Physics-guided Statistical Data Fusion for Reconstructing 3D Current Fields of Oceanic Eddies

Accurate reconstruction of three-dimensional ocean current fields is critical for understanding ocean dynamics and real-time conduct of modern oceanographic field campaigns, particularly for mesoscale eddy surveys. We propose a physics-guided modeling and learning framework for multi-source data fusion to estimate the three-dimensional (3D) current structure of oceanic eddies by integrating satellite altimetry and temperature data, ocean reanalysis data, and in situ drifting buoy observations. The approach leverages geostrophic balance, derived from the Navier-Stokes equations, to guide a neural network trained on GLORYS reanalysis data in inferring subsurface currents from surface conditions. The surface conditions were estimated using a high-dimensional linear mixed model, which integrates systematically biased satellite altimetry and sparse drifting buoy data, allowing for spatially adaptive bias correction and yielding more accurate and spatially coherent surface velocity fields. This framework was deployed in a September 2024 field campaign targeting a cyclonic eddy in the Kuroshio Extension, guiding a real-time control of seven underwater gliders. Compared with existing data products, our method demonstrated substantially improved accuracy in cross-validation with drifting buoys and stronger consistency with ADCP observations. The resulting glider trajectories provided enhanced spatial coverage of the eddy interior, enabling the first successful high-resolution controlled network survey of a mesoscale eddy.