# Impact of the Elevation Angle on CYGNSS GNSS-R
## 6 Results on the Surface Roughness and the Soil Moisture Effect
### Regional Case Studies

Table 4: Statistics (mean, standard deviation SD, kurtosis, and skewness) of the CyGNSS reflectivity \(\Gamma_{\rm LHCP,CyGNSS}\) distributions over the selected target areas (Argentinian Pampas, India, and Sudan). Figure 7: Histograms of the CyGNSS reflectivity \(\Gamma_{\rm LHCP,CyGNSS}\) over the selected target areas [(**a,b**) Argentinian Pampas, (**c,d**) India, and (**e,f**) Sudan] for (**a,c,e**) \(\theta_{\rm e}=[20,30]^{\circ}\), and (b,d,f) \(\theta_{\rm e}=[50,60]^{\circ}\). The histograms of \(\Gamma_{\rm LHCP,CyGNSS}\) over these target areas are displayed to complement the observations on the correlation coefficients (Figure 7). The corresponding statistics are also included in Table 4. Significant changes on the histograms were found from \(\theta_{\rm e}\approx\)[20,30]\({}^{\circ}\) (Figure 7a,c,e) to \(\theta_{\rm e}\approx\)[50,60]\({}^{\circ}\) (Figure 7b,d,f). The lowest mean \(\Gamma_{\rm LHCP,CyGNSS}\) and the highest standard deviation (SD) of the three target areas appeared over Sudan (Table 4). In this sense, it seems reasonable that the maximum correlation in Sudan was achieved over a significantly lower \(\theta_{\rm e}\) as compared to the Argentinian Pampas and India. A lower angular range was required to achieve a high enough signal coherence. A bimodal distribution (Figure 7f) was found over Sudan at \(\theta_{\rm e}\approx\)[50,60]\({}^{\circ}\), which was an additional factor that justified the lower angular variability over this particular target area (Table 2). The impact of a lower \(\theta_{\rm e}\) was quite evident in Figure 7e where the \(\Gamma_{\rm LHCP,CyGNSS}\) distribution turned into a unimodal one with a kurtosis \(\approx\)2.5, which tended to be like a Gaussian one. This indicated the presence of a coherent component in the total scattered electromagnetic field [15], and thus it is reasonable that the maximum correlation also appeared at this angular range. Over the Argentinian Pampas, the mean \(\Gamma_{\rm LHCP,CyGNSS}\) was higher than over India, and thus the maximum correlation appeared over a slightly higher \(\theta_{\rm e}\). For very low \(\theta_{\rm e}\approx\)[20,30]\({}^{\circ}\), the Pearson coefficients tended to decreases in all the selected target areas (Table 2), and this could be attributed to the lower \(\Gamma_{\rm LHCP,CyGNSS}\) dynamic range over this angular range. \(\Gamma_{\rm LHCP,CyGNSS}\), SMC, and h were geolocated over the specific target areas (Figure 8a-i) to further understand the effects of h on SMC estimation using GNSS-R. The averaged \(\Gamma_{\rm LHCP,CyGNSS}\) over Argentinian Pampas is shown in Figure 8a. The spatial pattern was clearly correlated with that of the SMAP-derived SMC (Figure 8b), which appeared to be the most important parameter. However, the impact of h was also relevant, especially on the upper-right side of Figure 8a-c. In this area, there was a sudden drop of h that enabled an increment of \(\Gamma_{\rm LHCP,CyGNSS}\) for nearly constant values of SMC. The spatial variability of \(\Gamma_{\rm LHCP,CyGNSS}\) was higher than radiometer data because of the higher resolution of GNSS-R, which was associated with the size of first Fresnel zone. The target area over India was selected because this was a relatively dry region with some SMC peaks, so as to complement the information obtained from the wet Argentinian Pampas. \(\Gamma_{\rm LHCP,CyGNSS}\) increased due to a positive gradient on SMC. This effect was lower than over the Argentinian Pampas because of the reduced roughness range h \(<\) 0.13 as compared to that over the Argentinian Pampas h\(<\) 0.16. This result agrees with the conclusions derived from Figure 6b,d,f, where the effect of surface roughness was shown to be more significant for h \(>\) 0.13. Finally, the averaged \(\Gamma_{\rm LHCP,CyGNSS}\) over Sudan showed two clearly differentiated spatial patterns that corresponded to SMC levels from moderate (0.2 \(<\) SMC \(<\) 0.3) to very high (0.4 \(<\) SMC \(<\) 0.5).