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

Abstract

One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are characterized by large anomalies of the time average of an observable over a long time. The framework of Donsker-Varadhan large deviation theory could therefore be useful for their analysis. In this paper we discuss how concepts and numerical algorithms developed in relation with large deviation theory can be applied to study extreme, rare fluctuations of time averages of surface temperatures at regional scale with comprehensive numerical climate models. We study the convergence of large deviation functions for the time averaged European surface temperature obtained with direct numerical simulation of the climate model Plasim, and discuss their climate implications. We show how using a rare event algorithm can improve the efficiency of the computation of the large deviation rate functions. We discuss the relevance of the large deviation asymptotics for applications, and we show how rare event algorithms can be used also to improve the statistics of events on time scales shorter than the one needed for reaching the large deviation asymptotics.

Applications of large deviation theory in geophysical fluid dynamics and climate science

“…Equation 30 however can still be of interest, as discussed in Sect. 4 and for different applications in [25,94,96,217,219].…”

“…Here we give a summary of a possible procedure, presented in more details in [217,224]. Let us assume that we have a time series of an observable A(t) from time 0 to time T .…”

“…A second way consists of computing the scaled cumulant generating function first, and then use the Gärtner-Ellis theorem to obtain the rate function [217,224]. This method has the advantage of not involving the estimate of a probability distribution and of requiring less data to achieve a similar precision.…”

“…In typical climate applications both methods require a substantial amount of data to go beyond the Gaussian fluctuations [96,217]. In the direct method the estimate of the non-Gaussian tails of the rate function is corrupted by the inability of properly computing the probability density function in ranges dominated by sparse data and outliers.…”

Introduction to the Special Issue on the Statistical Mechanics of Climate

“…Ragone [101] discuss critically how concepts and algorithms informed by large deviation theory can be applied to study persistent extreme events in climate and present an application focusing on persistent and spatially extended heat waves performed using a comprehensive climate models. A different angle on persistent extremes is given in the study by Caby et al [14], who provide a very informative review of the extremal index.…”