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A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates, and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer, rely on the assumption of statistical homogeneity or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique because of a gauge freedom. Here, it is argued that a Galilean-invariant subfilter-scale (SFS) flux is a suitable quantity to properly measure energy scale transfer in the ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale transfer of energy. The paper presents geographic maps of the energy scale transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions near the Gulf Stream and in the Equatorial Countercurrent have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extratropical energy scale transfer over regions of O (10 3 ) km in size.

Wind power inputs at the surface ocean are dissipated through smaller-scale processes in the ocean interior and turbulent boundary layer. Simulations suggest that seafloor topography enhances turbulent mixing and energy dissipation in the ocean interior. The ocean circulation is forced at a global scale by winds and fluxes of heat and fresh water. Kinetic energy is dissipated at much smaller scales in the turbulent boundary layers and in the ocean interior 1 , 2 , where turbulent mixing controls the transport and storage of tracers such as heat and carbon dioxide 3 , 4 . The primary site of wind power input is the Southern Ocean, where the westerly winds are aligned with the Antarctic Circumpolar Current 5 . The potential energy created here is converted into a vigorous geostrophic eddy field through baroclinic instabilities. The eddy energy can power mixing in the ocean interior 6 , 7 , 8 , but the mechanisms governing energy transfer to the dissipation scale are poorly constrained. Here we present simulations that simultaneously resolve meso- and submeso-scale motions as well as internal waves generated by topography in the Southern Ocean. In our simulations, more than 80% of the wind power input is converted from geostrophic eddies to smaller-scale motions in the abyssal ocean. The conversion is catalysed by rough, small-scale topography. The bulk of the energy is dissipated within the bottom 100 m of the ocean, but about 20% is radiated and dissipated away from topography in the ocean interior, where it can sustain turbulent mixing. We conclude that in the absence of rough topography, the turbulent mixing in the ocean interior would be diminished.

Rayleigh–Bénard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of atmospheric convection is the buoyancy source provided by the condensation of water vapour, but the presence of radiation, compressibility, liquid water and ice further complicate the system and our understanding of it. In this paper we present an idealized model of moist convection by taking the Boussinesq limit of the ideal-gas equations and adding a condensate that obeys a simplified Clausius–Clapeyron relation. The system allows moist convection to be explored at a fundamental level and reduces to the classical Rayleigh–Bénard model if the latent heat of condensation is taken to be zero. The model has an exact, Rayleigh-number-independent ‘drizzle’ solution in which the diffusion of water vapour from a saturated lower surface is balanced by condensation, with the temperature field (and so the saturation value of the moisture) determined self-consistently by the heat released in the condensation. This state is the moist analogue of the conductive solution in the classical problem. We numerically determine the linear stability properties of this solution as a function of Rayleigh number and a non-dimensional latent-heat parameter. We also present some two-dimensional, time-dependent, nonlinear solutions at various values of Rayleigh number and the non-dimensional condensational parameters. At sufficiently low Rayleigh number the system converges to the drizzle solution, and we find no evidence that two-dimensional self-sustained convection can occur when that solution is stable. The flow transitions from steady to turbulent as the Rayleigh number or the effects of condensation are increased, with plumes triggered by gravity waves emanating from other plumes. The interior dries as the level of turbulence increases, because the plumes entrain more dry air and because the saturated boundary layer at the top becomes thinner. The flow develops a broad relative humidity minimum in the domain interior, only weakly dependent on Rayleigh number when that is high.

Ocean circulation and dynamics can alter atmospheric CO 2 concentrations. Numerical modelling suggests that shifts in surface buoyancy loss and the location of upwelling can sequester CO 2 in the Southern Ocean during glacial periods. Atmospheric CO 2 concentrations over glacial–interglacial cycles closely correspond to Antarctic temperature patterns 1 . These are distinct from temperature variations in the mid to northern latitudes 2 , so this suggests that the Southern Ocean is pivotal in controlling natural CO 2 concentrations 3 . Here we assess the sensitivity of atmospheric CO 2 concentrations to glacial–interglacial changes in the ocean’s meridional overturning circulation using a circulation model 4 , 5 for upwelling and eddy transport in the Southern Ocean coupled with a simple biogeochemical description. Under glacial conditions, a broader region of surface buoyancy loss results in upwelling farther to the north, relative to interglacials. The northern location of upwelling results in reduced CO 2 outgassing and stronger carbon sequestration in the deep ocean: we calculate that the shift to this glacial-style circulation can draw down 30 to 60 ppm of atmospheric CO 2 . We therefore suggest that the direct effect of temperatures on Southern Ocean buoyancy forcing, and hence the residual overturning circulation, explains much of the strong correlation between Antarctic temperature variations and atmospheric CO 2 concentrations over glacial–interglacial cycles.

Future projections indicate the Atlantic Meridional Overturning Circulation (AMOC) will weaken and shoal in response to global warming, but models disagree widely over the amount of weakening. We analyze projected AMOC weakening in 27 CMIP6 climate models, in terms of changes in three return pathways of the AMOC. The branch of the AMOC that returns through diffusive upwelling in the Indo‐Pacific, but does not later upwell in the Southern Ocean (SO), is particularly sensitive to warming, in part, because shallowing of the deep flow prevents it from entering the Indo‐Pacific via the SO. The present‐day strength of this Indo‐Pacific pathway provides a strong constraint on the projected AMOC weakening. However, estimates of this pathway using four observationally based methods imply a wide range of AMOC weakening under the SSP5‐8.5 scenario of 29%–61% by 2100. Our results suggest that improved observational constraints on this pathway would substantially reduce uncertainty in 21st century AMOC decline. Plain Language Summary The Atlantic Meridional Overturning Circulation (AMOC) is a system of ocean currents that move warm surface waters from the south to the north of the Atlantic Ocean where they cool, sink, and return southward at depth. Changes in the AMOC would have wide‐ranging impacts on our climate. It is predicted to weaken as the climate warms during the 21st century, but the extent of weakening varies among different climate models. We show that AMOC weakening is greatest in models that have a large exchange of water between the AMOC and the Indo‐Pacific Ocean along a specific pathway. The magnitude of this ocean pathway, inferred from four observation‐based estimates of the global overturning circulation, is uncertain. By using these estimates and analyzing the relationship between the aforementioned ocean pathway and AMOC weakening across many climate models, we can predict how the real‐world AMOC will change. Our findings indicate that by 2100, under a high greenhouse gas emission scenario, the AMOC will weaken by 29%–61%. This highlights the importance of reducing differences between observational estimates of the ocean's overturning pathways to reduce uncertainty in future AMOC weakening and to improve the representation of these pathways in climate models. Key Points The magnitude of 21st century Atlantic Meridional Overturning Circulation (AMOC) weakening in CMIP6 models is highly correlated with an AMOC pathway into the Indo‐Pacific Ocean The real‐world “Indo‐Pacific diffusive” AMOC pathway inferred from observation‐based estimates is used to constrain future AMOC weakening Under high‐end greenhouse gas forcing, AMOC weakening based on this emergent constraint relationship ranges from 29% to 61% by 2100

The fast and slow components of global warming in a comprehensive climate model are isolated by examining the response to an instantaneous return to preindustrial forcing. The response is characterized by an initial fast exponential decay with ane-folding time smaller than 5 yr, leaving behind a remnant that evolves more slowly. The slow component is estimated to be small at present, as measured by the global mean near-surface air temperature, and, in the model examined, grows to 0.4°C by 2100 in the A1B scenario from the Special Report on Emissions Scenarios (SRES), and then to 1.4°C by 2300 if one holds radiative forcing fixed after 2100. The dominance of the fast component at present is supported by examining the response to an instantaneous doubling of CO₂ and by the excellent fit to the model’s ensemble mean twentieth-century evolution with a simple one-box model with no long times scales.

Arctic amplification has been proposed to promote temperature extremes by slowing the midlatitude jet and increasing the amplitude of its meanders. Observational and modeling studies have used a variety of metrics to quantify jet waviness. These studies show conflicting changes in jet waviness depending on the metric used and period examined. Here, we evaluate common metrics for dry idealized model simulations in which we apply polar warming of varying depth and meridional extent. In all simulations, polar warming increases the spatial extent of jet meanders, but reduces the magnitudes of ridges and troughs within the wave. As a result, geometric and anomaly‐amplitude measures of jet waviness can yield opposing responses. This contrast between metrics is particularly evident when warming extends into the midlatitudes. In all simulations, midlatitude temperature anomalies weaken as the poles warm, suggesting that a wavier jet need not imply stronger temperature extremes. Plain Language Summary The Arctic is warming faster than anywhere else on Earth, and this has been suggested to affect weather over midlatitude regions in Eurasia and North America. It has been proposed that, as the pole warms, the equator‐to‐pole temperature gradient is reduced and the atmospheric jet stream slows down and undergoes larger, slower‐moving meanders, which bring long‐lasting extreme temperatures. However, theories for understanding waves in the jet stream actually suggest that these waves could weaken when the equator‐to‐pole temperature gradient decreases. This study uses simple model simulations to test how different metrics for describing jet waviness respond when the pole is warmed. We find that the overall scale of meanders does seem to increase, but the associated temperature anomalies decrease, suggesting a wavier jet stream need not imply stronger temperature extremes. Key Points Spatial extent of midlatitude waves is increased by polar amplification Magnitudes of ridges and troughs within waves are decreased by polar amplification Accordingly, geometric, and anomaly‐amplitude measures of jet waviness can yield opposing responses

The variability and compensation of the meridional energy transport in the atmosphere and ocean are examined with the state-of-the-art GFDL Climate Model, version 2.1 (CM2.1), and the GFDL Intermediate Complexity Coupled Model (ICCM). On decadal time scales, a high degree of compensation between the energy transport in the atmosphere (AHT) and ocean (OHT) is found in the North Atlantic. The variability of the total or planetary heat transport (PHT) is much smaller than the variability in either AHT or OHT alone, a feature referred to as “Bjerknes compensation.” Natural decadal variability stems from the Atlantic meridional overturning circulation (AMOC), which leads OHT variability. The PHT is positively correlated with the OHT, implying that the atmosphere is compensating, but imperfectly, for variations in ocean transport. Because of the fundamental role of the AMOC in generating the decadal OHT anomalies, Bjerknes compensation is expected to be active only in coupled models with a low-frequency AMOC spectral peak. The AHT and the transport in the oceanic gyres are positively correlated because the gyre transport responds to the atmospheric winds, thereby militating against long-term variability involving the wind-driven flow. Moisture and sensible heat transports in the atmosphere are also positively correlated at decadal time scales. The authors further explore the mechanisms and degree of compensation with a simple, diffusive, two-layer energy balance model. Taken together, these results suggest that compensation can be interpreted as arising from the highly efficient nature of the meridional energy transport in the atmosphere responding to ocean variability rather than any a priori need for the top-of-atmosphere radiation budget to be fixed.

The influence of ocean circulation changes on heat uptake is explored using a simply-configured primitive equation ocean model resembling a very idealized Atlantic Ocean. We focus on the relative importance of the redistribution of the existing heat reservoir (due to changes in the circulation) and the contribution from anomalous surface heat flux, in experiments in which the surface boundary conditions are changed. We perform and analyze numerical experiments over a wide range of parameters, including experiments that simulate global warming and others that explore the robustness of our results to more general changes in surface boundary conditions. We find that over a wide range of values of diapycnal diffusivity and Southern Ocean winds, and with a variety of changes in surface boundary conditions, the spatial patterns of ocean temperature anomaly are nearly always determined as much or more by the existing heat reservoir redistribution than by the nearly passive uptake of temperature due to changes in the surface boundary conditions. Calculating heat uptake by neglecting the existing reservoir redistribution, which is similar to treating temperature as a passive tracer, leads to significant quantitative errors notably at high-latitudes and, secondarily, in parts of the main thermocline. Experiments with larger circulation changes tend to produce a relatively larger magnitude of existing reservoir redistribution, and a faster growing effective heat capacity of the system. The effective heat capacity is found to be sensitive to both vertical diffusivity and Southern Ocean wind.