# Classifying Inundation in a Tropical Wetlands Complex with GNSS-R
## 2 Theoretical Background
### Measurement Definition
Visually, the 7 km \(\times\) 7 km grid shows complete coverage of our study area, however, the contributions to each  
Figure 1: Semi-minor (\(b\) in Equation (3), \(n\) = 1) and semi-major (\(a\) in Equation (2), \(n\) = 1) axis dimensions of the first Fresnel zone as they vary with incidence angles associated with CYGNSS data. The size of the ellipse defining the first Fresnel zone varies: semi-major axis varies from 600 m to 2.8 km and semi-minor axis varies from 600 m to 1 km for incidence angles below 70\({}^{\circ}\). Figure 2: Comparison of two different gridding strategies considered for CYGNSS data over Pacaya-Samiria for a 14 day period from 8–21 May 2017: (**a**) fixed spatial resolution set to 7 km \(\times\) 7 km, where each grid cell represents the averaged power of all reflection signals with specular points falling within each cell. (**b**) Fixed spatial resolution set to approximately 500 m \(\times\) 500 m, such that the first Fresnel zone ellipse of each single measurement is mapped across multiple grid cells. grid cell value may come from just one specular point, of which the scattering area is not necessarily representative of the entire 7 km \(\times\) 7 km area (specially for coherent reflections, which have a scattering area that is significantly smaller than that of non-coherent reflections). In contrast, the 500 m \(\times\) 500 m grid shows large gaps in spatial coverage because it finely maps the first Fresnel zone, which is a better indicator of the surface (inundated wetlands) where most of the scattering is coming from. We therefore opted to use the 500 m \(\times\) 500 m grid in order to explore the data at its highest spatial resolution, while at the same time focusing on the coherent component of the signal, which is the most relevant to inundated wetlands. The CYGNSS data calibration is optimized for ocean surfaces. CYGNSS provides a number of variables in its dataset (Level 1, version 2.1): _raw_counts_ corresponds to uncalibrated power values produced by the DDM instrument (DDMI); _power_analog_ in Watts corresponds to the power computed from the raw counts corrected for quantization (L1a calibration); _brcs_ in m\({}^{2}\) corresponds to the bistatic radar cross section (BRCS), computed from the DDM power in Watts corrected by the geometry and antenna parameters (L1b calibration); and _ddm_nbrcs_ corresponds to the normalized BRCS computed from the BRCS corrected by the scattering area associated to each specular point. The scattering area pre-computed to normalize the BRCS is only valid for ocean measurements, therefore not suitable for the wetlands application focus of this study. For data over land, both variables _power_analog_ (L1a calibrated data, \(P_{\textit{coh}}\) in Equation 1) and _brcs_ (L1b calibrated data) can be used, since those only consider geometrical and instrument corrections. The expression for L1b calibrated data \(P_{L1b}\) (_brcs_ variable) is defined in Reference [44] as:  
\[P_{L1b}=\langle\sigma\rangle=\frac{P_{RX}(4\pi)^{3}}{P_{TX}\lambda^{2}G_{TX}G_ {RX}R_{PL}}, \tag{4}\]  
where \(R_{PL}=\frac{1}{R_{TX}{}^{2}R_{RX}{}^{2}}\) and \(P_{RX}\) correspond to the received power in Watts (_power_analog_ variable in the CYGNSS dataset, L1a calibrated data), and \(\langle\sigma\rangle\) is the BRCS (_brcs_ variable in the CYGNSS dataset, L1b calibrated data). There are two equivalent ways of obtaining reflectivity with currently available CYGNSS products: (1) using \(P_{\textit{coh}}\) (_power_analog_ dataset) and computing the reflectivity by solving for \(\Gamma\) in Equation (1), or (2) substituting Equation (1) into Equation (4) with \(P_{RX}=P_{\textit{coh}}\) and re-arranging the expression to write the \(\Gamma\) as a function of \(P_{L1b}\) (_brcs_ dataset):  
\[\Gamma=\ \frac{\left(R_{TX}+\ R_{RX}\right)^{2}R_{PL}}{\left(4\pi\right)}P_{L1b} \tag{5}\]  
We used _brcs_ data in CYGNSS dataset (\(P_{L1b}\)) to obtain \(\Gamma\), following Equation (5). The data was filtered following the same quality flag selection as defined in Reference [10].