## 1 Introduction
Research has shown that due to the stronger transmission of diffuse radiation in the canopy and avoidance of the light-saturation phenomenon of direct radiation in the canopy leaves, photosynthesis is more efficient under the action of diffuse radiation [14, 15, 16, 17]. [PERSON] _et al._ analyzed the impact of diffuse radiation on forest canopy GPP under the assumption that direct radiation can expose only sunlit leaves, but that diffuse radiation can expose both sunlit and shaded leaves [18]. The results showed that aerosols from human activities have increased the proportion of diffuse radiation and improved forest canopy GPP. [PERSON] _et al._ simulated GPP using changes in total PAR and the proportion of diffuse PAR by means of the MAESTRA model [19]. The results showed that increasing the proportion of diffuse radiation can improve the absorption and utilization efficiency of incident PAR on the forest canopy. Therefore, the diffuse radiation effects on vegetation canopy GPP cannot be ignored. Direct and diffuse radiation follow different transfer paths in the vegetation canopy, making their FPAR values different. To perform further research on the difference between direct and diffuse FPAR, it is necessary to analyze the variation characteristics of direct and diffuse FPAR. Using the SAIL (scattering by arbitrarily-inclined leaves) model, [PERSON] _et al._ explored the effects of background spectral reflectance and canopy optical and geometrical properties on the relationship between FPAR and SVI [20]. [PERSON] _et al._ also used the SAIL model to simulate radiation transfer inside the canopy. [PERSON] _et al._ simulated FPAR using a Monte Carlo model and analyzed the influencing factors of FPAR, such as solar zenith angle and LAI [21]. [PERSON] _et al._ also simulated FPAR based on a Monte Carlo model and analyzed the effects of soil background and leaf angle on vegetation canopy FPAR [12]. A previous study by the authors of this article used the SAIL model to simulate direct and diffuse FPAR under various weather and LAI conditions. The SAIL model is a radiation transfer model developed from the SUITS model [22]. The scattering and extinction coefficients of the SAIL canopy reflectance model are derived for the case of a fixed arbitrary leaf inclination angle and a random leaf azimuth distribution. The SAIL model includes the uniform model of G.H [PERSON] as a special case, and its main characteristics are that canopy variables, such as leaf area index and the leaf inclination distribution function, are used as input parameters and that it provides more realistic angular profiles of directional reflectance as a function of view angle or solar zenith angle [23, 24, 25]. In the SAIL model, the proportions of direct and diffuse radiation can be changed by means of the visibility parameter. The results showed that when visibility was set to 5 km, 15 km and 30 km, the contributions of diffuse FPAR to total FPAR were 52.6%, 29.3% and 21.7%, respectively [26]. The error between total and direct FPAR was reduced with increasing visibility and increased with decreasing LAI. The maximum relative error was 13.2%. Simulation analyses revealed that direct and diffuse FPAR varied with changes in environmental variables. Especially when visibility was low, diffuse FPAR was an important part of total FPAR, and therefore, when modeling FPAR, the diffuse part cannot be ignored. Because the transmission process is different for direct and diffuse FPAR, the two must be modeled separately. This separation helps improve FPAR inversion accuracy. [PERSON] and [PERSON] developed a look-up table method for inverse direct, diffuse and total FPAR based on a coupled soil-leaf canopy radiative transfer model (SLC), which could inverse the fraction of photosynthetically-active radiation absorbed by green elements [27]. Therefore, in this study, an FPAR inversion model was developed that distinguishes between direct and diffuse FPAR based on the principle of the energy budget balance.