4DVarGen: A 4D Variational-Inspired Generative Model for Eddy-Resolving Surface Ocean Reconstruction

Abstract

Sea surface variable reconstruction from sparse observations is a key ocean-science challenge. Traditional methods, such as the four-dimensional variational (4DVar) approach, rely on numerical models for background information, leading to high computational costs. Deep learning methods are more efficient but often fail to capture eddy dynamics, resulting in limited effective resolution. We propose 4DVarGen, a 4DVar-inspired generative framework for reconstructing sea surface variable fields at eddy-resolving scales from sparse remote-sensing observations. 4DVarGen establishes a mathematical equivalence between 4DVar and an observation-guided denoising process. Its key innovation is injecting the observation-likelihood gradient into denoising iterations, driving the generated trajectories to evolve in the direction of minimizing the 4DVar objective function toward a maximum a posteriori solution. Spatiotemporal priors learned by a diffusion model serve as background information, reducing computational costs and mitigating the adverse effects of Gaussian assumptions. Experiments show that 4DVarGen effectively leverages the temporal evolution patterns of sea surface temperature (SST) and sea surface height (SSH), as well as their dynamical mappings learned by the diffusion model, leading to improved reconstruction accuracy and effective resolution. Our model, pretrained on GLORYS12V1 reanalysis data, generates sea surface variable fields guided by real observations, achieving accuracy and effective resolution improvements of 18% and 58%, respectively, compared to GLORYS12V1. This study offers a novel framework for reconstructing Earth system states from sparse observations.