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This study investigates the use of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric sciences applications. In a first step, the needed underlying dynamical models are derived from data using a non-parametric model-based clustering framework. The covariant Lyapunov vectors are then approximated based on these data-driven models. The data-based numerical approach is tested using three well-understood example systems with increasing dynamical complexity, identifying properties that allow for a successful application of the method: in particular, the method is identified to require a clear multiple time scale structure with fast transitions between slow subsystems. The latter slow dynamics should be dynamically characterized by invariant neutral directions of the linear approximation model. [ABSTRACT FROM AUTHOR]

A statistical indicator for dynamic stability, known as the Υ indicator, is used to gauge the stability and, hence, detect approaching tipping points of simulation data from a reduced five-box model of the North Atlantic Meridional Overturning Circulation (AMOC) exposed to a time-dependent hosing function. The hosing function simulates the influx of fresh water due to the melting of the Greenland ice sheet and increased precipitation in the North Atlantic. The Υ indicator is designed to detect changes in the memory properties of the dynamics and is based on fitting auto-regressive moving-average models in a sliding window approach to time series data. An increase in memory properties is interpreted as a sign of dynamical instability. The performance of the indicator is tested on time series subject to different types of tipping, namely, bifurcation-induced, noise-induced, and rate-induced tipping. The numerical analysis shows that the indicator indeed responds to the different types of induced instabilities. Finally, the indicator is applied to two AMOC time series from a full complexity Earth systems model (CESM2). Compared with the doubling CO 2 scenario, the quadrupling CO 2 scenario results in stronger dynamical instability of the AMOC during its weakening phase. [ABSTRACT FROM AUTHOR]