## 3 Results
### Model Performance  
The SWH model performed well for both ET and GPP simulations. Collectively, the SWH model explained 65% of the variation in eight-day ET and 68% in GPP at the 63 sites (\(p<0.01\), Figure 2). By comparison, the MODIS ET algorithm explained 53% of the variations in ET (\(p<0.01\)). In general, both the SWH model and the MODIS ET algorithm underestimated ET at the sites or in the season with high ET.  
The model performance for ET and GPP prediction for each site and vegetation type is shown in Table 3. According to the \(R^{2}\) and RMSE of the model-measurement relationship, the SWH model performance was best in MF (0.82, 0.59 mm-day\({}^{-1}\)), DBF (0.82, 0.66 mm-day\({}^{-1}\)) and ENF (0.81, 0.64 mm-day\({}^{-1}\)), followed by shrubland (0.80, 0.67 mm-day\({}^{-1}\)), savanna (0.80, 0.78 mm-day\({}^{-1}\)), cropland (0.78, 0.71 mm-day\({}^{-1}\)) and wetland (0.76, 0.9 mm-day\({}^{-1}\)). However, the model performance was inferior in EBF (0.70, 0.75 mm-day\({}^{-1}\)) and grassland (0.68, 0.83, mm-day\({}^{-1}\)). This result indicates that, except for EBF, the model performs better in woody ecosystems than in herbaceous ecosystems.  
Compared with the MODIS algorithm, the SWH model yielded a higher \(R^{2}\) at 58 of the 63 sites and lower RMSE at 36 of the 63 sites. The bulk average \(R^{2}\) of the SWH model for all 63 sites was 0.13 higher (0.77 for SWH and 0.64 for MODIS), and the average RMSE was 0.11 mm-day\({}^{-1}\) lower (0.72 for SWH and 0.83 for MODIS). The performance of the two models was comparable for DBF,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Biome** & ** NDVI** & **SWC** & \(b_{2}\) & \(b_{3}\) & \(a_{1}\) & \(g_{0}\) & \(\varepsilon_{\text{max}}\) & \(d\) \\ \hline Cropland & 3.0 & 0.4 & 0.5 & 0.5 & 2.2 & 1.0 & 2.2 & 0.2 \\ Forest & 5.1 & 0.5 & 0.8 & 1.3 & 4.2 & 1.3 & 4.2 & 0.2 \\ Grassland & 3.6 & 1.7 & 2.5 & 1.1 & 2.5 & 1.8 & 2.5 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Sensitivities of modeled ET to changes (max\([VR_{+10\%}\), \(VR_{-10\%}]\)) in key variables and parameters. NDVI: Normalized Dynamic Vegetation Index; SWC: soil water content.  
savanna and shrubland, whereas SWH exhibited superior performance for EBF, wetland and MF (Figure 3).  
Figure 3: Mean difference between the model predictions (including the SWH model and the MODIS ET algorithm) and observations in terms of (**a**) the determinant coefficient of the model-observation relationship (\(R^{2}\)); and (**b**) the root mean square error (RMSE) for each plant functional type. The numbers in parentheses indicate the number of sites used in this study. The error bars indicate standard deviations.  
Figure 2: Performances of the SWH model in estimating: (**a**) evapotranspiration (ET); and (**b**) gross primary productivity (GPP); and the performance of the MODIS ET algorithm in estimating ET (**c**). All of the sites used in this study use an eight-day timescale (\(n=9012\)). ET_EC and GPP_EC are the ET and GPP derived from the measurements using eddy covariance (EC) systems.  
When the interpolated climate data were used as the input variables, the model predictions were also consistent with the observations (i.e., the annual values of GPP and ET at 43 non-Chinaflux sites in China published in the literature). The model explained 77% and 84% of the spatial variability of GPP and ET, respectively (Figure 4). Note that similar to the validation for flux sites at the eight-day scale, certain underestimations of both GPP and ET were observed for the sites (or years) with high GPP and ET values. In addition, the regionalized model (i.e., driving with interpolated climate data) also illustrated good performance at the eight-day timescale. The model explained 62% and 77% of the variations in ET and GPP, respectively (Figure S2).