# 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  
#### 4.2.1 Introduction  
A specific target area over South Asia was selected to further investigate topographic effects in \(\left\langle\left|Y_{\tau,\text{t,topo}}(\tau,\text{f})\right|^{2}\right\rangle\), without the influence of high levels of \(\sigma\), above ground biomass (AGB), and canopy height (CH). The coordinates of the selected target area were as follows: latitude = [5; 36]\({}^{\circ}\) and longitude = [64; 94]\({}^{\circ}\). The characteristics of this region enabled this study to be performed over a rich variety of terrains, including the Tibetan Plateau, Great Himalaya, Indo-Gangetic Plains, and Hindustan. As such, the impact of different topographic features in TE and \(\Gamma\) can be properly evaluated (Figures 4-6). In so doing, \(\left\langle\left|Y_{\tau,\text{t,topo}}(\tau,\text{f})\right|^{2}\right\rangle\) were classified in two groups to evaluate the effects of topography over two different scenarios. At \(\theta_{\text{e}}\)\(\sim\)[20; 30]\({}^{\circ}\), the main contribution to the generation of the reflected signal in a specular manner (elevation angle of the incident wave equals elevation angle of the scattered wave i.e., \(\theta_{\text{e,i}}\)= \(\theta_{\text{e,s}}\)= \(\theta_{\text{e}}\)) came from surface facets over high elevation mountains. Some low elevation areas could be occulted by the top of the mountains. On the other hand, at \(\theta_{\text{e}}\)\(\sim\)[80; 90]\({}^{\circ}\), both valleys and mountain peaks could reflect signals in a specular manner towards the CyGNSS. This study was additionally complemented with SMAP-derived SMC and its coefficient of variation (CV). A wide range of SMC levels could be observed. The highest SMC values were associated with both the Indo-Gangetic Plains and mountains regions in the West of Hindustan, while the lowest SMC levels were found over the Tibetan Plateau and the Thar Desert. The spatial patterns of SMC did not appear correlated with the topographic parameters. Significant SMC levels could be found over mountains but also over rivers basins. Figure 4: Regional scale study over a target area in South Asia. Different scientific observables and auxiliary data were depicted: (**a**) TPI, (**b**) TRI, (**c**) VRM, (**d**) \(\beta\), (**e**) TC, (**f**) PC, (**g**) CyGNSS-derived TE at \(\theta_{\rm e}\sim\) [20, 30] \({}^{\circ}\), (**h**) TE at \(\theta_{\rm e}\sim\) [80, 90] \({}^{\circ}\), (**i**) SMAP-derived SMC, (**j**) CyGNSS-derived \(\Gamma\) at \(\theta_{\rm e}\sim\) [20, 30] \({}^{\circ}\), (**k**) \(\Gamma\) at \(\theta_{\rm e}\sim\) [80, 90] \({}^{\circ}\), and (**l**) SMC CV. Figure 5: Parametric evaluation as a function of SMAP-derived SMC: (**a**,**d**,**g**,**j**) TPI, (**b**,**e**,**h**,**k**) TRI, and (**c**,**f**,**i**,**j**) VRM. Analysis of CyGNSS-derived TE at \(\theta_{\rm e}\sim\) [80, 90] \({}^{\circ}\) (**a**–**c**) and \(\theta_{\rm e}\sim\) [20, 30] \({}^{\circ}\) (**d**–**f**). Analysis of CyGNSS-derived \(\Gamma\) at \(\theta_{\rm e}\sim\) [80, 90] \({}^{\circ}\) (**g**–**i**) and \(\theta_{\rm e}\sim\) [20, 30] \({}^{\circ}\) (**j**–**l**). SMAP SMC data were used as an auxiliary product to help in the interpretation of the experimental results. The SMAP baseline accuracy requirement of 4% is not guaranteed over areas with very rough topography. SMC data are here provided with a lower accuracy. Nonetheless, 6 months of SMC data were averaged using a 0.1 \({}^{\circ}\) x 0.1 \({}^{\circ}\) latitude/longitude grid with a moving window of 0.2 \({}^{\circ}\) in steps of 0.1 \({}^{\circ}\). This strategy mitigated the effects of potential artefacts in SMAP-derived SMC. Additionally, this moving filter smoothed potential residual errors in the GMTED2010. Some errors have been reported in the literature. Figure 6: Parametric evaluation as a function of SMAP-derived SMC: (**a,d,g,j**) \(\beta\), (**b,e,h,k**) TC, and (**c,f,i,l**) PC.