A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere

TL;DR

This study uses large deviation theory on a simplified Earth-like atmospheric model to analyze the probability and structure of heat waves and cold spells, revealing universal scaling and the importance of intermediate spatial scales.

Contribution

It introduces a novel application of large deviation theory to atmospheric temperature extremes, demonstrating scale symmetry and the relevance of intermediate spatial scales for persistent events.

Findings

Rate functions agree across space and time after auto-correlation normalization.

Large deviations are more probable at intermediate spatial scales.

Rate functions effectively describe persistent heat waves and cold spells.

Abstract

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 spatial-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe spatially extended and temporally persistent heat waves or cold spells, if we consider temporal averages of spatial averages over intermediate spatial scales. Finally, we find out that large deviations are relatively more likely to occur when looking at these spatial averages performed over intermediate scales, thus pointing to the existence of weather patterns associated to the low-frequency variability of the atmosphere. Extreme value theory is used to benchmark our results.