## 5 Marine Gravity Recovery
### Model Construction
The residual gravity anomalies of GRAHY2 have maximum noise level, but the general trend of the gravity signals can be detected and was basically consistent with the other two results. An initial conclusion was that the HY-2 dataset could not be the only input observations to construct a 1\({}^{\prime}\)\(\times\) 1\({}^{\prime}\) resolution marine gravity anomaly model due to limited spatial resolution. In addition, the multi-satellite altimetry-captured gravity signals derived from WHU16 and NSOAS22 had more consistent distribution, but the latter had smoother features and smaller trajectory characteristics. Taking the 35\({}^{\circ}\)-40\({}^{\circ}\)N part of Region 1, for example, the signal distribution of positive and negative anomalies  
Figure 12: Global gravity anomaly model NSOAS22. was more integrated in Figure 13(c-1) than Figure 13(b-1). Another initial conclusion was that the tracking effect was effectively constrained and the final captured gravity signals were enhanced by incorporating HY-2 series measurements into a multi-satellite dataset. In other words, the HY-2 missions played an irreplaceable role in modeling global marine gravity. Therefore, validating the NSOAS22 model with HY-2 measurements is our main goal in the next section. Figure 13: Residual gravity anomaly of GRAHY2, WHU16 and NSOAS22 models in the six study regions and difference between NSOAS22 and WHU16 (the lowercase letters (**a–d**) represent GRAHY2, WHU16, NSOAS22 and difference between NSOAS22 and WHU16; the Arabic numbers (**1–6**) represent the study regions). To further highlight HY-2's contribution, the difference between NSOAS22 and WHU16 was also plotted as column d in Figure 13. The difference grid consistently reflected typical gravity signals in the six study regions, indicating that incorporating HY-2 data was helpful to capture more signals during the marine gravity recovery modeling. From the perspective of numerical value, statistical and histogram analysis of discrepancies between two models was executed. As shown in Table 8 and Figure 14, the discrepancies are concentrated within \(\pm 20\) mGal with approximate normal distribution and the largest deviation, respectively, reached 180.4 and \(-209.4\) mGal. The SD values indicated the difference in captured gravity signals, as well as caused errors by incorporating HY-2 altimetric data over the six study areas. The second validation was based on a comparison with shipborne gravity anomaly measurements along irregular tracks. This comparison provided a more independent assessment of model accuracy but was limited to special areas where high-quality shipborne data were available [34]. The accessible observations distributed by the national geophysical data center (NGDC) were globally distributed and each study region had several cruises and several thousand measurements. In addition to NSOAS22, other models also carried out the same validation as comparisons, which contained EGM2008, SS V31.1, DTU21, WHU16 and GRAHY2. The gravity anomaly of each model was interpolated according to the location of the shipborne measurements by the GRDTRACK command in generic mapping tools (GMT) and the difference was calculated for further statistics [35]. The initial and processed shipborne datasets were validated and the statistics are listed in Table 10. The former dataset was derived from NGDC shipborne measurements with the default value eliminated, while the latter was further processed following two steps. In step one, we eliminated the shipborne measurements according to discrepancies with the reference model larger than 15 mGal. The threshold was set by considering that the accuracy of altimetry-derived marine gravity over open oceans is usually 3-5 mGal and large deviations should not exceed 15 mGal under the triple criteria. For step 2, the shipborne data beyond three-times standard deviation, as checked by NSOAS22 for each cruise, were removed. The upper part in Table 10 shows that the average SD of discrepancies was larger than 7 mGal.