## 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
However, when substituting the downscaled LST into the LE model, the DisTrad-LST LE was 364.79 W\(\cdot\)m\({}^{-2}\), and the GWR-LST LE was 372.08 W\(\cdot\)m\({}^{-2}\), respectively, indicating that the errors caused by surface temperature nonuniformity cannot be ignored in the second landscape inhomogeneity condition. The land surface of EC15 is uniform and consists of pure pixels covering maize fields. Consequently, the temperature distribution at a resolution of 30 m was very homogeneous, and the ranges of the LST obtained using both downscaling methods displayed a range of 1.5 K. The temperature observed through in situ measurements was 301.99 K. For comparison, the temperature retrieved at the MODIS resolution was 302.94 K. The mean LE calculated using the MODIS-LST, DisTrad-LST and GWR-LST were 281.14 W\(\cdot\)m\({}^{-2}\), 287.05 W\(\cdot\)m\({}^{-2}\) and 287.95 W\(\cdot\)m\({}^{-2}\), respectively. For homogeneous areas, the differences among the three methods were not large (within 8 W\(\cdot\)m\({}^{-2}\)). The weakly heterogeneous land surface at EC11 contained barley and maize, and it displays the first condition of heterogeneity (i.e., nonlinear vegetation density variations among subpixels). The mean LE values calculated using the MODIS-LST, DisTrad-LST and GWR-LST were 585.45 W\(\cdot\)m\({}^{-2}\), 602.82 W\(\cdot\)m\({}^{-2}\) and 605.41 W\(\cdot\)m\({}^{-2}\), respectively. The improvements in H and LE by the temperature sharpening were not obvious as the improvements at EC04, which contains a totally different landscape. At EC11, the range of temperature-sharpening results is 1.6 K. The mean temperatures retrieved using the MODIS-LST, DisTrad-LST and GWR-LST were 300.66 K, 299.40 K and 299.69 K, respectively, and the observed ground-based temperature was 297.83 K. Hence, the LE differences between the DisTrad-LST LE and GWR-LST LE are small. However, compared to MODIS-LST, temperature sharpening can still decrease the heterogeneity that results from thermal dynamics. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Variable**} & \multicolumn{3}{c}{**MODIS-LST (W\(\cdot\)m\({}^{-2}\))**} & \multicolumn{3}{c}{**GWR-LST (W\(\cdot\)m\({}^{-2}\))**} & \multicolumn{3}{c}{**DisTrad\_LST (W\(\cdot\)m\({}^{-2}\))**} \\ \cline{2-10}  & \(R^{2}\) & **MBE** & **RMSE** & \(R^{2}\) & **MBE** & **RMSE** & \(R^{2}\) & **MBE** & **RMSE** \\ \hline EC04-H & 0.17 & \(-93.54\) & 96.64 & 0.28 & \(-74.57\) & 78.18 & 0.29 & \(-70.01\) & 74.23 \\ EC04-LE & 0.47 & 68.74 & 77.05 & 0.56 & 38.07 & 48.98 & 0.55 & 28.77 & 45.86 \\ \hline EC15-H & 0.53 & 57.17 & 75.43 & 0.76 & 55.51 & 71.96 & 0.66 & 48.73 & 69.50 \\ EC15-LE & 0.93 & \(-51.86\) & 70.99 & 0.95 & \(-48.82\) & 68.60 & 0.92 & \(-48.28\) & 65.10 \\ \hline EC11-H & 0.11 & 34.10 & 82.28 & 0.25 & \(-6.36\) & 57.61 & 0.21 & 7.11 & 57.11 \\ EC11-LE & 0.39 & \(-50.12\) & 86.96 & 0.53 & \(-15.23\) & 76.88 & 0.46 & \(-31.52\) & 51.64 \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison of the turbulent heat flux results at EC04, EC15 and EC11.