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We study in detail the role of covariant Lyapunov vectors and theirrespective angles for detecting transitions between metastable states indynamical systems, as recently discussed in several atmospheric scienceapplications. The underlying models are built from data by the dynamicalclustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximatedbased on these models. We test this data-based numerical approach at the handof three well-understood example systems with increasing dynamical complexity,identifying crucial properties that allow for a successful application of themethod: in particular, it turns out that the method requires a clear multipletime scale structure with fast transitions between slow subsystems which can bedynamically characterized by invariant neutral directions of the linearapproximation model.

Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors