Effect of stochastic perturbations on a low-order spectral model of the atmospheric circulation

Abstract

The dynamics of a low-order spectral model of the barotropic potential vorticity equation, forced by random perturbations, is studied as a function of the memory and intensity of the noise. The unperturbed deterministic system has three equilibria, and for arbitrary initial conditions trajectories in phase space always tend to one of the two stable equilibria representing preferent circulation patterns of the atmosphere. The noise forces the system to visit alternately the two attraction domains of the stable equilibria. During the transition, the system will remain for some time in a neighbourhood of the unstable equilibrium. This indicates that the latter is important for the atmospheric dynamics. Characteristic residence times in the attraction domains and in the domain near the unstable equilibrium are calculated by combined analytical and numerical methods. Furthermore the alternation of preferent states is studied with a discrete state Markov process model. It consists of three states, which are related to the equilibria of the low-order spectral model. Transition probabilities are derived from the characteristic residence times of the stochastically forced dynamical system. The eigenvalues of the Markov model yield information about the time scale over which the effect of the initial state is present in the system.