## 3 Methodology
### Input Variables
\begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{1}{c}{**Vegetation Indices**} & **Formulation** & **References** \\ \hline NDVI & \(\text{(NIR}-\text{R})/\text{(NIR}+\text{R})\) & [50] \\ (Normalized Difference Water Index) & \(\text{NPCI}\) & \(\text{(R}-\text{B})/\text{(R}+\text{B})\) & [51] \\ (Normalized pigment chlorophyll index) & \(\text{LSWI}\) & \(\text{(NIR}-\text{SWIR1)}/\text{(NIR}+\text{SWIR1)}\) & [52] \\ (Land Surface Water Index) & \(\text{SAVI}\) & \(1.5\times\text{(NIR}-\text{R})/\text{(NIR}+\text{R}+1.5)\) & [53] \\ (Soil Adjusted Vegetation Index) & \(\text{EVI}\) & \(2.4\times\text{(NIR}-\text{R})/\text{(NIR}+\text{R}+1)\) & [54] \\ (Enhanced Vegetation Index) & ExNDVI & \(\text{(NIR}+\text{SWIR2}-\text{R})/\text{(NIR}+\text{SWIR2}+\text{R})\) & [55] \\ (Extended NDVI) & \(\text{NIR}\times\text{R}/\text{G}^{2}\) & [56] \\ (Chlorophyll Vegetation Index) & \(\text{(NIR}/\text{G})-1\) & [57] \\ (Enhanced Vegetation Index) & \(\text{MDMI}\) & \(\text{(G}-\text{SWIR2)}/\text{(G}+\text{SWIR2)}\) & [58] \\ (Normalized Difference Moisture Index) & \(\text{MNDMI}\) & \(\text{(NIR}-\text{SWIR2)}/\text{(NIR}+\text{SWIR2)}\) & [59] \\ (Modified NDMI) & \(\text{AFRI}\) & \(\text{(NIR}-\text{0.66}\times\text{R})/\text{(NIR}+\text{0.66}\times\text{R})\) & [60] \\ \hline \hline \end{tabular} Note. B: Blue band. G: Green band. R: Red band. NIR: Near infrared band. SWIR1: Shortwave infrared 1 band. SWIR2: Shortwave infrared 2 band. Ts: surface temperature observed by Landsat.  
\end{table} 
Table 4: Definitions of input variables extracted from Landsat observations. SATDs were calculated as the difference between Ts with air temperature (Ta), Ta values were obtained from the study of [PERSON] et al. [62], and the nearest algorithm was employed to resample the Ta dataset from 1 km spatial resolution to 30 m.  
\[TVDI=\frac{Ts-Ts_{\text{min}}}{Ts_{\text{max}}-Ts_{\text{min}}} \tag{5}\]  
where Ts\({}_{\text{max}}\) and Ts\({}_{\text{min}}\) is the surface temperature of dry edge and wet edge. 3 Radiation energy  
Solar radiation is the primary energy source for water evaporation and plant photosynthesis. In this paper, four indicators are selected: downward shortwave radiation (R\({}_{\text{s\_down}}\), Equation (6)); upward shortwave radiation (R\({}_{\text{s\_up}}\), Equations (7) and (8)); downward longwave radiation (R\({}_{\text{l\_down}}\), Equation (9)); and upward longwave radiation (R\({}_{\text{l\_up}}\), Equation (10)). \[R_{s\_down}=\frac{G_{sc}\times\cos\theta\times\tau_{sw}}{{d_{r}}^{2}} \tag{6}\]  
\[R_{s\_up}=\alpha\times R_{s\_down} \tag{7}\]  
\[\alpha=\frac{(0.36\times B+0.13\times R+0.37\times NIR+0.09\times SWIR1+0.07 \times SWIR2-0.0018)-\alpha_{p}}{\tau_{sw}} \tag{8}\]  
\[R_{l\_up}=\varepsilon_{a}\sigma T^{4} \tag{9}\]  
\[R_{l\_down}=\varepsilon\sigma Ts^{4} \tag{10}\]  
where G\({}_{\text{SC}}\) represents the solar constant, taken as 1376 W/m\({}^{2}\); \(\theta\) represents the solar zenith angle; \(\tau_{\text{sw}}\) represents the atmospheric transmittance; d\({}_{r}\) represents the astronomical distance between the sun and the Earth; \(\alpha\) represents surface albedo; \(\alpha_{p}\) represents the influence of atmospheric path radiation, which is generally taken as 0.03; B, R, NIR, SWIR1, SWIR2 represent Blue band, Red band, Near infrared band, Shortwave infrared 1 band and Shortwave infrared 2 band observed by Landsat; \(\varepsilon_{a}\) and \(\varepsilon\) represent the atmospheric emissivity and surface emissivity, respectively; \(\sigma\) represents the Stefan-Boltzmann constant, taken as \(5.67\times 10^{-8}\) W/m\({}^{2}\)K\({}^{4}\). The specific calculation methods for these parameters can be referenced from the study of [PERSON] et al. [21]. 4 Others  
Considering the seasonal variations in phenology and climate that can influence plant physiological processes [2], we incorporated the Julian day (i.e., the day of the year, DOY) as one of the input variables. Figure 4 presents the ET and NEE variation with DOY.