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Richard J. Greatbatch

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-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

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 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

Abstract

No abstract available.

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Richard J. Greatbatch

Abstract

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

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 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
Trevor J. McDougall

Abstract

A method for modifying currently existing ocean models to make them non-Boussinesq has been advocated by McDougall, Greatbatch, and Lu and implemented in the Parallel Ocean Program model by Greatbatch et al. Here, theoretical justification is provided for combining the above modifications with the temporal residual mean (TRM) approach of McDougall and McIntosh. The TRM is a method for including the skew flux of tracers caused by the adiabatic stirring of mesoscale eddies in non-eddy-resolving ocean models. The paper provides the justification for simultaneously undertaking these two model improvements and the physical interpretation of the model variables in this situation.

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Torben Kunz
and
Richard J. Greatbatch

Abstract

The dynamical origin of the spectral and autocorrelation structure of annular variability in the troposphere is investigated by a deductive approach. Specifically, the structure of the power spectrum and autocorrelation function of the zonal-mean geopotential is analyzed for the case of a quasigeostrophic spherical atmosphere subject to a white noise mechanical forcing applied in a single Hough mode and concentrated at a particular level in the vertical, with vertically uniform Newtonian cooling and Rayleigh drag concentrated at a rigid lower boundary. Analytic expressions for the power spectrum are presented together with expressions for an approximate red noise (i.e., a Lorentzian-shaped) power spectrum. It is found that for an infinitely deep atmosphere the power spectrum can be well approximated by a red noise process for the first few Hough modes (associated with large Rossby heights), provided the distance from the forcing is not larger than about one Rossby height. When a frictional rigid lower boundary is included, however, the approximation is generally bad. The high-frequency part of the power spectrum exhibits near-exponential behavior and the autocorrelation function shows a transition from a rapid decay at short lags to a much slower decay at longer lags, if the thermal and mechanical damping time scales are sufficiently well separated. Since observed annular variability exhibits the same characteristics, the above results lead to the hypothesis that these characteristics may, to some extent, be intrinsic to the linear zonal-mean response problem—although the need for an additional contribution from eddy feedbacks is also implied by the results.

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Torben Kunz
and
Richard J. Greatbatch

Abstract

The wintertime northern annular mode (NAM) at the surface is known to undergo slow intraseasonal variations in association with stratospheric variability, which leads the surface signal by up to several weeks. The relative contributions, however, of potentially relevant stratosphere–troposphere coupling mechanisms are not yet fully understood.

In this study the relative roles of (i) the downward effect of the zonal-mean secondary circulation induced by quasigeostrophic (QG) adjustment to stratospheric wave drag and radiative damping and (ii) wave drag local to the troposphere are estimated. For this purpose, a spectral tendency equation of the QG zonal-mean zonal wind is derived and used, in a first step, to obtain the external mechanical forcing that, in the QG framework, drives exactly the observed stratospheric and tropospheric daily NAM. In a second step, the equation is then integrated in time to reconstruct the daily NAM, but with the forcing restricted to either stratospheric or tropospheric levels, each case leaving a characteristic NAM surface signal.

The relative roles of the above-mentioned mechanisms are found to be of similar quantitative importance, but to differ in a qualitative sense. The downward effect of stratospheric QG adjustment is responsible for the initiation of the NAM surface signal, whereas subsequently local tropospheric wave drag actively maintains and persists the signal over several weeks. Furthermore, the downward effect of QG adjustment to stratospheric radiative damping is shown to have only a minor impact, compared to that from stratospheric wave drag. The robustness of these conclusions is demonstrated by a sensitivity study with respect to various model parameters.

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Richard J. Greatbatch
and
Ping-ping Rong

Abstract

Northern Hemisphere summer (July–August) data from the NCEP–NCAR and ECMWF 40-yr Re-Analysis (ERA-40) reanalyses are compared with each other and with Trenberth's sea level pressure (SLP) dataset. Discrepancies in SLP and 500 hPa are mostly confined to a band connecting North Africa and Asia. In the NCEP–NCAR reanalysis, there is a negative offset in SLP over North Africa and Asia prior to the late 1960s, together with a similar problem in 500-hPa height, and in Trenberth's data there is a negative offset in SLP over Asia prior to the early 1990s. Both these offsets magnify the linear trend from 1958 to 2002 over North Africa and Asia in the NCEP–NCAR and Trenberth datasets. On the other hand, the interannual variability in the three datasets is highly correlated during the periods between these offsets. Compared to SLP and 500-hPa height, there is a more extensive area of discrepancy in 2-m temperature that extends eastward from North Africa across the subtropics into the Pacific, with an additional area of discrepancy over the Arctic and parts of the American continent. At 500 and 100 hPa, the biggest differences in the temperature time series are found in the Tropics, with a marked jump being evident in the late 1970s in the NCEP–NCAR, but not in the ERA-40, reanalysis that is almost certainly associated with the introduction of satellite data. On the other hand, all three datasets agree well over Europe. The summer North Atlantic Oscillation (NAO), defined here as the first EOF of summer mean SLP over the Euro-Atlantic sector, agrees well between the different datasets. The results indicate that the upward trend in the summer index in the 1960s is part of a longer-period interdecadal cycle, with relatively high index values also being found during the 1930s. The running cross correlation between the central England temperature record and the summer NAO shows a strong correlation throughout the last half of the twentieth century, but much reduced correlation in the early part of the twentieth century. It is not clear whether the change in correlation is real, or a data artifact, a topic that requires further research.

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Richard J. Greatbatch
and
Thomas Jung

Abstract

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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