A chaotically driven model climate: extreme events and snapshot attractors

Abstract. In a low-order chaotic global atmospheric circulation model the effects of deterministic chaotic driving are investigated. As a result of driving, peak-over-threshold type extreme events, e.g. cyclonic activity in the model, become more extreme, with increased frequency of recurrence. When the characteristic time of the driving is comparable to that of the undriven system, a resonance effect with amplified variance shows up. For very fast driving we find a reduced enhancement of variance, which is also the case with white noise driving. Snapshot attractors and their natural measures are determined as a function of time, and a resonance effects is also identified. The extreme value statistics of group maxima is found to follow a Weibull distribution.

[1]  Lai-Sang Young,et al.  Dimension formula for random transformations , 1988 .

[2]  Edward N. Lorenz,et al.  Irregularity: a fundamental property of the atmosphere* , 1984 .

[3]  Michael Ghil,et al.  Stochastic climate dynamics: Random attractors and time-dependent invariant measures , 2011 .

[4]  Grebogi,et al.  Multifractal properties of snapshot attractors of random maps. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[5]  Tamás Bódai,et al.  Fractal snapshot components in chaos induced by strong noise. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Edward Ott,et al.  Particles Floating on a Moving Fluid: A Dynamically Comprehensible Physical Fractal , 1993, Science.

[7]  Thomas M. Antonsen,et al.  Modeling fractal entrainment sets of tracers advected by chaotic temporally irregular fluid flows using random maps , 1997 .

[8]  D. Wilks.  Effects of stochastic parametrization on conceptual climate models , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  Memory effects in recurrent and extreme events. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Michael Ghil,et al.  Climate dynamics and fluid mechanics: Natural variability and related uncertainties , 2008, 1006.2864.

[11]  T. Palmer.  Extended-range atmospheric prediction and the Lorenz model , 1993 .

[12]  Shlomo Havlin,et al.  Return intervals of rare events in records with long-term persistence , 2004 .

[13]  Tamás Tél,et al.  Advection in chaotically time-dependent open flows , 1998 .

[14]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[15]  Andrey Shilnikov,et al.  Bifurcation and predictability analysis of a low-order atmospheric circulation model , 1995 .

[16]  Paul J. Roebber,et al.  Climate variability in a low-order coupled atmosphere-ocean model , 1995 .

[17]  Tamás Tél,et al.  Chaotic Dynamics: Introductory concepts , 2006 .

[18]  Michael Ghil,et al.  Recent forecast skill for the El Niño/Southern Oscillation , 1998 .

[19]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[20]  H. Kantz,et al.  Recurrence time analysis, long-term correlations, and extreme events. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  G. Nicolis,et al.  Extreme events in deterministic dynamical systems. , 2006, Physical review letters.

[22]  Klaus Fraedrich,et al.  Nonlinear Processes in Geophysics Extreme event return times in long-term memory processes near 1 / f , 2022 .

[23]  C. DaCamara,et al.  Multistability, phase diagrams, and intransitivity in the Lorenz-84 low-order atmospheric circulation model. , 2008, Chaos.

[24]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[25]  L. Arnold.  Random Dynamical Systems , 2003 .