Robust extremes in chaotic deterministic systems

This paper introduces the notion of robust extremes in deterministic chaotic systems, presents initial theoretical results, and outlines associated inferential techniques. A chaotic deterministic system is said to exhibit robust extremes under a given observable when the associated statistics of extreme values depend smoothly on the system's control parameters. Robust extremes are here illustrated numerically for the flow of the Lorenz model [E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963)]. Robustness of extremes is proved for one-dimensional Lorenz maps with two distinct types of observables for which conditions guaranteeing robust extremes are formulated explicitly. Two applications are shown: improving the precision of the statistical estimator for extreme value distributions and predicting future extremes in nonstationary systems. For the latter, extreme wind speeds are examined in a simple quasigeostrophic model with a robust chaotic attractor subject to nonstationary forcing. (C) 2009 American Institute of Physics. [doi:10.1063/1.3270389]