# Soil Moisture Retrieval from Multi-GNSS Reflectometry on FY-3E GNOS-II by Land Cover Classification
## 3 Methods
### Analysis of Terrain Roughness Attenuation  
For spaceborne GNSS-R measurements, large-scale roughness has a greater impact on DDM observations. This subsection presents an analysis of the terrain roughness attenuation on the observations of GNOS-II. Although there are two effects linked to topography and micro-topography, it is difficult to separate them. Thus, we compute the combined effect of both. The roughness attenuation effects could be represented below:  
\[Att_{\text{roughness}}=\Gamma_{soil}/\Gamma_{fresnel} \tag{7}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**IGBP** & **b** \\ \hline Evergreen Needleleaf Forest & 0.10 \\ Evergreen Broadleaf Forest & 0.10 \\ Deciduous Needleleaf Forest & 0.12 \\ Deciduous Broadleaf Forest & 0.12 \\ Mixed Forest & 0.11 \\ Closed Shrublands & 0.11 \\ Open Shrublands & 0.11 \\ Woody Savannas & 0.11 \\ Savannas & 0.11 \\ Grasslands & 0.13 \\ Permanent Wetlands & 0 \\ Cropland & 0.11 \\ Urban and Built-Up & 0.10 \\ Cropland Natural Vegetation Mosaic & 0.11 \\ Snow and Ice & 0.11 \\ Barren or Sparsely Vegetated & 0.11 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The setting of parameter b according to IGBP classifications.  
The reflectivity of the soil surface \(\Gamma_{soil}\) could be calculated with Equations (4) and (5), and the Fresnel reflectivity \(\Gamma_{fresnd}\) dependent on the surface soil dielectric constant \(\varepsilon\) and the incidence angle \(\theta\)[31]:  
\[\Gamma_{fresnd}=\left|R_{rl}(\theta)\right|^{2}=\frac{\left(\varepsilon-1 \right)^{2}\cos^{2}\theta(\varepsilon-\sin^{2}\theta)}{\left(\varepsilon\cos \theta+\sqrt{\varepsilon-\sin^{2}\theta}\right)^{2}} \tag{8}\]  
where \(R_{rl}\) represents the Fresnel reflection coefficient, and \(\theta\) is the incidence of the observation. Note that for GNSS-R measurements, the transmitted signal is in right hand circular polarization, and the reflected signal is in left hand circular polarization. The soil dielectric constant \(\varepsilon\) could be obtained using the Mironov dielectric constant model, with clay fraction, soil moisture reference data, and signal frequency as the inputs [34]:  
\[\varepsilon =\text{micronov}(C,\text{mv},\text{freq}) \tag{9}\]  
where C is the clay fraction obtained from the Open Land Map [35] and grided to ease grid of 9 km, mv is the soil moisture in volumetric from the SMAP soil moisture product at a resolution of 9 km, freq is the frequency of reflected signals from different GNSS systems.  
The soil dielectric constant was calculated from Equation (9). Then, the Fresnel reflectivity could be obtained by Equation (8). Finally, the predicted global roughness (topography) attenuation at a resolution of 36 km is presented in Figure 7. The predicted values on different incidence angles were averaged on each grid. Regions with high elevations have larger attenuation (negative value) because complicated terrain is usually found at high altitudes. Due to the spatial heterogeneity of topography, it is difficult to construct a model for worldwide application. For this reason, instead of constructing a physical model, the empirical change detection approach [13] is used in this study.