## 5 Marine Gravity Recovery  
### Model Construction  
The data qualities of the four HY-2 missions were proven from many perspectives in previous sections: SSH discrepancies at crossover points, resolution capabilities of geoid signals and calculation of vertical deflections. The goal of this paper was to evaluate the performance of the HY-2 missions in constructing a 1\({}^{\prime}\)\(\times\) 1\({}^{\prime}\) marine gravity model. Considering the sparse distribution of HY-2 measurements in cross-track directions, a high degree of interpolation was unavoidable when relying only on HY-2 measurements. Hence, we prepared three groups of input datasets for the model construction. The first was only the HY-2 measurements mentioned in Section 2.1. The second was a 2016 accumulated dataset for constructing the WHU2016 model: Geosat GM and ERM, ERS-1 GM and ERM, Envisat 30d and 35d, Jason-1 ERM and GM, CryoSat-2 and SARAL/AltiKa ERM data [32]. The third group is a combination of the two. The slopes-based method, which is based on the Laplace equation-deduced relationship between vertical deflections and gravity anomalies, was adopted in this study, for  
Figure 11: Distributional proportion of discrepancies between HY-2 along-track vertical deflections and XGM2019 model (unit: arcsec): Region 1, North Pacific; Region 2, South Pacific; Region 3, Mid-Pacific; Region 4, Indian Ocean; Region 5, North Atlantic; Region 6, South Atlantic. Figure 10: Distributional proportion of HY-2 along-track vertical deflections over study regions (unit: arcsec): Region 1, North Pacific; Region 2, South Pacific; Region 3, Mid-Pacific; Region 4, Indian Ocean; Region 5, North Atlantic; Region 6, South Atlantic. which a series of joint processing procedures was necessary. First, raw waveforms were retracked using the two-step waveform retracker and high-rate observations along profiles were uniformly resampled into 5 Hz to enhance the accuracy and density of available measurements. Second, along-track SSH measurements were calculated by adding correction items provided in the standard products to constrain the corresponding effects for path delay and geophysical environment. Third, the along-track SSH gradients were calculated, whereas the along-track gradients from the EGM2008 model were interpolated for preliminary verification to detect outliers. Fourth, Parks-McClellan low-pass filters were used uniformly to constrain the amplified high-frequency noise during the difference procedure. Fifth, the along-track residual vertical deflections were computed, during which the DOT2008A_n180 [33] and EGM2008 model are selected, respectively, to remove the effects of sea surface topography and geoid height by interpolating and subtracting from along-track observations. Sixth, the directional components of residual vertical deflection at gridding points were calculated. Then, the residual gravity anomalies were calculated using the FFT method according to the relationship formula between gravity anomaly and vertical deflection. Finally, a global marine gravity model over a range of 80\({}^{\circ}\)S-80\({}^{\circ}\)N with a 1\({}^{\prime}\)\(\times\) 1\({}^{\prime}\) grid interval was inverted after restoring the removed reference model. Following the previous procedure, the marine gravity model results were obtained based on three input datasets. For convenience of description, these three results derived from HY-2 missions only, multi-satellite dataset without HY-2 missions and multi-satellite dataset with HY-2 missions: GRAHY2, WHU16 and NSOAS22. The NSOAS22 gravity model is shown in Figure 12.  
Figures for the three final marine gravity anomalies after the remove-restore procedure were hard to distinguish. Hence, we directly plotted the residual gravity anomalies in the six study regions for better discernment. As shown in Figure 13, the lowercase letters a, b and c represent GRAHY2, WHU16 and NSOAS22, while the Arabic numbers 1 to 6 indicate the study regions.