## 1 Introduction  
Solar-induced chlorophyll fluorescence (SIF) is a phenomenon in which chlorophyll molecules in plants emit light in response to natural light. It is a byproduct of the light reaction process of photosynthesis [1, 2] and has been proven to serve as a proxy for gross primary productivity (GPP) in numerous studies [2, 3, 4, 5, 6]. The light energy absorbed by photosynthetic pigments can be dissipated through three main pathways: photosynthesis, heat dissipation, and fluorescence [2; 7]. SIF changes in sync with photochemical quenching and competes with heat dissipation under natural light conditions without stress, and it is closely tied to photosynthesis in the basic physiological and biochemical processes of plants [8; 9]. As such, SIF provides a more accurate measurement of photosynthetic ecological changes and has a more direct relationship with GPP compared with vegetation indices based on reflectance [10; 11]. There are currently many algorithms that can successfully retrieve SIF from ground-based and satellite-based observations [8; 9; 12; 13; 14]. However, the fluorescence photons observed at the canopy level only represent a fraction of the total SIF emission due to the effect of the radiative transfer process. After fluorescence photons are emitted by photosystems, they are absorbed and scattered by the leaf and canopy components and then escape to the canopy, where they are detected by sensors [2]. The red SIF is primarily affected by chlorophyll absorption within leaves, whereas the near-infrared SIF is primarily impacted by the scattering effect within the canopy [15]. The scattering and reabsorption effects result in different SIF-GPP relationships due to variations in canopy structure, such as leaf area, leaf orientation, and leaf clumping [16]. Furthermore, multiple scatterings inside the canopy during SIF transmission make the SIF observed from different angles vary, which demonstrates that canopy SIF is directional and not isotropic [17]. As a result, the canopy-level SIF differs from the leaf-level SIF and cannot be utilized to directly quantify changes in plant physiology [5; 18; 19]. To reduce the influence of the canopy structure and directional effect on the SIF-GPP relationship, it is necessary to downscale the SIF from canopy level to leaf level and obtain the leaf-level SIF which has a closer physiological coupling relationship with GPP. The fluorescence escape probability (f\({}_{\text{esc}}\)) represents the probability that the fluorescence emitted by photosystems escapes from the canopy and is an important bridge connecting the canopy SIF (SIF\({}_{\text{canopy}}\)) and the total SIF emitted by photosystems (SIF\({}_{\text{total}}\)). Their relationship can be expressed as follows [20; 21; 22; 23; 24; 25]:  
\[\text{SIF}_{\text{canopy}}=\text{SIF}_{\text{total}}\times\text{f}_{\text{esc }}=\text{PAR}\times\text{PAP}\times\Phi_{\text{SIF}}\times\text{f}_{\text{ esc}} \tag{1}\]  
where PAR is the incident photosynthetically active radiation; FAPAR is the fraction of photosynthetically active radiation absorbed by vegetation; \(\Phi_{\text{SIF}}\) is the fluorescence quantum yield. The weak absorption effect of leaves in the near-infrared band means that the fluorescence escape probability from photosystems to leaves can be approximated by the leaf albedo with a value around 1 [26], and the f\({}_{\text{esc}}\) in Equation (1) can be approximated as the fluorescence escape probability from leaves to the canopy and its unit is sr\({}^{-1}\). In recent years, a number of studies have concentrated on estimating f\({}_{\text{esc}}\), in other words, downscaling SIF from the canopy to the leaf level; however, a common problem in most of these approaches is that they are based on spectrally invariant properties and the assumption of a \"black soil background,\" assuming that the soil is a black body with a reflectance of 0, which absorbs all external radiation signals, regardless of the reflective property of the soil and the effects of multiple scatterings among soils and leaves.