## 5 Model Validation  
To evaluate the performance of the retrieval model, the ENVSAT ASAR image was used to retrieve soil moisture in Linze County at an incidence angle of 33.5\({}^{\circ}\) and a frequency of 5.4 GHz. From Tables 3 and 4, regression coefficients \(a\), \(b\), \(c\), and \(d\) can be obtained as shown in Equations (16) and (17).  
\[0.0030\mbox{ln}(mv)+0.0354\ln(Hrms)+0.0011\ln(Hrms)\ln(mv)+0.0838=10^{(\sigma_ {\rm ov}(\rm dB)/10)} \tag{16}\]  
\[0.0002\mbox{ln}(mv)+0.0041\ln(Hrms)+0.0001\ln(Hrms)\ln(mv)+0.0053=10^{(\sigma_ {\rm vh}(\rm dB)/10)} \tag{17}\]  
According to Equation (16), the following formula was obtained:  
\[Hrms=\mbox{e}^{\frac{10^{(\rm ov}(\rm dB)/10)-0.0838-0.0030\mbox{ln}(mv)}{0.0 054+0.0011\mbox{ln}(mv)}} \tag{18}\]  
By substituting Equation (18) into Equation (17), the soil moisture \(mv\) can be calculated by MATLAB. Similarly, the \(Hrms\) can be calculated. Then, the approach of 3-fold cross validation can be used to validate the model by in situ data. Figures 5 and 6 present the soil moisture and \(Hrms\) distribution map at the incidence angles of 33.5\({}^{\circ}\) and 26.3\({}^{\circ}\), respectively. Figure 5 shows that when the incidence angle was set to 33.5\({}^{\circ}\), the maximum value of soil moisture in the study area was 50%, and the maximum \(Hrms\) was 4 cm. When the incidence angle was set to 26.3\({}^{\circ}\), the maximum value of soil moisture in the study area was also 50%, and the maximum \(Hrms\) was also 4 cm. In Figure 5, the brown color indicates higher soil moisture content and \(Hrms\) and the purple color indicates lower soil moisture content and \(Hrms\). To evaluate the performance of the retrieval model, the retrieved and measured soil moisture values were compared, as shown in Figure 6. When the incidence angle varied from 33.5\({}^{\circ}\) to 26.3\({}^{\circ}\), R\({}^{2}\) of the retrieved and measured soil moisture decreased from 0.67 to 0.57, and RMSE increased from 2.53% to 5.4%. In the same situation, when the incidence angle varied from  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\theta\) (\({}^{\circ}\)) & \(a\) (\(\theta\)) & \(b\) (\(\theta\)) & \(c\) (\(\theta\)) & \(d\) (\(\theta\)) & \(\mathbf{R}^{2}\) \\ \hline
25 & 0.0002 & 0.0032 & 0.0001 & 0.0049 & 0.99 \\
30 & 0.0002 & 0.0038 & 0.0001 & 0.0052 &33.5\({}^{\circ}\) to 26.3\({}^{\circ}\), R\({}^{2}\) of the retrieved and measured _Hrms_ decreased from 0.64 to 0.51, and RMSE increased from 0.33 to 0.4 cm. The results show good consistency between simulated and measured data, but the inversion accuracy of soil moisture is higher than that of surface roughness. When the incidence angle varied from 33.5\({}^{\circ}\) to 26.3\({}^{\circ}\), the inversion accuracy of soil moisture and surface roughness decreased. Therefore, it is feasible to invert soil moisture and surface roughness using the empirical model.  
Figure 5: _Cont._  
Figure 6: Comparison between inverted and ground-measured soil moisture and _Hrms_: (**a**) soil moisture, \(\theta\) = 33.5\({}^{\circ}\); (**b**) soil moisture, \(\theta\) = 26.3\({}^{\circ}\); (**c**) _Hrms_, \(\theta\) = 33.5\({}^{\circ}\); (**d**) _Hrms_, \(\theta\) = 26.3\({}^{\circ}\).