Also from Notz and Stroeve 2018
“Also for the future, no substantial self amplification of the summer ice loss is expected. In particular, in all models that participated in CMIP5, the linear relationship between Arctic sea-ice cover and global-mean temperature holds until all sea ice is lost. This behavior already takes into account that in many regions, the ice-free duration during summer is becoming longer and longer, and that the ice cover as a whole is getting thinner. These factors are apparently not sufficient to overcome the stabilizing feedbacks and do not cause an acceleration of the summer sea-ice loss.”
This seems to put to rest hope for a slowdown in ASI losses due to the final ice being at higher latitude. Notz and Stroeve discuss and dismiss the opposite potential for reinforcing feedbacks to accelerate the rate of decline. That does not leave much room for a slow down.
Stroeve & Notz papers
To state that the linear relationship between sea ice loss and Arctic Global-mean(?) temperatures will hold until there is no more ice is heroic indeed.
How do they deal with September sea ice loss 1979 to 2019 of around 50% and volume loss of around 75% ? If both continue at the same linear rate then an arithmetical impossibility looms.
What got me started on all this was the discrepancy between the Extent and Volume trends. Since Extent has to reach zero at the same time as Volume, my query was how much longer before the Extent curve bends down to a necessary eventual reckoning with zero Volume? Shared Humanity's comment about ice going poof is worth more than what he supposes is its current market value! It got me to realize that the Extent curve does NOT have to bend down to meet the Volume trend, at least not until the last day.
Volume is a product of Extent x Thickness. We've lost about 76% of Volume (based on PIOMAS Sept. Volume trend for 2019 vs.1979), but only about 42% of Extent (based on NSIDC Sept. Extent trend line for 2019 vs. 1979).
The Extent value gets multiplied by the Thickness value to get Volume. So Extent can keep on floating down at a less steep slope until the point at which Thickness gets so thin that it falls prey to a warming event that takes Thickness down to zero. That is the "poof" moment when Extent suddenly catches up to Volume, i.e. they both reach zero.
Figure 6 in the Strove and Notz, 2018 cited in previous post shows that 10-day Extent losses of 1M km2 have occurred, and that losses of at least 0.5M km2 are not that rare. Thus, once Extent gets into the range of less than 2.0M to 1.5 km2, there is a possible and increasingly likely chance of a "poof" event of 0.5 to 1.0km2 scale that takes Extent below the arbitrary 1.0M km2 BOE threshold. That provides an indicator for how much longer Extent losses can continue at a slower pace than Volume losses before a fluctuation in Thickness creates a first time BOE.
The Sept. 2019 NSIDC Exent was 4.32M km2. As per NSIDC "The linear rate of sea ice decline for September extent from 1979 to 2019 is 82,400 square kilometers per year."
To reach the 2.0M Extent when a poof Event becomes possible, would require losing another 2.3M km2 of Sept Extent below the 2019 value of 4.3 (which is pretty much on the Trend line). By this reasoning, at 82k per year losses, losing 2.3M km2 would take another 28 years, i.e. 2047 before Extent in 50% of years would be within plausible range of a poof event.
This is later than I had expected, since Notz and Stroeve put the 50% chance of any single year going below 1.0M km2 as 2038. By 2047, Notz and Strove estimate that >95% of individual years will go below 1M km2.
Hmmm? So Extent trend alone does not end up at the expected date for 50% chance of BOE. That leaves Thickness losses as the missing factor that aligns the NSIDC Extent trend with the Notz and Stroeve BOE dates.
And that makes sense. Stroeve and Notz Fig. 5 show the decline of April ASI Thickness, and they cite the PIOMAS April Thickness trend as -0.28M per decade. Looking at PIOMAS Sept. thickness linear trend, I get a very similar -0.27M/decade trend. So by 2038, absent any acceleration or deceleration of Thickness losses, the average Sept. ice Thickness is likely to be near 0.51M. As Thickness declines from 1.022 (Sept. 2019) to 0.51M, the frequency of 0.5 to 1.0 km2 Extent losses in a 10-day period will certainly increase, and the magnitude of infrequent large scale Extent losses will also increase.
That is why extrapolation of the Extent loss curve alone yields BOE dates that are artificially late. Combine the continued Extent loss curve with an increasing (instead of static) scale for 10-day Extent losses (due to declining Thickness), then you can get dates to fit with the Notz and Stroeve estimate of 2038 for when 50% of years could reach BOE status of <1.0M km2.
In 20 years, the Extent trend goes to 4.32M - (0.084M x 20) = 2.67M km2. That is way too high to be taken down to 1.0 km2 by a 10-day Extent loss event if the September Thickness remained at the current ca. 1.02M. But much more likely when the average September Thickness is down to 0.51M.
So here we have the most likely poof moment scenario for when ASI goes below 1.0m km2. Around 2038, with Sept. Extent at ca. 2.7M km2
and Thickness is down to 0.5M, a 10-day event removes enough ice to take Extent below 1.0M km2. (This scenario also fits well enough with Archimid's April max vs. summer losses crossing trendlines.)
Of course, this is an event of arbitrary significance. The ice will begin refreezing and our long march to a hot Earth destiny will continue with ups and downs in ASI. Deniers will cite the fact that Arctic ice coverage in October increased over September to show that there is nothing to worry about.
As for thin ice melt acceleration, which is also where this adventure started, I stand corrected and have to yield to more educated minds that reversing the Thorndike curve is not legitimate in terms of thickness alone and thermodynamics. But as Shared Humanity noted, my gut still says that in a real world setting, younger, saltier, highest-surface-to-volume-ratio, more fractured, dispersed, thinner ice has a higher chance in a rolling ocean exposed to currents to get melted by export or to go poof due to flash melt, and that the chances for rapid Extent loss increases faster than the linear change in thickness. But now I'm just being stubborn.
I don't know if this convinces anybody else, and there remains the chance of some bonehead error that makes this all wrong, but thanks to the Stroeve and Notz articles I feel like I have some understanding for how the Extent, Thickness, and Volume trends will evolve over the next 20 years. The Emperors are well dressed indeed, and I retract my arrogant and ignorant allegations to the contrary.