## 1 Introduction  
Solar-induced chlorophyll fluorescence (SIF) is emitted from within the photosynthetic apparatus of all higher plants and is a good indicator of carbon assimilation and plant physiological status [1, 2]. Hence, SIF has been used to characterize the spatiotemporal dynamics of gross primary productivity (GPP), and strong correlations have been found between satellite-derived SIF and landscape-scale GPP across different biomes [3; 4; 5; 6; 7; 8]. Many research studies have reported a strong linear relationship between TOC (Top of Canopy) SIF and ecosystem-scale GPP over different biomes [9]. However, whether or not a universal linear relationship exists across biomes at ecosystem-scale is still an open question [6; 10]. Usually, GPP is calculated as the difference between NEE (Net Ecosystem Exchange) and ER (Ecosystem Respiration) [11], while the satellite-observed TOC SIF is calculated based on the directional canopy spectrum [12; 13; 14]. TOC SIF is only a part of the total emitted SIF of vegetation and is influenced by canopy structure and solar-viewing geometry. These factors weaken the relationship between SIF and GPP. For this reason, the total emitted SIF of vegetation (SIF emission from all leaves within the canopy) is more directly related to GPP than TOC SIF [13; 14]. Canopy radiative transfer models (RTMs) offer an easy and direct way to estimate the total emitted SIF through model inversion. This process amounts to the compensation of the observed TOC SIF for the structure-dependent multiple scattering and re-absorption events that occur from the leaves to sensor. Today, several SIF models have already been developed that are capable of this, including the one-dimensional (1-D) SIF RTM, such as the Soil-Canopy Observation of Photochemistry and Energy (SCOPE) balance model [15] and three-dimensional (3-D) SIF RTM, such as the FluorWPS model [16], the FluorFLIGHT model [17], and the Discrete Anisotropic Radiative Transfer (DART) model [18]. However, a lot of input parameters from leaf to canopy are needed for these models to carry out the inversion process, and these input parameters are not always available on a global scale. Spectral invariants theory (SIT) was developed and introduced to remote sensing to simplify the radiative transfer processes among leaf, shoot, and canopy [19; 20; 21]. When compared with RTMs, the radiation scattering processes within canopies can be characterized just by leaf albedo and three spectral invariant parameters: canopy interceptance (\(i_{0}\)), directional escape probability, and recollision probability under the assumption that soil background has no (or negligible) effects on canopy reflectance. Recently, a semi-empirical approach has been developed to estimate SIF escape probability by [PERSON] et al. [22]. Here canopy SIF scattering at far-red band is estimated using TOC pure vegetation reflectance, in addition to two other parameters, canopy interceptance and leaf albedo. These parameters are combined to estimate the SIF escape probability based on SIT (\(f_{yung}^{esc}=NIR_{v}/i_{o}\cdot\omega_{\lambda}\), \(NIR_{v}\) is defined as the vegetation canopy reflectance by vegetation, \(i_{o}\) is the canopy interceptance, and \(\omega_{\lambda}\) is the leaf albedo at the specific wavelength), which is finally used to derive total emitted SIF from observed TOC SIF. As stated above, canopy interceptance (\(i_{o}\)) is required for the estimation of SIF escape probability and not commonly available on a global scale. To address this problem, [PERSON] et al. [23] proposed a method to estimate the SIF escape probability using random forest with only TOC SIF and reflectance data. As this estimation method is based on an empirical approach, a more generalizable physical based approach is also sought. [PERSON] et al. [12] proposed an extended method for the estimation of SIF escape probability based on the concept of [PERSON] et al.