Let’s do the math!

Roger Pielke’s post which we criticized now has seven updates. Seven! He has protested, I would even say whined, that I and my readers have treated him unfairly. He has accused me of a lack of “professional courtesy” for such horrible deeds as blogging under a pseudonym. He even went to the trouble to dig up my real name and post my hometown location on his blog. How professionally courteous of you, Roger. That certainly advances our understanding of sea ice trends.

What he still hasn’t done is: the math.

Let’s be absolutely clear what Pielke’s post, and my criticism, are about. He’s trying to test the predictions of trends in northern hemisphere annual average sea ice extent from Vinnikov et al. (1999, Global Warming and Northern Hemisphere Sea Ice Extent, Science, 286, 1934-1937, doi:10.1126/science.286.5446.1934). Pielke claims that since 2006, the trend has “stopped and even reversed.”

Pielke didn’t even look at data for sea ice extent like Vinnikov et al., he only showed data for sea ice area, and he never looked at annual averages like Vinnikov et al., he only looked at daily data, and he never looked at raw area data he only looked at anomalies. None of that bothers me because Vinnikov et al. are interested in the trends, and the trends in anomaly are pretty much the same as those in annual averages, the trends in area are pretty much the same as those in extent. What does bother me is that Pielke saw fit to criticize a reader’s comment because the annual averages of the data Pielke used didn’t match the observations, or values for the GFDL model, plotted by Vinnikov et al. (who explicitly state that the estimates from the Hadley model are too low). Apparently he wasn’t even aware that he was averaging area and comparing that to extent, and for their absolute annual averages they tend to differ by about 2 million km^2. He’s aware of it now — but that seems to be the only mistake he’s willing to own up to.

Now Pielke suggests that I should analyze area data as well as extent data. I already did. Re-read the post and look at the 2nd and 3rd graphs. The 3rd is based on extent data from NSIDC, but the 2nd is based on area data from Cryosphere Today — the same data Pielke used.

Pielke has also protested that I’m ignoring Antarctic sea ice, and insists that I should analyze “insolation-weighted sea ice.” Why are you trying so hard to change the subject? Reminder: it’s about trends estimated by Vinnikov et al. 1999 of northern hemisphere annual average sea ice extent. Not Antarctica, not area, not insolation-weighted area, and not short-term trends anyway. Another reminder: you are the one who chose the subject. Considering that your claims have been shown false, even foolish, I guess we already know why you’re trying so hard to change the subject.

It’s very revealing that Pielke chooses to focus on the data since 2006. That’s a total of just a smidgen over 6 years of data. Yet he seems to want to compare recent short-term trends to those quoted in Vinnikov et al., for which the shortest time span having a reported trend was 16.8 years, and the computer model trends (which Pielke himself quotes for comparison purposes) are based on at least 21 years data. It’s the same old fake-skeptic trick we warned of, be especially wary of time spans that are too brief and areas that are too small.

The hilarious part is that even if you do allow this time span which is too brief, the trend is still squarely in the range given for recent trends by Vinnikov et al. I know because I already did the math. ROTFLMAO!

But let’s give Pielke credit for one thing. He did identify an interesting point in time related to Arctic sea ice extent. He utterly failed to realize that it’s not a “breakpoint” of the trend and certainly not a “stopped and even reversed” point of the trend, because he never bothered to do the math and find out what the trends are (in fact when we did it for him he refused to believe it).

It’s time to ignore Pielke altogether, because we actually are interested in what has been happening with Arctic sea ice. First let’s do as a reader suggested and compare observations to the model output reported in Vinnikov et al. 1999. Here’s Vinnikov’s graph, on which I’ve superimposed annual average extent from NSIDC data (in red):

I also put in a dashed line at 1999. Clearly, since then Arctic sea ice has declined more than expected according to Vinnikov et al. Quite a bit more. And although it shows up-and-down fluctuations on short time scales — just like the model output does! — there’s no sign of a stop, or reversal, of the trend. If you don’t believe me, do the math.

Nonetheless, something interesting happened around 2006. This is evident from the graph of anomalies:

The pattern of changes is different since that time. But is that a sign of a fundamental change in the trend? Not according to the math.

We can discover what it really means with a well-chosen wavelet analysis of the extent data (not anomalies but actual extent). Here’s the mean value according to that analysis:

No surprise there. We see short-term fluctuations — just like in the model output — but the trend continues downward. Now look at the plot of the amplitude (actually semi-amplitude) of the annual cycle (actually of the best-fit sinusoid to the annual cycle):

Bingo! That’s what really changed most recently (actually from about 2006 to 2008) — the amplitude of the annual cycle has increased by about 1 million km^2 (semi-amplitude increased by about 0.5 million km^2).

We can note the same thing by de-trending the data, then plotting each year on top of all the others, to compare the annual cycles apart from the trend. We’ll plot the cycles since 2006 in red:

Again we see that it’s the size of the annual cycle which changed.

This change is visible in the plot of anomalies because of the way anomalies are calculated. The usual way is to take each value and subtract the average value for the same time of year. For monthly data, for instance (and I’m using monthly extent data from NSIDC), we take each month’s value and subtract the average for that same month. That gives the anomaly plot already shown.

This has the effect of removing the average annual cycle from the data. But if the annual cycle changes, we won’t actually have subtracted the current annual cycle, we’ll have removed the average — and the difference between the current annual cycle and the long-term average annual cycle will remain. That’s why, after about 2006, the anomaly graph itself appears to show an annual cycle. We’re seeing the “leftover” annual cycle after removing its average.

There are ways to estimate a time-varying annual cycle, and remove that from the data, in order to compute anomaly values which take this effect into account. Here’s one example of anomalies computed this way:

We can plainly see what has happened to Arctic sea ice extent. There is a long-term decline — the trend — which continues, and which is faster now than it was just a few decades ago. There was an extreme dip in 2007, when the summer minimum reached record-low values. There was a “hiccup” after 2007, very much like the short-term fluctuations seen throughout the computer model results. And: there was a substantial increase in the size of the annual cycle.

Finally, what about testing the predictions of Vinnikov et al. 1999? Mostly the paper is about comparing computer model simulations to observed trends (using data available as of 1999). There’s actually very little discussion of prediction for future changes in Arctic sea ice extent. In fact, just about the only thing Vinnikov et al. say about that is this:

“Both models predict continued substantial sea ice extent and thickness decreases in the next century.”

That’s one computer model prediction which, so far at least, has been completely correct.

96 responses to “Let’s do the math!

  1. The science debate is interesting, but you might tone down the testosterone, FYI:


    [Response: Did he not accuse me of lack of professional courtesy specifically for blogging under a pseudonym?

    Did he not decide to post my name and hometown (not that I really care)? Is that not discourteous?

    Did he not write a post specifically to critique Vinnikov et al., then when it was criticized attempt to change the subject? Multiple times? Did he not accuse me of ignoring Antarctica? Did he not change the subject to sea ice area rather than extent, and “insolation-weighted area”? What do these have to do with the topic of his original post?

    Did he not explicitly state that the trend has “stopped and even reversed” — when he hadn’t even done the math?

    Did he not base his claim on only a bit more than six years of data? Are the model trends given in Vinnikov et al. not based on at least 21 year intervals? Is this not a case of Pielke choosing a time span which is too short? Is it not funny that even with his choice, the trend is still in the range from Vinnikov et al.?

    As for the “science debate,” there hasn’t been any. All we’ve seen is misrepresentation from Pielke, followed by misdirection in order to save face.]

  2. The only thing that surprises me is that you haven’t digressed to point out how silly his comments on Levitus et al. are.

  3. David Graves

    Went to Pielke the Elder’s re-re-re-re-re-re-revised post. Has taken his ball and gone home, he has–no new comments. So I will make this comment here rather than where it should be, on his blog. He insults Tamino over some non-existent hysteria about climate change in “Do the Math” because RPSr can’t be relied upon to think or analyze clearly and Tamino didn’t take his word for it. And A. Watts gets a tip of the cap? Yikes.

  4. He also requests that you do an insolation-weighted analysis: well, as I mentioned before, that’s pretty much been done: http://www.nature.com/ngeo/journal/v4/n3/full/ngeo1062.html

  5. Looks like P Sr. put some apendage or other into a dangerous piece of cognitive machinery and lost it. That deserves a vicarious ‘ouch’.

  6. Susan Anderson

    How many decades of more extremes does it take to agree we have more extremes?

  7. Susan Anderson

    There is an implied disrespect for the reader in the implication that they need to be told what to think about what someone – in this case Tamino – has said. When that characterization does not match the original, I would hope that the reader might notice the discrepancy and wonder where else they’ve been told what and how to think.

    This should be obvious but I’m afraid most people are conditioned to follow their leader of choice and not to trust their own ability to judge. This has been exploited and unfortunately leaves us with a population that appear unable or unwilling to develop and use their ability to think critically.

  8. Holy cow… i read your blogs often, Tamino, and i find them extremely informative! In fact, i have saved several to Word and shared them with some junior staff to instruct them on statistical analyses that are in line with some of the ground water monitoring statistics we often conduct.. I am not a climate scientist, however, i am an environmental engineer that specializes in landfill design and landfill gas recovery/energy conversion. I like to think i try to do my small part for the environment… and for generating non-fossil energy from landfill gas.

    i am responding because the comments seemed to start here based on “professional courtesy”… but i was stunned when i read from the RP Sr. blog the reference to your papers with Rahmstorf (2011) and with Annan, Schmidt, and Mann (2008)…

    … then he writes this:

    “His expertise clearly is in statistics, and he wants to apply this skill to climate analysis.

    He does have a quite good study published February 12 2012 titled

    Pine Beetle Infestation and Fire Risk in the Black Hills

    where he writes as part of his conclusion

    Surely, excessive rhetoric about the urgent fire danger posed by pine beetle infestation, sometimes to the point of hysteria, does not serve the public interest.

    [he should apply the same advice to his treatment of climate science]”


    So… what is he saying? the first two papers were written – i guess just written… as if Tamino is attempting to apply his statistics to climate science… and for some reason they don’t mean much… but the paper on fire risk due to Pine Beetle Infestation is actually a GOOD study because… it concluded there was no need for hysteria…?

    … does this imply the other two papers were NOT good because they… didn’t conclude there was no need for ‘hysteria’… ?

    … So are papers only good if they conclude what RP Sr. thinks they should? or wants them to?

    I am shocked because many years ago, i had RP Sr.’s website bookmarked… i used to frequent it often… with RealClimate and a few others… but the last few years… i no longer seem to understand what he’s talking about…

    • Gordon, I’ll make it worse: that pine beetle “study” was a blogpost. No offence meant to our host, but I still put blog posts a notch below actual scientific papers. So, Pielke Sr considers the papers irrelevant, and one blog post relevant. Why? Because he likes it conclusion, so much is clear.

      • Marco,

        Yeah, you’re absolutely right! I remember Tamino’s post… it was good… i guess i had assumed maybe he followed up with a real paper, but then of course, i should have noticed there are no such citations by RPSr and of course, it is very unlikely a real peer reviewed paper could have followed up from that post so quickly… those things take time… because you’ve got those other experts in the field reviewing and commenting (anonymously, by the way)… and revisions being made…

  9. Susan, your post reminds me of a great bumper sticker I saw not too long ago: Critical Thinking: The Other National Deficit! How ‘bout this….Let’s do the science and the math….with a very occasional local exception, glacial and sea ice are showing notable and persistent losses worldwide…. The temperature goes up; ice melts. It’s just one of the physical manifestations of a warming planet.

  10. Tamino,

    Thanks for this analysis. You know the differenc ebetween you and Pielke Senior is striking, you base your assertions following the analysis of the data, with the data guiding your claims and deductions. Pielke Senior on the other hand is in the unfortunate habit of making confident assertions before having even undertaken any qunatitative analysis. Worse still, when his errors are identified, he seems reluctant to back down and then delegates the analysis to others. Although, to his credit, seven updates later he seems to have taken some responsibility for his errors, so that is some progress. Unfortunately for Pielke though, his original gaffs and his propensity to speak first and analyze later won’t be forgotten by his fellow scientists.

    The amplified intra-seasonal cycle (i.e. difference between the minimum and maximum sea ice extent) since circa 2006 is interesting, but not unexpected. That it started before 2007 is telling (that reminds me, I distinctly remember when the new record low minimum was announced in late 2005), because modelling studies and theory suggested that the greatest loss was expected to occur during the summer months, while the greatest impact on the Arctic atmosphere would be felt in the fall and winter. This results in an amplified intra-seasonal cycle, and is thought to be primarily in response to a systematic thinning of the ice that started in the late eighties (e.g., Lindsay et al. 2009).

    But here is the key part, the amplified intra-seasonal cycle since 2006 or so, rather than being an indicator that the ice loss is has stabilized or reversed (as Pielke Senior appears to be suggesting) is in fact evidence that the Arctic ice is in a very fragile state on account of contiued thinning, positive feedbacks and a non-montonic decrease in summer extent. So in short, it is bad news.

  11. I got the Arctic area data from here:


    and get somewhat different results for an evolving trend than yours in the previous post (mine show a low at 2005, with 2006 and 2007 being slightly and progressively stronger in trend), but what I do notice from the absolute data is that (1) a parabolic fit since 1979 shows 2011 as being lower than the curve, (2) 2011 has the lowest area (this is without December data in, but the last time December area was as high as the current 2011 average was 2000), and (3) I do not see any sort of “reversal” in trend at any time period, nor one that continues past the 2005/2007 hiccup, nor one that seems to be outside of the range given by Vinnikov et al 1999 (all are either -500,000 km^2/yr or stronger).

    All values are clearly outside of (are stronger than) the model’s predictive bounds you gave on your previous post, though I don’t understand the discrepancy in the magnitudes of our numbers.

    I note how in Pielke’s most recent post, he’s now trying to suggest that it’s not that the sea ice is deviating from the model trend from the paper, but from its previous physical trend… I think? It’s a very serious goalpost shift if so, claiming that the trend in sea ice is no longer following an extremely fast fall is not the same as claiming it’s no longer following a more conservative prediction of rate of fall (and very different from the claim that such a trend is reversed). That’s what I garner he’s saying from how he links to Zach’s post. The former is false anyway.

    I’m not sure what other analysis Pielke is expecting though. He’s asking for the same analysis to be applied to area, though you provided that in the original post. It’s not like much more is needed besides such a graph as you provided or I provided here, the point is made clearly in it.

    • Ugh, I hate it when I make such goofs in writing – my previous might make more sense if changed to (emph. at change):

      “…nor one that seems to be **weaker** than the range given by Vinnikov et al 1999 (all are either -500,000 km^2/yr or stronger).

      All values are clearly outside of (are stronger than) the model’s predictive bounds you gave on your previous post…”

    • “I note how in Pielke’s most recent post, he’s now trying to suggest that it’s not that the sea ice is deviating from the model trend from the paper, but from its previous physical trend… I think?”

      I think his point, circa the 2nd or 3rd revision, was that the model shows a monotonically decreasing trend, which he sees as consistent with the ice anomaly through 2006, but not afterwards. A basic problem there is reading the polynomial fit as the model prediction, which must be what he’s doing as those are the only monotonically deceasing curves in his original post.

      Tamino’s shown that the only significant change is in noise amplitude of the annual anomaly. The point of my post was that Pielke didn’t make sense even in the eyecrometer sense if you plot both of his images on the same scale. First, the decline 2000-2006 is more remarkable than any apparent stall. Second, stalls, reversals etc of larger magnitude occur throughout the modeled and experimental records.

      • I was somewhat confused by his reference to your post Zach, it has seemed as though he thought you were supporting his point, but your post by itself didn’t inflect that. Thanks for the clarification.

  12. Roger, it’s kind of odd that I have to post here to have you read my comment, but whatever. I must say that your focus on “outing” Tamino looks pretty childish. Just about everybody who follows climate science online knows who he is and what he has published.

  13. Pielke is a gentleman, he conducts himself professionally and politely, he is open to changing his mind in the light of evidence. His blog is generally moderate and even handed. You do not have to agree with all he posts to find it a valuable and informative contribution to the subject. To visit the personal attacks on him that have been appearing on these threads only discredits those who make them.

    He may have made errors in his posts, but that is no excuse for taking a vituperative tone and indulging in speculation about his motives. Simply engage in a calm and factual discussion. I have to say that when a man like this declines to post his comments on your blog because of the chorus of irrelevant abuse which he knows and can see he will encounter, you are failing. WUWT is rightly criticised sometimes for the stridency of comments. You and your commenters are, regrettably, falling into the same trap, and thereby devaluing the contribution which your expertise would permit you to make. It is shooting yourselves in the foot.

    [Response: You are mistaken.

    When Pielke looks at a graph, sees what he *wants* to see, does zero analysis to confirm or deny or even to understand it, then uses that conclusion rooted in nothing but his inherent bias to throw mud on the work of other scientists (i.e., climate modelers), that’s a helluva long way from “gentleman.” At the very least it’s culpably incompetent, and it’s flirting with downright unethical. And … this is hardly an isolated incident.

    Digging up personal information to “out” someone is the opposite of gentlemanly behavior. It’s truly nasty, mean-spiritied behavior, at *best* the act of a petulant child.

    As for being “open to changing his mind,” bullshit. Getting him to admit error was worse than pulling teeth — how many updates did he post trying to resist the truth? He had to be dragged kicking and screaming, and in my opinion, in the end he only admitted error because it was so stinking obvious even Anthony Watts could see it. Also my opinion: he’s not the least bit sorry he jumped to mistaken conclusions to denigrate climate model results, he’s just sorry he got caught.

    Maybe what’s most irritating is how often and how desperately he kept trying to *change the subject* when faced with his mistakes. That’s just dishonesty, especially when *he* is the one who defined what the subject was in the first place.

    While he’s distorting the truth as a matter of course and of habit, it’s true that he does in fact use only polite language. That hardly makes a “gentleman.” One may smile, and smile, and be a villain still.]

    • Golly, it was a whole week from his erroneous post to the correction. Academic pi$$ing matches almost never are so quickly resolved. Tamino, you did fine work pointing out the fallacious nature of his reasoning, unimpeachable I’d venture. But please chill out a bit. Pielke may be stubborn, but a “villain”? That kind of talk just makes you look bad. As one of the scientific fathers of three-dimensional computer models of the atmosphere and a H-index off the charts, I think he has earned the right to offer whatever critiques he’d like. As his correction shows, he will accept when wrong. So, please, stick to the data.

      [Response: The fact that he admitted mistakes within a week had nothing to do with Pielke’s willingness to consider new evidence or his being a “nice guy.” It had everything to do with the fact that he was so abysmally wrong. If he had claimed that 2+2=5, then took an entire week to admit error — all the while trying desperately to change the subject in an act of outright intellectual dishonesty — he is hardly deserving of praise or of sympathy.]

      • Just to clarify a small point–when Tamino wrote that one may “smile and smile and be a villain still,” he was making a literary allusion–Act I, Scene 5 of Hamlet, to be precise:


        You can read that as calling Dr. Pielke a villain, but considering the context, a more likely interpretation (IMO–of course, Tamino can speak for himself) would be 1) that manners and intent need not be congruent in general, and 2) they are not so in the particular case at hand.

        [Response: You are correct.]

    • Tamino, you have won the ‘science’ debate by numbers and facts. Don’t be baited by concern trolls into a debate about manners.

    • Pielke is a gentleman, he conducts himself professionally and politely, he is open to changing his mind in the light of evidence.

      Having watched his performance over at SkS a few months back, this isn’t even close to true.

      And if he’s open-minded, why doesn’t he allow people to post responses to his blog?

    • The fact that you’d call someone who “outs” an anonymous poster a “gentleman” says all we need to know about you, Michel.

    • Susan Anderson

      I find this puzzling. I read both the Pielke and Tamino posts, and I found more ungentlemanly language in the former. The attack dog mentality, while perhaps couched in courteous language, was apparent in the unremitting criticism and the mischaracterization of what was going on.

      You have to be biased to get this from the material itself. Try reading both articles again and try again comparing the language. While there is a whole lot more science in Tamino’s, to my eye there’s a lot more attack in Pielke’s.

  14. Hell, you can even use the old iometer to see that
    Second, the first year ice area jumps about until the big melt of 2007, after which it takes a big jump. Makes sense, the old ice melted out, and usually the Arctic pretty much freezes over every winter. This winter may be different because the western end of the Arctic was pretty ice free this year.

    • Hey, I can even see this on my garden pond. Last year it grew to ~7inches thick, hung around for a month and then slowly melted over a week or so as the air temperature rose. This last year it all froze up to half an inch and then melted, no less than three times over the winter. So from this I deduce that the thinner the ice, the more variation in ice extent will be occasioned.

  15. I have been aware of the growing amplitude for some time. I think there are solid grounds for expecting this and perhaps it should get more analysis esp in volume terms. There are two competing feedbacks: In summer albedo feedback dominates, in winter thinner ice means more heat can be lost and more ice forms. The best case scenario is for the negative feedback to mean complete recovery of ice volume because if it gets that far the reason for faster ice growth disappears. While there is thick MYI still disappearing, this negative feedback hasn’t fully kicked in yet.

    Meanwhile on the melt side, with less MYI and more albedo feedback, the volume melted each year is likely to go up. Here is piomas data graphed:

    If a cautious extrapolation of the melt volume crosses the maximum volume, then this would seem to me to give a good cautious estimate of when we will get a few days of practically ice free arctic. It doesn’t look like there is enough of a period of growth to sensibly extrapolate the melt volume yet. Do these musings make sense?

  16. To ne, the Arctic sea ice extent/area calculations are a bit like counting the averaged Wolf Sunspot Number (or WSN anomaly over it’s ~11 year cycle (note the 11-year Sunspot cycle is nowhere’s nearly as cyclic as Earth’s annual seasonal cycle given the known periodicity of the Earth’s rotation about the Sun, but the basic point still stands, a sum of 11 or 12 or 13 zeros is only ever going to be never less than zero even though TSI may continue on it’s downward long term averaged path)).

    And since 2007 we are beginning to see the effects of adding zero’s (if you consider the core ice area to be ~3M km^2) to that calculation.

    So that at some point the North Pole becomes ice free, first for a day, then a few days, then perhaps for a month. or somesuch. Then (or in the meantime) the ~3M km^2 core ice field (area) also begins to shrink.

    The winter season then returns and we are back to say ~14M km^2 or ~15M km^2. Somehow, don’t ask me how, but somehow I think the Arctic winter ice field will always be there. Assuming this to be true, and the 1st year ice reaches an average thickness of say 1-2 m thick, then we will always return to an Arctic ice volume of say 20M km^3. That this is so is suggested in your next to last plot of the annual averaged detrended cycles, as the springtime ice extents (red lines) are running above the black lines (again this has to be so given the defined metric, lower minima are offset by higher (actually broader springtime) maxima.

    Anyways, at some point Arctic sea ice extent/area becomes somewhat meaningless. By that, I mean that at some point in the near-to-imtermediate future there will be an inflection point in the long term trends of extent/area/volume, and the limiting case is an asymptotic trendline to zero. This has to be so given the defined metric (be it extent/area/volume), as it can never go below zero.

    Have we reached that inflection point yet? I don’t think so given your presentation. But at some point we will hit that long term inflection point, as its defined by the very metric itself.

  17. What can you say?
    The adjective that surely must be appended to Pielke Sr is “untrustworthy,” or perhaps qualified more precisely as “entirely untrustworthy.” How else can you characterise this nonsense he writes?

    In his eighth update/correction (see link @ first comment in thread), he says he “made several methodological errors “ (although they are not described) & “did not properly explain my perspective on the analysis I presented. “ This was (i) Not to explain clearly why 2006 was chosen as a start year for his “analysis”. (ii) Why such a short period 2006-2011 was chosen as useful for this “analysis.” (iii) Why he is comparing Area anomalies with Extent anomalies.
    His answers? – (i) 2006 because he’d used it previously on Ocean Heat Content ‘trend’ analysis & the graph visually appeared to change after this date. (ii) If the long term trend changes, you have to look over less than the long term to spot it. (iii) “This was my more serious mistake,” he says because he simply assumed it would make no odds but he is now convinced otherwise by Tamino & Dana81 (although he cannot resist an obfuscating “although” to save a bit of face).

    All three answers are entirely worthless. Pielke Sr did no “analysis.” He just cherry-picked the latest extent/area anomaly and said that the long-term extent/area trend thus “has stopped and even reversed.“He wasn’t even fagged to plot the data on the same graph. So there was no “chosen start date” of a “relatively short time (period)” because there was no actual “analysis”.
    As for his admission of a serious mistake, what mistake? It doesn’t matter whether you use Area or Extent, the decline continues apace. There is certainly no significant divergence between the two. (See graph linked below.) And it is was a commenter Ned that pointed to the difference use of Extent/Area, not Tamino or Dana81.

    Pielke Sr is simply carrying out mass murder of straw men! How can anyone place any trust in anything he says? He has become entirely untrustworthy!

    Extent/area graph two clicks down here.

  18. Pielke Sr: In examing the Vinnikov et al 1999 paper, I did not explain that my use of their trend values to state that short term assessments have value for quantities which involve inertia (mass) such as heat and ice. If the sea ice area were to recover to its original area and thickness (for whatever reason), for example, it does not matter what its long term trend was. The long term trend (if there is one) would be reset. I have made this point often with respect to ocean heat content (e.g. see). It also applies to sea ice (although area is only one part of it).

    It’s unfortunate that Pielke does not maintain an open blog. I am curious as to why he believes that sea ice contains significant inertia. Whatever inertia there is, would be in multiyear ice. MYI is discussed in Maslanik 2011 and here</a<

    • Thanks for that, Ron.
      Pielke Sr: “If the sea ice area were to recover to its original area and thickness (for whatever reason), for example, it does not matter what its long term trend was. The long term trend (if there is one) would be reset.”

      Oh really? What an interesting world Roger lives in where trends can be reset by outliers and noise.

    • I also want to follow up on this. Roger, this seems rather odd. You say “if” sea ice area were to recover …” But for how long? A year, two years, a decade? It seems to me it will take many years of such a recovery to have an impact on the long term trend. It also seems you will take every opportunity to claim there is no trend … but surely you now realize the science is not on your side.

      Then you go on to state something odd: “Trend analysis, as being interpreted by Grant Foster and dana1981 is fundamentally an assumption that there is an overarching control on the long time period.”

      An assumption? I thought the analysis is evidence of a trend, not an assumption there is one.

    • I think I understand Pielke’s perspective a little bit better. Imagine the arctic ice as an initial value problem described by a system of equations where ice extent, area, and thickness are the initial values. Anytime those value ‘reset’ to their initial condition, you have essentially reset your system of equations to time ‘0’.

      But of course, there are a host of other variables that are in play. Ocean heat content, distribution and currents, salinity, insolation, atmospheric aerosols, black carbon, and GHG, and an evolving interplay between tropic and arctic air masses in a warming atmosphere.

      I’m not sure this perspective is entirely correct, because it doesn’t really speak to his ‘inertia’ comment, which implies a certain amount of memory in the system. Indeed, the ‘reset trend’ and ‘inertia’ comments seem somewhat in opposition.

      • Just read Post #2 / Update #1. I think that confirms the IVP viewpoint. I don’t think he is using the term inertia the way that I think of it – he is just pointing out that ice mass stores energy and requires energy to melt. Increased ice volume acts as a damp on melt – seasonal and multiyear. My point that the sea ice system is more than just ice parameters + insolation stands: it takes more than just returning ice extent/area/volume to a previous state to ‘reset’ the system.

    • “The trend would be reset” ???
      No, that’s not how it works.

      It’s like saying, “our team is losing 6-0″, but if we were to score 7 quick goals, we would win!”
      Pielke is no different of all other denialists who claim that the current warming (in this case, melting) doesn’t matter, because they are *convinced* a big cooling is just about to begin, so it will all balance out in the end…

    • “If the sea ice area were to recover to its original area and thickness (for whatever reason), for example, it does not matter what its long term trend was. The long term trend (if there is one) would be reset. ”

      This assertion implies two assumptions.

      The first is that the physics of ice melt are unaffected by the previous history of the ice, which to first order are true; it doesn’t make any difference in how many calories the ice takes to melt whether it accumulated over a hundred years or was frozen yesterday. There are second order effects, important for short term sea ice dynamics – how porous the ice is, how much brine it contains, and how its thickness effects its interaction with the weather(wind, rain) – but these mostly create short term noise which is removed by analyzing long term trends.

      The second implication is that the AGW forcing starting in 1980, which is providing the energy to melt more ice to lower minimum annual volumes(on average – it’s a noisy system), is the same as the forcing starting today. This is wishful thinking on Pielke’s part. Around 1980, there was more average annual NH snow cover, higher albedo, and less forcing than today – and Arrhenius knew this would happen. Atmospheric CO2 was ~330ppmv; today it’s ~390ppmv, and rising more quickly. If the Starship Enterprise were to wormhole its’ way back from the future to today, and use the transporter to move ice from Greenland into the Arctic, duplicating the area and thickness of 1980, the longterm trend would be faster going forward than it was from 1980 – because the forcing has increased, and will continue to increase.

      There is no doubt that there is a long term trend, and that AGW forcing is increasing.

      [Response: Captain, the additional climate forcing due to increased greenhouse gases will rapidly eliminate the transported ice, and will raise sea level because it originated as land-based ice. Changing to an energy technology which does not make the problem worse is simply logical.

      But HOW, Mr. Spock — HOW — CAN WE GET THEM — TO REALIZE — that it’s their own technology — that’s creating — the problem? Bones?

      Dammit, Jim, I’m a doctor, not a climate scientist!]

      • Scottie! Can you get the replicator to recreate the aliens’ transformer weapon? Yes, Captain! Just give me a couple of hours! Good! Then we could use it to transform the Republicans’ brains for the next six months — that might work!

      • SCOTTY: “Captain, the sea-ice…she’s breaking up… We need more di-Hydrogen crystals.”

    • Dr. Pielke: – “If the sea ice area were to recover to its original area and thickness (for whatever reason), for example, it does not matter what its long term trend was.”

      If there was a reset to previous conditions, yes, the long term trend would be gone.

      Of course, that includes ice volume (long since dropped from mid-20th century averages), multi-year ice (very little left), air temperature (check any/all of the temperature records), and very significantly, ocean heat content (one of Pielkes favorite alternatives to the surface temperature record, see Levitus et al. [2012] for increasing OHC over the last 50 years).

      If all of these were to go back to previous conditions, any long term trend would be irrelevant. But they have not, so Dr. Pielke’s assertions are simply nonsense – we have to deal with the world as we find it, not as we wish it would be!

  19. Would it be of use, or even possible, to look at what appears to be an increasing volatility (variance?) in the 3-day running averages? I am sure I am not expressing myself correctly, but I am trying to say that over the last few years the NSIDC curves, for example, seem to be increasingly less smooth. I think five years ago they were using a 3- or 5-day running average during the winter months, then switching to daily during the melt season — can’t be sure my memory is correct.

    • Don’t know what NSIDC is doing today, but the previous two seasons were, in fact, 5-day centered moving averages (I have digitized their melt season data from the previous two seasons, in doing so, I found that the most recent two days worth of data are adjusted as the 5-day centered moving average progresses). Meaning that two days ago has 5 days of data, one days ago has only 4 days of data, and today’s has only the most recent 3 day average.

      So if there now appears to be more “volitility” and NSIDC is currently using a 3-day centered moving average (It would appear to be the case as I believe they now state something to the effect of one day behind the current graph date (meaning a 3-day centered moving average using the current date, yesterday and the day before yesterday).

      At one time, I could have told you the amount of averaging applied to all 6 of the most common Arctic sea ice extent/area time series, and their definitions of extent. But it’s been awhile.

      • The NSIDC ‘melt-season’ graphs continue(1) to be smoothed using a 5-day rolling average. However, while they used to plot today’s/yesterday’s value by predicting tomorrow’s/&-the-next’s value, they just plot a ‘trailing average’ two days behind. See this link for an animated example of the change:-

        (1) There is some ambiguity about this very recent change in NSIDC methods as their website also mentions 9-day trailing averages.

        This 5-day smoothing has no bearing on the “volatility” of recent years which is present in the monthly data.

      • They just switched to a five-day trailing average:


        Also, the climatology used to be 9-day, so that curve is now more ‘jagged.’

      • So I think that clears up some confusion I had with respect to NSIDC’s use of climatology and their daily extent time series.

        In the past what NSIDC reported as the seasonal minimum was based on the 9-day climatology versus the 5-day average seen in their daily extent time series. But the 9-day climatology is nowhere to be seen (unless, of course, it’s used to define their monthly time series (but again the 9-day climatology time series itself is nowhere to be seen AFAIK)).

        Again, I know this from working on the previous two seasons of melt data, what NSIDC reports as the seasonal minimum does not agree with their own daily extent time series (And yes, I have all the daily extent time series graphs from those two previous melt seasons, which show that what NSIDC reports as the minima is somewhat higher than the minima seen on their daily extent time series plot, which I attribute to the difference between a 9-day vs 5-day averaging.)

        Also, the current 5-day trailing average is exactly the same as their previous 5-day centered average, just shifted to the right by two days (ignoring the most recent two days of extrapolation as shown in their previous daily extent time series).

        And thus, a very minor complaint I have had with the NSIDC daily extent time series. That very minor complaint being, could I download the gridded time series data and faithfully reconstruct the exact same underlying daily (or one day average) extent time series that NSIDC uses to produce the 5-day and 9-day time series? Remember this is across several satellites and differing grid densities (or so I would I assume, as we do know that the pole hole has a step change). And even the gridded data may have infilling of grid cells from prior/subsequent days (or might be reported as -999999 or somesuch).

        I’ve come to the conclusion that NSIDC does not release the actuals (the one day time series as constructed from the daily gridded time series) for one basic reason, they don’t want to appear to be somewhat subjective in their analysis of the daily gridded time series data (you know IF THAN statements in the code itself and what not).

        But just to be clear though, I don’t think the underlying algorithims would have much (if any) of an affect on the monthly and annual time series data themselves (assuming that a 9-day climatology is used throughout).

        [Response: My guess is that they don’t publish the daily gridded data because it takes work to do so, and to keep it updated, and they don’t have that work in their budget. If they did, it would generate more work as people ask for changes/revisions/etc. You could write to them and ask.]

  20. Ron, you could make the argument that there is significant hysteresis, but as you say inertia????

  21. Michel,
    A gentleman accepts correction graciously and admits he was wrong. He would have no need of mobile goalposts and continual prevarication. Such behavior is not only ungentlemanly, but unscientific. The most important thing about science is that it is definite–it is either right or it is wrong. If it is right, we can build upon it. If it is wrong, we can correct it, verify it and then build upon it. If instead we have a continually shifting position never clearly expressed, then what we have is bullshit. Bullshit is “not even wrong”. It allows no progress.

    When was the last time you read something truly illuminating on either Pielke’s or Aunt Judy’s blogs? When was the last time you came away saying, “Oh, so that’s how that works!?”

    Unfortunately, debates between science and antiscience always end up that way. Science has all the real evidence. All antiscience has is obfuscation and misanalysis of the evidence (e.g. analyzing a 6-year “trend”). Like it or not, Roger the Dodger is now firmly on the anti-science side.

  22. I gave up years ago when RP Sr flapped his hands about glacier mass loss, and I asked him to tell us what would satisfy him about glacier mass loss – he refused to answer, and some of my follow-up comments even got “lost” in moderation.



  23. Susan Anderson

    It came to me in the night what’s going on here. Apparently it is rude to criticize the science but not rude to criticize the person doing the science. In addition, the blog owner appears to be held responsible for what commenters say on the “side” disliked by the criticizer.

    Some people appear to have a small degree of confusion: there are two Dr. PIelkes, Sr. and Jr.

    Given the polarizability of the conversation, perhaps some commenters should modify their irritability. While completely natural, it is all too easy for people to take advantage of expressions of annoyance at all the repeated bafflegab going around.

    On ice, and other trends for that matter, I was thinking about my tendency to talk about weather over a relatively short period while keeping in my mind living historical experience (in my case, a bit under 60 years since I started being able to notice and remember, but there is my family as well) and being well aware of the difference between trends and incidents. The timeline is really in centuries – mostly the two for which we have somewhat and increasingly consistent records – and the horizontal grid markers are more like decades. That 200 years has a noticeable upward trend, with dips of more than a decade which do not alter the trend. When we talk about 10 years, 12 years, 15 years, or 30 years, we are thinking of them relative to the continuous trend. Naysayers will grab these amounts and take them out of context – hence the nonsense about making the old high the new low in 1998, or the fuss and mid-20th century dips, for example. If they will keep in mind the time is continuous, no matter how you measure it, they will get a better picture.

    On ice recovery, it happens every year. This should not be a counter in some weird game. As far as I’ve been able to learn from science and experience, the issue now is that this recovery is bigger every year and more durable ice is much more gone than area or extent.

    If you were cooling a drink, you would not shave an ice cube to a semblance of two dimensions. The cooling power and durability of the cube has to do with its volume.

  24. Pielke Sr now has another update, this time fronting the second post he made on this subject.
    He now features a graph of Ice Area/Extent Rolling Annual Averages by ‘yours truly’ which he describes as “very informative” (although he was less happy with my comment accompanying the link to the graph in the thread above. It was taken as insult although I am unapologetic. If a commentator continually writes fallacy, their comments are thus “entirely untrustworthy”. How can it be otherwise?)
    He writes that the graph confirms “a visual change in the character of the slope in ~2006” but he has been convinced that statistically 2006-to-date “is too short a time to determine if there is a real change in the character of Arctic sea ice decline.”
    (This second-hand reporting is daft. I do wonder if just cutting & pasting Pielke Sr’s Updates straight across here would be the thing to do.)

    So concerning Sea Ice decline, is this 2006/7 wobble are irrelevant as say the 1996/7 wobble? The anomaly certainly flaps around more after 2007, just as it flapped around more prior to 1996 (although less markedly so) although the decline in area/extent continues regardless.

    • Al,

      I think what we are seeing over these past five seasons, is somewhat related to my core ice field conjecture (which I mentioned above in a previous post). That being, that these past five seasons we are beginning to see erosion of the ~3M km^2 core ice field located directly above the Canadian Archipelago. The thicker, and much more likely to be, MYI.

      I think I’ll constuct the anomaly plot using a baseline of say 2006 (or 2007) to present (using either the UIUC daily area or NSIDC monthly extent time series). Not much of an anomaly period, I know, but it does shift the burden from the 2007-2011 era to earlier years. How that affects the “look” of the anomaly time deries, well, I don’t know.

      Or we could just go with Tamino’s last graphic as shown above.

      • EFS_Junior
        I’m not entirely surprised by the summer minimum extents given what’s happening temperature-wise up in the Arctic. Core ice or core Arctic, the warming is reaching into it.
        It’s the recent higher winter maximum extents that seems to need an explanation. Arctic winter air temperatures are higher than pre-2007. Ditto Arctic winter SST with the exception of 2004/5 (although 2011/2 looks to be a match to it & still has high extent.). Perhaps I should start graphing Bering Sea temperatures, it being outside the Arctic but inside the winter freeze. But I’m not sure I can fit it onto my graph of…. (Fingers crossed. I’m trying to link using HTML as the URL on these google images are longer than Friday!) ….Arctic SST anomalies.

  25. As an aside, GFDL R15 (circa 1990-1999) has left little trace of itself outside of some papers and IPCC modeling data. At first glance, I do not see any sea ice data files for SAR for this model. And in TAR, there seems to be a mix of references to GFDL R15 and R30, but the R15 references are seem to be only in text and the R30 references are in the model output tables leading me to believe that R30 may have come in a bit late but still in time to displace R15 for TAR modeling.

    “Transient responses of a coupled ocean–atmosphere model to gradual changes of atmospheric CO2”
    Manabe, Stouffer, Spelman, Bryan 1991

    If anyone has any pointers to the GFDL R15 source code, I would love a reference and a chance to examine the code.

  26. Brief history. The GFDL R15 atm model has origins in the 1970s

    Click to access petageo.pdf

    A comparison of GFDL R15 to R30
    A comparison of climate change simulations produced by two
    GFDL coupled climate models
    , Dixon, et al, 2002

    Click to access kd0301.pdf

  27. It seems that Pielke Sr. may be past his sell by date. In his post on Arctic Sea Ice trend, he seems to be unaware of some of the most important data relevant to his post, that is easily available to anyone who is interestsd. He claims:

    “In examing the Vinnikov et al 1999 paper, I did not explain that my use of their trend values to state that short term assessments have value for quantities which involve inertia (mass) such as heat and ice. If the sea ice area were to recover to its original area and thickness (for whatever reason), for example, it does not matter what its long term trend was. The long term trend (if there is one) would be reset. I have made this point often with respect to ocean heat content (e.g. see). It also applies to sea ice (although area is only one part of it).”

    The problem is that there is no evidence of any recovery in the mass of the ice in the data the we have, and in fact the mass of the sea ice has been decreasing much faster than the extent.


    Here is yet another foolish point that he makes that requires a retraction and an apology to his readers. It is sad that he is ruining his reputation as a scientist in this way.

    • Well, apart from the fact that Dr. Pielke’s first sentence is far from clear, his point appears to be incorrect if Tietsche et al (2011) may be trusted as a guide. The scenario Pielke describes is essentially the inverse of theirs: they virtually “erased” the sea ice, only to find that what they describe as “an equally rapid temporary recovery.” Since this implies that the albedo effect and other feedbacks in their models were not enough to make an ice-free July a true ‘tipping point,’ some rather liked this study. (The ice abruptly disappeared on July 1 in their model experiments, IIRC.)

      As Tietsche et al put it in their introduction:

      “This suggests that Arctic sea ice has a preferred equilibrium state that varies smoothly with the climatic forcing, and that there are
      recovery mechanisms that counteract the destabilizing ice–albedo effect after abrupt losses.

      But WRT to Dr. Pielke’s comment, Tietsche suggests–it does not imply!–that likely not only the trend would not be reset, the extent/area itself would not be reset for very long. That is, 1) the trend following the reset would evince accelerated extent/area loss, and 2) the extent area would relatively rapidly drop to pre-‘reset’ levels, at which point the trend would revert to previously observed rates.

      To be sure, I’m hand-waving here; it’s an assumption that the Tietsche model with its “preferred equilibrium state” works symmetrically (if at all.) But does the inverse suggestion have even that much support in the literature? If not, then why is it stated as if it were a fact?

  28. Were I writing for Pielke, I’d use the yearly rebounding of sea ice to posit a ceiling in the amount of energy due to albedo change. And leave it at that.
    With a good bit of the Arctic refreezing every winter, absent horrific warming, there will be a limit to the albedo effect.

    You can’t hide the facts, but you can bury the lede.

    • “With a good bit of the Arctic refreezing every winter, absent horrific warming, there will be a limit to the albedo effect.”

      Perhaps. But I think there is some modeling reason to think that a perenially ice-free Arctic Ocean is quite possible, difficult to imagine though that is from today’s perspective. (It wouldn’t be perfectly ice-free; it would be rather as the North Atlantic is ice-free today–mostly, but not completely.)

      If I get a chance later, I’ll see if I can retrieve something that looked at this.

  29. “…when sea ice covers the Arctic Ocean during fewer months of the year, the state of the Arctic becomes less stable and more susceptible to
    destabilization by the ice–albedo feedback. In a warming climate,
    as discussed above, this causes irreversible threshold behavior
    during the potential distant loss of winter ice, but not during the
    more imminent possible loss of summer (September) ice.

    “The relevance of any basic theory to the actual future evolution
    of the complex climate system must be carefully qualified.
    Because the time scale associated with the sea-ice response to a
    change in forcing may be decadal, and the time scale associated
    with increasing greenhouse gas concentrations may be similar,
    the system may not be operating close to a steady-state. In the
    gradual approach to steady-state under a continual change in
    forcing, the difference between a region of the steady-state
    solution with increased sensitivity to the forcing and an actual
    discontinuous bifurcation threshold (as in Fig. 3) could be
    difficult to discern. If greenhouse gas concentrations were
    reduced after crossing a bifurcation threshold, however, the
    possible irreversibility of the trajectory would certainly be expected
    to be relevant.”

    (Eisenman & Wettlaufer, 2009)

    Click to access 28.full.pdf

    But it might take as much as a quadrupling of CO2.

  30. Maybe all this talk of arctic ice melt should be put into a perspective of archealogical and historical sense. It would seem that during the last glacial period people lived in the arctic as recent finds have found, it would appear that the arctic has much less ice in a glacial period.

    [Response: No. It doesn’t.]

    If what you are saying about the trends in the arctic ice are true this portends the start of our next glacial period with all the problems it can bring to North America , Europe and northern Asia.

    I hope what you are putting forward is not true as the reverse of global warming is what it signifies.

    • Susan Anderson

      Wayne Jobs,

      If you have already done so, my apologies in advance. But it looks to me like you have not carefully read the article and the comments above. Several of these people have expended much effort to understand the subject matter, and are providing references to us and to each other about the state of knowledge.

      I suggest you look carefully at the more informed information above, and consider holding back on promoting some vague information that has been traveling around the internet, whether or not it fits what you want to believe. Unfortunately, the internet is an amplifier for information that fails to address the real state of things and this stuff about history is vague at best, and a lot of it simply wrong. These guys, on the other hand, are the real deal.

      A little exploration will leave you with a much better idea of how things work. If you have a standard question, SkepticalScience has made a job of collating the facts and is a goodish place to start.

      I am not a scientist so when the discussion gets technical I have to skip a bit or move on, but the drift is readily available for someone with an open mind and a willingness to think and learn.

    • @ Wayne Job

      “it would appear that the arctic has much less ice in a glacial period”

      Actually, the Arctic has less ice in an inter-glacial period, such as we are in now. The current level of ice in the Arctic is the lowest in historical times (Per Kinnard et al 2011, discussed here). A good synopsis of current conditions in context is Stroeve et al 2012.

      “this portends the start of our next glacial period with all the problems”

      Umm, not so much. This has been looked at before by climate scientists. Per Tzedakis et al 2012, “glacial inception would require CO2 concentrations below preindustrial levels of 280 ppmv” (for reference, we are at about 395 right now…and climbing). Earlier, Tyrrell et al 2007 examined this, concluding that we have already skipped the next glacial epoch. Furthermore, Tyrrell concludes that if we continue our present fossil fuel consumption, we will skip the next 5 glacial epochs. So no glacial epochs the next million years…

      Sleep well on the cold-that’s-not-coming. The climate changes wrought by the heat on its way…yeah, that’s worth losing sleep over.

      • For the interested, Steve Brown took a 5-part look at the last interglacial prior to this one. Part 5 is here, with links to the previous installments in the series.

  31. Horatio Algeranon

    First posted to the wrong thread…

    “Lord of the Updates”
    – by Horatio Algeranon (with some help from JRR Tolkien)

    Two Updates for the Jester’s on the net,
    Two for the Denier-lords in the Halls of Congress,
    One for the Public in their ways set,
    One for the Blogger Lord that you can guess
    In the Land of Shortrends where the statistics lie.

    One Update to rule them all, One Update to find them,
    One Update to bring them all and in the confusion bind them
    In the Land of Shortrends where the statistics lie.

    • Susan Anderson

      chortle, etc. … thanks.

      Why do we all keep thinking of mythical monsters, particularly from Tolkein? (question, rhetorical, frustrated realists for the time wasting of)

      • Susan Anderson

        and, darn it, why can’t a proof and spell. That’s Tolkien

        (and earlier, Job not Jobs)

      • Holly Stick

        Because certain people keep Tolkien through their hats? Snicker, snort!

      • Susan Anderson

        Holly Stick:

        and the mome raths* outgrabe … (nice pix and related information here)
        (“a rath is a sort of green pig” god’s teeth!)

        The Jabberwock might be useful with bafflegab.

        Apologies to anyone offended by for the extended limb – but what is a body to do, when to not laugh is to cry. It’s a backhanded tribute to wonderful Algeranon.

      • Holly Stick

        Ha! I just realized that must be where half of green eggs and ham comes from! Isn’t literature wonderful? I guess Horatio’s creativity is catching.

      • Horatio Algeranon

        Tolkien through your hat is bad enough, but some people seem to have a preference for Tolkien through their orcs.

        …and Horatio wrote about the Jabberblogger here

      • Susan Anderson

        Thanks Horatio. I spent a pleasant time over there. Very enjoyable interlude.

  32. My, Wayne, you’re making the rounds today, first blaming the “perambulations around our galaxy” at RC (I’m surprised it wasn’t Bore Holed) and now here with talk about an impending ice age return. You might want to look up the Milankovitch matrix insolaton forcing before you go off half-cocked, though. And, in the spirit of our host’s current post, be sure to do the math.

  33. The increased amplitude of the Arctic Sea Ice cycle has been detectable since 2002, but the people who talked about it were labeled “Alarmist” and ignored.

    It is the kind of thing that industrial process managers watch for, because it warns that “the system is out of control”, and about to “seek a new equilibrium”. (See the work of W. Ed Deming) That was “process control speak” for things are about to get real hot, real soon.

    The nearest equilibrium for the Arctic sea ice system is no summer ice, and with a high amplitude behavior, the sea ice system will find that equilibrium rather more quickly than the simulation models predict. (Some industries have rather better process simulation models than anything the IPCC dreams of, and still those models do not always warn when a process is about to go out of control.)

    Considering all related feedbacks, unexpected loss of sea ice is a significant event.

    Your loyal Alarmist,

    [Response: I don’t see evidence in the wavelet analysis of increased amplitude since 2002 (not until 2007). I also looked at the max-min difference for all years from 1979 to 2011, and similarly found no such evidence. What is your evidence for this statement?]

  34. I enjoy reading this blog and it’s analysis is enlightening, but I have one problem with the presentation. I have weak red colour sight (one of the more common colour weaknesses) and have very little contrast between red and black. When choosing colours to contrast on plots could you please not use red and black. I can’t see the point you are making in the annual cycle apart from trend graph as the lines are indistinguishable.

    [Response: I chose red and black precisely because for *me* they give the best contrast. It never occurred to me that it would be problem for others. I’ll try to take that into account in the future, but I can’t promise to be consistent. What colors would have good contrast for you?

    Do others have a similar problem?]

    • There are a lot of color contrast resources available. Googling “contrasting graph coloring” shows these, among others:

      Color Contrast Chart: http://www.accentsignage.com/media/colorchart.pdf
      MS Wheel of Color: http://msdn.microsoft.com/en-us/library/bb263947%28v=vs.85%29.aspx
      Choosing colors for Data Visualization: http://www.perceptualedge.com/articles/b-eye/choosing_colors.pdf

      The biggest problem with the red/black mix (which I also had a bit of trouble with) is that the grayscale intensity is very similar – whereas differing intensities provide a strong contrast. Pink, for example (although not my favorite graph color), is less saturated, has much more white, and would stand out over black on intensity alone – because it’s gray-scale value is a mid-tone gray, rather than black or white.

      • To expand on the contrast issues in graphics:

        Black and white versus colors require intensity contrast to show up well – a light yellow contrasts poorly with white, as a dark blue does with black.

        Colors of similar grayscale intensity can contrast well across hue, unless you run into issues such as red/green colorblindness (the most common, particularly in men, hence I avoid those as contrast colors). For that reason I tend to use opposites for maximal contrast, such as blue/yellow or red/cyan. In such cases I tend to drop the intensity of the yellow or cyan to better contrast with a white background.

        Saturation contrast is perhaps the least useful, unless showing a continuous spread (such as an image with adjacent pixels) – for some reason the human eye does not maintain as much of a distinction between red and pink over any distance. But if looking at something like a map image, saturation contrast can be used to show differences in a pleasing (if difficult to quantitate) fashion.

        I hope that’s helpful!

    • TrueSceptic

      Yes. Red/black and red/green are about the worst for me. Red/green is the most common form of colour blindness.

      Blue stands out really well for me against most colours except purple or mauve (which are part blue anyway). Yellow is good too, but only against a grey background (I find a pale grey background best overall).

      I find the first 2 colours that Wood For Trees uses bad for me too. I’ve emailed the owner about giving us a choice several times without reply.

  35. Do others have a similar problem?

    Yes, there’s an entire field of study within the broader realm of accessibility that addresses such issues.

    KR’s links are a start, here’s another that might help: “http://www.uxmatters.com/mt/archives/2007/02/ensuring-accessibility-for-people-with-color-deficient-vision.php”

  36. Nick Cox has suggested that blue and orange are two colors that appear very different across all of the common types of color vision problems. That seems to be supported by the three examples in Wikipedia.

    Following Nick’s advice leads me to somewhat garish graphs, but hopefully their content is clear.

    • Susan Anderson

      Sounds a good idea, and to improve the grey-scale (aka “value” which in color is the contrast of light and dark) contrast you could also use more of a navy (dark) blue.

  37. Can people just set their monitors to emphasize the colour contrasts that they have a hard time detecting? Or perhaps a website widget would allow preferences of the user to be saved?

    • There probably is a way, I know for Macs at least a simple contrast flip can be accomplished by pressing control + option + command + 8 (and can be reversed by the same method). The color opposites of red and black, though, are cyan and white, which might help for color blindness but which aren’t as different from each other as red/black.

  38. On the topic of bifurcations, there’s a new paper,
    A recent bifurcation in Arctic sea-ice cover
    Valerie N. Livina, Timothy M. Lenton
    Apologies if it’s a repeat.

    • Susan Anderson

      That is fascinating. Is there other information about this? I’m guessing the more likely further “abrupt change” would not be a “return to the normal state”.

      OTOH, there is Neven’s exploration with colleagues (in comments especially) of the new measurement discontinuity, which I assumed was partly due to a change of instrumentation and the inevitable calibration issues. This would not be the same thing, as Livina/Lenton was in 2007 and the new satellite is recent.

  39. Tamino: Is there anything to say about the apparent changes in variability in that NDSIC extent graph? Seem like the whole system is much more variable from 2006-2012 than it was 1997-2005. Is that significant?

    [Response: I’d say it’s only because of the change in the amplitude of the annual cycle after 2007. Note in the final graph, which compensates for this, that the variability is about the same throughout except for the extreme dip in summer/fall 2007.]

  40. Meanwhile: Heartland Institute billboards compare belief in global warming to mass murder

    “The people who still believe in man-made global warming are mostly on the radical fringe of society. This is why the most prominent advocates of global warming aren’t scientists. They are murderers, tyrants, and madmen.”

  41. Heartland has Godwinned the climate debate.

    Let’s see. We’ve got Alan West saying he’s got a list of Congressmen who are Communist party members. We’ve got Rush calling for climate scientists to be hunted down. We’ve got Ken the Cooch abusing his office to launch a witchhunt for Michael Mann.

    Isn’t it about time for someone to step up and say, “Have you, finally, no shame?” Maybe it’s time to start naming and shaming Heartland donors.

  42. jameshmclaren

    The increase in variability of sea ice extent is quite interesting in itself – not altogether surprising of course as it is no doubt a result of increasing GHG concentration putting more energy into the atmosphere, “stirring the pot” if you will. The irony is that increased variability is what climate change deniers are using, by cherry-picking years, to “disprove” warming.

    • Are you talking about the differences between winter and summer?? If so that appears to be a straightforward result of the decrease in multiyear ice.