Ocean mesoscale eddies constitute a crucial component of ocean energy cascade, engaging in energy exchange with large-scale circulations, submesoscale eddies, and internal waves. State-of-the-art ocean climate models, which partially resolve mesoscale eddies (i.e., eddy-permitting), often exhibit weaker and more surface-intensified eddy kinetic energy (EKE) than in higher-resolution simulations and observations. The energy backscatter scheme has been employed in eddy-permitting simulations to enhance the energy of mesoscale eddies by compensating for the excessive dissipation caused by the viscosity closure. In this scheme, a proper vertical structure for the backscatter coefficient is necessary to simulate a more realistic vertical distribution of kinetic energy. Here we propose a parameterization for the vertical structure of subgrid EKE and implement it within the backscatter scheme in idealized eddy-permitting simulations of MOM6. The parameterization is grounded in the observation that the EKE is surface-intensified and decays faster with depth at smaller horizontal scales. The diagnosed vertical structure of EKE from eddy-resolving simulations is well-captured by surface quasi-geostrophic (SQG) modes, whose vertical structure depends on the eddy horizontal scale, Coriolis parameter, and stratification profile. Based on the SQG mode, we formulate a scale-aware parameterization of the vertical structure, accounting for the variation of subgrid eddy scale with the model horizontal grid spacing. This vertical structure is then applied to the energy backscatter coefficient used in 1/2° and 1/4° idealized simulations of basin-scale ocean circulations. The diagnostics of these eddy-permitting simulations are compared to those of a 1/32° reference simulation. The inclusion of the vertical structure in the backscatter improves the simulation of global kinetic energy distributions, large-scale circulation pathways, and isopycnal structures, compared with the eddy-permitting simulations without backscatter or with a depth-independent backscatter. Sensitivity tests show that a more surface-intensified backscatter tends to result in weaker total kinetic energy and more tilted isopycnals. This work provides insights into the parameterization of mesoscale energetics and its vertical variation in eddy-permitting simulations.

Our ability to characterize and quantify the complex uncertainties surrounding future sea-level changes is crucial for coastal risk assessments and adaptation strategies. This study focuses on the role of steric and dynamic changes (i.e., sterodynamics) in sea level projections, particularly regarding their contribution to the uncertainty of global and regional sea level changes in relation to other components such as ice sheet dynamics. A probabilistic framework is used to estimate probability distributions of sea-level change for each component. Through variance decomposition, the total uncertainty in sea-level change is dissected into its constituent sources. Subsequently, the relative contribution of sterodynamics uncertainty is quantified across various regions, time frames, emission scenarios, and projection methodologies utilized to estimate future sea-level distributions. The contribution of sterodynamics to overall uncertainty reduces over time as the contribution from ice sheets becomes more pronounced. The spatiotemporal pattern of sterodynamic significance is not strongly dependent on future greenhouse gas emissions, yet its overall role is highly dependent on the representation (e.g., emulation) of ice sheets. When high-end, low-probability estimates of future Antarctic ice sheet contributions are excluded, sterodynamics remain a dominant source of regional sea-level uncertainty at the end of this century, particularly along the US East Coast and European coast. These regions are also identified as hotspots for future sea-level rise, indicating that sterodynamic processes will play a significant role in assessing coastal vulnerabilities there. This study suggests that ocean model development can most effectively reduce the overall uncertainty in future sea-level projections by focusing on these areas.

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.

Water Mass Transformation (WMT) theory provides conceptual tools that in principle enable innovative analyses of numerical ocean models; in practice, however, these methods can be challenging to implement and interpret, and therefore remain under‐utilized. Our aim is to demonstrate the feasibility of diagnosing all terms in the water mass budget and to exemplify their usefulness for scientific inquiry and model development by quantitatively relating water mass changes, overturning circulations, boundary fluxes, and interior mixing. We begin with a pedagogical derivation of key results of classical WMT theory. We then describe best practices for diagnosing each of the water mass budget terms from the output of Finite‐Volume Generalized Vertical Coordinate (FV‐GVC) ocean models, including the identification of a non‐negligible remainder term as the spurious numerical mixing due to advection scheme discretization errors. We illustrate key aspects of the methodology through the analysis of a polygonal region of the Greater Baltic Sea in a regional demonstration simulation using the Modular Ocean Model v6 (MOM6). We verify the convergence of our WMT diagnostics by brute‐force, comparing time‐averaged (“offline”) diagnostics on various vertical grids to timestep‐averaged (“online”) diagnostics on the native model grid. Finally, we briefly describe a stack of xarray‐enabled Python packages for evaluating WMT budgets in FV‐GVC models (culminating in the new xwmb package), which is intended to be model‐agnostic and available for community use and development.

We use a three-layer quasigeostrophic model to study the effects of sloping bottom topography on baroclinic instability in an ocean-like setting. Three layers allow for an interior potential vorticity gradient, a feature that is precluded by the use of a two-layer model. Material conservation of quasigeostrophic potential vorticity (QG PV) is expressed in terms of sloping background density interfaces, perturbations to the sloping interfaces, and the bottom slope. Linear stability analysis and numerical simulations of initial linear growth are used to demonstrate the dependence of topographic modifications to baroclinically unstable modes on background shear and stratification. Instabilities are classified according to their vertical structure, and the nature of topographic modification to baroclinically unstable modes is shown to correspond to instability type. Surface-intensified vertical shear of the background flow supports surface-intensified baroclinic instability that is less sensitive to bottom topography, compared to uniformly sheared background flow. When background shear is constant or close-to-constant, topography has a leading order effect on the vertical structure of the most baroclinically unstable mode. Upper-ocean stratification changes the lateral and vertical scales of the most unstable mode, with weaker upper-ocean stratification supporting high-wavenumber surface-intensified baroclinically unstable modes that are less sensitive to topography. We also present and assess a novel criterion that predicts the degree of surface intensification of the fastest-growing baroclinically unstable mode using only prescribed background properties, highlighting the role of interior potential vorticity in setting the most unstable mode's vertical structure. SIGNIFICANCE STATEMENT: Mesoscale eddies dominate ocean transient kinetic energy at time scales longer than a few days, playing a critical role in ocean dynamics, ocean biogeochemistry, and the climate system. Ocean eddies not captured by a model's resolution are represented through parameterizations. The changing strength of an eddy with depth, an important aspect of realistic parameterizations, has been attributed to the baroclinic instability that generates the eddy. We use a three-layer model to demonstrate and explain the essential mechanics of the vertical structure of baroclinic instability and clarify the relative roles of upper-ocean mean flow, upper-ocean stratification, and sloping bottom topography. We exhibit the importance of interior ocean dynamics when studying topographic effects on vertical structure, a feature precluded by two-layer models.

Understanding regional sea level variability is vital for assessing coastal risks beyond global mean sea level rise. While thermal expansion and meltwater dominate long-term changes, high-frequency sea level anomalies driven by atmospheric forcing contribute to coastal impacts. Using tide gauge observations and a hierarchy of global climate models (GFDL-CM4X; Griffies et al., JAMES, in review) with varying atmospheric (100km, 50km) and ocean (0.25-degree, 0.125-degree) horizontal grid spacing, we investigate how sea level variability and associated atmospheric drivers may change under a high emissions climate warming scenario (SSP5-8.5) for three time periods: 1993-2014, 2015-2034, and 2080-2099. Analysis of sea surface height (SSH) variability along the U.S. East Coast reveals that winter extreme sea level events are typically associated with Rex-block configurations which are characterized by high-pressure systems over Québec and offshore low-pressure systems. While the strength of the pressure gradient between the two weather systems remains consistent through the end of the century, the frequency of atmospheric blocking and storm events is projected to decrease by 2080-2099, particularly in higher-resolution models. Daily sea level variability declines across the model hierarchy, with varying contributions from inverse barometer effects depending on model resolution. The higher atmospheric resolution CM4X models suggest an emerging relationship between sea surface height anomalies and synoptic-scale pressure gradients by 2080-2099. This work demonstrates the importance of both atmospheric and ocean resolution in simulating coastal sea level variability and has important implications for understanding and predicting extreme sea level events in the future.

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 roughly more heat 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 the mesoscale dominance hypothesis for why CM4X-p125 shows such favorable thermal equilibration properties.

We assess the response of Antarctic sea ice, the Southern Ocean, and global climate to mass loss from the Antarctic continent in a new multi-model ensemble. Antarctic ice-mass loss from ice sheets and ice shelves is increasing and is projected to increase further as the climate warms. The fresh water entering the Southern Ocean due to this ice-mass loss has been proposed as a mechanism responsible for the lack of decline in Antarctic sea ice area between 1979 and 2015, in contrast to the sea-ice loss seen in the Arctic. The fresh water impacts sea ice by increasing the density gradient between the near-surface waters and deeper waters around the Antarctic continent, which inhibits vertical transport of warmer, deeper water to the surface. This results in surface cooling and increased sea ice growth, as has been shown in previous studies. Though this increased Antarctic ice-mass loss is expected to impact climate it is absent from almost all models in the current Coupled Model Intercomparison Project (CMIP6), which typically enforce that the continent remain in perpetual mass balance, with no gain or loss of mass over time. Further, previous non-CMIP6 model experiments that include changing Antarctic ice-mass loss suggest that the climate response depends on the model used, and that the reasons for this model dependence are not clear. We present results from the Southern Ocean Freshwater Input from Antarctica (SOFIA) Initiative, an international model intercomparison, in which freshwater is added to the ocean surrounding Antarctica to simulate the otherwise missing ice-sheet mass loss. This unique suite of models allows us compare the response to Antarctic mass loss across climate models, identify reasons for model discrepancies, and quantify the potential impact of the absence of increasing Antarctic ice-mass loss on Antarctic sea ice and climate. We will give an overview of the SOFIA initiative including the experiment design and participating models. We will present results from the “antwater” experiment outlined in the SOFIA protocol in which a constant freshwater input of 0.1 Sv is distributed evenly around the Antarctic continent at the ocean surface in an experiment with pre-industrial control forcing. We show that there is a spread of up to a factor of 3 across models in the Antarctic sea ice area response to identical freshwater forcing. There are also substantial differences in the spatial pattern of the sea ice response depending on the model used. We explore the dependence of the response on the mean state of Antarctic sea ice and the Southern Ocean in the pre-industrial control runs, as well as the response of the ocean stratification and oceanic deep convection in the models. We also explore the seasonality of the sea ice and oceanic response.

We formulate a new conceptual model, named “MT2”, to describe global ocean heat uptake, as simulated by atmosphere–ocean general circulation models (AOGCMs) forced by increasing atmospheric CO _2 , as a function of global-mean surface temperature change T and the strength of the Atlantic meridional overturning circulation (AMOC, M). MT2 has two routes whereby heat reaches the deep ocean. On the basis of circumstantial evidence, we hypothetically identify these routes as low- and high-latitude. In low latitudes, which dominate the global-mean energy balance, heat uptake is temperature-driven and described by the two-layer model, with global-mean T as the temperature change of the upper layer. In high latitudes, a proportion p (about 14 ∙ Ocean heat uptake efficiency correlates strongly with the AMOC. ∙ Global ocean heat uptake is not correlated with the AMOC. ∙ Transient climate response (TCR) is anticorrelated with the AMOC. ∙ T projected for the late twenty-first century under high-forcing scenarios correlates more strongly with the effective climate sensitivity than with the TCR.

Density-driven steric seawater changes are a leading-order contributor to global mean sea level rise. However, intermodel differences in the magnitude and spatial patterns of steric sea level rise exist at regional scales and often emerge during the spinup and preindustrial control integrations of climate models. Steric sea level results from an eddy- permitting climate model, GFDL CM4, are compared with a lower-resolution counterpart, GFDL-ESM4. The results from both models are examined through basin-scale heat budgets and watermass analysis, and we compare the patterns of ocean heat uptake, redistribution, and sea level differ in ocean-only [i.e., Ocean Model Intercomparison Project (OMIP)] and coupled climate configurations. After correcting for model drift, both GFDL CM4 and GFDL-ESM4 simulate nearly equivalent ocean heat content change and global sea level rise during the historical period. However, the GFDL CM4 model exhibits as much as a 40% increase in surface ocean heat uptake in the Southern Ocean and subsequent increases in horizontal export to other ocean basins after bias correction. The results suggest regional differences in the processes governing Southern Ocean heat export, such as the formation of Antarctic Intermediate Water (AAIW), Subpolar Mode Water (SPMW), and gyre transport between the two models, and that sea level changes in these models cannot be fully bias-corrected. Since the process-level differences between the two models are evident in the preindustrial control simulations of both models, these results suggest that the control simulations are important for identifying and correcting sea level-related model biases.

Using a recently developed 1/12th degree regional ocean model, we establish a link between U.S. East Coast sea level variability and offshore upper ocean heat content change. This link manifests as a cross-shore mass redistribution driven by an offshore thermosteric sea level response to subsurface warming or cooling. Approximately 50% of simulated monthly to interannual coastal sea level variance south of Cape Hatteras can be statistically accounted for by this mechanism, realized as a function of regional ocean hypsometry, gyre scale warming, and the depth dependence of density change. This response to offshore warming explains the nonstationarity of U.S. East Coast sea level covariance, a specifically observed and modeled behavior after similar to ${\sim} $ 2010. Since approximately 2010, elevated rates of sea level rise south of Cape Hatteras can be partly explained as the result of shoreward mass redistribution due to offshore subsurface warming within the North Atlantic subtropical gyre. These results reveal a mechanism that connects local coastal sea level to a broader region and identifies the influence of regional heat content changes on coastal sea level. This analysis presents a framework for identifying new regions that may be susceptible to enhanced sea level rise due to ocean warming and helps bridge the gap between quantifying large scale change and anticipating local coastal impacts that can make flooding and storm surge more acutely damaging.

The vertical structure of ocean eddies is generally surface-intensified, commonly attributed to the dominant baroclinic modes arising from the boundary conditions (BCs). Conventional BC considerations mostly focus on either flat- or rough-bottom conditions. The impact of surface buoyancy anomalies—often represented by surface potential vorticity (PV) anomalies—has not been fully explored. Here, we study the role of the surface PV in setting the vertical distribution of eddy kinetic energy (EKE) in an idealized adiabatic ocean model driven by wind stress. The simulated EKE profile in the extra-tropical ocean tends to peak at the surface and have an e -folding depth typically smaller than half of the ocean depth. This vertical structure can be reasonably represented by a single surface quasi-geostrophic (SQG) mode at the energy-containing scale resulting from the large-scale PV structure. Due to isopycnal outcropping and interior PV homogenization, the surface meridional PV gradient is substantially stronger than the interior PV gradient, yielding surface-trapped baroclinically unstable modes with horizontal scales comparable to or smaller than the deformation radius. These surface-trapped eddies then grow in size both horizontally and vertically through an inverse energy cascade up to the energy-containing scale, which dominates the vertical distribution of EKE. As for smaller horizontal scales, the EKE distribution decays faster with depth. Guided by this interpretation, an SQG-based scale-aware parameterization of the EKE profile is proposed. Preliminary offline diagnosis of a high-resolution simulation shows the proposed scheme successfully reproducing the dependence of the vertical structure of EKE on the horizontal grid resolution.

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West Antarctic Ice Sheet mass loss is a major source of uncertainty in sea level projections. The primary driver of this melting is oceanic heat from Circumpolar Deep Water originating offshore in the Antarctic Circumpolar Current. Yet, in assessing melt variability, open ocean processes have received considerably less attention than those governing cross-shelf exchange. Here, we use Lagrangian particle release experiments in an ocean model to investigate the pathways by which Circumpolar Deep Water moves toward the continental shelf across the Pacific sector of the Southern Ocean. We show that Ross Gyre expansion, linked to wind and sea ice variability, increases poleward heat transport along the gyre’s eastern limb and the relative fraction of transport toward the Amundsen Sea. Ross Gyre variability, therefore, influences oceanic heat supply toward the West Antarctic continental slope. Understanding remote controls on basal melt is necessary to predict the ice sheet response to anthropogenic forcing.

Due to their limited resolution, numerical ocean models need to be interpreted as representing filtered or averaged equations. How to interpret models in terms of formally averaged equations, however, is not always clear, particularly in the case of hybrid or generalized vertical coordinate models. We derive the averaged hydrostatic Boussinesq equations in generalized vertical coordinates for an arbitrary thickness weighted-average. We then consider various special cases and discuss the extent to which the averaged equations are consistent with existing model formulations. As previously discussed, the momentum equations in existing depth-coordinate models are best interpreted as representing Eulerian averages (i.e., averages taken at fixed depth), while the tracer equations can be interpreted as either Eulerian or thickness-weighted isopycnal averages. Instead we find that no averaging is fully consistent with existing formulations of the parameterizations in semi-Lagrangian discretizations of generalized vertical coordinate ocean models. Perhaps the most natural interpretation of generalized vertical coordinate models is to assume that the average follows the model’s coordinate surfaces. However, the existing model formulations are generally not consistent with coordinate-following averages, which would require “coordinate-aware” parameterizations that can account for the changing nature of the eddy terms as the coordinate changes. Alternatively, the model variables can be interpreted as representing either Eulerian or (thickness-weighted) isopycnal averages, independent of the model coordinate that is being used for the numerical discretization. Existing parameterizations in generalized vertical coordinate models, however, are usually not fully consistent with either of these interpretations. We discuss what changes are needed to achieve consistency.

The climatological mean barotropic vorticity budget is analyzed to investigate the relative importance of surface wind stress, topography and nonlinear advection in dynamical balances in a global ocean simulation. In addition to a pronounced regional variability in vorticity balances, the relative magnitudes of vorticity budget terms strongly depend on the length-scale of interest. To carry out a length-scale dependent vorticity analysis in different ocean basins, vorticity budget terms are spatially filtered by employing the coarse-graining technique. At length-scales greater than 10o (or roughly 1000 km), the dynamics closely follow the Topographic-Sverdrup balance in which bottom pressure torque, surface wind stress curl and planetary vorticity advection terms are in balance. In contrast, when including all length-scales resolved by the model, bottom pressure torque and nonlinear advection terms dominate the vorticity budget (Topographic-Nonlinear balance), which suggests a prominent role of oceanic eddies, which are of Ο(10-100) km in size, and the associated bottom pressure anomalies in local vorticity balances at length-scales smaller than 1000 km. Overall, there is a transition from the Topographic-Nonlinear regime at scales smaller than 10o to the Topographic-Sverdrup regime at length-scales greater than 10o. These dynamical balances hold across all ocean basins; however, interpretations of the dominant vorticity balances depend on the level of spatial filtering or the effective model resolution. On the other hand, the contribution of bottom and lateral friction terms in the barotropic vorticity budget remains small and is significant only near sea-land boundaries, where bottom stress and horizontal friction generally peak.

Abstract Deficiencies in upper ocean vertical mixing parameterizations contribute to tropical upper ocean biases in global coupled general circulation models, affecting their simulated ocean heat uptake and ENSO variability. To better understand these deficiencies, we develop a suite of ocean model experiments including both idealized single column models and realistic global simulations. The vertical mixing parameterizations are first evaluated using large eddy simulations as a baseline to assess uncertainties and evaluate their implied turbulent mixing. Global models are then developed following NOAA/GFDL's 0.25° nominal horizontal grid spacing OM4 (uncoupled) configuration of the MOM6 ocean model, with various modifications that target biases in the original model. We test several enhancements to the existing mixing schemes and evaluate them against observational constraints from Tropical Atmosphere Ocean moorings and Argo floats. In particular, we find that we can improve the diurnal variability of mixing in OM4 via modifications to its surface boundary layer mixing scheme, and can improve the net mixing in the upper thermocline by reducing the background vertical viscosity, allowing for more realistic, less diffuse currents. The improved OM4 model better represents the mixing, leading to improved diurnal deep‐cycle variability, a more realistic time‐mean tropical thermocline structure, and a better Pacific Equatorial Undercurrent.

The Weddell Gyre is one of the dominant features of the Southern Ocean circulation and its dynamics have been linked to processes of climatic relevance. Variability in the strength of the gyre's horizontal transport has been linked to heat transport toward the Antarctic margins and changes in the properties and rates of export of bottom waters from the Weddell Sea region to the abyssal global ocean. However, the precise physical mechanisms that force variability in the Weddell's lateral circulation across different time scales remain unknown. In this study, we use a barotropic vorticity budget from a mesoscale eddy active model simulation to attribute changes in gyre strength to variability in possible driving processes. We find that the Weddell Gyre's circulation is sensitive to bottom friction associated with the overflowing dense waters at its western boundary. In particular, an increase in the production of dense waters at the southwestern continental shelf strengthens the bottom flow at the gyre's western boundary, yet this drives a weakening of the depth-integrated barotropic circulation via increased bottom friction. Strengthening surface winds initially accelerate the gyre, but within a few years the response reverses once dense water production and export increases. These results reveal that the gyre can weaken in response to stronger surface winds, putting into question the traditional assumption of a direct relationship between surface stress and gyre strength in regions where overflowing dense water forms part of the depth-integrated flow.

The data and scripts used to generate the figures in the manuscript "Remote versus local impacts of energy backscatter on the North Atlantic SST biases in a global ocean model".

The editors of Journal of Advances in Modeling Earth Systems thank the 702 reviewers who provided 1362 reviews during 2022. Their hard work and insights, typically done anonymously, benefits authors, readers, and the broader science community.