The Tikhonov-L-curve regularization method for determining the best geoid gradients from SWOT altimetry

The Surface Water and Ocean Topography (SWOT) mission generates dense altimetry data that, when used in geoid gradient component estimations through least-squares collocation (LSC), lead to an ill-conditioned problem. Such problems also arise in geodetic network designs. This study introduces the Tikhonov-L-curve regularization to effectively address this challenge. By pinpointing the maximum curvatures of the L-curve, we discern optimal regularization parameters, countering issues stemming from the dense data of SWOT and the resulting ill-conditioned covariance matrices. Our approach not only stabilizes LSC solutions but also achieves gradient accuracies at 1-microrad levels compared to theoretical values. Additionally, we experimented with a strategic removal process that selectively eliminates adjacent geoid gradients. This technique considerably improves geoid gradient component determinations, especially evident at a threshold distance of 0.755 km within an 8′× 8′ data selection window. While our findings are rooted in simulated SWOT data, they are pivotal for future research intending to employ real SWOT data, anticipated by late 2023. This work serves as a precursor for marine gravity field determinations, emphasizing the importance of stabilized LSC solutions to avoid misleading seafloor signatures due to data compactness.