# _remote sensing_
## 3 Related Data and Correction Models in Cal/Val of Altimeters
### Datum of the In Situ SSH Measurements  
To accomplish the Cal/Val of altimeters, the datum of the three ATGs of WSCS were determined from 2019-2022 using the DGB [17]. The time length of each campaign was more than 3 h for each determination, and the distance between the DGB and the ATGs was less than 300 m. To obtain accurate coordinates, a Trimble Net R9 dual-frequency receiver and Trimble-Ti Chock Ring Antenna were equipped on DGB to decrease the impact of multi-path (MP1/2) effects [17]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PGS** & **N Slope** & **E Slope** & **U Slope** & **Noise Model** & **Solutions** \\ \hline ZWAN & \(-10.52\pm 0.35\) & \(30.74\pm 0.24\) & \(-2.05\pm 0.91\) & GGM & \\  & \(-10.52\pm 0.38\) & \(30.74\pm 0.24\) & \(-2.33\pm 0.80\) & GGM + WN & \\ \hline WLDD & \(-10.00\pm 0.29\) & \(31.25\pm 0.26\) & \(-1.73\pm 0.55\) & GGM & This research \\  & \(-10.01\pm 0.34\) & \(31.25\pm 0.27\) & \(-1.76\pm 0.59\) & GGM + WN & \\ \hline  & \(-10.80\pm 0.31\) & \(30.95\pm 0.21\) & \(-1.43\pm 0.68\) & GGM & \\  & \(-10.83\pm 0.29\) & \(30.95\pm 0.22\) & \(-1.59\pm 0.60\) & GGM + WN & \\ \cline{2-6} HKWS & \(-11.54\pm 0.18\) & \(32.57\pm 0.16\) & \(0.73\pm 0.52\) & \(-\) & SOPAC \\  & \(-11.40\pm 0.09\) & \(32.89\pm 0.14\) & \(0.32\pm 0.30\) & \(-\) & COMB \\  & \(-11.40\pm 0.10\) & \(32.94\pm 0.15\) & \(0.07\pm 0.30\) & \(-\) & JPL \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Estimated stations velocities (mm/year). Figure 3: Time-series of the coordinates of ZWAN and WLDD. The blue dots represent the raw coordinate processed by GAMIT/GLOBK. The red lines represent the results after removing the noise and geometric modelling. The quality of the DGB was checked using the Anubis software (version 3.7) in the campaigns [21]. The data were deleted if the MP1/2 was more than 0.5 m. The received Rinex data of DGB were processed using the accurate coordinates and the static Rinex data of the PGSs of WSCS are needed for the kinematic solutions of DGB. The kinematic DGB data were processed using the TRACK module of the GAMIT/GLOBK together with the final GNSS satellite clocks and orbits [22]. The kinematic results comprised the XYZ, NEU, and BLH coordinates and the integrated weighted RMS of the DGB. A low pass filter of five minutes was used to eliminate the impact of the dynamic ocean environment. Data suddenly affected by the impact will be deleted (Figure 4h). The U/H components of the kinematic solutions were used to set the datum for the ATGs. The overall precision of the SSH can be less than 15 mm. After three years of comparisons, the datum of the ATGs was set with an accuracy of less than 10 mm (Figure 4). This datum of the PGSs was WGS 84 ellipsoid with an equatorial radius of 6378.137 km and a flattening coefficient of 0.003352811, but have height differences with the S3A, HY-2B,  
Figure 4: Definition of the datum of the ATGs using the DGB. Panels (**a**–**i**) show the comparisons between the ATGs and the DGB from 2019–2021. The magenta lines in (**h**) represent the SSH of the DGB jumped suddenly. This may be caused by weak GNSS satellite coverage, multipath, or changes in the floating position (Reprinted/adapted with permission from Ref. [19]). HY-2C, and J3 altimeter, which have an equatorial radius of 6378.1363 km and a flattening coefficient of 1/298.257 [23]. This height difference was corrected using Equation (3):  
\[dh=-Wda+\frac{W}{a}(1-f)sin^{2}qdf \tag{3}\]  
where, \(dh\) was the changes of the height caused by reference ellipsoid transformation; \(da=a0-a\), \(df=f0-f\) were the corrections of the Semi-major Axis and flattening factor, respectively; \(a\) and \(a0\) were the Semi-major Axis of WGS 84 and altimeter satellite, respectively; \(f\) and \(f0\) were the Flattening Factor of the Earth of WGS 84 and altimeter satellite, respectively; \(\varphi\) was the latitude, and \(\mathrm{W}=\sqrt{1-\mathrm{e}^{2}\mathrm{sin}^{2}\varphi}\); \(e\) was the first eccentricity of an ellipsoid.