Stochastic aspects of climatic transitions-response to a periodic forcing

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.

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“…This concept of SR is far more complex than the classical SR concept of Nicolis (1982), which assumes stable equilibria.…”

Section: Discussionmentioning

confidence: 99%

“…This nonlinear amplification mechanism is called stochastic resonance (SR; Benzi et al 1981Benzi et al , 1982Nicolis 1982;Gammaitoni et al 1998). To put it in more general terms, stochastic resonance describes the synchronization between noiseinduced fluctuations and weak periodic forcing in nonlinear systems.…”

Section: Nonautonomous Stochastic Resonancementioning

confidence: 99%

Coherent Resonant Millennial-Scale Climate Oscillations Triggered by Massive Meltwater Pulses

Timmermann¹,

Gildor²,

Schulz³

et al. 2003

J. Climate

125

140

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“…The idea of approximation of diffusions in potential landscapes by appropriate finite state Markov chains in the context of stochastic resonance was suggested by Eckmann and Thomas [6], and C. Nicolis [15], and developed by McNamara and Wiesenfeld [14]. In this section we follow [17,13].…”

Section: The 'Effective Dynamics': Two-state Markov Chainmentioning

confidence: 99%

“…The paradigm of stochastic resonance (SR) emerged from papers by C. Nicolis [15] and Benzi et al [2,3,4] which were devoted to the mathematical explanation of the phenomenon of glacial cycles. The model they created is based on the following observations.…”

Section: Background and Paradigmmentioning

confidence: 99%

Stochastic Resonance: A Comparative Study of Two-State Models

Imkeller

Pavlyukevich

2004

Seminar on Stochastic Analysis, Random Fields and Applications IV

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Abstract. We consider a dynamical system describing the motion of a particle in a double well potential with a periodic perturbation of very small frequency, and an additive stochastic perturbation of amplitude ε. It is in stochastic resonance if the solution trajectories amplify the small periodic perturbation in a 'best possible way'. Systems of this type first appeared in simple energy balance models designed for a qualitative explanation of global glacial cycles. Large deviations theory provides a lower bound for the proportion of the amplitude and the logarithm of the period above which quasi-deterministic periodic behavior can be observed. However, to obtain optimality, one has to measure periodicity with a measure of quality of tuning such as spectral power amplification favored in the physical literature. In a situation where the potential switches discontinuously between two spatially antisymmetric double well states we encounter a surprise. Contrary to physical intuition, the stochastic resonance pattern is not correctly given by the reduced dynamics described by a two state Markov chain with periodic hopping rates between the potential minima which mimic the large (spatial) scale motion of the diffusion. Only if small scale fluctuations inside the potential wells where the diffusion spends most of its time are carefully eliminated, the Markov chain gives the correct picture.

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“…It has been initially proposed in the context of climate studies, as an explanation of the recurrence of ice ages [BPS81,BPSV82,BPSV83,Nic81,Nic82], and subsequently the phenomenon has been reported in other fields, such as biology and neurosciences, and extensively studied in many different physical settings. It is not possible here to account for the huge literature on the subject but we refer to [GHJM98] for a comprehensive review, while an exhaustive discussion of the literature in different fields can be found in [MSPA08].…”

Section: Introductionmentioning

confidence: 99%

A random dynamical systems perspective on stochastic resonance

et al. 2017

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Abstract. We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a nonautonomous forcing. We prove the existence of a unique global attracting random periodic orbit and a stationary periodic measure. We use the stationary periodic measure to define an indicator for the stochastic resonance.

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Stochastic aspects of climatic transitions-response to a periodic forcing

Cited by 257 publications

References 7 publications

Coherent Resonant Millennial-Scale Climate Oscillations Triggered by Massive Meltwater Pulses

Coherent Resonant Millennial-Scale Climate Oscillations Triggered by Massive Meltwater Pulses

Stochastic Resonance: A Comparative Study of Two-State Models

A random dynamical systems perspective on stochastic resonance

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