## 3 Methodology
### Developing GLOPEM Model and CEVSA Model : GLOPEM-CEVSA Model  
GLOPEM-CEVSA represents a coupling of two independently developed models (GLOPEM and CEVSA), which describes the processes and mechanisms of an ecosystem based on remotely sensed vegetation indices (Figure 2, Table 2). In this model, the autophagic respiration simulation is based on plant physiological and ecological processes. The GLOPEM-CEVSA model reflects the vegetation growth process. By using the spatially continuous remote sensing data, the spatial heterogeneity of the ecosystem is considered in the model, which may improve the accuracy of NPP simulation [16]. The most important feature of GLOPEM-CEVSA model is fPAR which could be retrieved by using remote sensing data to realize regional carbon flux simulation. In this paper, we improved the GLOPEM-CEVSA model, which uses MODIS atmosphere and land parameters to estimate model parameter fPAR and regional NPP. The model is based on a simplification of general radiation transfer equations [26]. The NDVI and the NDVI-derived Simple Ratio (SR) were used to estimate fPAR, which integrated fPAR\({}_{\mathrm{NDTVI}}\) model and fPAR\({}_{\mathrm{SR}}\) would provide an improved estimate [27]. The vegetation classification accuracy is taken into account in the simulation of fPAR, which highlights the difference in photosynthetically active radiation absorption of different vegetation types. Meanwhile, the differences among water vapor pressure, PAR, air temperature, the concentration of \(\mathrm{CO_{2}}\), and soil moisture are taken into account in the light efficiency model [28; 29]. This approach can reflect the physiological and ecological processes of vegetation. \[\mathrm{GPP}=\mathrm{PAR}\times\mathrm{FPAR}\times\mathrm{LUE} \tag{13}\]  
\[\mathrm{LUE}=\mathrm{PLUE}[\mathrm{S}(\mathrm{VPD})\cdot\mathrm{S}(\mathrm{PAR })\cdot\mathrm{S}(\mathrm{Ta})\cdot\mathrm{S}(\mathrm{CO_{2}})\cdot\mathrm{S}( \mathrm{SW})] \tag{14}\]  
\[\mathrm{NPP}=\mathrm{GPP}-\mathrm{Ra} \tag{15}\]  
Among them, the vegetation PAR absorption obtained by using the climatology radiation calculation method was used for the estimation. fPAR refers to vegetation PAR absorption, which is used to describe the canopy structure and the function of the energy material exchange rate in the process of biophysical variables. [PERSON] [18] uses the MODIS fPAR product to drive the model, but, in this paper, the precision of fPAR inversion with a space of 1 km and time scale of one month, was improved by Equations (16)-(19). It has been found that fPAR was linearly related with NDVI and SR, previous study has shown that the NDVI-based fPAR model (fPAR\({}_{\mathrm{NDTVI}}\)) and SR-based fPAR model (fPAR\({}_{\mathrm{SR}}\)) can overestimate or underestimate fPAR respectively, and then [PERSON] (1998) combines fPAR\({}_{\text{NDVI}}\) and fPAR\({}_{\text{SR}}\), which would provide exact assessment result [30]. \[\text{fPAR}=(\text{fPAR}_{\text{NDVI}}+\text{fPAR}_{\text{SR}})/2 \tag{16}\]  
\[\text{SR}=(1+\text{NDVI})/(1-\text{NDVI}) \tag{17}\]  
\[\text{fPAR}_{\text{NDVI}}=\frac{(\text{NDVI}-\text{NDVI}_{\text{i,min}})\times (\text{fPAR}_{\text{max}}-\text{fPAR}_{\text{min}})}{(\text{NDVI}_{\text{i,max }}-\text{NDVI}_{\text{i,min}})}+\text{fPAR}_{\text{min}} \tag{18}\]  
\[\text{fPAR}_{\text{SR}}=\frac{(\text{SR}-\text{SR}_{\text{i,min}})\times( \text{fPAR}_{\text{max}}-\text{fPAR}_{\text{min}})}{(\text{SR}_{\text{i,max}}- \text{SR}_{\text{i,min}})}+\text{fPAR}_{\text{min}} \tag{19}\]  
SR represents the ratio vegetation index. Studies show a good linear relationship among fPAR, NDVI, and SR. fPAR\({}_{\text{NDVI}}\) and fPAR\({}_{\text{SR}}\) represent the estimated fPAR, according to the SR and NDVI, respectively.