# Convergence of extreme value statistics in a two-layer quasi-geostrophic atmospheric model

## TL;DR

This study investigates the convergence of extreme value statistics in a high-dimensional atmospheric model, testing theoretical predictions related to universal properties of extreme events in chaotic systems.

## Contribution

It provides empirical analysis of extreme value convergence in a two-layer quasi-geostrophic model, highlighting the influence of forcing strength on universality.

## Key findings

- Closer agreement with theory under strong forcing
- Limited data and serial correlations affect extreme value estimates
- Weaker forcing shows less conformity to Axiom A flow predictions

## Abstract

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.