## 4 Results and Analysis
### Error Analysis
#### 4.4.1 Errors from \(R_{n}\) and G  
Since G is calculated from \(R_{n}\), this paper mainly analyzes the errors associated with \(R_{n}\). According to a sensitivity analysis of Equation (2), \(R_{n}\) is highly sensitive to \(R_{s}\downarrow\) and \(R_{L}\downarrow\), whereas the albedo and \(\varepsilon_{s}\) are less influential. The station validation results of \(R_{s}\downarrow\) and \(R_{L}\downarrow\) are shown in Table 8. The \(R^{2}\)  
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline
**Station** & **Date** & **EC-LST** & **GWR-LST** & **DisTrad-LST** & **EC-LE** & **GWR-LST-LE** & **DisTrad-LST-LE** & **Better** & **Difference** \\  & **(G)** & **(G)** & **(G)** & **(G)** & **(W\(\cdot\)m\({}^{-2}\))** & **(W\(\cdot\)m\({}^{-2}\))** & **(W\(\cdot\)m\({}^{-2}\))** & **Method** & **(W\(\cdot\)m\({}^{-2}\))** & **SHDI** \\ \hline EC02 & 22 August & 298.05 & 300.82 & 300.27 & 501.12 & 296.98 & 404.83 & DisTrad-LST & 8.85 & 0.19 \\ EC12 & 27 July & 300.53 & 300.47 & 300.26 & 587.07 & 572.50 & 580.31 & DisTrad-LST & 7.81 & 0.18 \\ EC09 & 15 August & 300.83 & 300.60 & 300.28 & 589.79 & 540.33 & 548.89 & GWR-LST & 8.56 & 0.15 \\ EC02 & 19 June & 301.40 & 304.69 & 304.59 & 502.00 & 372.76 & 380.41 & DisTrad-LST & 7.65 & 0.15 \\ EC17 & 2 September & 293.94 & 293.87 & 292.99 & 377.96 & 484.66 & 492.01 & GWR-LST & 7.35 & 0.15 \\ EC18 & 30 June & 310.05 & 310.68 & 310.16 & 192.94 & 161.38 & 169.33 & DisTrad-LST & 7.65 & 0.14 \\ EC14 & 8 July & 298.82 & 300.44 & 299.51 & 401.64 & 565.09 & 572.43 & DisTrad-LST & 7.34 & 0.14 \\ EC05 & 14 September & 297.53 & 298.27 & 297.07 & 260.87 & 278.14 & 270.8 & DisTrad-LST & 7.34 & 0.14 \\ EC13 & 19 June & 302.36 & 305.55 & 304.66 & 442.96 & 310.25 & 319.07 & DisTrad-LST & 8.82 & 0.13 \\ EC18 & 8 July & 311.35 & 314.44 & 314.63 & 146.48 & 140.93 & 148.20 & DisTrad-LST & 7.27 & 0.00 \\ SWW & 15 August & 315.29 & 314.42 & 314.59 & 164.55 & 158.74 & 166.00 & DisTrad-LST & 7.26 & 0.00 \\ SSW & 30 June & 316.98 & 314.71 & 314.20 & 184.81 & 192.14 & 199.33 & GWR-LST & 7.19 & 0.00 \\ EC10 & 3 August & 304.10 & 304.96 & 304.61 & 610.29 & 584.85 & 591.67 & DisTrad-LST & 7.09 & 0.00 \\ SSW & 22 August & 3148.55 & 315.02 & 315.70 & 196.74 & 55.15 & 48.04 & GWR-LST & 7.11 & 0.00 \\ EC07 & 2 September & 292.64 & 293.19 & 293.41 & 427.55 & 422.21 & 414.95 & GWR-LST & 7.26 & 0.00 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The site information for small differences between the two methods.  
MBE and RMSE values of \(R_{s}\downarrow\) were 0.81, 13.80 W\(\cdot\)m\({}^{-2}\), and 25.35 W\(\cdot\)m\({}^{-2}\), respectively. The accuracy of SSW is low. Because cloudy conditions occurred briefly on 27 July, few ground observations were obtained, and \(R_{s}\downarrow\) was significantly overestimated. After removing these data, the \(R^{2}\), MBE and RMSE values of \(R_{s}\downarrow\) were 0.87, 10.90 W\(\cdot\)m\({}^{-2}\), and 21.13 W\(\cdot\)m\({}^{-2}\), respectively.  
On overall, the \(R^{2}\), MBE and RMSE values of \(R_{L}\downarrow\) were 0.73, 0.28 W\(\cdot\)m\({}^{-2}\), and 21.24 W\(\cdot\)m\({}^{-2}\), respectively. As seen in Table 9, the accuracies at SD and SSW were low. The low accuracies at the SD station potentially resulted from high humidity, which resulted in low at-nadir brightness temperatures and low retrieved \(R_{L}\downarrow\). The models use surface temperature when estimating \(R_{L}\downarrow\) to approximate or substitute the near-surface temperature [24], and the inaccuracy of the SSW LST may influence the \(R_{L}\downarrow\) results.