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| Titel |
A stochastic perturbation theory for non-autonomous systems |
| VerfasserIn |
Woosok Moon, John Wettlaufer |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250091298
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| Publikation (Nr.) |
 EGU/EGU2014-5583.pdf |
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| Zusammenfassung |
| We develop a perturbation theory for a class of first order nonlinear non-autonomous
stochastic ordinary differential equations that arise in climate physics. The perturbative
procedure produces moments in terms of integral delay equations, whose order by order
decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of
noise are discussed and the question of how the nature of the noise influences the results is
addressed theoretically and numerically. By invoking the Martingale property, we rationalize
the transformation of the underlying Stratonovich form of the model to an Ito form,
independent of whether the noise is additive or multiplicative. The generality of the
analysis is demonstrated by developing it both for a Brownian particle moving in a
periodically forced quartic potential, which acts as a simple model of stochastic
resonance, as well as for our more complex climate physics model. The validity of
the approach is shown by comparison with numerical solutions. The particular
climate dynamics problem upon which we focus involves a low-order model for
the evolution of Arctic sea ice under the influence of increasing greenhouse gas
forcing ΔF0. The deterministic model, developed by Eisenman and Wettlaufer EW09
exhibits several transitions as ΔF0 increases and the stochastic analysis is used to
understand the manner in which noise influences these transitions and the stability of the
system.
Eisenman, I., and J.S. Wettlaufer, “Nonlinear threshold behavior during the loss of
Arctic sea ice,” Proc. Natl. Acad. Sci. USA, 106, 28–32, 2009. |
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