# Classifying Inundation in a Tropical Wetlands Complex with GNSS-R
## 3 GNSS-R Measurements
### GNSS-R Observable Definitions  
We used the following CYGNSS observables as inputs to the inundation classification algorithm: (1) peak SNR, (2) trailing edge slope (TES), (3) leading edge slope (LES), (4) width of the waveform (\(\Delta\)), and (5) the generalized linear observable (GLO). Peak SNR was computed as \(10 log_{10}\bigg{(}\frac{S_{max}}{N_{avg}}\bigg{)}\), where \(S_{max}\) is the maximum value (in raw counts) in a single DDM bin and \(N_{avg}\) is the average raw noise counts per bin, which was computed on board the satellite from the first 45 delay rows of the uncompressed DDM (before the data was compressed and sent to the ground). For our study, the peak SNR was corrected using the following coherent assumption: corrected peak SNR \(=\frac{(R_{TX}+R_{RX})^{2}}{P_{TX}\mathcal{C}_{TX}\mathcal{C}_{RX}}\) peak SNR (expressed in linear units). Peak SNR is sensitive to the reflectivity of the observed surfaces; inundated surfaces, covered or not by vegetation, have strong peak SNR as compared to non-inundated surfaces. The strongest peak SNR is observed for open water scenarios. TES and LES were computed as the slope of the reflectivity delay waveform. The reflectivity delay waveform is the result of integrating Equation 5 with the Doppler domain. TES slope is computed from reflectivity delay waveform values at delay bins m and m + 3, where m corresponds to the position of the peak of the waveform. LES slope is computed from reflectivity delay waveform values at delay bins m and m - 3. \(\Delta\) was defined as the width of the reflectivity delay waveform at 1/e of the peak value, and the threshold was selected from previous experience, as shown in References [46] or [47]. TES, LES, and \(\Delta\) are all shape-based observables and are directly linked to the coherency/incoherency of the scattering surface. Inundated surfaces show a more step reflectivity delay waveform, as those surfaces are dominated by coherence scattering. Non-inundated surfaces are dominated by a mix of coherency and incoherence scattering, and are characterized by a reflectivity delay waveform with a smaller slope. In Reference [48], the authors describe the effect of the PRN-dependent autocorrelation function (ACF) deviations on GNSS-R wind speed retrievals. The effect of the ACF deviations for ocean winds speeds under 20 m/s as 2-3 m/s, while the effect for ocean wind speeds of 40 m/s can be 7-8 m/s. The ocean surface produces highly incoherent returns, and the ACF deviations have a significant impact. For the surfaces under consideration (open water--coherent, inundated vegetation--coherently dominated, and non-inundated surfaces--mix of coherency and incoherency), the effect of the ACF deviations was considered negligible for this application. The GLO observable is based on principal component analysis (PCA) applied to the DDM samples, and was originally defined for the ocean domain in [PERSON] et al. [49]. In that study, the authors showed that the GLO increased the performance of the ocean wind speed retrieval algorithm in comparison to standard observables such as the DDM average (DDMA). The DDMA is the number of DDM samples around the specular point that are averaged together. For example, for a total of \(M\) samples, DDMA would be defined as \(DDMA=\ \frac{1}{M}\sum\limits_{i=1}^{M}\Gamma_{i}\), where \(\Gamma_{i}\) corresponds, in our case, to the \(M\) reflectivity samples \(\Gamma\) (Equation (5)) around the specular point. The DDMA observable can be defined by a more general expression, \(GLO=\sum\limits_{i=1}^{M}a_{i}\Gamma_{i}\), where the coefficients \(a_{i}\) are set to a constant value, i.e., for DDMA \(a_{i}=\frac{1}{M}\). Here, we propose that the optimal weight coefficients \(a_{i}\) be found, given the characteristics of the data ensemble. The optimal coefficients are found by applying PCA to a data ensemble. This data ensemble requires that the variability of the scenes selected to perform the PCA is representative of the type of area to be described.