# Classifying Inundation in a Tropical Wetlands Complex with GNSS-R
## 3 GNSS-R Measurements
### GNSS-R Observable Definitions
GLO is sensitive to the reflectivity of the observed surfaces, as peak SNR, i.e., inundated surfaces, covered or not by the vegetation, have high GLO values as compared to non-inundated surfaces. The highest GLO is observed for open water scenarios. The main difference between GLO and peak SNR is that GLO uses bins around the peak to reduce the noise by linearly combining them with optimal coefficients. In order to make the GLO coefficients general and inclusive of most tropical vegetated river basins, we derived the GLO coefficients by accounting for wide differences in land cover variability, surface conditions, biomass densities, and surface elevation. Therefore, we selected areas around the Congo river basin ([7\({}^{\circ}\)S, 12\({}^{\circ}\)E]-[5\({}^{\circ}\)N, 29\({}^{\circ}\)E] and Amazon river basin ([10\({}^{\circ}\)S, 77\({}^{\circ}\)W]-[2\({}^{\circ}\)N, 51\({}^{\circ}\)W] latitude-longitude boxes that contain these diverse conditions, and that include and are representative of the area under study (Pacaya-Samiria), and are inclusive of all tropical wetlands around rivers. In order to derive the GLO observable, we used CYGNSS data for those specific Amazon and Congo areas during the high-water season and the low-water season (corresponding to the same dataset used for training our algorithm and defined later in Section 3.2, after Table 2). In a dataset with this level of variability, many contributors can cause differences in the signal received. By observing the impact of standing water on the scattered signal in Figure 3, we assumed that the presence of water above the surface was the primary contributor to changes in the measurements. This assumption was tested later when the impact of the GLO observable in the classification algorithm was evaluated. In order to build the GLO observables we simplified the study to reflectivity delay waveforms instead of the whole reflectivity DDM (\(\Gamma\), Equation (5)); given that inundated areas exhibit a coherent dominant forward (specular) scattering, this assumption does not cause a significant loss of information. A delay waveform was obtained by integrating \(\Gamma\) over the Doppler domain (\(\Gamma_{int}\)). The PCA was then applied to the \(\Gamma_{int}\) samples corresponding to the delay bins m - 3:m + 3 (where m is the position of the maximum power). We retained up to the third principal component to yield GLO 1, GLO 2, and GLO 3 observables. This analysis generated three vectors (a\({}_{N}\)) of coefficients of size \(1\times 7\) for each vector, with N corresponding to the first, second, and third principal components, as shown in Table 1.  
These coefficients were applied to the waveform samples \(\Gamma_{int}\) in order to rotate the samples from the current space to a new orthogonal space. GLO observables were therefore computed as the linear combination of delay waveform \(\Gamma_{int}\) samples following Equation (6):  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Delay Bin (\(\tau_{i}\))** & \(a_{1}\) & \(a_{2}\) & \(a_{3}\) \\ \hline m \(-\) 3 & 0.0503 & \(-\)0.2030 & 0.4353 \\ m \(-\) 2 & 0.2125 & \(-\)0.4267 & 0.3853 \\ m \(-\) 1 & 0.4725 & \(-\)0.5186 & 0.0541 \\ M & 0.6625 & \(-\)0.0366 & \(-\)0.3698 \\ m + 1 & 0.4933 & 0.5582 & \(-\)0.0212 \\ m + 2 & 0.2089 & 0.4072 & 0. \[GLO_{N}=\sum_{\tau_{i}=m-3}^{m+3}a_{N}(\tau_{i})\Gamma_{int}(\tau_{i}), \tag{6}\]