## 4 Results and Analysis
### Compare of Heat Fluxes Calculated Using Different LST Datasets
#### 4.3.1 Validation of the DisTrad-LST and GWR-LST Heat Fluxes
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Date**} & \multicolumn{3}{c}{**GWR-LST-H (W-m\({}^{-2}\))**} & \multicolumn{3}{c}{**GWR-LST-LE (W-m\({}^{-2}\))**} & \multicolumn{3}{c}{**DisTrad-LST-H (W-m\({}^{-2}\))**} & \multicolumn{3}{c}{**DisTrad-LST-L (W-m\({}^{-2}\))**} \\ \cline{2-13}  & \(\mathbf{R^{2}}\) & **MBE** & **RMSE** & \(\mathbf{R^{2}}\) & **MBE** & **RMSE** & \(\mathbf{R^{2}}\) & **MBE** & **RMSE** & \(\mathbf{R^{2}}\) & **MBE** & **RMSE** \\ \hline
19 June & 0.48 & 42.25 & 50.73 & 0.77 & \(-\)52.60 & 46.05 & 0.44 & 44.48 & 54.26 & 0.75 & \(-\)55.32 & 50.24 \\
30 June & 0.68 & 21.57 & 47.84 & 0.79 & \(-\)40.65 & 81.01 & 0.67 & 23.22 & 48.69 & 0.79 & \(-\)42.71 & 82.20 \\
8 July & 0.65 & 40.22 & 76.59 & 0.81 & 44.42 & 91.87 & 0.67 & 26.57 & 72.65 & 0.81 & \(-\)27.89 & 92.50 \\
27 July & 0.68 & 34.22 & 65.88 & 0.86 & \(-\)50.86 & 81.81 & 0.67 & 33.71 & 66.13 & 0.84 & \(-\)49.54 & 84.35 \\
3 August & 0.42 & 48.83 & 64.82 & 0.67 & \(-\)68.88 & 49.11 & 0.44 & 45.30 & 61.60 & 0.71 & \(-\)65.03 & 44.42 \\
15 August & 0.41 & 21.48 & 70.59 & 0.76 & 42.67 & 91.76 & 0.41 & 18.82 & 68.20 & 0.76 & \(-\)39.74 & 90.18 \\
22 August & 0.42 & 40.85 & 70.82 & 0.73 & \(-\)50.27 & 43.15 & 0.43 & 35.74 & 68.32 & 0.72 & \(-\)44.76 & 43.53 \\
29 August & 0.65 & 42.69 & 65.61 & 0.80 & \(-\)75.42 & 53.66 & 0.70 & 30.44 & 57.71 & 0.80 & \(-\)61.00 & 45.45 \\
2 September & 0.39 & \(-\)27.66 & 68.57 & 0.59 & 8.12 & 54.35 & 0.40 & \(-\)26.16 & 66.25 & 0.59 & 6.36 & 52.04 \\
13 September & 0.37 & \(-\)36.46 & 77.01 & 0.42 & \(-\)51.49 & 49.67 & 0.38 & \(-\)37.90 & 86.83 & 0.34 & \(-\)3.57 & 61.06 \\
14 September & 0.38 & 16.01 & 68.17 & 0.41 & \(-\)33.41 & 52.40 & 0.38 & 23.00 & 79.91 & 0.33 & \(-\)40.64 & 62.01 \\ Overall & 0.66 & 6.69 & 51.32 & 0.75 & \(-\)26.52 & 47.38 & 0.68 & 3.66 & 49.03 & 0.76 & \(-\)23.17 & 45.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Validation results for the DisTrad-LST and GWR-LST heat fluxes. Figure 9: Maps of energy components, (**a**) GWR-LST-H; (**b**) GWR-LST-LE; (**c**) DisTrad-LST-H; and (**d**) DisTrad-LST-LE, on 19 June 2012.  
turbulent heat fluxes calculated using the MODIS-LST, GWR-LST and DisTrad-LST methods. For EC04, the LE calculated using the GWR-LST is more consistent with the in situ measurements than the LE calculated using the MODIS-LST; the MBE and RMSE are much smaller, the \(R^{2}\) is larger, and the MBE improves by 30.67 W\(\cdot\)m\({}^{-2}\). However, the LE calculated using the DisTrad-LST is more accurate than the LE calculated using the GWR-LST. For EC15, the differences between the three methods were small; however, the LE calculated using the GWR-LST is more accurate than the LE calculated using the MODIS-LST and DisTrad-LST for EC11. The reason is related to the land cover types within the flux contribution source area, which we discuss in Section 4.3.2. We also note that the difference in MBE between the heat fluxes determined from the downscaled LSTs and the MODIS-LSTs is larger at EC04 and EC11 than EC15. Figure 10 shows that the classes and temperatures of 10 \(\times\) 10 subpixels at 30 m correspond to the pixels within the MODIS pixels, which have a resolution of 990 m, at the EC tower. After temperature sharpening, the distribution of temperatures at a resolution of 30 m agrees with the classification. EC04 shows the temperature sharpening resulting from different methods on 19 June. The temperature retrieved at the MODIS resolution was 305.24 K. Compared with the in situ measurement of 314.04 K, the temperature was underestimated at a resolution of 990 m. The mean value of LE calculated using the MODIS-LST of the 10 \(\times\) 10 subpixels was 342.22 W\(\cdot\)m\({}^{-2}\), and the H was 158.96 W\(\cdot\)m\({}^{-2}\).