# 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
#### 4.2.2 Interpretation of the Empirical Results  
Figure 4 shows that TE increases and \(\Gamma\) decreases with increasing values of the heterogeneity variables i.e., TPI (Figure 4a), TRI (Figure 4b), and VRM (Figure 4c). Additionally, the measurements of \(\beta\) (Figure 4d), TC (Figure 4e), and PC (Figure 4f) have a clear impact on both observables. The ranges of TE and \(\Gamma\) are the same in all the plots. This strategy was assumed to provide intercomparable plots, and at the same time show full variability. Over the Himalayan mountains, the spreading of TE was very high (up to \(\sim\) 600 m) and \(\Gamma\) was very low (down to \(\sim\) -25 dB). On the other hand, an inverse behavior appeared over the Indo-Gangetic Plains. Here, the scattered electromagnetic field became mostly coherent at grazing angles because the exponential factor (Equation (4)) increased significantly with decreasing angles [40]. As a consequence, there was an increment of \(\Gamma\), which was distributed in a rather homogeneous manner (Figure 4j), despite the strong SMC gradient from east to west (Figure 4i). In Reference [40] it was previously found that the \(\Gamma\) dynamic range decreased at grazing angles. In other words, the sensitivity to SMC reduced at this geometry, which helps to justify the homogeneous distribution of \(\Gamma\). On the other hand, \(\Gamma\) appeared more associated with the variability of SMC in a nadir-looking configuration, despite being lower than at grazing angles [8; 40]. Figures 5 and 6 show the relationship of TE and \(\Gamma\) with the selected topographic parameters as a function of SMAP-derived SMC, over the two angular ranges used in this study \(\theta_{\rm e}\sim\)[20; 30] \({}^{\circ}\) and \(\theta_{\rm e}\sim\) [80; 90] \({}^{\circ}\): TPI (Figure 5a,d,g,j), TRI (Figure 5b,e,h,k), VRM (Figure 5c,f,i,l), \(\beta\) (Figure 6a,d,g,j), TC (Figure 6b,e,h,k), and PC (Figure 6c,f,i,l). The influence of SMC was evaluated at four differentiated ranges from \(\sim\)0 m\({}^{3}\)/m\({}^{3}\) to \(\sim\)0.4 m\({}^{3}\)/m\({}^{3}\) in steps of \(\sim\)0.1 m\({}^{3}\)/m\({}^{3}\). For low SMC \(\sim\) [0, 0.2] m\({}^{3}\)/m\({}^{3}\), the impact of the heterogeneity variables on both TE and \(\Gamma\) was quite strong in the ranges TPI- [-0.01, 0.01] m, TRI- [0, 20] m, and VRM- [0, 0.005] \({}^{\circ}\). This point could be just justified because for low SMC levels: (a) the geometrical properties of the scattering medium play a stronger role than the dielectric properties and (b) the GNSS-R observables become saturated for a smaller topographic roughness. Increasing SMC levels reduced the gradients because of the waveforms' peak power increment. Consequently, the 70% power threshold appeared at smaller TE values as compared to dry soils. The variability of TE with SMC was higher in a nadir-looking configuration than at grazing angles because of the lower topographic influence. On the other hand, \(\Gamma\) increased with increasing SMC in a nadir-looking configuration. However, it was roughly independent of SMC at grazing angles [8]. As such, the spreading of TE and the decrease of \(\Gamma\) showed a much more gradual evolution for increasing heterogeneity levels up to TE \(\sim\) 600 m and \(\Gamma\sim\) - 22 dB at \(\theta_{\rm e}\sim\) [80; 90] \({}^{\circ}\) and TE \(\sim\) 600 m and \(\Gamma\sim\) - 15 dB at \(\theta_{\rm e}\)- [20; 30] \({}^{\circ}\). Finally, it is pointed out that the topographic dynamic range of both GNSS-R parameters TE and \(\Gamma\) was higher for SMC \(\sim\) [0, 0.2] m\({}^{3}\)/m\({}^{3}\) than for SMC \(\sim\) [0.2, 0.4] m\({}^{3}\)/m\({}^{3}\). This observation is also attributed to the stronger influence of the geometrical properties for decreasing SMC levels. A similar behavior was also pointed out in the case of the small-scale surface roughness [40].