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

Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organizes phase space. We introduce a method to identify time-parameterized 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 utilizes the Ulam scheme for the generator of the transfer operator on a time-expanded domain. The new methodology is illustrated with an idealized 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.