## 2 Methodology
### Methods
#### 2.2.2 Calculation of FAPAR  
For a pixel (sample site), its FAPAR can be considered as the average of FAPAR within the pixel (sample site), encompassing both the green canopy distribution area and the non-green canopy distribution area. This can be calculated based on the canopy-scale FAPAR within the green canopy distribution area and the FVC in the pixel (sample site):  
\[\text{FAPAR}_{\text{pixel}}=\text{FAPAR}_{\text{canopy}}*\text{FVC} \tag{2}\]  
where \(\text{FAPAR}_{\text{pixel}}\) is the FAPAR at the pixel (sample site) scale, \(\text{FAPAR}_{\text{canopy}}\) is the canopy-scale FAPAR of the green vegetation canopy distribution area, FVC is the fractional vegetation coverage, and \(\text{FAPAR}_{\text{canopy}}\) in the green canopy distribution area can be expressed as:  
\[\text{FAPAR}_{\text{canopy}}=1-\text{e}^{-\text{k}*\text{LAI}_{\text{canopy}}} \tag{3}\]where k is the extinction coefficient, set at 0.5 [14,15], and \(\text{LAI}_{\text{canopy}}\) is the leaf area index of the green canopy distribution area.  
For LAI measured at the pixel (sample site) scale, it should reflect the average situation of LAI for that pixel (sample site), which can be defined as \(\text{LAI}_{\text{pixel}}\). This can be regarded as  
Figure 1: The conceptual models of the fraction of absorbed photosynthetically active radiation (FAPAR) for green vegetation canopy (FAPAR\({}_{\text{canopy}}\)) and FAPAR for a pixel (sample site) (FAPAR\({}_{\text{pixel}}\)). (**a**) Actual distribution of vegetation green canopy within pixels, where subpixels with green leaves present are green canopy distribution areas; (**b**) Average green canopy conditions at the pixel (sample site) scale under the Beer-Lambert’s law assumption, with green leaves evenly distributed in each subpixel. \(\text{LAI}_{\text{canopy}}\) is the amount of leaf area per unit of horizontal ground surface with green leaves present in Figure 1a and FAPAR\({}_{\text{canopy}}\) is the absorbed PAR by green leaves in the same area; \(\text{LAI}_{\text{pixel}}\) is the mean of leaf area per unit of horizontal ground surface within the whole pixel in Figure 1a and FAPAR\({}_{\text{pixel}}\) is the average of absorbed PAR by green leaves in the same area. FVC is the fractional vegetation coverage. The relationship between \(\text{LAI}_{\text{pixel}}\) and \(\text{LAI}_{\text{canopy}}\) can be expressed as \(\text{LAI}_{\text{pixel}}=\text{LAI}_{\text{canopy}}\) * FVC.  
Figure 2: The schematic flowchart of the presented FAPAR model. FAPAR, FAPAR\({}_{\text{pixel}}\), FAPAR\({}_{\text{canopy}}\), LAI\({}_{\text{pixel}}\), \(\text{LAI}_{\text{canopy}}\), and FVC were the same in Figure 1. NDVI: normalized difference vegetation index; NDVI\({}_{\text{max}}\) and NDVI\({}_{\text{min}}\): the 95 th and the 5 th percentile of NDVI over the growth period within the study area, respectively; R\({}^{2}\); coefficient of determination; RMSE: root mean squared error; Bias: mean prediction error; MAPE: mean absolute percentage error; MPE: mean percentage error; RPIQ: ratio of performance to interquartile range.  
the products of the canopy-scale \(\mathrm{LAI}_{\mathrm{canopy}}\) within the green vegetation canopy distribution area and FVC, thus expressed as:  
\[\mathrm{LAI}_{\mathrm{pixel}}=\mathrm{LAI}_{\mathrm{canopy}}*\mathrm{FVC} \tag{4}\]  
Consequently, \(\mathrm{LAI}_{\mathrm{canopy}}\) can be calculated based on the pixel (sample site) scale \(\mathrm{LAI}_{\mathrm{pixel}}\) and FVC:  
\[\mathrm{LAI}_{\mathrm{canopy}}=\frac{\mathrm{LAI}_{\mathrm{pixel}}}{\mathrm{ FVC}} \tag{5}\]  
\(\mathrm{LAI}_{\mathrm{pixel}}\) can be derived from MODIS LAI, and FVC can be inferred from MODIS NDVI as discussed in Section 2.2.1.