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Jochem Marotzke

Abstract

The length of time an ocean model and its adjoint should be integrated in determining a steady state compatible with observed data is investigated. The starting point is based upon a suggestion that only one time step is required. This method fails to converge to an acceptable solution when applied to a general circulation model (GCM) of the North Atlantic. Using a very coarse resolution GCM in an idealized geometry, the problem is traced to the interplay of convective adjustment and the very short integration time.

The general assimilation technique is explored using a very simple model, a linear first-order equation with forcing and damping. The model is unable to provide a dynamical coupling between the forcing and the model response, owing to a mismatch of integration time and adjustment time scale. Coupling can be enforced in the simple linear model through a careful choice of weighting factors, a strategy excluded in the GCM due to the presence of very fast processes like convective adjustment. An integration over a sufficiently long time can avoid the problems encountered. Experiments with the idealized GCM prove successful for longer integrations, and a tentative upper limit of 50 years is given for inversions aiming at the main thermocline structure.

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Jochem Marotzke

Abstract

Boundary mixing is implemented in an ocean general circulation model such that the vertical mixing coefficient k υ is nonzero only near side boundaries and in convection regions. The model is used in a highly idealized configuration with no wind forcing and very nearly fixed surface density to investigate the three-dimensional dynamics of the thermohaline circulation. For k υ = 20 × 10−4 m2 s−1 and lower, the meridional overturning strength to great accuracy is proportional to k 2/3 υ ; meridional heat transport is proportional to k 1/2 υ . The circulation patterns resemble those from runs with uniform vertical mixing, but vertical motion is entirely confined to the boundary regions. Near the western boundary, there is upwelling everywhere. Near the eastern boundary, there is a consistent pattern of downwelling above upwelling, with downwelling reaching deeper at high latitudes; this pattern is explained by convection and vertical advective–diffusive balance underneath.

For k υ = 30 × 10−4 m2 s−1 and higher, no steady solutions have been found; the meridional overturning oscillates on a timescale of about 25 years. A time-averaged thermally direct overturning cell is not supported dynamically because convection extends longitudinally across the entire basin, and upwelling near the western boundary does not lead to densities higher than at the eastern boundary.

Assuming uniform upwelling in the west, level isopycnals near the equator, and level isopycnals along the eastern boundary south of the outcropping latitude permits the analytic determination of convection depth at the eastern wall and hence the density difference between the eastern and western walls. This difference is at most one-quarter the surface density difference between high and low latitudes, and agrees in magnitude and latitudinal dependence with the numerical experiments. Scaling arguments estimate overturning strength as of the order of 10 × 106 m3 s−1 and confirm the 2/3 power dependence on k υ . The derivation also gives a dependence of overturning strength with latitude that agrees qualitatively with the numerical results. The scaling for the dependence of meridional heat transport on latitude agrees well with the model results; scaling for heat transport amplitude agrees less well but correctly predicts a weaker dependence on k υ than maximum overturning.

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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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Tong Lee
and
Jochem Marotzke

Abstract

A general circulation model of the Indian Ocean is fitted to monthly averaged climatological temperatures, salinities, and surface fluxes using the adjoint method. Interannual variability is minimized by penalizing the temporal drift from one seasonal cycle to another during a two-year integration. The resultant meridional overturning and heat transport display large seasonal variations, with maximum amplitudes of 18 and 22 (× 106 m3 s−1) for the overturning and 1.8 and 1.4 (× 1015 W) for heat transport near 10°S and 10°N, respectively. A dynamical decomposition of the overturning and heat transport shows that the time-varying Ekman flow plus its barotropic compensation can explain a large part of the seasonal variations in overturning and heat transport. The maximum variations at 10°N and 10°S are associated with monsoon reversal over the northern Indian Ocean and changes of the easterlies over the southern Indian Ocean. An external mode with variable topography has a moderate contribution where the Somali Current and the corresponding gyre reverse direction seasonally. Contribution from vertical shear (thermal wind and ageostrophic shear) is dominant near the southern boundary and large near the Somali Current latitudes. The dominant balance in the zonally integrated heat budget is between heat storage change and heat transport convergence except south of 15°S.

Optimization with seasonal forcings improves estimates of sea surface temperatures, but the annual average overturning and heat transport are very similar to previous results with annual mean forcings. The annual average heat transport consists of roughly equal contributions from time-mean and time-varying fields of meridional velocities and temperatures in the northern Indian Ocean, indicating a significant rectification to the heat transport due to the time-varying fields. The time-mean and time-varying contributions are primarily due to the overturning and horizontal gyre, respectively.

Inclusion of TOPEX data enhances the seasonal cycles of the estimated overturning and heat transport in the central Indian Ocean significantly and improves the estimated equatorial zonal flows but leads to unrealistic estimates of the velocity structure near the Indonesian Throughflow region, most likely owing to the deficiencies in the lateral boundary conditions.

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Marlene Klockmann
,
Uwe Mikolajewicz
, and
Jochem Marotzke

Abstract

This study analyzes the response of the Atlantic meridional overturning circulation (AMOC) to different CO2 concentrations and two ice sheet configurations in simulations with the coupled climate model MPI-ESM. With preindustrial (PI) ice sheets, there are two different AMOC states within the studied CO2 range: one state with a strong and deep upper overturning cell at high CO2 concentrations and one state with a weak and shallow upper cell at low CO2 concentrations. Changes in AMOC variability with decreasing CO2 indicate two stability thresholds. The strong state is stable above the first threshold near 217 ppm, and the weak state is stable below the second threshold near 190 ppm. Between the two thresholds, both states are marginally unstable, and the AMOC oscillates between them on millennial time scales. The weak AMOC state is stable when Antarctic Bottom Water becomes dense and salty enough to replace North Atlantic Deep Water (NADW) in the deep North Atlantic and when the density gain over the North Atlantic becomes too weak to sustain continuous NADW formation. With Last Glacial Maximum (LGM) ice sheets, the density gain over the North Atlantic and the northward salt transport are enhanced with respect to the PI ice sheet case. This enables active NADW formation and a strong AMOC for the entire range of studied CO2 concentrations. The AMOC variability indicates that the simulated AMOC is far away from a stability threshold with LGM ice sheets. The nonlinear relationship among AMOC, CO2, and prescribed ice sheets provides an explanation for the large intermodel spread of AMOC states found in previous coupled LGM simulations.

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Max Popp
,
Hauke Schmidt
, and
Jochem Marotzke

Abstract

A one-dimensional radiative–convective equilibrium model is used to investigate the influence of clouds on the onset of a runaway greenhouse under strong solar forcing. By comparing experiments with clear-sky conditions (clouds are transparent to radiation) to experiments with full-sky conditions (clouds are radiatively active), the authors find that the critical solar irradiance that is necessary to trigger a runaway greenhouse is increased from around 1.15–1.20 times the present-day total solar irradiance (TSI) on Earth S 0 for clear-sky conditions to around 1.40–1.45S 0 for full-sky conditions. Cloud thickness increases with TSI, leading to a substantially higher albedo, which in turn allows the climate to remain in equilibrium for markedly higher values of TSI. The results suggest that steady states with sea surface temperatures higher than 335 K exist for a large range of TSI. The thickening clouds in these states do not reduce the outgoing longwave radiation any more, implying that the thickening of clouds increases only their shortwave effect. This mechanism allows the column to remain in balance even at high sea surface temperatures. The authors find double equilibria for both clear-sky and full-sky conditions, but the range for which they occur extends to considerably higher values of TSIs for full-sky conditions. Moreover, when clouds are included in the radiative transfer calculations, climate instabilities are no longer caused by longwave effects but by the cloud albedo effect.

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Barry A. Klinger
and
Jochem Marotzke

Abstract

A coarse resolution, three-dimensional numerical model is used to study how external parameters control the existence and strength of equatorially asymmetric thermohaline overturning in a large-scale, rotating ocean basin. Initially, the meridional surface density gradient is directly set to be larger in a “dominant” hemisphere than in a “subordinate” hemisphere. The two-hemisphere system has a broader thermocline and weaker upwelling than the same model with the dominant hemisphere only. This behavior is in accord with classical scaling arguments, providing that the continuity equation is employed, rather than the linear vorticity equation.

The dominant overturning cell, analogous to North Atlantic Deep Water formation, is primarily controlled by the surface density contrast in the dominant hemisphere, which in turn is largely set by temperature. Consequently, in experiments with mixed boundary conditions, the dominant cell strength is relatively insensitive to the magnitude Q S of the salinity forcing. However, Q S strongly influences subordinate hemisphere properties, including the volume transport of a shallow overturning cell and the meridional extent of a tongue of low-salinity intermediate water reminiscent of Antarctic Intermediate Water.

The minimum Q S is identified for which the steady, asymmetric flow is stable; below this value, a steady, equatorially symmetric, temperature-dominated overturning occurs. For high salt flux, the asymmetric circulation becomes oscillatory and eventually gives way to an unsteady, symmetric, salt-dominated overturning. For given boundary conditions, it is possible to have at least three different asymmetric states, with significantly different large-scale properties. An expression for the meridional salt transport allows one to roughly predict the surface salinity and density profile and stability of the asymmetric state as a function of Q S and other external parameters.

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Jochem Marotzke
and
David W. Pierce

Abstract

The authors identify spatial and temporal scales in a one-dimensional linear, diffusive atmospheric energy balance model coupled everywhere to a slab mixed layer of fixed depth. Mathematically, the model is identical to a heat conducting rod, which over its entire length both radiates and is in contact with a large but finite“reservoir.” Three characteristic timescales mark, respectively, the atmosphere’s adjustment to a sea surface temperature (SST) anomaly, the decay of a pointwise SST anomaly, and the radiative decay of a large-scale SST anomaly. The first and the third of these timescales are associated with diffusive length scales characterizing, respectively, the distance over which heat is diffused in the atmosphere before being lost to the ocean beneath, and the distance over which heat is diffused in the coupled system before being radiated to space. For spatial scales between the two diffusive lengths, the SST anomaly does not decay exponentially but with the square root of time; this regime has not previously been identified. Apparent discrepancies between published discussions of diffusive length scales are reconciled.

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Steven R. Jayne
and
Jochem Marotzke

Abstract

The rectified eddy heat transport is calculated from a global high-resolution ocean general circulation model. The eddy heat transport is found to be strong in the western boundary currents, the Antarctic Circumpolar Current, and the equatorial region. It is generally weak in the central gyres. It is also found to be largely confined to the upper 1000 m of the ocean model. The eddy heat transport is separated into its rotational and divergent components. The rotational component of the eddy heat transport is strong in the western boundary currents, while the divergent component is strongest in the equatorial region and Antarctic Circumpolar Current. In the equatorial region, the eddy heat transport is due to tropical instability waves, while in the western boundary currents and the Antarctic Circumpolar Current the large eddy heat transports arise from the meandering of the currents. Stammer's method for estimating the eddy heat transport from an eddy diffusivity derived from mixing length arguments, using altimetry data and the climatological temperature field, is tested and fails to reproduce the model's directly evaluated eddy heat transport in the equatorial regions, and possible reasons for the discrepancy are explored. However, in the Antarctic Circumpolar Current region and to a lesser extent in the western boundary currents, the model's eddy heat transport is shown to have some qualitative agreement with his estimate.

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Jeffery R. Scott
and
Jochem Marotzke

Abstract

The large-scale consequences of diapycnal mixing location are explored using an idealized three-dimensional model of buoyancy-forced flow in a single hemisphere. Diapycnal mixing is most effective in supporting a strong meridional overturning circulation (MOC) if mixing occurs in regions of strong stratification, that is, in the low-latitude thermocline where diffusion causes strong vertical buoyancy fluxes. Where stratification is weak, such as at high latitudes, diapycnal mixing plays little role in determining MOC strength, consistent with weak diffusive buoyancy fluxes at these latitudes. Boundary mixing is more efficient than interior mixing at driving the MOC; with interior mixing the planetary vorticity constraint inhibits the communication of interior water mass properties and the eastern boundary. Mixing below the thermocline affects the abyssal stratification and upwelling profile but does not contribute significantly to the meridional flow through the thermocline or the ocean's meridional heat transport. The abyssal heat budget is dominated by the downward mass transport of buoyant water versus the spread of denser water tied to the properties of deep convection, with mixing of minor importance. These results are in contrast to the widespread expectation that the observed enhanced abyssal mixing can maintain the MOC; rather, they suggest that enhanced boundary mixing in the thermocline needs to be identified in observations.

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