## 3 Earth Surface Effects on GNSS-R Relevant to Land Applications
### Global Scale  
The global one-year averaged maps (1 September 2015 to 1 September 2016) provided in this study are useful for the global scale study. Signal-to-Noise Ratio (SNR) values are presented for H-Pol and V-Pol respectively in Figure 5a,b over the Earth's land surface. High SNR peaks correspond to bare soil regions with high soil moisture content such as the Pampas of Argentine, the Great Lakes regions in the US, Northern India, or the Northern Yakutia region in Russia. There are also high power peaks over regions such as the Sahara Desert despite the low soil moisture values. This effect will be investigated at a regional scale. In regions with significant amount of AGB, the SNR values are lower despite high values of soil moisture content because of the effect of signal attenuation (Figure 5a,b). The PR values (Figure 5c) show good correlation (Pearson linear correlation factor r \(\sim\)\(-0.6\)) to soil moisture content by comparing them to SMAP's radiometer data (Figure 5d). It appears higher PR values are associated with larger waveform spreading (Pearson linear correlation factor r \(\sim\)\(0.4\)). These results are clearly illustrated in Figures 5c and 6a-d. In regions with higher PR and little vegetation  
Figure 4: Definition of the trailing and leading edge width over a sample waveform. (Greenland, Australia, the Sahara Desert, the Gobi Desert, the Arabian Desert, and the Kalahari Desert) waveform spreading is larger than regions with higher values of above ground vegetation (Amazonian and Boreal forests), and lower waveform spreading. Figure 5: SMAP over-land power waveform analysis using one-year averaged values: (**a**) Signal-to-Noise Ratio H-Pol [dB]; (**b**) Signal-to-Noise Ratio V-Pol [dB]; (**c**) Polarimetric Ratio [dB]; (**d**) Global distribution of time-averaged retrieved surface soil moisture based on SMAP radiometer observations and application of the multi-temporal dual-channel algorithm by [PERSON] et al [34; 35]. Volumetric soil moisture measured for the first few centimeters (in fact the penetration depth depends on the soil mineralogical content and the moisture). For a given elevation angle, the level of signal depolarization depends on the surface roughness, and the scatterer type through the scattering coefficient \(\sigma^{0}\). Therefore, the SMAP data set, which has an approximately constant elevation angle of \(\theta_{\mathrm{e}}\)-55\({}^{\circ}\), is useful to analyze the GNSS-R sensitivity to  
Figure 6: SMAP over-land power waveforms shape analysis: (**a**) leading edge width H-Pol [m]; (**b**) leading edge width V-Pol [m]; (**c**) trailing edge width H-Pol [m]; and (**d**) trailing edge width V-Pol [m]. changes in the dielectric constant. Figure 5c shows the good sensitivity of the PR for different levels of Above Ground Biomass (ABG), from \(\sim\)100 ton/ha for boreal forests to \(\sim\)350 ton/ha for tropical rainforests (Figure 7a). The transitions zones from arid to dense vegetation areas are well represented in Africa and Asia from the North to the South. Over dense vegetation areas, the PR takes negative values, which suggests that the vertical stalks scatter more vertically polarized waves. These maps show that this observable depends on dielectric and scattering property changes over biomass and wetlands (see Amazon river and lakes regions). This is the reason that explains the behaviour in Figure 8a,b where there are two types of waveforms: those with higher power levels corresponding to areas over the Amazon river and riparian forest, and those corresponding only to tropical forests with lower power level because of signal attenuation [11; 36]. The attenuation due to vegetation is \(\mathrm{L}^{\mathrm{anopy}}=\mathrm{e}^{\tau^{\mathrm{canopy}}/\cos\theta_{ \mathrm{inc}}}\), where \(\tau^{\mathrm{canopy}}\) is the nadir optical depth of the vegetation layer [11]. Over the Amazon river and riparian forests the SNR ranges from \(\sim\)15 dB to \(\sim\)30 dB depending on the proportions of land signal contamination.