## 2 Materials and Methods
### Other ET Partitioning Methods  
Due to the lack of observation data for E and T at the 16 cropland sites, three different and widely used ET partitioning methods are selected to indirectly evaluate the performance of the machine learning model in T estimation and estimate the T/ET values of different typical crops. The three ET partitioning methods are the transpiration estimation algorithm proposed by [PERSON] et al. [36] (hereafter, N18), the underlying water use efficiency method proposed by [PERSON] et al. [30] (hereafter, Z16), and the ET partitioning method based on the leaf and ecosystem water use efficiency and the stomatal conductance model proposed by [PERSON] et al. [31] (hereafter, Y22). The three methods are developed based on eddy covariance measurements and differ in their physical and physiological knowledge of ecosystem (i.e., theoretical foundations) and prerequisites. The three ET partitioning methods have been validated by many previous studies [38]. All of the three ET partitioning methods also used the half-hourly eddy covariance dataset. The N18 method is developed based on ecosystem water use efficiency (WUE) and uses an RF model to estimate T. First, the N18 method selects some periods when T is close to ET (i.e., ET \(\approx\) T) in which WUE can be considered as GPP/T (Equation (7)). Then, the RF model is used to train those WUE data during the selected periods and subsequently predict the WUE of the whole observation period at each site. T is finally calculated as the ratio of GPP and predicted WUE as follows [36]:  
\[WUE_{ET\approx T}=RF(X)_{P}=\frac{GPP}{T} \tag{7}\]  
where \(X\) is a set of features. \(P\) is the prediction percentile of RF model, and the recommended 75 th percentile was used in this study. The Z16 method relies on the concept of underlying WUE (uWUE) and defines the apparent uWUE (uWUEa, Equation (8)) that is associated with ET and the potential uWUE (uWUEp, Equation (9)) that is associated with T. This method assumes that the uWUEp is constant for each flux site if the vegetation type of the site is homogeneous, and its value \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **Parameters** \\ \hline ANN & nneurons & [20; 20; 20] \\ epochs & [50; 300; 50] \\ ExtraTrees & max\_depth & [3; 15; 1] \\  & n\_estimators & [50; 1000, 50] \\  & learning\_rate & [0.05, 0.4, 0.05] \\ GBDT & max\_depth & [3; 15; 1] \\  & n\_estimators & [50; 1000, 50] \\  & learning\_rate & [0.05, 0.4, 0.05] \\ LightGBM & max\_depth & [3; 15; 1] \\  & n\_estimators & [50; 1000, 50] \\ RF & max\_depth & [3; 15; 1] \\  & n\_estimators & [50; 1000, 50] \\  & learning\_rate & [0.05, 0.4, 0.05] \\ XGBoost & max\_depth & [3; 15; 1] \\  & n\_estimators & [50; 1000, 50] \\ \hline \hline \end{tabular} Note: [20; 20; 20] means from 20 to 200 with intervals of 20.  
\end{table} 
Table 2: Range of tuning parameters for the ANN, ExtraTrees, GBDT, LightGBM, RF, and XGBoost models. is close to the maximum value of uWUE\({}_{\text{a}}\) when T is approximately equal to ET at some periods during the growing season [30]. \[uWUE_{a}=\frac{GPP\sqrt{VPD}}{ET} \tag{8}\]  
\[uWUE_{p}=\frac{GPP\sqrt{VPD}}{T} \tag{9}\]  
\[\frac{T}{ET}=\frac{uWUE_{a}}{uWUE_{p}} \tag{10}\]  
Here, \(uWUE_{a}\) is calculated using the linear regression at the daily scale, and \(uWUE_{p}\) is calculated using the 95 th percentile regression of all half-hourly data. T/ET is then estimated as the ratio of uWUE\({}_{\text{a}}\) to uWUE\({}_{\text{p}}\). The Y22 method is based on the difference between leaf and ecosystem WUEs and a stomatal conductance model [31]. For Y22, it uses two WUE variables to calculate T/ET, and the two WUE variables, ecosystem WUE (WUE\({}_{\text{eco}}\)) and ecosystem transpiration WUE (iWUE\({}_{\text{eco}}\)), are defined as follows:  
\[\frac{T}{ET}=\frac{WUE_{eco}}{iWUE_{eco}} \tag{11}\]  
\[WUE_{eco}=\frac{GPP}{ET} \tag{12}\]  
\[iWUE_{eco}=\frac{GPP}{T} \tag{13}\]  
According to the [PERSON]'s law and the stomatal conductance model developed by [PERSON] et al.