Reconstructing the Global Ocean from the Historical Observing Record with Generative Data Assimilation

The ocean absorbs most of the heat trapped by greenhouse gases, but until the mid-2000s it was measured only sparsely. It remains unclear how much of the past ocean, including its interior, these measurements can determine. We address this question with score-based data assimilation, in which a diffusion model trained on MIROC6 climate-model simulations learns the distribution of coupled ocean--atmosphere trajectories and is conditioned on historical observations, without running a general circulation model (GCM). Three experiments separate the sources of error: a perfect-model test against withheld MIROC6 members, a cross-model test against CESM2, and a real-world reconstruction over 1950--2020 from surface temperature, sea-level pressure, and subsurface temperature and salinity profiles. In model-world tests, the historical record determines the large-scale upper ocean back to 1950, including interior modes such as the Pacific thermocline tilt and Labrador Sea temperature at 1500~m, recovered through their learned covariance with the observed fields. In the upper ocean this covariance transfers across structurally different GCMs and, where independent data allow a test, to the real ocean. Unassimilated sea-surface height tracks satellite altimetry at large scales (median correlation 0.41), and basin-scale heat content agrees with observational products after 1990, with an earlier warm offset that is largest in the South Pacific. As observations thin out, the reconstruction increasingly follows the prior. In the cross-model test this shows up as modest biases in 300--700~m heat content and Arctic sea-ice trends and as a missed Antarctic sea-ice decline. The ensemble is underdispersed in all three experiments.