stochastic dynamics of climate states I

The physical and mathematical understanding of real world as well as simulation based virtual world phenomena in climate dynamics needs support by stochastically reduced low dimensional climate models. The scope of models building the background of this project range from simple models for glacial metastability through multi-stable box models of thermohaline circulation to models for the El Nino Southern Oscillation, from linear to delay stochastic oscillators. Their mathematical backbone is non-linear stochastic differential equations with external periodic or internal feedback forcing. Their effective dynamics features transitions between metastable climate states given by the minima of complex potential functions that describe the non-linear environment. The stochastic analysis of these dynamical climate systems focuses on asymptotic properties such as attractors, bifurcations, hystereses, stochastic resonance, and Lyapunov stability. The research in this project will concentrate on the following subjects. Most importantly, motivated by periodically forced climate transitions in simple models, we shall develop the mathematical understanding of the physical paradigm of spontaneous phase transitions and stochastic resonance. To this end, subjects such as quality measures of noise tuning will be studied. A second focus is on (local) Lyapunov exponents and stochastic stability questions for non-linear systems, a topic important for predictability in reduced climate models. The underpinning of Hasselmann's stochastic reduction of climate models through scale separation has to be seen as a topic for the long run, preceded by numerical case studies of simple coupled ocean-atmosphere models.