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Henk A. Dijkstra
and
J. David Neelin

Abstract

Within one of the simplest models that represents thermohaline transport in the ocean, a two-dimensional Boussinesq model under mixed boundary conditions, the relationship between multiple equilibria in a flux-corrected model and an uncorrected model is considered. Flux-correction procedures are used in some climate models to maintain a climate state close to observed, compensating for model errors by introducing artificial fluxes between model components. A correction procedure used in many ocean or ocean–atmosphere models of the thermohaline circulation involves calculating the freshwater flux required to maintain observed surface salinity and then specifying this flux. In the prototype system here, one model solution is chosen as the “true” solution and flux correction is applied to model versions with different parameters. When the flux correction is not too large, it is qualitatively successful, particularly in reproducing the equilibrium state for which the correction is designed. However, other equilibria are more strongly affected, and the connections between equilibria are changed. Furthermore, areas in parameter space exist with multiple equilibria in the flux-corrected case that have a unique state in the uncorrected case. Care should thus be used in drawing conclusions on the existence of multiple equilibria and the stability of the thermohaline circulation when a flux-correction procedure is used. Guidelines are provided to help distinguish spurious equilibria in a flux-corrected model. The computation of an uncorrected equilibrium is useful, even if it does not resemble observations.

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Henk A. Dijkstra
and
J. David Neelin

Abstract

Coupled processes between the equatorial ocean and atmosphere control the spatial structure of the annual-mean state in the Pacific region, in particular the warm pool–cold tongue structure. At the same time, coupled processes are known to be responsible for the variability about this mean state, in particular the El Niño–Southern Oscillation phenomenon. In this paper, the connection between both effects of coupling is considered by investigating the linear stability of fully coupled climatologies in an intermediate coupled model. The new element here is that when parameters—such as the coupling strength—are changed, the potential amplification of disturbances can be greatly influenced by a simultaneous modification of the mean state. This alters the stability properties of the coupled climatology, relative to the flux-corrected cases that have been previously studied. It appears possible to identify a regime in parameter space where ENSO-like unstable modes coincide with a reasonable warm pool–cold tongue structure. These unstable modes are mixed SST–ocean dynamics modes, that is, they arise through an interaction of oscillatory modes originating from ocean dynamics and oscillatory SST modes. These effects are qualitatively similar in this fully coupled problem compared to the flux-corrected problem, but the sensitivity of the ENSO mode to parameters and external variations is larger due to feedbacks in the climatology.

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J. Dayid Neelin
and
Henk A. Dijkstra

Abstract

This sequence of papers examines the role of dynamical feedbacks between the ocean and the atmosphere in determining features of the tropical climatology. A stripped-down, intermediate, coupled ocean-atmosphere model is used to provide a prototype problem for the Pacific basin. Here the authors contrast the fully coupled case with the case where flux correction is used to construct the climatology. In the fully coupled case, the climatology is determined largely by feedback mechanisms within the ocean basin: winds driven by gradients of sea surface temperature (SST) within the basin interact with the ocean circulation to maintain SST gradients. For all realistic cases, these lead to a unique steady solution for the tropical climatology. In the flux-corrected case, the artificially constructed climatology becomes unstable at sufficiently large coupling, leading to multiple steady states as found in a number of coupled models. Using continuation methods, we show that there is a topological change in the bifurcation structure as flux correction is relaxed toward a fully coupled case; this change is characterized as an imperfection and must occur generically for all flux-corrected cases. The cold branch of steady solutions is governed by mechanisms similar to the fully coupled case. The warm branch, however, is spurious and disappears. The dynamics of this and consequences for coupled models are discussed. Multiple steady states can be ruled out as a mechanism for El Niño in favor of oscillatory mechanisms. The important role that coupled feedbacks are suggested to play in establishing tropical climatology is referred to as “the climatological version of the Bjerknes hypothesis."

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Henk A. Dijkstra
and
J. David Neelin

Abstract

The influence of coupled process on the climatology of the tropical Pacific is studied in a model for the interaction of equatorial SST, the associated component of the Walker circulation, and upper-ocean dynamics. In this part, the authors show how different physical mechanisms affect the spatial pattern of the Pacific warm pool and cold tongue in this coupled climatology. When model parameters give a suitable balance between effects of upwelling and thermocline depth on sea surface temperature and for suitable atmospheric parameters, a good prototype for the observed cold-tongue configuration is produced. This is largely determined by coupled ocean-atmosphere processes within the basin. Presence of an easterly wind s~ component produced by factors external to the Pacific basin can be important in setting up a cooling tendency, but this is magnified and modified by a chain of nonlinear feedbacks between trade winds and ocean dynamics affecting the SST gradient within the basin. These feedbacks determine a preferred spatial pattern that does not strongly depend on the form of the external wind stress and that tends to place the cold tongue in the cast-central basin. Although robust to external influences, this pattern is sensitive to the balance of coupled process. Parameter changes can produce warm-pool-cold-tongue patterns significantly different from observed but resembling some noted in coupled CTCMS.

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Henk A. Dijkstra
and
J. David Neelin

Abstract

The present Atlantic thermohaline circulation is dominated by deep water formation in the north despite the fact that surface buoyancy forcing has relatively modest latitudinal asymmetry. Many studies have shown that even with buoyancy forcing that is symmetric about the equator, spontaneous symmetry breaking can produce a single overturning cell with intense sinking in the north. This occurs by salt advection at sufficiently large freshwater forcing. In this symmetry-breaking case, a southern-sinking solution and a symmetric solution are also possible. A simple coupled ocean–atmosphere model of the zonally averaged thermohaline circulation is used to examine the effect of latitudinal asymmetries in the boundary conditions. The greater continental area in the Northern Hemisphere, combined with the slight asymmetry in the observed freshwater flux, induce a strong preference for the northern-sinking solution. Examining the relation to the solution under symmetric conditions, the salt-advection mechanism still acts to enhance the overturning circulation of the northern-sinking branch, but multiple equilibria are much less likely to occur within the realistic parameter range. The most plausible shift between equilibria for paleoclimate applications would be between a strong northern-sinking branch and a weak northern-sinking branch that is an asymmetric version of the thermally driven solution. However, this is possible only in a very limited range of parameters. There is a substantial parameter range where the northern-sinking branch is unique. The role of the fractional region of air–sea interaction at each latitude is substantial in producing north–south asymmetry.

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Lianke A. te Raa
and
Henk A. Dijkstra

Abstract

In this paper, an explanation is proposed for the changes in the amplitude of multidecadal variability found in the GFDL climate model when different restoring salinity fields in the flux adjustments were considered. This explanation arises from a study of the stability of three-dimensional thermohaline flows in an idealized coupled ocean–atmosphere model. The shape of the freshwater flux affects the stability properties of the thermohaline flows, in particular the growth rate of a stable interdecadal mode. The physics of this change in decay rate is explained by analyzing the energy conversions in the flows. Under a stronger freshening of the northern North Atlantic, the interdecadal mode destabilizes, which can result in an increase of the amplitude of the multidecadal variability.

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Henk A. Dijkstra
,
Juan A. Saenz
, and
Andrew McC. Hogg

Abstract

Oscillatory behavior of the Atlantic meridional overturning circulation (MOC) is thought to underlie Atlantic multidecadal climate variability. While the energy sources and sinks driving the mean MOC have received intense scrutiny over the last decade, the governing energetics of the modes of variability of the MOC have not been addressed to the same degree. This paper examines the energy conversion processes associated with this variability in an idealized North Atlantic Ocean model. In this model, the multidecadal variability arises through an instability associated with a so-called thermal Rossby mode, which involves westward propagation of temperature anomalies. Applying the available potential energy (APE) framework from stratified turbulence to the idealized ocean model simulations, the authors study the multidecadal variability from an energetics viewpoint. The analysis explains how the propagation of the temperature anomalies leads to changes in APE, which are subsequently converted into the kinetic energy changes associated with variations in the MOC. Thus, changes in the rate of generation of APE by surface buoyancy forcing provide the kinetic energy to sustain the multidecadal mode of variability.

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Leela M. Frankcombe
,
Anna von der Heydt
, and
Henk A. Dijkstra

Abstract

The issue of multidecadal variability in the North Atlantic has been an important topic of late. It is clear that there are multidecadal variations in several climate variables in the North Atlantic, such as sea surface temperature and sea level height. The details of this variability, in particular the dominant patterns and time scales, are confusing from both an observational as well as a theoretical point of view. After analyzing results from observational datasets and a 500-yr simulation of an Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) climate model, two dominant time scales (20–30 and 50–70 yr) of multidecadal variability in the North Atlantic are proposed. The 20–30-yr variability is characterized by the westward propagation of subsurface temperature anomalies. The hypothesis is that the 20–30-yr variability is caused by internal variability of the Atlantic Meridional Overturning Circulation (MOC) while the 50–70-yr variability is related to atmospheric forcing over the Atlantic Ocean and exchange processes between the Atlantic and Arctic Oceans.

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Matthijs den Toom
,
Henk A. Dijkstra
,
Andrea A. Cimatoribus
, and
Sybren S. Drijfhout

Abstract

The impact of atmospheric feedbacks on the multiple equilibria (ME) regime of the Atlantic meridional overturning circulation (MOC) is investigated using a fully implicit hybrid coupled model (HCM). The HCM consists of a global ocean model coupled to an empirical atmosphere model that is based on linear regressions of the heat, net evaporative, and momentum fluxes generated by a fully coupled climate model onto local as well as Northern Hemisphere averaged sea surface temperatures. Using numerical continuation techniques, bifurcation diagrams are constructed for the HCM with the strength of an anomalous freshwater flux as the bifurcation parameter, which allows for an efficient first-order estimation of the effect of interactive surface fluxes on the MOC stability. The different components of the atmospheric fluxes are first considered individually and then combined. Heat feedbacks act to destabilize the present-day state of the MOC and to stabilize the collapsed state, thus leaving the size of the ME regime almost unaffected. In contrast, interactive freshwater fluxes cause a destabilization of both the present-day and collapsed states of the MOC. Wind feedbacks are found to have a minor impact. The joint effect of the three interactive fluxes is to narrow the range of ME. The shift of the saddle-node bifurcation that terminates the present-day state of the ocean is further investigated by adjoint sensitivity analysis of the overturning rate to surface fluxes. It is found that heat feedbacks primarily affect the MOC stability when they change the heat fluxes over the North Atlantic subpolar gyre, whereas interactive freshwater fluxes have an effect everywhere in the Atlantic basin.

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Claudia E. Wieners
,
Henk A. Dijkstra
, and
Will P. M. de Ruijter

Abstract

In recent years it has been proposed that a negative (positive) Indian Ocean dipole (IOD) in boreal autumn favors an El Niño (La Niña) at a lead time of 15 months. Observational analysis suggests that a negative IOD might be accompanied by easterly anomalies over the western Pacific. Such easterlies can enhance the western Pacific warm water volume, thus favoring El Niño development from the following boreal spring onward. However, a Gill-model response to a negative IOD forcing would lead to nearly zero winds over the western Pacific. The authors hypothesize that a negative IOD—or even a cool western Indian Ocean alone—leads to low-level air convergence and hence enhanced convectional heating over the Maritime Continent, which in turn amplifies the wind convergence so as to cause easterly winds over the western Pacific. This hypothesis is tested by coupling an idealized Indian Ocean model and a convective feedback model over the Maritime Continent to the Zebiak–Cane model. It is found that, for a sufficiently strong convection feedback, a negative (positive) IOD indeed forces easterlies (westerlies) over the western Pacific. The contribution from the eastern IOD pole dominates. IOD variability is found to destabilize the El Niño–Southern Oscillation (ENSO) mode, whereas Indian Ocean basinwide warming (IOB) variability dampens ENSO, even in the presence of convection. The influence of the Indian Ocean on the spectral properties of ENSO is dominated by the IOB, while the IOD is a better predictor for individual ENSO events.

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