Global Properties and Local Structure of the Weather Attractor over Western Europe

Abstract

An analysis of the West European climate over short time scales is performed by means of time series of the 500 mb geopotential height at nine different meteorological stations. The characterization of the dynamics is based on the computation of the dimensions of manifolds on which the systems evolve. For this purpose several embedding techniques are used and compared. All methods give similar results, namely, that the data in different stations seem to derive from a single deterministic dynamical system spanning a relatively low-dimensional manifold embedded in a low dimensional phase space. The estimation of the most significant Lyapounov exponents of the global system gives evidence that the nature of the dynamics is chaotic. The average e-folding time scale of the “growth of errors” associated with divergence of nearby initial conditions is found to be a few weeks. A more involved analysis reveals that the Western European weather attractor is highly nonuniform, expressing the fact that the stability properties of the trajectories depend on their position on the manifold. It is found that the predictability time in the regions of the attractor which correspond to low geopotential heights is slightly above one month decreasing to about two weeks for high geopotential values. The connection between these estimates and the error growth time determined from numerical models of weather prediction is discussed.