  We study in detail the role of covariant Lyapunov vectors and their
respective angles for detecting transitions between metastable states in
dynamical systems, as recently discussed in several atmospheric science
applications. The underlying models are built from data by the dynamical
clustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximated
based on these models. We test this data-based numerical approach at the hand
of three well-understood example systems with increasing dynamical complexity,
identifying crucial properties that allow for a successful application of the
method: in particular, it turns out that the method requires a clear multiple
time scale structure with fast transitions between slow subsystems which can be
dynamically characterized by invariant neutral directions of the linear
approximation model.
