## 1 Introduction
[PERSON] et al. [27] proposed that f\({}_{\text{esc}}\) could be accurately estimated using near-infrared reflectance, canopy interception (\(i_{0}\)), and leaf albedo in the near-infrared band (\(\omega_{N}\)), assuming no soil reflectance (f\({}_{\text{esc}}=\text{Ref}_{\text{NIR}}/i_{0}\cdot\omega_{N}\)), which laid the foundation for the study of f\({}_{\text{esc}}\) estimation. [PERSON] et al. [15] used this model to estimate f\({}_{\text{esc}}\) from canopy reflectance based on random forest regression, effectively avoiding the difficulties of estimating \(i_{0}\) and \(\omega_{N}\) in the model. [PERSON] et al. [28] further simplified the parameters in the model by developing the near-infrared reflectance of vegetation index (NIRv) to isolate the contribution of soil and vegetation to canopy reflectance and using FAPAR to approximate \(i_{0}\) in the denominator. Similarly, [PERSON] et al. [26] derived fluorescence escape probability formulas for the red and near-infrared bands based on reflectance and FAPAR, respectively, and applied them to correct long-term ground observation data of SIF. [PERSON] et al. [29] later showed that it was challenging to estimate FAPAR and f\({}_{\text{esc}}\) in the near-infrared band separately using canopy reflectance alone; however, the product of the two could be well replaced with a new vegetation index, the fluorescence-corrected vegetation index (FCVI), which was shown to be in good agreement with spectrally invariant properties. Among the above-mentioned SIF-downscaling methods, the semi-empirical model proposed by [PERSON] et al. [28] is simple and accurate, facilitating the use of current in situ or remotely sensed NIRv and FAPAR datasets for f\({}_{\text{esc}}\) estimation. As a result, [PERSON] et al. 's model has been widely used and can be expressed as:  
\[\text{f}_{\text{esc}}\approx\frac{\text{NIRv}}{i_{0}\times\omega_{N}}=\frac{ \text{NDVI}\times\text{Ref}_{\text{NIR}}}{i_{0}\times\omega_{N}}\approx\frac{ \text{NIRv}}{\text{FAPAR}} \tag{2}\]  
where f\({}_{\text{esc}}\) is a dimensionless quantity, different from f\({}_{\text{esc}}\) (unit: sr\({}^{-1}\)) in Equation (1). For ease of understanding, the f\({}_{\text{esc}}\) values in the following sections are all expressed as dimensionless quantities. The canopy interception, \(i_{0}\), is approximated by FAPAR. The leaf single scattering albedo in the near-infrared band (leaf reflectance + transmittance), \(\omega_{N}\), is taken to be constant and equal to 1. Although the use of NIRv in the model is intended to eliminate the effect of soil reflectance, in practice, NIRv as a pure vegetation signal is controversial because soil reflectance impacts the calculation of the normalized difference vegetation index (NDVI). Additionally, the approximation of \(i_{0}\) with FAPAR relies on the assumption that soil reflectance is 0 [29]. Hence, the NIRv/FAPAR model proposed by [PERSON] et al. does not completely eliminate the impact of soil reflectance, which remains a key source of uncertainty in f\({}_{\text{esc}}\) estimation, especially for sparse vegetation. The influence of soil reflectance on f\({}_{\text{esc}}\) estimation can be seen in two aspects: its impact on the calculation of pure vegetation reflectance and on the scattering process between the canopy and soil. To thoroughly correct the effect of soil reflectance, we aim to add a correction factor that includes soil reflectance to the simple NIRv/FAPAR model to increase the precision of f\({}_{\text{esc}}\) and leaf-level SIF estimation in the near-infrared band. First, we used the Soil-Canopy-Observation of Photosynthesis and the Energy Balance (SCOPE) model to simulate the training dataset. Then, we employed the Gaussian process regression (GPR) algorithm to model the correction factor, obtaining the improved f\({}_{\text{esc}}\) modeling method accounting for soil reflectance (f\({}_{\text{esc}\_\text{GPR-SR}}\) model).