## 4 Vertical Deflections
### Along-Track Vertical Deflection  
Compared with the targeted vertical deflection information at 1\({}^{\prime}\times 1^{\prime}\) grid points, the spatial distribution of crossover points determined in Section 4.1 was relatively sparse. A more common approach is to directly construct the relationship between directional components at grid points and the along-track vertical deflection at each measuring point. The  
Figure 9: Distributional proportion of discrepancies between HY-2 directional components and XGM2019 model: Region 1, North Pacific; Region 2, South Pacific; Region 3, Mid-Pacific; Region 4, Indian Ocean; Region 5, North Atlantic; Region 6, South Atlantic. latter is obtained in a differential operation among the along-track adjacent measurements of geoid heights. The difference calculation effectively suppressed the influence of long-wavelength error items, such as radial orbit, instrumental and atmospheric propagation errors, as well as inaccurate geophysical environmental corrections. Hence, the accuracy of along-track vertical deflections depended on, but also was distinguished from, the accuracy of SSH observations. In this section, the performance of the HY-2 missions is evaluated from the perspective of along-track vertical deflection. The experimental data for calculating along-track vertical deflections were exactly the same as the data sequences in Section 3.2. The XGM2019 (d/o) gravity model was also used for validation. Moreover, a triple-standard-deviation criterion was adopted by comparing model values to eliminate gross errors in measurement. The statistical results are listed in Table 7, indicating that all HY-2 missions obtained reliable along-track vertical deflections. The standard deviations of discrepancies with the XGM2019 model range from 0.86 arcsec to 1.79 arcsec over six study regions. The average accuracy for HY-2A, HY-2B, HY-2C and HY-2D is, respectively, 1.46, 1.05, 1.09 and 1.01 arcsec. Recent missions, including HY-2B, HY-2C and HY-2D, obviously had better performance compared to HY-2A, which was the first experimental satellite and no longer distributed data. Moreover, we analyzed the distributional proportion of the along-track vertical deflections as well as their discrepancies with the XGM2019 model over the six research regions, which are, respectively, shown in Figures 10 and 11. In Figure 10, the distributional proportion is, respectively, consistent in prograde orbit group (HY-2C and HY-2D) and retrograde orbit group (HY-2A and HY-2D). Histograms of the two groups were approximately symmetrical along the axis of 0 value. Since we selected ascending passes for the retrograde orbit group and descending passes for the prograde orbit group, the calculated along-track deflections at similar locations had similar values but opposite signs. Figure 11 shows that the discrepancies with the XGM2019 model are concentrated at 0 arcsec with approximate normal distribution. The proportions of model discrepancies within 1 arcsec were over 30%, of which the performance of HY-2A is far below average. In addition, HY-2B and HY-2D accorded better with XGM2019 in Region 3 (Mid-Pacific) and Region 6 (South Atlantic) and the corresponding proportions were larger than 40%. HY-2D was superior in most cases, while HY-2C performed better in Region 1 (North Pacific). Generally, the determined along-track vertical deflections were reliable for all HY-2 missions, but there were quality gaps between HY-2A and the other HY-2 missions.