In the lecture Dr. BODAI Tamás will demonstrate the effects of driving, i.e., time-dependent (periodic, chaotic, and noisy) forcing applied to a well-known low-order chaotic model of global atmospheric circulation due to Lorenz (1984).
Extreme value statistics can be pursued by the method of block maxima. In autonomous dynamical systems the extreme value distributions are known to be Weibullian (of negative shape parameter) and related to the fractal dimension of the chaotic attractor. Having introduced a bounded driving, the statistics is still Weibullian in the limit, but for shorter observational times Frechet-type distributions can be observed as well. It is also typical that the convergence to the limiting extreme value distribution is slow and nonmonotonic.
Deterministic drivings result in shape parameters larger in modulus than stochastic drivings, but otherwise strongly dependent on the particular type of driving, living a fingerpring on the extreme value statistic. The maximal effects of deterministic drivings are found to be more pronounced, both in magnitude and variability of the extremes, than white noise, and the latter has a stronger effect than red noise. Numerical results can be unreliable, however, and an extreme value theory for driven systems is yet lacking. This, interesting recent observations, and its strong practical relevance make extreme value statistics a dynamic field of research.
The effect of the time scale of driving is also evaluated. When it becomes comparable to some characteristic internal time scale of the model climate, we find that the magnitude and relative frequency of the extremes, in terms of the maximal excursion and the kurtosis of the parent distribution, becomes maximal. This appears to be a novel type of resonance.
Finally, Dr. BODAI Tamás will present a probabilistic prediction scheme of peak-over-threshold extreme events. It is based on the use of a long time series and the monitioring of precursors. The goodness of the prediction is assessed in terms of Receiver Operating Characteristic (ROC) curves (comparing the rates of true positive predictions and false alarms). This measure of predictability is compared to the more conventional finite-time Maximal Lyapunov Exponent, and their dependence on the threshold level and prediction lead-time is investigated. We find a characteristically different behaviour from simple stochastic processes, in terms of nontrivial/nonmonotonic dependences. |
Education
2004 – 2009 PhD in Engineering Sciences, School of Engineering, University of Aberdeen
1999– 2004 MSc in Mechanical Engineering,
Budapest University of Technology and Economics
2002 – 2004 Specialised in Applied Mechanics and Mechatronics
1995 – 1999 Zipernowsky Károly Secondary Technical School, Pécs Employment
2013 – Department of Theoretical Meteorology, KlimaCampus/
Meteorological Institute, University of Hamburg
2011 – 2013 Max Planck Institute for the Physics of Complex Systems
2010 – 2011 Department of Theoretical Physics, Loránd Eötvös University 2008 –2010 Green Ocean Energy Limited |
