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Jürgen Willebrand

Abstract

Quasi-geostrophic wind fields over the northern parts of the Pacific and Atlantic Oceans are calculated from synoptic surface pressure data for the four-year period 1973–76. Maps of mean and rms wind stress and of mean wind stress curl are given. Spectral and cross-spectral analysis reveals the dominant space and time scales of atmospheric disturbances. At periods shorter than 10 days, eastward traveling cyclones dominate the atmospheric variability. At longer time scales the atmospheric spectra are white in frequency and symmetric with respect to wavenumber, and there is no preferred direction of propagation. Differences between the spectra of pressure, wind and wind stress are discussed.

To estimate the amount of fluctuations at high wavenumbers which are not present in smoothed synoptic maps, direct wind observations from two weather stations in the North Atlantic are analyzed and compared to synoptic data. It is found that the smoothing is severe for fluctuations with a period shorter than 10 days, but is less important on longer time scales.

It is demonstrated that the most important parameters of the frequency-wavenumber spectrum of atmospheric pressure can be inferred from wind and pressure observations at a single weather station, provided the relationship between geostrophic and surface winds is known. The method can be utilized in areas of sparse spatial resolution (e.g., Southern Hemisphere) to infer horizontal scales and propagational characteristics of the atmospheric fields.

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Carsten Eden and Jürgen Willebrand

Abstract

A model of the Atlantic Ocean was forced with decadal-scale time series of surface fluxes taken from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis. The bulk of the variability of the oceanic circulation is found to be related to the North Atlantic oscillation (NAO). Both realistic experiments and idealized sensitivity studies with the model show a fast (intraseasonal timescale) barotropic response and a delayed (timescale about 6–8 yr) baroclinic oceanic response to the NAO. The fast response to a high NAO constitutes a barotropic anticyclonic circulation anomaly near the subpolar front with a substantial decrease of the northward heat transport and an increase of northward heat transport in the subtropics due to changes in Ekman transport. The delayed response is an increase in subpolar heat transport due to enhanced meridional overturning and due to a spinup of the subpolar gyre. The corresponding subpolar and subtropical heat content changes could in principle act as an immediate positive feedback and a delayed negative feedback to the NAO.

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Stefan Rahmstorf and Jürgen Willebrand

Abstract

Ocean climate models traditionally compute the surface heat flux with a restoring boundary condition of the form Q = λ(T *To). This implies an atmosphere of fixed temperature and breaks down when large-scale changes in the ocean circulation are considered, which have a feedback effect on atmospheric temperatures.

To include this important feedback, a new thermal boundary condition of the form Q = γ(T *To) − μ∇2(T *To) is proposed. This is derived from an atmospheric energy balance model with diffusive lateral heat transport. The effects of this new parameterization are examined in experiments with the GFDL modular ocean model for two model basins. “Conveyor belt” circulation states are compared using traditional mixed boundary conditions and our new coupling. With the new coupling, a realistic temperature contrast is obtained between the North Atlantic and the Pacific, caused by free adjustment of surface temperature to the oceanic heat transport.

The results show that a temperature feedback involving horizontal heat transport regulates the overturning rate of the conveyor. A second feedback involving vertical convection of heat stabilizes the conveyor belt when freshwater anomalies are added to the North Atlantic, making it harder to interrupt convection and trigger a halocline catastrophe.

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Jochem Marotzke and Jürgen Willebrand

Abstract

A general circulation model with a highly idealized geometry is used to investigate which fundamentally different equilibria of the global thermohaline circulation may exist. The model comprises two identical basins representing the Atlantic and Pacific oceans, which are connected by a circumpolar channel in the south. The model circulation is driven, in addition to wind forcing by restoring the sea surface temperature to prescribed values and specified freshwater fluxes in the surface salinity budget (mixed boundary conditions). The boundary conditions are symmetric with respect to the equator and identical for both oceans.

Four fundamentally different, stable steady states are found under the same set of boundary conditions. Two of the equilibria show both oceans in the same state, with high-altitude deep-water formation occuring either in both northern or in both southern oceans, respectively. Two additional equilibria exist in which the thermohaline circulations of the basins differ fundamentally from each other: one ocean forms deep water at northern high latitudes, while the other has a much weaker circulation with sinking in the Southern Hemisphere. One of these equilibria qualitatively corresponds to today's global thermohaline circulation pattern (conveyor belt).

It is demonstrated that a transition from one equilibrium to another can be accomplished by relatively small differences in the freshwater fluxes. The preference and sensitivity of the steady states depends critically on the freshwater forcing applied.

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Nils H. Rix and Jürgen Willebrand

Abstract

The compatibility of the Gent and McWilliams thickness mixing parameterization with perturbation thickness fluxes evaluated from eddy-resolving North Atlantic model results is investigated. After extensive spatial and temporal averaging, a linear correlation between the parameterized fluxes and those calculated directly from model fluctuations in the subtropics could be found. A direct estimate of a constant mixing parameter κ could be inferred in the order of 1.0 × 107 cm2 s−1.

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Hans-Jörg Isemer, Jürgen Willebrand, and Lutz Hasse

Abstract

An inverse technique is used to adjust uncertain coefficients and parameters in the bulk formulae of climatological air-sea energy fluxes in order to obtain an agreement of indirect estimates of meridional heat transport with direct estimates in the North Atlantic Ocean. Three oceanographic estimates of ocean heat transport at the equator, at 25°N, and 32°N are compatible with meteorological evidence provided that the uncertainties of both direct and indirect estimates are taken into account. The transport coefficient CE for estimation of the latent heat flux is the major contributor to the overall uncertainty in estimates of ocean heat transport. The constraint of 1 PW northward transport across 25°N leads to a set of parameterizations for which the parameter adjustments are only less than half as large as the estimated uncertainties. Based on this set of constrained parameterizations monthly climatological fields of the individual fluxes in the North Atlantic Ocean are computed which are consistent with direct transport estimates.

With a larger set of heat transport observations this method will provide a possibility to discriminate between various bulk formulations, and to obtain more accurate estimates of the air-sea energy flux.

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Carsten Eden, Richard J. Greatbatch, and Jürgen Willebrand

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 estimated using an optimization technique. In this case, |κ| can be reduced or increased by construction, but the regions where κ < 0 are still present and the optimized rotational fluxes also remain similar to a priori values given by the theoretical considerations. A previously neglected component (ν) of the bolus velocity is associated with the horizontal flux of buoyancy along, rather than across, the mean buoyancy contours. The ν component of the bolus velocity is interpreted as a streamfunction for eddy-induced advection, rather than diffusion, of mean isopycnal layer thickness, showing up when the lateral eddy fluxes cannot be described by isotropic diffusion only. All estimates show a similar large-scale pattern for ν, implying westward advection of isopycnal thickness over much of the subtropical gyre. Comparing ν with a mean streamfunction shows that it is about 10% of the mean in midlatitudes and even larger than the mean in the Tropics.

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Aike Beckmann, Claus W. Böning, Cornelia Köberle, and Jürgen Willebrand

Abstract

Global mean and eddy fields from a four-year experiment with a 1/6° × 1/5° horizontal resolution implementation of the CME North Atlantic model are presented. The time-averaged wind-driven and thermohaline circulation in the model is compared to the results of a 1/3° × 2/5° model run in very similar configuration. In general, the higher resolution results are found to confirm that the resolution of previous CME experiments is sufficient to describe many features of the large-scale circulation and water mass distribution quite well. While the increased resolution does not lead to large changes in the mean flow patterns, the variability in the model is enhanced significantly. On the other hand, however, not all aspects of the circulation have improved with resolution. The Azores Current Frontal Zone with its variability in the eastern basin is still represented very poorly. Particular attention is also directed toward the unrealistic stationary anticyclones north of Cape Hatteras and in the Gulf of Mexico.

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Peter R. Gent, Jurgen Willebrand, Trevor J. McDougall, and James C. McWilliams

Abstract

It is shown that the effects of mesoscale eddies on tracer transports can be parameterized in a large-scale model by additional advection and diffusion of tracers. Thus, tracers are advected by the effective transport velocity, which is the sum of the large-scale velocity and the eddy-induced transport velocity. The density and continuity equations are the familiar equations for adiabatic, Boussinesq, and incompressible flow with the effective transport velocity replacing the large-scale velocity. One of the main points of this paper is to show how simple the parameterization of Gent and McWilliams appears when interpreted in terms of the effective transport velocity. This was not done in their original 1990 paper. It is also shown that, with the Gent and McWilliams parameterization, potential vorticity in the planetary geostrophic model satisfies an equation close to that for tracers. The analogy of this parameterization with vertical mixing of momentum is then described.

The effect of the Gent and McWilliams parameterization is illustrated by applying it to a strong, sloping two-dimensional front. The final state is that the front is flat, corresponding to a state of minimum potential energy. However, the amount of water of a given density has not been changed and there has been no flow across isopycnals. These properties are not preserved with horizontal diffusion of tracer. Finally, the Levitus dataset is used to estimate the effects of the Gent and McWilliams parameterization. The zonal mean meridional overturning streamfunction for the eddy-induced transport velocity has a maximum of 18 Sverdrups near the Antarctic Circumpolar Current. The associated poleward heat transport is 0.4 petawatts. The maximum poleward heat transport in the Northern Hemisphere is 0.15 petawatts at 40°N. These values are the same order of magnitude as estimates from observations and regional eddy-resolving ocean models.

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