## 5 Discussion on Potential Applications of the Data Products
### Surface Characterization Using Coherence of the Reflected Signal  
Most of the GNSS-R missions can only provide the power of the reflected signal at low sampling rate (e.g., 1-4 Hz), which corresponds to a spatial sampling resolution of 1.5-7 km. Instead, the complex waveform products can provide both amplitude and phase information of the reflected signal at a higher sampling rate (1000 Hz), which makes it possible to characterize the surface parameters at higher spatial sampling resolutions. Here we demonstrate the use of high sampling rate complex waveform for surface characterization over around Lake Rousseau in Florida. One track of complex waveform data with the reflected signal from Galileo PRN 31 is used in this demonstration. The corresponding raw IF data set is collected by the CYGNSS FM02 satellite on 13 September 2018. The coherence coefficient of the reflected signal is used as the main observable in this exercise, which can be generated directly with the post-processing software introduced in Section 4.3. The coherence coefficient between two successive complex waveforms is defined as  
\[\Gamma^{\mathrm{r}}(t_{k}+\frac{t_{\mathrm{c}}}{2})=\frac{z^{\mathrm{r}}_{ \mathrm{peak}}(t_{k})z^{\mathrm{r}}_{\mathrm{peak}}{}^{*}(t_{k}+t_{\mathrm{c} })}{\left|z^{\mathrm{r}}_{\mathrm{peak}}(t_{k})\right|\left|z^{\mathrm{r}}_{ \mathrm{peak}}(t_{k}+t_{\mathrm{c}})\right|} \tag{8}\]  
in which \(z^{\mathrm{r}}_{\mathrm{peak}}\) is the peak amplitude of the waveform. Then, the complex coherence coefficient can be further averaged to generate the mean coherent coefficient as  
\[\overline{\Gamma^{\mathrm{r}}}(t_{0}+\frac{M+1}{2}t_{\mathrm{c}})=\frac{1}{ M}\left|\sum_{m=0}^{M-1}\Gamma^{\mathrm{r}}(t_{m}+\frac{t_{\mathrm{c}}}{2})\right| \tag{9}\]  
in which \(M\) is the number of coherent coefficients to generate their mean value. From (8) and (9), it can be seen that the mean coherence coefficient is mainly determined by the phase differences between the successive complex waveforms. For the GNSS signal reflected from smooth surface, it can be assumed that the phase of the complex waveform does not change significantly within a short period of time (e.g., in 2 ms). Thus,the coherent average of the coherent coefficient results in a relative high mean coherent coefficient (close to 1). While for the reflected signal from rough surface, diffuse scattering can be the dominate component, and the phase differences between the successive complex waveforms are more random. In this case, the mean coherent coefficient is close to 0. Figure 7 shows an overlay of of the mean coherent coefficient in a Google Earth historical image, which clearly shows the consistence between high coherent coefficient pixels and the presence of inland water bodies. Note that the number of averaged coherence coefficients in (9) is 20 (i.e., \(M=20\)) in this processing, which corresponds to an along-track resolution of \(\sim\)120 m. This resolution can be adapted to characterize flood inundation dynamics at appropriate scales by using different coherent integration times or number of averaged coherence coefficients. It is noted that a similar approach has been attempted using the CYGNSS raw IF data collected over Mississippi River in [27], and this new analysis presented here is just to provide the users a simply example on how to extract observables from the complex waveform for different geophysical application. It is also remarkable that a similar algorithm will be also implemented as the HydroGNSS mission's Level 2 inundation detection processor. However, the impact of dense vegetation and saturated soil on the performance of such detector should be further investigated. Note that CYGNSS mission has made dedicated raw IF data collections over inundation regions as well as tropical wetlands, e.g., Amazon basin, Mississippi watershed, Yucatan Lake, Florida Everglades and White River watershed.