Sea Ice Forecasts

For several years, I’ve forecast the Arctic sea ice extent to be observed during September (when it reaches its minimum). For the most part my forecasts have been successful, although I was farther off this year than previously because sea ice extent dipped well below the existing trend line — and that’s how I make my predictions, by extending the existing trend line for September sea ice extent, 1 year into the future.

Here’s the base data for this method, September average sea ice extent from NSIDC, together with the model used to make the forecast:

The model is simple: a quadratic function of time. Fitting this to the observed data and extrapolating a year forward gives the prediction: 4.03 +/- 0.9 million km^2.

That’s one way — and it has worked well in the past. But there are others. For instance if I smooth the observed data with my modified lowess smooth and extend that a year forward, I get this:

This method gives a lower prediction, only 3.91 million km^2. That’s because, even though the model has less “curvature” in the later years, it has a steeper slope compared to the previous model:

I prefer model 2 to model 1, not just because it gives smaller overall residuals, but also because it fits the endpoints of the data (especially at the beginning) better. But their predictions are not really that different

But wait — there’s more! Some of you may recall that when you transform ice extent to the latitude of the ice edge, the data reveal more consistent behavior over time. For one thing, the trend rates (by linear regression) don’t vary so much throughout the year, being more consistent from one month to another and one season to another. For another thing, if you look at sea ice anomaly (the difference between a given month’s extent and the average for that same month), there’s a clear pattern which emerges in 2007:

What happened is that the annual cycle got bigger — greater difference between winter and summer extent. This is also clear if we us a time-frequency method (in this case, windowed Fourier analysis) to study the size (i.e., amplitude) of the annual cycle directly:

The graph shows the semi-amplitude, which is just half the amplitude of the fundamental Fourier component. Since 2007 it has been much greater, indicating a considerably larger annual difference between minimum and maximum extent.

Some people have even made a big deal about this. For instance, Roger Pielke Sr. interpreted it as a sign that “since 2006, the reduction has stopped and even reversed..” This is grossly mistaken, but he simply didn’t do the math. Judith Curry interprets it as a sign of a change point, an idea which falls to pieces when you consider latitude rather than extent, but Judith tends to consider anything that looks funny as a “regime shift” so she can blame sea ice loss on anything and everything at the same time. As for doing the math, I can’t recall ever having seen that from her.

If we plot latitude anomaly rather than extent anomaly, there’s no sign of “change point” or “regime shift” in 2007:

Note that the trend is upward because the ice is retreating northward. There are visual signs of, perhaps, an annual-cycle change from 2004 to 2008, but they’re easily within the boundaries of natural variation, not evidence of the kind of changes Curry wishes she could blame sea ice change on. She really needs to learn to “do the math.” I’m not holding my breath.

We can take the values of September sea ice latitude and fit a quadratic trend to make a prediction for next year, just as we did with extent:

The prediction is for the ice edge to reach latitude 79.09N, which corresponds to an extent of 4.10 million km^2 — a wee bit higher than the forecast from using extent alone.

And yet again, we can extrapolate the smoothed curve rather than just a quadratic model, using the latitude rather than extent data:

This model predicts the ice edge will reach latitude 79.29N, with extent equal to 3.97 million km^2.

So there you have it, four models, all statistical, with four different — but only slightly so — predictions. For the record, the “old method” predicts 4.03, but (for not entirely scientific reasons) I think I prefer the final model at 3.97. And you can attach a “+/- 0.9” to both of them.

The fact that all these models give nearly the same forecast is simply a reflection of the fact that they’re all short-range statistical forecasts based on the same central idea: that the trend will continue. There will be fluctuation of course, and at +/- 0.9 it can be considerable. But I don’t expect 2013 to break the 2012 record, in fact I don’t expect the 2012 record to be broken until 2015 or 2016, and possibly even a few years later. That’s the nature of fluctuation, even when the trend continues. And I do expect that the trend will continue, for a very simple reason: global warming.


40 responses to “Sea Ice Forecasts

  1. I do expect the words “sea ice recovery” will figure prominently on denier blogs about this time next year. This will be the case even if (as is likely) the Antarctic Sea Ice Extent is less than this year.

    Thanks for the analysis.

  2. Why do you not make a prediction based on the reduction volume? De prediction for volume (look at Neven’s website for the graphs from Wipneus) seam to be pretty good…

  3. The situation up there is getting interesting. Rec’d (to friends) at FB. I haven’t checked what the sun is doing, are we going down yet on this (projected) mini cycle of 24?

  4. Timothy (likes zebras)

    Thanks for linking to the post about latitude – I didn’t read your blog back then, and it was something I was starting to write code to analyse, for my own interest. Glad that I can read a paper and look at some data instead.

    Although extrapolation becomes more inaccurate the further one extends it forward, it is interesting to compare your latitude-based trend with those from PIOMAS volume estimates. Over on Neven’s sea ice blog they like to show a Gompertz-extrapolation of PIOMAS volume (calculated by Wipneus I think) and this suggests an ice-free September as early as 2016.

    I would guesstimate that your final two methods would predict an ice-free September as, relatively, late as 2025-2030.

  5. Timothy (likes zebras)

    I found Eisenman’s sea-ice latitude data to have a play with it, but the numbers I found don’t match the ones in your graphs. For example, and most obviously, in September 1979 the daily values I have found all exceed 76.7N, whereas your average for the month is about 75N.

    The data I found is at

    Also this only extends to the end of January 2010.

    Do you have a different source of data? Did you calculate your own latitudes from NSIDC extent maps?

    [Response: In the supplemental info, Eisenman gives a 5th-order polynomial approximation to transform extent to latitude, which is what I used. Perhaps there are significant differences from map-based estimates, or perhaps I made an error in coding the approximation.]

  6. I’m puzzled.
    Recent data of September minimum Arctic sea-ice VOLUME from PIOMAS (Pan-Arctic Ice Ocean Modeling and Assimilation System), for example shown on Neven’s blog, give the following:

    “Yearly minimum sea ice volume for the 2005-2012 period (in km3):

    2005: 9159
    2006: 8993
    2007: 6458
    2008: 7072
    2009: 6893
    2010: 4428
    2011: 4017
    2012: 3263”

    Simple extrapolation of that data by linear regression gives a zero minimum Arctic sea-ice volume (whatever that means) as soon as about 2016, yet similar extrapolation of Arctic sea-ice EXTENT graphs show zero extent is not reached until many years later. Why is there this difference in the extrapolated timing of zero minimum sea-ice volume and extent?

    • Slioch,

      It’s because ice has thinned as well as contracted in area. If you lose 20% of area, and 40% of thickness, you’ve lost 50% of volume.

      The amount of sea covered by ice is of interest for albedo calculations and feedbacks, but when it comes to measuring how much of the stuff we have left, volume is the best metric. As the ice continues to thin, it becomes easier to melt large areas quickly (especially if helped by mechanical mixing like we saw in the big storm this year). Whether ice free conditions arrive in 2016 or 2056, you will see a crash in area / extent in the few years leading up to that time.

      As Wieslaw Maslowski has said: “In the end, it will just melt away quite suddenly…”

      • FrankD
        Well, yes, I can see that volume is likely to decrease more rapidly than area or extent in the early stages (in your example by 50% (strictly, 52%) of volume for a 20% decrease in area). And I can see that it may not be possible easily to extrapolate to zero area/extent from early data because of that. But, dammit, when you’ve got zero volume you’ve also got zero area, so I suppose my query morphs into the question, “why don’t we just rely on the volume data to extrapolate to the ice-free in September state and not bother with the area/extent data, (which are necessary for computing albedo changes).” Perhaps the answer lies in the inevitable lower accuracy of the volume data.
        Nonetheless, I find that PIOMAS volume data pretty compelling, getting, as it does, to zero with just a few short years of extrapolation. It is not a long extrapolation, so that, if the volume data is at all accurate, zero cannot be more than a few years away, if the trend continues.

      • Wadhams said that, Frank! :-)

    • Given that both methods should converge on zero at the same time, something is wrong. I’m thinking maybe the choice of function to model the sea ice extent. But given that using the data itself to generate the curve doesn’t change things much…

      • John, having mulled over it a bit I am inclined to the following:
        FrankD’s suggestion would seem to explain the apparent divergence between area and volume predictions of the September zero end point in the early stages of melting. KAP, November 22, 2012 at 11:24 pm, describes what will probably happen close to the zero point. In other words, I assume the measurements both of area and volume, are accurate enough to be useful and that the extrapolation of the volume, not area, graph gives by far the better indication of the September zero point.
        If so, we only have a very few years to wait to see if that is correct.

      • I think exponential trend would be better:

  7. A “numerological” observation, just for amusement…

    I suppose one reason you might not “expect” a new record minimum next year (more so than you would have this time last year, maybe) is that, in the recent record (from 1980), the maximum number of excursions of the data points in one direction (extent loss or gain) is 3.

    The up/down data point excursion frequencies are:

    f_u1=7, f_u2=4, f_u3=0
    f_d1=6, f_d2=3, f_d3=2

    So, since 1980, there has yet to be an uptick for >2 consecutive years and there has yet to be a downward excursion for >3 consecutive years.

    Well, they do say records are there to be broken, but I’m going for an uptick, too.

  8. I am relieved [if that’s] the right word that you don’t think 2013 or even 2014 will be another record low, my interest in ice extent/volume was initially just keeping abreast of climate change trends it is now a matter of business. I have always been involved in growing things, whether landscapes or trees and now food, on an anecdotal level what happens in the Arctic effects crops.

    Farmers are never happy with the weather because they grow different things but 2007 and 2012 have been very poor harvests across the board here in Wales. 2012 has been the worst with sheep farmers having to supplement grass [with low sugar content] with cake [cereal], arable farmers have seen a 20% fall in production and potato harvest is non existent in some places [the impact of cod/wet weather]. Between 2008-2011 we have had very dry springs, 2012 was the hottest March on record, so expecting trends I invested in irrigation-

    If there is a direct connection between the jet stream and Ice vol/ext trends at least give a possible picture and means to adapt. If it were possible a more robust prediction would help me choose what to sow.

    I would be interested in seeing how the Ice extent matched say UK potato harvest for each year.

    • My prediction: welcome to the new normal. Sea ice will never recover to the levels of pre-2007. What you’ve been getting recently is what to expect, except more so. Plan accordingly.

  9. For a forward prediction, wouldn’t something sigmoidal be appropriate? I would have thought that the last of the multiyear ice north of the arctic archipelago would take disproportionately long to disappear.

  10. But naturally if it jogs up, idiot boy and idiot girl will be saying the decline is over.

    • Indeed, but still…

      I don’t expect 2013 to break the 2012 record, in fact I don’t expect the 2012 record to be broken until 2015 or 2016, and possibly even a few years later.

      I hope Tamino’s right! I might not be ‘cheering’ for records in melting season ’13. Last melting season scared me a bit.

  11. Apologise for the off topic comment but have you seen

    “…greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated, and the perceived relationship between these variables is a spurious regression phenomenon…”

    It’s probably not worth your time debunking – but I am sort of interested in what are “Polynomial cointegration tests” and why they show the relationship between the forcings and temperature is a spurious regression

    • Apologies for being OT also from my side. Pete, the paper has already been thoroughly debunked (long before submission to ESDD) by our host himself more than 2 years ago: Not-a-random-walk
      The authors managed to fool the ESD editor who, to be blunt, utterly failed to pick up this nonsense (plus the even more obvious nonsense in the 2nd reviewer comment).
      James Annan has this to say on his blog:

      Tamino, great post on sea ice trends once again! Thanks a lot! I go with model 2.

  12. Would a calculation using ice volume and thickness trends together be a better fit to the data to date? Of course, this is adding an extra parameter, so a slight increase in r2 may not actually give abetter fit. However, I’m wondering if this might catch the increasing downturn since 2005, and the issue that volume is predicted to go to 0 before area does, at current predictions.

  13. Circa 1998, I started plotting the standard deviation of monthly ice area, and by 2002 it pointed to a change in the system, suggesting a change in the system equilibrium within a decade (e.g., a sea ice melt back.)

    More recently, I have been estimating the mechanical strength of the ice (ability to resist storms) combined with estimates of available latent heat to generate storms. Last spring this said that Arctic in 2012 would have record sea ice melt, but not approach sea ice free conditions. Now it says, that in 2013 the Arctic will approach or achieve sea ice free conditions.

    The cumulative effect of global warming is that there is more heat in the Arctic. It takes about 1 calorie to warm a gram of ice from -1.5C to -0.5C. Then it takes 80 cal to warm that gram of water to 0.5C. This discontinuity on the heat content of ice means that statistics done based on the temperature of the system or geographic extent of the ice, contain inherent errors. Statistics on the system should be done on the basis of Gibbs Energy.

    A region of ice can contain some of its heat of fusion and still look like ice. The final disappearance of the ice is disconcertingly abrupt. At its melting point, ice does not do smooth curves as measured by temperature or geographic extent. It does not melt from south to north, it melts from the top down and from the bottom up. When these two processes meet, there is no more ice.

    The assumption of a North-South temperature gradient is left over from a time before global warming. Sometimes its there,and sometimes its not.

    • Absolutely correct, and as a person who lives on a lake which is ice-covered every winter, and who has watched that lake melt every year for 30 years, believe me, folks: ice area, or ice extent, is spectacularly unhelpful in predicting when the ice goes away. Typically, my lake goes from 95% cover to 0% cover in one day, after spending months at 100% cover. It just drops off a cliff. It’s not that there’s no warning, it’s that the *area* isn’t the warning you should look for.

  14. How about a prediction of this years maximum?
    I say a couple days later and about 200K higher than last year, with the extent exceeding the 30 year average.
    And I predict hay.
    And I am a card-carrying Hansenite.

  15. There’s also this thing called “radiation physics” which says there damn well is a connection between greenhouse gases and surface temperature.

  16. Well, as some commenters before, I find forcasts based on area/edge much less reliable than based on volume at this stage. Yes, volume data is built on evaluations and area data is is built on observations, but…

  17. I understand the trend is caused by warming (AGW), and the noise is weather. We do not know, perhaps cannot know – from the “physics” – which statistical function describes the trend best. That is, exactly how the trendline will continue. (We know it´s down, of course.)
    On the question of a record low extent next year, we basically don´t know, because of the noise of weather. But the likelihood of a new record seems very much dependent on what caused the sharp downtick this year. The more it was influenced by weather (the August storm? Some other factor?), the less likely that we will see a new low for extent in 2013. On the other hand, if the weather actually was favourable for ice, then the 2012 downtick is most likely a sign of an increased downward trend (caused by the reduction in volume of ice). Which makes a record low extent next year much more likely, of course.

    • David B. Benson

      The August cyclonic storm broke off a huge portion of the ice and forced over to Wrangell Island. The ocean is shallow there and that prompts melting.

  18. David B. Benson

    VOLUME 81, NUMBER 3 PHYSICAL REVIEW LETTERS 20 JULY 1998 Indication of a Universal Persistence Law Governing Atmospheric Variability Eva Koscielny-Bunde, Armin Bunde, Shlomo Havlin, H. Eduardo Roman, Yair Goldreich, and Hans-Joachim Schellnhuber*&match=all
    appears relevant to this forecast.

  19. David B. Benson

    GEOPHYSICAL RESEARCH LETTERS, VOL. 39, L09705, doi:10.1029/2012GL051241, 2012
    Greenland ice core evidence for spatial and temporal variability of the Atlantic Multidecadal Oscillation
    Petr Chylek, Chris Folland, Leela Frankcombe, Henk Dijkstra, Glen Lesins, and Manvendra Dubey
    also appears to be relevant in that the AMO and AO appear to have some forecastability (if that is a word).

  20. I’ve provided links to my own exponential fits to PIOMAS data here. These are 2012 updates of similar fits done at the end of the 2011 melt season. The 2012 extrapolations show little change. The summer becomes ice free in 2015, and the *winter* ice pack disappears by 2028. Quadratic fits (which don’t fit the shape of the trend nearly as well as exponential functions) predict zero summer ice by 2017, and zero winter ice by 2040.

    The exponential PIOMAS fits, which include the 2012 minimum, are here:

    We are now so close to zero summer ice that this is no longer an extrapolation into the distant future. That future is nearly upon us, and I think we will see a widespread collapse of the summer sea ice within the next 2-3 years.


    • How much of a sea temperature increase does your exponential extrapolation indicate? Does that make physical sense?

  21. David,
    Past trends (ice core data) are not predictive for nonlinear feedback systems under different forcing conditions. Out of control systems behave differently than systems in control, .The AMO was a function of a system in control.

    Any nonlinear feedback system that shows a persistent trend in any major parameter is moving away from equilibrium, and is likely to suddenly go out of control. The Hockey Stick is a temperature trend that indicates our weather system is moving out of control. We need to apply systems thinking to this issue.

    With the weather system out of control, the AMO (and PDO) are not likely to have the same significance. In the past, the AMO was the signal and AGW was just noise, now AGW is the signal and the AMO is just noise. The Hockey Stick is a bigger signal than the AMO ever was, and even the Hockey Stick understates Arctic warming as correctly expressed as Gibbs energy.

    The 2012 Arctic cyclone broke up the sea ice which is now on the order of a thousand times weaker than it was 30 years ago (beam strength). This increased the ice’s surface area, allowing faster melting. The cyclone pumped heat from sun warmed, open ocean waters over the ice pack, accelerating melt. A plume of cold water sank under the ice pack, drawing sun warmed surface water into the edges of the ice pack. This accelerated melt.

    It is a different system. The old rules do not apply.

    • David B. Benson

      As best as I can tell the PDO matters almost not at all (except to the fishermen in the Pacific Northwest and western Alaska). The AMO has some effect on southern Greenland but none to speak of on northern Greenland. The AO is another matter and there is as yet no reason to doubt it continues.

      The other paper, by Koscielny-Bunde et al., makes a good case for statistical persistence. I doubt that has suddenly disappeared.

      Nonetheless, the arctic sea ice is clearly in a down trend (and has been since at least 1922). The two papers I mentioned don’t directly aid in offering a trend analysis but rather indirectly merely suggest some matters to be kept in mind. In particular, it would perhaps help to see a graph of the AO for the last 100 years or so.

  22. Arctic Sea Ice Volume: PIOMAS, Prediction, and the Perils of Extrapolation (RC) is worth a look. Esp section titled “Extrapolation”.

    “[Another] issue that may foil prediction by extrapolation: The period over which the function is fit must be sufficiently long to include adequate long-term natural variability in the climate system. The goodness of fit over the fitting period unfortunately may be misleading… By fitting a smooth function to a sea ice time series (e.g. PIOMAS) one might easily be tempted to assume that the smooth fit represents the forced (e.g. greenhouse) component and the variation about the curve is due to natural variability. But natural variability can occur at time scales long enough to affect the fit. We have to remember that part of the observed trend is likely due to natural variability (Kay et al. 2011, Winton, 2011) and may therefore have little to do with the future evolution of the sea ice trajectory… Natural variability at these time scales (order of 30 years) may very well make prediction by extrapolation hopeless.”

    Note I have no problem whatsoever with Taminos 1yr extrapolation but I have been seeing much much longer ones being thrown around in blog comments without any accompanying argument as to why the extrapolation is reasonable.

  23. I presented this results as extrapolations, not predictions. Clearly, extrapolation is a risky business, and interpreting extrapolations as predictions means assuming all sorts of caveats. Of course, a longer record would be nice — but what you see if what we have to work with. Of courser, natural variability is an issue. However, having said all of this, the simple exponential fit does appear to capture the information content present on the PIOMAS ice volume record. The residuals from this fit appear to randomly (and normally) distributed about zero:

    GIven that the extrapolation to zero summer ice is a short extrapolation (3 years) compared to the length of the the entire data set (30+ years), and the present fit captures all of the information content of the existing data record, I do not think it unreasonable to present this 3-yr extrapolation as a reasonable outcome.

    • Mostly agree with you Phil and my comment wasn’t aimed at you nor anyone else on this thread. However, “and zero winter ice by 2040” is the kind of stuff I was talking about. IMO, it is not even worth mentioning that fact – “if we use this fit and extrapolate, this is the result”. The potential to (non-intentionally) mislead exists and outweighs anything we can take from it. Just my opinion tho

  24. I think the y axis on the September latitude Model 4 graph is mislabeled. Shouldn’t it be latitude instead extent?