Qinghua,
Thank you for referring to Armour et al 2011.
They say:
“Although we find that CCSM3 does not show evidence of a summer sea ice tipping point, the variance in summer Arctic sea ice area increases in the model as the climate warms [Holland et al., 2008; Goosse et al., 2009]. The increase in variance may plausibly be related to a reduction in stability, or alternatively it may be driven by other factors such as reduced geographic muting of ice edge variability [Goosse et al., 2009; Eisenman, 2010] or an overall thinning of the ice pack [Notz, 2009]. However, in light of the present findings, it does not appear to be associated with a loss of stability altogether. Given that these same processes are expected to be at work in nature, variance in the observed sea ice cover may similarly be an unreliable indicator of an approaching threshold.”
Livina & Lenton 2013 say on potential Arctic sea ice tipping points:
http://www.the-cryosphere.net/7/275/2013/tc-7-275-2013.pdf"there has been an abrupt and persistent jump in the amplitude of the seasonal cycle of Arctic sea-ice cover in 2007 (Ditlevsen, 2012), but the underlying causal mechanism remains uncertain. We describe this as a (non-bifurcation) “tipping point”, because it involved an abrupt, qualitative change in the sea-ice dynamics, without any evidence for a large forcing perturbation; i.e. the abruptness resides in the internal dynamics of the Arctic climate system."
And Serreze 2011 says:
http://www.nature.com.sci-hub.cc/nature/journal/v471/n7336/full/471047a.html"with ice-free summers, the ocean picks up a great deal of extra heat, delaying autumn ice growth. If there was a tipping point, this summer heat gain would lead to ice cover the following spring being thin enough to completely melt out over the following summer. Instead, so much ocean heat is lost during the darkness of the polar winter that enough ice grows to survive the next summer’s melt."
The question seems to be: will it? Or will Arctic amplification feedbacks cause much of this extra heat uptake to stay in the Arctic? If so, how large will this amplification be? Even if there is no irreversibility, there still could maybe be an acceleration in ice loss. It seems a risk we can't ignore yet.
Also if we look again at fig 8 of Walsh et al 2016 (attached):
http://onlinelibrary.wiley.com/doi/10.1111/j.1931-0846.2016.12195.x/fullIt shows maybe 0.5 million km2 decadal variability from 1850-1925 and about 1 million km2 from 1925-2000. Why has this decadal variability apparently grown? Could it be due to AGW? In that case maybe part of the 1.05 million km2 loss from 1979-1988 to 2007-2016 is not fully due to natural variability, but also partly to AGW, say 50% of it? In that case natural variability would have caused about 20% of ice loss since 1979 instead of 40%. Or how would this argument be mistaken?