Richard J. Greatbatch

A note on the representation of steric sea level in models that conserve volume rather than mass

This note discusses the representation of steric sea level in ocean circulation models. Changes in steric sea level are caused when changes in the density of the water column imply an expansion or contraction of the column. Models usually make the Boussinesq approximation and conserve volume, rather than mass, and so do not properly represent expansion or contraction. This means that although expansion/contraction is included in the equation of state, it is not accounted for by the model dynamics. In this note, we examine the equation governing the time evolution of the sea level displacement. It is shown that requiring conservation of mass, rather than volume, introduces a new term to this equation. A simple example is used to show the relationship of the new term to the surface buoyancy flux. The equilibrium response to the new term has two parts. One part consists of the Goldsbrough and Stommel gyres, for which, in the ocean interior, vortex stretching due to the local expansion/contraction of the water column is balanced by changes in planetary vorticity. The other part corresponds to the “inverse barometer.” The effect is to adjust sea level by a globally uniform but timevarying factor, determined by the net expansion/contraction of the global ocean. Since this correction is globally uniform, it has no dynamical significance. Both the Goldsbrough/Stommel gyres and the inverse barometer solution are missing from models as currently formulated. This does not represent a serious error. However, if comparison is made with observations of sea level, model-calculated sea level should be adjusted by a globally uniform, time-varying factor, determined by the net expansion/contraction of the global ocean. This would be important for assessing the likely rise in sea level in response to global warming.

Multidecadal Thermohaline Circulation Variability Driven by Atmospheric Surface Flux Forcing

Previous analyses of an extended integration of the Geophysical Fluid Dynamics Laboratory coupled climate model have revealed pronounced multidecadal variations of the thermohaline circulation (THC) in the North Atlantic. The purpose of the current work is to assess whether those fluctuations can be viewed as a coupled air‐sea mode (in the sense of ENSO), or as an oceanic response to forcing from the atmosphere model, in which large-scale feedbacks from the ocean to the atmospheric circulation are not critical. A series of integrations using the ocean component of the coupled model are performed to address the above question. The ocean model is forced by suitably chosen time series of surface fluxes from either the coupled model or a companion integration of an atmosphere-only model run with a prescribed seasonal cycle of SSTs and sea-ice thickness. These experiments reveal that 1) the previously identified multidecadal THC variations can be largely viewed as an oceanic response to surface flux forcing from the atmosphere model, although air‐ sea coupling through the thermodynamics appears to modify the amplitude of the variability, and 2) variations in heat flux are the dominant term (relative to the freshwater and momentum fluxes) in driving the THC variability. Experiments driving the ocean model using either high- or low-pass-filtered heat fluxes, with a cutoff period of 20 yr, show that the multidecadal THC variability is driven by the low-frequency portion of the spectrum of atmospheric flux forcing. Analyses have also revealed that the multidecadal THC fluctuations are driven by a spatial pattern of surface heat flux variations that bears a strong resemblance to the North Atlantic oscillation. No conclusive evidence is found that the THC variability is part of a dynamically coupled mode of the atmosphere and ocean models.

A diagnosis of interpentadal circulation changes in the North Atlantic

Diagnostic calculations of the circulation in the North Atlantic are described. Three basic cases are considered: the climatological mean state and the circulation in the pentads 1955–1959 and 1970–1974. Density data from Levitus (1982, 1989) are used as input together with the annual mean wind stress field of Hellerman and Rosenstein (1983) for the climatological case and wind stress data derived from the Comprehensive Ocean-Atmosphere Data Set for the 1950s and 1970s. The results suggest that the Gulf Stream was some 30 Sv weaker in the 1970–1974 pentad than in the pentad 1955–1959. About 20 Sv of this is due to a dramatic weakening of the circulation of the subtropical gyre. This is traced to a change in bottom pressure torque associated with the bottom topography on the western side of the Mid-Atlantic Ridge. This same general area is also shown to be important for enhancing the transport of the climatological mean subtropical gyre above that predicted by the flat-bottomed Sverdrup relation. The remaining 10 Sv is due to a weakening of the cyclonic gyre in the continental slope region south of Atlantic Canada and north of the Gulf Stream. This too is associated with a change in bottom pressure torque. We find that changes in the density field above 1500 m depth contribute about half of the transport change. It is not clear how reliable is the estimate of the remaining half. This is because it is dependent on changes in the analyzed density field at depths greater than 1500 m, and these could be a result of insufficient or unreliable data. No significant change in the total transport of the subpolar gyre is diagnosed by our calculations. In order to interpret the results we have split the joint effect of baroclinicity and relief (JEBAR) term into two parts: a part associated with bottom pressure torque and a part associated with compensation by the density stratification for the effect of variable bottom topography. This leads to a natural division of the volume transport stream function Ψ into three parts; Ψ = Ψ W + Ψ C + Ψ B. Ψ W is calculated using wind forcing alone and assumes a uniform density ocean. Ψ C is the difference between this and the stream function, Ψ S, calculated using the flat-bottomed Sverdrup relation. It is driven by that part of JEBAR associated with density compensation. Finally, Ψ B is the difference between Ψ and Ψ S and is that part of Ψ driven by bottom pressure torque. (Ψ C + Ψ B) then gives the total contribution to Ψ from the JEBAR term. We find that for the climatological mean subpolar gyre, density compensation is particularly important, with bottom pressure torque displacing the gyre southward rather then enhancing its transport. For the subtropical gyre, density compensation plays less of a role. Almost all the difference between the two pentads occurs in the bottom pressure torque part.

A Reexamination of the polar Halocline Catastrophe and Implications for Coupled Ocean-Atmosphere Modeling

Abstract In this paper, the physical mechanism of the polar halocline catastrophe (PHC) is reexamined with emphasis on the role played by the surface heat flux. It is argued that, in a coupled ocean–atmosphere system, thermal changes in the atmospheric state in response to changes in heat flux from the ocean weaken the feedback responsible for the PHC. So far, the PHC has been observed in models that use mixed boundary conditions; that is, the freshwater flux is specified, but the surface temperature is relaxed to a specified value. Previous explanations of the PHC have focused on the role of the freshwater flux in establishing a freshwater cap and shutting off the deep convection. However, the establishment of a freshwater cap reduces the depth of the water column that is cooled by surface heat loss. As a consequence, the surface temperature is reduced. Since the difference between this and atmospheric restoring temperature is now less, there is a corresponding reduction in the surface heat loss to the a...

On the Response of the Ocean to a Moving Storm: The Nonlinear Dynamics

Abstract A novel and efficient numerical method is used to investigate the nonlinear equations of motion for the upper layer of a two-layer ocean in which the lower layer is infinitely deep and at rest. The efficiency is achieved by seeking solutions that are in a steady state, translating in equilibrium with the storm. Oscillations are found in the wake of the storm. Two features of the response are attributed to the nonlinear terms in the equation of motion: 1) a rapid transition from a maximum in the downwelling phase, to a maximum in the upwelling phase of each oscillation, followed by a gradual relaxation to the next downwelling maximum; and 2) a displacement of the maximum response, usually to the right of the storm track, by ∼40 km. It is shown that the horizontal pressure gradient terms can be neglected from the momentum equations for “fast”, “large” storms, in which case a Lagrangian integration can be performed, following fluid particles. This enables feature 1) to be attributed to the along-tra...

On the Response of the Ocean to a Moving Storm: Parameters and Scales

Abstract This paper has two purposes: One is to present a new and efficient multilevel numerical model for calculating the response of the ocean to a moving storm; the second is to show how, on a time scale of a few inertial periods following the arrival of the storm, the maximum horizontal and vertical velocities found in the wake can be calculated using a linear Ekman model and a knowledge of that part of the change in the depth of the wind mixed layer due to entrainment. This is demonstrated over a range of experiments with the multilevel numerical model. These integrate the full nonlinear equations of motion with realistic ocean stratification and involve substantial entrainment of water into the wind mixed layer. It is also shown that on this time scale, the horizontal currents are confined near the surface but that the vertical velocity field extends throughout the depth of the ocean. It is shown in Appendix B that the wind forcing need only be “large” or “fast” for the forced response not to feel t...

Exploring the Relationship between Eddy-Induced Transport Velocity, Vertical Momentum Transfer, and the Isopycnal Flux of Potential Vorticity

Abstract Gent et al. have emphasized the role of the eddy-induced transport (or bolus) velocity as a mechanism for redistributing tracers in the ocean. By writing the momentum equations in terms of the isopycnal flux of potential vorticity, the author shows that any parameterization of the eddy-induced transport velocity must be consistent with the conservation equation for potential vorticity. This places a constraint on possible parameterizations, a constraint that is satisfied by the Gent and McWilliams parameterization only if restrictions are placed on the diffusivity coefficient. A new parameterization is suggested that is the simplest extension of Gent and McWilliams based on the potential vorticity formulation. The new parameterization parameterizes part of the time-mean flow driven by the Reynolds stress terms in addition to the eddy-induced transport velocity. It is also shown that the eddy-induced transport velocity can always be written as the Ekman velocity associated with the vertical deriva...

A Diagnosis of Thickness Fluxes in an Eddy-Resolving Model

Abstract Output from an eddy-resolving model of the North Atlantic Ocean is used to estimate values for the thickness diffusivity κ appropriate to the Gent and McWilliams parameterization. The effect of different choices of rotational eddy fluxes on the estimated κ is discussed. Using the raw fluxes (no rotational flux removed), large negative values (exceeding −5000 m2 s−1) of κ are diagnosed locally, particularly in the Gulf Stream region and in the equatorial Atlantic. Removing a rotational flux based either on the suggestion of Marshall and Shutts or the more general theory of Medvedev and Greatbatch leads to a reduction of the negative values, but they are still present. The regions where κ < 0 correspond to regions where eddies are acting to increase, rather than decrease (as in baroclinic instability) the mean available potential energy. In the subtropical gyre, κ ranges between 500 and 2000 m2 s−1, rapidly decreasing to zero below the thermocline in all cases. Rotational fluxes and κ are also esti...

Enhanced vertical propagation of storm-induced near-inertial energy in an eddying ocean channel model

The interaction between inertial oscillations generated by a storm and a mesoscale eddy field is studied using a Southern Ocean channel model. It is shown that the leakage of near-inertial energy out of the surface layer is strongly enhanced by the presence of the eddies, with the anticyclonic eddies acting as a conduit to the deep ocean. Given the ubiquity of the atmospheric storm tracks (a source of near-inertial energy for the ocean) and regions of strong ocean mesoscale variability, we argue that this effect could be important for understanding pathways by which near-inertial energy enters the ocean and is ultimately available for mixing.

A Damped Decadal Oscillation in the North Atlantic Climate System

A simple stochastic atmosphere model is coupled to a realistic model of the North Atlantic Ocean. A north–south SST dipole, with its zero line centered along the subpolar front, influences the atmosphere model, which in turn forces the ocean model by surface fluxes related to the North Atlantic Oscillation. The coupled system exhibits a damped decadal oscillation associated with the adjustment through the ocean model to the changing surface forcing. The oscillation consists of a fast wind-driven, positive feedback of the ocean and a delayed negative feedback orchestrated by overturning circulation anomalies. The positive feedback turns out to be necessary to distinguish the coupled oscillation from that in a model without any influence from the ocean to the atmosphere. Using a novel diagnosing technique, it is possible to rule out the importance of baroclinic wave processes for determining the period of the oscillation, and to show the important role played by anomalous geostrophic advection in sustaining the oscillation.