## 2 Materials and Methods
### TDS-1 Data Set  
#### 2.1.1 TDS-1 Observables at a Glance  
The TDS-1 data used in this study spans over a period from September 2014 to July 2017. Figure 1 shows different TDS-1 GNSS-R observables. The interested reader is referred to [5] for a detailed introduction to GNSS-R techniques and a description of the different observables. Figure 1a shows the SNR computed from the peak of the DDM to the average noise floor computed for delay lags before the reflected signal, which basically follows the behavior of the peak of the DDM. As it can be appreciated, there is an increased noise around the Equator in the East Pacific, Atlantic, and Indian Oceans due to Satellite Based Augmentation System (SBAS) reflected signals which will have to be compensated for ([6], Figure 12). Figure 1b shows the values of the peak of the DDM. It is higher over iced sea and land, where there is a coherent reflection component, but also around the Plata river mouth in Argentina, the Eastern part of the Sahara desert, and South East Asia. Figure 1c shows the standard deviation of the peak of the DDM computed from ten 1 s consecutive samples. It is reasonably constant, except in a few tracks, where it is surprisingly low, i.e., the peak of the DDM is nearly constant, and in very specific events when it is anomalous large (see [7] for more detailed study). Finally, Figure 1d shows a parameter to measure the spread of the DDM in the Delay and frequency Doppler domains. This parameter is smaller over ice (specular reflection) and over dense vegetation than over most other areas, but it is surprisingly low also over mountains and the ocean. A more detailed analysis is presented below.  
Figure 2 shows the histograms of the DDM spread parameters in (a) delay, and (b) Doppler frequency, over land regions only computed as:  
\[\sigma_{\tau}=\sqrt{\sum_{j=-5}^{5}\text{DDM}(i_{0},j)\cdot\frac{(j-j_{0})^{2}}{ \sum_{j=0}^{11}\text{DDM}(i_{0},j)}} \tag{1a}\]  
\[\sigma_{f_{d}}=\sqrt{\sum_{j=-5}^{5}\text{DDM}(i,j_{0})\cdot\frac{(i-i_{0})^{2}} {\sum_{j=0}^{11}\text{DDM}(i,j_{0})}} \tag{1b}\]  
where \(i\) and \(j\) are the indices of the Delay and Doppler coordinates and \(i_{0}\) and \(j_{0}\) are the coordinates of the peak of the DDM (steps: 0.25 C/A chips \(\times\) 500 Hz).  
As it can be observed, the histograms present a multimodal behavior, i.e., the probability density function (pdf) can be decomposed as the sum of several pdf's (\"bell\"-like curves, separated by vertical dotted lines). In the case of the PDF delay spread some \"modes\" can be somehow arbitrarily separated at 0.9, 1.2, and 1.7, and in the PDF Doppler frequency spread at 0.82 and 1.92 (local minima of the PDF).  
Figure 1: Sample TechDemoSat-1 (TDS-1) data: (**a**) SNR [dB] computed as the ratio of the peak of the Delay Doppler Maps (DDM) to the noise; (**b**) DDM peak; (**c**) standard deviation of the peak; and (**d**) waveform spread figure of merit.  
Figure 2: pdf’s of the DDM spread parameters over land only: (**a**) delay (units = 0.25 \(\times\) C/A chips) and (**b**) Doppler frequency (units = 500 Hz bins).  
Trying to understand better this behavior, Figure 3a shows the land pixels corresponding to the regions identified in Figure 2 for \(\sigma_{\tau}\leq 0.9\) and \(\sigma_{fd}\leq 0.82\). Figure 3b shows a surface topography flag computed as the convolution of a \(1^{\circ}\times 1^{\circ}\) Digital Elevation Model (DEM) with a \(\left[\begin{array}{cc}1&-1\\ -1&1\end{array}\right]\) kernel, followed by a thresholding for absolute values larger than 125. As it can be appreciated while comparing Figure 3a,b, is that DDM spread parameters \(\sigma_{\tau}\leq 0.9\) and \(\sigma_{fd}\leq 0.82\) can be used as a proxy to detect when DDMs are affected by topography effects.