## 4 Results and Analysis
### Validation of Heat Fluxes Calculated Using MODIS LSTs  
Before comparing the two downscaled LSTs in calculating surface heat fluxes, we must verify the LE model by comparing the remote sensing-estimated fluxes with the ground-based measurements. In this section, the MODIS LSTs, which have a resolution of 990 m, are resampled to a spacing of 30 m using the nearest neighbor method. The resampled LSTs and the surface VNIR variable, which have resolutions of 30 m, are applied to the LE algorithm. Figure 7 provides the turbulent heat flux results (which are termed the MODIS-LST heat fluxes) calculated using the MODIS LST data on 19 June 2012. The spatial distribution of the turbulent heat fluxes is related to the underlying land cover. The LE values are lower in areas covered by buildings and uncultivated land, including land patches in the desert areas, barren areas, and Gobi regions, and they are higher in the water-covered and agricultural areas within the oasis. Comparing Figure 7c,d, we see that the LE values (H values) of the barren areas in the southwest are higher (lower) than those of the desert areas in the southeast. Because the barren areas in the southwest border the Oilian Mountains, this result is due to snow melt and the downward movement of water. Comparing the four maps, we see that Figure 7c,d display obvious \"boxy\" anomalies, which are due to our direct use of the MODIS LSTs. In recent years, many researchers have employed the footprint model in validating remote sensing-based LE estimates. When combined with the flux contribution source areas, this model solves the problems associated with mismatches between observed values and remote sensing-based estimates and leads to better results ([PERSON] and [PERSON], 2001; [PERSON], 2017; [PERSON], 2017). In this study, we employ a user-friendly tool that is based on the Eulerian analysis flux footprint model proposed by [PERSON] and [PERSON] (2001) to calculate the footprints of the function parameters ([PERSON], 2017; [PERSON], 2017). Based on the relative weights of the pixels in which the source area is located, we determine the remote sensing-based estimates with the same spatial representation range as the observed values. The results of the footprint validation are shown in Figure 8 and Table 4. The \(R^{2}\), MBE, and RMSE values of LE are 0.75, \(-\)59.78 W\(\cdot\)m\({}^{-2}\), and 73.15 W\(\cdot\)m\({}^{-2}\), respectively, and those of H are 0.63, 38.90 W\(\cdot\)m\({}^{-2}\), and 77.26 W\(\cdot\)m\({}^{-2}\), respectively. The accuracy of LE is impacted by \(R_{n}\), surface G, and H, because it is calculated as a residual term. All of the input parameters may contribute to the error in LE; these errors are discussed in Section 4.4. As shown in Figure 8, the majority of the LE values are large because June, July, August, and September constitute the growing season, when soil moisture is adequate and ET is strong. ET leads to substantial reductions in air temperature; thus, the surface and air temperature gradient is small, leading to low values of H. The points with small LE values are influenced by uncultivated land. Within our study area, the barren areas, desert areas and Gobi regions make up the uncultivated land.