# First Evaluation of Topography on GNSS-R: An Empirical Study Based on a Digital Elevation Model
## 4 Understanding the Effects of Rough Topography on GNSS-R Space-Borne Data  
### Global Scale  
The main goal of this work was to study the impact of rough topography on CyGNSS-derived TE & \(\Gamma\) as a function of SMAP-derived SMC. As a first step, the selected topographic parameters (Figure 2), TWI (Figure 3a), CyGNSS-derived TE and \(\Gamma\) (Figure 3b,c), and SMAP-derived SMC (Figure 3d) were displayed over the complete coverage of the Earth's surface enabled by CyGNSS. SMC data were derived based on the V-pol single channel algorithm [37; 38]. Corrections for roughness, effective surface temperature, and vegetation water content (VWC) were also applied. Six months of CyGNSS and SMAP data were selected from 1 August 2018 to 31 January 2019. This specific time period was selected because the AGC was disabled in July 2018, so as to improve the performance in the estimation of \(\Gamma\)(Equation (17)). The selected temporal length was as large as possible at the time of starting this work. All the parameters were averaged using a \(0.1^{\circ}\times 0.1^{\circ}\) latitude/longitude grid with a moving window of \(0.2^{\circ}\) in steps of \(0.1^{\circ}\). This gridding strategy enabled the analysis using auxiliary data and different sensors. The resulting spatial resolution was \(\sim\) 20 km \(\times\) - 20 km at equatorial latitudes, which was wide enough to account for the across-track spreading \(\sim\) 20 km of the DDMs due to \(\left\langle\left|\mathrm{Y_{r,incoh}}(\tau,\mathrm{f})\right|^{2}\right\rangle\). Figure 3: (**a**) TWI, (**b**) CyGNSS-derived \(\Gamma\) (dB), (**c**) CyGNSS-derived TE (m), and (**d**) Soil Moisture Active Passive (SMAP)-derived SMC (m\({}^{3}\)/m\({}^{3}\)). CyGNSS and SMAP data correspond to a temporal window of six months (1 August 2018 to 31 January 2019). The parameters were displayed over the CyGNSS coverage over land surfaces. Overall, it was found that the spreading of TE was low \(\sim\)[100, 250] m and \(\Gamma\) is high \(\sim\) [\(-\)10, \(-\)3] dB over flat areas with low topographic heterogeneity and small surface elevation gradients (Figures 2 and 3). Over these areas, the scattering was quite specular and the coherence of the Earth-reflected GPS signals could be assumed to be high [35]. Under these circumstances,\(\left\langle\left|Y_{\tau,\text{t,colon}}(\tau,\text{f})\right|^{2} \right\rangle\gg\left\langle\left|Y_{\tau,\text{t,colon}}(\tau,\text{f})\right| ^{2}\right\rangle\). Thus, the power of the reflected signals could be assumed to be roughly independent of the platform's height (Equation.4). This point justifies the strong values of \(\Gamma\) and the reduced spreading of the waveforms. SMC was high over regions that do not always correspond to flat areas (Figure 3d). On the other hand, the spatial patterns of TE & \(\Gamma\) showed a certain agreement with TWI. An exception is found over e.g., tropical rainforests. Here, the spreading of TE was high and \(\Gamma\) was low because specular reflection is weakened by vegetation attenuation, \(\gamma\), and vegetation structure contributes to diffuse scattering, both of which significantly modify the shape of \(\left\langle\left|Y_{\tau,\text{t,topo}}(\tau,\text{f})\right|^{2}\right\rangle\)[39]. A more quantitative analysis is performed at a regional scale over an area with little vegetation and low small-scale surface roughness. Over desert areas e.g., Sahara, Kalahari, and Australia it was found that \(\Gamma\) was also quite high, despite SMC being almost negligible. This aspect was previously attributed to the effect of sub-surface scattering over rich sand content areas [6; 9]. In very dry conditions, GNSS-R observables have shown a certain sensitivity to the soil moisture at deeper levels [8]. In addition, specular scattering over areas with high TWI could significantly increase \(\Gamma\), despite SMC being low (Figure 3). Indeed, TE was rather low over areas with high TWI, which is an additional indication of the specular nature of the scattering.