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Henk A. Dijkstra

Abstract

The spectral origin of the recently discovered multidecadal modes (MMs) and centennial modes (CMs) is explained. These modes appear in the linear stability analysis of thermohaline-driven flows in a single-hemispheric ocean basin. It is shown that both classes of modes arise through interaction of so-called sea surface temperature (SST) modes. These SST modes are damped and nonoscillatory for the unforced (motionless) flow. They become oscillatory under small thermal forcing through mode merging that is induced by the meridional overturning circulation. The type of merger responsible for each class of modes explains many features—for example, why CMs can be found in two-dimensional models whereas MMs cannot—of the patterns of the modes at realistic forcing strength.

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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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Maurice J. Schmeits
and
Henk A. Dijkstra

Abstract

For a long time, observations have indicated that the Kuroshio in the North Pacific Ocean displays bimodal meandering behavior off the southern coast of Japan. For the Gulf Stream in the North Atlantic Ocean, weakly and strongly deflected paths near the coast of South Carolina have been observed. This suggests that bimodal behavior may occur in the Gulf Stream as well, although less pronounced than in the Kuroshio. Evidence from a high-resolution ocean general circulation model (OGCM) and intermediate complexity models is given to support the hypothesis that multiple mean paths of both the Kuroshio and the Gulf Stream are dynamically possible. These paths are found as multiple steady states in an intermediate complexity shallow-water model. In the OGCM, transitions between similar mean paths are found, with the patterns having similarity to the ones in observations as well. To study whether atmospheric noise can induce transitions between the multiple steady states, a stochastic component is added to the annual mean wind stress forcing in the intermediate complexity model and differences between the transition behavior in the Gulf Stream and Kuroshio are considered.

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Wilbert Weijer
and
Henk A. Dijkstra

Abstract

For the first time, the (linear) stability of the global ocean circulation has been determined explicitly. In a low-resolution general circulation model, a steady state is computed directly by solving the elliptic boundary value problem. The stability of this solution is determined by solving the generalized eigenvalue problem. Although the steady global circulation is (linearly) stable, there are two interesting oscillatory modes among the least stable ones, with periods of about 3800 and 2300 yr. These modes are characterized by buoyancy anomalies that propagate through the ocean basins as they are advected by the global overturning circulation. The millennial timescale is set by the time it takes for anomalies to travel, at depth, from the North Atlantic to the North Pacific. Further analyses confirm that the advective feedback between the steady flow and buoyancy anomalies is an essential process in the propagation mechanism. The growth rate of the millennial modes is controlled by vertical mixing. It is argued that these internal ocean modes may be a relevant mechanism for global climate variability on millennial timescales.

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Eric Simonnet
and
Henk A. Dijkstra

Abstract

In idealized models that aim to understand the temporal variability of the wind-driven ocean circulation, low-frequency instabilities associated with so-called oscillatory gyre modes have been found. For the double-gyre case, the spectral origin of these modes as well as the physical mechanism of the instability is explained. In a barotropic quasigeostrophic model, the low-frequency modes arise spontaneously from the merging between two nonoscillatory eigenmodes. Of the latter two, one is called here the P-mode and is responsible for the existence of multiple steady states. The other is called the L-mode and it controls the intensity of the gyres. This merging turns out to be robust over a hierarchy of models and can even be found in a low-order truncated quasigeostrophic model. The latter model is used to determine the physical mechanism of the instability. The low-frequency oscillation results from the conjugate effects of shear- and symmetry-breaking instabilities and is free of Rossby wave dynamics.

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Leela M. Frankcombe
and
Henk A. Dijkstra

Abstract

Observations of sea ice extent and atmospheric temperature in the Arctic, although sparse, indicate variability on multidecadal time scales. A recent analysis of one of the global climate models [the Geophysical Fluid Dynamics Laboratory Climate Model, version 2.1 (CM2.1)] in the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change has indicated that Arctic Ocean variability on these time scales is associated with changes in basin-wide salinity patterns. In this paper the internal modes of variability in an idealized Arctic Basin are determined by considering the stability of salinity-driven flows. An internal ocean mode with a multidecadal time scale is found, with a spatial pattern similar to that obtained in the analysis of the CM2.1 results. The modes propagate as a “saline Rossby wave” induced by the background salinity gradient.

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