  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.
