  In light of the rapid recent retreat of Arctic sea ice, the extreme weather
events triggering the variability in Arctic ice cover has drawn increasing
attention. A non-Gaussian $\alpha$-stable L\'evy process is thought to be an
appropriate model to describe such extreme event. The maximal likely
trajectory, based on the nonlocal Fokker-Planck equation, is applied to a
nonautonomous Arctic sea ice system under $\alpha$-stable L\'evy noise. Two
types of tipping times, the early-warning tipping time and the
disaster-happening tipping time, are used to predict the critical time for the
maximal likely transition from a perennially ice-covered state to a seasonally
ice-free one, and from a seasonally ice-free state to a perennially ice-free
one, respectively. We find that the increased intensity of extreme events
results in shorter warning time for sea ice melting, and that an enhanced
greenhouse effect will intensify this influence, making the arrival of warning
time significantly earlier. Meanwhile, for the enhanced greenhouse effect, we
discover that increased intensity and frequency of extreme events will advance
the disaster-happening tipping time, in which an ice-free state is maintained
throughout the year in the Arctic Ocean. Finally, we identify values of L\'evy
index $\alpha$ and noise intensity $\epsilon$ in $\alpha \epsilon$-space that
can trigger a transition between the Arctic sea ice state. These results
provide an effective theoretical framework for studying Arctic sea ice
variations under the influence of extreme events.
