## 2 Methods  
According to the principle of the energy budget balance, the relationship between surface albedo and FPAR can be expressed in Equation (1):  
\[(1-\alpha)=A_{sol}+FPAR \tag{1}\]  
where \(\alpha\) is the surface albedo. Therefore, \((1-\alpha)\) is the proportion of the radiance absorbed by the land surface, which can be divided into two parts, one is that absorbed by vegetation, namely \(FPAR\), the other is that absorbed by soil, noted as \(A_{sol}\). In our proposed model, FPAR was separated into two parts, direct \(FPAR\) and diffuse \(FPAR\), as expressed in Equation (2):  
\[FPAR=(1-k)\times FPAR_{dir}+k\times FPAR_{diff} \tag{2}\]  
where \(FPAR\) is the total \(PAR\), \(FPAR_{dir}\) is the fraction of absorbed direct \(PAR\) reaching the top of the canopy, \(FPAR_{diff}\) is the fraction of absorbed diffuse \(PAR\) reaching the top of the canopy and \(k\) is the proportion of diffuse \(PAR\). Firstly, in order to distinguish direct and diffuse \(FPAR\), instead of the surface albedo (\(\alpha\)), the black sky albedo integrated from 400 to 700 nm (\(\omega\)) and the white-sky albedo integrated from 400-700 nm (\(\alpha_{w}\)) need to be used in the model. The derivation of the equation for calculating direct \(FPAR\) is described as follows. The incident light can be divided into the part irradiated to the vegetation and the part irradiated to the soil. The probability of the incident light irradiating to the vegetation is \((1-P_{gap})\), and the probability of the incident light irradiating to the soil is \(P_{gap}\). \(P_{gap}\) is:  
\[P_{gap}=\exp[-LAI\times\Omega(\theta_{s})\times G(\theta_{s})/\mu_{s}] \tag{3}\]  
where \(\Omega(\theta_{s})\) and \(G(\theta_{s})\) are, respectively, the clumping index of foliage and the projection coefficient of the solar zenith angle \(\theta_{s}\)[11,28]; \(\mu_{s}\) is the cosine of \(\theta_{s}\). If only considering the condition of the direct incident light absorbed by the land surface, Equation (1) can be written as Equation (4). \[(1-\alpha_{s})=A_{sol\text{-}dir}+FPAR_{dir} \tag{4}\]  
\(A_{soil}\) can be expressed as:  
\[A_{soil\text{-}dir}\ =\ \alpha_{d}\times P_{gap} \tag{5}\]  
where \(\alpha_{d}\) is the absorptivity of the soil background. If the multiple scattering between soil background and vegetation canopy is not considered, \(FPAR_{dir}\) can be expressed as:  
\[FPAR_{dir}\ =\ \alpha_{L\text{-}dir}\times(1-P_{gap}) \tag{6}\]  
where \(\alpha_{L}\) is the absorptivity of the vegetation canopy. Therefore, the portion of sunlight directly absorbed by the vegetation canopy and the soil background can be expressed as:  
\[(1-\alpha_{{}_{b}})=\alpha_{{}_{d}}\times P_{gap}+\alpha_{{}_{L-dir}}\times(1-P_{ gap}) \tag{7}\]  
If the soil absorptivity \(\alpha_{d}\) is \(a\) times the vegetation canopy absorptivity \(\alpha_{L}\), the formulas for these can be expressed as:  
\[\alpha_{{}_{d}}\ =\ a_{dir}\alpha_{{}_{L-dir}} \tag{8}\]  
\[(1-\alpha_{{}_{b}})\ =\ a_{dir}\times\alpha_{{}_{L-dir}}\times P_{gap}+\alpha_{{} _{L-dir}}-\alpha_{{}_{L-dir}}\times P_{gap} \tag{9}\]  
\[(1-\alpha_{{}_{b}})\ =\ \alpha_{{}_{L-dir}}\times[1+(\alpha_{dir}-1)P_{gap}] \tag{10}\]  
\[FPAR=(1-k)\times FPAR_{dir}+k\times FPAR_{diff} \tag{2}\]0  
\[FPAR=(1-k)\times FPAR_{dir}+k\times FPAR_{diff} \tag{2}\]1  
The derivation of the equation for calculating diffuse FPAR is described as follows. The openness of the crown at the top of the canopy \(K_{open}\) is used, which describes how much of the PAR scattered by the ground passes through the crown to the top of the canopy. \(K_{open}\) can be expressed as in Equation (13) [29]:  
\[FPAR=(1-k)\times FPAR_{dir}+k\times FPAR_{diff} \tag{2}\]2  
If only considering the condition of the direct incident light absorbed by the land surface, Equation (1) can be written as Equation (14).