Abstract. We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction.Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems. Both these results have implications for the study and prediction of natural hazards and their human impacts.

No abstract

The time‐dependent properties of the Fokker–Planck equation corresponding to a zero‐dimensional climate model, showing bistable behavior and subject to a weak external periodic forcing are analyzed. Conditions under which the response is amplified are found analytically. In this way the possibility of transitions between climatic states is established. The results are illustrated by the 100,000‐yr periodicity of the eccentricity of the earth's orbit, in connection with glaciation cycles.

The propagation of extreme events in space is analyzed for a class of dynamical systems giving rise to spatiotemporal chaos. It is shown that this process can be mapped into a generalized random walk, whereby the mean square displacement increases linearly in time and there is a nonvanishing probability for jumps beyond first neighbors. The relative roles of the local dynamics and of the spatial coupling are identified.

No abstract

No abstract

A comprehensive bifurcation analysis of a low-order atmospheric circulation model is carried out. It is shown that the model admits a codimension-2 saddle-node-Hopf bifurcation. The principal mechanisms leading to the appearance of complex dynamics around this bifurcation are described and various routes to chaotic behavior are identified, such as the transition through the period doubling cascade, the breakdown of an invariant torus and homoclinic bifurcations of a saddle-focus. Non-trivial limit sets in the form of a chaotic attractor or a chaotic repeller are found in some parameter ranges. Their presence implies an enhanced unpredictability of the system for parameter values corresponding to the winter season.

The Fokker‐Planck equation corresponding to a zero‐dimensional climatic model showing bistable behavior is analyzed. A climatic potential function is introduced, whose variational properties determine the most probable states of the stationary probability distribution. A study of the time‐dependent properties leads to the identification of the characteristic time scales of evolution.