## 2 Materials and Methods
### Experiment Design  
Considering that cropland E is affected by many factors, we categorized those factors into six groups and assessed the impacts of different combinations on the accuracy of E estimation. Here, the six groups of the considered influencing factors comprise time variable (TIME), meteorological factors (VPD, USTAR, TA, and LW), sensible heat flux (H), ecosystem respiration (RECO), soil variable (SWC1), and vegetation variables (NDVI, EVI, and LAI). Among these variables, TIME is used to represent the annual and seasonal variation in E. VPD, USTAR, TA, and LW describe the impact of atmospheric water demand on E. H is tightly linked to ET (or LE) through the energy balance equation. RECO is related to soil temperature. SWC1 directly influences soil evaporation, and NDVI, EVI, and LAI indirectly affect E through vegetation cover. To evaluate the impacts of different feature combinations on the accuracy of E estimation, we designed a series of experiments (A1-A8, Table 1). Specifically, A1-A6 investigated the individual influence of each group feature. A7 focused on the combined effect of factors other than meteorological features on soil evaporation. This was because previous research had shown that meteorological factors had a significant impact when using machine learning models to predict evaporation [37; 55]. While A8 provided a comprehensive evaluation of all factors. Apart from that, other feature combinations within A2 to A6 were also tested (Supplementary Table S3). Through these experiments, we aimed to comprehensively understand how these factors affected the accuracy of E estimation and to obtain the most suitable feature combination for cropland T/ET estimation.  
In this study, all the six machine learning models were individually built and optimized at each cropland site. The nighttime E dataset was randomly split into two parts: 80% for training and 20% for testing. A forward-chaining cross-validation approach was used during the training process to prevent overfitting. All variables were standardized to minimize the effect of the absolute scale on the E estimation accuracy of the machine learning models. For the ExtraTrees, GBDT, LightGBM, RF, and XGBoost models, the parameters were optimized using both random search and grid search. While for the ANN model, it had one hidden layer, and the rectified linear unit was used as the activation function. The weights of the hidden layer were updated using the backpropagation algorithm. Two parameters of the ANN model, i.e., the number of neurons in the hidden layer (nneurons) and iteration (epochs), were optimized using the trial-and-error approach and ranging from 20 to 200 with intervals of 20 and from 50 to 300 with intervals of 50, respectively. The optimized parameters and their ranges for the six machine learning models are listed in Table 2. Other additional parameters were set as their default values.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Experiments** & **Input Features** \\ \hline A1 & TIME \\ A2 & TIME + VPD + USTAR + TA + LW \\ A3 & TIME + H \\ A4 & TIME + RECO \\ A5 & TIME + SWC1 \\ A6 & TIME + NDVI + EVI + LAI \\ A7 & TIME + H + RECO + SWC1 + NDVI + EVI + LAI \\ A8 & TIME + VPD + USTAR + TA + LW + H + RECO + SWC1 + NDVI + EVI + LAI \\ \hline \hline \end{tabular} Note: TIME is timestamp variable, VPD is vapor pressure deficit, USTAR is friction velocity, TA is air temperature, LW is longwave incident radiation, H is sensible heat flux, RECO is ecosystem respiration, SWC1 is the top layer soil water content, NDVI is normalized difference vegetation index, EVI is enhanced vegetation index, and LAI is vegetation leaf area index.  
\end{table}
Table 1: The eight experiments with different combinations of input features (TIME, VPD, USTAR, TA, LW, H, RECO, SWC1, NDVI, EVI, and LAI) used in this study.  
In addition, we provided the specific values of each optimized parameter at the 16 cropland sites in Supplementary Table S4.