From Sea Surface Height to Velocity - A Machine Learning Approach
Inferring upper-ocean velocity from altimetric sea surface height (SSH) remains challenging below 50~km, scales now resolved by the Surface Water and Ocean Topography (SWOT) mission. Conventional methods rely on geostrophic or cyclogeostrophic balance. Here, we demonstrate that deep learning can predict the full velocity vector from SSH and environmental data and recover derivative-based diagnostics, including spectral energy flux. We trained a U-Net encoder--decoder on hourly fields from the pre-SWOT Cape Basin extraction of the LLC4320 ocean simulation, with 1.5-km grid spacing ($11.8$--$15.8^\circ$E, $41$--$45^\circ$S). Inputs were SSH, sea surface temperature (SST), and wind stress; targets were horizontal velocities at the surface and 50~m, where wind influence is weaker. At 50~m, the best model achieves a speed RMSE of $0.049\,\mathrm{m\,s^{-1}}$, 29% lower than the geostrophic approximation. Predicted relative vorticity has a correlation of 0.93, compared with 0.75 for the geostrophic approximation. The model also recovers divergence with a correlation of 0.66, whereas geostrophic velocity is nondivergent by definition. Tests of training strategies yield four findings: SSH gradients outperform raw SSH as inputs; wind stress is the most useful covariate for total velocity prediction; SST benefits vary seasonally; and including vorticity and divergence in the loss improves accuracy. These results offer a path for transferring high-fidelity simulation physics to SWOT applications, where kilometer-scale SSH snapshots contain superposed balanced and unbalanced signals.