## 5 Discussion  
Based on the findings of this study, it can be inferred that utilizing remote sensing Vegetation Indices (VIs) to correlate with ET and NEE yields reasonably accurate results. In comparison to the SEB-based and LUE-based models, these empirical models offer a simpler, more efficient approach while reducing the dependency on meteorological data. Typically, widely used distributed meteorological datasets like GLDAS and MERRA possess relatively low spatial resolutions (ranging from 0.25\({}^{\circ}\) to 0.625\({}^{\circ}\)), necessitating a spatial downscaling \begin{table}
\begin{tabular}{l l r r r r r r} \hline \hline
**Variable** & **Metrics** & **XX** & **LC** & **DX** & **GT** & **HL** & **YC** \\ \hline ET & Samples & 22 & 170 & 18 & 20 & 18 & 163 \\  & \(R^{2}\) & 0.79 & 0.79 & 0.61 & 0.71 & 0.51 & 0.87 \\  & RMSE (mm) & 1.76 & 1.11 & 2.28 & 1.59 & 2.12 & 0.94 \\ NEE & Samples & 37 & 179 & 36 & 31 & 38 & 168 \\  & \(R^{2}\) & 0.42 & 0.67 & 0.36 & 0.76 & 0.80 & 0.76 \\  & RMSE (gC/m\({}^{2}\)) & 5.45 & 1.87 & 3.88 & 2.86 & 3.25 & 1.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistics of the validation conducted in different sites. Figure 9: The spatial distribution of estimated ET based on this study (**a**) MODIS (**b**); NEE based on this study (**c**) and MODIS (**d**). procedure before they can be effectively paired with high-resolution remote sensing data. This downscaling process, however, introduces additional uncertainties to data accuracy, as noted by [PERSON] et al. [65], and subsequently increases the uncertainties inherent in SEB-based and LUE-based models [21; 26]. Furthermore, previous research has confirmed the limited accuracy of these distributed meteorological datasets [66; 67; 68]. In contrast, empirical models circumvent these errors, but they have a drawback in terms of limited explanatory power [69; 70]. In this study, we employed three regression algorithms (MLR, RFR, and BPNN) to fit multiple types of variables with ET and NEE, observing varying fitting accuracies (refer to Figure 7). Among them, RFR consistently achieved the highest accuracy. As a representative ensemble learning algorithm, RFR derives its final estimates by averaging multiple decision trees. This approach ensures more stable results and effectively mitigates the impact of anomalous samples [71]. Consequently, RFR has been widely used in remote sensing applications for various indicators, such as soil water content estimation [4], crop yield prediction [45; 46], and remote sensing image classification [72], often outperforming other machine learning algorithms. MLR also demonstrated considerable accuracy in estimating ET and NEE, particularly when highly correlated variables were included. Furthermore, MLR exhibited stability even with the introduction of additional variables with lower correlation. These less informative variables for ET or NEE estimation could be downweighted by assigning smaller fitting coefficients in MLR. It should be noted that MLR struggles with handling complex nonlinear problems, and from the results, we see that the estimation of NEE is even more challenging, thus the accuracy of MLR is quite limited. In contrast, BPNN struggled more with processing irrelevant input variables. As a neural network algorithm, BPNN typically requires a substantial sample size and is sensitive to anomalous samples or variables with limited explanatory power [4; 73]. In general, the regression algorithms employed in this study exhibited satisfactory fitting, but some errors persisted. Firstly, while the empirical models minimized uncertainties from input variables, such as by foregoing meteorological data, the geographical registration, radiometric calibration, and atmospheric correction processes inherent to Landsat data cannot fully guarantee the absolute accuracy and objectivity of the obtained Vegetation Indices (VIs) or surface temperature in portraying the actual situation [74; 75].