# Impact of the Elevation Angle on CYGNSS GNSS-R
## 6 Results on the Surface Roughness and the Soil Moisture Effect
### Regional Case Studies
The sensitivity to SMC was based on the difference between the dielectric properties of water and soil. Here, the sensitivity of \(\Gamma_{\text{LHCP,CyGNSS}}\) to SMC was analyzed over these selected target areas (Figure 6a-f). In so doing, the selected \(\theta_{\text{e}}\) ranges corresponded to those with the maximum Pearson correlation coefficient between \(\Gamma_{\text{LHCP,CyGNSS}}\) and SMC (Table 2). Figure 6a,c,e shows the scatter plots of \(\Gamma_{\text{LHCP,CyGNSS}}\) and SMC as a function of different h levels. Land cover-types over Pampas and India were croplands with moderate mean roughness: h\({}_{\text{Pampas}}\approx\) 0.1 (Figure 6b) and h\({}_{\text{India}}\approx\) 0.11 (Figure 6d). The mean roughness over Sudan was higher: h\({}_{\text{Sudan}}\approx\) 0.15 (Figure 6f). The slopes of the linear regressions were \(\approx\)26 dB/(m\({}^{3}\)/m\({}^{3}\)), \(\approx\)37 dB/(m\({}^{3}\)/m\({}^{3}\)), and \(\approx\)50 dB/(m\({}^{3}\)/m\({}^{3}\)) respectively over the target areas, while the RMSE was \(\approx\)2.5 dB, \(\approx\)3 dB and \(\approx\)3.3 dB. In Sudan there was a smaller SMC variability and a significant dynamic range (Figure 6e). This explained the higher slope of the fit. On the other hand, the higher roughness h explained the higher RMSE and SD (Table 4). Overall, a good sensitivity of \(\Gamma_{\text{LHCP,CyGNSS}}\) to SMC was found over the three selected target areas. Figure 6b,d,f is useful to further understand the impact of h on the sensitivity to SMC [Pampas (Figure 6a), India (Figure 6c), and Sudan (Figure 6e)]. \(\Gamma_{\text{LHCP,CyGNSS}}\) decreased with an increase in h for nearly constant levels of SMC, and at the same time this rate of change depended on the mean SMC level. For lower SMC levels, \(\Gamma_{\text{LHCP,CyGNSS}}\) decreased significantly for a high h parameter, while \(\Gamma_{\text{LHCP,CyGNSS}}\) appeared to be roughly independent of h for higher levels of SMC. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\theta_{\text{e}}\) & **Semi-Minor Axes [m]** & **Semi-Major Axes [m]** \\ \hline \(90^{\circ}\) & 311 & 311 \\ \(80^{\circ}\) & 313 & 317 \\ \(70^{\circ}\) & 321 & 341 \\ \(60^{\circ}\) & 334 & 385 \\ \(50^{\circ}\) & 355 & 463 \\ \(40^{\circ}\) & 388 & 603 \\ \(30^{\circ}\) & 440 & 880 \\ \(20^{\circ}\) & 532 & 1555 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Size of the semi-major and semi-minor axis of the first Fresnel zone for the CyGNSS scenario, as a function of the elevation angle \(\theta_{\text{e}}\). Figure 6: Scatter plots over specific target areas [(**a,b**) Argentinian Pampas, (**c,d**) India, and (**e,f**) Sudan] of (**a,c,e**) the CyGNSS reflectivity \(\Gamma_{\rm LHCP,CyGNSS}\) vs soil moisture content (SMC) as a function of surface roughness parameter h and (**b,d,f**) the CyGNSS reflectivity \(\Gamma_{\rm LHCP,CyGNSS}\) vs. surface roughness parameter h as a function of SMC. The selected elevation angles \(\theta_{\rm e}\) ranges corresponded to the maximum Pearson correlation coefficient between \(\Gamma_{\rm LHCP,CyGNSS}\) and SMC (Table 2). The robust fit regression lines are shown in green. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Pampas** & **India** & **Sudan** \\ \hline
**Mean [dB]**; \(\theta_{\rm e}=[50,60]^{\circ}\) & \(-10.6\) & \(-12.2\) & \(-14.5\) \\
**Mean [dB]**; \(\theta_{\rm e}=[20,30]^{\circ}\) & \(-5.2\) & \(-8.4\) & \(-9.2\) \\ SD [dB] \(\phi_{\rm e}=[50,60]^{\circ}\) & \(3.9\) & \(2.5\) & \(6.4\) \\
**SD [dB]**; \(\theta_{\rm e}=[20,30]^{\circ}\) & \(2.5\) & \(2.5\) & \(4\) \\
**Kurtosis**; \(\theta_{\rm e}=[50,60]^{\circ}\) & \(5.8\) & \(3.5\) & \(1.96\) \\
**Kurtosis**; \(\theta_{\rm e}=[20,30]^{\circ}\) & \(4.1\) & \(2.8\) & \(2.5\) \\
**Skewness**; \(\theta_{\rm e}=[50,60]^{\circ}\) & \(-1.5\) & \(-0.6\) & \(0\) \\
**Skewness**; \(\theta_{\rm e}=[20,30]^{\circ}\) & \(-0.5\) & \(0\) & \(-0.1\) \\ \hline \hline \end{tabular}
\end{table}