Area vs Extent

Because of a very interesting discussion in the comment section of the last SIE update, I've decided to report some more on the area and extent figures. Although it deserves a blog post of its own, I unfortunately lack the skills and time to produce the necessary graphs. But some of the commenters are busy with this, so I will probably be adjusting and expanding this post, making it more comprehensive, this coming week.

As we have seen ever since atmospheric patterns changed radically since the beginning of the month and caused extent melt rates to stall in a big way, the ice pack, instead of being compacted and transported out of Fram Strait, has been diverging and spreading out over the Arctic Ocean. So much in fact that halfway through the month we started to notice 'holes' in the ice pack where relatively large leads and patches of blue ocean water were increasingly becoming visible.

Because of this phenomenon of cyclones dominating over the Central Arctic (preventing for instance the setting up of a stable and strong positive Arctic Dipole Anomaly, a key factor in 2007's record minimum extent) and causing the ice pack to be spread out, an interesting thing might be happening with regards to sea ice area and sea ice extent, both different methods of calculating the total surface of ocean water that is covered with sea ice. 

I keep forgetting how this works, and other people probably do too, so I think we can't have enough explanations and analogies to stress the differences between both methods. The Arctic is divided up into grid cells, measuring 25 km x 25 km. For every grid cell that contains an ice concentration (percentage of the seawater that is covered by sea ice) of at least 15%, the whole surface area of the grid cell, 625 square km is added up to the total extent number. For sea ice area the surface area of every grid cell that is covered with sea ice is added to the total, except grid cells that have an ice concentration lower than 15%.

Say, for instance, we have three grid cells. One is covered with 10% ice, the second with 50% ice and the third with 100% ice. The first grid cell has less than 15% ice concentration and so isn't counted, but the other two are. Total extent is thus 1,250 square km (two grid cells of 625 km). For total area we take 10%, 50% and 100% of the surface areas of the grid cells, adding up to 937.5 square km (0 + 312.5 + 625). Total area will practically always be lower than extent.

Here is a great graph made by Larry Hamilton that shows us the monthly decline in area and extent from 1979 till now:

Of course, we know that IJIS reports its extent numbers on a daily basis, forming the basis of my SIE updates. Unfortunately, although they also have a sea ice area graph that looks just like the extent graph, they do not provide a spreadsheet or document with sea ice area data for us to download and play around with. Cryosphere Today has a regularly updated sea ice area document, but they only do area, not extent. NSIDC does have numbers for both methods. Larry Hamilton's graph is based on them and professional statistician Tamino has used the same numbers in his recent blog post, Sea Ice Curiosity, where he subtracted area numbers from extent numbers:

2007 is blue, 2008 is green, 2009 is brown, 2010 is red.

But unfortunately these are monthly numbers. And we can't wait for that. We Arctic junkies like to be fed data on a daily, near real-time basis, thank you very much. That's why some of the commenters of the Arctic Sea Ice blog have downloaded IJIS extent numbers and CT area numbers to play around with. Even though it isn't a perfect combination of data, it's still interesting to subtract the numbers from each other or divide them.

Why is this interesting? Mostly, it tells us something about how much the ice pack is spread out. When the pack gets compacted area and extent will come closer together. For instance in Tamino's graph we can see that during winter the difference between extent and area - when area is subtracted from extent - fluctuates between 1 and 2 million square km. But in the melting season the gap gets greater. This is because ice is melting, gets spread out and melt ponds start to form.

The last aspect is important as I believe it is the key factor in the early peaks of 2007 and 2010 to a lesser extent. When air temperatures get high enough and the sun reaches its maximum elevation around summer solstice melt ponds start to form on the ice, fooling satellite sensors into believing this is open water. For extent numbers this isn't so much a problem because a melt pond would have to get really big to cover a grid cell of 625 square km in such a way (more than 85%) for it to not be counted. With area however every percent of the surface that doesn't look like ice gets added to the total, making sea ice area numbers go much lower than extent numbers. But at this point in the melting season melt ponds aren't that big any longer, having been drained or starting to freeze over again, so we are mostly looking at the spreading of ice when fiddling around with area and extent numbers.

We are now entering the zone of speculation. I will probably alter and adjust this final part of the blog post as numbers and graphs are being crunched by commenters and there is still a lack of clarity on several points.

Like I said some of the commenters on this blog have started combining area and extent numbers from Cryosphere Today and IJIS respectively. To be more precise, they are dividing area by extent to see if the resulting percentages have been dipping in the last few weeks.

I have finally managed to create a spreadsheet that combines the numbers. What I did was download IJIS extent data and CT area data and arrange all the numbers in this spreadsheet.

For instance here's the percentage (area/extent) for the 30th of July:

2006 72.4%
2007 69.3%
2008 70.5%
2009 74.3%
2010 65.7%

FrankD came up with different numbers because he managed to divide IJIS area numbers (probably by inferring them from the IJIS area graph) with IJIS extent numbers, which of course would be much better than using numbers from different organisations who use different methods and algorithms to calculate their numbers. Nevertheless I've decided to post his preliminary graph, because it is the thing we are looking for:

 

Unfortunately the 2010 trend line stops around July 8th, the point at which we'd expect the percentage to drop because of sea ice area dropping faster than extent, or in other words: because the ice pack kept a relative same shape at the exterior, but started to become less concentrated in parts of the interior, as shown by the 'holes' we have seen on MODIS satellite images.

I have followed up on a tip from Nick Barnes and produced my first graph with Google Chart Tools. It is showing daily area/extent percentages for the month of July:

In all years the percentages drop, but this year stands out. The number for July 31st 2010 is 63.8%. According to my data the minimum was reached on the following dates in previous years:

• September 25th 2006: 67.2%
• August 20th 2007: 60.6%
• August 14th 2008: 60.2%
• September 10th 2009: 64.7%

Larry Hamilton produced another graph with the NSIDC monthly area and extent data that shows how over the last 30 years the yearly minimum of ice area as a percentage of extent has dropped:

Okay, that's it for now. My poor little alpha brains can't take anymore. Stay tuned for more (when I have recovered).

Comments

[L. Hamilton]

Neven, my apologies, there's a typo in the 7/30 version of my cycle plot. A corrected 8/1 version is here:
http://img.photobucket.com/albums/v224/Chiloe/Climate/Cycle_Arctic_extent_4.png

[Neven]

Thanks, Larry. I've switched to your new graph.

[Andrew Xnn]

Wow!

So, 2010 is standing out with the lowest area/extent percentage (65.7%) compared to the previous low years; lower than 2007 and in stark contrast to 2009. In other words, it is primed for compaction/export more so than any previous year.

Also, from the "Trends in ice area and extent by month 11/1978 - 6/1010" graph, it looks like October, September, August and July pretty much in that order have had the largest anomalies over the past few years. It will likely be an interesting next 3 months.

[L. Hamilton]

Andrew, graph's title should of course read "11/1978-6/2010", not through "6/1010" as I mistyped it. If anyone else wants a typo-free version, it's here:

http://img.photobucket.com/albums/v224/Chiloe/Climate/Cycle_Arctic_extent_4.png

Once the July numbers are posted by NSIDC, and for that matter August & September, I'll update the graph at that same URL.

[Artful Dodger]

Neven, could you comment on how you are handling the 'data hole' at the North Pole for your computations? Thanks!

[Neven]

AD, I'm using a very useful technique called 'ignoring'. ;-)

Do you think I should add a certain number to the area total? The 0.31 million square km Tamino mentions, or do they use a different number over at CT?

[Artful Dodger]

Neven, no single technique is perfect; each has merits and drawbacks. It is most important simply to document your method, so your results are reproducible.

[Lord Soth]

With such a huge difference between area and extent, there is a possibility that the extent may decrease late into September or early October. It would take the right weather condtions, but a little bit of nilas or thin ice, between the pack in early autumn; will not stop the compaction with the fall storms blowing in the right direction.

[Neven]

AD, what I did was download IJIS extent data and CT area data and arrange all the numbers in this spreadsheet.

You guys tell me what I did wrong, and then I'll continue tomorrow. Because if I did something wrong I have made a fool of myself enough as it is.

[L. Hamilton]

Here is what the ratio of area (adjusted as described earlier) to extent looks like, by month, 11/1978 to 6/2010. The ratio tends to be highest, just below 90%, in March. There is no apparent trend in these high points.

Most years the ratio of area to extent reaches a low point in August. In the 1980s and early 90s such low points remained above 70%, but unlike the maximum ratio, the minimum has a downward trend over time -- so that within-year variation in area/extent has increased.

http://img.photobucket.com/albums/v224/Chiloe/Climate/area_vs_extent1.png

[Andrew Xnn]

Another interesting graph L. Hamilton...

So, as late as 2006, the August Minimum could have passed for "normal".
However since then, every year has been exceptional with the previous extreme year being 1998.

The last 4 years, including 2010 have been exceptional.

[Neven]

Larry, as usual I have stolen your excellent graph for this blog post. Thanks a lot.

[Jon Torrance]

Hard to see how we can do anything other than ignore any north pole data hole the CT area data may have until we know for sure how large such a hole might be and how, if at all, they adjust their area numbers to deal with it. For that matter, I have no idea how IJIS deals with any data hole at the north pole in their area data - they explain what they do with extent just fine but I don't recall reading a similarly detailed explanation of how they produce their area chart.

[Bfraser]

Great blogging, Neven.

But I noticed something wrong with the example that you gave on the definition of area versus extent. According to nsidc,

http://nsidc.org/arcticseaicenews/faq.html#area_extent

they apply a "filter" of 15% to their area computation, so the 10% cell in your example would count as 0, rather than 6.25 km^2.

And, finally, yes, following the fate of the arctic ice is more exciting that following cricket.

[Neven]

Thanks, Bfraser, I'll change the text. Jon Torrance told me the same thing in a previous thread, but I misunderstood, thinking the 15% threshold only applied to extent.

I read that NSIDC explanation only a short while ago, but overlooked this definition for area. I practically copied their example off the top of my head, haha. Copypaste could have saved me the trouble and the mistake. :-)

[Phil263]

Very interesting graphs and meaningful analysis, just a few thoughts though.

I am not so sure about what meaningful value we can attach to the area/extent ratio inasmuch as the ice area represents a surface of of ice that can be distributed very differently within the ice extent. What I mean by that is that you can 4 million sqkm of ice made up of a big chunk of 95% concentrated ice and a large area of say 15-30% concentration. This ice pack would behave very differently from an ice pack of the same area but with an homogeneous concentration between 70 % and 90%. Ice at 25 % concentration is likely to melt away within a few weeks, while 70% + concentration ice is more likely to be a temporary melt which will quickly refreeze.
I am sorry if I haven't made myself clear enough. What I want to say in a nitshell is that an analysis with a breakdown of ice extent into different rates of concentration might be a much better predictive tool that just an area/ extent ratio. This being said, I undertsand that this may not easy to do.

[Artful Dodger]

Yes Phil, the Area/Extent statistic as formulated will not capture fine detail. Primarily because we do not have 'per grid' data, A/E masks a good deal of signal due to spatial averaging. Further, there is temporal averaging (2 days for IJIS, 5 for NSIDC) that masks changes that occur over a shorter period.

Still, as Larry Hamilton's graph above clearly demonstrates, there is a useful signal embedded in the A/E statistic, which is what I was hoping to see when I suggested it's use.

[Neven]

And it more or less confirms what we have been seeing on satellite images and ice concentration maps in the past 2-3 weeks, with the 'holes' and everything. Despite its flaws I still think it's an interesting metric to be comparing with previous years in this final phase of the melting season. It might give a sense of how much potential for compaction there is (the final outcome of which is depending on atmospheric conditions of course).

[Artful Dodger]

Lord Soth said | August 01, 2010 at 21:23

"With such a huge difference between area and extent, there is a possibility that the extent may decrease late into September or early October. It would take the right weather condtions, but a little bit of nilas or thin ice, between the pack in early autumn; will not stop the compaction with the fall storms blowing in the right direction."

Hi Lord Soth,

I made a similar prediction on June 27. If the DA returns this Fall, we will continue to loose Sea Ice due to advection through Fram Strait well after the melt is over. I stand by my earlier prediction of Sep 24 - Oct 4 as the date for Sea Ice Minimum 2010.

[Anu]

Area decline has slowed down the last two days:
http://www.ijis.iarc.uaf.edu/seaice/extent/AMSRE_Sea_Ice_Area.png

Extent decline is picking up speed again.
The latest value : 6,820,469 km2 (August 1, 2010)
A 101,562 sq km drop (pre-correction):
http://www.ijis.iarc.uaf.edu/seaice/extent/AMSRE_Sea_Ice_Extent_L.png

This suggests some compaction at the sea ice coasts, or perhaps some melt ponds draining through ice that has melted through.

Beaufort Sea ice is poised for more heavy melts:
ftp://ftp-projects.zmaw.de/seaice/NEAR_REAL_TIME/Arc_latest_large.png

Both Arctic sea ice area and extent are currently 2nd lowest on record for August 1st.

[Evilreductionist.blogspot.com]

In terms of average loss from here on in, we should see it getting to around 5.3 million by the end of August. If there is some ice loss in September, we could get to 4.7 or 4.8. Maybe my pessimism was misplaced. I would really like it if sea ice extent this year reflected the true state of the ice, if you understand what I mean by that.

[Artful Dodger]

To further handicap the August horserace, here is the average daily SIE change for 2002-09: (sorted from largest to smallest)

Year  Avg/Day
2008  -70,121
2004  -64,657
2007  -57,041
2002  -54,797
2009  -48,654
2003  -46,764
2005  -45,000
2006  -37,697

[FrankD]

Hi Neven,

You are correct, I downloaded the area graph and read the values off that, just counting pixels. Its far from perfect:
1. Data from later years obscures data from earlier so there's a bit of guess work involved.
2. Resolution - at high res, the line is 2-6 pixels thick, so I had to pick a reasonable centre
3. Trying to smooth out the data - my counts yielded about 52 data points (pixels) per month which I then smoothed out into 30/31 days. To do that I simply rounded the fraction (for example, in July: x / 52 * 31) to the nearest day of the month. Where there was one data point for a day I used that, where there were two I took the mean. That gave me one value per day.

I then divided the result by the published daily extent data. and graphed the resulting percentages, using the same colours as IJIS.

So in the detail its quite crude, but I figured it was close enough for my intent of examining gross trends. Perhaps IJIS can be persuaded to release the raw area data.

The original cut out at 8th July because I was doing this while cooking soup for the hungry tribe and didn't pay enough attention to the detail. Problem now fixed, new area graph downloaded and comparison charted. I've uploaded a new version to 31 July here:
http://img687.imageshack.us/img687/7026/areaoverextent2.png

Still haven't had a chance to really look at it and work out what it means, but I note that the percentage troughs in mid-August. After that, I guess the ice gets a little more compacted (same area, smaller extent), or we start to see leads and polynyas freezing over (greater area, same extent). Finally, a month after bottoming out, area and extent both start to shoot up.

Frank

[Neven]

FrankD, I'm impressed with what you have come up with, especially after having struggled yesterday to get that Google Chart Wizard to do what I want. I'm putting a second area/extent post up today with just the graphs, including yours. Thanks again.

[Steve Bloom]

Fun Arctic trivia:

Today I happened across this map of the De Long Islands (just NE of the New Siberian Islands) showing a boundary for the permanent ice. I don't know when the map dates to, but not any more!

A couple of them may be technically U.S. territory (a result of yet another failed attempt to find a Northeast Passage), although if the Russians thought there was any threat the claim would be carried through on they probably would have changed the names from Henrietta and Jeannette. Anyway, there's material for a joke there somewhere.

[toby]

Excellent chart, FrankD, it shows that 2010 is more like its "sisters" 2007,8 & 9 than the earlier years. An argument against a recovery!

[IceMan]

Neven,

Nice discussion on the extent vs. area issue and a nice figure showing the trend. We've been calling the ratio of the two "compactness". See quote from this paper:

"The compactness of the ice pack (the ratio of ice
area to ice extent) in August, the month of minimum
compactness, has been decreasing in the last 20 yr because
the area is declining faster than the extent. A less
compact ice pack is more easily moved to one side of
the basin and thus allows for greater variability in the
ice extent"

http://psc.apl.washington.edu/lindsay/pdf_files/Lindsay%20etal%202009%20JClim%20-%202007%20follows%20thinning%20trend.pdf
http://psc.apl.washington.edu/lindsay/pdf_files

Regards
Axel

[Neven]

Thanks a lot, Axel! So compactness it is.

That's a great paper. Am reading it as we speak.

I hope you saw that there is a follow-up to this post.

[Artful Dodger]

Nice to know that the experts are on the ball, too! Thanks, Iceman. I hope you'll stay with us here at Neven's blog and continue to share your knowledge. Welcome!