## 3 Results
### Differences in Model Accuracy Between Bione Types  
Most of the biome types showed an overestimation of FAPAR\({}_{\rm MOD}\). Grass savanna, desert, arctic tundra, tallgrass prairie, cropland, temperate needleleaf forest, and temperate mixed forest showed an overestimation of FAPAR\({}_{\rm MOD}\), and boreal forest and tropical broadleaf evergreen forest showed underestimation. The overestimated biomes ranged from 0.088 to 0.280 for Bias and 25.1% to 350.1% for MPE. Boreal forest and tropical broadleaf evergreen forest had Bias of \(-\)0.012 and \(-\)0.066, respectively, and MPE of \(-\)1.9% and \(-\)6.9%. Among overestimated biomes, cropland and grass savanna had the most prominent overestimation of FAPAR\({}_{\rm MOD}\) with MPE of 350.1% and 333.8%, respectively. This was followed by arctic tundra and desert with MPE of 168.3% and 111.2%, respectively. Figure 3: The accuracies in FAPAR estimation for FAPAR\({}_{\rm MOD}\), FAPAR\({}_{\rm LAI}\), and FAPAR\({}_{\rm FVC}\): (**a**) the accuracy of FAPAR\({}_{\rm MOD}\); (**b**) the accuracy of FAPAR\({}_{\rm LAI}\); (**c**) the accuracy of FAPAR\({}_{\rm FVC}\). FAPAR\({}_{\rm MOD}\), FAPAR\({}_{\rm LAI}\), and FAPAR\({}_{\rm FVC}\) are FAPAR from MODIS FAPAR products, FAPAR calculated using Beer-Lambert’s law based on the MODIS LAI products, and the improved FAPAR that uses Beer-Lambert’s law by considering FVC, respectively. FAPAR, FAPAR\({}_{\rm MOD}\), FAPAR\({}_{\rm LAI}\), FAPAR\({}_{\rm FVC}\), FVC, R\({}^{2}\), RMSE, Bias, RPIQ, MAPE, and MPE were the same in Figure 2. CI refers to the confidence interval. The accuracy of FAPAR\({}_{\rm LAI}\) is higher than that of FAPAR\({}_{\rm MOD}\), and the accuracy of FAPAR\({}_{\rm FVC}\) is superior to that of FAPAR\({}_{\rm LAI}\). Then came the temperate mixed forest and tallgrass prairie, with MPE of 41.3% and 72.9% for the two sites in temperate mixed forest and 50.6% for tallgrass prairie. The least overestimated was the temperate needleleaf forest with an MPE of 25.1% (Figure 4 and Table 2). For biome types overestimated by FAPARMOD, FAPARLAI and FAPARFVC estimated FAPAR with clearly lower overestimates compared to FAPARMOD, with FAPARFVC being more clearly lower. The MAPE of FAPARLAI varied from 27.3 to 217.0%, with an average reduction of 32.3% compared to FAPARMOD; the MPE varied from 9.1 to 203.6%, with an average reduction of 37.0% compared to FAPARMOD; and the RPIQ of FAPARLAI varied from 0.20 to 3.01, with an average increase of 31.4% compared to FAPARMOD. The MAPE of FAPARFVC varied from 19.2 to 154.7%, with an average reduction of 55.8% compared to FAPARMOD; the MPE varied from \(-\)15.0 to 141.4%, with an average reduction of 71.4% in terms of quantity compared to FAPARMOD; and the RPIQ of FAPARFVC varied from 0.10 to 4.55, with an average increase of 89.8% compared to FAPARMOD (Figure 4 and Table 2). Figure 4: The accuracies for FAPAR estimation in different biome types. FAPAR was the same in Figure 1. FAPARMOD, FAPARLAI, FAPARFVC, FVC, R\({}^{2}\), RMSE, Bias, RPIQ, MAPE, MPE, and CI were the same in Figure 3. For biome types overestimated by FAPARMOD, FAPARLAI and FAPARFVC estimated FAPAR with clearly lower overestimates compared to FAPARMOD, with FAPARFVC being more clearly lower. For the biome types underestimated by FAPARMOD, the underestimation of FAPAR was more severe for FAPARLAI and FAPARFVC, especially for FAPARFVC. For the biome types underestimated by FAPAR\({}_{\text{MOD}}\), the underestimation of FAPAR was more severe for FAPAR\({}_{\text{LAI}}\) and FAPAR\({}_{\text{FVC}}\), especially for FAPAR\({}_{\text{FVC}}\). The MPE of FAPAR\({}_{\text{LAI}}\) for boreal forest was \(-4.7\%\), which is \(141.9\%\) higher in terms of quantity compared to FAPAR\({}_{\text{MOD}}\), but the underestimation of FAPAR\({}_{\text{LAI}}\) for tropical broadleaf evergreen forest was improved, with an MPE of \(-1.85\%\), which is \(73.2\%\) lower in terms of quantity compared to FAPAR\({}_{\text{MOD}}\).