Three-Dimensional Parameterization of Submesoscale Eddy From HiSea-II Imagery

The detection of submesoscale eddies is limited by altimeter resolution and the complex dynamics of eddy formation and dissipation, resulting in an incomplete understanding of their structure. The advent of multiband high-resolution satellites, such as HiSea-II, enables more detailed observations of submesoscale eddies. This study presents a comprehensive methodology for parameterizing eddy properties. We model eddy morphology using a logarithmic spiral expression and employ deep learning and partial differential equations to extract streamlines representing the static transport state. The spiral is then fitted to parameterize attributes such as core location, radius, and polarity. Furthermore, a three-dimensional logarithmic spiral is introduced to characterize the eddy vertical extent. Analysis of 21 submesoscale eddies in 9 HiSea-II images demonstrates that our proposed method surpasses an existing deep-learning model in accuracy by about 70% for the eddy core position. Validation using reanalysis ocean current data and high-resolution Chlorophyll-a concentration data confirms that these eddies have a radius of 3.7 $\pm$ 2.5 km and a mean depth of 42 m. This approach overcomes the limitations of altimeter-based eddy observations in nearshore regions, provides a novel and precise parameterization of submesoscale eddies in optical imagery, and enhances the utility of multiband high-resolution SmallSats such as HiSea-II.