## 2 Materials and Methods
### Modeling  
#### 2.2.1 TL-LUE Model  
The TL-LUE model [12] is based on MODIS GPP [40] and the Boreal Ecosystem Productivity Simulator (BEPS) model [41]. Model validation was performed at both the site [42; 43] and the regional scale [44]. Additional information on the model was introduced in [12; 42; 43]. The model parameters used for the TL-LUE models followed [PERSON] et al. [43].  
GPP was calculated with the following Equation (3):  
\[\text{GPP}=(\varepsilon_{\text{msu}}\times\text{APAR}_{\text{su}}+\varepsilon_ {\text{msh}}\times\text{APAR}_{\text{sh}})\times f(\text{VPD})\times f(T_{\text {amin}}) \tag{3}\]  
where \(\varepsilon_{\text{msu}}\) and \(\varepsilon_{\text{msh}}\) are the maximum LUE of sunlit and shaded leaves, respectively; APARsu and APARsh are the absorbed PAR of sunlit and shaded leaves, respectively; and \(f(\text{VPD})\) and \(f(T_{\text{amin}})\) are stress factors of Vapour Pressure Deficiency (VPD) and air temperature, respectively. APARsu and APARsh were calculated with the following Equations (4) and (5):  
\[\text{APAR}_{\text{su}}=(1-\alpha)\times[\text{PAR}_{\text{dir}}\times\cos( \beta)/\cos(\theta)+(\text{PAR}_{\text{diff}}-\text{PAR}_{\text{diff},\text{u} })/\text{LAI}+C]\times\text{LAI}_{\text{su}} \tag{4}\]  
\[\text{APAR}_{\text{sh}}=(1-\alpha)\times[(\text{PAR}_{\text{diff}}-\text{PAR} _{\text{diff},\text{u}})/\text{LAI}+C]\times\text{LAI}_{\text{sh}} \tag{5}\]  
where \(\alpha\) is albedo; PARdiffu is diffuse radiation under the canopy; \(C\) is multiple scattered radiation; \(\beta\) is the leaf angle, which was considered to be \(60^{\circ}\); \(\theta\) is the solar zenith angle; PARdiff and PARdir are incoming direct and diffuse radiation, respectively ([PERSON] et al., 1999). LAIsu and LAIsh are the LAI of sunlit and shaded leaves and was calculated with Equations (6) and (7):  
\[\text{LAI}_{\text{su}}=2\times\cos(\theta)\times(1-\exp(-0.5\text{LAI}/\cos( \theta))) \tag{6}\]  
\[\text{LAI}_{\text{sh}}=\text{LAI}-\text{LAI}_{\text{su}} \tag{7}\]  
On the basis of Equations (3)-(5), GPP derived from diffuse radiation can be calculated with the following Equation (8):  
\[\text{GPP}_{\text{diff}}=\Big{(}\varepsilon_{\text{msu}}\times\Big{(}(1- \alpha)\times\frac{\text{PAR}_{\text{diff}}-\text{PAR}_{\text{diff}}}{\text{ LAI}}\Big{)}\times\text{LAI}_{\text{msu}}+\varepsilon_{\text{msh}}\times\Big{(}(1- \alpha)\times\frac{\text{PAR}_{\text{diff}}-\text{PAR}_{\text{diff}}}{\text{ LAI}}\Big{)}\times\text{LAI}_{\text{msh}}\Big{)}\times f(\text{VPD})\times g(T_{\text{A}}\min) \tag{8}\]  
where GPPdiff and GPPdir are GPP contributed by diffuse and direct radiation, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Latitude (\({}^{\circ}\))** & **Longitude (\({}^{\circ}\))** & **Years** & **Vegetation Types** \\ \hline Xishuanggbanna (XSBN) & 21.95 & 101.2 & 2003–2012 & BF \\ Dinghushan (DHS) & 23.17 & 112.53 & 2003–2011 & BF \\ Ailaoshan (ALS) & 24.54 & 101.03 & 2009–2011 & BF \\ Luancheng (LC) & 37.88 & 114.68 & 2009–2012 & CROP \\ Yucheng (YC) & 36.83 & 116.57 & 2003–2012 & CROP \\ Haibei2 (HB) & 37.61 & 101.33 & 2003–2012 & GRASS \\ Neimeng (NM) & 43.53 & 116.67 & 2004–2012 & GRASS \\ Duolun (DL) & 42.03 & 116.28 & 2010–2012 & GRASS \\ Dangxiong (DX) & 30.5 & 91.07 & 2004–2011 & GRASS \\ Changbaishan (CBS) & 42.4 & 128.1 & 2003–2011 & MF \\ Qianyanzhou (QYZ) & 26.73 & 115.07 & 2003–2012 & NF \\ Huitong (HT) & 26.79 & 109.59 & 2008–2012 & NF \\ Haibei1 (HBG) & 37.67 & 101.33 & 2003–2012 & Shrub \\ \hline \hline \end{tabular}
\end{table}
Table 3: Specifications for the 13 flux tower sites. (BF means broad-leaved forest; CROP means crop; GRASS means grass; MF means mixed forest; NF means needle-leaved forest; Shrub means shrubland).