Freddy Bouchet, ENS Lyon and CNRS, France – Københavns Universitet

Freddy Bouchet, ENS Lyon and CNRS, France

Title: Large deviation theory applied to climate dynamics

We will review some of the recent developments in the theoretical and mathematical aspects of the non-equilibrium statistical mechanics of climate dynamics. At the intersection between statistical mechanics, turbulence, and geophysical fluid dynamics, this field is a wonderful new playground for large deviation theory. It involves large deviation theory for stochastic partial differential equations, homogenization, and rare event algorithms.

We will discuss two paradigmatic examples. First, we will study extreme heat waves, as an example of rare events with a huge impact. We will explain how algorithms based on large deviation theory allow to sample rare heat wave at a numerical cost that is several orders of magnitude smaller than a direct numerical simulation. This will improve drastically the study of the dynamics of these extreme events, in climate models, in relation with climate change.

A a second example, we will study rare trajectories that suddenly drive turbulent flows from one attractor to a completely different one, in the stochastic barotropic quasigeostrophic equation. This equation, a generalization of the stochastic two dimensional Navier–Stokes equations, models Jupiter's atmosphere jets. We discuss preliminary steps in the mathematical justification of the use of averaging, derive an effective action for large deviations, compute transition rates through Freidlin–Wentzell theory, and instantons (most probable transition paths).

This talk is based on works with Francesco Ragone and Jeroen Wouters (heat waves) on one hand, and  Brad Marston, Eric Simonnet, Tomas Tangarife, and Eric Woillez (large deviations for quasi geomorphic turbulence) on the other hand.