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Richard J. Greatbatch

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Richard J. Greatbatch

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A framework for mesoscale eddy parameterization based on density-weighted averaging at fixed height is developed. The method uses the fully non-Boussinesq equations of motion and is connected to the equations carried by Boussinesq ocean models only after the averaged equations have been developed. The framework applies to the continuity, tracer, and momentum equations within a single formalism. Two methods for applying parameterizations in ocean models are obtained. The first, based on the tracer equation, corresponds to the approach commonly taken when including eddy effects in ocean models. The second puts the forcing for the eddy-induced transport into the averaged momentum equation where it appears as the divergence of a generalized Eliassen–Palm flux.

It is then shown how to solve for the tracer transport velocity. The solutions form a family closely related to the temporal residual mean (TRM) velocity of McDougall and McIntosh, valid to O(α 3), where α is perturbation amplitude. The analysis is extended to obtain a family of exact solutions for the eddy-induced mass transport, valid at any order in perturbation amplitude. It is also shown how to obtain a generalization of the TRM to take account of diffusion and time dependence in the instantaneous equations. The solution suggests that the tracer transport velocity could be different for different tracers, depending primarily on the structure of the mean field. This conclusion also applies in the case of isopycnal averaging; it is not a result that is peculiar to averaging at fixed height.

Finally, it is shown how the non-Boussinesq analysis presented in the paper can be modified to analyze output from eddy-resolving, Boussinesq ocean models.

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Richard J. Greatbatch

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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-track advection terms and 2) to be associated with the cross-track advection terms. When the horizontal pressure gradient terms are more important, feature 1) remain but the maximum response is displaced, in the wake, to the left of the track from the right. It is shown that even a symmetric storm can produce a strongly asymmetric response. Finally, results are compared with observations of the response of the ocean to hurricanes.

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Richard J. Greatbatch

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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 the effect of the ocean stratification and to extend through the depth of the ocean in this way.

The parameter which determines the horizontal structure of the response, in coordinates scaled with respect to the scale L of the storm, is k = U/Lf. Here U is the storm translation speed and f the Coriolis parameter. This parameter also determines the magnitude of the response, after suitable nondimensionalization.

Finally, it is shown how to apply these results to an interpretation of observations and other model results.

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Richard J. Greatbatch

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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 derivative of a horizontally directed eddy stress. The author shows how the eddy stress is related to the “inviscid pressure drag” or “form drag” associated with the eddies, although the correspondence is not exact.

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Richard J. Greatbatch and Allan Goulding

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An efficient numerical model is used to solve the linear barotropic equations of motion with North Atlantic bottom topography and seasonal wind forcing. The model domain extends from 10°S to 80°N and from 0° to 100°W with 1° × 1° resolution. Seasonal transport and sea level variations predicted by the model are compared with the available data.

The most striking result from our study is the ability of the model to reproduce features of the observed annual cycle of sea level. The model reproduces most of the features at stations on the southeastern seaboard of the United States noted by Blaha, although with reduced amplitude. We demonstrate the influence of offshore transport variations on our model response at these stations and suggest that perhaps the coastal sea level record provides evidence for the transport variations in deep water, offshore from the Gulf Stream, that are predicted by the model. We have also looked at the model response at stations farther north and on the eastern side of the North Atlantic. We find that the model results often show little agreement with data from which the offshore deep-water steric signal has been removed. Indeed, better agreement is generally found (at least in phase) with data corrected only for atmospheric pressure variations. This suggests that seasonally varying baroclinic coastal currents and/or JEBAR have an important influence on North Atlantic coastal sea level at these stations (a possible exception being St. John's, Newfoundland).

The model results compare favorably with the observed transport variations through the Florida Straits, although, in common with Anderson and Corry's study, the amplitude is underestimated. We demonstrate that our model transports are influenced by winds north of 50°N and that this influence is felt all along the eastern seaboard of North America. The model cannot, however, account for the annual cycle of transport in the Gulf Stream off Cape Hatteras noted by Halkin and Rossby. However, it does explain why Thompson et al. were unable to find any correlation between fluctuations in the Labrador Current and predictions based on the North Atlantic wind stress field. It also predicts a sea level response at Nain, Labrador, similar to that detected by these authors in the observed sea level record.

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Annika Drews and Richard J. Greatbatch

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This article investigates the dynamics and temporal evolution of the Atlantic multidecadal variability (AMV) in a coupled climate model. The model contains a correction to the North Atlantic flow field to improve the path of the North Atlantic Current, thereby alleviating the surface cold bias, a common problem with climate models, and offering a unique opportunity to study the AMV in a model. Changes in greenhouse gas forcing or aerosol loading are not considered. A striking feature of the results is the contrast between the western and eastern sides of the subpolar gyre in the model. On the western side, anomalous heat supply by the ocean plays a major role, with most of this heat being given up to the atmosphere in the warm phase, largely symmetrically about the time of the AMV maximum. By contrast, on the eastern side, the ocean anomalously gains heat from the atmosphere, with relatively little role for ocean heat supply in the years before the AMV maximum. Thereafter, the balance changes with heat now being anomalously removed from the eastern side by the ocean, leading to a reduced ocean heat content, behavior associated with the establishment of an intergyre gyre at the time of the AMV maximum. In the warm phase, melting sea ice leads to a freshening of surface waters northeast of Greenland that travel southward into the Irminger and Labrador Seas, shutting down convection and terminating the AMV warm phase.

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Richard J. Greatbatch and Jian Lu

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In the Stommel box model, the strength of the overturning circulation is parameterized in terms of the density (and hence the pressure) difference between the two boxes. Straub has pointed out that this parameterization is not consistent with the Stommel–Arons model for the abyssal circulation. In particular, the zonally averaged density field implied by the Stommel–Arons model is unrelated to the strength or the direction of the meridional overturning circulation. Here, the inconsistency is examined using the abyssal circulation model of Kawase and a variant to include the effect of Southern Hemisphere wind forcing. The important parameter is R, the ratio of two timescales: the timescale for a perturbation to the density field to propagate, by either wave or advective processes, from a high-latitude source to the equator and the timescale for the dissipation of a perturbation to the density field by diapycnal mixing. If the model is forced only by a deep water source in the northern basin, it is found that the model behaves like the Stommel–Arons model when R ≪ 1 (the “weak” damping regime) and like the Stommel box model when R ≫ 1 (the “strong” damping regine). Estimates of R suggest that coarse-resolution models generally reside in or near the Stommel box model regime (R ≫ 1), which is probably why these models generally support the Stommel box model hypothesis and corroborate the momentum-based closure used in zonally averaged models. On the other hand, it is not clear that the real world is also in the strong damping regime. Indeed, it is easy to obtain estimates for R, using realistic parameter values, that sit in the weak damping regime. It is shown that, even in the weak damping regime (R ≪ 1), adding forcing by the Southern Hemisphere circumpolar westerlies generally moves the model into the Stommel box model regime. It therefore is concluded that, at least in the context of the Kawase model, the inconsistency noted by Straub can be removed by including the effect of Southern Hemisphere wind forcing and that the Stommel box model approach probably has wider applicability than is suggested by estimates of R alone.

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Wenju Cai and Richard J. Greatbatch

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Recent observational study on the compensation for the North Atlantic Deep Water (NADW) outflow suggested that the compensation flow loops into the south Indian Ocean, whereby the compensating water gains heat and salt before returning to the South Atlantic. A question arises as to whether the heat and salt gain from the south Indian Ocean plays a significant role in determining the thermohaline circulation associated with the NADW formation. Many low-resolution ocean general circulation models (OGCMs) for coupled atmosphere–ocean studies fail to produce an Agulhas leakage. The consequence of this missing leakage in these climate models remains unclear. This study examines the role played by the Agulhas leakage in the compensating process for the NADW outflow, and assesses the feasibility of low-resolution ocean climate models. The authors do this in a series of numerical experiments using the Bryan–Cox global OGCM coupled to Schopf's zero heat capacity atmospheric model.

The model confirms that in the presence of the Agulhas leakage, the compensating route includes a loop extending into the southwestern Indian Ocean. Part of the compensating water flows to the Indian Ocean through this loop, and returns with Indian Ocean water to the South Atlantic via the Agulhas leakage. All of the compensating water flows with the Benguela Current. A small branch of the Benguela Current then breaks away from the main stream at about 15°S and heads for the North Atlantic.

The Agulhas leakage decreases only slightly when the NADW formation is suppressed. Most of the reduction occurs in the intermediate water. A comparison of model runs suggests that the contribution by the Indian Ocean water is less than 35% of the total compensating water leaving the South Atlantic and that the majority of the Indian Ocean contribution is intermediate water. Most of the South Atlantic area gains heat from the atmosphere, and the northward heat transport in the South Atlantic associated with the compensation can be sustained by this heat gain. The heat gain accompanies a conversion of intermediate water into surface water, providing the surface water source for the compensating water.

The southwestern Indian Ocean loop of the compensating flow provides a pathway whereby the compensating water may gain heat and salt from the Indian Ocean. In an experiment where the loop is suppressed, the Atlantic water cools and freshens. However, the cooling and freshening process hardly changes the density field, leading to an almost identical rate of the NADW formation and strength of the NADW outflow, with or without the Agulhas leakage.

That the majority of the compensating water, whether through the leakage or the Drake Passage, is intermediate water clears the way for the use of low-resolution OGCMs in climatic studies in terms of the compensation for the NADW outflow.

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Richard J. Greatbatch and Thomas Jung

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In this paper, a version of the European Centre for Medium-Range Weather Forecasts (ECMWF) operational model is used to (i) diagnose the diabatic heating associated with the winter North Atlantic Oscillation (NAO) and (ii) assess the role of this heating in the dynamics of the NAO in the model. Over the North Atlantic sector, the NAO-related diabatic heating is dominated above the planetary boundary layer by the latent heat release associated with precipitation, and within the boundary layer by vertical diffusion associated with sensible heat flux from the ocean. An association between La Niña–El Niño–type conditions in the tropical Pacific and the positive/negative NAO is found in model runs using initial conditions and sea surface temperature (SST) lower boundary conditions from the period 1982–2001, but not in a companion set of model runs for the period 1962–81. Model experiments are then described in which the NAO-related diabatic heating diagnosed from the 1982–2001 control run is applied as a constant forcing in the model temperature equation using both 1982–2001 and 1962–81 model setups. To assess the local feedback from the diabatic heating, the specified forcing is first restricted to the North Atlantic sector alone. In this case, the model response (in an ensemble mean sense) is suggestive of a weak negative feedback, but exhibits more baroclinic structure and has its centers of action shifted compared to those of the NAO. On the other hand, forcing with only the tropical Pacific part of the diabatic heating leads to a robust model response in both the 1982–2001 and 1962–81 model setups. The model response projects on to the NAO with the same sign as that used to diagnose the forcing, arguing that the link between the tropical Pacific and the NAO is real in the 1982–2001 control run. The missing link in the corresponding run for 1962–81 is a result of a change in the tropical forcing between the two periods, and not the extratropical flow regime.

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