Home > climate > Renowden’s Threnody Reprised

Renowden’s Threnody Reprised

2012 October 13


Two years ago, Gareth Renowden posted a piece titled FIVE YEARS (THRENODY FOR ARCTIC SEA ICE). He modeled changes in arctic sea ice extent as a function of linear trends in sea ice volume and “thickness.” The result was an accelerating decline in sea ice extent; it might have been the first such ‘accelerating decline’ chart I had seen. I bookmarked it for later review. Now here we are, two years later…

Gareth took PIOMAS volume and divided it by NSIDC sea ice extent to calculate a notional “thickness.” He then determined the linear trends for both the volume and the thickness over a 21 year period (1990-2010) and a 10 year period (2001-2010). He then used the trend projectons for volume and thickness to project extent.

I’ve reproduced his methods in the following two charts, the first for the 21 year trends and the second for the 10 year trend. The sea ice volume and extent for 2010 and 2011 have been added; note the four “cross-hair” data points.

There were three things about Gareth’s work that seemed odd to me. The first is that he used sea ice extent rather than area. The second is that he extended his projections from the last data point (2010), rather than from the trend value for 2010. And the last is that thickness remains positive even as volume goes negative.

In the following two charts, I have “corrected” Gareth’s method by using sea ice area and by projecting the trend from the 2010 trend value and not the 2010 data value. The 10 year “zero” date is moved from 2016 to 2017.

It’s pretty obvious that projections of the 21 year trends do a poor job of predicting volume and area values for 2011 and 2012. The ten year trends do better.

But as a “model”, this is still a piss poor model. It is a model in which the volume goes zero (and beyond!) but for which the thickness remains greater than zero. Recall that thickness is a calculated, notional value based on extent or area. The fact that the notional thickness trend isn’t falling in proportion with the volume trend simply indicates that the real sea ice extent and area aren’t falling at the same proportion as the PIOMAS volume. It appears that the arctic sea ice is getting thinner proportionally faster than it is retreating.

And the same chart as the last but extended over the entire time series…

I quote Gareth’s original post from 2010

Gareth (2010): Bottom line: if the relationship between ice volume and extent evident in the NSIDC and PIOMAS data over the last 21 years continues in the near future, then the Arctic will be effectively ice-free in late summer sometime between 2015 and 2020. One interesting observation: the 10 year trend chart above suggests that 2007′s record minimum extent could remain unbroken next year, and the ice would still be on course to disappear within five years. If there’s any upside at all to this message (and I’m struggling to find one) it is perhaps that such a rapid and visible loss of sea ice might finally persuade the international community to take urgent action to reduce the atmospheric carbon load. What a seasonally ice-free Arctic might mean for global climate is something I shall look into a future post.

Source here: threnody.R

  1. 2012 October 13 at 1:34 pm

    Model predictions and extrapolations as in http://neven1.typepad.com/blog/2012/10/naive-predictions-of-2013-sea-ice.html make no sense to me at all. I cannot think of any reason why sea ice reduction rate should level off as it approaches zero. Thus, OTOH, Renowden’s predictions, and yours above, look eminently reasonable.

  2. 2012 October 13 at 6:13 pm

    One reason why it might level off and never reach zero is the possibility that there will always be *some* multi-year ice. That winds and currents will always pile up some ice along the “west” side of the Arctic Ocean, along Greenland and Ellesmere Island, thick enough to survive the summer. So I don’t think “absolute zero” ice as the minimum is a given.

  3. 2012 October 14 at 1:01 am

    Thanks for revisiting my “piss poor” model, Ron… 😉

    It was naive, in the sense that Neven uses it, but I do think it captures the essence of what’s going on in the Arctic – and that’s an excess of heat in compared with heat out. And I think I’ll happily stick with my original. I struggle to see how the sea ice at minimum (beyond a rump of multi-year ice stuck to the north of the archipelago) can survive the decade.

  4. Ned
    2012 November 16 at 6:58 am

    There are other reasons why the curve might “level off” as it approaches zero. Perhaps it is easier to melt ice around the fringes of the ice cap than in the center (higher solar zenith angle, more solar radiation absorbed by water due to angular dependence of absorptance; proximity to warm currents from the Atlantic/Pacific). Because the area of ice in a given latitude band decreases as you move toward the poles, the rate of loss of extent would tend to slow down over time. Of course, there are other factors that might negate this. But the point is that it’s not unreasonable to expect that there might be a sigmoid shape to the volume curve over time.

    So far, though, there doesn’t seem to be much sign of a slowdown as we approach zero.

  1. 2012 October 15 at 6:26 am
Comments are closed.