## 5 Marine Gravity Recovery
### Model Construction
It should be noted that most of the NGDC shipborne measurements were \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experimental Region** & **Ship Num** & **EGM2008** & **V31.1** & **DTU21** & **NSOAS22** & **WHU16** & **GRAHY-2** \\ \hline \multicolumn{8}{c}{Comparison with original NGDC shipborne data} \\ \hline
1 & 154307 & 8.9969 & 8.4055 & 8.4498 & 8.6485 & 8.7617 & 9.5523 \\
2 & 223215 & 6.7261 & 6.1551 & 6.0829 & 6.4873 & 6.4206 & 7.9747 \\
3 & 183428 & 7.0148 & 6.5585 & 6.5938 & 6.6597 & 6.6070 & 7.2480 \\
4 & 100646 & 5.8313 & 5.2628 & 5.2111 & 5.2717 & 5.3690 & 6.6649 \\
5 & 77656 & 8.2512 & 8.0527 & 8.0360 & 8.2659 & 8.1806 & 8.8939 \\
6 & 106374 & 10.0158 & 9.6352 & 9.6369 & 9.9101 & 9.7588 & 10.5042 \\ Average & - & 7.8060 & 7.3449 & 7.3350 & 7.5405 & 7.5162 & 8.4730 \\ \hline \multicolumn{8}{c}{Comparison with NGDC shipborne data after a gross error elimination} \\ \hline
1 & 130048 & 4.8749 & 4.3306 & 4.3088 & 4.6215 & 4.8435 & 6.0770 \\
2 & 197434 & 4.8451 & 4.2817 & 4.2640 & 4.3932 & 4.5215 & 6.2772 \\
3 & 153836 & 4.1413 & 3.9048 & 3.8843 & 3.7998 & 3.9424 & 4.6622 \\
4 & 68245 & 4.8880 & 4.3855 & 4.3446 & 4.1921 & 4.4148 & 5.8480 \\
5 & 55325 & 5.5377 & 5.2586 & 5.2472 & 5.2753 & 5.3840 & 6.1715 \\
6 & 88587 & 4.3236 & 3.6457 & 3.6818 & 4.0168 & 3.8482 & 5.1531 \\ Average & - & 4.7684 & 4.3011 & 4.2884 & 4.3831 & 4.4924 & 5.6981 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistics of difference between shipborne measurements and typical gravity models (unit: mGal): Region 1, North Pacific; Region 2, South Pacific; Region 3, Mid-Pacific; Region 4, Indian Ocean; Region 5, North Atlantic; Region 6, South Atlantic. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**SD(Model)** & **Region 1** & **Region 2** & **Region 3** & **Region 4** & **Region 5** & **Region 6** \\ \hline SD (DTU21-NSOAS22) & 2.1984 & 2.1382 & 1.2778 & 1.8634 & 1.7846 & 1.7260 \\ SD (V31.1-NSOAS22) & 2.2945 & 2.2386 & 1.4460 & 1.9923 & 1.8450 & 1.7619 \\ SD (V31.1-DTU21) & 1.2943 & 1.4832 & 1.1498 & 1.3503 & 1.2564 & 1.1988 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Statistics of difference between NSOAS22, DTU21 and SS V31.1 (unit: mGal): Region 1, North Pacific; Region 2, South Pacific; Region 3, Mid-Pacific; Region 4, Indian Ocean; Region 5, North Atlantic; Region 6, South Atlantic. accumulated 40 years ago, so the data quality could not be guaranteed. Furthermore, these altimetry-derived models generally have a smaller SD than EGM2008, indicating that the altimetry measurements captured new gravity signals after a remove-restore procedure. Meanwhile, GRAHY2 had the highest noise level due to a limited spatial distribution and excessive interpolation. The SD values in the lower part of Table 10 showed similar variation regularity with a smaller numerical magnitude. Moreover, the number of shipborne measurements involved in validating decreased significantly. The eliminating rates were, respectively, 15.7%, 11.5%, 16.1%, 32.2%, 28.8% and 16.7% in the study regions. Due to the constraints of navigational and observational accuracy before the 1990s, the relatively large rejection ratio was also acceptable. In conclusion, the validation accuracy between NSOAS22 and NGDC shipborne data was between 3.8 and 5.3 mGal, which was superior to EGM2008, WHU16 and GRAHY2. The accuracy gap among our latest result and the worldwide recognized models (DTU21 and SS V31.1) was still detectable but tiny.