# Impact of the Elevation Angle on CYGNSS GNSS-R
## 6 Results on the Surface Roughness and the Soil Moisture Effect
### Global Analysis  
The angular evolution of \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) was studied averaging at steps of \(\theta_{e}=10^{\circ}\) from \(\theta_{e}=20^{\circ}\) to \(\theta_{e}=90^{\circ}\) using different ranges of h (Figure 4a) and SMC (Figure 4b). The averaging was performed  
Figure 3: Close-up of one-month (from 20 September to 20 October 2017) averaged CyGNSS bistatic reflectivity \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) for a grazing angle geometry with \(20^{\circ}<\theta_{e}<40^{\circ}\), over differentiated target areas over land: (a) croplands, and (b) Amazonian rainforests. At this geometry, the major axes of the Fresnel zone is \(\approx\)1.6 km. using data from the eight satellites of the CyGNSS constellation (the maximum of eight different DDMs were used in the averaging). The rate of change of \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) was larger as h increased. At the same time, the larger the roughness, the lower \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) was at all the selected SMC levels (Figure 5). Figure 5 also shows two differentiated \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) angular ranges: \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) decreased from \(\theta_{\mathrm{e}}\)\(\approx\) 85\({}^{\circ}\) to \(\theta_{\mathrm{e}}\)\(\approx\) 55\({}^{\circ}\), and it increased from \(\theta_{\mathrm{e}}\)\(\approx\) 55\({}^{\circ}\) to \(\theta_{\mathrm{e}}\)\(\approx\) 25\({}^{\circ}\). \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) included contributions from both coherent and incoherent scattering regimes in both angular ranges. The main difference between both scattering regimes was on the combination of the electromagnetic field vectors. \(\sigma^{0}_{\mathrm{LHCP,coh}}\) came from the coherent combination of the signals scattered on the individual facets within the first Fresnel zone. \(\sigma^{0}_{\mathrm{LHCP,incoh}}\) was the result of the random combination of electromagnetic waves coming from other scatterers within the glistening zone that added together at the receiving antenna. If the combination was totally coherent, \(\Gamma_{\mathrm{LHCP,coh}}\) accounted for all the reflected power. In the case of diffuse scattering, the random signs of the electric field cross-products cancelled out \(\sigma^{0}_{\mathrm{LHCP,coh}}\), and the reflected power was given by \(\sigma^{0}_{\mathrm{LHCP,incoh}}\). The changes on the angular evolution of \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) depended on the dominant scattering mechanism. In the interpretation of Figure 5 it should be considered that the averaging of the reflectivity was performed over the complete land-surface coverage enabled by CyGNSS, including bare soil, deserts, rough topography areas, and highly vegetated areas such as rainforests. As such, these results provide the average response of \(\Gamma_{\mathrm{LHCP,CyGNSS}}\) as a function of \(\theta_{\mathrm{e}}\). Figure 4: (**a**) Effective surface roughness parameter h over the Earth. (**b**) One-month (from 20 September to 20 October 2017) averaged SMAP-radiometer derived Soil Moisture Content (SMC). \(\Gamma_{\text{LHCP,cyGNSS}}\) decreased in the first range (from \(\theta_{\text{e}}\approx 85^{\circ}\) to \(\theta_{\text{e}}\approx 55^{\circ}\)) because the incoherent scattering was dominant over the coherent one. The coherent integration time \(\text{T}_{\text{c}}\) is an important parameter that influences the ratio of the coherent-to-incoherent scattering components, and in this experiment it was set to \(\text{T}_{\text{c}}\) = 1 ms. A longer \(\text{T}_{\text{c}}\) would limit the incoherent scattering term, so as to increase the coherent-to-incoherent ratio because it would better filter out the noise and the volume scattering term [32]. Previous research activities also found a transition from an incoherent to coherent scattering regime over the ocean surface [42; 51], where \(\Gamma_{\text{LHCP,incoh}}\) is dominant for high \(\theta_{\text{e}}\)[52]. Theoretical simulations were performed in Reference [52] to study the evolution of the incoherent reflected power as a function of \(\theta_{\text{e}}\).