Helmholtz–Hodge decomposition-based 2D and 3D ocean surface current visualization for mesoscale eddy detection

Ocean surface current (or ocean flow) visualization plays a significant role in the understanding of dynamical processes of ocean. It has been a hot research topic in both computer science and oceanography. Ocean surface current is a turbulent flow field mixing of multi-scale ocean dynamics such as large-scale ocean circulations (\(100\,\hbox {km}\sim\)), mesoscale eddies (10–\(100\,\hbox {km}\)), submesoscale processes (1–\(10\,\hbox {km}\)). Mesoscale eddies, which are strong but short-life movement relative to the large-scale ocean circulations, have great importance on the transportation of ocean water masses, momentum and energy. However, their detection and recognition, which are treated as the foundation of exploring their dynamical mechanisms, is still a challenging issue. For one thing, in the mixed ocean flow field, different ocean flows depended and influence with each other making existing methods difficult to identify among them. For another, mesoscale eddies are active signals on the ocean. They may change their forms and velocities at any time. This challenges existing works to deal with their boundary ambiguity and unremitting transitions. To solve these problems, this paper proposes a novel 2D and 3D ocean surface current visualization approach based on an amended Helmholtz–Hodge decomposition (HHD), which can be widely used for mesoscale eddy detection. In our method, HHD decomposes each mixed ocean flow field to two components: curl component and divergence component. Different ocean flows can be represented by these two components independently. In addition, to improve the performance of eddy identification and to reveal the 3D structure of ocean flows simultaneously, HHD transforms the 2D ocean flow field to 3D potential surfaces. Finally, comprehensive experiments are performed on both global and local ocean flow field (Black Sea and Mediterranean Sea) calculated from satellite maps of sea level anomaly to verify our method. Experimental results demonstrate the good effectiveness of our method.