## 4 Results  
### Results from Three Machine Learning Algorithms  
Among all three models, SVR models resulted in the lowest performances, as the RMSE and rRMSE were always the highest at all study sites (Figure 4). RF yielded similar or slightly better performances than Cubist, with RMSE less than 2.5 mm/8 days for US sites and 5.7 mm/8 days for Korean sites; rRMSEs were less than 20% at the US sites and less than 15% at Korea sites, which is within the range of the MODIS ET product accuracy (rRMSE around 25%) [10]. Performances of all models have similar temporal patterns, with increasing errors (both RMSE and rRMSE) during growing seasons (June-September) and decreasing errors during leaf-off seasons (October-December). Figure 5 shows the average importance of the eleven Landsat indicators resulting from all RF models and their ranks. Importance of a variable is measured by the increase in MSE when the variable is permuted. Greater increase in MSE indicates higher importance of the variable. Table 5 shows the mean and standard deviation of linear correlation coefficients (\(\rho\)) between Landsat indicators and MODIS ET calculated at all dates or only during growing seasons. From Figure 5 and Table 5, the  
Figure 4: Root Mean Square Error (RMSE) and relative RMSE (rRMSE%) of Support Vector Regression (SVR), Random Forest (RF), and Cubist models at: Site 1 (**a,b**); Site 2 (**c,d**); Site 3 (**e,f**); and Site 4 (**g.h**). variable importance in RF models was largely consistent with the correlations between the variables and MODIS ET. Among the eleven indicators, NDVI, EVI, and SAVI that are related to vegetation greenness and growth conditions were ranked the most important in ET modeling. Permuting values of NDVI could lead to as much as a 7.2 mm/8 days ET bias. The correlation coefficients between these variables and MODIS ET were also highest with positive relationships (\(\rho>0.69\) when averaged at all dates and \(\rho>0.73\) during growing seasons, \(p\)-value \(<0.0001\)). Variables representing vegetation moisture status including NDIIb7 and NDWI were ranked the fourth and fifth. As is shown in Table 5, correlations between NDIIb7, NDWI and MODIS ET were slightly weaker than NDVI/EVI/SAVI but still strong and significant (\(\rho=0.68\) and \(-0.67\), respectively, for all seasons and \(\rho=0.79\) and \(-0.76\) for growing seasons). LST and TVDI are also negatively related to ET as increasing temperature usually corresponds to dry conditions resulting in less evapotranspiration. Although previous studies have shown that temperature-related variables have a dominant impact on satellite-based daily ET estimation, the correlation coefficients between LST and ET are only \(-0.59\) on average in our study and those between TVDI and ET were only \(-0.32\) when all seasons were considered. LST/TVDI were overall ranked less important than vegetation greenness and moisture  
Figure 5: Importance of the 11 variables represented by the average increase in Mean Squared Error (MSE) of evapotranspiration (ET) resulted from all RF models at the four sites. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{2}{c}{**All Dates**} & \multicolumn{2}{c}{**Growing Season (June–September)**} \\ \cline{2-5}  & **Average \(\rho\)** & **Standard Deviation of \(\rho\)** & **Average \(\rho\)** & **Standard Deviation of \(\rho\)** \\ \hline NDVI & 0.72 & 0.31 & 0.82 & 0.13 \\ EVI & 0.70 & 0.31 & 0.76 & 0.13 \\ SAVI & 0.69 & 0.23 & 0.73 & 0.14 \\ NDIIb7 & 0.68 & 0.35 & 0.79 & 0.16 \\ NDWI & \(-0.67\) & 0.23 & \(-0.76\) & 0.13 \\ MSAVI & 0.68 & 0.31 & 0.75 & 0.14 \\ LST & \(-0.59\) & 0.29 & \(-0.73\) & 0.15 \\ NDMI & \(0.66\) & 0.31 & 0.75 & 0.19 \\ D1609 & \(-0.42\) & 0.21 & \(-0.62\) & 0.16 \\ Albedo & \(-0.38\) & 0.24 & \(-0.44\) & 0.22 \\ TVDI & \(-0.32\) & 0.39 & \(-0.60\) & 0.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Correlation coefficients between Landsat variables and MODIS ET. indices.