## 4 Results and Discussion
### Soil Moisture Estimation  
The soil moisture estimation was performed by applying the LUT described in Section 3.3. Figure 5 shows the relationship between measured and predicted soil moisture when using the WCM to reduce the effect of vegetation. We observed that all the predicted soil moisture was overestimated when the soil moisture less than 19 vol.%. This phenomenon may be explained by the strong influence of vegetation. When the vegetation is characteristically sparse, the backscattering increment from vegetation exceeded the soil backscattering reduction due to vegetation attenuation [2]. The biomass of these plots is less than 0.3 kg/m\({}^{2}\). Thus, the vegetation is sparse, it may cause that the attenuation on soil backscattering is lower than the backscattering increment from vegetation. Therefore, the soil moisture in these plots was overestimated. The relationship between the measured and estimated volumetric soil moisture using the modified model is graphically represented in Figure 6. A linear relationship between the predicted and measured soil moisture (Figure 6) was observed, which suggests that the method described here could be effectively used to estimate soil moisture in an alpine prairie. However, as shown in Figure 6, the soil moisture values in wetter area had larger deviations from the 1:1 line than those in the relatively dryer area. In other words, there were larger retrieval errors in the wetter area than in the dryer area. This may be due to the high sensitivity of backscattering to changes in soil moisture with low soil water content; however, for wet soil, the backscattering is less sensitive [51]. This behavior may also be explained by the lower sensitivity of the IEM \(\sigma^{o}\) to soil moisture under wet conditions [52], and the IEM simulations show saturation behavior before the actual radar signals [53]. It may indicate that this method is problematic for estimating soil moisture under wet conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Vegetation condition** & **Model** & **HH Polarization** & **VV Polarization** \\ \hline  & & \(R^{2}\) & RMSE & \(R^{2}\) & RMSE \\ \hline
**Density vegetation** & Basic model & 0.78 & 1.58 & 0.74 & 1.63 \\
**conditions** & Modified model & 0.81 & 1.23 & 0.78 & 1.61 \\
**Sparse vegetation** & Basic model & 0.25 & 2.65 & 0.15 & 2.93 \\
**conditions** & Modified model & 0.73 & 1.77 & 0.74 & 1.79 \\ \hline \end{tabular}
\end{table} 
Table 2: Performance achieved on test samples using the basic model and modified model. The result reveals that volumetric soil moisture may be estimated with a maximum error of \(\pm\)24.8% (Figure 6). The errors in the soil moisture estimation were not merely from the simulation and inversion. They could also be partially caused by the data preprocessing. The main error sources that cause poor soil moisture estimates are as follows: (1) Because of measurement uncertainty and the ill-posed problem, the mean values were used as the inverse results when the solution was not unique. If a randomly solution was selected as the inverse result, the maximum error of the estimated soil moisture was \(\pm\)64.6%; (2) Errors in the percentage of vegetation cover and LAI calculated from the optical imagery may have directly introduced errors into the soil moisture retrieval. The percentage of relative error was small for LAI; (3) In some areas of the image, the topography may cause errors in the inversion. Topographic distortions in the side-looking SAR image cannot be easily corrected in the mountainous area. As shown in Figure 4, model errors in the relatively flat area were lower than 2 dB. However, in the areas with high relief and steep slopes, model errors could be higher than 6 dB. Figure 4: The absolute error map of the model simulation. It suggesting that soil moisture estimation by model inversion was not reliable in these areas; (4) The acquisition times for the ascending and descending orbits of Radarsat-2 are different (morning and evening).