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In light of the rapid recent retreat of Arctic sea ice, the extreme weatherevents triggering the variability in Arctic ice cover has drawn increasingattention. A non-Gaussian $\alpha$-stable L\'evy process is thought to be anappropriate model to describe such extreme event. The maximal likelytrajectory, based on the nonlocal Fokker-Planck equation, is applied to anonautonomous Arctic sea ice system under $\alpha$-stable L\'evy noise. Twotypes of tipping times, the early-warning tipping time and thedisaster-happening tipping time, are used to predict the critical time for themaximal likely transition from a perennially ice-covered state to a seasonallyice-free one, and from a seasonally ice-free state to a perennially ice-freeone, respectively. We find that the increased intensity of extreme eventsresults in shorter warning time for sea ice melting, and that an enhancedgreenhouse effect will intensify this influence, making the arrival of warningtime significantly earlier. Meanwhile, for the enhanced greenhouse effect, wediscover that increased intensity and frequency of extreme events will advancethe disaster-happening tipping time, in which an ice-free state is maintainedthroughout the year in the Arctic Ocean. Finally, we identify values of L\'evyindex $\alpha$ and noise intensity $\epsilon$ in $\alpha \epsilon$-space thatcan trigger a transition between the Arctic sea ice state. These resultsprovide an effective theoretical framework for studying Arctic sea icevariations under the influence of extreme events.

The tipping times in an Arctic sea ice system under influence of extreme events