  We employ the framework of the Koopman operator and dynamic mode
decomposition to devise a computationally cheap and easily implementable method
to detect transient dynamics and regime changes in time series. We argue that
typically transient dynamics experiences the full state space dimension with
subsequent fast relaxation towards the attractor. In equilibrium, on the other
hand, the dynamics evolves on a slower time scale on a lower dimensional
attractor. The reconstruction error of a dynamic mode decomposition is used to
monitor the inability of the time series to resolve the fast relaxation towards
the attractor as well as the effective dimension of the dynamics. We illustrate
our method by detecting transient dynamics in the Kuramoto-Sivashinsky
equation. We further apply our method to atmospheric reanalysis data; our
diagnostics detects the transition from a predominantly negative North Atlantic
Oscillation (NAO) to a predominantly positive NAO around 1970, as well as the
recently found regime change in the Southern Hemisphere atmospheric circulation
around 1970.
