I got lucky

As most of you are aware, I had predicted that the 2010 minimum of arctic sea ice extent as measured by JAXA would be 4.78 million km^2. This turned out to be a remarkably close prediction, because the minimum (so far, which is probably but not certainly this year’s actual minimum) was 4.813594 million km^2. I was off by less than 1 percent.

Why was my prediction so close? There’s a very simple, and correct, answer to that: I got lucky.

My prediction was actually 4.78 +/- 0.95 million km^2. It was based on extrapolating the existing trend (a nonlinear trend) one year into the future. Since the existing trend appears to be continuing unabated, it’s no surprise that the observed figure was within my predicted range. It is a surprise that it was so close; there was only about a 1-in-40 chance that it would end up as close as it did.

Here in fact is the data on which I based my prediction and the trend line fit to that data:

The prediction itself, together with its 95% confidence interval, is the red dot on the right with error bars. It’s kind of hard to see the red dot because the black “x” marking the observed value is so close to it.

Now let’s get to the important point.

The observed value is almost dead on the value expected from extrapolating the existing trend. That means that this year’s observation not only utterly fails to contradict the existing trend, it actually supports its unabated continuation. The evidence from this year is in, and it says plainly: the existing trend continues.

In fact any value within the predicted range would lead to the same conclusion. Even if Steve Goddard’s prediction had turned out to be exactly correct and this year’s minimum had been 5.500000 million km^2, it would still be within the expected range of the existing trend. Make no mistake: this year’s data confirms the existing trend.

But if it had ended up as 5.5 million km^2, you can bet that Steve Goddard and Anthony Watts and their readers would be crowing about how it demonstrated a “recovery” of arctic sea ice extent. In fact, some of their readers have stated that the actual observed value is evidence of further recovery! How stupid can you be?

The arctic is warning us. Global warming is real. It’s caused by human activity. And it’s gonna be bad.

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49 responses to “I got lucky

  1. Hence the quip that WUWT really stands for “We Use Wishful Thinking.” But really it’s not new; it’s just another instance of the eternal truth that humans can be extremely adept at rationalizing their preferred conclusions.

    It’s highly unfortunate, of course, that the inability of denialists to look at reality with clear eyes hinders everyone’s ability to take the necessary steps to protect our environment and well-being.

  2. Tamino, can you please continue the curve down to Zero so we can have an idea about… when it would occur ? Perhaps having the error bar on the Years?

    (or is this just statistically stupid?)

    [Response: The trend model I used (a quadratic model) will dive below zero in the year 2030. However, it's a bad model for prediction. In general, polynomials are excellent for interpolation but highly unreliable for extrapolation more than a few time steps into the future.]

    • From a simple physical consideration of the system (OK, too much staring at Cryosphere Today maps), there is always going to be an area of ice just north of Greenland that is very hard to melt, which probably means that totally ice free conditions cannot happen. And in the other direction, the constricted nature of the Arctic basin puts a limit on how far the ice can expand.

      Typically in this case you’d expect an S- shaped curve in response to temperature changes, in this case complicated by the lags in the system.

      But you’d have to ask a more expert statistician than myself (or at least one with enough time) to dig the relevant formulae out.. I’m too busy asking Dr Curry annoying questions at the moment.

      • Right — good points. Maybe winds and currents will change up there, though, and maybe by 2030 with ice thinning and even sea level rising a few cm, perhaps the strongholds for ice won’t be so strong. Nevertheless, one has to wonder when NSIDC will stop reporting the decline in terms of % per decade.

      • Ice accumulates at the northern shores of Greenland and the eastern part of the Canadian archipelago due to the Transpolar Drift, and it does form a bastion of old ice. It will be the last to go, no doubt.

        But when there’s not much left “upstream” in the Drift to accumulate, well–I have to think that that bastion will fall, too. I think that there will be a longish period where “essentially ice-free” summers accommodate the existence of a few bergs floating around to imperil the new shipping lanes of the Arctic Basin.

  3. Your props from me are here: http://theidiottracker.blogspot.com/2010/09/open-mind-calls-it.html. Well done!

    Don’t keep us in suspense. What does this simple but successful method prognosticate for 2011?

  4. Well done Tamino,

    Now the lottery this Saturday… got any tips?

    [Response: Get lucky.]

  5. As an explanatory tool for two points you make (you were lucky wrt where within the prediction interval the observation landed; polynomial fits are good for interpolation), perhaps a figure showing the predicted range around the line would be valuable. Looks like you might be unlucky in retrospectively estimating 1996 (using a jackknife sort of procedure, if my terminology is correct).

  6. There is dumb luck, but in your case it was smart luck.

  7. Horatio Algeranon

    “It’s kind of hard to see the red dot because the black “x” marking the observed value is so close to it.” (from the book “How to brag without really bragging.”)

    Normally we wouldn’t be able to see Watts and Company’s red dot either…cuz it’s usually off in the next pond over, moving around like aeuglena, trying to find it’s way to the light.

  8. Indeed, few years are so close to the quadratic fit as this year. Anyway, it supports your extrapolation.

    Congratulations for your deserved luck.

  9. I find it amusing to ponder how Some People would treat a nearly perfect prediction like this, ala Goddard and Watts, as you suggest. Not only would they use it as proof of whatever snake oil they were peddling that particular month or week or day, but they would consider it Proof of their expertise and data analysis skills and probably a strong indicator of their ability to satisfy a lover.

    Instead, Tamino points out how he got the number (via a process that seems to have much more merit than anything from Those Other Guys) and humbly says it was luck.

    I definitely like the reality-enhanced tribe better.

    • Horatio Algeranon

      “…a strong indicator of their ability to satisfy a lover.”

      Prolly why Goddard didn’t use Tamino’s quadratic fit (which looks kinda droopy), and instead stuck with the tried and true linear (aka missionary) fit.

    • Well said, Lou. I was thinking the exact thing today. Thanks for putting my thoughts into words.

  10. Well done Tamino, and as others said, good on you for being modest about your prediction and the significance of the actual value being so close. I’m intrigued by the potential future – as you say the polynomial fit is not good for extrapolation, but worth noting is the polynomial fit through Sept PIOMAS data reaches zero much sooner (within this decade), relatively few steps further along it’s curve. So I wonder if we’ll see a rapid acceleration in extent loss to follow the volume loss into zero (of course assuming the volume data is somewhere close to reality). If so, Arctic ice will make headlines in the next year or two.

  11. Here’s my news story on what permafrost experts think the decline means – yes its going to be bad: Arctic Ice in Death Spiral, Thaws Permafrost — Risks Climate Catastrophe

  12. Philippe Chantreau

    Incidentally, Cryosphere Today is showing some interesting stuff. Antarctic sea ice has dropped significantly below normal, bringing the global sea ice area anomaly below anything recorded since 2007, and indeed pretty darn close to 2007. Be prepared to hear that, in Goddardworld, the recovery is almost complete…

  13. Extent/area accounts for only two dimensions of ice cover, and measures of the third are still rudimentary (pre-Cryosat 2). It would be a mistake to use only area/extent when considering how the ice cover may evolve, because you can have a low volume covering a large area if the ice is thin. At some point, however, the thin ice will melt out over summer and you may get a sudden steep reduction — a bit like pond ice disappearing when the weather warms. It sits there covering the pond, getting thinner and thinner, and then disappears all of a sudden…

    What we do know of sea ice volume (PIOMAS) shows that the ice is currently at a record low volume — eyeballing the anomaly versus average (-9.5 x 10^3 km3/13 x 10^3) suggests that at minimum the ice volume was about 3.5 x 10^3 km3. The anomaly trend over the full record is -3.5 x 10^3 km3 per decade. Ten years… But the anomaly trend over the last decade is nearer 1,000 km3 per year. Three to four years. But if you allow for a rump of stubborn thick ice north of the Canadian Archipelago, both of those numbers will reduce, depending on how big you believe it might be.

    One key point: the heat accumulating in the Arctic (sufficient to melt 1,000 km3 of ice per annum) is not going to stop accumulating just because the summer ice is gone. It will warm the ocean, delaying the onset of the autumn freeze. Eventually, the accumulated heat will exceed the Arctic’s normal winter energy loss, and the ocean will be ice free in winter. Back of the envelope? Before mid century.

    • Gareth, do you have a citation to any studies showing a winter ice-free Arctic Ocean any time this century? I find that hard to believe (yeah, yeah, the fallacy of personal incredulity…). Wouldn’t an ice-free ocean lose heat more rapidly than an ice-covered ocean, providing a negative feedback?

      I find it noteworthy that in recent years, while summer ice has declined rapidly, winter ice has not declined as much.

      • No cites, just the back of an envelope (actually a Post-It note, if you really want to know). The logic works like this: consider the overall heat budget for the Arctic. The positive terms currently exceed the negative by the heat required to melt 1,000 km3 of ice per annum. We can estimate the average annual heat loss by looking at the difference between annual vol(max) and vol(min) — the amount of ice that freezes up over winter. Ignoring feedbacks, at some point the heat accumulated in the ocean will exceed the annual loss, and there will be no freeze — just a lot of chilling. The first signs of this happening are already there in the area/extent curves. The biggest anomalies always happen after minimum, as the onset of freezing is delayed…

        Are there negative feedbacks? Quite possibly, and I’d be very interested in a discussion of what they might be. But we do know that the Arctic can get very warm (during the Pliocene, at 390ppm CO2, for example), so I suspect that eventually the heat accumulation wins. How soon is an open question. My calculations suggest within 50 years, but I’m no physicist, and I have no more mathematical qualifications than Monckton, so it would nice if somebody checked my working… ;-)

      • …do you have a citation to any studies showing a winter ice-free Arctic Ocean any time this century?

        Abbot & Tzipperman, 2008, “Sea ice, high-latitude convection, and equable climates.”
        Unless my memory betrays me (it’s been some time since I read it) with CO2 levels possible this century winter ice-free state is stable with cloud cover and heat transport into the Arctic keeping temperatures high enough to avoid freezing. Check out the final line of the conclusions which seems to support what I remember:
        We finally investigated various CO2, OHT, and AHT values and found that the ice-free state is stable for values that may be reasonable for the Arctic ocean during the late Cretaceous and early Paleogene (OHT = 0, CO2 = 250–2000 ppm, AHT = 80–100% modern). OHT = Ocean Heat Transport, AHT = Atmspheric Heat Transport.

  14. Gareth wrote: “. . .you can have a low volume covering a large area if the ice is thin. At some point, however, the thin ice will melt out over summer and you may get a sudden steep reduction — a bit like pond ice disappearing when the weather warms.”

    Indeed, we saw something of that pattern this summer; from an early stage in the melt season we had much more widespread areas of comparatively low concentration on the Cryosphere Today maps. Then in July, when the weather turned favorable to ice conservation, with cloudy skies and no Arctic Dipole pattern, extent loss slowed. But at the same time, you could see concentrations dropping gradually, and you knew that at some point, some of those areas would hit the 15% “knee” and drop off the map–and indeed, that did happen as the season advanced further.

    Although the El Nino that helped fuel the high temperatures of late 2009 and the first half of 2010 has faded into a La Nina, the troposphere seems not to be cooling very fast. It will be interesting indeed to see whether freeze-up is–shall I say, “sluggish?”–once again, and how the next melt season plays out. It wouldn’t surprise me if there’s a whole lot of relatively thin ice once again in 2011.

  15. “I got lucky”?

    Mixing up your blog titles with your fb status updates?

    Nice work on completely skewering WUWT, and actually a good example of how setting aside complications and focusing on simplicity can do very well in predicting the gross features of complicated systems. You didn’t need a supercomputer to model every chunk of ice in the arctic to make a good prediction.

  16. WUWT’s touting a new paper that says Arctic Sea Ice is more extensive than any time in the past 9000 years.

    McKay 2010


    [Response: It says no such thing. I recommend reading the paper before reporting what it says.]

    • You’re not kidding, Tamino!

      From the abstract:

      Results indicate a decrease in sea-ice cover and a corresponding, albeit much smaller, increase in summer sea-surface temperature over the past 9000 years. . .”

      “The results of this study clearly show that sea-ice cover in the western Arctic Ocean [because their data was sediment from the Chukchi Sea only] has varied throughout the Holocene. ”

      “More importantly, there have been times when sea-ice cover was less extensive than at the end of the 20th century.” Ah, finally the kernel of truth that WUWT used to create their distortion.

      • Rattus Norvegicus

        And of course, the fact that SST;s might have been higher during the early holocene is no great shakes because early holocene NH insolation was geater than at present.

        Sort of an epic fail. And of course the graph provided by the site he linked to (and I can’t figure out whether it is satirical or not) uses a Dr. Inferno approved trick of inverting the graph.

    • Note also that McKay is not a “new” paper. It was published in 2008. Somebody went digging around, to find something to throw up against the wall. Characterizing it as “news” is just a bit disingenuous of Mr. Watts.

  17. Speaking about predictions, this is off topic but I was trying to find Tamino’s post where he used statistical analysis to show when according to the warming trends the Earth was likely to have one year whose temps were greater than 1998′s (assuming you use that date as the year for the highest temps). I failed tracking it down, but IIRC it was pre-2012. Is this correct?

  18. Philippe Chantreau

    A small kernel Kevin, which is to qualified with this.

    “If both the observed and reconstructed time series are correct, then the last part of the 20th century must have been particularly cold compared with the mid- to late Holocene in the Chukchi Sea, which is opposite to what is seen in the Eastern Arctic and Northern Baffin Bay (e.g. De Vernal et. al 2008).”

  19. First thing I did – even before finishing reading the WUWT post on 9000 years of ‘Arctic sea ice coverage’ – was read the paper. The Cuckhi sea is a small area of the Arctic ocean. Had a few tries at pointing this out, how the title and post hugely misrepresented the paper, but the bald, blind rejection of what was clear in the paper was extraordinary. Talk about blinkers.

    Being a maths dunce, I tried to figure out comparative area. The Chukchi Sea is ~600 000 sq/km.s. The entire Arctic ocean is ~14 million sq km. That’s about 4%, but is there a special calculus for percentage area?

    • Barry,

      Have you seen this?


      Watts and co. are full of it. From Polyak et al. (2010):

      “The current reduction in Arctic ice cover started in the late 19th century, consistent with the rapidly warming climate, and became very pronounced over the last three decades. This ice loss appears to be unmatched over at least the last few thousand years and unexplainable by any of the known natural variabilities.”

  20. A sideslip, but still within topic parameters, I think–I’ve just published a farewell to the melt season online that some may enjoy:


  21. Philippe Chantreau

    Barry, you could use the same “percentage calculus” that Goddard used when looking at Western snow pack, that would be funny…

  22. Because NSIDC don’t publish their daily data, we are a little in the dark about the September mean extent until next week. I have estimated it by taking the daily IJIS data for the month to date, extending the most recent 5-day trend (which is fairly linear) to the next 3 days, and calculating a monthly mean: 5.09 Mkm^2. NSIDC numbers seem to be about 0.2 Mkm^2 below IJIS at this time of year, so I predict an NSIDC September mean of something like 4.9 Mkm^2.

    • Thanks, Nick. I’m also curious to see what data about volume comes out. There seems to be a pretty widespread feeling that we may have just had the lowest volume minimum ever–and PIOMAS model results from earlier in the summer seems to make that conclusion nearly inescapable if it is correct–but I haven’t seen anything quantitative on that so far.

      • There’s very little real data on volume; everyone (with the quite plausible exception of secret military research) seems to be working from scant datasets held together with models like PIOMAS. What you should be waiting for is the first live numbers from Cryosat 2, which is our first instrument to actually measure volume. Based on area and extent, and on the ice quality I see on MODIS, I’m expecting the PIOMAS numbers to be more-or-less borne out by Cryosat 2: in particular that September ice volumes are now below 5000 km^3 and falling dramatically each year. But it wouldn’t come as a huge shock to me if it shows that PIOMAS is off by (say) 30%, and that the rate of decline is more gradual.

    • I was right about this; NSIDC September mean is indeed 4.90 Mkm^2.

  23. Cryosat should start some important new time series. But absolute volume estimates, directly comparable to earlier estimates, might not be Cryosat’s strength. Measurement methods differ and we won’t have overlapping satellite observations.