# Impact of the Elevation Angle on CYGNSS GNSS-R
## 4 Data and Methods  
In this work, the impact of the elevation angle \(\theta_{\text{e}}\) on CyGNSS experimental reflectivity \(\Gamma_{\text{LHCP,CyGNSS}}\) was empirically evaluated as a function of the effective surface roughness parameter h and SMC. CyGNSS Level 1 Science Data Record Version 2.0 [25] is used to estimate \(\Gamma_{\text{LHCP,CyGNSS}}\) and SMAP Enhanced Level 3 product [46] is selected to provide h and SMC data. These observables are described here for an enhanced understanding of the experimental results. CyGNSS experimental reflectivity \(\Gamma_{\text{LHCP,CyGNSS}}\): The calibrated reflected and direct DDMs are used to estimate the power waveform peaks \(\text{Y}_{\text{r,Peak,LHCP}}\) and \(\text{Y}_{\text{d,Peak,RHCP}}\). They are computed using a coherent integration time of \(\text{T}_{\text{c}}=1\) ms and 1000 samples to perform an incoherent averaging. The estimation of the CyGNSS reflectivity was obtained by applying the following algorithm:  
\[\Gamma_{\text{LHCP,CyGNSS}}=\left\langle\left|\text{Y}_{\text{r,Peak,LHCP}} \right|^{2}\right\rangle\!\left/\left\langle\left|\text{Y}_{\text{d,Peak,RHCP}} \right|^{2}\right\rangle\right. \tag{5}\]  
after compensating for the antennas' gain patterns versus the gain at the corresponding boresight direction [down-looking gain \(\approx 14.5\) dB, \(\theta_{\text{e}}=62^{\circ}\) and up-looking gain \(\approx 4.7\) dB, \(\theta_{\text{e}}=90^{\circ}\)], and the difference of both gains at boresight. The compensation of the antennas' gain was performed as a function of \(\theta_{\text{e}}\), with a precision of four decimals. The half-power beamwidth (\(-3\) dB) of each down-looking CyGNSS antenna was \(\approx\)30\({}^{\circ}\), and the \(-6\) dB field-of-view was \(\approx 45^{\circ}\). On the other hand, each antenna pointed to the Earth's surface with an inclination angle of 28\({}^{\circ}\) (antenna boresight). As such, GNSS signals reflected at lower \(\theta_{\text{e}}\approx\) [20,40]\({}^{\circ}\) could be accurately collected through the main lobe of each antenna. Effective surface roughness parameter h: It was empirically estimated based on the Moderate Resolution Imaging Spectroradiometer (MODIS) Geosphere-Biosphere Program (IGBP) land cover classes [47, 48]. h is an estimation of the factor \(4k^{2}\sigma_{\text{RMS}}^{2}\) in the surface reflectivity term in Equation (4). As such, this parameterization provided an improved performance as compared to previous global constant values-based algorithms [49], because it incorporated the diversity of the land surface. h values for different land cover types are included in the SMAP Tau-Omega parameter look-up table, at a spatial scale of 9 km. The use of physical roughness parameters, such as correlation length and RMS height, requires in situ characterization, which is time-consuming and it is not feasible at a global scale. Thus, the SMAP effective roughness parameter was selected for this study, although the ultimate accuracy of the MODIS IGBP land cover types used for the roughness parameter estimation in the SMAP algorithm needs to be further evaluated. This effective parameter accounts for the dependence of surface roughness with SMC, while physical parameters do not. A heterogeneous distribution of the water when the soil dries out more water at specific target areas creates variations in the actual roughness of the soil that is not considered by the physical parameters. Further research should also account for the effects of roughness dynamics. Over specific target areas it has been reported [50] that the actual soil roughness is slightly higher as compared to the estimation provided by physical roughness parameters. Future studies covering a large variety of areas could help to optimize the estimation of the effective roughness parameter at a global scale. Soil Moisture Content (SMC): SMC was estimated using the single channel algorithm at V-Pol, when the optimal Earth's surface conditions are identified.