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We quantify the volume transport and watermass transformation rates of the global overturning circulation using the Estimating the Circulation and Climate of the Ocean version 4 release 4 (ECCOv4r4) reanalysis product. The ECCO solution shows large rates of intercell exchange between the mid‐depth and abyssal cells, consistent with other recent inferences. About 10 Sv of North Atlantic deep water enters the abyssal cell in the Southern Ocean and is balanced by a similar amount of apparrent diapycnal upwelling in the Indo‐Pacific. However, much of the upwelling in ECCO's deep ocean is not associated with irreversible watermass transformations, as typically assumed in theoretical models. Instead, a dominant portion of the abyssal circulation in ECCO is associated with isopycnal volume tendencies, reflecting a deep ocean in a state of change and a circulation in which transient tendencies play a leading role in the watermass budget. These volume tendencies are particularly prominent in the Indo‐Pacific, where ECCO depicts a cooling and densifying deep ocean with relatively little mixing‐driven upwelling, in disagreement with recent observations of deep Indo‐Pacific warming trends. Although abyssal ocean observations are insufficient to exclude the trends modeled by ECCO, we note that ECCO's parameterized diapycnal mixing in the abyssal ocean is much smaller than observational studies suggest and may lead to an under‐representation of Antarctic Bottom Water consumption in the abyssal ocean. Whether or not ECCO's tendencies are realistic, they are a key part of its abyssal circulation and hence need to be taken into consideration when interpreting the ECCO solution. Plain Language Summary: We analyze results taken from the Estimating the Circulation and Climate of the Ocean (ECCO) state estimate in order to investigate the internal structure and watermass budget of the global ocean's large‐scale circulation. The ECCO solution supports the modern view of an interconnected global ocean with substantial exchange between the overturning circulation of the Atlantic and that of the Indo‐Pacific via the Southern Ocean. However, our investigation also reveals that the density structure of much of the deep ocean in the ECCO product is in a state of change, and that these changes play a key role in the watermass budget of the circulation. These results reveal disagreement between the model's representation of the deep ocean and the prevailing theoretical depictions of the ocean's large‐scale circulation, which generally assume that the circulation is in a steady state. Disagreement between ECCO's deep ocean mixing rates and independent estimates indicate that the trends in ECCO may be biased, but deep ocean observations are insufficient to conclusively infer the true trends. Key Points: The meridional overturning circulation (MOC) in Estimating the Circulation and Climate of the Ocean version 4 release 4 (ECCOv4r4) exhibits substantial linkage between the mid‐depth and abyssal cellsTransient isopycnal volume change plays a key role in the watermass budget of the MOC in ECCOECCO's transient interior state must be taken into account when interpreting its climatological state [ABSTRACT FROM AUTHOR]

There are two distinct parameterizations for the restratification effect of mesoscale eddies: the Greatbatch and Lamb (1990, GL90, https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485%5f1990%5f020%5f1634%5fopvmom%5f2%5f0%5fco%5f2.xml?tab%5fbody=abstract-display) parameterization, which mixes horizontal momentum in the vertical, and the Gent and McWilliams (1990, GM90, https://journals.ametsoc.org/view/journals/phoc/20/1/1520-0485%5f1990%5f020%5f0150%5fimiocm%5f2%5f0%5fco%5f2.xml) parameterization, which flattens isopycnals adiabatically. Even though these two parameterizations are effectively equivalent under the assumption of quasi‐geostrophy, GL90 has been used much less than GM90, and exclusively in z‐coordinate models. In this paper, we compare the GL90 and GM90 parameterizations in an idealized isopycnal coordinate model, both from a theoretical and practical perspective. From a theoretical perspective, GL90 is more attractive than GM90 for isopycnal coordinate models because GL90 provides an interpretation that is fully consistent with thickness‐weighted isopycnal averaging, while GM90 cannot be entirely reconciled with any fully isopycnal averaging framework. From a practical perspective, the GL90 and GM90 parameterizations lead to extremely similar energy levels, flow and vertical structure, even though their energetic pathways are very different. The striking resemblance between the GL90 and GM90 simulations persists from non‐eddying through eddy‐permitting resolution. We conclude that GL90 is a promising alternative to GM90 for isopycnal coordinate models, where it is more consistent with theory, computationally more efficient, easier to implement, and numerically more stable. Assessing the applicability of GL90 in realistic global ocean simulations with hybrid coordinate schemes should be a priority for future work. Plain Language Summary: Ocean models are complex simulations run on large supercomputers, and are useful for predicting changes in ocean circulation and climate. Ocean models divide the globe into grid cells. Choosing many, very small grid cells is not feasible because the simulations would take too much time and would be too expensive. Therefore, the grid cells in most ocean models are not small enough to simulate mesoscale eddies. Mesoscale eddies are swirling motions that are less than 100 km wide and play an important role in transporting heat and carbon throughout the ocean. To still account for the effects of mesoscale eddies, one can use approximate "parameterizations." Which parameterization is "best" is an ongoing research question. This paper compares two parameterizations that simulate the effect of mesoscale eddies in two distinct ways: the commonly used Gent and McWilliams (1990, https://journals.ametsoc.org/view/journals/phoc/20/1/1520-0485%5f1990%5f020%5f0150%5fimiocm%5f2%5f0%5fco%5f2.xml) parameterization and the less commonly used Greatbatch and Lamb (1990, https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485%5f1990%5f020%5f1634%5fopvmom%5f2%5f0%5fco%5f2.xml?tab%5fbody=abstract-display) parameterization. This paper shows that the two parameterizations impact ocean circulation in a very similar way, and that for a certain class of models the Greatbatch and Lamb (1990, https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485%5f1990%5f020%5f1634%5fopvmom%5f2%5f0%5fco%5f2.xml?tab%5fbody=abstract-display) parameterization has advantages because it is more consistent with physical and mathematical theory, is easier to code, and leads to faster computations. Key Points: We compare the Greatbatch and Lamb (1990, GL90, https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485%5f1990%5f020%5f1634%5fopvmom%5f2%5f0%5fco%5f2.xml?tab%5fbody=abstract-display) and the Gent and McWilliams (1990, GM90, https://journals.ametsoc.org/view/journals/phoc/20/1/1520-0485%5f1990%5f020%5f0150%5fimiocm%5f2%5f0%5fco%5f2.xml) parameterizations in an isopycnal ocean modelGL90 leads to very similar flow as GM90, for non‐eddying through eddy‐permitting resolutionWe argue, however, that for isopycnal coordinate models GL90 is more consistent with theory than GM90 [ABSTRACT FROM AUTHOR]

Energy exchanges between large-scale ocean currents and mesoscale eddies play an important role in setting the large-scale ocean circulation but are not fully captured in models. To better understand and quantify the ocean energy cycle, we apply along-isopycnal spatial filtering to output from an isopycnal 1/32° primitive equation model with idealized Atlantic and Southern Ocean geometry and topography. We diagnose the energy cycle in two frameworks: 1) a non-thickness-weighted framework, resulting in a Lorenz-like energy cycle, and 2) a thickness-weighted framework, resulting in the Bleck energy cycle. This paper shows that framework 2 is more useful for studying energy pathways when an isopycnal average is used. Next, we investigate the Bleck cycle as a function of filter scale. Baroclinic conversion generates mesoscale eddy kinetic energy over a wide range of scales and peaks near the deformation scale at high latitudes but below the deformation scale at low latitudes. Away from topography, an inverse cascade transfers kinetic energy from the mesoscales to larger scales. The upscale energy transfer peaks near the energy-containing scale at high latitudes but below the deformation scale at low latitudes. Regions downstream of topography are characterized by a downscale kinetic energy transfer, in which mesoscale eddies are generated through barotropic instability. The scale- and flow-dependent energy pathways diagnosed in this paper provide a basis for evaluating and developing scale- and flow-aware mesoscale eddy parameterizations. Significance Statement: Blowing winds provide a major energy source for the large-scale ocean circulation. A substantial fraction of this energy is converted to smaller-scale eddies, which swirl through the ocean as sea cyclones. Ocean turbulence causes these eddies to transfer part of their energy back to the large-scale ocean currents. This ocean energy cycle is not fully simulated in numerical models, but it plays an important role in transporting heat, carbon, and nutrients throughout the world's oceans. The purpose of this study is to quantify the ocean energy cycle by using fine-scale idealized numerical simulations of the Atlantic and Southern Oceans. Our results provide a basis for how to include unrepresented energy exchanges in coarse global climate models. [ABSTRACT FROM AUTHOR]

We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence. [ABSTRACT FROM AUTHOR]

Building on previous work using single-basin models, we here explore the time-dependent response of the Atlantic meridional overturning circulation (AMOC) to a sudden global temperature change in a two-basin ocean–ice model. We find that the previously identified mechanisms remain qualitatively useful to explain the transient and the long-term time-mean responses of the AMOC in our simulations. Specifically, we find an initial weakening of the AMOC in response to warming (and vice versa for cooling), controlled by the mid-depth meridional temperature contrast across the Atlantic basin. The long-term mean response instead is controlled primarily by changes in the abyssal stratification within the basin. In contrast to previous studies we find that for small-amplitude surface temperature changes, the equilibrium AMOC is almost unchanged, as the abyssal stratification remains similar due to a substantial compensation between the effects of salinity and temperature changes. The temperature-driven stratification change results from the differential warming/cooling between North Atlantic Deep Water and Antarctic Bottom Water, while the salinity change is driven by changes in Antarctic sea ice formation. Another distinct feature of our simulations is the emergence of AMOC variability in the much colder and much warmer climates. We discuss how this variability is related to variations in deep-ocean heat content, surface salinity, and sea ice in the deep convective regions, both in the North Atlantic and in the Southern Ocean, and its potential relevance to past and future climates. [ABSTRACT FROM AUTHOR]

Changes in the Southern Ocean (SO) surface wind stress influence both the meridional overturning circulation (MOC) and stratification not only in the SO but in the global oceans, which can take multiple millennia to fully equilibrate. We use a hierarchy of models to investigate the time-dependent response of the MOC and low-latitude pycnocline depth (which quantifies the stratification) to SO wind stress changes: a two-layer analytical theory, a multicolumn model (PyMOC), and an idealized general circulation model (GCM). We find that in both the GCM and PyMOC, the MOC has a multidecadal adjustment time scale while the pycnocline depth has a multicentennial time scale. The two-layer theory instead predicts the MOC and pycnocline depth to adjust on the same, multidecadal time scale. We argue that this discrepancy arises because the pycnocline depth depends on the bulk stratification, while the MOC amplitude is sensitive mostly to isopycnals within the overturning cell. We can reconcile the discrepancy by interpreting the "pycnocline depth" in the theory as the depth of a specific isopycnal near the maximum of the MOC. We also find that SO stationary eddies respond very quickly to a sudden wind stress change, compensating for most of the change in the Ekman-driven MOC. This effect is missing in the theory, where the eddy-induced MOC only follows the adjustment of the pycnocline depth. Our results emphasize the importance of depth dependence in the oceans' transient response to changes in surface boundary conditions, and the distinct role played by stationary eddies in the SO. Significance Statement: Our work resolves the question of why previous theories predict the ocean density structure to adjust to a change in the winds over the Southern Ocean within centuries, while climate models indicate that this adjustment takes thousands of years. The question is important because it is related to our understanding of how the ocean responds to potential climate change scenarios. Our results emphasize the importance of depth dependence in the density response (i.e., the upper ocean adjusts faster than the deep ocean), suggesting that future theoretical advancement should be made with careful considerations of the ocean's vertical structure. Our results also highlight the role of stationary meanders in the Southern Ocean's Antarctic Circumpolar Current, whose influence has not been included in the existing theories. [ABSTRACT FROM AUTHOR]

A toy model for the deep ocean overturning circulation in multiple basins is presented and applied to study the role of buoyancy forcing and basin geometry in the ocean's global overturning. The model reproduces the results from idealized general circulation model simulations and provides theoretical insights into the mechanisms that govern the structure of the overturning circulation. The results highlight the importance of the diabatic component of the meridional overturning circulation (MOC) for the depth of North Atlantic Deep Water (NADW) and for the interbasin exchange of deep ocean water masses. This diabatic component, which extends the upper cell in the Atlantic below the depth of adiabatic upwelling in the Southern Ocean, is shown to be sensitive to the global area-integrated diapycnal mixing rate and the density contrast between NADW and Antarctic Bottom Water (AABW). The model also shows that the zonally averaged global overturning circulation is to zeroth-order independent of whether the ocean consists of one or multiple connected basins, but depends on the total length of the southern reentrant channel region (representing the Southern Ocean) and the global ocean area integrated diapycnal mixing. Common biases in single-basin simulations can thus be understood as a direct result of the reduced domain size. [ABSTRACT FROM AUTHOR]

Earth system models (ESMs) project that global warming suppresses biological productivity in the Subarctic Atlantic Ocean as increasing ocean surface buoyancy suppresses two physical drivers of nutrient supply: vertical mixing and meridional circulation. However, the quantitative sensitivity of productivity to surface buoyancy is uncertain and the relative importance of the physical drivers is unknown. Here, we present a simple predictive theory of how mixing, circulation, and productivity respond to increasing surface buoyancy in 21st-century global warming scenarios. With parameters constrained by observations, the theory suggests that the reduced northward nutrient transport, owing to a slower ocean circulation, explains the majority of the reduced productivity in a warmer climate. The theory also informs present-day biases in a set of ESM simulations as well as the physical underpinnings of their 21st-century projections. Hence, this theoretical understanding can facilitate the development of improved 21st-century projections of marine biogeochemistry and ecosystems. [ABSTRACT FROM AUTHOR]

A subgrid‐scale eddy parameterization is developed, which makes use of an explicit eddy kinetic energy budget and can be applied at both "non‐eddying" and "eddy‐permitting" resolutions. The subgrid‐scale eddies exchange energy with the resolved flow in both directions via a parameterization of baroclinic instability (based on the established formulation of Gent and McWilliams) and biharmonic and negative Laplacian viscosity terms. This formulation represents the turbulent cascades of energy and enstrophy consistent with our current understanding of the turbulent eddy energy cycle. At the same time, the approach is simple and general enough to be readily implemented in ocean climate models, without adding significant computational cost. The closure has been implemented in the Modular Ocean Model Version 6 and tested in the "Neverworld" configuration, which employs an idealized analytically defined topography designed as a testbed for mesoscale eddy parameterizations. The parameterization performs well over a range of resolutions, seamlessly connecting non‐eddying and eddy‐resolving regimes. Key Points: A scale‐aware energy budget‐based eddy parameterization is introducedBidirectional energy transfer between resolved flow and subgrid scales can be representedThe parameterization allows for a smooth transition between non‐eddying and eddying resolution regimes [ABSTRACT FROM AUTHOR]

Changes in deep-ocean circulation and stratification have been argued to contribute to climatic shifts between glacial and interglacial climates by affecting the atmospheric carbon dioxide concentrations. It has been recently proposed that such changes are associated with variations in Antarctic sea ice through two possible mechanisms: an increased latitudinal extent of Antarctic sea ice and an increased rate of Antarctic sea ice formation. Both mechanisms lead to an upward shift of the Atlantic meridional overturning circulation (AMOC) above depths where diapycnal mixing is strong (above 2000 m), thus decoupling the AMOC from the abyssal overturning circulation. Here, these two hypotheses are tested using a series of idealized two-basin ocean simulations. To investigate independently the effect of an increased latitudinal ice extent from the effect of an increased ice formation rate, sea ice is parameterized as a latitude strip over which the buoyancy flux is negative. The results suggest that both mechanisms can effectively decouple the two cells of the meridional overturning circulation (MOC), and that their effects are additive. To illustrate the role of Antarctic sea ice in decoupling the AMOC and the abyssal overturning cell, the age of deep-water masses is estimated. An increase in both the sea ice extent and its formation rate yields a dramatic "aging" of deep-water masses if the sea ice is thick and acts as a lid, suppressing air–sea fluxes. The key role of vertical mixing is highlighted by comparing results using different profiles of vertical diffusivity. The implications of an increase in water mass ages for storing carbon in the deep ocean are discussed. [ABSTRACT FROM AUTHOR]

Increasing computational resources are starting to allow global ocean simulations at so-called “eddy-permitting” resolutions, at which the largest mesoscale eddies can be resolved explicitly. However, an adequate parameterization of the interactions with the unresolved part of the eddy energy spectrum remains crucial. Hyperviscous closures, which are commonly applied in eddy-permitting ocean models, cause spurious energy dissipation at these resolutions, leading to low levels of eddy kinetic energy (EKE) and weak eddy induced transports. It has recently been proposed to counteract the spurious energy dissipation of hyperviscous closures by an additional forcing term, which represents “backscatter” of energy from the un-resolved scales to the resolved scales. This study proposes a parameterization of energy backscatter based on an explicit sub-grid EKE budget. Energy dissipated by hyperviscosity acting on the resolved flow is added to the sub-grid EKE, while a backscatter term transfers energy back from the sub-grid EKE to the resolved flow. The backscatter term is formulated deterministically via a negative viscosity, which returns energy at somewhat larger scales than the hyperviscous dissipation, thus ensuring dissipation of enstrophy. The parameterization is tested in an idealized configuration of a primitive equation ocean model, and is shown to significantly improve the solutions of simulations at typical eddy-permitting resolutions. [ABSTRACT FROM AUTHOR]