Michael Ghil
Ecole Normale Supérieure & UCLA

Title: Climate Change & Climate Variability: A Unified Mathematical Framework

Abstract: The climate system is nonlinear, heterogeneous and complex; it exhibits variability on many space and time scales. Its dynamical behavior results from a plethora of physical, chemical and biological processes. Hence, it is typically studied across a hierarchy of models, from low-dimensional systems of ordinary differential equations (ODEs) to infinite-dimensional systems of partial and functional differential equations (PDEs and FDEs). The theory of differentiable dynamical systems (DDS) has provided a road map for climbing this hierarchy and for comparing theoretical results with observations.

The climate system is also subject to time-dependent forcing, both natural and anthropogenic, e.g. solar luminosity variations, volcanic eruptions and changing greenhouse gas concentrations. Hence increased attention has been paid recently to applications of the theory of non-autonomous and random dynamical systems in order to describe the way that this complex system changes on time scales comparable to a human lifetime and longer. This talk will review the road from the classical applications of DDS theory to low-dimensional climate models, with no explicit time dependence, to current efforts at applying nonautonomous and random dynamical systems theory to high-end climate models governed by PDEs and FDEs, deterministic as well as stochastic.

Host: Michael Tippett