## 4 Result and Discussion  
### Retrieval of Daily Reference Evapotranspiration  
The optimization of the three ML models (RF, GBM, and XGBoost) was conducted through the training process, followed by the blind test for the optimized models. The accuracy statistics of the three models were very similar, although the RF showed slightly better performance (Table 2). We chose the RF model because it is a commonly used machine learning model of which maintenance and rebuilding are more convenient. Figure 5 shows the accuracy statistics of the blind test of the RF model. The MBE was 0.007 mm/day, including unbiased predictions without over- or under-estimation. The MAE was 0.790 mm/day, the RMSE was 1.038 mm/day, and the CC was 0.870, indicating quite a strong accordance with the KMA in situ data. A scatterplot also shows that the test retrieval for the 3,184 cases was successful, with few deviations from the 1:1 line. \begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & **MBE** & **MAE** & **RMSE** & **CC 1** \\ \hline Random forest (RF) & 0.007 & 0.790 & 1.038 & 0.870 \\ Gradient boosting machine (GBM) & 0.010 & 0.820 & 1.068 & 0.862 \\ Extreme gradient boosting (XGBoost) & 0.000 & 0.786 & 1.039 & 0.869 \\ \hline \end{tabular} \({}^{1}\)\(p\)-value \(<\) 0.001.  
\end{table} 
Table 2: Accuracy comparison of the three machine-learning (ML) models. Figure 4: Conceptual diagram of 10-fold calibration/validation with random sampling [42]. The importance of 9 variables was evaluated based on permutation feature importance (PFI) [41] (Table 3). Relative humidity, land surface temperature, and air temperature accounted for about 70% of the importance of all variables. The transport of water vapor from the soil and vegetation to the atmosphere is mainly controlled by the heat transfer between the land surface and the atmosphere [44]. Relative humidity (PFI = 33.2%) is directly associated with the vapor pressure deficit (VPD) \((e_{s}-e_{a})\) in the PM equation, which represents the capacity of the diffusion of water vapor to the atmosphere. Under the conditions of sufficient soil moisture, a high VPD and low relative humidity result in high evapotranspiration (Figure 6a). Although the degree of stomatal opening, which is associated with the transpiration rate, can be decreased under extremely dry conditions of very high VPD, the plant transpiration is generally increased by the high evaporative capacity [45]. The land surface temperature (PFI = 25.1%) and the air temperature (PFI = 11.9%) can influence the relative humidity. Indeed, the land surface temperature had a positive relationship with ET\({}_{0}\) (Figure 6b), as mentioned in the previous studies [46]. The evaporation can increase if high thermal energy is available to convert the liquid water to water vapor under a sufficient supply of water. Figure 5: Scatterplot for the Korea Meteorological Administration (KMA) in situ daily ET\({}_{0}\) vs. estimated daily ET\({}_{0}\) in the blind test of the RF model in the croplands of South Korea, 2013–2019, with the accuracy statistics in terms of the mean bias error (MBE), mean absolute error (MAE), root mean square error (RMSE), and correlation coefficient (CC). \(\text{ET}_{0}\) is not directly controlled by rainfall or vegetation phenology, according to the definition of \(\text{ET}_{0}\). However, the high-priority variables of the \(\text{ET}_{0}\) model can have direct or indirect relationships with the other variables, such as rainfall and vegetation (NDVI, LAI, and FPAR). Hence, the variables with lower importance should not be considered unnecessary for the AI modeling of \(\text{ET}_{0}\) to cope with the nonlinearity between the variables. Figure 7 shows that the estimation errors were not significantly influenced by wind speed. Further, the errors were decreased when the wind was strong because the aerodynamic resistance, which is generally governed by wind speed, has less fluctuation against the wind speed under strong winds [47].