Several people have mentioned (I think the first I heard of it was from the Rabett) that at the moment, Arctic sea ice is exceptionally fragmented. It has even been suggested that we should expect a precipitous decline over the next week or so, by some accounts because of a possible imminent storm. I don’t know whether or not such prognostications are true, but I am motivated to look at the relationship between the two most common measures of sea ice, its area and its extent.
Sea ice extent is defined as the area of ocean which has at least 15% ice cover, whereas sea ice area is simply the area of the sea ice itself. When the ice is completely connected rather than fragmented, the two measures will be the same. It turns out, however, that the ice is usually somewhat fragmented, and when it is the extent of the sea ice is larger than the sea ice area. The two measures taken together can give us at least a rough idea of how much the ice is fragmented.
We can easily compare them in two different ways: by taking the difference (extent minus area) and by taking the ratio (extent divided by area). The Arctic Sea Ice Blog does one version of this (actually the ratio of area to extent rather than extent to area), but uses daily extent data from JAXA which only begin in 2002. I’ll use monthly data from NSIDC (and add back in the size of the “hole” at the pole which is unobserved, accounting for the fact that the size of the unobserved area changed in mid-1997) in order to extend the analysis over a longer time span. Here’s the extent-area difference over time:
The most obvious feature is an annual cycle, with the difference being greatest during late summer/early fall when ice cover is approaching its annual minimum. Here’s the ratio over time:
Again we see an obvious annual cycle, but for the ratio we can also see an increase over time during the peak summer/fall months.
It behooves us to remove the annual cycle by computing anomaly values as a given month’s value minus the average for that same month. Here’s the difference anomaly:
There’s no obvious pattern, although there are many extreme values during more recent years. Here’s the ratio anomaly:
For ratio, the overall increase over time is again evident.
We can look at the annual cycle in detail by plotting each year’s difference or ratio on top of the other years. Here’s the difference, by month, up through 2006 (the y-axis is mislabelled “Ratio” but the title is correctly “Difference”):
This serves to define the “normal” annual pattern in extent-area difference. It increases in June, is greatest in July, sometimes dips below average in September, and often shows a secondary rise during October. But during the record-smashing year 2007 a unique pattern element emerged:
The value during June was much larger than in previous years. The September dip was on the low side and the October rise on the high side, but it’s the exceptional June value that really stands out.
The following years, 2008 through 2011, returned to the previous pattern. Here’s the data, I’ve left the dots on 2007 and added 2008 through 2011, which are kinda hard to pick out since they don’t really deviate from what happened before:
But this year again shows essentially the same oddity observed in 2007, namely, an exceptionally high value during June:
Could this June extremity in extent-area difference be a harbinger of things to come? Might it signify that this year will emulate 2007 in showing an exceptionally low sea ice minimum? After all, 2007 wasn’t just low, it was exceptionally so — it didn’t just continue the declining trend, it deviated from that trend, with truly dramatic ice loss. If the June extent-area difference is a sign of that, then we might witness an astounding loss of Arctic sea ice again this year, not just a continuation of the trend, but an exceptional low, even well below the expected value due to trend.
A similar story emerges from examination of the ratio rather than the difference. Here’s the pattern up to 2006:
Again, something unique happened in 2007:
The ratio was much higher than before during June, and also set new records for July, August, and October. The following years 2008 through 2011 saw new records for August but a return to the previous pattern for other months:
Yet again, 2012 has repeated the unusual pattern of 2007:
There are new record highs for June and July. Again I wonder, is this a harbinger of a 2012 repeat of the “fall-off-the-cliff” drop in Arctic sea ice we witnessed in 2007? It certainly suggests that for June and July, the ice was more fragmented than in previous years.
And there is indeed quantitative evidence of this greater degree of fragmentation — both from the extent-area difference and the extent/area ratio. It will be interesting to see what August brings, and even more interesting to note this year’s minimum values (for both extent and area) in September. Signs point to a new record low, and there is the possibility that it could be not just a record-breaker, but a record-obliterator just like in 2007.
Finally, for those who enjoy the animated graphs here are the differences and ratios over time (click the graphs!):
Open Mind 
Could you do some kind of regression to show that months with high extent/area ratios have high extent declines in the subsequent month?
Stats are one thing, but phsyical processes another. Without implying that I understand the latter (not at all, in fact), but this year’s weather conditions are markedly different from those in 2007. To simplify: in the four ‘busiest’ months of the melting season (mid-May to mid-September) 2007 had ideal conditions for ice decline during practically the whole period, with a very late minimum.
2012, however, is looking much more like 2010. From mid-May to mid-June conditions were good for ice decline and decline it did. But then the weather turned, and it hasn’t really switched back since. 6 weeks of weather that stopped 2010 and 2011 dead in their tracks, but 2012 keeps going strong (see this blog post for a comparison). It doesn’t have heavy ice transport through Fram Strait or ocean heat flux through Bering Strait, like in 2007, but it doesn’t seem to matter. This in my view is very strong evidence that the ice is thinner than it was in 2007.
I think what makes 2007 and 2012 so similar in the graphs in the blog post above, is heavy melt ponding. Both years seemed to have a lot of that, which implies that a lot of solar energy reached the Arctic, particularly in May and June. But where compaction played a big part in the 2007 minimum record, 2012 is seeing a lot of divergence, which is why the ratio is even ‘worse’ than 2007.
Now, first we have to see what the effect will be of that big, intense cyclone on the ice pack, especially the weak looking ice on the Pacific side of the Arctic. Then things will depend on what the weather does after this week. If it stays unfavourable, I’m not sure if 2012 can keep going strong, as air temperatures will start to drop. If it starts to resemble 2007 weather conditions and we do not see a repeat of last year’s early minimum, the record sea ice area minimum will be shattered. The record extent minimum will very probably be broken as well.
Was going to ask if you’d made a prediction for this year’s September minimum, and rediscovered your estimate given in October last year.
Would you be inclned to revise your estimate based on the area/extent analysis above?
Making my prediction at 4.25 million km2.
[Response: The impact of higher-than-usual June extent/area difference or ratio is not yet firmly established. So I’ll leave my prediction as is.]
To build on all this, thinner, younger ice is more subject to fragmentation. It is important to not lose sight of the physical basis of the statistics which describe it.
Taminos estimate last October seems to be for September average, not minimum. If Barrys prediction of 4.25 is for minimum (NSIDC), it will not be a record.
Though interesting, I think the harbinger hypothesis here is speculative. NevenA´s explanation of the physical processes involved seems to make sense. As I understand it, it implies that an unusual extent-area difference in June like 2007 will increase the chances of an extraordinarily low minimum, but this won´t necessarily be the result.
My guess, based on the information from NevenA, and eyeballing the curves of the last years, is that 2012 will set a record minimum for extent, but not “extraordinarily low” (compared to 2007).
It seems obvious that the weather conditions in the last month of the melt season will have a considerable influence on the final number, and we all know the weather is unpredictable:-)
So guessing a number really has to be a guess, and I go for 4.11 m km2.
Careless language – I meant the September average, which would be a record at 4.25 mil sq/km.
Tamino neglects to cite his own previous work in this space:
That post and comments were influential on discussion at Neven’s, where some similar musing had been getting traction for a little bit but needed an injection of capital.
The wheels on the blogs go round and round…
:-)
Hi Tamino,
Do you have any comments on this one:
http://www.fas.org/irp/agency/dod/jason/statistics.pdf
It’s not peer-reviewed because it’s DoE/DoD work, but I find it amazing that nobody has followed that idea since then ?
Poul,
The Jason study is pretty well known. It’s just a straightforward application of extreme value statistics to temperature time series. It’s a report, not an innovation. I’m not sure whey you think has not been followed up. Actuaries do this type of analysis all day long.
The reason I ask, is that I do not see this (obscure) branch of statistics mentioned or used in any of the climate science papers I have read. Given its claimed discriminating power (assigning odds 1:100.000 in 1992) it seems to me that it would readily be able to tie individual extreme events directly to global warming.
Extreme value statistics is not really all that obscure. As I said, it’s very important in insurance and finance. I’ve also used it for radiation hardness assurance. The problem is that for extreme values, you are of necessity dealing with the tail of the distribution and so relatively few events. That is fine if you are looking at a stationary series, but if you are interested in changes, you will of necessity be working with a small sample, and so your conclusions will not be rigorous.
If you are interested in this stuff, I believe Gumbel’s text is now available as a paperback from Dover
A constant Extent-Area difference, and increasing ratio can be explained by dividing the ice pack into two zones – a central zone where concentration is 100%, and a fringe zone where concentration is reduced. Then assume that the whole ice pack and the central zone shrink, while the fringe zone remains the same size and the same concentration.
I was about to paste this from neven’s blog but there’s a new post that expands on it
“Apocalypse wrote:
The blog link is:
https://sites.google.com/site/apocalypse4real/home/sea-ice-concentration-and-thickness-comparison “
A relative ice free Arctic is not a good thing as a little research will show it is the norm in an ice age. Not what the world needs right now.
I think you meant *not* the norm in an ice age.
I think you are doing your research in the wrong places. Try Polyak et al (2010) for an alternate view.