# 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
### Regional Scale
#### 4.2.3 Sensitivity of CyGNSS to TWI vs. SMC  
The strong influence of primary terrain attributes on GNSS-R observables (Figures 5 and 6) triggered the sensitivity study of TE and \(\Gamma\) with TWI vs. SMC. To do so, a specific target area (Latitude \(\sim\)[20; 27]\(\,\,\)\({}^{\circ}\) and Longitude \(\sim\)[72; 84]\(\,\,\)\({}^{\circ}\)) was selected with a strong gradient of SMC, and a wide topographic heterogeneity (Figure 7). Figure 8 shows the density scatter plots of \(\Gamma\) vs. TWI at \(\theta_{\rm e}\)\(\sim\)[20; 30]\(\,\,\)\({}^{\circ}\) (Figure 8a) and \(\theta_{\rm e}\)\(-\)[80; 90]\(\,\,\)\({}^{\circ}\) (Figure 8b), \(\Gamma\) vs. SMC at \(\theta_{\rm e}\)\(\sim\)[20; 30]\(\,\,\)\({}^{\circ}\) (Figure 8c) and \(\theta_{\rm e}\)\(-\)[80; 90]\(\,\,\)\({}^{\circ}\) (Figure 8d), TE vs. TWI at \(\theta_{\rm e}\)\(-\)[20; 30]\(\,\,\)\({}^{\circ}\) (Figure 8e) and \(\theta_{\rm e}\)\(\sim\)[80; 90]\(\,\,\)\({}^{\circ}\) (Figure 8f), and TE vs. SMC at \(\theta_{\rm e}\)\(-\)[20; 30]\(\,\,\)\({}^{\circ}\) (Figure 8g) and \(\theta_{\rm e}\)\(-\)[80; 90]\(\,\,\)\({}^{\circ}\) (Figure 8h).  
Both observables TE and \(\Gamma\) are more correlated with TWI than with SMC (Table 1). This point could be justified because the potential presence of inland water bodies over areas with high TWI have a stronger impact on GNSS-R observables than SMC. In this analysis, areas with high elevation and very rough topography (i.e., Himalayan mountains) were excluded (Figure 7) because SMAP-derived SMC could have some uncertainties over areas with very rough topography. As such, SMC is delivered within the baseline accuracy in this target area.  
The Pearson correlation coefficients increased at grazing angles because of the stronger impact of topography at this geometry as compared to a nadir-looking configuration. On the other hand, the correlation of TE and \(\Gamma\) with SMC is almost negligible despite the moderate-to-high SMC dynamic range \(\sim\)[0, 0.4] m\({}^{3}\)/m\({}^{3}\). The slopes of the linear regressions were also included in Table 1, for both angular ranges. It is found that the sensitivity of TE to TWI and SMC increased at grazing angles, while that of \(\Gamma\) was stronger in a nadir-looking configuration in agreement with the results in Reference [8]. This empirical evidence suggests that topographic features can determine the main spatial pattern of Earth's surface reflectivity, at least over some specific target areas.  
Figure 7: Close up of the area selected for the sensitivity analysis of CyGNSS observables to TWI and SMAP-derived SMC.  
Figure 8: Density scatter plots over North India target area: CyGNSS-derived \(\Gamma\) vs. TWI at (**a**) \(\theta_{\rm e}\)\(\sim\) [20, 30] \({}^{\circ}\) and (**b**) \(\theta_{\rm e}\)\(\sim\) [80, 90] \({}^{\circ}\). \(\Gamma\) vs. SMAP-derived SMC at (**c**) \(\theta_{\rm e}\)\(\sim\) [20, 30] \({}^{\circ}\) and (**d**) \(\theta_{\rm e}\)\(\sim\) [80, 90] \({}^{\circ}\). TE vs. TWI at (**e**) \(\theta_{\rm e}\)\(\sim\) [20, 30] \({}^{\circ}\) and (**f**) \(\theta_{\rm e}\)\(\sim\) [80, 90] \({}^{\circ}\). TE vs. SMC at (**g**) \(\theta_{\rm e}\)\(\sim\) [20, 30] \({}^{\circ}\) and (**h**) \(\theta_{\rm e}\)\(\sim\) [80, 90] \({}^{\circ}\).  
Finally, it is worth pointing out that these results at a regional scale support qualitative results obtained at a global scale (Figure 1). As such, attention should be paid when analyzing GNSS-R data because soils saturated by the effect of topography could introduce confounding effects with respect to the impact of SMC.