## 2 Materials and Methods
### Model Performance and Sensitivity Analysis  
With the calculated biome-specific parameters and soil water content being estimated with the bucket scheme, we evaluated the model with two independent datasets of ET and GPP. The first dataset was the in situ measurements at the 63 flux tower sites, and the second was the GPP and ET in ecosystems in China extracted from published literature (see the details in Section 2.3). The driving meteorological variables for this first dataset were the in situ measurements at the tower sites and were the 10-km interpolated products for the second dataset.  
The determinant coefficients of the relationship between model and observation (\(R^{2}\)) and the root mean square error (RMSE) were used to quantify the difference between the model predictions and observations:  
\[RMSE=\sqrt{\frac{\sum\left(O_{i}-M_{i}\right)^{2}}{N}} \tag{7}\]  
where \(O_{i}\) and \(M_{i}\) are the observed and modeled values, respectively. \(N\) is the total number of observations at one site.  
Sensitivity analysis is a critical step in the identification of the potential parameters and driving variables that cause model uncertainty. Some advanced methodologies for performing sensitivity analysis have been developed in recent years [41]. Here, we conducted a conventional one-at-a-time sensitivity analysis. This method involves varying the model parameters individually while fixing the remaining parameters [42]. We ran the SWH model by increasing or decreasing each of the model parameters or driving variables by 10% while fixing the others. The model output sensitivity (in %) was calculated as the relative differences in mean daily ET between the model runs (\(run_{+10\%}\) or \(run_{-10\%}\)) and the reference run (\(run_{base}\)):  
\[VR_{+10\%}=100\times\frac{\left|run_{base}-run_{+10\%}\right|}{run_{base}} \tag{8}\]  
\[VR_{-10\%}=100\times\frac{\left|run_{base}-run_{-10\%}\right|}{run_{base}} \tag{9}\]  
The maximum value between \(VR_{+10\%}\) and \(VR_{-10\%}\) was regarded as the sensitivity of the modeled ET to the selected parameter or the driving variable. In the sensitivity analysis, we mainly focused on the six estimated parameters with large variability among the sites (Table 1). In addition, because the soil water content was estimated and the NDVI product may have large uncertainty under cloudy weather conditions, these two driving variables were also included in the sensitivity analysis.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Biome** & \(b_{\mathbf{2}}\) & \(b_{\mathbf{3}}\) (**s-m\({}^{-1}\)**)** & \(a_{\mathbf{1}}\) & \(g_{\mathbf{6}}\) (**mol-m\({}^{-2}\).s\({}^{-1}\)**)** & \(\varepsilon_{\mathbf{max}}\) (**mg CO\({}_{2}\) \(\mu\)mol\({}^{-1}\) PPFD**) & \(d\) (**mm**) \\ \hline Cropland & 3.8 (0.7) & 643 (234) & 7.5 (3.8) & 0.028 (0.025) & 0.0022 (0.0003) & 303 (95) \\ Forest & 3.5 (0.8) & 724 (215) & 9.0 (5.4) & 0.005 (0.004) & 0.0011 (0.0003) & 244 (110) \\ Grassland * & 3.4 (0.9) & 508 (279) & 10.3 (4.2) & 0.017 (0.021) & 0.0012 (0.0005) & 188 (95) \\ \hline \hline \end{tabular}  
* The number of flux sites of savanna, wetland and shrubland is too small to estimate their parameters with acceptable confidence. Considering these biomes types are physically close to grassland and the values of optimized parameters are also close, we combines the four biome types and use the same parameter set. PPFD: photosynthetic photon flux density (\(\mu\)mol\(\cdot\)m\({}^{-2}\).s\({}^{-1}\)).  
\end{table}
Table 1: Look-up table of model parameters for each biome type. The values in parentheses are standard deviations.