## 3 Results  
### Performance of Different Correction Factors for \(\mathrm{f_{esc}}\) Estimation  
As discussed in Section 2.3, vegetation indices should be included in the correction factor of the model. In this study, NDVI, SR, EVI2, and PVI were evaluated. The determination coefficient (R\({}^{2}\)), root mean square error (RMSE), and mean absolute error (MAE) were used to evaluate the models' performance. As depicted in Figure 4, model \(\mathrm{f_{esc}}/\frac{\mathrm{NIRv}}{\mathrm{FAPAR}}\) performed significantly better than model \(\mathrm{f_{esc}}-\frac{\mathrm{NIRv}}{\mathrm{FAPAR}}\). However, changing the vegetation indices had little effect on the R\({}^{2}\) values. By comparing other performance evaluation indices (Table 5), we found that NDVI performed best under all circumstances, including sparse vegetation. NDVI is the most extensively used of over 40 vegetation indices [46] and has been proven as a reliable representation of LAI and FVC [47; 48]. Hence, NDVI was finally chosen as the vegetation index in the correction factor. \begin{table}
\begin{tabular}{c c} \hline \hline
**VIs** & **References** \\ \hline \(\mathrm{NDVI}=(\mathrm{R_{780}}-\mathrm{R_{678}})/(\mathrm{R_{780}}+\mathrm{R_{ 678}})\) & [41] \\ \(\mathrm{SR}=\mathrm{R_{780}}/\mathrm{R_{678}}\) & [42] \\ \(\mathrm{EVI2}=\frac{2.5\times(\mathrm{R_{780}}-\mathrm{R_{780}})}{\mathrm{R_{78 0}}+2.4\times\mathrm{R_{780}}+1}\) & [43] \\ \(\mathrm{PVI}=\sqrt{(\mathrm{R_{780}^{soil}}-\mathrm{R_{780}^{veg}})^{2}+( \mathrm{R_{678}^{soil}}-\mathrm{R_{678}^{veg}})^{2}}\) & [44] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: VIs used for the calculation of the correction factor (R\({}_{780}\), R\({}_{710}\), and R\({}_{678}\) represent the reflectance at 780 nm, 710 nm, and 678 nm, respectively). When the inputs of the model were the combination of NDVI and \(Ref_{soil}\) and the output was \(f_{\text{esc}}/\frac{\text{NIRv}}{\text{FAPAR}}\), the model performance R\({}^{2}\) reached 0.850, indicating that \(f_{1}\) (\(Ref_{soil}\), \(NDVI\)) can explain 85% of the remaining part of \(f_{\text{esc}}\) from the NIRv/FAPAR model. Even for sparse canopies (LAI < 2), R\({}^{2}\) reached 0.690. Therefore, the improved \(f_{\text{esc}}\) model in the near-infrared band accounting for soil reflectance (referred to as the \(f_{\text{esc}\_\text{FPR-SR}}\) model) is defined as follows:  
\[f_{\text{esc}}=\frac{\text{NIRv}}{\text{FAPAR}}\times f_{1}(Ref_{soil}\,,\ NDVI) \tag{8}\]
0.954 and RMSE decreasing from 0.100 to 0.012. The results demonstrate that the f\({}_{\text{esc,GPR-SR}}\) model provides a better estimation of f\({}_{\text{esc}}\) in the near-infrared band and has high estimation accuracy for sparse vegetation. Furthermore, we calculated the coefficient of variation (CV) of the canopy SIF simulated by the SCOPE model and the leaf SIF estimated by the f\({}_{\text{esc,GPR-SR}}\) model and NIRv/FAPAR model for each set of different LAI values with only the VZA changing and the remaining parameters fixed (Figure 7). The smaller the CV value, the less the SIF is affected by the directional effect. The CV of canopy SIF for different LAI values is much larger than that of leaf SIF due to the anisotropic scattering within the canopy. Apparently, compared with the NIRv/FAPAR model, the CV of leaf SIF estimated by the f\({}_{\text{esc,GPR-SR}}\) model is smaller, and the gap between the results of the two models is more obvious for sparse vegetation. The result suggests that our f\({}_{\text{esc,GPR-SR}}\) model can reduce the directional effect of canopy SIF more effectively compared with the NIRv/FAPAR model. Figure 5: Comparison of f\({}_{\text{esc}}\) in the near-infrared band (760 nm) estimated by (**a**) the NIRv/FAPAR model (f\({}_{\text{esc}}\) (NIRv/FAPAR)) and (**b**) the f\({}_{\text{esc,GPR-SR}}\) model (f\({}_{\text{esc}}\) (GPR-SR)) with the f\({}_{\text{esc}}\) simulated by the SCOPE model.