The Surface Water and Ocean Topography (SWOT) satellite is expected to observe the sea surface height (SSH) down to scales of ∼10-15 kilometers. While SWOT will reveal submesoscale SSH patterns that have never before been observed on global scales, how to extract the corresponding velocity fields and underlying dynamics from this data presents a new challenge. At these soon-to-be-observed scales, geostrophic balance is not sufficiently accurate, and the SSH will contain strong signals from inertial gravity waves — two problems that make estimating surface velocities non-trivial. Here we show that a data-driven approach can be used to estimate the surface flow, particularly the kinematic signatures of smaller scales flows, from SSH observations, and that it performs significantly better than directly using the geostrophic relationship. We use a Convolution 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 joint distributions, we show that the CNN works well when inertial gravity wave amplitudes are weak. When the wave amplitudes are strong, the model may produce distorted results; however, an appropriate choice of loss function can help filter waves from the divergence field, making divergence a surprisingly reliable field to reconstruct in this case. We also show that when applying the CNN model to realistic simulations, pretraining a CNN model with simpler simulation data improves the performance and convergence, indicating a possible path forward for estimating real flow statistics with limited observations.

Mesoscale eddies modulate the stratification, mixing and dissipation pathways, and tracer transport of oceanic flows over a wide range of spatiotemporal scales. The parameterization of buoyancy and momentum fluxes associated with mesoscale eddies thus presents an evolving challenge for ocean modelers, particularly as modern climate models approach eddy-permitting resolutions. Here we present a parameterization targeting such resolutions through the use of a subgrid mesoscale eddy kinetic energy budget (MEKE) framework. Our study presents two novel insights: (1) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent-McWilliams along-isopycnal transport; (2) a dominant factor in ensuring a physically-accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2$^\circ$ and 1/4$^\circ$ resolution idealized models with backscatter applied to the equivalent barotropic mode. Remarkably, the global kinetic and potential energies, isopycnal structure, and vertical energy partitioning show significantly improved agreement with a 1/32$^\circ$ reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy-permitting regime.

The understanding and representation of energetic transfers associated with ocean mesoscale eddies is fundamental to the development of parameterizations for climate models. We investigate the influence of eddies on flow vertical structure as a function of underlying dynamical regime and grid resolution. We employ the GFDL-MOM6 in an idealized configuration and systematically consider four horizontal resolutions: 1/4, 1/8, 1/16, and 1/32 degree. We analyze the distributions of potential and kinetic energy, decomposed into barotropic and baroclinic, and eddy and mean parts. Kinetic energy increases and potential energy decreases as resolution increases and captures more baroclinically-unstable modes. The dominant trend in vertical structure is an increasing fraction of kinetic energy going into the barotropic mode, particularly its eddy component, as eddies are increasingly resolved. We attribute the increased baroclinicity at low resolutions to inaccurate representation of vertical energy fluxes, leading to suppressed barotropization and energy trapping in high vertical modes. We also explore how the underlying dynamical regime influences energetic pathways. In cases where large-scale flow is dominantly barotropic, resolving the deformation radius is less crucial to accurately capturing the flow’s vertical structure. We find the barotropic kinetic energy fraction to be a useful metric in assessing vertical structure. In the highest-resolution case, the barotropic kinetic energy fraction correlates with the scale separation between the deformation scale and the energy-containing scale, i.e. the extent of the eddy-driven inverse cascade. This work suggests that mesoscale eddy parameterizations should incorporate the energetic effects of eddies on vertical structure in a scale-aware, physically-informed manner.

Fronts, at both mesoscale and submesoscales, are generally hypothesized to play a significant role in mediating the transfer of tracers from the surface boundary layer into the interior. With the advent of computational capabilities numerous high resolution modeling studies have shown the enhancement of of vertical velocities with increasing horizontal resolution. In a carefully designed setup of an idealized channel partially blocked by meridional topography and forced by steady forcing, idealization of the Antarctic Circumpolar Current, we vary the horizontal resolution as the control parameter, and analyze the impact of enhanced vertical velocities on tracer subduction. It is found that the submesoscale-permitting simulations flux far more tracer downward than the lower resolution simulations, the 1km simulation takes up 50\% more tracer compared to the 20km simulation, despite the increased restratifying influence of the resolved submesoscale processes. A spectral decomposition of the flow and fluxes illuminated the relative importance of scales, and the inefficiency of inertia-gravity waves in influencing tracer transport. To further understand the physical dynamics in these simulations we diagnosed how energy was being transferred between the mean and eddy kinetic and potential energy reservoirs (Lorenz energy cycles), and if changing the resolution influenced this exchange. In particular we focussed on separating the dynamics of the energy cycles that are active in the interior of the water column and those that are trapped near the surface. We also analyzed the inter-lengthscale exchange of energy to understand the detailed spectral dynamics of the turbulence that is resolved. Lastly, and probably most relevant to SWOT, we looked at the energy budgets in terms of velocity and pressure structure functions, to assess the potential for the future SWOT mission to directly measure the inter-scale energy transfers at the ocean surface.

The Gent-McWilliams (GM) and Redi eddy parameterizations are essential features to ocean climate models. GM helps to maintain stratification, balancing the steepening of isopycnals by Ekman forcing and convection with a relaxation that dissipates potential energy adiabatically. The Redi parametrization represents unresolved isopycnal mixing of tracers, while keeping diabatic mixing small. Due to its direct impact on the simulated circulation, research has focused more on theories for the GM than Redi coefficient, the latter typically being set equal to the former without justification. Theories for the GM coefficient invariably rely on an assumption of down-gradient eddy buoyancy fluxes, despite that estimates of the latter in eddy-resolving models and nature often show up-gradient tendencies. When tuned to values of O(500) $m^2s^{-1}$, GM-based simulations are able to reproduce observed ocean stratification. By contrast, observational estimates of along-isopycnal mesoscale diffusivity (the Redi part) are typically an order of magnitude larger. Setting the Redi coefficient to the too-small GM value results in serious errors in biogeochemical tracers like oxygen. Here I will describe an alternate approach that requires only small changes to the existing infrastructure and resolves the discrepancy in values. The idea relies on three results: (1) materially-conserved tracers are mixed down-gradient, with diffusivities well-estimated by mixing-length theory; (2) the mixing rate of tracers and potential vorticity (PV) are very similar; (3) eddy PV and buoyancy fluxes are related through an integral relationship derived from quasigeostrophic theory. Therefore, I argue that PV flux theories should be applied to setting the Redi coefficient, with the GM coefficient determined diagnostically. This idea is explored using a high-resolution MITgcm simulation of an idealized Southern Ocean channel, run with 10 independent tracers, each driven by different mean gradients. The tracers are used to extract an estimate of the mixing tensor, and hence of the mixing coefficients in question.