# First Evaluation of Topography on GNSS-R: An Empirical Study Based on a Digital Elevation Model
## 6 Conclusions  
Several topographic parameters, TPI, TRI, VRM, \(\beta\), TC, and PC were derived from the \(\sim\)250 m GMTED2010 DEM. The impact of these parameters on different GNSS-R observables TE and \(\Gamma\) was assessed over land surfaces as a function of SMAP-derived SMC and \(\theta_{\mathrm{e}}\). A parametric study was then performed over a target area in South Asia. For low SMC levels, TE and \(\Gamma\) presented a strong fluctuation from flat surfaces to areas with moderate topographic roughness. On the other hand, increasing SMC levels reduced the gradients. Additionally, it was found that the sensitivity of both observables to SMC increased in a nadir-looking configuration as compared to grazing angles. As a final remark, TE and \(\Gamma\) converged with increasing levels of TPI, TRI, VRM, and \(\beta\); while they diverge with increasing levels of TC and PC for different SMC values.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Topographic Wetness Index (TWI)**} & \multicolumn{3}{c}{**SMC [m\({}^{3}\)/m\({}^{3}\)]**} \\ \hline  & **TE [m]** & \(\Gamma\) [dB]** & **TE [m]** & \(\Gamma\) [dB]** & **TE [m]** & \(\Gamma\) [dB]** & **TE [m]** & \(\Gamma\) [dB]** \\ \hline  & [20, 30] \({}^{\circ}\) & [20, 30] \({}^{\circ}\) & [80, 90] \({}^{\circ}\) & [80, 90] \({}^{\circ}\) & [20, 30] \({}^{\circ}\) & [20, 30] \({}^{\circ}\) & [80, 90] \({}^{\circ}\) & [80, 90] \({}^{\circ}\) \\ r & \(-\)0.63 & 0.59 & \(-\)0.50 & 0.48 & \(-\)0.08 & 0.27 & \(-\)0.06 & 0.30 \\ RMSE & 95.3 & 1.7 & 68.5 & 2.7 & 121.9 & 2.1 & 80.7 & 2.8 \\ Slope & \(-\)75.13 & 1.40 & \(-\)18.65 & 1.57 & \(-\)175.21 & 8.4078 & \(-\)63.47 & 13.55 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistics (Pearson correlation coefficient r, RMSE, and slope of the linear fits) of the scatter plots of CyGNSS-derived TE and \(\Gamma\) with TWI and SMAP-derived SMC over the selected target area over North India.  
In the last part of this study, the sensitivity of TE and \(\Gamma\) to TWI and SMC was evaluated over a specific target region in North India, with a strong SMC gradient and a wide topography heterogeneity. Areas with very rough topography were excluded. The Pearson correlation coefficients of TE and \(\Gamma\) with TWI were rather high. On the other hand, the correlation with SMC was almost negligible. This empirical evidence suggests that topographic features could determine the main spatial patterns of \(\Gamma\), at least over some areas. TWI provided an indication of the relative propensity of soils to become saturated to the surface due to the effect of the local topography.  
Present and future applications of GNSS-R for Earth Observation over land surfaces could benefit from the results of this work. Accuracy on geophysical parameters retrieval e.g., SMC, could be improved after properly calibrated reflected DDMs. The estimation of SMC based on GNSS-R observables relies on their ability to represent the dielectric constant of the soil. However, topography significantly distorts these observables. The empirical relationships that were found between the selected topographic parameters and the observables pave the way to compensate underestimated SMC levels due to topographic roughness. Future work should include ground truth data to further validate these results.  
Conceptualization, methodology, software, investigation, and writing-original draft preparation by [PERSON]-[PERSON]; supervision, by [PERSON] and [PERSON].  
This research received no external funding.  
This research was carried out with the support grant of a [PERSON] postdoctoral research fellowship from the Spanish Ministerio de Ciencia, Innovacion y Universidades, reference FJCI-2016-29356.  
The authors declare no conflict of interest.