## 2 Data and Methods
### Methods  
#### 2.2.1 Models Used  
TL-LUEn, TL-LUE, and MOD17 models were used in this study. The MOD17 algorithm is described in detail in [PERSON] _et al._[8, 91]. It relies on the assumption that GPP is linearly related to APAR [11, 12, 92]. The TL-LUE model stems from the MOD17 algorithm and discriminates the differences of upper and bottom canopy in receiving direct radiation and diffuse radiation and in their LUE. As a consequence, canopy GPP simulated by TL-LUE nonlinearly changes with incoming PAR. The TL-LUEn adopts the same methodology as the TL-LUE model to separate sunlit and shaded leaves and calculate their APAR. However, it takes the rectangular hyperbolic model to calculate GPP for sunlit and shaded leaves. The MOD17, TL-LUE, and TL-LUEn models are described in Equations (1-3), respectively, _i.e._,  
\[G\!P\!P\!=\!\!\varepsilon_{\text{max}}\!\times\!\!\text{PAR}\!\times\!\!f \!PAR\!\times\!\!f\!\left(\!V\!PD\!\right)\!\times\!\!g\!\left(\!T_{\!a\!min}\!\! \right) \tag{1}\]  
\[G\!P\!P\!=\!\left(\!\!\varepsilon_{\text{max}}\!\times\!APAR_{\text{max}}\! \times\!\!LAI_{\text{max}}\!+\!\varepsilon_{\text{m}\!sh}\!\times\!APAR_{\text {m}\!sh}\!\times\!LAI_{\text{m}\!sh}\!\right)\!\times\!\!f\!\left(\!V\!PD\! \right)\!\times\!\!g\!\left(\!T_{\!a\!min}\!\!\right) \tag{2}\]  
\[G\!P\!P\!=\!\!\left(\!\!\frac{\varepsilon_{m}\!\times\!APAR_{\text{max}}\! \times\!\beta}{\varepsilon_{m}\!\times\!APAR_{\text{max}}\!+\!\beta}\!\times\! LAI_{\text{max}}\!+\!\frac{\varepsilon_{m}\!\times\!APAR_{\text{m}\!sh}\!\times\!\beta}{ \varepsilon_{m}\!\times\!APAR_{\text{m}\!sh}\!+\!\beta}\!\times\!LAI_{\text{ m}\!sh}\!\right)\!\times\!f\!\left(\!V\!PD\!\right)\!\times\!\!g\!\left(\!T_{\!a\!min}\!\!\right) \tag{3}\]  
where \(\varepsilon_{max}\) is the maximum LUE in MOD17; _fPAR_ is the fraction of PAR absorbed by vegetation and calculated from LAI using the Beer's Law (_fPAR_=1-e\({}^{-k^{\star}Ld}\), where \(k\) is the light extinction coefficient and set as 0.5 as [23]); \(\varepsilon_{m}\!su\) and \(\varepsilon_{m}\!sh\) are the maximum LUE of sunlit and shaded leaves in TL-LUE, respectively; \(\varepsilon_{m}\) is the quantum yield when incident PAR approaches zero and \(\beta\) is the maximum canopy photosynthetic flux density at light saturation in TL-LUEn [13]; _f(VPD)_ and \(g(T_{amin})\) denote the constrains imposed by atmospheric vapor pressure deficit (VPD) and minimum air temperature, respectively, and are used to downscale the maximum LUE values to real ones. _APAR\({}_{msu}\)_ and _APAR\({}_{msh}\)_ are the PAR absorbed by sunlit and shaded leaves per unit \(LAI\); \(LAI_{msu}\)_ and \(LAI_{msh}\) are the leaf area index for sunlit and shaded leaves. In above equations, the two attenuation scalars, _f(VPD)_ and \(g(T_{amin})\), range from 0 (total inhibition) to 1 (no inhibition) and are calculated using the same formulas for MOD17, TL-LUE, and TL-LUEn. Parameters _VPD\({}_{max}\)_, _VPD\({}_{min}\)_, _T\({}_{amin\_min}\)_, and _T\({}_{amin\_max}\)_ used to calculate _f(VPD)_ and \(g(T_{amin})\) depend on vegetation types [91] and are listed in Table 2.  
In Equations (2) and (3), _APAR\({}_{msu}\)_ and _APAR\({}_{msh}\)_ are calculated as: \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Site Name** & **Country** & **Lat. (\textasci{})** & **Long. (\textasci{})** & **Veg.** & **Opti.** & **Vali.** & **Reference** \\  & & & & **Type** & **Years** & **Years** & **Years** \\ \hline Vaira Ranch (VRA) & USA & 38.41 & \(-\)120.95 & GRASS & 2003,2004 & 2007 & [PERSON] _et al._ (2004) [85] \\ [PERSON] (VSA) & Belgium & 50.31 & 6.00 & MF & 2001,2002 & 2003 & [PERSON] _et al._ (2001) [88] \\ Willow Creek (WCR) & USA & 45.81 & \(-\)90.08 & BF & 2003 & 2005 & [PERSON] _et al._ (2004) [89] \\ [PERSON] (WET) & Germany & 50.45 & 11.46 & NF & 2002 & 2003 & [PERSON] _et al._ (2009) [90] \\ \hline \hline \end{tabular}
\end{table}