  Abrupt and irreversible winter Arctic sea-ice loss may occur under
anthropogenic warming due to the collapse of a sea-ice equilibrium at a
threshold value of CO$_2$, commonly referred to as a tipping point. Previous
work has been unable to conclusively identify whether a tipping point in Arctic
sea ice exists because fully-coupled climate models are too computationally
expensive to run to equilibrium for many CO$_2$ values. Here, we explore the
deviation of sea ice from its equilibrium state under realistic rates of CO$_2$
increase to demonstrate how a few time-dependent CO$_2$ experiments can be used
to predict the existence and timing of sea-ice tipping points without running
the model to steady-state. This study highlights the inefficacy of using a
single experiment with slow-changing CO$_2$ to discover changes in the sea-ice
steady-state, and provides an alternate method that can be developed for the
identification of tipping points in realistic climate models.
