Surface to Seafloor: A Generative AI Framework for Decoding the Ocean Interior State

TL;DR

The paper tackles the problem of inferring the ocean interior state from surface observations by introducing a probabilistic, score-based diffusion framework that samples subsurface velocity and buoyancy fields conditioned on surface data. Using an idealized 15-level double-gyre testbed, the authors demonstrate that the method can recover mean circulation and mesoscale structures while providing meaningful uncertainty estimates, with predictive skill diminishing as surface information is degraded or inference depth increases. This approach highlights the value of generative, uncertainty-aware procedures for ocean state estimation in underconstrained regimes and suggests pathways for integrating surface data with interior dynamics in data assimilation. The work lays a foundation for probabilistic, 4D ocean reconstructions using surface observations and paves the way for combining high-resolution satellite data with physics-based simulations in climate modeling.

Abstract

Understanding subsurface ocean dynamics is essential for quantifying oceanic heat and mass transport, but direct observations at depth remain sparse due to logistical and technological constraints. In contrast, satellite missions provide rich surface datasets-such as sea surface height, temperature, and salinity-that offer indirect but potentially powerful constraints on the ocean interior. Here, we present a probabilistic framework based on score-based diffusion models to reconstruct three-dimensional subsurface velocity and buoyancy fields, including the energetic ocean eddy field, from surface observations. Using a 15-level primitive equation simulation of an idealized double-gyre system, we evaluate the skill of the model in inferring the mean circulation and the mesoscale variability at depth under varying levels of surface information. We find that the generative model successfully recovers key dynamical structures and provides physically meaningful uncertainty estimates, with predictive skill diminishing systematically as the surface resolution decreases or the inference depth increases. These results demonstrate the potential of generative approaches for ocean state estimation and uncertainty quantification, particularly in regimes where traditional deterministic methods are underconstrained or ill-posed.

Figures (11)

• Figure 1: Snapshots of the ocean state from a double-gyre simulation. Each column is a different ocean state, and each row is a fixed moment in time. The first row consists of year 20, the middle row year 200, and the last row year 300. The columns are the sea surface height, the zonal velocity $U$, the meridional velocity $V$, the vertical velocity $w$, and the temperature $T$. The velocities and temperature are evaluated at a 400-meter depth.
• Figure 2: Evolution of $L^1$ norms in time. We show the average value of the absolute value of various fields (see Equation \ref{['l1_error']}) as a function of time in years on a logarithmic scale. The surface fields are in quasi-statistical equilibrium, whereas the fields near the bottom of the domain are still converging, especially for the temperature field. The different colors represent the discarded spin-up data (blue), training data (red), and test data (orange) for training a score-based diffusion model.
• Figure 3: Statistical inference of the ocean interior state from SSH. Given the SSH input field (left column), we reconstruct the ocean state: the velocity component fields $U, V, W$, and temperature $T$ (second column). All fields are generated simultaneously. We show the mean over 100 samples predicted by the neural network (third column) and two representative samples (fourth and fifth column). The absolute difference between the AI mean and the OsC ground truth is displayed in the second-to-last column alongside the AI standard deviation in the last column.
• Figure 4: Statistical inference of zonal velocity given the different resolutions of the free surface. Given the sea surface height at several coarse-grained resolutions (first column), we show the output of the generative AI model ensemble in the subsequent columns. We show the average value over 100 samples predicted by the neural network (second column) and representative samples (third, fourth and fifth columns). The pointwise standard deviation of the generative AI ensemble is in the last column. The latitudinal resolutions of SSH are, from top to bottom, 200 kilometers, 800 kilometers, 1,600 kilometers, and 3,200 kilometers.
• Figure 5: Comparison of the AI ensemble mean to the OsC temporal mean. Using fully coarse-grained SSH as inpute to the network, we generate 100 samples and calculate point-wise statistics. We compare these ensemble statistics to the temporal analog of the ocean simulation over the training period.