## 4 Results and Analysis  
### Accuracy Assessment of the LST Downscaling Results  
The performance of the DisTrad downscaling method and the GWR-based LST downscaling algorithm can be evaluated from qualitative and quantitative perspectives. The qualitative analysis was performed by visual examination of the results. The quantitative analyses were performed using the root mean square error (RMSE), the mean bias error (MBE), and the coefficient of determination (\(R^{2}\)). Figure 4 displays the spatial pattern of the LST data downscaled using DisTrad and GWR on 19 June 2012. For comparison, the spatial distribution of the MODIS LST is also shown. In comparison with the MODIS LST, both the DisTrad- and GWR--downscaled LST data effectively enhance the spatial resolution while preserving the characteristics and spatial distribution of the MODIS LST. Moreover, the results of the two models provide a more detailed description of the spatial variability of the thermal characteristics of the surface. However, a smoothing effect is observed in the LST downscaled using GWR when compared to the DisTrad-estimated LST because the regression process is based on the minimum mean square error (MMSE). Methods based on the MMSE tend to underestimate high values and overestimate low values; thus, the predicted parameters are frequently smoothed [(57; 23)]. The ground-based land surface temperature (\(T_{S}\)) was calculated using the Stefan-Boltzmann law from the AMS measurements of the longwave radiation fluxes [(58)]:  
\[T_{s}=\left[\frac{L^{\uparrow}-(1-\varepsilon_{s})\cdot L^{\downarrow}}{ \varepsilon_{s}\cdot\sigma}\right]^{\frac{1}{2}} \tag{10}\]  
where \(L^{\uparrow}\) and \(L^{\downarrow}\) are the in situ surface upwelling and atmospheric downwelling longwave radiation, respectively, and \(\varepsilon_{S}\) is the surface broadband emissivity, which is regarded as the value of the HJ-1B pixel corresponding to the AMS. Figure 5 shows the comparison of the LSTs obtained using the two downscaling methods with the ground-based measurements of land surface temperatures. As seen in Figure 5l, the \(R^{2}\), MBE and RMSE of the DisTrad downscaled LSTs are 0.83, 0.62 K and 2.59 K, respectively, and these values reflect better results than those associated with the GWR downscaled LSTs (0.82, 0.75 K, 2.66 K). On the whole, the differences between the two methods are not remarkable. However, the method that displays better performance varies depending on the date examined. For example, the GWR downscaled LSTs are better than the DisTrad downscaled LSTs on 19 June, 30 June, 13 September and 14 September, whereas DisTrad is superior to GWR on 8 July, 27 July, 3 August,  
Figure 4: Spatial distribution of **(a)** the MODIS LST; **(b)** the DisTrad downscaled LST; and **(c)** the GWR downscaled LST on 19 June 2012. 15 August, 22 August, 29 August and 2 September. The reason for these differences between the two techniques may be related to changes in land surface parameters (i.e., NDVI and albedo); the study period covers the entire life cycle of plants, extending from when they begin to grow to when they grow rapidly and eventually wither. The MBE difference between the DisTrad downscaled LSTs and the GWR downscaled LSTs ranges from \(-\)0.49 K-0.2 K, and the RMSE difference is \(-\)0.47 K-0.42 K. The results of the two methods vary substantially on 8 July and 29 August. Figure 5: Comparison of the results of the two LST downscaling approaches with measured data. To determine the reasons for the above phenomenon, we calculated the contributions of the different independent variables to the LSTs on each date separately by calculating the normalized regression coefficients [19]. The results are shown in Figure 6. The ability of the individual independent variables to explain the LSTs determines the accuracy of the two methods. NDVI explains only 49.39% and 47.09% of the LSTs on 19 June and 30 June, respectively, which is lower than the combination of albedo and DEM.