Scott A Martin , Georgy Manucharyan, Patrice Klein

Estimating the surface ocean state at mesoscale eddy-resolving scales is essential for understanding the role of eddies in climate and marine ecosystems. Satellites provide multi-modal observations through sea surface height, temperature (SST), and salinity (SSS). However, each variable is observed with varying resolutions and sparsity, while some variables, such as surface currents, are not yet observed by satellites. All these variables must be accurately reconstructed across scales to study eddy dynamics. Dynamical data assimilation (DA) struggles to accurately reconstruct eddies since, to respect the equations of motion, it must reconstruct both the surface and interior ocean state, but the interior is sparsely observed. Relaxing this requirement and focusing only on the surface could improve surface state estimation, but a new method is required to ensure reconstructions remain physically realistic. Here, we introduce a score-based generative data assimilation (GenDA) framework for jointly reconstructing key surface ocean variables at eddy-resolving scales from multi-modal satellite observations. GenDA uses a two-stage approach: training a score-based diffusion model on a simulation to generate realistic ocean states before employing this as a Bayesian prior to assimilate sparse observations and generate state estimates. The learned diffusion prior leads to coherence between variables and realism across scales. By synergizing low-resolution SSS with high-resolution SST observations, GenDA improves the SSS resolution. Remarkably, GenDA can infer unobserved surface currents using only satellite observables, suggesting the learned prior encodes physical relationships between variables. Applied to real observations, GenDA demonstrates strong generalizability compared to regression-based deep learning and outperforms state-of-the-art dynamical DA.