## 2 Study Area and Data Collection
### Flux Data  
In this study, the flux tower observations obtained from ChinaFLUX ([[http://www.chinaflux.org](http://www.chinaflux.org)]([http://www.chinaflux.org](http://www.chinaflux.org))) were used for the model evaluation, and the six flux tower sites located exclusively within the cropland ecosystem were used for estimating water and carbon fluxes. Figure 1 illustrates the positions of these six sites, while Table 2 provides detailed information about them. For in situ carbon flux measurements, we relied on the net ecosystem exchange (NEE, measured in gC/m\({}^{2}\)) recorded by the flux towers. Similarly, the latent heat flux (LE, measured in W/m\({}^{2}\)) observed by the flux towers served as our in situ water flux, which we converted to evapotranspiration (ET, in mm) using Equation (1).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Bands ID** & **Wavelength** & **Description** & **Temporal/Spatial Resolution** \\ \hline \multirow{6}{*}{ Landsat 7 Level 2, Collection 2, Tier 1} & SR\_B1 & 0.452–0.512 \(\upmu\)m & blue surface reflectance & 16 day/30 m \\  & SR\_B2 & 0.533–0.590 \(\upmu\)m & green surface reflectance & 16 day/30 m \\  & SR\_B3 & 0.636–0.673 \(\upmu\)m & red surface reflectance & 16 day/30 m \\  & SR\_B4 & 0.851–0.879 \(\upmu\)m & near infrared surface reflectance & 16 day/30 m \\  & SR\_B5 & 1.566–1.651 \(\upmu\)m & & 16 day/30 m \\  & ST\_B6 & 10.40–12.50 \(\upmu\)m & surface temperature (K) & 16 day/30 m (resampled from 100 m) \\  & SR\_B7 & 2.107–2.294 \(\upmu\)m & shortwave infrared 2 surface reflectance & 16 day/30 m \\  & SR\_B2 & 0.452–0.512 \(\upmu\)m & blue surface reflectance & 16 day/30 m \\  & SR\_B3 & 0.533–0.590 \(\upmu\)m & green surface reflectance & 16 day/30 m \\  & SR\_B4 & 0.636–0.673 \(\upmu\)m & red surface reflectance & 16 day/30 m \\  & SR\_B5 & 0.851–0.879 \(\upmu\)m & near infrared surface reflectance & 16 day/30 m \\  & SR\_B6 & 1.566–1.651 \(\upmu\)m & shortwave infrared 1 surface reflectance & 16 day/30 m \\  & SR\_B7 & 2.107–2.294 \(\upmu\)m & shortwave infrared 2 surface reflectance & 16 day/30 m \\  & ST\_B10 & 10.60–11.19 \(\upmu\)m & surface temperature (K) & 16 day/30 m \\ \hline \hline \end{tabular}
\end{table}
Table 1: Satellite data description.  
Figure 1: Study area. Note: the land use type data were obtained from the Resource and Environment Science and Data Center (RESDC), China Academy of Science ([[https://www.resdc.cn/](https://www.resdc.cn/)]([https://www.resdc.cn/](https://www.resdc.cn/))).  
\[ET=\frac{LE}{\lambda} \tag{1}\]  
where \(\lambda\) is the latent heat vaporization. For the EC observation system, it should be noted that the energy balance closure issue was often found, i.e., the available energy (net radiation (Rn, W/m\({}^{2}\)) minus ground heat flux (G, W/m\({}^{2}\))) is not equal to the sum of LE and sensible heat flux (H, W/m\({}^{2}\)). Therefore, the energy balance closure ratio (EBCR, Equation (2)) was used to filter the flux data [1]:  
\[EBCR=\frac{H+LE}{Rn-G} \tag{2}\]  
where the energy fluxes were all calculated at the daily scale. Only the measurements with EBCR more than 80% were used in this study. Moreover, the Bowen ratio method was used to forcing the energy closure of the selected measurements (Equation (3)) [43]:  
\[LE_{cor}=\frac{Rn-G}{H+LE}\times LE \tag{3}\]  
where \(LE_{cor}\) is the corrected latent heat flux. After matching the satellite data (after cloud mask) and filtering using EBCR, totally 411 samples of ET and 490 samples of NEE were used in this study. The flux observation sensors were installed at the 40 m height, and the observation frequency is 30 min, while the observation data were taken at the statistic to daily scale to match the results from the proposed model. Figure 2a,b shows the histogram of observed ET and NEE.