  A statistical indicator for dynamic stability known as the $\Upsilon$
indicator is used to gauge the stability and hence detect approaching tipping
points of simulation data from a reduced 5-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 $\Upsilon$ indicator is designed to detect changes in the memory
properties of the dynamics, and is based on fitting ARMA (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 show 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.
