## 2 Study Area and Datasets
### Determination of Input Remote Sensing Data  
#### 2.2.1 Fraction of Vegetation Cover and Surface Emissivity  
The fraction of vegetation cover (\(f\)) is calculated from the normalized difference vegetation index (NDVI) values, which are estimated from the surface reflectances of ASTER bands 2 and 3 with pixel resolution of 15 m. The reflectances are obtained through the image atmospheric correction using the MODTRAN model. The value of \(f\) is calculated from the following equation [37, 38, 39]:  
\[f_{c}=\frac{NDVI-NDVI_{\text{min}}}{NDVI_{\text{max}}-NDVI_{\text{min}}} \tag{1}\]  
where \(NDVI_{\text{min}}\) represents the normalized vegetation index of bare soil, and \(NDVI_{\text{max}}\) represents the maximum value of the normalized vegetation index. However, the spectral signature of land surface varies due to factors including mineralogy, moisture content and grain size, and also those associated with differences in species, plant health, leaf water content, and other factors [40]. Most of \(NDVI_{\text{min}}\) and \(NDVI_{\text{max}}\) values need local calibration [37, 38, 39]. In this study, \(NDVI_{\text{min}}\) and \(NDVI_{\text{max}}\) were calculated from the 2 nd and more than 95 th percentiles of the statistical NDVI histogram of the study area image, respectively [39]; the \(NDVI_{\text{min}}\) values were set to 0.05, while the \(NDVI_{\text{max}}\) were set to 0.85 for the study area.  
Although ASTER standard products of LST and emissivity have been widely used, significant uncertainty in the Temperature and Emissivity Separation algorithm often occurs in areas of high and low spectral contrast [41], which could introduce relative large errors in LST estimation. In addition,  
Figure 1: Spatial distribution and ground photographs of the six vegetation surface sites in this study. The upper left image is the landscape of the experimental HiWATER-MUSOEXE area, and the study area is the black rectangle with a length of 13 km and a width of 11 km.  
uncertainty from the atmospheric corrections also leads to errors in LST estimation. Here, a hybrid procedure was utilized to estimate the surface emissivity from the ASTER image using the NDVI Thresholds Method-NDVI\({}^{\text{THM}}\) in this study [42] and applying the radiative transfer algorithms with atmospheric profiles measured from Zhangye Meteorological Observation radiosondes at ASTER overpassed time [43]. The NDVI\({}^{\text{THM}}\) method obtains the surface emissivity considering different cases:  
(a) NDVI \(<0.2\), here the pixels consist of bare soil. The surface emissivity values can be calculated from the surface reflectivity (\(\rho_{\text{red}}\)) in the red channel:  
\[\varepsilon=1-\rho_{red} \tag{2}\]  
(b) NDVI \(>0.5\), here, the pixels are considered fully vegetated, and the surface emissivity distribution is calculated from _in situ_ measurements of vegetation emissivity.  
(c) \(0.2\leq\text{NDVI}\leq 0.5\), here, the given surface is considered as a mixture of bare soil and vegetation. The emissivity of a heterogeneous surface is then expressed as [39]  
\[\varepsilon=\varepsilon_{c}f_{c}+\varepsilon_{s}\left(1-f_{c}\right)+d\varepsilon \tag{3}\]  
In Equation (3), \(\varepsilon_{c}\) and \(\varepsilon_{s}\) are the emissivities of full vegetation and bare soil, respectively, which were calculated from _in situ_ measurements [39] and \(f_{c}\) is the fraction of vegetation cover. The term \(d\varepsilon\) is given as:  
\[d\varepsilon=\left(1-\varepsilon_{s}\right)\varepsilon_{c}F(1-f_{c}) \tag{4}\]  
where \(F\) is a shape factor whose value depends on the geometrical structure of the vegetation, the mean value is 0.55.