High-resolution probabilistic estimation of three-dimensional regional ocean dynamics from sparse surface observations

Abstract

The ocean interior regulates Earth's climate but remains sparsely observed due to limited in situ measurements, while satellite observations are restricted to the surface. We present a depth-aware generative framework for reconstructing high-resolution three-dimensional ocean states from extremely sparse surface data. Our approach employs a conditional denoising diffusion probabilistic model (DDPM) trained on sea surface height and temperature observations with up to 99.9 percent sparsity, without reliance on a background dynamical model. By incorporating continuous depth embeddings, the model learns a unified vertical representation of the ocean states and generalizes to previously unseen depths. Applied to the Gulf of Mexico, the framework accurately reconstructs subsurface temperature, salinity, and velocity fields across multiple depths. Evaluations using statistical metrics, spectral analysis, and heat transport diagnostics demonstrate recovery of both large-scale circulation and multiscale variability. These results establish generative diffusion models as a scalable approach for probabilistic ocean reconstruction in data-limited regimes, with implications for climate monitoring and forecasting.

Figures (7)

• Figure 1: Schematic of the depth-aware conditional DDPM framework for three-dimensional ocean reconstruction. Sparse observations of SSH and SST are used with a log-normalized continuous depth coordinate and used as conditioning inputs to a conditional denoising diffusion probabilistic model (DDPM). A single unified model is trained across nine discrete depth levels and learns a continuous vertical representation of the ocean interior. During inference, the model reconstructs T, S, U, and V fields not only at trained depths but also at previously unseen depths within the training range, enabling vertical interpolation without memorizing discrete layers.
• Figure 2: Sparse surface observations and depth-aware DDPM reconstruction of subsurface ocean variables at three depths. Panel a shows sparse satellite SSH and SST observations on February 13, 2023, which are used to reconstruct 3D ocean states in panel b. Panel b shows subsurface ocean variables, including T, S, U, and V is shown over the Gulf of Mexico at three different depths: 55 m, 318 m, and 1062 m. The DDPM reconstructions (top row) are compared with the corresponding ground-truth fields from the GLORYS reanalysis (bottom row) for each depth. Only three depths are displayed here for clarity, and reconstructions at the other depths are included in the Supplementary Material. White areas indicate land/bathymetry. As depth increases, the valid ocean domain decreases due to bathymetric constraints, resulting in a larger land mask at deeper levels.
• Figure 3: Averaged Fourier power spectra for subsurface ocean variables at three depths. The power spectra of T, S, U, and V is displayed for 100 test samples at three different depths: 55 m, 318 m, and 1062 m. Power spectra from the DDPM reconstructions are compared with the corresponding GLORYS reanalysis reference across spatial wavenumbers.
• Figure 4: Quantitative evaluation of reconstructed subsurface variables across depths and models. Reconstruction performance for T, S, U, and V across 100 test samples. Columns correspond to various evaluation metrics, including normalized RMSE (NRMSE), correlation coefficient (CC), and SSIM. Results are compared across three models: DDPM, UNet+DDPM, and FNO+DDPM. Rows show results at three depths: 55 m, 118 m, and 1062 m.
• Figure 5: Meridional heat-flux longitude--depth transects at $26^\circ$N on 13 February 2023. Longitude--depth transects of meridional heat flux for the GLORYS reanalysis dataset (Truth) and the DDPM reconstruction are shown over the longitude range $[-99^\circ, -74^\circ]$.