Ice Cover is Not “Stabilizing”

NOTE: for a brief, non-technical summary of this post see the UPDATE at the end. To get there, go to the full post (not just the blog’s home page), then click here.

Real data are the combination of signal and noise. By noise I don’t just mean measurement error. I mean the stochastic part of the process. That includes naturally occuring noise in the system itself — those ubiquitous wiggles up and down and up and down and down and up, that never cease but never really get anywhere. They’re not part of the trend, they’re noise. If you want to know what the trend is then you have to account for the noise.

If you claim that “ice cover is stabilising,” then you better be talking about the trend. You damn well better not be basing that conclusion on the effect of those ubiquitous wiggles that never cease but never get anywhere.


Here, for instance, is some data for Arctic sea ice area according to Cryosphere Today (for convenience I’ve transformed them to 0.02-year averages — roughly weekly — which won’t have any notable effect on the analysis which follows):

uiuc

I’ve also shown a lowess smooth to indicate the trend. In addition to trend the data show noise, with lots of up-and-down variation. It’s not just point-to-point jitter, there’s persistent noise here, which reflects the fact that the noise shows autocorrelation. But it’s still noise, it still shows nonstop wiggles that don’t get anywhere and have nothing to do with the trend, or with whether or not “ice cover is stabilising.”

We can even see some of those more persistent wiggles if we smooth the data with a “faster” lowess smooth (shorter time constant) like this:

uiuc2

One might be tempted to think that those wiggles represent “cyclic variation” with period around 5.4 years. One would be mistaken.

We can use the residuals from the first smooth (in the first graph) to estimate the parameters of the noise — in particular, its size and its autocorrelation. We could, for that matter, use the residuals from the second, “faster” smooth, which would likely underestimate the impact of the noise, but we’ll do it both ways anyway.

Then we’ll create some purely artificial noise, which we know (by design) has no trend at all, certainly no change in its trend. Nothing. Nada. Zip. We’ll create AR(1) noise with the same lag-1 autocorrelation, and the same standard deviation, as the residuals from the smoothed sea ice area anomaly data — two versions, one for the “slow” smooth and one for the “fast” smooth. If we apply various methods of estimating the trend to the artificial data, we can get an idea how uncertain their estimates are — because any nonzero trend (or change in trend) indicated for the artificial data isn’t real. It’s just response to the noise.

How shall we estimate the trend? Here’s one way — and not a bad one at all. We’ll apply a Gaussian filter/derivative filter to the data. The derivative filter just computes the ratio of the data differences to the time differences, simulating “differentiation” and estimating the rate of change. Those are bound to show a lot of wild point-to-point fluctuation, so the Gaussian filter will smooth that out and give a sensible estimate.

We do need to be aware, however, that a derivative filter is a high-pass filter and a Gaussian is a low-pass filter, so the two in tandem are a bandpass filter. The center of the passband will suddenly look strong, whether it’s meaningful or not, and unless we’re aware of this we’ll be tempted to conclude that there’s “cyclic variation” when there isn’t.

We also need to choose a timescale for the Gaussian filter. Let’s use a 1-year filter. And, although Gaussian filters can be applied right up to the edge of time span of the data, there are “edge effects” which degrade precision — so we’ll chop off two timescales from the beginning and end just to keep things “clean.”

If we apply that rate-of-change estimation method to the actual sea ice area anomaly data from Cryosphere Today, we get this:

uiuc_rate

One might be tempted to think that all those fluctuations, those smooth ascents and descents, are real signs of change in the trend of sea ice area. But it would be downright foolish not to account for the fact that there will be fluctuations in the estimated rate, simply due to noise — those ubiquitous fluctuations that never get anywhere and have nothing to do with whether or not “ice cover is stabilising.”

The mean rate over the entire time span is a loss of about 50,000 km^2/yr. We’re most interested in how much variation the rate shows — so let’s subtract the mean rate to show just the variations from mean. This makes the graph look the same but the zero point is different):

uiuc_rate_0

We can estimate the size of the irrelevant noise fluctuations by applying the same rate-estimation method to the artificial data. For the “slow” residuals, the very first artificial data set (the only one I bothered to create) gave this:

ar1_rate

It’s probably more informative to compare the variation in rate from the artificial, trendless data directly to the variation in rate from the real data:

rate_compare

Result: The variations in rate-of-change of sea ice area anomaly data are no bigger, no faster, no sharper, no more or less smooth, in fact not really distinguishable from the variations in rate-of-change of random noise with similar size and autocorrelation.

We can do the same with artificial noise generated using the parameters estimated from the residuals to the “fast” smooth. The very first artificial data set (the only one I bothered to create) gave this:

rate_compare2

Result: The variations in rate-of-change of sea ice area anomaly data are no bigger, no faster, no sharper, no more or less smooth, in fact not really distinguishable from the variations in rate-of-change of random noise with similar size and autocorrelation.

Conclusion: There is no evidence that the variations in rate-of-change of sea ice area anomaly data estimated using this method are anything but the result of random noise. The mean rate-of-change is meaningful; sea ice area has certaintly declined. But the variations mean nothing because they’re no bigger than the uncertainty in those estimates.

If you didn’t bother to estimate, or even consider the existence of, uncertainty in your estimated rate of change then you’d probably reach false, in fact downright ridiculous conclusions. Like “ice cover is stabilising.”

You’d be mistaken. If you also declared “cyclic variation” which isn’t real, and said in no uncertain terms that the scientists who actually study sea ice need to get their act together because they’re missing the really important stuff, then you’d be thought a fool. Because of your hubris.

Why does the given method show such large unrealistic fluctuations? The Gaussian+derivative filter is like applying this filter to the original data:

filter2

Note that it reaches its maximum and minimum at times +1 and -1 years, because that’s the timescale of the Gaussian filter. Therefore, it’s hardly exactly equal to, but is somewhat (very roughly) akin to estimating the rate of change at time t by taking the average around time t = +1 years, subtracting the average around time t = -1 years, then dividing by 2.

That’s a valid way to estimate the rate of change. But when there’s noise, especially the kind of autocorrelated noise shown by sea ice area, it’s not a very precise way. One can hardly expect such an estimate, based as it is on such a short timescale, not to show large uncertainty due to random noise — uncertainty as large or larger than the rate-of-change itself.

There’s a lot more to Arctic sea ice area data, and sea ice extent data, and sea ice volume data. There are better ways to compute anomaly which account for some of the recent changes, and better enable us to estimate the properties of the noise as well as see just how unstable the Arctic ice pack is. But, that will be the topic of another post.

UPDATE

I get the impression this post has enough math to sail right “over the head” of some readers. So, here’s the brief not-too-technical summary.

Bottom line: take random noise with the same characteristics (size and autocorrelation) as the noise in real sea ice area data. Apply the same rate-estimation method used by Greg Goodman. What you get is wiggles just like he got — same size, same time scale. It’s because the noise — all by itself — will create them.

Conclusion #1: the wiggles he found are no evidence at all of any changes in the rate of sea ice loss.

Conclusion #2: Greg Goodman not only didn’t estimate the uncertainty in his analysis, he ignored its very existence.

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37 responses to “Ice Cover is Not “Stabilizing”

  1. I’m reminded by Tamino (and RC, SkSc, etc.etc.) why “Intelligent Design” will NEVER gain a foothold in the public school systems as science: …there are just too many dedicated, competent, honest, articulate and willing people who will prevent it from anything but the most short-term, local, false-victories. For them, I’m hugely impressed and grateful.

    Too bad that Climate doesn’t lend itself, at least not yet, to that sort of immediate, decisive and assured victory in the public arena.

    I understand way too little of what Tamino, et.al., are doing but it’s clear that the fake-skeptics and liars and willfully ignorant will one day acknowledge that, even “back then,” the science was clear and the conclusions sound and they were outclassed at every turn.

    My wordy way as a non-scientist of saying, “Thanks, Tamino, I’m hugely impressed and grateful.” (Also, my brain just doesn’t work like yours. Your stuff with Goodman just blows me away.)

    • Gavin's Pussycat

      > but it’s clear that the fake-skeptics and liars and willfully ignorant will one day acknowledge that

      If wishes were horses…

      • I didn’t say the truly crazy and conspiratorialists. But even Watts and Monckton will someday admit it.

  2. Thank you! I wished for treatment of the uncertainties, and lo! and behold…

  3. Tamino,

    “…..as well as see just how unstable the Arctic ice pack is”

    Here is a link to IR satellite imagery for the Beaufort sea region. A region previously dominated by year round and very thick multi-year sea ice.

    But now it looks like a broken egg shell near the time of year when the Arctic ice is at its maximum extent. A crumpled shell of its former self.

  4. thanks again for not treating me as an idiot… however I don’t really understand the wiggles. The issue is simple- fake sceptics can treat everyone as statistically illiterate [in the area of statistics] telling the truth is a lot slower method of communication. I’m still struggling although I do get the basics and imagine it to be similar to processing audio which I do using high and low gain passes and similar ‘tools’ to clean up sound.

    [Response: Bottom line: take random noise with the same characteristics (size and autocorrelation) as the noise in real sea ice area data. Apply the same rate-estimation method used by Greg Goodman. What you get is wiggles just like he got -- same size, same time scale. It's because the noise -- all by itself -- will create them.

    Conclusion #1: the wiggles he found are no evidence at all of any changes in the rate of sea ice loss.

    Conclusion #2: Greg Goodman not only didn't estimate the uncertainty in his analysis, he ignored its very existence.

    I've added this brief summary as an UPDATE at the end of the post.]

  5. Susan Anderson

    For anyone not yet agog about the doings over at Neven’s, this:
    http://neven1.typepad.com/blog/2013/03/the-cracks-of-dawn.html#more

    In addition, while I have infinite respect for all you scientific types, I would suggest that observation is a useful part of reality. For a layperson like myself, it seems a ton of new observational information is pouring in, and it all points clearly to the same developments scientists are trying to understand and quantify. I don’t think it’s necessary to separate the two and value one over the other (perhaps I’m misdescribing, but it seems to me the theory is being outstripped by the reality).

  6. I’ve a feeling that Goodman would see your AR(1) noise series as obviously and completely different than the Cryosphere Today series in that the last two years of CT rates are headed towards zero, (i.e. ‘stabilizing’) while the last few years of rates for your AR(1) series is headed away from zero (which would mean things are ‘destabilizing’).

    In finance, it seems folks are a lot more willing to understand noise and trends, and the difference between sober and shitty advice. As a stock market analogy, it seems you are saying the rate of return is negative and there is no evidence that beta is changing, (and for an example, here’s what a similar random, negative alpha, same beta series would look like) while someone focusing on the noise is saying the stock is below expectations and ‘stabilizing’ since it seems to be heading back up towards zero (clearly, Tamino’s fake stock isn’t hot like my mathy analysis of CRYOT shows: buy-buy-buy!)

    In terms of ice and climate change, a meaningful “stabilization” would mean that we should expect the ice years into the future to be about the same as we now. I certainly do not see that.

    If Yahoo! finance charted Cryosphere Today, CO2, and temperature, etc., the way they do DJIA and VXD, it might help.

  7. Maple Leaf,

    As I’ve only just posted elsewhere, Here’s a paper from 1991 who’s figure one shows ice that could pass for now, but it was in 1983.
    http://www.igsoc.org/journal.old/37/127/igs_journal_vol37_issue127_pg319-322.pdf

    In that year the ice was dominated by MYI. In my opinion the reason this break up is significant is rather more subtle.

    Thanks for the post Tamino.

  8. One point: Errors like Goodmans don’t require malice, just an unfamiliarity with the tools, methods and statistics used. Accompanied in his case with a severe Dunning–Kruger effect and some arrogance, mind you.

    If you don’t know the consequences of your tools (in this case, the band-pass filtering done by differencing/smoothing), you can and will be led astray – you have to be able to judge whether those consequences are significant. This happens all the time in signal processing.

    If Goodman had come in with an observation, framed by his technique, and said “Look what I found – it seems interesting, what are folks thoughts on this?”, it could sparked a good discussion, with everyone (including him) learning from it. That’s always helpful; “Never do this” is very important. And if his analysis pointed out something that proved solid and interesting, even better!

    It’s unfortunate that he approached matters with a fixed opinion: that his dilettante analysis outmatched those of people who study these issues for a living…

  9. Greg Goodman

    Right, assuming I will not be censored again and will be able reply to all the shouts of “hubris”, incompetence, etc , let’s start by reviewing what I actually posed on RC rather than what everyone else wants to read into it and the words they want to put into my mouth.

    Greg Goodman says:
    7 Mar 2013 at 7:09 AM

    http://climategrog.files.wordpress.com/2013/03/ddt_arctic_ice.png

    We only hear about run-away melting in Artic ice but looking at all the daily data available for over 30 years now we also see there are strong “unforced” cyclic variations up there too.

    This plot is rate of change so the zero line represents neither loss not gain.

    The media tend to focus on one day per year in September. Scientists need to dig a bit deeper. What is happening up there is a lot more interesting than simple melting.

    Thorough investigation of the daily satellite ice data could give important clues to a better understanding of the “internal” fluctuations in the climate system: the part that, so far, models have trouble reproducing.

    =========

    [Response: Nobody tried to "put words in your mouth." Take another look at the first post where you got pwned. I already quoted your entire RC comment, verbatim.]

    So I did NOT say that scientists were only looking at one day per, I said “media tend to focus on one day per year”. Slight difference which seems to have escaped some of the those without enough attention span to read a whole sentence without forgetting what the first half said.

    The one phrase that was apparently highly “offensive” to some was “scientists need to dig a bit deeper”. Now I did not say all scientists have no idea and I can do better than any of them, which do go by comments you would think was the case.

    [Response: Your implication was clear: that scientists need to dig deeper because your analysis revealed what they had missed. So: I'm calling you a liar.

    You were mistaken about your analysis. Your arrogance in assuming you had found something they had missed rather than merely suggesting it as an interesting possibility worthy of investigation, is hubris. Clinging to the vain hope that you're still right even after you've been shown the error of your ways twice, is pathetic.]

    But scientists (and anyone else interested in how it will develop) do need to dig deeper, there is only a very superficial understanding of the large fluctuations driving the rate of change in ice area. CO2 alone won’t explain why melting accelerated from 1997 to 2007 and slowed since. Neither will it explain the markedly different pattern in those years.

    [Response: You still refuse to get it. You have not shown any evidence at all that Arctic sea ice loss slowed since 2007. You still don't seem to get the difference between variations caused by trend and those caused by noise. You still have no clue about the statistical uncertainty of your rate estimates, other than what I've computed for you. In fact you still seem to be in denial of its very existence.

    Repeating that scientists "do need to dig deeper" is again arrogance -- and you don't even get that. Of course there's a lot still to learn, but when you say scientists "need to dig deeper" all you show is that you're clueless about how hard they are working on it and the limitations of current knowledge. If you want to claim that you were just pointing out how much we have yet to understand rather than implying that you and your genius had seen further than they, then again I'll call you a liar.]

    My final comment about models got rewritten as :
    == … “internal fluctuations” which, of course, those inadequate computer models just can’t handle.== as though it was some outrageous bit of “climate denial”.

    Well in fact the models don’t reproduce the short term variation at all well, certainly not before 1950 This is recognised and is currently the one of the main areas where efforts are being made to improve the models. This is not me slandering models , modellers or anyone else , it’s simple the state of the art.

    [Response: You're not just arrogant and ignorant of sea ice loss, but also about "the models." Many of them reproduce the short-term variation well, some even reproduce known phenomena like el Nino/la Nina. But none of them reproduce the actual observed short-term variation because it is stochastic. You might as well complain that a random number generator is inadequate because it failed to reproduce the exact same sequence of random numbers observed from a natural phenomenon. For the sake of other readers I will mention that I don't expect you to "get" this, either.

    Models need a lot of improvement. You are the last person qualified to critique them, and perhaps the worst to assist in such efforts.]

    The RC thread was simple headed:
    A new open thread – hopefully for some new climate science topics…

    I think the rate of change of Arctic shows variations that are at least interesting, so at the invitation of this thread I posted a suggestion with a graph. Not a research paper, just a few lines on blog comment. Someone at RC must have thought it at least of interest for it to have got through moderation.

    So why has this created to such vitriolic response and merited two full articles on this site to try and trash me? Perhaps it’s more significant than I thought.

    Tamino’s AR1 test is an interesting (though clearly anecdotal one-off) check.

    [Response: It's an illustration that random noise with properties similar to that in real sea ice data reproduces the same kinds of fluctuations that your analysis found. Which makes it proof that your analysis fails to establish any non-random fluctuation in the rate of sea ice loss. Your ego won't allow you to acknowledge that. Everyone else sees it plainly. You have made yourself into a laughingstock.]

    Sure , there are ups and downs, rounded by the gaussian filter but no apparent order. Now looking at the real data, there is clearly a change in pattern between 1997 and 2007.

    Now, if that is purely a result of my inept use of a one year filter to remove annual noise, why don’t we see similar “random” patterns in the AR1 test data?

    [Response: We do.]

    Why didn’t the same “bandpass” filter exaggerate some intermediate and insignificant pseudo cycle out of the AR1 series and produce similar multi-year cycle of some arbitrary frequency?

    [Response: Are you kidding? Seriously -- you must be kidding, right? Because it does.]

    Much play has been made of the frequency response of combination of diff and gaussian , perhaps Tamino could also post the frequency response of his Loess [sic] filters for comparison.

    [Response: Wherefore the "[sic]“? You seem to know as little about what I did as about what you did. From Wikipedia: “LOESS and LOWESS (locally weighted scatterplot smoothing) are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model.”]

    Before giving too much weight to the Fourier analysis of the ice area time series to draw conclusions, perhaps someone should examine its stationarity and that of the differential series. Augmented Dickey-Fuller Test perhaps….

    [Response: Gosh ... the only one who drew faulty conclusions about ice area time series is: you. Your mention of the augmented Dickey-Fuller test is just a very lame attempt to show off that you've heard of some statistical tests. You're no more interested in the stationarity of the stochastic fluctuations than you were in the uncertainty level of your rate estimates -- but you're desperate to avoid facing the fact that your conclusions were completely unjustified because your analysis was grossly incompetent.

    I've wasted far more than enough time on you. Add mine to the (probably growing) list of sites at which you are not welcome.]

    • Greg, your comment should have been something like this:

      “I’ve been trying to investigate whether or not the Arctic sea ice (extent, area, and volume) trends contain any sort of short-term cycle, perhaps driven by the dynamics of other cycles. I’ve come up with a methodology that produces what appears to be a 5.4 year cycle, but I don’t know if I’m fooling myself (i.e. bad methodology). If anyone has a moment to take a quick look, I’ve got the methodology spelled out here (link). Thanks.”

      Note that I didn’t add in any detailed awareness of the uniqueness of annual melt/freeze conditions, the decline of ice quality (producing conditions without precedent in the modern period), the differences between the trends in extent/area/volume, or the loss of multi-year ice (the dregs of which are currently slowly being sliced to ribbons). Each of those realities should make detecting the signal of a very light short-term cycle very difficult (uncertain). Awareness of that was not in the original post. Just out of curiosity, before you were disabused of the 5.4 year cycle notion, what physical processes were you thinking about attributing it to, in theory?

    • “CO2 alone won’t explain why melting accelerated from 1997 to 2007 and slowed since. Neither will it explain the markedly different pattern in those years.”

      Huge straw man–nobody claims that CO2 explains all short-term trends in sea ice or anything else climatic. There’s a reason that RC calls its open threads “Unforced Variations.”

      Which is not to say that investigating those variations is not a good idea…

      Or easy to do.

    • Greg,
      Just curious. Have you ever published a peer-reviewed paper? Thje reason I ask is because you do not seem to understand what scientists go through when publishing.

    • “Tamino’s AR1 test is an interesting (though clearly anecdotal one-off) check.”

      Indeed, in fact exactly the sort of sanity check that Greg ought to have performed before promulgating his theory. Self-skepticism is at the heart of good science and good statistics, which is why the expectation is normally that we show statistically significant evidence to support a hypothesis *before* publishing, or take steps to show that the effect we are interested in cannot be explained by random chance.

    • Now, if that is purely a result of my inept use of a one year filter to remove annual noise, why don’t we see similar “random” patterns in the AR1 test data?

      [Response: We do.]

      Why didn’t the same “bandpass” filter exaggerate some intermediate and insignificant pseudo cycle out of the AR1 series and produce similar multi-year cycle of some arbitrary frequency?

      [Response: Are you kidding? Seriously -- you must be kidding, right? Because it does.]

      #######
      Ha. For him not to be kidding, this must mean that he still believes that his analysis is significantly different from noise. He’s neglected or misunderstood the point of your https://tamino.files.wordpress.com/2013/03/attenuate.jpg plot. His analysis is indeed a “bandpass”, centered around ~5 years, and will “exaggerate insignificant pseudo cycles” around that period.

      Given how Greg’s reacted, I don’t think Tamino could have picked a better example.

      Oh my: “If that is not the case it would suggest that there is something in that data that he feels strong need to suppress.

      I did intend to write this up at some time in the future. Foster’s reaction makes me think this may merit more immediate attention.” — Greg Goodman at http://climategrog.wordpress.com/2013/03/11/open-mind-or-cowardly-bigot/

      I’d bet these “statistical significance” tests will be in on the conspiracy as well.

      It it all works out for Greg, these aperiodic cycles with an amplitude of 1/10th of the signal are never going to explain more than 1/10th of the change, even if they are attributable to something real.

      If this was a stock market data analysis, it would be as feeble as saying Apple (e.g.) is due for a buy because a pattern in the yearly moving average of the daily rate of return looks like it almost explains 10% of the price change–you’d be better off reading press releases.

      • Quiet Waters

        “Open Mind or Cowardly Bigot”
        Note that Greg has turned comments off on this & his other post on Tamino…

    • Greg Goodman, I agree with you.

      In fact, I think your argument is so strong that I’m surprised you didn’t submit it to a peer-reviewed professional journal.

    • On his blog, Goodman writes

      “Now, because of the 12 month gaussian filter they both smooth curves of a similar scale. However, there is no obvious pattern in the AR1 model. No repetition of peaks at equal spacings.

      The series of equally spaced cycles broken by a 10 year period of accelerating ice loss is certainly not reproduced by the AR1 test data. ”

      In other words, he looks at Tamino’s graphs showing the filtered cryosphere data and filtered AR1 noise, and concludes that they are competely different, when in fact they show exactly the same *important* characteristics. And that’s his fundamental problem – he cannot, or will not, distinguish between the important characteristics of data and the irrelevant ones. He cannot, or will not, distinguish between signal and noise.

      I wonder if this problem, which is very common among the fake skeptics, is a natural human tendency (effectively a form of pareidolia) that good scientists train themselves out of; or is it a sign of the DK-afflicted? Certainly the fake sceptics will scream long and loud about the tiniest wiggles in a graph while completely ignoring the huge trend. Is this a deliberate tactic of distraction on their part, or are they really *unable* to see beyond the noise?

      Purely speculation of course, but I wonder if there’s a correlation between conspiracy ideation and pareidolia? (Could be a paper for Lewandowsky in that!)

  10. Are you planning to comment or publish on Tung and Zhou?

    http://depts.washington.edu/amath/research/articles/Tung/journals/Tung_and_Zhou_2013_PNAS.pdf

    They seem to be claiming that they can see their 70 or is it 40 year cycle in Foster & Rahmstorf. It seems rather obvious to me that they are not justified in extending the method back further because they seem to assuming that the prior flat spots are due to their cycles, rather than the known physical causes I’ve seen assigned to them.

    [Response: I hadn't planned to. What they actually claim about F&R 2011 is that the trend is due to the AMO. I think Tung & Zhou are too enamored of imaginary cycles -- like a lot of people.]

  11. I am shaking my head at the notion that a supposedly smaller decrease rate proves that something is wrong with either theory or models with regard to GHG and sea-ice changes. A reduced loss rate, or even a small increase in minimum ice cover over several years actually show that the models may be better than found in the current situation. Why do I claim this?

    Most climate models underestimate the recent loss of ice in the Arctic. However many (most?) models have periods in the model future where the loss rate is as large as currently observed. These periods of ice-loss is sometimes followed by a flattening or even a small increase in minimum ice-cover for up to a decade before the reduction continues.

  12. I’m a little worried that two or three giant dollops of misguided nonsense are being left in public view within this discussion of the rate of change of Arctic sea ice cover and thus perhaps there is a danger that they may give an inaccurate ‘take-away’ from the discussion.

    To address this, I present exhibit A, a graph of Sea Ice Area 1979 to date. and exhibit B a graph showing the rate of change of that data (although actually SIE not SIA, the outcome is the same).

    (1) Goodman suggests that while folk get so exercised over the annual minimum SIA (or SIE), a lot of analysis goes a-begging. This is why he is so insistent that he uses daily data.
    Goodman’s suggestion is misplaced.
    As well as the annual minimum, the world also gets quite obsessive about the annual maximum. Despite what Goodman implies, if you combine the annual Max & Min the wobbly average SIA record appears. (Compare red & yellow in the first graph linked above.) So does the wobbly differential of that average that Goodman smooths to create his pretty sine waves.

    (2) The pretty sine waves that appear from Goodman’s analysis are not present in the raw data. They are purely an artifact of Goodman’s data processing. The raw data is far less smooth. There are the same series of ups and downs within the data, be it Goodman’s graph, SIA SIE running averages or a max+min running average. They are not equi-spaced and are only smooth because Goodman smoothed them. Their apparent regularity is an artifact of Goodman’s data processing. (Examine the purple trace in the second graph linked above that shows a rolling 12-month average of SIE).

    (3) The idea that there has been some sort of stabilisation in Arctic Sea ice cover since 2007 and what that might have entailed has not been well addressed here. If 2007 is cherry-picked as a low point and (in Goodman’s words) the “acceleration” not followed by a “stabilising” period of “deceleration,” that is if the rate of loss continued at that shown in Goodman’s graph, we would have witnessed the first Ice-free Arctic summer by now.
    “Stabilisation” is far from apparent when the massaged data presented by Goodman is replaced by more realistic representations. If you wish, call it 2 years off for good behaviour but do remember such wobbles are not unprecedented within the 33 year record. (See what Goodman’s cherry-picked “stabilisation” actually looks like in the first graph linked above.)

    • Al,
      I agree that Greg’s analysis is utterly misguided. However, I’m wondering whether it might be repeated with arctic ice volume to produce something meaningful. After all, Greg’s contention that the “acceleration has stopped” is just another way of saying that the Arctic is cold in the frigging winter. However, we know that a lot of the ice is thin, crappy one-year ice. If there were really recovery, we’d expect the decrease in volume to be decelerating as well. What do you think?

      [Response: Two opinions: First, volume is a more physically relevant measure, but the data are less certain. Second, his analysis is not unlike a "moving trend estimate" using 2-to-3 year long trends. That's just too short a time scale for such trends to be meaningful, it only shows the fluctuations. If you want to study the fluctuations, fine -- but don't make claims like "stablizing" on that kind of evidence.]

      • I did a quick plot of the differential of the rolling annual PIOMAS average just for a look-see. (Sorry, I’ve not uploaded it to show) Of course, the trace of the PIOMAS annual rolling average is steeper than the SIA/SIE trace. It also has bigger wobbles and 2007 is no longer such a feature. So anyone trying to do a Greg with PIOMAS meets the problem of 2010 having a bigger downward trend wobble than 2007. Unlike SIA/SIE, there was a healthy distribution of ‘wobble sizes’ but it being the output of a model, I myself would be wary of even analysing its fluctuations too deeply.

  13. Horatio Algeranon

    “The Speed of the Bounce of Noisiness”
    – Horatio’s rendition of “The Speed of the Sound of Loneliness” by John Prine (Sorry for blaspheming a truly amazing song)

    You come on right and you come on surely
    You come on big when you’re looking small
    You come to fight so you come on surly
    Sometimes you don’t come on at all

    Chorus
    So what in the world’s come over you
    And what in science’ name have you done
    You’ve graphed the speed of the bounce of noisiness
    You’re out there graphing just to look like you won

    Well I got an Earth that burns with a fever
    And I got a thinning and a melting ice
    How can a trend that has lasted “forever”
    Mathemagically stabilize?

    Chorus

    It’s the 5-year mean on a deathful spiral
    That’s crossed a record low today
    Well, how can you talk about a “cycle”
    When you messed up with Fourier?

    Chorus

    You’re out there graphing just to look like you won
    You’re out there graphing just to look like you won
    You’re out there graphing just to look like you won

  14. Horatio Algeranon

    Horatio wrote “Noise” a while back, but (unfortunately) it seems particularly apt

    “Noise”
    – Horatio Algeranon’s perversification of yet another beautiful song
    (“Words”, by the Bee Gees)

    Cycle an everlasting cycle
    A cycle could bring a Prize to me
    Don’t ever let me find it gone
    ‘Cause that would bring the flies to me

    CO2 has lost it’s glory
    Let’s start a brand new story
    Now Mike Mann
    Right now
    There’ll be no other time
    and I can show you
    How Mike Mann

    Engage in everlasting noise
    And dedicate it all to me
    And I will give you all my cherries
    I’m here if you should call on me

    You think that I don’t even mean
    A single graph displayed
    It’s only noise, and noise is all
    I have to take your warmth away

    You think that I don’t even mean
    A single graph displayed
    It’s only noise, and noise is all
    I have to take your trend away

    It’s only noise, and noise is all
    I have to take your trend away

  15. I am always amused by the frequent claims (usually made by someone who doesn’t know what they are doing) to have ‘found the unicorn’, that tiny bit of information that overturns all of science, the piece that everyone else has overlooked. This usually appears as a statement similar to: “Look, if you divide by _2_ you get a completely different answer!”. And that is presented with the full expectation that their contribution will make scientists reconsider everything they have been doing.

    On rare, very rare, occasions, the unicorn might be real. Far more often, however, the apparent contradiction is due to a simple error, one that has likely been made over and over again – and if you present your ideas with even a wee bit of humility, with the possibility that you might be wrong, you are likely to learn something. And in a very useful sense the discussion may well educate all readers on one of the “never do this” issues.

    If on the other hand (as seen in these last two threads) you make a pronouncement of your virtuous clarity, having already concluded that you are right and all others are wrong, and even worse if when faced with facts, you double down on the foolishness – well, then, you aren’t learning anything.

    You still educate the readers, though – you teach them that your analysis is unlikely to be correct…

    • Horatio Algeranon

      claims to have ‘found the unicorn’

      ..or the unicycle

      Unicorns and unicycles
      Both are hard to ride
      But, at least, the unicorn
      Is stable cuz it’s wide

      • but unicorns are hard to ride
        even though they may be wide
        just ask your local physicist
        unicorns do not exist!

        and sound scientific arguments that sea ice extent is stabilising (other than at zero) seem unlikely to be significantly more common!

  16. David Sanger

    Considering the first sea ice area anomaly Cryosphere Today graph above, it “sure looks like” most of the graph is in the negative region anyway, which “sure looks like” a decline in sea ice area over time, notwithstanding any imaginary cycles.

  17. Don Gisselbeck

    Greg sounds like the sort of person who shows up at a supported bike ride and lectures the mechanic about bike repair.

  18. “If it’s a boy, I’ll call it after myself. If it’s a girl I’ll call it Victoria. But if, as I strongly suspect, it’s nothing but piss and wind, I’ll name it after you.”

    “The Greg Goodman, …..”

    Leave it all at this Tamino, no more, its piss and wind and unworthy of your time.

    Thanks for your work, time and effort, I enjoy the site.
    Ronz

  19. Horatio Algeranon

    “Stabiliesation”
    – by Horatio Algeranon

    Arctic-ice is stabiliesed
    Temperature is decreased
    Sea-level rise is annulliesed
    Reality is deceased.