## 3 Results
### Comparison of ANN Model with Different Input Data  
The input data of ANN in the ANN-PM model includes meteorological data (Ta, P, SW, Ca, and VPD) and remote sensing data (NIRv and NDVI). We investigate the accuracy  
Figure 4: A three-dimensional graph between the number of hidden layers, the number of neurons, and RMSE/MAE/R\({}^{2}\) of the training and validation datasets of the ANN-PM model. (**a1**) is the RMSE of the training, (**a2**) is the RMSE of the validation, (**b1**) is the MAE of the training, (**b2**) is the MAE of the validation, (**c1**) is the R\({}^{2}\) of the training, (**c2**) is the R\({}^{2}\) of the validation. RMSE is the root mean square error, MAE is the mean absolute error, and R\({}^{2}\) is the determination coefficient. of estimating ET using the optimized ANN-PM (two hidden layers and 48 neurons in each layer) with several combinations of input data (Table 3). Figure 5 shows the comparisons between the predicted ET values and the measured values of cropland ET in the training, validation, and test datasets across all flux sites. Figure 5: Scatter plots between the predicted ET values and the observed ET values measured from the flux tower in the training, validation, and test datasets of the ANN-PM model. (**a1–a3**) is the scatter plot between the predicted ET values and the observed ET values measured from the flux tower of the ANN-PM model using meteorological data in the three datasets, (**b1–b3**) is the scatter plot using meteorological data and NDVII, (**c1–c3**) is the scatter plot using meteorological data and NDVII and NIRv, (**d1–d3**) is the scatter plot using meteorological data and NDVII and NIRv and SWIR. As shown in Figure 5, all the employed models provide different accuracies under different input combinations. The accuracy of predicted ET values differs significantly depending on the model types and input combinations. Except for the second input combination, all input combinations show the highest R\({}^{2}\) in the training stage (Figure 5(a1,c1,d1)). The ranks of the input combinations under investigation in terms of prediction accuracy are (the value in parentheses after RMSE indicates the percentage of RMSE relative to the observed value): the fourth input combination (R\({}^{2}\) = 0.831-0.837, RMSE = 18.52-18.91 W m\({}^{-2}\) (38.42-38.86%), MAE = 12.63-13.00 W m\({}^{-2}\)), the third input combination (R\({}^{2}\) = 0.83, RMSE = 19.09-19.50 W m\({}^{-2}\) (39.84-40.46%), MAE = 13.27-13.41 W m\({}^{-2}\)), the second input combination (R\({}^{2}\) = 0.81-0.82, RMSE = 19.25-19.84 W m\({}^{-2}\) (39.94-41.05%), MAE = 13.05-13.51 W m\({}^{-2}\)), and the first input combination (R\({}^{2}\) = 0.71-0.73, RMSE = 23.76-24.58 W m\({}^{-2}\) (49.29-50.75%), MAE = 16.05-16.47 W m\({}^{-2}\)). In the testing stage, the models of the third input combination and fourth input combination have identical performance in estimating ET, both of which performed superior to the second input combination and the first input combination in predicting ET. These results confirm that the model using all input variables (meteorological data and three remote sensing data factors (NDVI, NIRv, SWIR)) achieves the best performances (RMSE = 18.52-18.91 W m\({}^{-2}\) (38.42-38.86%), MAE = 12.63-13.00 W m\({}^{-2}\), and R\({}^{2}\) = 0.831-0.837) compared with those using a subset of all the variables. However, the model using meteorological data and two remote sensing data factors (NDVI and NIRv) is also capable of predicting ET with acceptable accuracy, having the RMSE and MAE values of 19.09-19.50 W m\({}^{-2}\) (39.84-40.46%) and 13.27-13.41 W m\({}^{-2}\), respectively. When using only meteorological data, the model shows degraded performance with larger errors (RMSE = 23.76-24.58 W m\({}^{-2}\) (49.29-50.75%) and MAE = 16.05-16.47 W m\({}^{-2}\)) and smaller determination coefficients (R\({}^{2}\) = 0.71-0.73).