## 2 Data and Methods  
### The Revised EC-LUE Model and Parameterization  
We used the revised Eddy Covariance Light Use Efficiency (EC-LUE) model to evaluate its potential for improving GPP estimates. The revised EC-LUE model integrated the impacts of atmospheric CO\({}_{2}\) concentration, the limitation of atmosphere water demand (i.e., vapor pressure deficit, VPD), and radiation components on GPP [8], and substantially improved its capability for reproducing interannual variability of GPP compared to the original EC-LUE [27]. The revised EC-LUE model simulated GPP as the following expression:  
\[GPP=PAR\times FPAR\times\varepsilon_{max}\times C_{s}\times min\left(T_{s},W_{s}\right) \tag{1}\]  
where _PAR_ (MJ m\({}^{-2}\)) is the incident photosynthetically active radiation; _FPAR_ is the fraction of photosynthetically active radiation absorbed by plants; \(\varepsilon_{\max}\) (g C m\({}^{-2}\) MJ\({}^{-1}\)) is the maximum light use efficiency; C\({}_{8}\) represents the downward regulation scalar of atmospheric CO\({}_{2}\) concentration; and \(T_{s}\) and \(W_{s}\) are the temperature scalar and water scalar on LUE, respectively. The value of \(C_{s}\) and environmental stress factor (\(T_{s}\) and \(W_{s}\)) ranged from 0 to 1. More detailed information about \(C_{s}\) was summarized by [8]. \(C_{s}\), \(T_{s}\), \(W_{s}\) and _FPAR_ were calculated as follows:  
\[C_{s}=\frac{C_{i}-\theta}{C_{i}+2\theta} \tag{2}\]  
\[T_{s}=\frac{\left(T_{a}-T_{min}\right)\times\left(T_{a}-T_{max}\right)}{\left( T_{a}-T_{min}\right)\times\left(T_{a}-T_{max}\right)-\left(T_{a}-T_{opt} \right)\times\left(T_{a}-T_{opt}\right)} \tag{3}\]  
\[W_{s}=\frac{VPD_{0}}{VPD_{0}+VPD} \tag{4}\]  
\[FPAR=1.24\times NDVI-0.168 \tag{5}\]  
where \(\theta\) (ppm) is the CO\({}_{2}\) compensation point in the absence of dark respiration, and \(C_{i}\) (ppm) is the CO\({}_{2}\) concentration in the intercellular air spaces of the leaf. \(T_{min}\), \(T_{opt}\) and \(T_{max}\) represent the minimum, optimum, and maximum temperatures for terrestrial vegetation photosynthesis (\({}^{\circ}\)C), respectively. The default values of _Tmin_, _Topt_ and _Tmax_ are set to 0 \({}^{\circ}\)C, 40 \({}^{\circ}\)C and 20.33 \({}^{\circ}\)C, respectively [27], and _VPD\({}_{0}\)_ is the empirical half-saturation coefficient for the _VPD_ constraint [8]. We used the Markov chain Monte Carlo (MCMC) method to calibrate the parameters of the revised EC-LUE models through the ground-GPP observations using Landsat and MODIS NDVI, respectively. The prior value for each parameter was set as uniform, and the range for each parameter was set as described in [28]. We conducted the parameter optimization at a total of 78 FLUXNET sites across 10 vegetation types. More details on the model optimization process are presented in [28]. We first set the prior value for each parameter with an interval as described in [28], and then optimized three parameters (\(\varepsilon_{max}\), \(\theta\) and \(VPD_{0}\)) of the revised EC-LUE model for each vegetation type. Observations from odd-numbered years from all sites for each vegetation type were used to optimize the model performance, while observations from even-numbered years were used to evaluate the model performance. Two sets of parameters of the revised EC-LUE model were then generated, based on two NDVI datasets, at 30 m and 500 m spatial resolution, respectively. Finally, we compared the performance of the model with their own optimized parameters at 30 m and 500 m spatial resolution, respectively. We used the coefficient of determination (\(R^{2}\)), and root mean squared error (_RMSE_) to evaluate the model performance, and used the standard deviation (SD) and coefficient of variation (CV) to assess the heterogeneity of the FLUXNET footprint. R\({}^{2}\) and RMSE were calculated as follows.