## 3 Results  
### Evaluation on the Three \(C_{d}\) Models  
#### 3.1.1 Validation Accuracy at Site Scale  
Based on the corresponding samples shown in Table 3, the accuracy of the three \(C_{d}\) model was calculated separately, and then they were inter-compared with the common samples. Meanwhile, the accuracy of the two existing models before and after calibration was also presented. \begin{table}
\begin{tabular}{l l l l l} \hline  & \multicolumn{2}{l}{**Training**} & \multicolumn{2}{l}{**Validation**} \\ \cline{2-5}  & \(C_{d}\) & & \(R_{ni}\) & \(R_{nd}\)* \\ \cline{2-5}  & **Time** & **No. of Samples** & **No. of Samples** & **No. of Samples** \\ \hline \multirow{4}{*}{\(S\) Model} & 12:00 & 5393 & 2315 & \\ \cline{2-5}  & 13:00 & 5288 & 2267 & 4992 \\ \cline{2-5}  & 14:00 & 5147 & 2206 & \\ \hline \(R\) Model & 10:00–11:00 & 7730 & 3314 & 3314 \\ \hline \multirow{4}{*}{New Model} & 9:30–12:30 (30 min an interval) & & \\ \cline{2-5}  & Vegetated & 31,450 & 13,624 & 4668 \\ \cline{2-5}  & Non- & \multirow{2}{*}{18,431} & \multirow{2}{*}{7759} & \multirow{2}{*}{2730} \\ \cline{1-1} \cline{2-5}  & vegetated & & & \\ \hline \multicolumn{5}{l}{Common validation samples: No. = 517} \\ \hline \end{tabular}
\end{table} 
Table 3: The training and validation samples for the three \(C_{d}\). S Model  
Table 4 gives the calibrated and original coefficients of \(S\) Model at each of the three moments 12:00 hour, 13:00 hour, and 14:00 hour. Relatively, among the three groups of coefficients, the difference in \(a_{3}\) before and after calibration was the largest, especially at 14:00 hour. Additionally, the training accuracy of \(S\) Model at the three moments was very similar to one other with the range of R\({}^{2}\) being 0.91-0.92, RMSE being18.07-18.91 Wm\({}^{-2}\), and Bias being \(-\)1.02-\(-\)1.23 Wm\({}^{-2}\), respectively. Against the corresponding validation samples, the validation results of \(S\) Model overall and at specific moments, which was represented by the accuracy of the estimated \(R_{nd}\) (named as \(R_{nd\text{-}Cd\text{-}SM}\)) calculated by using the \(C_{d}\) derived from \(S\) model, were calculated and presented in Figure 4. In Figure 4a, the top chart represents the validated RMSE and rRMSE of the calculated \(R_{nd\text{-}Cd\text{-}SM}\) before (the bar and dash dot line in red) and after (the bar and dash dot line in blue) calibration, respectively, and the table below represents the corresponding validated Bias. Figure 4b and c display the overall validation accuracy of \(R_{nd\text{-}Cd\text{-}SM}\) when using the original and calibrated coefficients, respectively. The validation accuracy of \(S\) model at the three moments was also similar. It turns out that the estimation accuracy of \(S\) model was significantly improved after calibrating with the more comprehensive training samples at all three moments, with the overall validated RMSE (rRMSE) decreasing by 19.59 Wm\({}^{-2}\) (18%) and the magnitude of Bias decreasing by 30.53 Wm\({}^{-2}\). Among the three specific moments, the model performance improved the most at 14:00 hour, with the RMSE (rRMSE) decreasing by 29.35 Wm\({}^{-2}\) (27%) and the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Time**} & \multicolumn{2}{c}{**Original Coefficient**} & \multicolumn{2}{c}{**Calibrated Coefficient**} \\ \cline{2-7}  & \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{a_{3}}\) & \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{a_{3}}\) \\ \hline
12:00 & \(-\)7 \(\times\) 10\({}^{-6}\) & 0.0026 & 0.0756 & \(-\)7.483 \(\times\) 10\({}^{-6}\) & 0.0026 & 0.0383 \\
13:00 & \(-\)8 \(\times\) 10\({}^{-6}\) & 0.0028 & 0.0820 & \(-\)7.486 \(\times\) 10\({}^{-6}\) & 0.0026 & 0.0375 \\
14:00 & \(-\)7 \(\times\) 10\({}^{-6}\) & 0.0027 & 0.1240 & \(-\)7.862 \(\times\) 10\({}^{-6}\) & 0.0027 & 0.0467 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The original and calibrated coefficients of S Model.