Metastability in simple climate models: Pathwise analysis of slowly driven Langevin equations

Nils Berglund and Barbara Gentz
Stoch. Dyn. 2:327-356 (2002)

Proceedings of the Second Workshop on Stochastic Climate Models, Chorin, Germany, July 2001

We consider simple stochastic climate models, described by slowly time-dependent Langevin equations. We show that when the noise intensity is not too large, these systems can spend substantial amounts of time in metastable equilibrium, instead of adiabatically following the stationary distribution of the frozen system. This behaviour can be characterized by describing the location of typical paths, and bounding the probability of atypical paths. We illustrate this approach by giving a quantitative description of phenomena associated with bistability, for three famous examples of simple climate models: Stochastic resonance in an energy balance model describing Ice Ages; hysteresis in a box model for the Atlantic thermohaline circulation; and bifurcation delay in the case of the Lorenz model for Rayleigh-Bénard convection.

2000 Mathematics Subject Classification: 37H20 (primary), 60H10, 34E15, 82C31 (secondary).

Keywords and phrases: Stochastic resonance, dynamical hysteresis, bifurcation delay, double-well potential, first-exit time, scaling laws, Lorenz model, thermohaline circulation, white noise, coloured noise.

 

Journal Homepage Published article: 10.1142/S0219493702000455 MR1943556 Zbl1090.86001

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