Stochastic aspects of climatic transitions-Additive fluctuations

Nicolis, C.; Nicolis, Grégoire

doi:10.1111/j.2153-3490.1981.tb01746.x

Cited by 195 publications

(93 citation statements)

References 17 publications

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“…A simple conceptual model is Brownian motion in a one-dimensional potential landscape [11,12,27] described by the Langevin equationż…”

Section: Conceptual Dynamical Models: Bistability Versus Relaxation Omentioning

confidence: 99%

Analysis and modelling of glacial climate transitions using simple dynamical systems

Kwasniok

2013

Phil. Trans. R. Soc. A.

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Glacial climate variability is studied integrating simple nonlinear stochastic dynamical systems with palaeoclimatic records. Different models representing different dynamical mechanisms and modelling approaches are contrasted; model comparison and selection is based on a likelihood function, an information criterion as well as various long-term summary statistics. A two-dimensional stochastic relaxation oscillator model with proxy temperature as the fast variable is formulated and the system parameters and noise levels estimated from Greenland ice-core data. The deterministic part of the model is found to be close to the Hopf bifurcation, where the fixed point becomes unstable and a limit cycle appears. The system is excitable; under stochastic forcing, it exhibits noisy large-amplitude oscillations capturing the basic statistical characteristics of the transitions between the cold and the warm state. No external forcing is needed in the model. The relaxation oscillator is much better supported by the data than noise-driven motion in a one-dimensional bistable potential. Two variants of a mixture of local linear stochastic models, each associated with an unobservable dynamical regime or cluster in state space, are also considered. Three regimes are identified, corresponding to the different phases of the relaxation oscillator: (i) lingering around the cold state, (ii) rapid shift towards the warm state, (iii) slow relaxation out of the warm state back to the cold state. The mixture models have a high likelihood and are able to capture the pronounced time-reversal asymmetry in the ice-core data as well as the distribution of waiting times between onsets of Dansgaard–Oeschger events.

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“…A simple conceptual model is Brownian motion in a one-dimensional potential landscape [11,12,27] described by the Langevin equationż…”

Section: Conceptual Dynamical Models: Bistability Versus Relaxation Omentioning

confidence: 99%

Analysis and modelling of glacial climate transitions using simple dynamical systems

Kwasniok

2013

Phil. Trans. R. Soc. A.

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“…As the prototype model of stochastic resonance (SR), the overdamped bistable system was used to describe the earth's climatic change [1][2][3]. Since then, the bistable systems have been studied and researched for characterizing SR phenomena and the applications in diverse scientific fields [4][5][6][7][8][9][10][11], such as biological systems [5,6], brownian ratchet [7], neuron models [9], nanomechanical systems [8,10], Vibration analysis and faults diagnosis in mechanical systems [11].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of bistable systems for binary signal detection in symmetric non-Gaussian noise

Zhang

et al. 2010

Probabilistic Engineering Mechanics

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“…In the case of additive noise (g[x] = constant and not null) Eq. (18) is reduced to the expression found by Nicolis and Nicolis (1981) and by Wilks (2008) (Eq. [11]).…”

Section: Remains Valid On the Other Hand If G(x)mentioning

confidence: 99%

“…This approach has been used in the analysis of one-dimensional stochastic differential equations forced with additive noise (g = constant). Nicolis and Nicolis (1981) and Wilks (2008) found the following expression to calculate the potential function V(x),…”

Section: Potential Function In the Steady State Of A Stochastic Systemmentioning

confidence: 99%

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Analysis of the simulated global temperature using a simple energy balance stochastic model

Moreles

Martínez‐López

2016

ATM

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Este trabajo presenta un estudio de la respuesta de la variabilidad simulada de la temperatura global a parametrizaciones estocásticas aditivas y multiplicativas de flujos de calor, junto con una descripción de la variabilidad de largo plazo en términos de procesos autorregresivos simples. Para simular la temperatura global de la Tierra se utilizó un modelo climático de balance de energía promediado globalmente, acoplado a un modelo oceánico termodinámico. Se encontró que procesos autorregresivos simples explican la variabilidad de la temperatura en el caso de parametrizaciones aditivas; sin embargo, en el caso de parametrizaciones multiplicativas, la descripción de la variabilidad de la temperatura involucraría procesos autorregresivos de orden superior, lo cual sugiere la presencia de mecanismos complejos de retroefecto originados por el forzamiento multiplicativo. Asimismo, se encontró que las parametrizaciones multiplicativas produjeron una estructura compleja que emula de manera cercana procesos climáticos observados. Finalmente, se propone un nuevo enfoque para describir la estabilidad de un sistema estocástico general unidimensional en estado estacionario, a través de su función potencial. A partir de una expresión analítica de la función potencial se profundizó en la descripción de un sistema estocástico. ABSTRACTThis work presents a study of the response of the simulated global temperature variability to additive and multiplicative stochastic parameterizations of heat fluxes, along with a description of the long-term variability in terms of simple autoregressive processes. The Earth's global temperature was simulated using a globally averaged energy balance climate model coupled to a thermodynamic ocean model. It was found that simple autoregressive processes explain the temperature variability in the case of additive parameterizations; whereas in the case of multiplicative parameterizations, the description of the temperature variability would involve higher order autoregressive processes, suggesting the presence of complex feedback mechanisms originated by the multiplicative forcing. Also, it was found that multiplicative parameterizations produced a rich structure that emulates closely observed climate processes. Finally, a new approach to describe the stability in the steady state of a general one-dimensional stochastic system, through its potential function, was proposed. From an analytical expression of the potential function, further insight into the description of a stochastic system was provided.

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Stochastic aspects of climatic transitions-Additive fluctuations

Cited by 195 publications

References 17 publications

Analysis and modelling of glacial climate transitions using simple dynamical systems

Analysis and modelling of glacial climate transitions using simple dynamical systems

Evaluation of bistable systems for binary signal detection in symmetric non-Gaussian noise

Analysis of the simulated global temperature using a simple energy balance stochastic model

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