# _remote sensing_
## 3 Related Data and Correction Models in Cal/Val of Altimeters
### Tidal Differences  
The tidal differences in Cal/Val of altimeters were usually determined by global/regional tide models [12]. Here, we collected the tide models of FES2014 (ftp://ftp-access. aviso.altimetry.fr, accessed on 6 July 2023), HAMTIDE 12 ([[ftp://ftp-icdc.cen.uni-hamburg](ftp://ftp-icdc.cen.uni-hamburg)]([ftp://ftp-icdc.cen.uni-hamburg](ftp://ftp-icdc.cen.uni-hamburg)). de/hamtide/, accessed on 18 February 2023), EOT20 ([[https://www.seanoe.org/data/0068](https://www.seanoe.org/data/0068)]([https://www.seanoe.org/data/0068](https://www.seanoe.org/data/0068)) 3/79489/, accessed on 9 July 2023), DTU16 ([[ftp://ftp.space.dtu.dk](ftp://ftp.space.dtu.dk)]([ftp://ftp.space.dtu.dk](ftp://ftp.space.dtu.dk)), accessed on 28 August 2023), NAO99 Jb ([[https://www.miz.nao.ac.jp/staffs/nao99/index_En.html](https://www.miz.nao.ac.jp/staffs/nao99/index_En.html)]([https://www.miz.nao.ac.jp/staffs/nao99/index_En.html](https://www.miz.nao.ac.jp/staffs/nao99/index_En.html)), accessed on 4 September 2019), GOT4.10 ([[https://earth.gsfc.nasa.gov/geo/data/ocean-tide-models](https://earth.gsfc.nasa.gov/geo/data/ocean-tide-models)]([https://earth.gsfc.nasa.gov/geo/data/ocean-tide-models](https://earth.gsfc.nasa.gov/geo/data/ocean-tide-models)), accessed on 9 July 2023) to maintain the tidal differences (Table 2). The precision of the tide models was evaluated by comparing with the water level data from four in situ tide gauge stations, including three ATGs placed on the three islands of WSCS and one tide station of Hong Kong (No. B329, Figure 2) derived from the Global Sea Level Observing System (GLOSS, [[http://uhslc.soest.hawaii.edu/data/](http://uhslc.soest.hawaii.edu/data/)]([http://uhslc.soest.hawaii.edu/data/](http://uhslc.soest.hawaii.edu/data/)), accessed on 19 July 2023) [24; 25; 26; 27; 28]. The cubic interpolation method was used to obtain the harmonic constants of the ocean tide models of the tide gauge locations. The in situ tidal harmonic constants were analyzed using the t_tide model (version 1.5), which can perform classical harmonic analysis for periods of about 1 year or shorter [29]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tide Model** & **Facility** & **Resolution** & **Number of Tidal** \\  & **(Degree)** & **Constituents** \\ \hline FES2014 & Archiving, Validation, and Interpretation of Satellite & 1/16 & 34 \\  & Oceanographic (AVISO) & 1/8 & 17 \\ HAMTIDE12 & The Deutsches Geodätsches Forschungsinstitut, Technical & 1/8 & 17 \\  & University of Munich (DGFI-TUM) & 1/16 & 10 \\ DTU16 & Technical University of Denmark (DTU) & 1/16 & 10 \\ NAO99 Jb & National Astronomical Observatory (NAO) & 1/12 & 16 \\ GOT4.10 & National Aeronautics and Space Administration (NASA) & 1/8 & 16 \\ EOT20 & DGFI-TUM & 1/8 & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The participating global ocean tide models. The vector differences of the amplitude and phase of tidal components between the in situ data and model predicted values are given by Equation (4) [30; 31; 32]:  
\[\text{vector}=[\frac{1}{2}(\text{H}_{\text{model}}\text{cos}(\text{G}_{\text{ model}})-\text{H}\text{cos}(\text{G}))^{2}+\frac{1}{2}(\text{H}_{\text{model}} \text{sin}(\text{G}_{\text{model}})-\text{H}\text{sin}(\text{G}))^{2}]^{1/2} \tag{4}\]  
where the H\({}_{\text{model}}\) and G\({}_{\text{model}}\) represent the amplitude and Greenwich phase lag of a tide constituent given by the global tide models, respectively;  
The H and G are the amplitude and Greenwich phase lag derived from in situ tide gauges, respectively.