## 2 Data and Methods
### Sensitivity Analysis  
We applied the one-at-a-time sensitivity method [28] to compute the sensitivity of annual GPP, ET and WUE simulated by the MODIS GPP and ET algorithms to input daily meteorological variables,remotely-sensed variables and model parameters (Table 2) at the eight ChinaFLUX sites. We computed GPP, ET and WUE using the MODIS algorithms in the year 2005, given that each of the input variables or model parameters increases or decreases 10%, 20% and 30%, while the other parameters are fixed. The model run (\(run_{+10\%}\) or \(run_{-10\%}\)) had \(+10\%\) or \(-10\%\) variations for a chosen variable or parameter and the reference run (\(run_{\text{base}}\)) used default values. The sensitivity of modeled variables to the selected parameter or driving variables was calculated as the following equation [29, 30]:  
\[\text{S}=\text{max}\left(\frac{|\text{run}_{+10\%}-\text{run}_{\text{base}}|} {\text{run}_{\text{base}}},\frac{|\text{run}_{-10\%}-\text{run}_{\text{base}}| }{\text{run}_{\text{base}}}\right)\times 100 \tag{6}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ID** & **Symbol** & **Definition** & **Units** &
\begin{tabular}{c} **Used for GPP** \\ **or ET** \\ \end{tabular} \\ \hline \multicolumn{5}{c}{**Driving Variable**} \\ \hline
1 & \(T_{\text{min}}\) & minimum air temperature & \({}^{\circ}\)C & GPP, ET \\
2 & \(T_{\text{mean}}\) & mean air temperature & \({}^{\circ}\)C & ET \\
3 & \(T_{\text{day}}\) & daytime air temperature & \({}^{\circ}\)C & ET \\
4 & \(T_{\text{night}}\) & nighttime air temperature & \({}^{\circ}\)C & ET \\  & & fraction of absorbed & & \\
5 & FPAR & photosynthetically-active radiation & - & GPP, ET \\
6 & RH & relative humidity & \% & ET \\
7 & VPD & water vapor deficit & Pa & GPP, ET \\
8 & LAI & leaf area index & m\({}^{2}\cdot\)m\({}^{-2}\) & ET \\
9 & \(\alpha\) & albedo & - & ET \\
10 & \(R_{\text{s}}\)\({}_{\text{i}}\) & downward shortwave radiation & J\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\) & GPP, ET \\ \hline \multicolumn{5}{c}{**Model Parameter**} \\ \hline
11 & \(LUE_{\text{max}}\) & maximum light use efficiency & kg\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)d\({}^{-1}\cdot\)MJ\({}^{-1}\) & GPP \\
12 & \(T_{\text{min\_close}}\) & threshold value below which & \({}^{\circ}\)C & GPP, ET \\  & & the stomatal close completely & & \\
13 & \(T_{\text{min\_open}}\) & threshold value upon which there will & \({}^{\circ}\)C & GPP, ET \\  & & be no temperate stress & & \\
14 & VPD\({}_{\text{open}}\) & threshold value below & Pa & GPP, ET \\  & & which the stomatal close completely & & \\  & & the threshold value upon & Pa & GPP, ET \\
15 & VPD\({}_{\text{close}}\) & which there will be no water stress & & \\
16 & \(gl\_sh\) & leaf conductance to sensible & & \\  & & heat per unit LAI & & \\
17 & \(gl\_e\_wv\) & leaf conductance to evaporated & & \\  & & water vapor per unit LAI & & \\
18 & \(C_{\text{L}}\) & mean potential stomatal & & \\  & & conductance per unit leaf area & & \\
19 & \(rbl\_min\) & minimum value of totalaerodynamic & & \\  & & resistance to vapor transport & & \\
20 & \(rbl\_max\) & maximum value of total aerodynamic & & \\  & & resistance to vapor transport & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Input driving variables and model parameters in the MODIS gross primary production (GPP) and evapotranspiration (ET) algorithms.  
MODIS eight-day data of albedo, LAI and FPAR in 3 \(\times\) 3 homogenous pixels (3 \(\times\) 3 km) around the center of eight flux towers were downloaded from the University of Oklahoma ([[http://www.eomf.ou.edu](http://www.eomf.ou.edu)]([http://www.eomf.ou.edu](http://www.eomf.ou.edu))). To remove the effect of cloud cover, we used the harmonic analysis of time series (HANTS) algorithm to obtain the temporal interpolation of LAI and FPAR at a daily time step. Gap-filled half-hourly temperature, relative humidity, VPD and incoming solar radiation measured at the flux towers were aggregated to a daily step.