{\tau 2(x,t)}\times w_{\tau(x,t)} \times\varepsilon_{max} \tag{5}\]  
where \(T_{\tau 1}\), \(T_{\tau 2}\), \(w_{\tau}\) and \(\varepsilon_{max}\) indicate the effects of low and high temperature, soil moisture and the maximum light-used applied on LUE. \(\varepsilon_{max}\) values in gC/mol\(\cdot\)MJ\({}^{-1}\) are provided in Table 2.  
The VPM Model  
The vegetation photosynthetic model (VPM) is one of the satellite-based production efficiency models (PEMs) that estimates GPP as the product of light absorbed by chlorophyll of the vegetation (\(APAR_{Chl}\)) or vegetation canopy (\(APAR_{Cmopy}\)) and efficiency \(\varepsilon_{\rm g}\) to convert the absorbed energy to carbon fixed by plants through photosynthesis [17; 37]. In this study, we have estimated GPP by considering these two above-stated vegetation phenological processes effects through the following equations (Equations (6) and (7)). \[GPP_{VPM}Chl=APAR_{Chl}\times\varepsilon_{g} \tag{6}\]  
\[GPP_{VPM}Canopy=APAR_{Cmopy}\times\varepsilon_{g} \tag{7}\]