## 2 Method and Data  
### Models  
#### 2.1.1 Globem-Cevsa  
GLOPEM-CEVSA represents a coupling of two independently developed models (GLO-PEM and CEVSA), and describes the processes and mechanisms of an ecosystem based on remotely sensed vegetation indices and the simulation of the physiological processes (Figure 1) [9,32]. Founded on the concept of production efficiency, the GLO-PEM model uses satellite remote sensing data to estimate GPP and NPP [22, 38, 39]. The GLO-PEM approach has previously been applied successfully at both the regional and global scale [22, 40, 41, 42, 43]. The CEVSA model is an ecosystem process and mechanism model developed to describe the carbon cycles of terrestrial ecosystems. CEVSA has been applied to simulate net ecosystem productivity (NEP) at the regional and global scale [44, 45, 46]. The combination of these models, the GLOPEM-CEVSA model, can thus simulate GPP, NPP, and NEP. Here, we mainly focus on the evaluation of the GPP product as it is impacted by FPAR data from different sources.  
According to production efficiency logic, we estimated GPP by assuming a linear relationship between the incoming photosynthetically active radiation (PAR), the fraction of PAR absorbed by the vegetation (FPAR), the potential conversion efficiency or carbon yield of absorbed energy (\(\varepsilon^{*}\)), and the reduction of \(\varepsilon^{*}\) caused by environmental factors (\(\sigma\)) (Equation (1)) [9, 22, 43].  
\[GPP=PAR\times FPAR\times\varepsilon^{*}\times\sigma \tag{1}\]  
GLO-PEM and the newly developed GLOPEM-CEVSA model differ from other production efficiency models in that these models do not assign a fixed value for potential light use efficiency for each vegetation type. Instead, they are based on quantum yield that is affected by, among other factors, photosynthetic pathway, temperature, and the CO\({}_{2}\)/O\({}_{2}\) specificity ratio [22, 43, 47], which are given in Appendix. We estimated \(\sigma\) using critical environmental factors known to impact stomatal conductance [43], according to the below equation:  
Figure 1: Framework of the GLOPEM-CEVSA model. GLOPEM-CEVSA represents the coupling of the GLObal Production Efficiency Model (GLO-PEM, shown by solid lines) with the Carbon Exchange between Vegetation, Soil and Atmosphere (CEVSA) model (shown by dashed lines). A detailed description of this model is available in [9, 32].  
\[\sigma=f(T)\times f(\delta_{q})\times f(\delta_{\theta}) \tag{2}\]  
where _f(T)_, _f_(\(\delta_{q}\)) and _f_(\(\delta_{\theta}\)), respectively, represent the effects of air temperature (_T_), specific humidity deficit (\(\delta_{q}\)), and soil moisture (\(\delta_{\theta}\)) on stomatal conductance [43]. The temperature effect, _f_(_T_), reaches the maximum (1.0) at the optimum temperature and tapers off for warmer or cooler temperatures [48]:  
\[f(T)=\frac{(T-T_{min})(T-T_{max})}{(T-T_{max})(T-T_{max})(T-T_{opt})^{2}} \tag{3}\]  
where \(T\) is air temperature ( \(\mathrm{\SIUnitSymbolCelsius}\)) and _Tmin_, _Topt_ and _Tmax_ are respectively the minimum, optimum and maximum temperatures ( \(\mathrm{\SIUnitSymbolCelsius}\)).  
\[f(\delta_{q})=\begin{cases}1-0.05\delta_{q}&0<\delta_{q}\leq 15\\ 0.25&\delta_{q}>15\end{cases} \tag{4a}\] \[\delta_{q}=\mathrm{Qw}(T)-q \tag{4b}\]  
where \(\delta_{q}\) is the specific humidity deficit (\(\mathrm{g}\mathrm{g}^{-1}\)), \(\mathrm{Qw}(T)\) is the saturated specific humidity at the air temperature, and \(q\) is the specific humidity of the air. The effect of soil moisture is given as:  
\[f(\delta_{\theta})=1-\exp(0.081(\delta_{\theta}-83.03) \tag{5}\]  
where \(\delta_{\theta}\) is the soil moisture deficit (mm) in the top 1.0 m of soil. The soil moisture deficit is defined as the difference between saturated water content and actual water content, which is calculated with the algorithms described in [21].