  We search for the signature of universal properties of extreme events,
theoretically predicted for Axiom A flows, in a chaotic and high dimensional
dynamical system by studying the convergence of GEV (Generalized Extreme Value)
and GP (Generalized Pareto) shape parameter estimates to a theoretical value,
expressed in terms of partial dimensions of the attractor, which are global
properties. We consider a two layer quasi-geostrophic (QG) atmospheric model
using two forcing levels, and analyse extremes of different types of physical
observables (local, zonally-averaged energy, and the average value of energy
over the mid-latitudes). Regarding the predicted universality, we find closer
agreement in the shape parameter estimates only in the case of strong forcing,
producing a highly chaotic behaviour, for some observables (the local energy at
every latitude). Due to the limited (though very large) data size and the
presence of serial correlations, it is difficult to obtain robust statistics of
extremes in case of the other observables. In the case of weak forcing,
inducing a less pronounced chaotic flow with regime behaviour, we find worse
agreement with the theory developed for Axiom A flows, which is unsurprising
considering the properties of the system.
