## 4 Discussion  
### Effect of Soil Reflectance on Estimating \(f_{\text{esc}}\)  
The scattering and reabsorption of SIF photons within the canopy are governed by the same physical mechanisms as the scattering and reabsorption of reflected radiation photons. When incident light enters the canopy from the top, it can either pass through the canopy and reach the soil surface through the gaps or interact with leaves in the canopy. Photons intercepted by the canopy are scattered and reabsorbed several times, and some escape from the canopy while others are absorbed by leaves. Photons absorbed by leaves in the PAR range (400-700 nm) can stimulate fluorescence photons with a 640-850 nm wavelength range [27]. Emitted fluorescence will also escape from the canopy after multiple scatterings and reabsorptions inside the canopy and leaves. In practice, soil background has a specific reflectance spectrum and is not \"black.\" Ignoring the influence of atmospheric radiative transfer and multiple scatterings between soil and canopy (considering only single scattering), the photons captured by the sensor mainly come from three sources: (1) photons (including emitted fluorescence photons) that escape upward from the canopy to the sensor; (2) incident photons that pass through the canopy, reach the soil surface, and are reflected to the sensor; (3) photons (including emitted fluorescence photons) escaping downward from the canopy that reach the soil \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Vegetables and Crops**} & \multicolumn{2}{c}{**Gold Coin Grass**} & \multicolumn{2}{c}{**Winter Wheat**} \\ \cline{2-7}  & \(\mathbf{R^{2}}\) & **RMSE** & \(\mathbf{R^{2}}\) & **RMSE** & \(\mathbf{R^{2}}\) & **RMSE** \\ \hline \(\text{SIF}_{\text{ canopyy}}\) & 0.883 & 0.187 & 0.750 & 0.195 & 0.944 & 0.071 \\ \(\text{SIF}_{\text{leaf}}^{\text{NIRv/PAPR}}\) & 0.955 & 0.709 & 0.891 & 0.612 & 0.966 & 0.683 \\ \(\text{SIF}_{\text{leaf}}^{\text{GPR-SR}}\) & 0.950 & 0.646 & 0.901 & 0.518 & 0.970 & 0.511 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(\text{R}^{2}\) and RMSE values of the line correlation between \(\text{APAR}_{\text{green}}\) and SIF for samples of various species with \(\text{FVC}\leq 0.8\). The units of RMSE for the \(\text{APAR}_{\text{green}}\)–\(\text{SIF}_{\text{ canopyy}}\) relationship and the \(\text{APAR}_{\text{green}}\)–\(\text{SIF}_{\text{leaf}}\) relationship are \(\text{mW}/\text{m}^{2}/\text{nm}/\text{sr}\) and \(\text{mW}/\text{m}^{2}/\text{nm}\), respectively. Figure 10: Correlation between \(\text{APAR}_{\text{green}}\) and (**a**) canopy-level SIF (\(\text{SIF}_{\text{ canopyy}}\)), (**b**) leaf-level SIF estimated by the NIRv/PAPR model (\(\text{SIF}_{\text{leaf}}^{\text{NIRv/PAPR}}\)), and (**c**) leaf-level SIF estimated by the \(\text{f}_{\text{esc\_GPR-SR}}\) model (\(\text{SIF}_{\text{leaf}}^{\text{GPR-SR}}\)) for different species (vegetables and crops, gold coin grass, and winter wheat) in the case of \(\text{FVC}\leq 0.8\). The black solid lines and the equations are the linear regression lines and models for all samples with \(\text{FVC}\leq 0.8\). The finer colored lines are the linear regression lines of the species that correspond in color. and are reflected to the sensor. It is worth mentioning that the downward-escaping SIF photons from the canopy may be absorbed by the soil; however, this can be ignored as the lower leaves receive less light and thus produce fewer SIF photons [15]. Consequently, the SIF photons captured by the sensor come from two main sources: the contribution of pure vegetation canopy and the contribution of soil single scattering, and soil reflectance affects both. [PERSON] et al. [27] proposed a basic model to estimate \(\mathrm{f_{esc}}\) based on spectrally invariant theory, where \(\mathrm{f_{esc}}=\mathrm{Ref_{NIR}}/i_{0}\cdot\omega_{N}\), ignoring the contribution of soil scattering to the fluorescence signal captured by the sensor. The near-infrared reflectance in the numerator clearly contains the effect of soil reflectance.