Colloquium Mathematics - S. Baars, University Groningen

Titel: Numerical methods for studying transition probabilities in stochastic ocean-climate models

Abstract:

Small scale variability in the present day climate may have large effects on the global ocean circulation. Examples of this small scale variability are fluctuations in the amount of freshwater that are caused by the melting of the Greenland ice sheet. These fluctuations may lead to a weakening of the global ocean circulation, which in turn may lead to a cooling of a few degrees in Europe. To predict the probability of such a transition event, computations have to be performed with large scale models of the ocean circulation. Existing techniques, however, are not sufficiently efficient, and therefore new methodology has to be developed, of which three novel methods are introduced in my thesis.

The first method is a multilevel preconditioner for the Navier-Stokes equations discretized on a staggered grid. The second method is an iterative method for solving generalized Lyapunov equations, which especially performs well in a continuation context. The last method is a method for computing actual transition probabilities in high-dimensional problems. During this presentation, we briefly discuss the first two methods, but will mainly focus on the computation of transition probabilities.
We demonstrate the workings of the methods on an idealized two-dimensional ocean circulation model. In the future, they may be used to compute probabilities of transitions in realistic high resolution three-dimensional climate models.