A large deviation theory-based analysis of heat waves and cold spells in a simplified model of the general circulation of the atmosphere

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 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

Computation of Extreme Values of Time Averaged Observables in Climate Models with Large Deviation Techniques

“…From our analysis it appears that the large deviation limit per se can not be used to characterize heat waves: due to the presence of the seasonal cycle in the real world, heat waves are of interest up to time period of a season, about 90 days, that as we have seen is far from the time scales for which the large deviation rate function gives meaningful informations. In a recent paper, [13] performed a large deviation analysis of surface temperatures using the model Puma, which consists in the dynamical core of Plasim, obtaining faster convergence rates than what we observe. Puma is essentially Plasim without physical parameterizations, which are substituted by Newtonian cooling.…”

“…Note that [13] obtained very symmetric large deviation functions of surface temperature from simulations with the dynamical core of the same model, and noted that the symmetry was likely unrealistic and caused by the lack of a proper representation of moist processes in the model. The fact that in a version of the model that properly takes into account water phase transitions in the atmosphere the rate function is rather asymmetric confirms their observation.…”

“…With a climate model this is computationally unfeasible. However, equation (13) can be used to compute a very precise estimate of the scaled cumulant generating function in a neighborhood of k * . Using (15) an estimator of λ(k) iŝ…”

“…In [26] we used a rare event algorithm developed for the computation of Donsker-Varadhan type large deviation functions, and applied it to study rare heat waves, although for durations shorter than what necessary to be in the large deviation limit. [13] recently performed a comparison of extreme value theory and large deviation theory based approaches to study time and space averages of climatic observables in an idealized general circulation model. Considering the increasing interest in time persistent climate extremes, it is of interest to explore more in depth the applicability of large deviation theory to study rare fluctuations of time averages of climatic observables, and to discuss the methodological challenges one faces to perform this type of analysis.…”

The physics of climate variability and climate change

“…First, it has helped formulate rare events algorithms able to nudge a climate model towards representing preferentially the class of extreme events of interest (Ragone et al, 2018). Second, it has provided a solid theoretical and numerical basis for the study of spatially extended or temporally persistent temperature extremes (Gálfi et al, 2019). Large Deviation Theory has also been recently used to study multiscale and coupled atmosphere-ocean instabilities in a hierarchy of climate models (De Cruz et al, 2018;Vannitsem and Lucarini, 2016).…”