  It has been widely debated whether Arctic sea-ice loss can reach a tipping
point beyond which a large sea-ice area disappears abruptly. The theory of
dynamical systems predicts a slowing down when a system destabilises towards a
tipping point. In simple stochastic systems this can result in increasing
variance and autocorrelation, potentially yielding an early warning of an
abrupt change. Here we aim to establish whether the loss of Arctic sea ice
would follow these conceptual predictions, and which trends in sea ice
variability can be expected from pre-industrial conditions toward an Arctic
that is ice-free during the whole year. To this end, we apply a model hierarchy
consisting of two box models and one comprehensive Earth system model. We find
a consistent and robust decrease of the ice volume's annual relaxation time
before summer ice is lost because thinner ice can adjust more quickly to
perturbations. Thereafter, the relaxation time increases, mainly because the
system becomes dominated by the ocean water's large heat capacity when the
ice-free season becomes longer. Both trends carry over to the autocorrelation
of sea ice thickness in time series. These changes are robust to the nature and
origin of climate variability in the models and hardly depend on the balance of
feedbacks. Therefore, characteristic trends can be expected in the future. As
these trends are not specific to the existence of abrupt ice loss, the
prospects for early warnings seem very limited. This result also has
implications for statistical indicators in other systems whose effective mass
changes over time, affecting the trend of their relaxation time. However, the
robust relation between state and variability would allow an estimate of
sea-ice variability from only short observations. This could help one to
estimate the likelihood and persistence of extreme events in the future.
