## 3 Methodology
### Analysis Method  
According to conditions, such as surface roughness, incident angle, and vegetation type, GNSS signals experience two types of reflections: coherent scattering with identical incident and reflection angles; and, incoherent scattering, which has randomly distributed reflection angles. The scattering type can be determined by the maximum value and shape and magnitude of values around the maximum value in the DDM, as shown in Figure 2 and described in [13]. Theoretically, coherent scattering corresponds to a sharp peak in the DDM, because it has less obstacles for disrupting the original signal. An incoherent signal can be shown broadening around the maximum value as compared to signals from  
Figure 2: Example of the Delay Doppler Map (DDM) in (**a**) 2D plot and (**b**) 3D plot using observation results from v 2.1 Level 1 CYGNSS data measured by satellite 1 on 1 Jan 2019 in the case of specular point on land. X and Y axis in both plots denote the number of pixels in Doppler bin and delay bin, respectively. coherent scattering. Because a GNSS satellite broadcasts at the microwave frequency, both of the scattering signals are measured simultaneously by a nadir antenna. The measured signal power, \(P_{tot}\), from the nadir antenna can simply be expressed as the summation of coherent scattering \(P_{coh}\) and incoherent scattering \(P_{incoh}\), as in Equation 1.  
\[P_{tot}=P_{coh}+P_{incoh} \tag{1}\]  
In recent research, it is reported that the presence of an inland water body is associated with coherent reflection over land according to the spaceborne motivated observation and the extracting method developed for coherent scattering signals from an observed DDM by applying the Woodward ambiguity function [42]. Nevertheless, a restricted incident angle approach is used in this analysis to make the analysis process less complicated. As mentioned previously, higher incident angles have large opportunities for observing coherent scattering signals, given the concept that a small incident angle will increase the signal-to-noise ratio at the receiver and be applicable for neglecting coherent scattered signals from GNSS satellites. It was shown by [43] that the incident angles of less than \(35^{\circ}\) are able to represent the coherent scattering; thus, incident angles less than \(20^{\circ}\) from CYGNSS data are applied in this computation. The incident angle of \(20^{\circ}\) presenting the most correlated results has been selected to apply the computation progress in this analysis. Equation (2) describes the coherent scattering equation, which is used to calculate the reflectivity \(\Gamma\) using the bi-static geometry of GNSS-R with coherent scattered signal power from the DDM [44]. \[\Gamma_{lr}\;(\theta)=\frac{(4\pi)^{2}\;(P_{DDM}-N)(R_{r}+R_{t})^{2}}{\lambda^ {2}\;G_{r}\;G_{t}\;P_{t}} \tag{2}\]  
Where \(P_{DDM}\) is the peak value of DDM scattered power that is calculated from the raw count in CYGNSS data; N denotes the noise floor; \(R_{t}\) and \(R_{r}\) are the distant of transmitter and receiver from specular point, respectively; \(G_{t}\;P_{t}\) is the transmitter equivalent isotopically radiated power (EIRP); and, \(G_{r}\) represents the receiver antenna gain in the direction of the specular point. In addition, the subscript 'lr' on the left-hand side expresses the polarization of incident signals and reflected signals, and r and t on the right-hand side indicate the reflected signals and direct signals, respectively. All of the variables are obtained from the v2.1 Level 1 CYGNSS product, as denoted. The Fresnel coefficient, \(\mathcal{R}\), is another important parameter in this analysis is that describes the reflection and transmission of electromagnetic radiation when an incident on an interface between different media occurs.