# Impact of the Elevation Angle on CYGNSS GNSS-R
## 6 Results on the Surface Roughness and the Soil Moisture Effect
### Regional Case Studies  
Specific target areas with little vegetation over Argentina, India, and Sudan (Figures 6-8) were selected for this section because they allowed for the evaluation of the impact of SMC and h in the angular evolution of \(\Gamma_{\rm LHCP,CyGNSS}\), excluding the effects of rough topography and high vegetation. The coordinates of these target areas are the following ones: Argentinian Pampas (Lat = \([-37,-30]^{\circ}\), Lon = \([-65,-60]^{\circ}\)), India (Lat = \([22,29]^{\circ}\), Lon = \([70,77]^{\circ}\)) and Sudan (Lat = \([4,10]^{\circ}\), Lon = \([25,33]^{\circ}\)). The land cover-types were croplands (Pampas and India) and savannahs (Sudan), where the signal penetration depth was high, so as to minimize the vegetation effects. The Pearson correlation coefficient r of \(\Gamma_{\rm LHCP,CyGNSS}\) and SMC was calculated for each target area at steps of \(\theta_{\rm e}\) = \(10^{\circ}\) from \(\theta_{\rm e}\) = \(20^{\circ}\) to \(\theta_{\rm e}\) = \(90^{\circ}\) (Table 2). The maximum Pearson coefficients r\({}_{\rm Pampas}\)\(\approx\) 0.78, r\({}_{\rm India}\)\(\approx\) 0.72, and r\({}_{\rm Sudan}\)\(\approx\) 0.74 were found, respectively, at \(\theta_{\rm e}\)\(\approx\)\([60,70]^{\circ}\) and h\({}_{\rm Pampas}\)\(\approx\) 0.1, \(\theta_{\rm e}\)\(\approx\)\([50,60]^{\circ}\) and h\({}_{\rm India}\)\(\approx\) 0.11, and \(\theta_{\rm e}\)\(\approx\)\([30,40]^{\circ}\) and h\({}_{\rm Sudan}\)\(\approx\) 0.15. These coefficients were gradually achieved at lower \(\theta_{\rm e}\) for increasing mean values of h over these target areas. As such, the angular ranges associated with an improved correlation coefficient depend on h. A lower \(\theta_{\rm e}\) was required to increase the signal coherence with an increase in h, in agreement with the [PERSON] criterion that establishes a surface (without vegetation and without rough topography) could be considered smooth if the phase difference between two reflected electromagnetic waves was lower than \(\pi/2\) rad:  
\[\sigma_{\rm RMS}<\frac{\lambda}{8\sin\theta_{\rm e}} \tag{6}\]  
where \(\lambda\) was the signal wavelength that at the L-band was \(\approx\)20 cm. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\theta_{\rm e}\) & **Pampas** & **India** & **Sudan** \\ \hline \([80,90]^{\circ}\) & 0.73 & 0.62 & 0.68 \\ \([70,80]^{\circ}\) & 0.77 & 0.68 & 0.69 \\ \([60,70]^{\circ}\) & 0.78 & 0.71 & 0.68 \\ \([50,60]^{\circ}\) & 0.76 & 0.72 & 0.65 \\ \([40,50]^{\circ}\) & 0.71 & 0.72 & 0.68 \\ \([30,40]^{\circ}\) & 0.60 & 0.70 & 0.74 \\ \([20,30]^{\circ}\) & 0.36 & 0.6 The angular dependence seemed to be lower over the Sudan target area (savannahs), which was characterized by a significantly higher effective surface roughness parameter. In this situation, \(\sigma_{\text{LHCP,incoh}}^{0}\) was high even for low \(\theta_{\text{e}}\) and thus the power fluctuations of \(\Upsilon_{\text{r,Peak,LHCP}}\) were more linked to the size of the first iso-delay ellipse (much larger than that of the first Fresnel zone), which minimized the impact of \(\theta_{\text{e}}\). Nonetheless, there was a non-negligible increment of the correlation for \(\theta_{\text{e}}\approx\) [30,40]\({}^{\circ}\). The impact of \(\theta_{\text{e}}\) was clearer over Argentinian Pampas and India (croplands). This experimental evidence was a symptom that over smoother surfaces (e.g., croplands), the correlation of \(\Gamma_{\text{LHCP,CyGNSS}}\) and SMC was improved when the coherent scattering regime started to be the dominant one because: (a) A higher spatial resolution (smaller first Fresnel zone), as compared to that at lower \(\theta_{\text{e}}\), minimized the effects of land cover heterogeneity (Table 3). (b) \(\sigma_{\text{LHCP,coh}}^{0}\) was mainly related to surface scattering. The use of a higher \(\Upsilon_{\text{c}}\) would improve the sensitivity of GNSS-R to SMC [16] because it would filter out the power fluctuations linked to the incoherent scattering term.