Arctic Sea Ice: Death Spiral Continues

Now that August numbers for sea ice area and extent are available from NSIDC, let’s update the prediction of the upcoming September value.


This September we’re sure to see either the lowest or the 2nd-lowest extent value on record. This is clear from looking at daily data from JAXA (this year’s data in red):

We can even take a close-up look at the summer/fall, to see that we’ve almost passed into second place already even though these data only go up to the end of August:

If we look at the monthly averages from NSIDC we see that for August, extent was 2nd-lowest on record (and very nearly as low as 2007):

As for area (rather than extent), this August beat 2007 for lowest on record:

That’s important, because when it comes to predicting September extent, August area turns out to be a better predictor than August extent.

July’s values similarly portend a record minimum this year. For this July, both extent and area were the lowest on record:

If we model the September extent as a function of August values for both extent and area, the model predicts a September value of 4.35 million km^2, which would not break the 2007 record (but it’s close to the NSIDC record of 4.30). However, if we also use extent and area data from July, the model has better AIC value and predicts a September extent of 4.17 +/- 0.4 million km^2 — which would be a new record low:

All this would indicate that it’s likely (but only slightly more likely than not, about 5-to-3 odds) that this September will break the 2007 record.

On the other hand …

If we look at JAXA data, the August 31st value is 4.744 million km^2. This already makes it the 3rd-lowest annual minimum on record, and knocking on the door of being 2nd-lowest (a door it should cross very soon).

Even so, it we compute the changes from the present date (August 31) to the annual minimum in order to estimate how much further it might dip this year, then subtract those values from the present extent, we expect the JAXA minimum to end up somewhere between 4.21 and 4.60 million km^2. Of course, that’s the JAXA minimum not the NSIDC September value which we’re trying to predict, but those two numbers tend to be pretty darn close.

What’s the bottom line? If I had to bet (which thank goodness I don’t), I’d say the odds are just about 50-50 that this year’s NSIDC September extent will set a new record low. Of course, a lot depends on the weather! In fact, the next week or even the next few days may show a sudden turn for the better or the worse, so this 50-50 proposition may become much more lopsided within a handful or two of days.

However it finally turns out, this much is abundantly clear: the trend continues. The reason: global warming. But I’ll make another prediction: if 2011 doesn’t break the 2007 record, then some fake skeptics will refer to the continuing decline as a “recovery,” and/or find an excuse to explain away this year’s appallingly low value as a weather phenomenon in hopes of drawing attention away from the trend. Probably at WUWT.

About these ads

77 responses to “Arctic Sea Ice: Death Spiral Continues

  1. I’m rooting for a record! So when’s our next El Nino to pull the global temps up above their 35-year trend line?

  2. “Probably at WUWT.”

    I’ll predict that any numbers greater than the 2007 extent or area will be certain to be called a recovery at WUWT and if the numbers are
    worse they will be put down to a “natural cycle”.

  3. Immediately before and after your last figure you day “July 31″ when you should, I think, say “August 31″.

    [Response: Indeed! Thanks, it’s now fixed.]

  4. Jbar, we’re not done with the tragedy yet.
    It’s way too soon to be starting the farce.

  5. In “Temperature Prediction: the next few months” pd posted a link to a summary of the ERA arctic temperature reconstruction from 1979 to present. One of the interesting points about this data is that there is very little trend in July and August mean temperature over this period- a time when arctic sea ice has been collapsing. Winter temperatures have been soaring though.

    Evidently, the drops in sea ice extent have a lot less to do with warm summers than with much warmer winters. My best explanation/hypothesis for this is that warmer winters produce much thinner ice which can then melt much faster in the slightly warmer summers.

    • Meh, scratch what I said above (not that it’s all wrong).

      I’ve looked at the data a bit closer and it turns out ice extent minima do correlate better with summer temperatures than winter temperatures if you use the ERA data between 66N and 80N, i.e. where the melting actually occurs.

      But it’s still really hard to explain much of the year-to-year ice variance with year-to-year temperature variance.

      • My 66N data are between 66N and 90N. Anyway correlation is strong:

      • I calculated 66N to 80N by assuming:

        T_66_to_90 = a*T_66_to_80 + b*T_80_to_90

        where ,
        a = (24^2-10^2)/(24^2)
        b = (10^2)/(24^2)

        basically I assumed an area-weighted average where the area was proportional to the square of the “latitudinal” distance from the pole, which I believe is relatively accurate near the poles.

      • pd,

        As for your plot, the problem for me is that while there is enough correlation to explain the trend, there wasn’t enough to explain the year-to-year variation.

        I was trying to come up with something that could predict ice extent within +/- 0.2 million km2.

      • “I was trying to come up with something that could predict ice extent within +/- 0.2 million km2.”

        Well, some part of this year-to-year variation is obviously coused by the weather pattern, so i don’t think that you can predict ice extent with such accuracy.

    • Indeed. Also, more exposed water (either leads/polynyas, melt ponds or outright open sea) allows more evaporative cooling during the melt season, AND the melting itself takes up heat. Both factors tend to hold the surface temperatures down.

  6. JBar: looks like we wont be seeing an El Nino this year, at least:

    http://www.bom.gov.au/climate/ahead/ENSO-summary.shtml

    Maybe next year…

    Ernst K: Doesn’t the ice melting itself constrain arctic air temperatures over summer?

  7. “What’s the bottom line? If I had to bet (which thank goodness I don’t), I’d say the odds are just about 50-50 that this year’s NSIDC September extent will set a new record low.”

    Does that mean your central estimate at the time of making the post would be 4.3 mil sq/km, same as 2007 September min?

    [Response: Yes.]

  8. 2007 and 2011 are so close together, does it really matter if 2011 “beats” 2007? Looking at past years, we’ve seen this drama played out over and over, always with the same result. The damned line is going to continue ricocheting like a superball thrown down a mineshaft, frequently bouncing up, mostly dropping.

    On the other hand, “As the World Turns” was fascinating to many people, even though we knew the plot wheel was going to take us to the same place on a regular cycle. Lots of redundancy there, too, until the show vanished.

  9. “However it finally turns out, this much is abundantly clear: the trend continues. The reason: global warming.”
    I have some difficulty to see the exact reason why you’re saying that – if the debate is about the cause of the variation, how can a mere confirmation of the variation help to distinguish between different explanations ? all your analysis simply shows that something has changed in the last decade, but it doesn’t favor a particular explanation. And the 2000-2010 period is *not* characterized by a particularly strong warming , so I think that attributing the ice melting to GW requires some explanation of why it didn’t happen much earlier …. any idea ?

    [Response: Please abandon such mistaken beliefs.

    A helluva lot more has happened than just “something has changed in the last decade.” Arctic sea ice was in rapid decline before 2000, so rapid that it’s overwhelmingly statistically significant in spite of just 21 years of data. In fact the decline is significant even if you use only September data (rather than all 12 months) and only data prior to 2000.

    Furthermore, the 2000-2010 period is characterized by a particularly strong warming — look at zonal data for the Arctic region. Using just data since 2000, the warming trend is significant! And the slope is huge — a full degree C/decade.

    This post is not about attribution. But the attribution is clear.]

  10. “the next week or even the next few days may show a sudden turn for the better or the worse,”

    I don’t know how to feel anymore. If I believed a new record low would help change the attitudes of political leaders to begin a John-Kennedy-type national/world project to eliminate fossil fuels, I would feel good about it. But I don’t believe that.

  11. Ernst,

    Try a five-year moving average.

  12. Apparently global winding is a popular idea over at WUWT.

  13. On the other hand, volume:

    3 stddev off the mean and 1 stddev worse than 2007. Much less ice this year than in 2007.

  14. I’ve been following the last two seasons on Neven’s Arctic Ice blog, which is a very active and interesting site. I recommend it heartily. One thing I would like to point out is that the changes in volume are just plain terrifying, much more than changes in extent or area. The melt season has been, weather-wise, kind of meh, yet we are heading for a record low year, and might exceed 2007 extent record, when 2007 set the record after a season of weather marvelously hostile to ice. As Tamino answers, how? Global warming. Because the volumes of ice are plummeting. Because average ice thickness has gone from 2-3 meters to 0.9 m. And if you go to Neven’s site, you will see jpegs from the Healy and Polarstern voyages to the North Pole that will show you the ice there is just, as is used on Neven’s site, a Slush Puppy. This year may well set a record for extent. But anytime now, there will be a combination of Flash Melting and bad weather, and we won’t have to figure out the differences in methodology between Cryosat 2, AMSR-E, NSIDC, or JAXA. Zero will just be zero.

  15. Here’s a new graphic comparing time series of August means (NSIDC, Uni Bremen, JAXA, Cryosphere Today) over 1972-2011:

  16. Two other graphs that I’m updating frequently (while the season lasts) follow the 1-day minimum extent 1972-present,

    and area, 1979-present,

  17. More depressing than the impending 4.(something) million km^2 value for 2011 minimum Arctic sea ice extent is the fact that almost exactly the same numerical prefix will occur for the 2011 minimum Arctic sea ice volume, in thousands of km^3.

    And this is in spite of the fact that the ASI volume is departing from a 1979 to 2010 mean of around 12 thousand km^3, and a 1979 value of around 17 thousand km^3.

    Leaders all around the planet should be sitting up and paying very careful attention…

    • Gavin's Pussycat

      Leaders all around the planet should be sitting up and paying very careful attention…

      Oh they do, with all that oil and gas to be had… as the Gore says it, ‘junkies searching for the veins in their toes’

  18. Ah, I see that Jeffrey Davis beat me to it.

    A salient lesson in remembering to refresh before posting.

  19. What’s most interesting to me is that this year is so close to record year 2007, but without 2007 weather conditions. That really says something (well, the same as last year, but with more emphasis).

  20. The damned line is going to continue ricocheting like a superball thrown down a mineshaft, frequently bouncing up, mostly dropping.

    Doug, that’s a great simile.

    Only question now is how many more bounces before it reaches the bottom of the mine…

    • Ned.

      One of my favourite metaphors is that of the hyperbolic coin funnel, where rolling coins oscillate further and closer to the central axis, with occasional seemingly inexplicable excursions even further out, or almost to the centre, before returning to the overall pattern of ever-decreasing circuits.

      The nice thing about this metaphor is that it strikingly demonstrates the death spiral that is the subject heading of this thread…

      http://vimeo.com/5366199

      • [edit]

        [Response: No embedded video in comments please.]

      • Horatio Algeranon

        “The Brain Drain”
        – by Horatio Algeranon

        As sea ice funnels down the drain
        The climate “skeptics” go insane
        Down is up and melt is freeze
        And thin is thicken, if you please.

  21. Tamino, I find your prediction somehow sound in terms of statistics (no objections raised here), but my “short term variation” view gives me some caveats and I have find myself difficult to decide. But I would like to comment on some short term predictions anyway (and it is not sound science, anyway, but just some observations I’ve spotted):
    - the winds will favor spreading of ice more than compacting, and given the very low temps currently around the pole (regarding to USCGC Healy, about 18 F at 88 deg N), this will promote refreeze of any open water in that area
    - the ice in many area is much more dispersed than it was in 2007, which saw its lower min extent not just due to melt, but compaction against Greenland and northern CA islands (note that min area in 2007 was not much lower than in 2010 and 2008 and 2011 to speak).
    - there are large areas of warmer than usual waters in Laptev, Chuckchi and Beaufort seas.
    All in all, I think we will almost certainly see at least second lowest extent this year, but unless winds do not shift, I wouldn’t bet on lowest so far extent (but I am not so sure about betting on the lowest so far area). Anyway, the trend has confirmed itself and min value is already almost at your quadratic trend line prediction. And yes, the title of the blog post is correct.

  22. P.S. I am using weather forecasts from ECMWF and GFS available at http://www.wetterzentrale.de (trying to eyeball winds form isobars).

  23. Slightly OT, but related, is all the increased traffic in the Arctic. How long before we totally wreck it?

    Northern Sea Route setting Arctic commerce records

  24. Let me expand a little on my earlier comments about arctic temperature and sea ice.

    For a while now I have been trying to make a simple tamino-esque model of arctic sea ice that didn’t assume a linear or quadratic time trend. I wanted the temperature data to do that directly.

    Unfortunately, this requires good arctic temperature data because global temperature data don’t do much better than a linear time trend. I can think of a number of reasons for this:

    1) arctic temperatures are under sampled and therefore there is too much noise in arctic temperature data to make good sea ice estimates

    2) a large fraction of the energy for melting could be coming from the arctic ocean, which should warm much more steadily than the arctic surface temperature, therefore producing a large steady underlying warming trend

    3) ice dynamics are responsible for much of the year-to-year variation

    4) the spatial temperature distribution plays a large roll in year-to-year variation

    I suspect all these factors confound my attempts to use arctic temperature data to explain year-to-year sea ice variation. I’ve lost all confidence that arctic temperatures can do for sea ice what ENSO does for global temperature.

  25. Ernst K,

    I started pondering along similar lines, and ended up working on the energy implications of volume loss. The matter is however staggeringly complex – I couldn’t see my way through it. In the end I gave up and just posted what I’d got, see here.

    As for a death-spiral, the energy anomaly implied by the 2010 sea-ice volume anomaly is currently half of the annual range in sea-ice energy/volume.* I find that staggering.

    *The idiot-check for this is simply to compare PIOMAS anomaly and seasonal cycle volume – here.

  26. Continuing with the prediction for Sea Ice Extent using a Kalman filter on the extent data the filter did pretty well for August after getting roughed up a bit by July’s very low measured value. Back on Aug 2nd or so a predicted value of 5.44 million sqkm with 1 sigma of .5457 million sqkm was reported. The measured value of extent for August was 5.52 million sqkm. That value is about 25% below the monthly average (7.22 milion sqkm).

    So that’s about 18.5% below the average for July and now 25% for August.

    September is predicted at 4.98 million sq km at a 1 sigma of .545 million sqkm. If the prediction is correct Sept would come in at 25% below average (6.58 milion sqkm). Assuming the the SD is correct, if the extent is one SD higher than predicted it would be about 16% below monthly average.

  27. I have put my prediction based on 31 Aug data up at

    http://neven1.typepad.com/blog/2011/09/september-search-outlook-contribution.html

    The prediction is for 4.45+/- 0.32 m km^2

    I got the RMSE down to .134 m.

    Since July the rate of decline has been slower than the july data would suggest so the 4.17 looks a little out of date to me. You haven’t attempted to predict the falls from Aug 31 which I think helps reduce the error estimate.

    However, I could be falling into the trap of overfitting with far too many variables I can play with in what I have done. Any comments?

  28. Andrew Montford, aka Bishop Hill aka the moron’s moron, thinks that because the Swedes are hanging on to their icebreakers, there’s really no arctic ice crisis. Thus, as superheroes are wont to do, with a single bound, they were free.

    A less than passing acquaintance with reality, summer and winter, planets, axial tilts etc. helps too for such a distinguished “science” writer.

    • IIRC, the Baltic had record amounts of ice in winter 2011 with cruise ships stuck, yet all of the > 250,000 square Km ice [peaking on March 5 per MASIE data] melted out in 2.5 months. Yes, the Swedes reasonably hold on to their icebreakers, global warming not being a linear event on the thermometer as most sane would have understood by now.

  29. Death Spiral at WUWT:
    Website reader poll results submitted as predictions to the SEARCH sea ice outlook,

    http://www.arcus.org/search/seaiceoutlook/2011/august

    June 5.5
    July 5.1
    August 5
    September 4.5

    That’s a loss rate of 310,000 square kilometers of mental ice per month. You don’t need a weatherman to know which way the wind blows.

  30. We need a new sea ice outlook to see who can best guess what the collective mind of WUWT will guess next, kind of a meta-SEARCH.

    I’m curious too about the rationale for their pessimistic new ice estimates. The traditional theories about 60 year cycles, El Nino, recovery, it’s the wind, and “Bastardi says” all got tossed under the bus this year as it became crushingly obvious they were wrong. One of their thinkers will no doubt provide a new “anything but CO2″ explanation for why the arctic is melting, since it is.

    Icebreakers and soot, maybe that’s good enough for the sceptics.

    • Expect to hear this soon:

      September Sea Ice extent model with a 62 year cycle (R=+0.85):

      Sept Extent = 1.439*sin(0.1012*year-205.8) – 0.0006647*year + 7.404

      2011 prediction = 4.89 +/- 0.97 million km2 (2 std. dev. range)
      2012 prediction = 4.81 +/- 0.97 million km2
      2017 prediction = 4.63 +/- 0.97 million km2
      2048 prediction = 7.48 +/- 0.97 million km2

      The model can’t be used to hindcast because good quality sea ice data only exists after 1979.

      “Can we wait for this confirmation before implementing any policy?”

      (note: I’m posting this as a joke, but the equation and stats are real).

      • Ernst K,

        Do you have a link to that model?. I’m curious because the prediction and standard deviation for 2011 are similar to what I got with a Kalman filter based model.

      • All I did was use Excel’s solver utility to fit the following equation to the 1979-2010 arctic September sea ice extent:

        Extent = A sin (Bt+C) + Dt + F

        The above equation produced the minimum total absolute error.

        The reason it “works” is because the 1979-2010 data looks a fair amount like the crest and descending portion of a sine wave. It should surprise no one that it fits pretty well, no matter how ridiculous its underlying assumptions are.

      • Sine wave models (or quadratic, for that matter) don’t work as well for the extent time series going back to 1972 that has been produced by University of Bremen researchers:

        [Response: Do you have a link for the U.Bremen data?]

      • The Uni Bremen time series has not yet been published; new reports are in progress. So far as I know that’s the most up to date graphic. Note that it shows August means (through 2011) instead of the usual September.

      • Tamino, I thought of a slightly more helpful answer I should have given. 1-day minimum values from the Uni Bremen 1972-2011 time series appear in this graphic, which I’m updating daily for Neven’s Sea Ice blog.

      • Hmmm. An obvious case for a guest post at WUWT. We all know how little it takes.

  31. Send that in to the Journal of Mayan Pottery, suggest three friends to review it, and you could be the next Galileo.

  32. As of Oktober, there _will_ be recovery. The climate populists will have us know, like every winter :)

    • For now. However, it’s not impossible that at some point there will be no refreezing. Very good if you want to drill for oil offshore Alaska, Canada or Siberia, very bad for everything else..

  33. Ernst K,

    I see. Thanks very much.

  34. The area of Arctic sea ice, as reported by Cryosphere Today, edged very slightly below 2007 today to set a new record low.

    http://neven1.typepad.com/blog/2011/08/the-modern-area-of-ice.html

  35. Philippe Chantreau

    Yes, and NSIDC has the current extent about to cross below 2007. The slope of the current melt (over at least past 2 weeks) compared to the average at this time of the year is interesting, considering that, to my knowledge, there is no ongoing weather situation especially conducive to fast late season melt. I could be wrong on that, but if I’m right, we might simply be witnessing the “new normal” for September.

  36. And there’s a chance that weather situation might change in the coming days…

    2011 weather patterns started deviating from 2007 weather patterns somewhere mid-July. It’s amazing, but this year is proving that weather conditions are only as dominant in determining area/extent as the ice allows them to be.

  37. El Chichon, I meant, sorry.

  38. The regression on that data is

    Area = 140.426 – 0.0681484 Year
    N = 33, R^2 = 78%, t -10.4, p < 1.41 x 10^-11

    Indicating that the Arctic minimum sea ice area has been dropping 68,000 km^2 per year, on average, for the last 33 years. That's about half the size of Pennsylvania, I think.

  39. What it proves is that the Arctic sea ice is not stable. In the present stage of global warming it cannot exist in summertime anymore. Staggering indication of the magnitude of recent climate change.

    • I was reflecting this morning–thanks in part to the estimable L. Hamilton–that the *volume* this year is just 25% of the highest minimum. Not so coincidentally (perhaps), it occurred in the first year of the record, 1979, when the minimum was 16.9K km3.

      This year? 4.3 K–so far.

      In basically one human generation.

  40. Horatio Algeranon

    “Watterecovery of sea ice”
    – by Horatio Algeranon

    Watterecovery of sea ice it is
    For paddling polarbears, indeed pure bliss.
    For oil tankers it’s heaven sent
    So all their money won’t be spent
    On moving arctic oil to market
    (They’ll only have to pay to park it).

  41. Sept 28/11, Arctic ice appears to be back in the growth zone, may I ask what happened to “likely”? Any record set? How about “probably”? Did the decline go and hide?
    It appears to me that the scientific method has won again. WAG’s and models can never supersede direct observation.

    [Response: As a comment on my my prediction this is a miserable failure. Bit if it’s your attempt to be snotty, well done!

    This year broke the record for lowest extent according to the Univ. of Bremen, but not according to JAXA or NSIDC. However it *did* break the record for lowest sea ice area according to Cryosphere Today. And how does that compare to my prediction? Quoting from the post:

    What’s the bottom line? If I had to bet (which thank goodness I don’t), I’d say the odds are just about 50-50 that this year’s NSIDC September extent will set a new record low.

    We haven’t yet seen this year’s NSIDC September extent, yet it’s expected to miss a new record low — but not by much.

    More to the point (again quoting from the post):

    However it finally turns out, this much is abundantly clear: the trend continues. The reason: global warming.

    ]

    • Winnipegman:

      The first line of the second paragraph in Tamino’s post is

      “This September we’re sure to see either the lowest or the 2nd-lowest extent value on record.”

      Perhaps you can explain what you think that sentence means.

  42. “WAG’s and models can never supersede direct observation.”

    No matter how many faux skeptics insist otherwise. . .

  43. Philippe Chantreau

    Winnipegman, thank you for demonstrating once again how competent fake skeptics are. You’re making everybody feel all warm inside, and, as it turns out, outside as well, especially in the Arctic.
    I can’t help to wonder if you have even look at the sea ice numbers. Lowest area. 2nd lowest extent. Tamino’s predictions exactly on point. Steven Goddard was forecasting around 5 million sq. km, how did that pan out?
    Seriously, what were you thinking?

  44. My response goes a little like this.

    Duly noted that the work “likely” is now missing. I am not caring why.

    Torsten, I think that that statement covers an extremely short span of years to be making any long term predictions. If there was a tried and true way to predict just what the extent of the polar ice cap was, year to year, back to say 1850 I would be happy, Wanna make me orgasmic? Lets go to 500 A.D.. 25 years is not long enough to predict trends.

    Kevin, I am hurt, nay, insulted. Not a FAUX? Nope, I am real.

    Phillippe, I appreciate being called competent. However, both you and Kevin have it wrong. I am not a skeptic. Never have been. I firmly believe that the earth as a complete system is warming up. By the way, using your words, ” fake skeptic”, would that make me a warmist? I am already a believer.

    [Response: On the contrary, you are a fake skeptic. You claim that 25 years is not long enough to “predict trends” (perhaps you mean to *establish* a trend). But when the signal-to-noise ratio is as large as it is for Arctic sea ice, 25 years is plenty. More than enough. And by the way, the satellite record is longer than 25 years.

    A real skeptic who lacks sufficient evidence expresses doubt, not disbelief. And a real skeptic doesn’t make claims without *investigating*. We have considerable data on Arctic sea ice prior to the satellite era, enough to estimate its history stretching back to the start of the 20th century and before, by Kinnard, for the HadISST data set, and the Walsh & Chapman data set. Even longer ago, there’s an impressive array of proxy data which was studied for a recent review of the long-term history of Arctic sea ice. You should read it. Actually, you should have read it before commenting.

    Making foolish false statements about trends, claiming disbelief without investigating, bemoaning the lack of data which apparently you didn’t bother to look for, doesn’t make you a skeptic.

    And the word “likely” is still in the post, exactly where it has been all along — your snide implication notwithstanding.]

    • Philippe Chantreau

      I don’t know what you are and I don’t know what you believe. I read what you wrote and it is very much like what fake skeptics (search the site for a definition, it means exactly what it says) spew out all the time.

      “Sep 28 and the ice is in the growing zone.” I can’t see what the point of that remark is. How exactly is that unexpected or inconsistent with the multi-year decline? Are we to accept a melt that lasts until October as a normal thing?

      “Any record set?”
      Lowest sea ice area.
      “Did the decline go and hide?”
      No, as a cursory look on any ice monitoring site will reveal. As a matter of fact, I am pretty sure that this year’s numbers neatly inscribe themselves within the accelerating downward trend already identified by our host, although numerical analysis would have to confirm that. Arctic sea ice area has not seen a significant (i.e. more than 250k sq.km above the 79-08 mean) positive anomaly for the past 8 years.

      These 2 pieces of information were extremely easy to find. That you felt a need to come here and ask these questions, whether rethorical or not, indeed demonstrated your level of competence. No need to thank me.

  45. “Kevin, I am hurt, nay, insulted. Not a FAUX? Nope, I am real.”

    Did I say that was you?

    If the shoe fits. . .

  46. September 2011 mean ice extent from the University of Bremen is 4.6 million km^2, which by coincidence is exactly that predicted by a Gompertz curve estimated from their 1972-2010 time series. I just posted a note at Neven’s Sea Ice blog showing this curve, and speculating about what it implies for next year and beyond.

    http://neven1.typepad.com/blog/2011/10/september-2011-sea-ice-extent-looking-ahead.html