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

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 this thesis. The first is a method for solving large systems of equations, the second is a method that describes sensitivity to fluctuations far away from transitions, and the last method efficiently computes actual probabilities of transitions in large scale models. We demonstrate the workings of these 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.