We study temporally persistent and spatially extended extreme events of temperature anomalies, i.e. heat waves and cold spells, using large deviation theory. To this end, we consider a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature in the mid-latitudes. We find that, after a re-normalisation based on the integrated auto-correlation, the rate function one obtains at a given latitude by looking locally in space at long time averages agrees with what is obtained, instead, by looking locally in time at large spatial averages along the latitude. This is a result of scale symmetry in the spatio-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature PAPER: Interdisciplinary statistical mechanics

No abstract

The climate is a complex, chaotic system with many degrees of freedom. Attaining a deeper level of understanding of climate dynamics is an urgent scientific challenge, given the evolving climate crisis. In statistical physics, many-particle systems are studied using Large Deviation Theory (LDT). A great potential exists for applying LDT to problems in geophysical fluid dynamics and climate science. In particular, LDT allows for understanding the properties of persistent deviations of climatic fields from long-term averages and for associating them to low-frequency, large-scale patterns. Additionally, LDT can be used in conjunction with rare event algorithms to explore rarely visited regions of the phase space. These applications are of key importance to improve our understanding of high-impact weather and climate events. Furthermore, LDT provides tools for evaluating the probability of noise-induced transitions between metastable climate states. This is, in turn, essential for understanding the global stability properties of the system. The goal of this review is manifold. First, we provide an introduction to LDT. We then present the existing literature. Finally, we propose possible lines of future investigations. We hope that this paper will prepare the ground for studies applying LDT to solve problems encountered in climate science and geophysical fluid dynamics.

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. We study the convergence of GEV (Generalized Extreme Value) and GP (Generalized Pareto) shape parameter estimates to the theoretical value, which is expressed in terms of the partial information dimensions of the attractor. We consider a two-layer quasi-geostrophic atmospheric model of the mid-latitudes, adopt two levels of forcing, and analyse the extremes of different types of physical observables (local energy, zonally averaged energy, and globally averaged energy). We find good agreement in the shape parameter estimates with the theory only in the case of more intense forcing, corresponding to a strong chaotic behaviour, for some observables (the local energy at every latitude). Due to the limited (though very large) data size and to the presence of serial correlations, it is difficult to obtain robust statistics of extremes in the case of the other observables. In the case of weak forcing, which leads to weaker chaotic conditions with regime behaviour, we find, unsurprisingly, worse agreement with the theory developed for Axiom A flows.

Elucidating the statistical properties of extreme meteo-climatic events and capturing the physical processes responsible for their occurrence are key steps for improving our understanding of climate variability and climate change and for better evaluating the associated hazards. It has recently become apparent that large deviation theory is very useful for investigating persistent extreme events, and specifically, for flexibly estimating long return periods and for introducing a notion of dynamical typicality. Using a methodological framework based on large deviation theory and taking advantage of long simulations by a state-of-the-art Earth System Model, we investigate the 2021 North America Heatwave. Indeed, our analysis shows that the 2021 event can be seen as an unlikely but possible manifestation of climate variability, whilst its probability of occurrence is greatly amplified by the ongoing climate change. We also clarify the properties of spatial coherence of the 2021 heatwave and elucidate the role played by the Rocky Mountains in modulating hot, dry, and persistent extreme events in the Western Pacific region of North America.