## Data, Methodology and Results
### Methodology
#### 2.2.2 Ocean Tidal Correction  
Predicting \(H_{\text{T}}\) at a given location and time requires tidal analysis based on the tidal model, that is, the separation and estimation of tidal parameters, and the prediction of tides based on these parameters. In order to facilitate the prediction of tides, the tide is decomposed into a superposition of sine waves with different periods and amplitudes. Each different sine wave represents a different tidal constituent, and the superposition of all these sine waves constitutes a tidal wave that changes with time. The main method of modern tidal analysis and prediction is the harmonic analysis method, which is to estimate the amplitude and phase of a tidal constituent with a specified period. That is, to solve the tidal harmonic constants according to the tidal height expression and the actual observation data, so that the total tidal height can be obtained. 1. Extracting the harmonic constants of the tidal constituents. The harmonic constants are extracted from a barotropic tidal solutions of the TPXOS model to predict tide. The prediction obtains the global barotropic inverse tidal solutions based on the Ohio State University (OSU) Tidal Inversion Software (OTIS) used with TPXO model. At the reflection time \(t\) and the geodetic coordinates \((b,l)\), the tidal height \(h\) for a single constituent of frequency \"\(w\)\" is given by [PERSON] et al., [30]:  
\[h(b,\,l,\,t)=f_{\text{u}}(b,\,l,\,t)\,\text{Re}\,[h(b,\,l)\text{exp}\,\,\{ \text{i}\,\,[w(t-t_{0})+P(t_{0})+f_{\text{h}}(b,\,l,\,t)]\}], \tag{5}\]where \(P\) is the astronomical argument for the constituent at initial time \(t_{0}\),\(f_{\rm u}\) and \(f_{\rm h}\) are nodal corrections. The amplitude \(A\) and phase \(K\) are given by [PERSON] et al., ([PERSON] et al., 2010):  
\[A=|h|, \tag{6}\]  
\[K=\arctan[-{\rm Im}(h)/{\rm Re}(h)]. \tag{7}\]  
2. Performing harmonic analysis to predict tidal height. Based on the harmonic constants of the tidal constituents, the total tidal height \(H_{\rm T}\) is solved by harmonic analysis, as follows ([PERSON] et al., 2010), [PERSON] et al. (2010):  
\[H_{\rm T}(b,\,l,t)\ =\ L\ +\sum\limits_{j=1}^{\rm n}{h{\rm j}}\ =\ L\ +\sum \limits_{j=1}^{\rm n}{f_{\rm j}(b,\,l,t)\ A_{\rm j}(b,\,l,t)\ \cos[t/w{\rm j}\ +\ V_{\rm j} \,(t)\ -\ K_{\rm j}(b,\,l,t)]}. \tag{8}\]  
where \(L\) is the average sea surface height during observation, and \(n\) is the number of tidal constituents. From Equations (3) and (8), \(\sigma_{\rm X}\), \(\sigma_{\rm Y}\), \(\sigma_{\rm Z}\) for each iteration can be expressed as:  
\[\left[ \begin{array}{c}\sigma_{\rm X}\\ \sigma_{\rm Y}\\ \sigma_{\rm Z}\end{array} \right]=\left[ \begin{array}{c}L\cos(b)\cos(l)+\cos (b)\cos(l)\sum\limits_{j=1}^{n}{f_{\rm j}A_{\rm j}\cos(t/w_{\rm j}+V_{\rm j}- \rm K_{\rm j})}\\ L\cos(b)\sin(l)+\cos(b)\sin(l)\sum\limits_{j=1}^{n}{f_{\rm j}A_{\rm j}\cos(t/w _{\rm j}+V_{\rm j}-\rm K_{\rm j})}\\ L\sin(b)+\sin(b)\sum\limits_{j=1}^{n}{f_{\rm j}A_{\rm j}\cos(t/w_{\rm j}+V_{\rm j }-\rm K_{\rm j})}\end{array} \right]. \tag{9}\]  
After \(m\) times iterative correction, the cut-off threshold is satisfied, the total tidal time-varying elevation correction components \(\omega_{\rm X}\), \(\omega_{\rm Y}\), \(\omega_{\rm Z}\) are as follows:  
\[\left[ \begin{array}{c}\omega_{\rm X}\\ \omega_{\rm Y}\\ \omega_{\rm Z}\end{array} \right]=\left[ \begin{array}{c}\sum\limits_{p=1}^{m} \sigma_{\rm X}\\ \sum\limits_{p=1}^{m}\sigma_{\rm Y}\\ \sum\limits_{p=1}^{m}\sigma_{\rm Z}\end{array} \right].