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Abstract Surface and upper-ocean measurements of mesoscale eddies have revealed the central role they play in ocean transport, but their interior and deep ocean characteristics remain undersampled and underexplored. In this study, mooring arrays, sampling with high vertical resolution, and a high-resolution global atmosphere–ocean coupled simulation are used to characterize full-depth mesoscale eddy vertical structure. The vertical structure of eddy kinetic energy, e.g., partitioning of barotropic to baroclinic eddy kinetic energy or vertical modal structure, is shown to depend partly on bathymetric slope and roughness. This influence is contextualized alongside additional factors, such as latitude and vertical density stratification, to present a global landscape of vertical structure. The results generally reveal eddy vertical structure to decay with increasing depth, consistent with theoretical expectations relating to the roles of surface-intensified stratification and buoyancy anomalies. However, at high latitudes and where the seafloor is markedly flat and smooth (approximately 20% of the ocean’s area), mesoscale eddy vertical structures are significantly more barotropic by an approximate factor of 2–5. From a climate modeling perspective, these results can inform the construction, implementation, and improvement of energetic parameterizations that account for the underrepresentation of mesoscale eddies and their effects. They also offer expectation as to a landscape of eddy vertical structure to be used in inferring vertical structure from surface measurements. Significance StatementThis work addresses the question of how do ocean seafloor features (bathymetry) affect the vertical structure of ocean currents and eddies? Seafloor features modify eddies in complex ways not often accounted for in global ocean simulations. We analyze high-resolution velocity observations, find diverse structures at four mooring sites, and consider how sloping and rough bathymetry change distributions of eddy kinetic energy throughout the water column. Comparison to theory and model output reveals a relationship between vertical structure and bathymetry. These results show that vertical structures vary significantly with bathymetry, density stratification, and latitude and contribute to model development efforts to reproduce the effects of eddy turbulence without explicit representation. These results also enhance interpretations of more numerous surface observations. 

Abstract This paper is Part II of a two‐part paper that documents the Climate Model version 4X (CM4X) hierarchy of coupled climate models developed at the Geophysical Fluid Dynamics Laboratory. Part I of this paper is presented in Griffies et al. (2025a,https://doi.org/10.1029/2024MS004861). Here we present a suite of case studies that examine ocean and sea ice features that are targeted for further research, which include sea level, eastern boundary upwelling, Arctic and Southern Ocean sea ice, Southern Ocean circulation, and North Atlantic circulation. The case studies are based on experiments that follow the protocol of version 6 from the Coupled Model Intercomparison Project. The analysis reveals a systematic improvement in the simulation fidelity of CM4X relative to its CM4.0 predecessor, as well as an improvement when refining the ocean/sea ice horizontal grid spacing from the of CM4X‐p25 to the of CM4X‐p125. Even so, there remain many outstanding biases, thus pointing to the need for further grid refinements, enhancements to numerical methods, and/or advances in parameterizations, each of which target long‐standing model biases and limitations. 

Abstract Recent scaling theories for the eddy fluxes in the two-layer quasigeostrophic (QG) model assume a flat-bottom boundary. Here, we discuss an organizing principle for how rough topography (i.e., topography with length scales similar to or smaller than the eddy scale) modifies the fully developed state of baroclinic turbulence. In particular, we focus on random, homogeneous topography in the two-layer QG model on anfplane, forced by a zonal shear and dissipated by linear drag. We present a suite of numerical simulations using idealized monoscale topography, systematically modifying the topographic length and height scales and the strength of the drag. We outline the dependence of the eddy diffusivityD, barotropic eddy energyE, and eddy mixing length, on the two nondimensional control parameters:, controlling the strength of the drag, and, controlling the strength of topographic–advective interactions. Two distinct regimes are identified and quantitatively predicted by a regime transition parameterα, which depends on bothand. Onceαsurpasses ancritical value, all eddy scales are reduced below their flat-bottom values and become much less sensitive to the drag coefficient. Spectral energy budgets reveal that energy pathways are importantly reorganized in this regime compared to the flat-bottom limit. We show how this phenomenology extends to more realistic, multiscale topography and to three-layer QG simulations. 

Abstract We present the GFDL‐CM4X (Geophysical Fluid Dynamics Laboratory Climate Model version 4X) coupled climate model hierarchy. The primary application for CM4X is to investigate ocean and sea ice physics as part of a realistic coupled Earth climate model. CM4X utilizes an updated MOM6 (Modular Ocean Model version 6) ocean physics package relative to CM4.0, and there are two members of the hierarchy: one that uses a horizontal grid spacing of (referred to as CM4X‐p25) and the other that uses a grid (CM4X‐p125). CM4X also refines its atmospheric grid from the nominally 100 km (cubed sphere C96) of CM4.0–50 km (C192). Finally, CM4X simplifies the land model to allow for a more focused study of the role of ocean changes to global mean climate. CM4X‐p125 reaches a global ocean area mean heat flux imbalance of within years in a pre‐industrial simulation, and retains that thermally equilibrated state over the subsequent centuries. This 1850 thermal equilibrium is characterized by roughly less ocean heat than present‐day, which corresponds to estimates for anthropogenic ocean heat uptake between 1870 and present‐day. CM4X‐p25 approaches its thermal equilibrium only after more than 1000 years, at which time its ocean has roughlymoreheat than its early 21st century ocean initial state. Furthermore, the root‐mean‐square sea surface temperature bias for historical simulations is roughly 20% smaller in CM4X‐p125 relative to CM4X‐p25 (and CM4.0). We offer themesoscale dominance hypothesisfor why CM4X‐p125 shows such favorable thermal equilibration properties. 

Abstract Mesoscale eddies modulate the stratification, mixing, tracer transport, and dissipation pathways 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: (a) both the potential and kinetic energy effects of eddies may be parameterized via a kinetic energy backscatter, with no Gent‐McWilliams along‐isopycnal transport; (b) a dominant factor in ensuring a physically‐accurate backscatter is the vertical structure of the parameterized momentum fluxes. We present simulations of 1/2° and 1/4° 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° reference solution. Our work provides guidance on how to parameterize mesoscale eddy effects in the challenging eddy‐permitting regime. 

Abstract The use of coarse resolution and strong grid‐scale dissipation has prevented global ocean models from simulating the correct kinetic energy level. Recently parameterizing energy backscatter has been proposed to energize the model simulations. Parameterizing backscatter reduces long‐standing North Atlantic sea surface temperature (SST) and associated surface current biases, but the underlying mechanism remains unclear. Here, we apply backscatter in different geographic regions to distinguish the different physical processes at play. We show that an improved Gulf Stream path is due to backscatter acting north of the Grand Banks to maintain a strong deep western boundary current. An improved North Atlantic Current path is due to backscatter acting around the Flemish Cap, with likely an improved nearby topography‐flow interactions. These results suggest that the SST improvement with backscatter is partly due to the resulted strengthening of resolved currents, whereas the role of improved eddy physics requires further research. 

Abstract Coupled climate simulations that span several hundred years cannot be run at a high‐enough spatial resolution to resolve mesoscale ocean dynamics. Recently, several studies have considered Deep Learning to parameterize subgrid forcing within macroscale ocean equations using data from ocean‐only simulations with idealized geometry. We present a stochastic Deep Learning parameterization that is trained on data generated by CM2.6, a high‐resolution state‐of‐the‐art coupled climate model. We train a Convolutional Neural Network for the subgrid momentum forcing using macroscale surface velocities from a few selected subdomains with different dynamical regimes. At each location of the coarse grid, rather than predicting a single number for the subgrid momentum forcing, we predict both the mean and standard deviation of a Gaussian probability distribution. This approach requires training our neural network to minimize a negative log‐likelihood loss function rather than the Mean Square Error, which has been the standard in applications of Deep Learning to the problem of parameterizations. Each estimate of the conditional mean subgrid forcing is thus associated with an uncertainty estimate–the standard deviation—which will form the basis for a stochastic subgrid parameterization. Offline tests show that our parameterization generalizes well to the global oceans and a climate with increasedlevels without further training. We then implement our learned stochastic parameterization in an eddy‐permitting idealized shallow water model. The implementation is stable and improves some statistics of the flow. Our work demonstrates the potential of combining Deep Learning tools with a probabilistic approach in parameterizing unresolved ocean dynamics. 

Abstract The resolution of climate models is limited by computational cost. Therefore, we must rely on parameterizations to represent processes occurring below the scale resolved by the models. Here, we focus on parameterizations of ocean mesoscale eddies and employ machine learning (ML), namely, relevance vector machines (RVMs) and convolutional neural networks (CNNs), to derive computationally efficient parameterizations from data, which are interpretable and/or encapsulate physics. In particular, we demonstrate the usefulness of the RVM algorithm to reveal closed‐form equations for eddy parameterizations with embedded conservation laws. When implemented in an idealized ocean model, all parameterizations improve the statistics of the coarse‐resolution simulation. The CNN is more stable than the RVM such that its skill in reproducing the high‐resolution simulation is higher than the other schemes; however, the RVM scheme is interpretable. This work shows the potential for new physics‐aware interpretable ML turbulence parameterizations for use in ocean climate models.