## 2 Data Processing and Analysis Method
### OTL Model and Tidal Signal Analysis  
OTL displacement predicted by a model is usually based on the Green's function [6], which is determined by the adopted Earth model and represents the response characteristics of the solid Earth to mass loading. The OTL displacement \(u\) for a location \(r\) is as follows:  
\[u(r)=\int\limits_{\Omega}\rho G(|r-r^{\prime}|)Z(r^{\prime})d\Omega \tag{2}\]  
where \(Z\) is a vector expression of the tide at \(r^{\prime}\) provided by the ocean tide model; \(\Omega\) represents the global ocean area; \(\rho\) is the density of sea water; and \(G\) is the Green's function, characterizing the load deformation caused by the unit mass of sea water. In this paper, eight recent ocean tide models were considered: FES2014b, GOT4.10c, TPXO.8, DTU10, EOT11a, HAMTIDE, NAO99b, and OSU12 [31; 32]. The OTL displacements predicted by the FES2014b and GOT4.10c models based on the STW105 Earth model were provided by the International Mass Loading Service [33], for which the density of sea water was set to 1025 kg/m\({}^{3}\). The predictions of the OTL displacements by FES2014b, TPXO.8, DTU10, EOT11a, HAMTIDE, NAO99b, and OSU12 were provided by the Ocean Tide Loading Provider [34], for which the density of sea water was set to 1030 kg/m\({}^{3}\). The FES2014b and TPXO.8 tide models based on the Preliminary Reference Earth Model (PREM) were calculated with CARGA [7]. The DTU10, EOT11a, HAMTIDE, NAO99b, and OSU12 tide models based on the Gutenberg-Bullen A Earth model were calculated with OLFG/OLMPP [35]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **Longitude (E)** & **Latitude (N)** & **Ellipsoidal Height/m** & **Data Length/d** & **\% of Gross Errors** \\ \hline HKFN & \(114^{\circ}08^{\prime}17^{\prime\prime}\) & \(22^{\circ}29^{\prime}41^{\prime\prime}\) & 41.212 & 3628 & 1.57\% \\ HKKT & \(114^{\circ}04^{\prime}00^{\prime\prime}\) & \(22^{\circ}26^{\prime}41^{\prime\prime}\) & 34.576 & 3640 & 1.06\% \\ HKLT & \(113^{\circ}59^{\prime}48^{\prime\prime}\) & \(22^{\circ}25^{\prime}05^{\prime\prime}\) & 125.922 & 3650 & 1.23\% \\ HKMW & \(114^{\circ}00^{\prime}11^{\prime\prime}\) & \(22^{\circ}15^{\prime}21^{\prime\prime}\) & 194.946 & 3529 & 4.58\% \\ HKNP & \(113^{\circ}53^{\prime}38^{\prime\prime}\) & \(22^{\circ}14^{\prime}57^{\prime\prime}\) & 350.672 & 3643 & 1.15\% \\ HKOHH & \(114^{\circ}13^{\prime}43^{\prime\prime}\) & \(22^{\circ}14^{\prime}52^{\prime\prime}\) & 166.401 & 3646 & 1.08\% \\ HKPC & \(114^{\circ}02^{\prime}16^{\prime\prime}\) & \(22^{\circ}17^{\prime}05^{\prime\prime}\) & 18.130 & 3638 & 1.23\% \\ HKSC & \(114^{\circ}08^{\prime}28^{\prime\prime}\) & \(22^{\circ}19^{\prime}20^{\prime\prime}\) & 20.239 & 3594 & 2.61\% \\ HKSL & \(113^{\circ}55^{\prime}41^{\prime\prime}\) & \(22^{\circ}22^{\prime}19^{\prime\prime}\) & 95.297 & 3652 & 0.92\% \\ HKSS & \(114^{\circ}16^{\prime\prime}09^{\prime\prime}\) & \(22^{\circ}25^{\prime}52^{\prime\prime}\) & 38.713 & 3645 & 1.11\% \\ HKST & \(114^{\circ}11^{\prime}03^{\prime\prime}\) & \(22^{\circ}23^{\prime}43^{\prime\prime}\) & 258.704 & 3651 & 0.93\% \\ HKWS & \(114^{\circ}20^{\prime}07^{\prime\prime}\) & \(22^{\circ}26^{\prime}03^{\prime\prime}\) & 63.791 & 3652 & 0.89\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: WGS84 coordinates and the Gross Error elimination rate for the 12 stations. A total of nine OTL models were obtained, and we refer to them as GOT4.10c + STW, FES2014b + STW, FES2014b + PREM, TPX0.8 + PREM, DTU10 + GB, EOT11a + GB, HAMTIDE + GB, NAO99b + GB, and OSU12 + GB, respectively. After modeling the body tide in the GPS data processing, the GPS-estimated tidal deformation is mainly made up of the OTL displacement. A tidal constituent can be conveniently expressed in terms of the in-phase and out-of-phase amplitudes of the phasors on the complex plane [13].