## 2 Methodology  
### Data Collection and Preprocessing  
The LAI and FAPAR ground observations utilized in this study were obtained from the BigFoot Project and three in situ measured grassland sites in Senegal, West Africa [20, 43]. The BigFoot in situ measured LAI was the 8-day cell LAI averaged over 25 1 \(\times\) 1 km cells as the LAI for the site within 5 \(\times\) 5 km of the site, and the 8-day cell LAI over 25 1 \(\times\) 1 km cells was converted to cell FAPAR using the Beer-Lambert's law which was averaged as the BigFoot in situ measured FAPAR for the site [43]. For the three grass savanna in situ measured sites in Senegal, West Africa, LAI and FAPAR were measured on the day of the observation [20]. The aforementioned data were obtained using the online image digitization software WebPlotDigitizer at the following URL: [[https://apps.automeris.io/wpd4/](https://apps.automeris.io/wpd4/)]([https://apps.automeris.io/wpd4/](https://apps.automeris.io/wpd4/)) (accessed on 9 February 2025). This software digitizes the mean value of each sample based on plots from the relevant literature (Table 1).  
For MODIS LAI and FAPAR data, the BigFoot Project's data were also obtained by digitizing their mean values directly based on plots in the relevant literature. Data for West Africa, Senegal, were obtained by digitizing the researchers' interpolated daily data  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Site Name** & **Latitude** & **Longitude** & **Biome Types** & **Year** & **References** \\ \hline NOBS & 55.885 & 98.477 & boreal forest & 2002 & [44] \\ KONZ & 39.089 & \(-\)96.571 & tallgrass prairie & 2000 & [43] \\ AGRO & 40.007 & 88.292 & cropland (corn and soybean) & 2000 & [45] \\ HARV & 42.529 & \(-\)72.173 & temperate mixed forest & 2002 & [46] \\ TUND & 71.272 & \(-\)156.613 & arctic tundra & 2002 & [43] \\ SEVI & 34.351 & \(-\)106.690 & desert & 2002 & [47] \\ TAPA & 2.870 & \(-\)54.949 & tropical broadleaf evergreen forest & 2004 & [43] \\ METL & 44.451 & 121.573 & temperate needleleaf forest & 2002 & [48] \\ CHEQ & 45.945 & \(-\)90.272 & temperate mixed forest & 2000 & [43] \\ Dahra & 15.000 & \(-\)15.443 & grass savanna & 2001; 2002 & [20] \\ Tesseke North & 15.885 & \(-\)15.081 & grass savanna & 2002 & [20] \\ Tesseke South & 15.796 & \(-\)15.083 & grass savanna & 2002 & [20] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Data sources for the data used in this study.  
from the MODIS LAI/FPAR products (MOD15) at the corresponding observation sites in the relevant documents. In the non-growth period, the GPP should be zero. To decrease the impact of GPP estimation from non-growth periods, this study only used data over the growth period. The beginning and the end of the growth period and peak vegetation growth periods were determined according to the GPP changes. GPP generally starts to grow rapidly at the beginning of the growth period, gradually wilts after reaching the mature (peak) stage, and remains stable at the end of the growth period. When GPP reached a high and relatively stable state over the growth period, this period was considered the peak growth period; other periods were considered as off-peak vegetation growth periods.  
The Normalized Difference Vegetation Index (NDVI) data utilized in this study are from the MODIS reflectance products (MOD09Q1.061), which has a temporal resolution of eight days and a spatial resolution of 250 m. The aforementioned data were employed to reduce noise using the Savitzky-Golay filtering method [49]. The FVC utilized in this study was calculated through NDVI data [50; 51], and the FVC was calculated using the following equation:  
\[\text{FVC}=\frac{\text{NDVI}-\text{NDVI}_{\text{min}}}{\text{NDVI}_{\text{max}} -\text{NDVI}_{\text{min}}} \tag{1}\]  
where NDVI is the NDVI value for the current pixel (sample site), \(\text{NDVI}_{\text{max}}\) is the 95 th percentile of NDVI over the growth period within the study area, and \(\text{NDVI}_{\text{min}}\) is the 5 th percentile of NDVI for the growth period within the study area.