Tailored method for optimizing deflection of the vertical model using multi-directional geoid gradients from SWOT/KaRIn observations

The Surface Water and Ocean Topography mission (SWOT), equipped with the Ka-band Radar Interferometer (KaRIn), provides groundbreaking two-dimensional sea surface heights (SSHs), bringing new potential for optimizing the deflection of the vertical (DOVs). However, conventional DOV modeling—combining along- and cross-track geoid gradients with equal weights—fail to fully exploit the potential of SWOT/KaRIn observations and overlook the spatial variability in precision. We present a tailored method for optimizing DOVs estimation. The method combines geoid gradients in the along-track, cross-track, diagonal (forward and backward) directions with adaptive weighting. The refined weights are employed to exploit the potential of each geoid gradient based on the relationship between the standard deviation of SSHs and the significant wave height. To mitigate data gaps, prior and locally averaged geoid gradients are incorporated in the gaps and overlapping regions. SWOT/KaRIn-derived DOVs and gravity anomalies from the science-phase observations are validated against shipborne gravity in the Philippine Sea. Results indicate that the DOV model derived by the tailored method—particularly by combining triple-directional (along, cross, and diagonally forward) geoid gradients with refined weights—achieves a 7.3% improvement in accuracy over the conventional method. The supplement of additional geoid gradients is critical for mitigating leakage errors caused by missing or reduced observations in the gap regions. Furthermore, the gravity anomaly model recovered from DOVs by stacking 17-cycle observations achieved an accuracy of 2.97 mGal, representing a 7.2% improvement over single-cycle observations. The clear advantages of SWOT/KaRIn observations are gradually emerging in marine gravity recovery.