Ocean overturning circulation requires a continuous thermodynamic transformation of the buoyancy of seawater. The steeply sloping isopycnals of the Southern Ocean provide a pathway for Circumpolar Deep Water to upwell from mid depth without strong diapycnal mixing 1-3 , where it is transformed directly by surface fluxes of heat and freshwater and splits into an upper and lower branch 4-6 . While brine rejection from sea ice is thought to contribute to the lower branch 7 , the role of sea ice in the upper branch is less well understood, partly due to a paucity of observations of sea-ice thickness and transport 8,9 . Here we quantify the sea-ice freshwater flux using the Southern Ocean State Estimate, a state-of-the-art data assimilation that incorporates millions of ocean and ice observations. We then use the water-mass transformation framework 10 to compare the relative roles of atmospheric, sea-ice, and glacial freshwater fluxes, heat fluxes, and upper-ocean mixing in transforming buoyancy within the upper branch. We find that sea ice is a dominant term, with di erential brine rejection and ice melt transforming upwelled Circumpolar Deep Water at a rate of ∼22 × 10 6 m 3 s −1 . These results imply a prominent role for Antarctic sea ice in the upper branch and suggest that residual overturning and wind-driven sea-ice transport are tightly coupled.The Southern Ocean State Estimate (SOSE) is an ice/ocean data assimilation produced for the time period January 2005 through December 2010. (See Methods and Supplementary Information for SOSE details and validation.) The bulk freshwater fluxes at the ocean surface south of 50 • S, as estimated by SOSE, are summarized in Fig. 1a. When sea ice forms, nearly all of the salt remains behind in the underlying seawater (a process called brine rejection); when the ice melts, liquid freshwater is returned to the ocean. Direct open-ocean precipitation minus evaporation (0.28 fwSv) and glacial ice melt (0.05 fwSv) are both smaller than net sea-ice melt (0.50 fwSv) and brine rejection (0.36 fwSv). (Bulk freshwater volume fluxes are given in units of freshwater sverdrups 11 , 1 fwSv = 10 6 m 3 freshwater s −1 3.15 × 10 4 Gt freshwater per year.) Melt exceeds brine rejection because sea ice incorporates snowfall at a rate of 0.14 fwSv. Moreover, wind-driven sea-ice transport creates a freshwater conveyor belt from the Antarctic coast to the open ocean 12 , leading to sharp gradients in freshwater flux. The spatial structure of the sea-ice redistribution is assessed in Fig. 1b by comparing the annual mean freshwater flux leaving the atmosphere, land and glaciers (left panel) with that entering the ocean (right panel); the difference is due to sea-ice freshwater redistribution (middle panel, vectors show the ice thickness transport). From the atmosphere, widespread precipitation over the Southern Ocean leads to a broadly distributed downward freshwater flux with a characteristic magnitude of 0.5 m yr −1 , and glacial ice melt provides a stronger freshwater source near the Antarctic coas...

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Mesoscale eddies play a major role in the transport of tracers in the ocean. Focusing on a sector in the east Pacific, the authors present estimates of eddy diffusivities derived from kinematic tracer simulations using satellite-observed velocity fields. Meridional diffusivities are diagnosed, and how they are related to eddy properties through the mixing length formulation of Ferrari and Nikurashin, which accounts for the suppression of diffusivity due to eddy propagation relative to the mean flow, is shown. The uniqueness of this study is that, through systematically varying the zonal-mean flow, a hypothetical “unsuppressed” diffusivity is diagnosed. At a given latitude, the unsuppressed diffusivity occurs when the zonal-mean flow equals the eddy phase speed. This provides an independent estimate of eddy phase propagation, which agrees well with theoretical arguments. It is also shown that the unsuppressed diffusivity is predicted very well by classical mixing length theory, that is, that it is proportional to the rms eddy velocity times the observed eddy size, with a spatially constant mixing efficiency of 0.35. Then, the suppression factor is estimated and it is shown that it too can be understood quantitatively in terms of easily observed mean flow properties. The authors then extrapolate from these sector experiments to the global scale, making predictions for the global surface eddy diffusivity. Together with a prognostic equation for eddy kinetic energy and a theory explaining observed eddy sizes, these concepts could potentially be used in a closure for eddy diffusivities in coarse-resolution ocean climate models.

An eddy-resolving numerical model of a zonal flow, meant to resemble the Antarctic Circumpolar Current, is described and analyzed using the framework of J. Marshall and T. Radko. In addition to wind and buoyancy forcing at the surface, the model contains a sponge layer at the northern boundary that permits a residual meridional overturning circulation (MOC) to exist at depth. The strength of the residual MOC is diagnosed for different strengths of surface wind stress. It is found that the eddy circulation largely compensates for the changes in Ekman circulation. The extent of the compensation and thus the sensitivity of the MOC to the winds depend on the surface boundary condition. A fixed-heat-flux surface boundary severely limits the ability of the MOC to change. An interactive heat flux leads to greater sensitivity. To explain the MOC sensitivity to the wind strength under the interactive heat flux, transformed Eulerian-mean theory is applied, in which the eddy diffusivity plays a central role in determining the eddy response. A scaling theory for the eddy diffusivity, based on the mechanical energy balance, is developed and tested; the average magnitude of the diffusivity is found to be proportional to the square root of the wind stress. The MOC sensitivity to the winds based on this scaling is compared with the true sensitivity diagnosed from the experiments.

.[1] Velocities derived from AVISO sea-surface height observations, adjusted to be nondivergent, are used to simulate the evolution of passive tracers at the ocean surface. Eddy mixing rates are derived from the tracer fields in two ways. First, the method of Nakamura is applied to a sector in the East Pacific. Second, the Osborn-Cox diffusivity is calculated globally to yield estimates of diffusivity in two dimensions. The results from the East Pacific show weak meridional mixing at the surface in the Southern Ocean (<1000 m 2 s À1, consistent with previous results) but higher mixing rates (~3000-5000 m 2 s À1 ) in the tropical ocean. The Osborn-Cox diagnostic provides a global picture of mixing rates and agrees reasonably well with the results from the East Pacific. It also shows extremely high mixing rates (~10 4 m 2 s À1 ) in western boundary current regions. The Osborn-Cox diffusivity is sensitive to the tracer initialization, which we attribute to the presence of anisotropic mixing processes. The mixing rates are strongly influenced by the presence of a mean flow nearly everywhere, as shown by comparison with an eddy-only calculation, with the mean flow absent. Finally, results are compared with other recent estimates of mixing rates using Lagrangian and inverse methods.Citation: Abernathey, R. P., and J. Marshall (2013), Global surface eddy diffusivities derived from satellite altimetry,

Meridional cross sections of effective diffusivity in the Southern Ocean are presented and discussed. The effective diffusivity, K eff , characterizes the rate at which mesoscale eddies stir properties on interior isopycnal surfaces and laterally at the sea surface. The distributions are obtained by monitoring the rate at which eddies stir an idealized tracer whose initial distribution varies monotonically across the Antarctic Circumpolar Current (ACC). In the absence of observed maps of eddying currents in the interior ocean, the advecting velocity field is taken from an eddy-permitting state estimate of the Southern Ocean (SOSE). A threedimensional advection-diffusion equation is solved and the diffusivity diagnosed by applying the Nakamura technique on both horizontal and isopycnal surfaces. The resulting meridional sections of K eff reveal intensified isopycnal eddy stirring (reaching values of ;2000 m 2 s 21 ) in a layer deep beneath the ACC but rising toward the surface on the equatorward flank. Lower effective diffusivity values (;500 m 2 s 21 ) are found near the surface where the mean flow of the ACC is strongest. It is argued that K eff is enhanced in the vicinity of the steering level of baroclinic waves, which is deep along the axis of the ACC but shallows on the equatorial flank. Values of K eff are also found to be spatially correlated with gradients of potential vorticity on isopycnal surfaces and are large where those gradients are weak and vice versa, as expected from simple dynamical arguments. Finally, implications of the spatial distributions of K eff for the dynamics of the ACC and its overturning circulation are discussed.

The processes that determine the depth of the Southern Ocean thermocline are considered. In existing conceptual frameworks, the thermocline depth is determined by competition between the mean and eddy heat transport, with a contribution from the interaction with the stratification in the enclosed portion of the ocean. Using numerical simulations, this study examines the equilibration of an idealized circumpolar current with and without topography. The authors find that eddies are much more efficient when topography is present, leading to a shallower thermocline than in the flat case. A simple quasigeostrophic analytical model shows that the topographically induced standing wave increases the effective eddy diffusivity by increasing the local buoyancy gradients and lengthening the buoyancy contours across which the eddies transport heat. In addition to this local heat flux intensification, transient eddy heat fluxes are suppressed away from the topography, especially upstream, indicating that localized topography leads to local (absolute) baroclinic instability and its subsequent finite-amplitude equilibration, which extracts available potential energy very efficiently from the time-mean flow.