Identifying the onset and decay of quasi-stationary families of almost-invariant sets with an application to atmospheric blocking events

Abstract

Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organises phase space. We introduce a method to identify time-parameterised families of almost-invariant sets in time-dependent dynamical systems, as well as the families' emergence and disappearance. In contrast to coherent sets, which may freely move about in phase space over time, our technique focuses on families of metastable sets that are quasi-stationary in space. Our straightforward approach extends successful transfer operator methods for almost-invariant sets to time-dependent dynamics and utilises the Ulam scheme for the generator of the transfer operator on a time-expanded domain. The new methodology is illustrated with an idealised fluid flow and with atmospheric velocity data. We identify atmospheric blocking events in the 2003 European heatwave and compare our technique to existing geophysical methods of blocking diagnosis.

arXiv comment31 pages (up from 29 in the previous version), 10 figures, originally submitted to Chaos on 27/06/2024, accepted on 05/11/2024. Alterations to manuscript have been made in October 2024 following comments and suggestions from referees, including the addition of new references, the correction of typos and the inclusion of additional information