**3. Results**

### *3.1. Reduce the Effects of Surface Roughness and Vegetation*

Figure 5 shows the correlation of *σ*◦ and Δ*σ* with the SM observations. There is no apparent correlation between the original *σ*◦ and SM, with a Pearson correlation coefficient (r) of 0.06. However, after subtracting the winter reference *σ*w, the r between Δ*σ* and SM reached 0.76. In Figure 5a, the sensitivity of the radar signal to SM is weakened by the effect of surface roughness. The comparison of SM with *σ*◦ and Δ*σ* has proven that our method is able to reduce the effect of surface roughness and essentially improve the sensitivity of radar signals to SM.

**Figure 5.** Relationship between the *σ*◦ and the SM measurements. (**a**): none-corrected *σ*◦and SM; (**b**): Δ*σ* and SM.

NDVI and NDMI jointly characterize the contribution of vegetation to the retrieval of SM. As shown in Figure 6, NDVI and NDMI have high correlations with SM, with r of 0.76 and 0.74, respectively. The results indicate that NDVI and NDMI are suitable for characterizing the vegetation contribution in *σ*◦ of the study area.

**Figure 6.** Relationship between the vegetation parameters and the SM measurements at the site. (**a**): NDVI and SM; (**b**): NDMI and SM.

### *3.2. SM Retrieval Algorithm and Validation*

Table 3 lists the model coefficients and R<sup>2</sup> value of 10,000 regressions. The coefficients which generate the highest weighted R<sup>2</sup> were set as the optimal coefficients. The SM retrieval algorithm is expressed as follows:

$$\text{NM} = 0.02 \times \Delta \sigma + 0.24 \times \text{NDVI} + 0.28 \times \text{NDMI} + 0.003 \tag{8}$$

As illustrated in Table 3 and Figure 7, the retrieved result is satisfactory, with R<sup>2</sup> and RMSE reaching 0.82 and 0.07 m3/m3, respectively. As shown in Table 3, the mean values of the 10,000 sets of regression coefficients are very close to the optimal values, and the standard deviation is also relatively small. It indicates that the model coefficients are relatively stable, and not largely influenced by different divisions of training and validation samples, which demonstrates the robustness of the model.

**Figure 7.** Comparison of SM-retrieved results with measurement data.


**Table 3.** The optimal coefficients are selected after the regression analysis. Mean is the mean value of each coefficient, STD is the standard deviation, and OPT is the optimal coefficient solution.

### *3.3. Map of Retrieved SM*

Figure 8 shows retrieved SM on eight days of S1 acquisitions with the grid spacing of 50 m × 50 m. The white areas in the retrieval results are caused by post-processing, where water bodies, mountain shadows, and anomalous areas are masked. To better show the spatial distribution characteristics of SM, Figure 9 was made by overlaying the spatial distribution map of SM with the topographic map. In hill areas with undulating terrain, SM is usually higher. In order to show the complexity of the spatial distribution of SM in mountainous areas of the permafrost region, this study designed two transect lines to further show the SM variation in the hill areas and extracted the SM values corresponding to the two transect lines, as shown in Figure 10. The variability of SM in hill areas is well presented. It demonstrates the high variability of SM, which could not be revealed by coarse SM products.

**Figure 8.** The map of SM retrieval results for thawing seasons 2018 and 2019 after post −processing.

Figure 11 shows the relationship between the spatial and temporal CV and the mean SM in this study area. The CV tends to decrease with increasing mean SM in both spatial and temporal dimensions, which shows that the variability of SM is higher in drier environments and lower in wetter environments. This pattern is related to the water-holding capacity of the soil and its spatial variability [83]. The large differences in the CV in different regions are related to the soil water content, bulk density, and soil texture [22,84,85]. In permafrost areas, the physicochemical properties of soils vary greatly in different areas of topography and vegetation cover, resulting in a high spatial heterogeneity of SM. In addition, the high CV in areas of low SM may also be explained by frequent precipitation and strong evapotranspiration during the thawing season.

**Figure 9.** The spatial distribution of the SM and the location of the two transect lines.

**Figure 10.** The SM values for the two transect lines. (**a**): Red transect line; (**b**): Black transect line.

**Figure 11.** The corresponding CV for each mean SM interval. (**a**): Spatial; (**b**): Temporal.
