## 2 Materials and Methods
### Materials
#### 2.1.2 GMAO Meteorological Reanalysis Data  
The MODIS GPP Collection 6 (MOD17A2H, C6) data used in this paper implement Global Modeling and Assimilation Office (GMAO) Reanalysis data for direct meteorological inputs. The current version of GMAO is an hourly time step dataset with 0.5 latitude degree by 0.625 longitude degree resolution. For every flux tower site, hourly meteorological data including air temperature  
\begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline
**Site Name** & **Country** & **Lat.** & **Lon.** & **Biome Type** & **MAT** & **MAP** & **Data Period** \\ \hline Virasoro(AR-Vir) & Argentina & \(-\)28.24 & \(-\)56.19 & ENF & 21.6 & 1433 & 2010–2012 \\ Alice Springs(ALU-ASM) & Australia & \(-\)22.28 & 133.25 & ENF & 22.2 & 390 & 2010–2013 \\ Riggs Creek(ALU-Rig) & Australia & \(-\)36.65 & 145.08 & GRA & 15.4 & 418 & 2011–2013 \\ Whorom(AU-Wurm) & Australia & \(-\)36.67 & 145.03 & EBF & 15.7 & 411 & 2011–2013 \\ Lonzee(BE-Lon) & Belgium & 50.55 & 4.75 & CRO & 10.0 & 800 & 2004–2014 \\ Velsalam(BE-Vie) & Belgium & 50.31 & 6.00 & MF & 7.8 & 1062 & 2001–2014 \\ Santerman-NS-Logged Forest(BR-Sa3) & Brazil & \(-\)30.2 & \(-\)54.97 & EBF & 26.1 & 2044 & 2001–2004 \\ Ontario-Grounding River(CA-Gro) & Canada & 48.22 & \(-\)82.16 & MF & 1.3 & 831 & 2003–2014 \\ Billy King-grassland(C-BK2) & Czech Republic & 49.49 & 18.54 & GRA & 6.7 & 1316 & 2006–2011 \\ Hainich(DE-Hai) & Germany & 51.08 & 10.45 & DBF & 8.3 & 720 & 2001–2012 \\ Sorce-LilleBogeskov(DK-Sor) & Denmark & 55.49 & 11.64 & DBF & 8.2 & 660 & 2001–2012 \\ Grignon(FR-Gr) & France & 48.84 & 1.95 & CRO & 12.0 & 650 & 2001–2014 \\ Puchaohron(FR-Fue) & France & 43.74 & 3.60 & EBF & 13.5 & 883 & 2001–2013 \\ Arkansas(GH-Ank) & Ghana & 5.27 & \(-\)2.69 & EBF & 26.0 & 1900 & 2011–2012, 2014 \\ Renon/Ritter(IT-Rene) & Italy & 46.59 & 11.43 & ENF & 4.7 & 809 & 2001–2013 \\ Sardilla Pasture(PA-SPs) & Panama & 9.31 & \(-\)79.63 & GRA & 26.5 & 2350 & 2007–2009 \\ Curtice Walter-Berger cropland(US-CRT) & USA & 41.63 & \(-\)83.35 & CRO & 10.1 & 849 & 2011–2013 \\ Walnut Guck Kendall Grasslands(US-Wkg) & USA & 31.74 & \(-\)109.94 & GRA & 15.6 & 407 & 2004–2014 \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of FLUXNET eddy covariance tower sites used in this study. Site descriptions include name (site ID), country, latitude and longitude (lat./lon., decimal degrees), general biome type, mean annual temperature (MAT, \({}^{\circ}\)C), mean annual long-term precipitation (MAP, mm) and years of measurements. ENF: evergreen needleleaf forests; EBF: evergreen broadleaf forests; DBF: deciduous broadleaf forests; MF: mixed forests; GRA: grasslands; CRO: croplands.  
(T\({}_{\rm air}\), \({}^{\circ}\)C), specific humidity (SH, kg\(\cdot\)kg\({}^{-1}\)), surface pressure (Pres, Pa) and SWRad (W\(\cdot\)m\({}^{-2}\)) during 2001-2014 were downloaded from NASA Goddard Space Flight Center [35]. Through data preprocessing, key parameters including the daily average air temperature (T\({}_{\it argg}\), \({}^{\circ}\)C), daily minimum air temperature (T\({}_{\it min}\), \({}^{\circ}\)C), daytime average VPD (VPD\({}_{\it argg}\), Pa) and daily total SWRad (MJ\(\cdot\)m\({}^{-2}\)\(\cdot\)d\({}^{-1}\)) were obtained at a 0.5\({}^{\circ}\)\(\times\) 0.625\({}^{\circ}\) spatial resolution. Using a spatial nonlinear interpolation scheme developed by [PERSON] et al. (2005) [12], we further interpolated the GMAO data down to the 500-m MOD17A2H pixel spatial resolution. In order to make comparisons between reanalysis meteorological data and observed meteorological data, the same spatial nonlinear interpolation method was also employed to interpolate the GMAO data to EC flux tower locations [36].