Thermohaline circulation hysteresis: A model intercomparison

Rahmstorf, Stefan; Crucifix, Michel; Ganopolski, Andrey; Goosse, Hugues; Kamenkovich, Igor; Knutti, Reto; Lohmann, Gerrit; Marsh, Robert; Mysak, Lawrence A.; Wang, Zhaomin; Weaver, Andrew J.

doi:10.1029/2005gl023655

Cited by 404 publications

(421 citation statements)

References 37 publications

(33 reference statements)

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“…The state-of-the-art climate models used for the IPCC projections [29] cannot be used to study the last million years of Earth's history, not only because they are too computationally expensive, but because they do not take into the right considerations the processes which dominate the Earth dynamics on such long time scales. On the other hand, Earth Models of Intermediate complexity [9,23], which are tailored for such problems, are definitely not competitive if our aim is to describe the variability of the present climate and the short-term climate change. The problem of providing a satisfactory description of the dynamical processes that cannot be explicitly be represented has long been addressed at various levels of rigour by the climate community [20,31,11,10,3,28,22].…”

Section: Introductionmentioning

confidence: 99%

Disentangling multi-level systems: averaging, correlations and memory

Wouters¹,

Lucarini²

2012

J. Stat. Mech.

151

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We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way to parametrize the effect of the coupling as a function of only the variables of a system of interest. Our focus is on describing the impacts of the coupling on the long-term statistics rather than on the finite-time behaviour. By direct calculation, we find that, at first order, the coupling can be surrogated by adding a deterministic perturbation to the autonomous dynamics of the system of interest. At second order, there are additionally two separate and very different contributions. One is a term taking into account the second order contributions of the fluctuations in the coupling, which can be parametrized as a stochastic forcing with given spectral properties. The other one is a memory term, coupling the system of interest to its previous history, through the correlations of the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to treat this case, we present an extension to Ruelle's response theory able to deal with integral operators. We discuss our results in the context of other methods previously proposed to disentangle the dynamics of two coupled systems. We emphasize that our results do not rely on assuming a time scale separation, and, if such a separation exist, can be used equally well to study the statistics of the slow as well as that of the fast variables. By recursively applying the technique proposed here, we can treat the general case of multilevel systems.

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Section: Introductionmentioning

confidence: 99%

Disentangling multi-level systems: averaging, correlations and memory

Wouters¹,

Lucarini²

2012

J. Stat. Mech.

151

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show abstract

“…Heavily parametrized 'simple' models often capture numerous equilibria, hysteresis and abrupt changes [1], but for full-complexity models of the type used in the Intergovernmental Panel on Climate Change reports, the results are different [127]. Multiple equilibria and hysteresis have rarely been seen in fullcomplexity models with notable exceptions [134], and therefore may be mere artefacts of simpler models.…”

Section: (D) Comparisons Between Modelling and Datamentioning

confidence: 99%

“…However, there are important differences between models for key characteristics of the climate such as the sensitivity of ocean circulation to freshwater input in the North Atlantic [1]. Such model-dependent features indicate an important sensitivity to model boundary conditions for these abrupt changes in climate that is yet to be fully understood.…”

Section: (D) Comparisons Between Modelling and Datamentioning

confidence: 99%

“…On time scales of decades to millions of years, the ocean plays a key role in modulating and controlling global climate, including heat redistribution [1,2], the carbon cycle [3] and the hydrologic cycle [4]. If we are to make predictions about the response of the Earth to perturbations, either natural or anthropogenic, then we need a mechanistic understanding of the ocean's behaviour.…”

Section: Introductionmentioning

confidence: 99%

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Palaeoceanography: motivations and challenges for the future

Robinson

Siddall

2012

Phil. Trans. R. Soc. A.

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The ocean interacts with the atmosphere, biosphere and cryosphere in a complex way, modulating climate through the storage and transport of heat, nutrients and carbon. As such, it is important that we understand the ways in which the ocean behaves and the factors that can lead to change. In order to gain this understanding, we need to look back into the past, on time scales from recent decadal-scale change, through the abrupt changes of the Pleistocene and back to times when the Earth's climate was significantly different than the Holocene. A key challenge facing the field of palaeoceanography is to combine data and modelling in a common framework. Coupling palaeo-data and models should improve our knowledge of how the Earth works, and perhaps of more direct societal relevance, might enable us to provide better predictive capabilities in climate modelling. In this discussion paper, we examine the motivations, past successes and challenges facing palaeoceanographic studies. We then suggest a number of areas and approaches that we believe will allow palaeoceanography to continue to provide new insights into processes that affect future climate change.

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“…[4][5][6] This is very hard or impossible to do with large, complex systems, such as the climate, so one may instead build models of varying complexity and perform experiments on these models instead. 7,8 A third approach is to look at the statistics of some measurable variable of the system, usually a time series of this variable, as these may reveal something about the future behaviour without the need for a detailed model of the system. [1][2][3] All three approaches are potentially useful sources of information, particularly when taken together.…”

Section: Introductionmentioning

confidence: 99%

Detection of bifurcations in noisy coupled systems from multiple time series

Williamson

Lenton

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Bifurcations in nonstationarity noise dynamic systems: The basins of attraction and the problems of predictability of final states AIP Conf. Proc. 502, 655 (2000) We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system. V C 2015 AIP Publishing LLC. Abrupt changes in complex systems such as the human body, ecosystems, or the climate system can have unwelcome and expensive consequences. Ideally, given one or more time series of some measurable variables, one would like an early warning method to indicate whether an abrupt change is imminent. Abrupt changes can result from crossing a bifurcation in the underlying dynamical system. Recently, there has been a burgeoning body of work on the detection of approaching bifurcation in noisy systems whose deterministic dynamics are assumed to be approximated by a first order ordinary differential equation (ODE) of one dynamical variable. These methods work by looking for the system's recovery from noisy perturbations becoming more sluggish, a phenomenon known as critical slowing down. This is a generic feature of approaching bifurcations in systems modelled by autonomous first order differential equations of one dynamical variable with additive white noise, where the behaviour is decay toward a fixed point. However, it is not always possible to approximate parts of a complex system in such reduced manner. For example, the climate system can display coupled, oscillatory, or chaotic behaviour. Here, we make a direct g...

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Thermohaline circulation hysteresis: A model intercomparison

Cited by 404 publications

References 37 publications

Disentangling multi-level systems: averaging, correlations and memory

Disentangling multi-level systems: averaging, correlations and memory

Palaeoceanography: motivations and challenges for the future

Detection of bifurcations in noisy coupled systems from multiple time series

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