121 research outputs found
Coherent Resonat millenial-scale climate transitions triggered by massive meltwater pulses
The role of mean and stochastic freshwater forcing on the generation of millennial-scale climate variability in the North Atlantic is studied using a low-order coupled atmosphere–ocean–sea ice model. It is shown that millennial-scale oscillations can be excited stochastically, when the North Atlantic Ocean is fresh enough. This finding is used in order to interpret the aftermath of massive iceberg surges (Heinrich events) in the glacial North Atlantic, which are characterized by an excitation of Dansgaard–Oeschger events. Based on model results, it is hypothesized that Heinrich events trigger Dansgaard–Oeschger cycles and that furthermore the occurrence of Heinrich events is dependent on the accumulated climatic effect of a series of Dansgaard–Oeschger events. This scenario leads to a coupled ocean–ice sheet oscillation that shares many similarities with the Bond cycle. Further sensitivity experiments reveal that the timescale of the oscillations can be decomposed into stochastic, linear, and nonlinear deterministic components. A schematic bifurcation diagram is used to compare theoretical results with paleoclimatic data
Basin bifurcations, oscillatory instability and rate-induced thresholds for AMOC in a global oceanic box model
The Atlantic Meridional Overturning Circulation (AMOC) transports substantial
amounts of heat into the North Atlantic sector, and hence is of very high
importance in regional climate projections. The AMOC has been observed to show
multi-stability across a range of models of different complexity. The simplest
models find a bifurcation associated with the AMOC `on' state losing stability
that is a saddle node. Here we study a physically derived global oceanic model
of Wood {\em et al} with five boxes, that is calibrated to runs of the FAMOUS
coupled atmosphere-ocean general circulation model. We find the loss of
stability of the `on' state is due to a subcritical Hopf for parameters from
both pre-industrial and doubled CO atmospheres. This loss of stability
via subcritical Hopf bifurcation has important consequences for the behaviour
of the basin of attraction close to bifurcation. We consider various
time-dependent profiles of freshwater forcing to the system, and find that
rate-induced thresholds for tipping can appear, even for perturbations that do
not cross the bifurcation. Understanding how such state transitions occur is
important in determining allowable safe climate change mitigation pathways to
avoid collapse of the AMOC.Comment: 18 figure
Oscillators and relaxation phenomena in Pleistocene climate theory
Ice sheets appeared in the northern hemisphere around 3 million years ago and
glacial-interglacial cycles have paced Earth's climate since then. Superimposed
on these long glacial cycles comes an intricate pattern of millennial and
sub-millennial variability, including Dansgaard-Oeschger and Heinrich events.
There are numerous theories about theses oscillations. Here, we review a number
of them in order to draw a parallel between climatic concepts and dynamical
system concepts, including, in particular, the relaxation oscillator,
excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all
theories of ice ages reviewed here feature a phenomenon of synchronisation
between internal climate dynamics and the astronomical forcing. However, these
theories differ in their bifurcation structure and this has an effect on the
way the ice age phenomenon could grow 3 million years ago. All theories on
rapid events reviewed here rely on the concept of a limit cycle in the ocean
circulation, which may be excited by changes in the surface freshwater surface
balance. The article also reviews basic effects of stochastic fluctuations on
these models, including the phenomenon of phase dispersion, shortening of the
limit cycle and stochastic resonance. It concludes with a more personal
statement about the potential for inference with simple stochastic dynamical
systems in palaeoclimate science.
Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages,
Dansgaard-Oeschger eventsComment: Published in the Transactions of the Philosophical Transactions of
the Royal Society (Series A, Physical Mathematical and Engineering Sciences),
as a contribution to the Proceedings of the workshop on Stochastic Methods in
Climate Modelling, Newton Institute (23-27 August). Philosophical
Transactions of the Royal Society (Series A, Physical Mathematical and
Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on
request to author and on http://www.uclouvain.be/ito
An Organizing Center for Thermohaline Excitability
The bifurcation behavior of a conceptual heat–salt oscillator model is analyzed by means of numerical continuation methods. A global (homoclinic) bifurcation acts as an organizing center for the dynamics of the simplified convective model. It originates from a codimension-2 bifurcation in an extended parameter space. Comparison with earlier work by Cessi shows that the intriguing stochastic thermohaline excitability can be understood from the bifurcation structure of the model. It is argued that global bifurcations may play a crucial role in determining long-term variability of the thermohaline circulation
Millennial Variability in an Idealized Ocean Model: Predicting the AMOC Regime Shifts
A salient feature of paleorecords of the last glacial interval in the North Atlantic is pronounced millennial variability, commonly known as Dansgaard–Oeschger events. It is believed that these events are related to variations in the Atlantic meridional overturning circulation and heat transport. Here, the authors formulate a new low-order model, based on the Howard–Malkus loop representation of ocean circulation, capable of reproducing millennial variability and its chaotic dynamics realistically. It is shown that even in this chaotic model changes in the state of the meridional overturning circulation are predictable. Accordingly, the authors define two predictive indices which give accurate predictions for the time the circulation should remain in the on phase and then stay in the subsequent off phase. These indices depend mainly on ocean stratification and describe the linear growth of small perturbations in the system. Thus, monitoring particular indices of the ocean state could help predict a potential shutdown of the overturning circulation
Dansgaard-Oeschger events: tipping points in the climate system
Dansgaard-Oeschger events are a prominent mode of variability in the records
of the last glacial cycle. Various prototype models have been proposed to
explain these rapid climate fluctuations, and no agreement has emerged on which
may be the more correct for describing the paleoclimatic signal. In this work,
we assess the bimodality of the system reconstructing the topology of the
multi--dimensional attractor over which the climate system evolves. We use
high-resolution ice core isotope data to investigate the statistical properties
of the climate fluctuations in the period before the onset of the abrupt
change. We show that Dansgaard-Oeschger events have weak early warning signals
if the ensemble of events is considered. We find that the statistics are
consistent with the switches between two different climate equilibrium states
in response to a changing external forcing (e.g. solar, ice sheets...), either
forcing directly the transition or pacing it through stochastic resonance.
These findings are most consistent with a model that associates
Dansgaard-Oeschger with changing boundary conditions, and with the presence of
a bifurcation point.Comment: Final typeset version freely available at: Clim. Past, 9, 323-333,
2013 www.clim-past.net/9/323/2013/ doi:10.5194/cp-9-323-201
Homoclinic bifurcations in the quasi-geostrophic double-gyre circulation
The wind-driven double-gyre circulation in a rectangular basin goes through several dynamical regimes as the amount of lateral friction is decreased. This paper studies the transition to irregular flow in the double-gyre circulation by applying dynamical systems methodology to a quasi-geostrophic, equivalent-barotropic model with a 10-km resolution.The origin of the irregularities, in space and time, is the occurrence of homoclinic bifurcations that involve phase-space behavior far from stationary solutions. The connection between these homoclinic bifurcations and earlier transitions, which occur at larger lateral friction, is explained. The earlier transitions, such as pitchfork and asymmetric Hopf bifurcation, only involve the nonlinear saturation of linear instabilities, while the homoclinic bifurcations are associated with genuinely nonlinear behavior. The sequence of bifurcations—pitchfork, Hopf, and homoclinic—is independent of the lateral friction and may be described as the unfolding of a singularity that occurs in the frictionless, Hamiltonian limit of the governing equations.Two distinct chaotic regimes are identified: Lorenz chaos at relatively large lateral friction versus Shilnikov chaos at relatively small lateral friction. Both types of homoclinic bifurcations induce chaotic behavior of the recirculation gyres that is dominated by relaxation oscillations with a well-defined period.The relevance of these results to the mid-latitude oceans\u27 observed low-frequency variations is discussed. A previously documented 7-year peak in observed North-Atlantic variability is shown to exist across a hierarchy of models that share the gyre modes and homoclinic bifurcations discussed herein
The Mid-Pleistocene Transition induced by delayed feedback and bistability
The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr
glacial-interglacial cycles that occurred roughly 1 Myr ago, is often
considered as a change in internal climate dynamics. Here we revisit the model
of Quaternary climate dynamics that was proposed by Saltzman and Maasch (1988).
We show that it is quantitatively similar to a scalar equation for the ice
dynamics only when combining the remaining components into a single delayed
feedback term. The delay is the sum of the internal times scales of ocean
transport and ice sheet dynamics, which is on the order of 10 kyr. We find
that, in the absence of astronomical forcing, the delayed feedback leads to
bistable behaviour, where stable large-amplitude oscillations of ice volume and
an equilibrium coexist over a large range of values for the delay. We then
apply astronomical forcing. We perform a systematic study to show how the
system response depends on the forcing amplitude. We find that over a wide
range of forcing amplitudes the forcing leads to a switch from small-scale
oscillations of 41 kyr to large-amplitude oscillations of roughly 100 kyr
without any change of other parameters. The transition in the forced model
consistently occurs near the time of the Mid-Pleistocene Transition as observed
in data records. This provides evidence that the MPT could have been primarily
a forcing-induced switch between attractors of the internal dynamics. Small
additional random disturbances make the forcing-induced transition near 800 kyr
BP even more robust. We also find that the forced system forgets its initial
history during the small-scale oscillations, in particular, nearby initial
conditions converge prior to transitioning. In contrast to this, in the regime
of large-amplitude oscillations, the oscillation phase is very sensitive to
random perturbations, which has a strong effect on the timing of the
deglaciation events
Regimes of low-frequency variability in a three-layer quasi-geostrophic ocean model
The temporal variability of the midlatitude double-gyre wind-driven ocean circulation is studied in a three-layer quasi-geostrophic model over a broad range in parameter space. Four different types of flow regimes are found, each characterized by a specific time-mean state and spatio-temporal variability. As the lateral friction is decreased, these regimes are encountered in the following order: the viscous antisymmetric regime, the asymmetric regime, the quasi-homoclinic regime and the inertial antisymmetric regime. The variability in the viscous and the inertial antisymmetric regimes (at high and low lateral friction, respectively) is mainly caused by Rossby basin modes. Low-frequency variability, i.e.on interannual to decadal time-scales, is present in the asymmetric and quasi-homoclinic regime and can be related to relaxation oscillations originating from low-frequency gyre modes. The focus of this paper is on the mechanisms of the transitions between the different regimes. The transition from the viscous antisymmetric regime to the asymmetric regime occurs through a symmetry-breaking pitchfork bifurcation. There are strong indications that the quasi-homoclinic regime is introduced through the existence of a homoclinic orbit. The transition to the inertial antisymmetric regime is due to the symmetrization of the time-mean state zonal velocity field through rectification effects
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