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Jan D. Zika and Trevor J. McDougall

Abstract

The conservation equations of heat, salt, and mass are combined in such a way that a simple relation is found between the known volume flux of Mediterranean Water entering the North Atlantic Ocean and the effects of lateral and vertical mixing processes. The method is a form of inverse method in which the only unknowns are the vertical and lateral diffusivities. For each isohaline contour on each neutral density surface the authors develop one equation in two unknowns, arguing that other terms that cannot be evaluated are small. By considering several such isohaline contours, the method becomes overdetermined for each density layer, and results are found for both the vertical and lateral diffusivity that vary smoothly in the vertical direction, giving some confidence in the method.

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Jan D. Zika, Trevor J. McDougall, and Bernadette M. Sloyan

Abstract

The tracer-contour inverse method is used to infer mixing and circulation in the eastern North Atlantic. Solutions for the vertical mixing coefficient D, the along-isopycnal mixing coefficient K, and a geostrophic streamfunction Ψ are all direct outputs of the method. The method predicts a vertical mixing coefficient O(10−5 m2 s−1) in the upper 1000 m of the water column, consistent with in situ observations. The method predicts a depth-dependent along-isopycnal mixing coefficient that decreases from O(1000 m2 s−1) close to the mixed layer to O(100 m2 s−1) in the interior, which is also consistent with observations and previous hypotheses. The robustness of the result is tested with a rigorous sensitivity analysis including the use of two independently constructed datasets.

This study confirms the utility of the tracer-contour inverse method. The results presented support the hypothesis that vertical mixing is small in the thermocline of the subtropical Atlantic Ocean. A strong depth dependence of the along-isopycnal mixing coefficient is also demonstrated, supporting recent parameterizations for coarse-resolution ocean models.

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Clothilde E. Langlais, Stephen R. Rintoul, and Jan D. Zika

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The Southern Hemisphere westerly winds have intensified in recent decades associated with a positive trend in the southern annular mode (SAM). However, the response of the Antarctic Circumpolar Current (ACC) transport and eddy field to wind forcing remains a topic of debate. This study uses global eddy-permitting ocean circulation models driven with both idealized and realistic wind forcing to explore the response to interannual wind strengthening. The response of the barotropic and baroclinic transports and eddy field of the ACC is found to depend on the spatial pattern of the changes in wind forcing. In isolation, an enhancement of the westerlies over the ACC belt leads to an increase of both barotropic and baroclinic transport within the ACC envelope, with lagged enhancement of the eddy kinetic energy (EKE). In contrast, an increase in wind forcing near Antarctica drives a largely barotropic change in transport along closed f/H contours (“free mode”), with little change in eddy activity. Under realistic forcing, the interplay of the SAM and the El Niño–Southern Oscillation (ENSO) influences the spatial distribution of the wind anomalies, in particular the partition between changes in the wind stress over the ACC and along f/H contours. This study finds that the occurrence of a negative or positive ENSO during a positive SAM can cancel or double the wind anomalies near Antarctica, altering the response of the ACC and its eddy field. While a negative ENSO and positive SAM favors an increase in EKE, a positive ENSO and positive SAM lead to barotropic transport changes and no eddy response.

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Jan D. Zika, Matthew H. England, and Willem P. Sijp

Abstract

The thermohaline streamfunction is presented. The thermohaline streamfunction is the integral of transport in temperature–salinity space and represents the net pathway of oceanic water parcels in that space. The thermohaline streamfunction is proposed as a diagnostic to understand the global oceanic circulation and its role in the global movement of heat and freshwater. The coordinate system used filters out adiabatic fluctuations. Physical pathways and ventilation time scales are naturally diagnosed, as are the roles of the mean flow and turbulent fluctuations. Because potential density is a function of temperature and salinity, the framework is naturally isopycnal and is ideal for the diagnosis of water-mass transformations and advective diapycnal heat and freshwater transports. Crucially, the thermohaline streamfunction is computationally and practically trivial to implement as a diagnostic for ocean models. Here, the thermohaline streamfunction is computed using the output of an equilibrated intermediate complexity climate model. It describes a global cell, a warm tropical cell, and a bottom water cell. The streamfunction computed from eddy-induced advection is equivalent in magnitude to that from the total advection, demonstrating the leading-order importance of parameterized eddy fluxes in oceanic heat and freshwater transports. The global cell, being clockwise in thermohaline space, tends to advect both heat and salt toward denser (poleward) water masses in symmetry with the atmosphere’s poleward transport of moisture. A reprojection of the global cell from thermohaline to geographical coordinates reveals a thermohaline circulation reminiscent of the schematized “global conveyor.”

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Ryan M. Holmes, Jan D. Zika, and Matthew H. England

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The rate at which the ocean moves heat from the tropics toward the poles, and from the surface into the interior, depends on diabatic surface forcing and diffusive mixing. These diabatic processes can be isolated by analyzing heat transport in a temperature coordinate (the diathermal heat transport). This framework is applied to a global ocean sea ice model at two horizontal resolutions (1/4° and 1/10°) to evaluate the partioning of the diathermal heat transport between different mixing processes and their spatial and seasonal structure. The diathermal heat transport peaks around 22°C at 1.6 PW, similar to the peak meridional heat transport. Diffusive mixing transfers this heat from waters above 22°C, where surface forcing warms the tropical ocean, to temperatures below 22°C where midlatitude waters are cooled. In the control 1/4° simulation, half of the parameterized vertical mixing is achieved by background diffusion, to which sensitivity is explored. The remainder is associated with parameterizations for surface boundary layer, shear instability, and tidal mixing. Nearly half of the seasonal cycle in the peak vertical mixing heat flux is associated with shear instability in the tropical Pacific cold tongue, highlighting this region’s global importance. The framework presented also allows for quantification of numerical mixing associated with the model’s advection scheme. Numerical mixing has a substantial seasonal cycle and increases to compensate for reduced explicit vertical mixing. Finally, applied to Argo observations the diathermal framework reveals a heat content seasonal cycle consistent with the simulations. These results highlight the utility of the diathermal framework for understanding the role of diabatic processes in ocean circulation and climate.

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Jan D. Zika, Bernadette M. Sloyan, and Trevor J. McDougall

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The strength and structure of the Southern Hemisphere meridional overturning circulation (SMOC) is related to the along-isopycnal and vertical mixing coefficients by analyzing tracer and density fields from a hydrographic climatology. The meridional transport of Upper Circumpolar Deep Water (UCDW) across the Antarctic Circumpolar Current (ACC) is expressed in terms of the along-isopycnal (K) and diapycnal (D) tracer diffusivities and in terms of the along-isopycnal potential vorticity mixing coefficient (K PV). Uniform along-isopycnal (<600 m2 s−1) and low vertical mixing (10−5 m2 s−1) can maintain a southward transport of less than 60 Sv (Sv = 106 m2 s−1) of UCDW across the ACC, which is distributed largely across the South Pacific and east Indian Ocean basins. For vertical mixing rates of O(10−4 m2 s−1) or greater, the inferred transport is significantly enhanced. The transports inferred from both tracer and density distributions suggest a ratio K to D of O(2 × 106) particularly on deeper layers of UCDW. Given the range of observed southward transports of UCDW, it is found that K = 300 ± 150 m2 s−1 and D = 10−4 ± 0.5 × 10−4 m2 s−1 in the Southern Ocean interior. A view of the SMOC is revealed where dense waters are converted to lighter waters not only at the ocean surface, but also on depths below that of the mixed layer with vertical mixing playing an important role.

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Ryan M. Holmes, Jan D. Zika, and Matthew H. England

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, in a comment on , argue that under the incompressible Boussinesq approximation the “sum of the volume fluxes through any kind of control volume must integrate to zero at all times.” They hence argue that the expression in for the change in the volume of seawater warmer than a given temperature is inaccurate. Here we clarify what is meant by the term “volume flux” as used in and also more generally in the water-mass transformation literature. Specifically, a volume flux across a surface can occur either due to fluid moving through a fixed surface, or due to the surface moving through the fluid. Interpreted in this way, we show using several examples that the statement from quoted above does not apply to the control volume considered in . then derive a series of expressions for the water-mass transformation or volume flux across an isotherm G in the general, compressible case. In the incompressible Boussinesq limit these expressions reduce to a form (similar to that provided in ) that involves the temperature derivative of the diabatic heat fluxes. Due to this derivative, G can be difficult to robustly estimate from ocean model output. This emphasizes one of the advantages of the approach of , namely, G does not appear in the internal heat content budget and is not needed to describe the flow of internal heat content into and around the ocean.

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Jan D. Zika, Trevor J. McDougall, and Bernadette M. Sloyan

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A method is developed for estimating the along-isopycnal and vertical mixing coefficients (K and D) and the absolute velocity from time-averaged hydrographic data. The method focuses directly on transports down tracer gradients on isopycnals. When the tracer considered is salinity or an appropriate variable for heat, this downgradient transport constitutes the along-isopycnal component of the thermohaline overturning circulation. In the method, a geostrophic streamfunction is defined that is related on isopycnals by tracer contours and by the thermal wind relationship in the vertical. Volume and tracer conservation constraints are also included. The method is overdetermined and avoids much of the signal-to-noise error associated with differentiating hydrographic data in conventional inverse methods. The method is validated against output of a layered model. It is shown to resolve both K and D, the downgradient isopycnal transport, and the mean flow on isopycnals in the North Pacific and South Atlantic.

Importantly, an understanding is established of both the physics underlying the method and the circumstances necessary for an inverse method to determine the mixing rates and the absolute velocity. If mixing is neglected, the method is the Bernoulli inverse method. At the limit of zero weight on the tracer-contour equations the method is a conventional box inverse method. Comparisons are drawn between each method and their relative merits are discussed. A new closed expression for the absolute velocity is also presented.

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Joakim Kjellsson, Kristofer Döös, Frédéric B. Laliberté, and Jan D. Zika

Abstract

The zonal and meridional components of the atmospheric general circulation are used to define a global thermodynamic streamfunction in dry static energy versus latent heat coordinates. Diabatic motions in the tropical circulations and fluxes driven by midlatitude eddies are found to form a single, global thermodynamic cycle. Calculations based on the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) dataset indicate that the cycle has a peak transport of 428 Sv (Sv ≡ 109 kg s−1). The thermodynamic cycle encapsulates a globally interconnected heat and water cycle comprising ascent of moist air where latent heat is converted into dry static energy, radiative cooling where dry air loses dry static energy, and a moistening branch where air is warmed and moistened. It approximately follows a tropical moist adiabat and is bounded by the Clausius–Clapeyron relationship for near-surface air. The variability of the atmospheric general circulation is related to ENSO events using reanalysis data from recent years (1979–2009) and historical simulations from the EC-Earth Consortium (EC-Earth) coupled climate model (1850–2005). The thermodynamic cycle in both EC-Earth and ERA-Interim widens and weakens with positive ENSO phases and narrows and strengthens during negative ENSO phases with a high correlation coefficient. Weakening in amplitude suggests a weakening of the large-scale circulation, while widening suggests an increase in mean tropical near-surface moist static energy.

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Jan D. Zika, Willem P. Sijp, and Matthew H. England

Abstract

Vertical transport of heat by ocean circulation is investigated using a coupled climate model and novel thermodynamic methods. Using a streamfunction in temperature–depth coordinates, cells are identified by whether they are thermally direct (flux heat upward) or indirect (flux heat downward). These cells are then projected into geographical and other thermodynamic coordinates. Three cells are identified in the model: a thermally direct cell coincident with Antarctic Bottom Water, a thermally indirect deep cell coincident with the upper limb of the meridional overturning circulation, and a thermally direct shallow cell coincident with the subtropical gyres at the surface. The mechanisms maintaining the thermally indirect deep cell are investigated. Sinking water within the deep cell is more saline than that which upwells, because of the coupling between the upper limb and the subtropical gyres in a broader thermohaline circulation. Despite the higher salinity of its sinking water, the deep cell transports buoyancy downward, requiring a source of mechanical energy. Experiments run to steady state with increasing Southern Hemisphere westerlies show an increasing thermally indirect circulation. These results suggest that heat can be pumped downward by the upper limb of the meridional overturning circulation through a combination of salinity gain in the subtropics and the mechanical forcing provided by Southern Hemisphere westerly winds.

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