Reconstruction of Surface Kinematics from Sea Surface Height Using Neural Networks

The Surface Water and Ocean Topography (SWOT) satellite is expected to observe sea surface height (SSH) down to scales approaching similar to 15 km, revealing submesoscale patterns that have never before been observed on global scales. Features at these soon-to-be-observed scales, however, are expected to be significantly influenced by internal gravity waves, fronts, and other ageostrophic processes, presenting a serious challenge for estimating surface velocities from SWOT observations. Here we show that a data-driven approach can be used to estimate the surface flow, particularly the kinematic signatures of smaller scale flows, from SSH observations, and that it performs significantly better than using the geostrophic relationship. We use a Convolutional Neural Network (CNN) trained on submesoscale-permitting high-resolution simulations to test the possibility of reconstructing surface vorticity, strain, and divergence from snapshots of SSH. By evaluating success using pointwise accuracy and vorticity-strain-divergence joint distributions, we show that the CNN works well when inertial gravity wave amplitudes are relatively weak. When the wave amplitudes are strong, reconstructions of vorticity and strain are less accurate; however, we find that the CNN naturally filters the wave-divergence, making divergence a surprisingly reliable field to reconstruct. We also show that when applied to realistic simulations, a CNN model pretrained with simpler simulation data performs well, indicating a possible path forward for estimating real flow statistics with limited observations. Satellite measurements of sea surface height (SSH) have for the past few decades provided weekly global estimates of upper ocean currents at scales larger than approximately 100 km. The new Surface Water and Ocean Topography satellite promises to improve the resolution of these SSH observations. However, these new observations will introduce a new challenge, since a simple physics-based diagnostic relationship does not exist between the SSH and upper ocean currents for the finer scales that will now be visible. Here we show that a neural network can be used to estimate the surface flow from SSH observations. In particular, our trained neural networks are able to use SSH to predict aspects of upper-ocean currents that may be particularly useful for improving estimates of oceanic transport of heat and other tracers. Neural networks reasonably reconstruct surface vorticity, strain and divergence, from sea surface heightNeural networks naturally filter wave divergence, leaving only the desired divergence associated with frontsTransfer learning shows promise when task-specific data is limited but data from reasonably close simulations is available