Alistair Adcroft

Mesoscale eddies contribute to ocean transport and are a major sink of available potential energy (APE). When unresolved or only partially resolved, their effects must be parameterized to simulate a realistic large‐scale state. Traditionally, this is achieved via the Gent‐McWilliams (GM) parameterization, which represents the eddy‐induced transport as an adiabatic advection built from a downgradient diffusive closure for the horizontal flux. While effective at capturing the bulk APE removal by eddies, the downgradient diffusive framework limits the structural accuracy of the parameterized fluxes, which in reality can contain significant upgradient and cross‐gradient components. Additionally, at eddy permitting resolutions, GM can negatively impact the resolved eddies, and is often turned off in regions where eddies are partially resolved. Here we present a novel data‐driven parameterization that is not constrained to be diffusive, and can capture the full structure of the eddy‐induced thickness fluxes while extracting APE and without overly negative impacts on the resolved flow. It is both flow‐aware and scale‐aware, and its magnitude can be tuned using an O(1) non‐dimensional number. Features like non‐dimensional inputs/outputs, lateral non‐locality, flow‐dependent coordinates, and range limitation improve the generalization of the data‐driven scheme. A small neural network is used, ensuring low cost and ease of implementation. The parameterization performs skillfully in offline evaluation, especially at scales smaller than the largest eddies. It is implemented in NOAA s MOM6 and is skillful in online tests in two‐layer idealized simulations of a zonal channel and a wind‐driven gyre, at eddy‐permitting and non‐eddying resolutions.

The accurate computation of pressure gradients in ocean models is essential for simulating ocean and climate processes. Inaccurate computation can result in spurious velocities on the order of real ocean flows, particularly in quiescent ice shelf cavities. We introduce improvements to a finite volume discretization of the pressure gradient force, required with a sloped ocean surface boundary beneath ice shelves and when model layers intersect with ice shelves and bathymetry. We demonstrate the sensitivity of pressure gradient force calculations to choices of sub‐grid cell pressure, density and geopotential distributions. Our method results in a marked improvement in the simulation of pressure gradient forces in idealized ice shelf cavities, with spurious velocities reduced to order m or smaller in quiet, linear stratification test cases. These velocities are substantially smaller than the magnitude of real ocean flows beneath ice shelf cavities, providing confidence in their simulated flows. Though we provide methods to reduce spontaneous motion from very thin ocean layers subject to numerical errors, these methods could be further improved, as could the small spurious flows that remain with nonlinear stratification.

We introduce FloeNet, a graph neural network trained to emulate the Geophysical Fluid Dynamics Laboratory global sea ice model, SIS2. FloeNet is a mass‐conserving model, emulating 6‐hr mass and area budget tendencies related to sea ice and snow‐on‐sea‐ice growth, melt, and advection. We train FloeNet using SIS2 data from a reanalysis‐forced ice‐ocean simulation and test its ability to generalize to pre‐industrial and 1% CO ₂ forcing conditions. FloeNet outperforms a non‐conservative model at reproducing sea ice and snow‐on‐sea‐ice mean state, trends, and inter‐annual variability, with volume anomaly correlations above 0.96 in the Antarctic and 0.76 in the Arctic, across all forcings. FloeNet also produces the correct thermodynamic‐dynamic response to forcing, enabling physical interpretability of emulator output. Finally, we show that FloeNet outputs high‐fidelity coupling‐related variables, including ice‐surface temperature, ice‐to‐ocean salt flux, and melting energy fluxes. We hypothesize that FloeNet will improve polar climate processes within existing atmosphere and ocean emulators.

Ocean circulations are strongly constrained by rotation and stratification, making potential vorticity (PV) a key dynamical property. Specifically, PV is conserved following water parcels in the absence of diabatic forcing and friction—a desirable feature for isopycnal ocean models. Here, we devise a finite‐volume discretization for PV fluxes in the vector‐invariant formulation of shallow‐water equations. The scheme adopts a seventh‐order weighted essentially non‐oscillatory reconstruction of PV on the Arakawa C‐grid while ensuring PV conservation. To prevent PV singularities arising from vanishing layer thickness—typical in isopycnal ocean models—we propose a thickness weighting for the PV reconstruction. The scheme is implemented in the Modular Ocean Model 6 (MOM6) dynamical core and tested through idealized simulations of baroclinic geostrophic turbulence and wind‐driven double gyres. Compared with existing discretizations in MOM6 that conserve energy and/or potential enstrophy, the new scheme not only substantially reduces dispersive errors but also yields a weak potential enstrophy dissipation near grid scales, and thus permits stable time integration without superfluous horizontal viscosity. Additionally, the scheme supports a strong inverse energy cascade and exhibits an elevated eddy kinetic energy. These properties in turn lead to more realistic ocean energetics in eddy‐permitting simulations for which the energy input by surface wind stress is dissipated through bottom drag. In terms of computational efficiency, the scheme leads to notable improvement in energy spectra in eddy‐permitting simulations with a minor increase in total cost by . Results here are promising for improving the simulation of ocean eddies and large‐scale circulations for climate applications.

Global ocean models exhibit biases in the mean state and variability, particularly at coarse resolution, where mesoscale eddies are unresolved. To address these biases, parameterization coefficients are typically tuned ad hoc. Here, we formulate parameter tuning as a calibration problem using Ensemble Kalman Inversion (EKI). We optimize parameters of a neural network parameterization of mesoscale eddies in two idealized ocean models at coarse resolution. The calibrated parameterization reduces errors in the time‐averaged fluid interfaces and their variability by factors of 1.7–3.3 compared to the unparameterized model, depending on the metric and configuration. The EKI method is robust to noise in time‐averaged statistics arising from chaotic ocean dynamics. Furthermore, we propose an efficient calibration protocol that bypasses integration to statistical equilibrium by carefully choosing an initial condition. These results demonstrate that systematic calibration can substantially improve coarse‐resolution ocean simulations and provide a practical pathway for reducing biases in global ocean models.

Traditional numerical global climate models simulate the full Earth system by exchanging boundary conditions between separate simulators of the atmosphere, ocean, sea ice, land surface, and other geophysical processes. This paradigm allows for distributed development of individual components within a common framework, unified by a coupler that handles translation between realms via spatial or temporal alignment and flux exchange. Following a similar approach adapted for machine learning‐based emulators, we present SamudrACE: a coupled global climate model emulator which produces centuries‐long simulations at 1‐degree horizontal, 6‐hourly atmospheric, and 5‐daily oceanic resolution, with 145 2D fields spanning 8 atmospheric and 19 oceanic vertical levels, plus sea ice, surface, and top‐of‐atmosphere variables. SamudrACE is highly stable and has low climate biases comparable to those of its components with prescribed boundary forcing, with realistic variability in coupled climate phenomena such as ENSO that is not possible to simulate in uncoupled mode.

Large ocean data assimilation (DA) increments are concentrated in the mixed layer, indicating persistent biases in vertical mixing. These increments can therefore be used to derive bias corrections. Previous studies developed full‐depth climatological temperature and salinity corrections from these increments, known as the Ocean Tendency Adjustment (OTA). In this work, we develop a machine learning (ML) model trained on DA outputs from the GFDL SPEAR system to predict state‐dependent temperature corrections within three mixed layer depths (3 × MLD), targeting vertical‐mixing biases. The trained ML model is implemented online in MOM6 to produce both DA simulations and free runs within the coupled SPEAR system. Compared with OTA, the ML scheme more effectively reduces upper‐ocean analysis increments in DA runs. In 10‐year free runs, the ML approach better represents mixed layer depth, reducing overly deep biases by capturing restratification. However, applying ML corrections alone degrades sea surface temperature (SST) climatology due to subsurface drift, reflecting processes not targeted by the mixed‐layer‐focused ML scheme. This drift can be mitigated by applying residual OTA corrections, which represent climatological DA increments not captured by the ML scheme. With this treatment, the ML correction scheme improves long‐term SST climatology and outperforms OTA. The workflow developed here is generalizable to any climate model with an ocean DA system and offers a promising pathway for reducing long‐standing model biases.

Neural networks offer novel ways to parameterize unresolved ocean mixing but are challenging to interpret. Here, we derive compact equations that reproduce the behavior of neural networks trained on a second‐moment closure data set. The resulting interpretable expressions employed in a physics‐based first order closure scheme match neural‐network performance in global forced simulations. They expose a structural error in the baseline physics‐based scheme and describe how surface friction velocity, buoyancy flux, rotation, and boundary layer depth regulate diffusivity. The equations reveal a shift in the mixing peak toward the surface under stabilizing conditions and toward the mid‐boundary layer depth under convective conditions. The diffusivity amplitude (set by the velocity scale) is controlled by surface shear and buoyancy flux. Equations yield a transparent, efficient, and physically grounded vertical diffusivity applicable for ocean models.

Surface mixed‐layer dynamics play a crucial role in modulating the climate as it is the oceanic layer that directly communicates with the atmosphere. The resolution of global ocean models is, however, often restricted to ; this is too coarse to adequately resolve mixed‐layer processes, and we depend on parametrizations. One of such parametrizations is the mixed‐layer eddy (MLE) parametrization. Here, we compare the performance of two MLE parametrizations [Fox‐Kemper et al. (2011, https://doi.org/10.1016/j.ocemod.2010.09.002 hereon BFF11) and Bodner et al. (2023, https://doi.org/10.1175/jpo-d-21-0297.1 hereon BOD23)], and document their impact in three global ocean simulations. Upon tuning, and diagnosing submesoscale‐permitting truth simulations, the MLE efficiency coefficient in BOD23 ranges between the values of 0.003–0.038, while 0.06 to 0.07 for BFF11. We find that the spatial distribution of mixed‐layer depth and ventilation of the abyssal ocean, using the ideal‐age tracer and Atlantic Meridional Overturning Circulation as its proxy, are sensitive to the interaction between MLE parametrizations and ocean surface boundary‐layer mixing schemes.