WIAS Preprint No. 696, (2001)

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


  • Berglund, Nils
  • Gentz, Barbara

2010 Mathematics Subject Classification

  • 37H20 60H10 34E15 82C31


  • Stochastic resonance, dynamical hysteresis, bifurcation delay, double-well potential, first-exit time, scaling laws, Lorenzmodel, thermohaline circulation, white noise, coloured noise


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.

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