Stochastische Dynamik von Klimazuständen II

The physical and mathematical description of climate phenomena in the real world as well as the simulation of climate dynamics needs support by stochastically reduced models of low dimensions. The models used in this project range from simple models for glacial metastability in multistable box models of thermohaline circulation to models of El Nino Southern Oscillation, from linear to stochastic delay oscillators. Their mathematical basis is based on non-linear stochastic differential equations with external periodic or internal feedback excitation. The effective dynamics of these equations shows transitions between the metastable climate states given by minima of complex potential functions.

The stochastic analysis of these dynamic climate systems focuses on asymptotic properties such as attractors, bifurcations, hysteresis, stochastic resonance and Lyapunov stability.

The research in this further project will concentrate on the following priorities. Motivated by periodically stimulated climate transitions in simple models, we will first develop the mathematical understanding of the physical paradigms of the spontaneous phase transitions and the stochastic resonance. For this, topics such as quality measures for noise tuning are considered.

A second focus is on (local) Lyapunov exponents and the stochastic stability for nonlinear systems, an important question for predictability in reduced climate dynamics. Prepared by numerical case studies of simply coupled ocean atmosphere models, the underpinning of Hasselmann's stochastic reduction of climate models by separating the time scales must be seen as a long-term research goal.