## 3 Results and Analysis
### Sensitivity to Different Types of Soil Compositions  
The previous cases illustrate the importance and the sensitivity of the input variables for the permittivity retrieval in GNSS-R. The permittivity has a positive relationship with soil moisture content [54]. The relationship between soil permittivity and soil moisture is given by the soil permittivity models [54; 55; 56], so several static measurements were performed by the Remote Sensing Group at Politecnico di Torino in 2016. Among them, two typical types of soils that were chosen intentionally here to investigate the variable importance sensitivity for GNSS-R soil moisture content.  
In Tables 1 and 2, the composition (volume percentage and type of sand, clay) of the soil was reported in detail. According to the United States Department of Agriculture (USDA) Classification System, the two types of soil belong to the loamy sand and silty clay loam textural classes, respectively [59]. These different soil compositions that were used in the soil models for the permittivity to retrieve the soil moisture content here, and also for the subsequent ground-truth measurement.  
The parameters of the sensitivity to the permittivity retrieval were studied in the previous case and showed that the order of the variable importance was clear and quite stable. In this case, we illustrated the sensitivity analysis for the input variables to soil moisture retrieval. The more samples \(n\) we had, the results were more stable and precise, so the optimization parameters were _estimators_ = 2000, \(n=5000\), regarding the parameter \(col-sample-tree=0.5\) and 0.6 (Figure 8) respectively. In Figure 8, the loamy sand (a) and silty clay loam soil (b) case had similar behavior. The processed \(SNR\) was the most sensitive parameter and the \(\theta\) was the opposite. These variables in the two plots illustrated the same order as before. The highest contribution was observed when \(col-sample-tree=0.6\), with the maximum of the importance of 0.7 (70%). The same as before, the value of the variable \(\theta\) (elevation angle) was much lower than the \(Pn\) (receiver noise) and \(G_{r}\) (receiver gain), which denotes the minimum value of nearly zero indicating that the variable \(\theta\) was almost not sensitive to the output (soil moisture content) in this case. It also confirms that it is a less important input parameter in soil moisture retrieval of GNSS-R.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Coarse Sand** & **Fine Sand** & **Very Fine** & **Coarse Silt** & **Fine Silt (\%)** & **Clay (\%)** & **Organic** \\
**(\%)** & **(\%)** & **Sand (\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline
15.5 & 50.1 & 16.1 & 5.3 & 8.2 & 4.8 & 1.4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Composition of the loamy sand soil (Grugliasco experiment) [53].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Coarse Sand** & **Fine Sand (\%)** & **Fine Sand (\%)** & **Coarse Silt (\%)** & **Fine Silt (\%)** & **Clay (\%)** & **Organic** \\
**(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline
1.1 & 10.5 & 6.4 & 44.5 & 36.8 & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Composition of the silty clay loam soil (Agliano experiment) [53].