Transfer operators, climate sensitivity and the topology of random attractors

CHARÓ, GISELA D.; ROBIN DURAND; DENISSE SCIAMARELLA; MICKAEL CHECKROUN; MICHAEL GHIL

California

Conferencia; 2020 SIAM Mathematics of Planet Earth; 2020

Society for Industrial and Applied Mathematics

Transfer operators have attracted considerable attention in recent work on the dynamics of the climate system, whether it be geophysical fluid dynamics or other components of the system. In this talk, we report on two aspects of this work. First, the connection between Ruelle-Pollicott (RP) resonances, mixing, and model sensitivity will be described, and the role of the RP resonances in low-frequency variability (LFV) of the atmosphere and oceans will be emphasized. Second, we introduce the analogy between phase-space and physical-space flows into the study of the homology groups and topological tipping points (TTPs) of random climate attractors. In this analogy, Lagrangian and Eulerian descriptions of the physical-space flows correspond to the usual dynamics in phase space and the transfer operator description, respectively. Recent results on the algebraic topology of the random attractor of the stochastically perturbed Lorenz convection model will be presented.