## 4 Method and Discussion
### The Bistatic Radar Equations  
Radar is a system for detecting targets and deriving information such as position, velocity, and reflectivity signature from the detected objects [40]. It transmits a signal and receives the echo after it is reflected by a target. The types of radar systems based on the location of the transmitter (TX) and the receiver (RX) can be divided into colocated or monostatic radars, which measure backscattered signals, and separated or bistatic radars, which measure forward-scattered signals. The main difference between monostatic and bistatic radars is the separation of the transmitter and receiver [41]. Figure 6 shows monostatic and bistatic constellation for satellites. Figure 4: Moderate-Resolution Imaging Spectroradiometer (MODIS) images of the study area (**A**) before the flooding on 8 January 2020, and (**B**) during the flood on 13 January 2020. The dark blue regions are the inundated areas. The clouds in the image are shown with light blue which can be distinguished from the inundated areas [39]. Figure 5: Methodology flowchart based on the bistatic radar concept and using CYGNSS data. Figure 6: Simple schematic view of mono (**A**) and bistatic (**B**) radars constellation for satellite remote sensing. The CYGNSS and GPS constellations form a bistatic radar system. The GPS satellites transmit circularly polarized microwave signals which are collected by the CYGNSS reflectometry receivers after forward-scattering from the Earth's surface. The scattered signals contain valuable information about the physical properties of the reflecting surface. Inland waters can be detected by CYGNSS, assuming a coherent forward-scattering mechanism [33; 34; 42]. The peak value of coherent scattered power is defined as [22; 23; 43]:  
\[P_{RL}^{coh}=\frac{P_{R}^{t}\ G^{t}\ G^{r}}{\left(d_{ts}+d_{sr}\right)^{2}} \left(\frac{\lambda}{4\pi}\right)^{2}\Gamma_{RL} \tag{1}\]  
where \(P_{RL}^{coh}\) is the peak value of coherently received power, \(R\) denotes the right-handed circular polarization (RHCP) GPS transmit antenna, and \(L\) is related to the left-handed circular polarization (LHCP) of forward-scattered signals collected by the downward-looking antenna. \(P_{R}^{t}\) is the transmitted power, \(G^{t}\) is the gain of the transmitter antenna, \(G^{r}\) is the gain of the receiver antenna, \(\lambda\) is the GPS L1 wavelength (\(\sim\)0.19 m), and \(d_{ts}\) is the distance between the specular reflection point and the GPS transmitter, while \(d_{sr}\) is the distance between the specular reflection point and the GNSS-R receiver and \(\Gamma_{RL}\) is the surface reflectivity along with the incidence angle. In addition to the mentioned parameters \(P_{RL}^{coh}\) is affected by system noise. Therefore, signal-to-noise ratio (SNR) could be defined as:  
\[SNR=\frac{P_{RL}^{coh}}{N}=\frac{P_{R}^{t}\ G^{t}\ G^{r}}{\left(d_{ts}+d_{sr} \right)^{2}}\Big{(}\frac{\lambda}{4\pi}\Big{)}^{2}\frac{\Gamma_{RL}}{N} \tag{2}\]  
where \(N\) is the noise value. Since the magnitude of the SNR is not equal to the reflected power, the surface reflectivity or corrected SNR along with the incidence angle could be computed using:  
\[SNR_{c}=\frac{\Gamma_{RL}}{N}=SNR\frac{\left(d_{ts}+d_{sr}\right)^{2}}{P_{R}^{ t}G^{t}\ G^{r}}\left(\frac{4\pi}{\lambda}\right)^{2} \tag{3}\]  
Finally, the \(SNR_{c}\) in decibel (dB) is:  
\[SNR_{c\ dB}=SNR_{dB}+10\log(\frac{\left(d_{ts}+d_{sr}\right)^{2}}{P_{R}^{t}G^{ t}\ G^{r}}\left(\frac{4\pi}{\lambda}\right)^{2} \tag{4}\]  
This parameter (\(SNR_{c\ dB}\)) is strongly related to the hydrological conditions of the land surface [18; 34].