## 2 Material and Methods
### Model Evaluation  
#### 2.4.1 Model Performance Measurement  
The model performance evaluation metrics used in the study include root mean square error (RMSE), mean absolute error (MAE), and determination coefficients (R2). The calculations of these metrics are shown in Table 4.  
RMSE is the standard deviation between the predicted and true values, reflecting the degree that the predicted values explain the true values [54]. MAE is the mean error of evaluating a set of predictions and is the average value of the absolute difference between predicted and experimental values on test samples, but MAE is less sensitive to extreme values than RMSE [55]. R2 is determined by drawing a scatter plot between the observed and predicted value. Lower RMSE, MAE, and higher R2 correspond to a better performance of the model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Evaluation Parameters** & **Formula** \\ \hline RMSE & \(\sqrt{\frac{\sum_{i=1}^{m}(f^{i}-\overline{w})^{2}}{m}}\) \\ MAE & \(\frac{\sum_{i=1}^{m}|f^{i}-\overline{w}|}{\overline{m}}\) \\ R2 & \(\left(\frac{\sum_{i=1}^{m}\left(\left(\overline{w}^{i}-\overline{w}\right) \right)\left(f^{i}-\overline{f}\right)}{\sqrt{\sum_{i+1}^{m}\left(\left( \overline{w}^{i}-\overline{w}\right)^{2}\right)}\sqrt{\sum_{i=1}^{m}\left(f^{i} -\overline{f}\right)^{2}}}\right)^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Calculation formula of evaluation parameters. RMSE is the root mean square error, MAE is the mean absolute error, and R2 is the determination coefficients. _fi_: Predicted value: \(\overline{f}\)i Mean value of the predicted values; _yi_: Experiment value; \(\overline{y}\overline{i}\). Mean value of the observed values; _m_: Total amount of experimental data.  
2.4.2. Evaluating the Model Used to Estimate ET under Dry Climate  
Modeling ET in dry regions is more challenging than in other regions, especially for croplands. Because the water status of croplands is affected by irrigation, and the information of irrigation on a regional scale is difficult to obtain. On the other hand, in arid areas, most of the precipitation is consumed in the process of ET, and inadequate water supply could substantially limit the growth of crops in these regions. Therefore, accurate estimation of ET plays an important role in the sustainable development of agriculture in arid areas. Research on modeling ET in dry climates can facilitate rational cropland irrigation, maintaining stable crop production in dry regions.  
We analyzed the performance of the models we trained in estimating ET under a dry climate. The aridity index (AI) is a means and tool to determine the drought degree and range of a certain period quantitatively, and it is also an indicator of the degree of dry and wet in a region. The calculation formula of the AI is as follows [56]:  
\[\text{AI}=\frac{\text{P}}{\text{PET}} \tag{4}\]  
where AI is aridity index, PET is potential evapotranspiration, and P is the average precipitation. The AI calculation of each site is limited to the time range covered by the site. Low AI corresponds to a dry climate. We selected the sites with the AI values below 0.5 as arid areas by calculating the AI values of each flux site.