## 2 Methods
### Selection of Vegetation Indices (VIs)
\begin{table}
\begin{tabular}{c c c c c} \hline  & **GCOM-C/SGLI** & \multicolumn{3}{c}{**TERRA/MODIS**} \\
**Band Name** & **Wavelength (nm)** & **Width** & **Wavelength (nm)** & **Width** \\ \hline \(\rho_{\rm{blue}}\) & 443 & 10 & 469 & 20 \\ \(\rho_{\rm{green}}\) & 530 & 20 & 555 & 20 \\ \(\rho_{\rm{red}}\) & 673.5 & 20 & 655 & 50 \\ \(\rho_{\rm{NIR}}\) & 868.5 & 20 & 858.5 & 35 \\ \hline \end{tabular}
\end{table} 
Table 1: Global Change Observation Mission-Climate (GCOM-C)/ second-generation global imager (SGLI) and TERRA/MODIS spectral bands (showing only bands 1 to 4). _Remote Sens._**2012**, \(4\)  
\[\mathrm{SR}=\frac{\rho_{\mathrm{NIR}}}{\rho_{\mathrm{red}}} \tag{6}\]  
(6) The **green NDVI (GNDVI)**[50] is a better VI at a higher LAI and is good at detecting chlorophyll. The GNDVI can detect a wider range of chlorophyll compared to the NDVI. \[\mathrm{GNDVI}=\frac{\rho_{\mathrm{NIR}}\ \ \begin{table}
\begin{tabular}{l l l l l l l l} \hline
**Site Name** & **CA-Let** & **_JP-TMK_** & **_JP-TKY_** & **_JP-Mase_** & **_JP-FJY_** & **US-Dki_** & **TH-SKR** \\ (data year) & 2002, 2003 & 2002, 2003 & 2003, 2004 & 2002, 2003 & 2003, 2004 & 03 & 2002, 2003 \\ \hline
**City** & Lethbridge & Hokkaido & Takayama & Tsukuba & Yamanashi & Ne & Sakazert \\
**Country** & Canada & Japan & Japan & Japan & Japan & USA. & Thailand \\
**Latitude** & 49.7097N & 42.7377N & 36.1467N & 36.0547N & 35.4547N & 35.9717N & 14.4927N \\
**Longitude** & \(-\)112.9407W & 141.5197E & 137.4237E & 140.027E & 138.762E*E & \(-\)79.0937W & 101.916E \\
**Plant Functional Types** & Cg grass, Arctic & NDT & BDT,Temperature & Crop & NRT,Temperature & Cg grass & BET,Tropical \\
**Dominant species** & Short/mixed grass & Japanese & Deedicous Okd, & Rice & Japanese red & Tall fesco,C3 & Directorcap \\  & prairie (C3C4) & Larch & Birch & pine & grass and fofs & \\
**Tree age (years)** & - & 45 & 50 & - & 90 & 1 & - \\
**Elevation (m)** & 960 & 140 & 1420 & 13 & 1030 & 163 & 535 \\
**Cansey height (m.)** & - & 16 & 15-20 & 1.2 & 20 & 0.1–1 & 35 \\
**Flux measurement** & 4 & 27 & 25 & 3 & 25.4 & 3 & 45 \\
**height (m)** & & & & & & & \\
**Annual** & 5.36 & 6.61 & 7.2 & 12.9 & 10.1 & 15.5 & 24.1 \\
**avg. air temp. (C)** & & & & & & & \\
**U\({}^{\star}\) threshold (m/s)** & 0.2 & 0.3 & 0.5 & 0.1 & 0.12 & 0.2 & 0.2 \\
**Reference** & [PERSON] _et al._ & [PERSON] _et al._ & [PERSON] _et al._ & [PERSON] _et al._ & [PERSON] _et al._ & [PERSON] _et al._ & [PERSON] _et al._ \\  & 2005 & 2007 & 2005 & 2005 & 2012 & 2004 & 2007 \\ \hline \end{tabular} Plant Functional Types (PFTs) 1. NET, temperate = Needleleaf (Pergeon Temperature Trees 2. NDT = Needleleaf Desidous Trees 3. BET, Tropical = Broadleaf Pergreen Tropical Trees = 4.BDT,Temperature = Broadleaf Desidous Temperate Trees, U\({}^{\star}\) = friction velocity.  
\end{table} 
Table 2: Description of the study sites representing seven plant functional types. 3.3 Satellite-Scale Data Set: EC Flux Data and MODIS Spectral Reflectance of Seven Plant Functional Types  
Seven EC flux tower sites were selected from Bonan, 1996 [62]. These sites correspond to seven of dominant plant functional types. We selected study sites on the basis of online availability and accessibility of necessary parameters. Details of each site are summarized in Table 2. The study sites were representative of C3 grass, arctic (CA-Let); needleleaf deciduous trees (JP-TMK); broadleaf deciduous trees, temperate (JP-TKY); crop-paddy fields (JP-Mase); needleleaf evergreen trees, temperate (JP-FJY); C3 grass (US-Dk1); and broadleaf evergreen trees, tropical (TH-SKR). All of the EC flux data were used to calculate Pmax_capacity using the light-response curve.