## 4 Discussion
### Superiority of the \(\mathrm{f_{esc,GPR-SR}}\) Model  
At present, some studies on SIF downscaling have considered soil reflectance; however, these studies lacked clarity and had significant uncertainties. [PERSON] et al. [15] proposed a SIF-downscaling approach where the ratio of \(\mathrm{f_{esc}}\) to the bi-directional reflectance factor was obtained through SCOPE model simulations and the hypothesis of \"black soil\" was ignored in the machine learning process. However, they did not explicitly account for the effect of soil reflectance. [PERSON] et al. [52] developed a method to derive the global soil-resistant \(\mathrm{SIF_{total}}\) (\(\mathrm{SIF_{total-SR}}\)) using satellite data. However, their method used an approximation of the observed minimum reflectance to soil reflectance that is uncertain and relied on LAI and clumping index (CI) satellite data, which also propagated uncertainties in \(\mathrm{SIF_{total}}\). Notably, [PERSON] et al. [53] proposed using NIRvH with minimal soil impacts by making use of the spectral shape changes in the red-edge region to calculate true vegetation near-infrared  
Figure 11: Relationship between \(\mathrm{f_{esc}}\) and NIRv simulated by the SCOPE model. The small circles in the figure represent the average values of different NIRv segments. The six curves in different colors represent the six soil spectral curves used in the SCOPE simulations. reflectance. We used 9000 validation samples simulated by the SCOPE model to verify the performance of the NIRvH2/FAPAR model to estimate \(\mathrm{f_{esc}}\) (Figure S4). Compared with the results in Figure 5, it can be found that our model is also superior to the NIRvH2/FAPAR model (R2 = 0.885, RMSE = 0.051), possibly because of uncertainties in NIRvH itself, including the assumption that NIRvH2 is based on a linear increase in the reflectance of soil in the red-edge region which is not always correct. [PERSON] et al. [54] suggested that supervised machine learning methods trained on appropriate training datasets could construct accurate predictive models and overcome difficulties in physical modeling. [PERSON] et al. [55] also noted that while traditional parametric models are easy to interpret, they can be limited in their expression for complex datasets. Hence, in this study, we chose to build our \(\mathrm{f_{esc\_GPR\_SR}}\) model using a machine learning method. We proposed to add a correction factor composed of soil reflectance and NDVI to the widely used NIRv/FAPAR model suggested by [PERSON] et al. [28], in order to explicitly account for the effect of soil reflectance. This not only preserved the advantages of the NIRv/FAPAR model's simplicity, ease of computation, and clear physical meaning but also compensated for its lack of explicit consideration of soil reflectance's effect on \(\mathrm{f_{esc}}\) estimation. We tested the performance of various machine learning algorithms and found that exponential GPR was the best training model. Directly using the machine learning model to estimate \(\mathrm{f_{esc}}\) may lead to poor model robustness due to too many model input parameters, so the correction factor \(f\) (\(\mathrm{f_{sail}}\), \(\mathit{VI}\)) with fewer parameters was only trained using the exponential GPR method, which helped to reduce the number of input parameters and improve the model's robustness. Moreover, it ensured that the improvement was carried out on the basis of retaining the physical meaning of the original NIRv/FAPAR model as much as possible. We demonstrated the superiority of our model by combining simulation data with field data. The validation results of SCOPE model simulations (Section 3.2.1) showed that the \(\mathrm{f_{esc}}\) estimated by the \(\mathrm{f_{esc\_GPR\_SR}}\) model was in good agreement with the true \(\mathrm{f_{esc}}\) values, even under sparse vegetation, and it can significantly eliminate the influence of direction effect.