## Data, Methodology and Results
### Methodology  
#### 2.2.1 Correction Positioning  
This study was carried out under the WGS-84 coordinate system, in the Earth centered, Earth fixed frame. The previous study corrected the static-state elevation error of the reflection reference surface and positioned the specular reflection point on geoid. Based on the [PERSON] method, the specular reflection point is initially positioned on the reference ellipsoid. Steps of the positioning are as follows [13; 15]:  
1. Position of \(M\). In Figure 2, \(O\) is the center of the earth, and the vectors of the specular point, the receiver and the transmitter are respectively \(\overset{\rightarrow}{S}\), \(\overset{\rightarrow}{R}\) and \(\overset{\rightarrow}{T}\). \(M\) is the intersection of the \(OS\) extension line and the \(TR\) connection line. \(R^{\prime}\) is the mirror point of \(R\) to \(OM\), and \(M^{\prime}\) is the mirror point of \(M\) to \(RR^{\prime}\), then [PERSON] et al., [15]:  
\[\overset{\rightarrow}{M}=\overset{\rightarrow}{R}+H_{\text{R}}/(H_{\text{R} }+H_{\text{T}})\overset{\rightarrow}{\left(\overset{\rightarrow}{T}- \overset{\rightarrow}{R}\right)} \tag{1}\]  
2. Calculation and correction of the initial position of the specular reflection point. The latitude \(b\) and the longitude \(l\) of the specular point \(S\) are the same as those of \(M\), thus the geoid undulation \(H_{\text{G}}\) of \(S\) can be calculated using EGM2008 model according to \(b\) and \(l\). Then \(H_{\text{G}}\) is introduced in the process of transforming the geodetic coordinates of the specular reflection point into the spatial coordinates, which are shown in Equation (2) [PERSON] et al. [13]:  
\[\left[ \begin{array}{c}X\\ Y\\ Z\end{array} \right]=\left[ \begin{array}{c}(N+H_{\text{G}})\cos(b)\cos(l)\\ (N+H_{\text{G}})\cos(b)\sin(l)\\ [N(1-e^{2})+H_{\text{G}}]\sin(b)\end{array} \right]=\left[ \begin{array}{c}N \cos(b)\cos(l)+\varepsilon_{\text{X}}\\ N\cos(b)\sin(l)+\varepsilon_{\text{Y}}\\ N(1-e^{2})\sin(b)+\varepsilon_{\text{Z}}\end{array} \right] \tag{2}\]  
where \(N=a/\sqrt{1-e^{2}\sin^{2}(b)}\), \(a\) is the long radius of the WGS-84 reference ellipsoid, \(e\) is the first eccentricity of the ellipsoid. In Equation (2), the elevation correction \(\varepsilon_{\text{X}}\), \(\varepsilon_{\text{Y}}\), and \(\varepsilon_{\text{Z}}\) of the specular reflection point in the \(X\), \(Y\) and \(Z\) directions are \(H_{\text{G}}\)cos(\(b\))cos(\(l\)), \(H_{\text{G}}\)cos(\(b\))sin(\(l\)), \(H_{\text{G}}\)sin(\(b\)), respectively. Equation (2) only considers the correction of the static-state elevation error, the geoid still has time-varying elevation difference from the instantaneous sea surface. On the basis of static-state elevation correction, the tidal height at the time and position of the specular reflection point is  
Figure 2: The GNSS-R specular reflection point positioning geometry [13]. introduced into the coordinate transformation to perform time-varying elevation correction, and Equation (2) becomes:  
\[\left[ \begin{array}{c}X\\ Y\\ Z\end{array} \right]=\left[ \begin{array}{c}(N+H_{\text{G}}+H_{\text{T}})\cos(b) \cos(l)\\ (N+H_{\text{G}}+H_{\text{T}})\cos(b)\sin(l)\\ [N(1-e^{2})+H_{\text{G}}+H_{\text{T}}]\sin(b)\end{array} \right]=\left[ \begin{array}{c}N\cos(b)\cos(l)+\varepsilon_{\text{X}}+\sigma_{\text{X}}\\ N\cos(b)\sin(l)+\varepsilon_{\text{Y}}+\sigma_{\text{Y}}\\ N(1-e^{2})\sin(b)+\varepsilon_{\text{Z}}+\sigma_{\text{Z}}\end{array} \right] \tag{3}\]  
where \(H_{\text{T}}\) is the time-varying elevation correction. Tidal height is predicted based on the TPXOS model according to \(b,l\) and the reflection time \(t\) contained in the TDS-1 data. The tidal time-varying elevation correction \(\sigma_{\text{X}}\), \(\sigma_{\text{Y}}\), and \(\sigma_{\text{Z}}\) of the specular reflection point in the \(X\), \(Y\) and \(Z\) directions are \(H_{\text{T}}\)cos(\(b\))cos(\(l\)), \(H_{\text{T}}\)cos(\(b\))sin(\(l\)), \(H_{\text{T}}\)sin(\(b\)), respectively.