Nonlinear threshold behavior during the loss of Arctic sea ice

Abstract

In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or ''tipping point'') beyond which the ice-albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice-albedo feedback. Here, we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that although the ice-albedo feedback promotes the existence of multiple ice-cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea-ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely.Arctic climate ͉ bifurcation ͉ climate change ͉ tipping point T he retreat of Arctic sea ice during recent decades (1) is believed to be augmented by the difference in albedo (i.e., reflectivity) between sea ice and exposed ocean waters (2). Because bare or snow-covered sea ice is highly reflective to solar radiation, the increasing area of open water that is exposed as sea ice recedes leads to an increase in absorbed solar radiation, thereby contributing to further ice retreat. A number of recent studies have discussed the possibility that this positive ice-albedo feedback will cause the rapidly declining annual minimum (September) sea-ice cover to cross a critical threshold, after which the sea ice will melt back on an irreversible trajectory to a seasonally ice-free state (3-9).Heuristically, one might expect in a simple annual mean picture of the Arctic Ocean that completely ice-covered and ice-free stable states could coexist under the same climate forcing. The ice-free state would remain warm because of the absorption of most incident solar radiation, whereas the icecovered state would reflect most solar radiation and remain below the freezing temperature. In such a picture, these two stable states would be separated by an unstable intermediate state in which the Arctic Ocean is partially covered by ice and absorbs just enough solar radiation such that it remains at the freezing temperature: Adding a small amount of additional sea ice to this unstable state would lead to less solar absorption, cooling, and a further extended sea-ice cover. If the background climate warmed, the unstable state would require an increased ice extent to reflect sufficient solar radiation to remain at the freezing temperature. Beyond a critical threshold, the background climate would become so warm that the ice-covered state would reach the freezing temperature. At this point the stable ice-covered state and ...

The future of ice sheets and sea ice: Between reversible retreat and unstoppable loss

“…Hence, even if an ice cover were stable in this simple energybalance model for today's climate, it might well become unstable in a future warmer climate with a smaller ε: In such a climate, the transition to a smaller ice cover could be strongly nonlinear. A similar result, but for a different reason as discussed in Arctic Sea Ice, is also found in more-complex modeling studies (1,9).…”

“…Given that more complex models usually employ more realistic representations of heat transport, it was expected that they might not show the small ice-cap instability. Recently, a number of studies found that it is indeed probable that no such instability exists for the loss of Arctic summer sea ice, whereas an instability might well exist for the transition from a seasonally ice-covered Arctic Ocean to an Arctic Ocean that is virtually free of sea ice throughout the entire year (1,7,9).…”

Trends, noise and re-entrant long-term persistence in Arctic sea ice

“…In a study of the forecast skill of a linear empirical model, Lindsay et al (2008) found no skill in predicting detrended data for time scales of three or more months. Finally, the rapid decay in ice area anomalies is also found in climate models (see Armour et al 2011b and references therein) and this is argued to underlie the lack of hysteresis associated with the loss of summer sea ice in both global models and theoretical treatments such as in Eisenman & Wettlaufer (2009). The corpus of these studies led to the general conclusion of rapidly decaying correlations and hence compromised predictability.…”

Arctic Climate Tipping Points

“…The year that the North Pole becomes seasonally ice-free will likely be seen as a 'tipping point' by non-experts. Whilst politically important, several authors argue it is unlikely that such a transition involves an irreversible bifurcation (Eisenman and Wettlaufer 2009;Tietsche et al 2011) (as in Fig. 1a).…”

“…year-round) ice is more likely to represent a bifurcation (Fig. 1a), where the system can switch rapidly and irreversibly from one state (with seasonal ice) to another (without any) (Eisenman and Wettlaufer 2009). However, the tipping point for year-round ice loss requires around 13°C warming at the North Pole (Winton 2006).…”