## 2 Materials and Methods
### Satellite-Based Re Estimations  
Re is mainly composed of two components, autotrophic respiration by plants (Ra) and heterotrophic respiration by heterotrophic microorganisms (Rm) [75]. Ra is the sum of respiration from all plant components, including leaves, stems, flowers of aboveground biomass and roots of underground biomass, which generally depend on current photosynthate [43], and thus couple closely with GPP [42]. Rm is mainly composed of microbial respiration of plant residues and soil organic matter decomposition [43], which is strongly exponentially correlated to temperature variation under water-unlimited conditions [42; 44]. Thus in this study, we also considered the LSWI as a water index for regulating the Re variation as Equation (14) [44].  
\[Re=Ra+Rm=a\times GPP+b\times e^{(c\times LST+d^{*}LSWI+e^{*}LSWI^{2})} \tag{14}\]  
where Re is the satellite-based ecosystem respiration estimations. GPP can be estimated from all the seven methods we mentioned above (Figure 1), and we selected those which have no significant biases for GPP_EC. LST is the land surface temperature that is the average of daytime and nighttime land surface temperature extracted from MOD11A2. \(a\), \(b\), \(c\), \(d\) and \(e\) are regression parameters. Based on the GPP_EC, we trained the satellite-based Re model separately in growing season (GS) and non-growing season (NG) from 2009 to 2011 (Table 1). In NG, we assumed GPP approaches zero thus we adjusted the parameter of \(a\) as zero.  
Based on our preliminary test for Equation (14), we found the effect of LSWI on Re estimation was insignificant (\(p>0.05\)) for all separate seasons from 2009 to 2011 (parameters of \(d\) and \(e\) in Table 1). Therefore, we simplified Equation (14) for further Re estimations (Equation (15)).  
\[Re=Ra+Rm=a\times GPP+b\times e^{(c\times LST)} \tag{15}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Year** & **Period** & \(\mathbf{a}\) & \(\mathbf{b}\) & \(\mathbf{c}\) & \(\mathbf{d}\) & \(\mathbf{e}\) & \(\mathbf{R^{2}}\) & \(\mathbf{p}\) \\ \hline \multirow{2}{*}{2009} & GS & 0.195 * & 2.631 ** & 0.044 ** & 1.691 & 9.551 & 0.56 & *** \\  & NG & 0 & 2.009 *** & 0.044 *** & 1.828 & 14.714 & 0.78 & *** \\ \hline \multirow{2}{*}{2010} & GS & 0.293 ** & 6.436 ** & -0.012 * & 1.138 & -4.209 & 0.84 & *** \\  & NG & 0 & 2.085 *** & 0.015 * & 6.569 & 53.088 & 0.17 & *** \\ \hline \multirow{2}{*}{2011} & GS & 0.517 *** & 2.712 * & -0.057 * & -0.449 & 55.408 & 0.71 & *** \\  & NG & 0 & 1.058 *** & 0.061 ** & 5.655 & 45.792 & 0.30 & *** \\ \hline \multirow{2}{*}{All} & GS & 0.268 *** & 3.657 *** & 0.017 * & 1.875 * & 7.562 & 0.54 & *** \\  & NG & 0 & 1.652 *** & 0.045 *** & 5.151 & 42.125 & 0.38 & *** \\ \hline \hline \end{tabular}
* Correlation is significant at \(p<0.05\), ** \(p<0.01\), and *** \(p<0.001\) level (two-tailed test, \(\alpha=0.05\)). GS, growing season (\(n=21\) for a particular year from 2009 to 2011). NG, non-growing season (\(n=25\)).  
\end{table}
Table 1: Regression parameters for the satellite-based ecosystem repiration (Re) estimations based on tower-based gross primary production (GPP) and Re measurements (Equation (14)).