Dr. Vera Melinda Galfi
- Extreme events in chaotic nonlinear systems, like the atmosphere or the climate
- Large deviations and their connection to persistent extreme events
- Analysis of linear instabilities based on covariant Lyapunov vectors
- Application of limit laws from extreme value theory and large deviation theory to geophysical data
The driving force behind my research is the desire to understand complex, chaotic dynamical systems, like the atmosphere or the climate system. To achieve this, I apply methods of dynamical systems theory, extreme value theory, large deviation theory and statistical mechanics to geophysical data. My aim is to go beyond the pure data analysis ant try to understand piece by piece the system itself until an overall view of it emerges.
In my Ph.D. thesis I have analysed extreme values of energy observables in a two-layer quasi-geostrophic atmospheric model from the perspective of extreme value theory for dynamical systems. I have shown based on numerical simulations that, under certain conditions, the statistics of extreme events can be related to general dynamical properties of the system producing these events. This is in accordance with theoretical results. Consequently, extreme events have universal properties, and the extraordinary is related to the general. This is true in the so-called asymptotic regime, where the mathematical limit laws are valid and the information about memory / persistence is lost. However, real world phenomena happen outside the asymptotic regime, and the study of persistent events is immensely important for human society, especially in the context of climate change.
As a further part of my Ph.D. thesis, I have analysed persistent temperature events, like heat waves or cold spells, in a simple general circulation model of the atmosphere (PUMA) by using Large Deviation Theory (LDT). I have found that persistent events can be interpreted and analysed as large deviations of spatially averaged observables. The spatial averaging has to be performed over an area corresponding to the typical scale of the event of interest. Another important finding of my Ph.D. work is the universality of temporal and spatial large deviations, in the sense that both are described by the same universal rate function. This is a different type of universality than the one mentioned above, and is related to the Taylor "frozen turbulence" hypothesis.
In my current work, I analyse linear instabilities in a quasi-geostrophic, coupled ocean-atmopshere model (MAOOAM) by using covariant Lyapunov vectors. This work is part of the DFG-funded TRR 181 project "Energy transfers in the atmosphere and oceans".
- Galfi, V.M., V. Lucarini, and J. Wouters, 2019: A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere. J. Stat. Mech, 2019, 033404, https://doi.org/10.1088/1742-5468/ab02e8.
- Galfi, V.M., 2018: Mathematics of extreme events in atmospheric models. Phd Thesis, Hamburg: Universität Hamburg. https://doi.org/10.17617/2.3016821.
- Galfi, V.M., T. Bodai, and V. Lucarini, 2017: Convergence of extreme value statis tics in a two-layer quasi-geostrophic atmospheric model. Complexity, 2017, 5340858, https://doi.org/10.1155/2017/5340858.