## 2 Data and Methods
### Methods
#### 2.2.1 Models Used

Table 1: _Cont.__Remote Sens._**2015**, \(7\)  
\[APAR_{{}_{min}}=(1-\alpha)\times\left[PAR_{{}_{dir}}\times\frac{\cos(\varphi)}{ \cos(\theta)}+\frac{PAR_{{}_{dir}}-PAR_{{}_{dir}}}{LAI}+C\right] \tag{4}\]  
\[APAR_{{}_{min}}=(1-\alpha)\times\left[\frac{PAR_{{}_{dir}}-PAR_{{}_{dir}}}{LAI}+C\right] \tag{5}\]  
where \(\alpha\) is the albedo varying with vegetation types (Table 2), \(PAR_{{}_{dir}}\) and \(PAR_{{}_{dir}}\) are the diffuse and direct components of incoming PAR, respectively, and they are empirically calculated (see Equation (6)); \(PAR_{{}_{dir},u}\) is the diffuse PAR under the canopy and calculated following [24]; (\(PAR_{{}_{dir}}-PAR_{{}_{dir},u}\))/\(LAI\) denotes the absorbed diffuse PAR per unit leaf area within the canopy; \(C\) indicates multiple scattering of total PAR within the canopy [24]; \(\varphi\) is the mean leaf-sun angle and set as 60\({}^{\circ}\)[24]; \(\theta\) is the mean solar zenith angles of half an hour, a day, and 8 days. The average solar zenith angle in each half an hour is calculated according to latitude, Julian day, and local time [93]. The average solar zenith angle in a given day is calculated according to latitude and Julian day [24]. The 8-day average solar zenith angle is the mean of the daily average solar zenith angles during the 8 days period. Diffuse and direct PAR are empirically partitioned as [24]:  
\[PAR_{{}_{dir}}=(0.943+0.734R-4.96R^{2}+1.796R^{3}+2.058R^{4})\times PAR \tag{6}\]  
where \(PAR_{{}_{dir}}\) is the estimated diffuse PAR; \(R\) is the sky clearness index (\(R\)=\(S\)/(\(So\)\(\cos\)\(\theta\))), \(S\) and \(S_{\theta}\) are the incoming solar radiation on the ground surface and solar constant (1367 Wm\({}^{-2}\)), respectively. In the conversion of incoming solar radiation into PAR, a constant of 0.5 is used [23] (PAR=0.5S). \(LAI_{{}_{min}}\) and \(LAI_{{}_{min}}\) in Equations (2) and (3) are calculated as [24]:  
\[LAI_{{}_{min}}=2\times\cos(\theta)\times\left(1-\exp\left(-0.5\times\Omega \times\frac{LAI}{\cos(\theta)}\right)\right) \tag{7}\]  
\[LAI_{{}_{min}}=LAI-LAI_{{}_{min}} \tag{8}\]  
where \(\Omega\) is the clumping index, which changes with land cover types, season and solar zenith angle. It was only assigned according to vegetation types here (Table 2) since spatially and temporally variant data are not available for this parameter. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Vegetation Type\({}^{*}\)** & **DBF** & **ENF** & **EBF** & **MF** & **GRASS** & **CROP** & **savannas** & **OS** & **WS** \\ \hline \(\varepsilon_{\max}\) (g C/MJ)** & 1.044 & 1.008 & 1.259 & 1.116 & 0.604 & 0.604 & 0.888 & 0.774 & 0.768 \\ T\({}_{min,max}\) (\({}^{\circ}\)C) & 7.94 & 8.31 & 9.09 & 8.5 & 12.02 & 12.02 & 8.61 & 8.8 & 11.39 \\ T\({}_{min,min}\) (\({}^{\circ}\)C) & \(-8\) & \(-8\) & \(-8\) & \(-8\) & \(-8\) & \(-8\) & \(-8\) & \(-8\) & \(-8\) \\ VPD\({}_{max}\) (kpa) & 4.1 & 4.1 & 4.1 & 4.1 & 4.1 & 4.1 & 4.1 & 4.1 & 4.1 \\ VPD\({}_{min}\) (kpa) & 0.93 & 0.93 & 0.93 & 0.93 & 0.93 & 0.93 & 0.93 & 0.93 & 9.3 \\ Albedo & 0.18 & 0.15 & 0.18 & 0.17 & 0.23\({}^{\rm a}\) & 0.23\({}^{\rm b}\) & 0.16 & 0.16 & 0.23 \\ Clumping index (\(\Omega\)) & 0.8 & 0.6 & 0.8 & 0.7 & 0.9 & 0.9 & 0.8 & 0.8 & 0.8 \\ \hline \hline \end{tabular}  
*DBF: deciduous broadleaf forest; ENF: evergreen needleaf forest; EBF: evergreen broadleaf forest; MF: mixed forest; GRASS: grassland; CROP: cropland; savannas: savannas; OS: open shrublands; WS: woody savannas; \({}^{\rm a}\)[PERSON] _et al._[94]. \({}^{\rm b}\)[PERSON] _et al._[95]. \({}^{\rm c}\)[PERSON] _et al._[96]; \({}^{\rm**}\)[PERSON] _et al._[91].  
\end{table} 
Table 2: Model parameters used for different vegetation types.