One Look at a Graph

Paul Homewood objects to the U.K. Met Office telling people that “Arctic sea ice decline continues.” Of course his opinion is echoed at WUWT.

It’s Paul Homewood whose claims are false.


He says,


One look at their graph shows this is patently not true, despite grossly misleading linear fit, intended to fool people.

What graph, you wonder? This one:

It shows each year’s minimum sea ice extent in the Arctic. The amount of ice changes with the seasons: more in winter/spring, less in summer/fall, and each year it reaches its minimum some time in September; the graph shows how much ice remained even at the year’s lowest point.

Here’s my version, which I think is a bit easier to see:

I included a best-fit straight line (by least squares regression, shown as the red line), as did the U.K. Met Office.

Paul Homewood says he knows what’s really going on:


It is very easy to show that Arctic sea ice has stabilised. As their graph itself shows, there have only been three years since 2007 with lower ice extent than that year, and eleven have had higher extents.

Also the average of the last ten years is higher than 2007’s extent.

It’s obvious that this is how Paul Homewood sees the graph:

He’s drawing a rather bold conclusion from a very short time span and a very small number of data values. He himself says:


In itself, this is too short a period to make any meaningful judgements. But that is no excuse for the Met Office to publish such a manifest falsehood.

I find it ironic that he says outright “this is too short a period to make any meaningful judgements,” just after saying that “It is very easy to show that Arctic sea ice has stabilised.”

The linear fit shown by the U.K. Met Office (and in my 1st graph too) is estimated by least squares regression, which not only gives us an estimate of the rate (i.e., how fast is the variable rising or falling), it also estimates the uncertainty in our estimate.

I computed linear fits for both time spans discussed by Paul Homewood: the pre-2007 values and the post-2007 values (shown as red lines in the graph of how Homewood sees things). This gives me an estimate of the rate, and of its uncertainty, for each time span separately, which enables me to compute the likely range in which their rates fall. I can then compare their estimates to see how different they are, and I’ll do so with this graph showing the ranges for each interval:

For the first interval (pre-2007), the annual minimum extent of arctic sea ice was definitely declining, at a rate estiated at 55,000 km^2/year, but not less than 35,000 km^2/year or more than 75,000 km^2/year. For the later interval (post-2007), we can’t tell from the available data whether it’s rising or falling, be we can put limits on its rate. It’s not increasing faster than 47,000 km^2/yr, nor decreasing faster than 69,000 km^2/year.

Think about that. Using only the data since 2007, sea ice might be increasing or it might be decreasing faster than it was before. The rate estimate is too uncertain to tell. But Paul Homewood believes he can tell — by just “one look at their graph.”


Unlike Paul Homewood, I’m far more interested in what’s really happening to arctic sea ice than in heaping scorn at the U.K. Met Office.

First and foremost, the yearly minimum is only one day out of the year. We have sea ice extent data throughout the year, and what happens during the rest of the year counts. Instead of using the annual minimum, let’s use the annual average. To avoid losing the most recent data, I’ll compute the yearly average for October throught the following September rather than the usual (but arbitrary) January through December. I’ll also omit October 1978 through September 1979 because that year is incomplete. I get this:

I wonder what Paul Homewood will conclude from “one look at the graph.”

The annual averages show much less fluctuation than the annual minima, so we can estimate things like rates of change with greater precision. I find that there is statistical evidence that the rate changed over time. One model of such changes uses three straight-line segments with their changes chosen to best-fit the data, like this:

This fit also enables us to estimate the rates, and their uncertainties (and therefore likely ranges), for each time span. Here they are:

From this analysis, I estimate the rate of change of Arctic sea ice extent as follows: from 1979 to 2002 it decreased at a rate of 31,000 (+/- 9,000) km^2/year; from 2002 to 2007 it decrease super-fast, at a rate of 143,000 (+/- 36,000) km^2/year; since 2007 it has declined at a rate of 42,000 (+/- 15,000) km^2/year.

Note that during the final time span, post-2007, the rate is negative with statistical significance. That wasn’t true for the annual minima, mainly because the degree of fluctuation of the yearly minimum is so much bigger than the degree of fluctuation for the anual average, that our rate estimate from annual minimum is far more uncertain. So much more so, we can’t even tell with confidence whether it’s increasing or decreasing.

But with the annual averages, the answer is clear. Using only data since 2007, we can still show the statistically significant decline in Arctic sea ice.

Just like the U.K. Met Office said.

As for “Arctic sea ice has stabilised,” no — it hasn’t.

I think I know Paul Homewood’s method of analyzing climate data: one look at a graph, to see what you want to see.


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28 responses to “One Look at a Graph

  1. I had noticed that a couple of days ago as well Tamino. What’s more neither Mr. Homewood or Mr. Watts have deigned to publish my Arctic alter ego’s suggestion that they brush up on their statistics.

    Here’s the abstract of my forthcoming preprint on the subject:

  2. It looks like, especially in light of the last figure, the rate of shrinkage was strongly affected by something 2002-2007, which further research may determine. The same sort of research might also determine if there is some factor that might have cause the ice to stabilize since 2007, although I think my research dime would be better spent trying to see what was going on during 2002-2007.

  3. … And I bet the 0.5 quantile (median) would be more stable still. But of course you are entirely correct. The only statistical raise-of-an-eyebrow I might make with UK Met is their attempt to fit a line to such an extreme quantile in the first place. I know, however, they do regularly produce series of ice minima, so perhaps the line was just a quick remark.

  4. Susan Anderson

    I don’t think it is appropriate to assume that the Arctic has “stabilized” just because of the exceptional years 2007 and 2012. As far as I can see, there is very little long-term/thick ice remaining, and assigning previous highs as new lows is a typical tactic of those who wish to undermine the real information, as we saw with the 1998 El Nino. As I see it, a look at all recent years shows months-long losses that demonstrate the reverse of “stabilization”.

    • Hi Susan, Long time no see!

      Of course the Arctic hasn’t “stabilised”, but there is a valid physical reason for an apparent “brief slowdown” in the rate of September minimum extent reduction, as revealed by Tamino’s statistical analysis. If you want to dig deeper than the ASIF thread linked above then please see this 2011 paper by Armour et. al.:

      Click to access Armouretal2011.pdf

      “We can expect the thicker MY ice to thin at a greater rate than the thinner FY ice.”

      As you point out, there are a wide range of other metrics that should be considered when assessing the “health” of the sea ice cover over the Arctic Ocean. Area at minimum instead of extent being one obvious one!

      It seems safe to conclude that Paul & Anthony haven’t considered any of them?

  5. Yes, as Susan implies, volume is what we really care about.

    • Is volume what we really care about?

      The volume of melt will tell us how much heat has been used to melt sea-ice, but that’s not the only important thing.

      The two-dimensional measures are critically important in terms of the ice albedo feedback – which is one of the ways in which the melt has an impact on the rest of the world. But then that would be most important in looking at the figures for May, June and July, when solar radiation is at its greatest, rather than the September minimum.

      I also don’t think we should dismiss the importance of September ice extent being easy to measure – having the longest possible historical record to compare against is not something to dismiss lightly. How good is the historical ice volume data? How far back does it go?

      What I’d be really interested in is whether many Argo buoys have made it into the Arctic Ocean, and whether we have good estimates of changes in ocean heat content for the Arctic Ocean. I want to know how much extra heat is being absorbed by the Arctic Ocean as it melts from the edges earlier in the year.

      One proxy for that is to look at the two-dimensional statistics again, and see how late the autumn freeze-up is.

      • Hi Misfratz,

        Of course volume isn’t all we care about! As you point out, 2 dimensions is far more relevant than 3 when considering albedo, and area is more relevant than extent. See for example Nico Sun’s “Albedo-Warming Potential”:

        https://cryospherecomputing.tk/awp.html

        Then that “potential” may or may not be realised. To a considerable degree that didn’t happen during peak insolation this summer.

        However it seems to me we’re drifting away from the point of Tamino’s original post, or at least my interpretation of it outlined at the top. Try and discuss these sort of subtleties at WUWT and see how far you get. Paul and Anthony and assorted other “skeptics” systematically shut down learned but “alarmist” or even “realist” comment. However I note that Tamino managed to slip a little something past Anthony’s gatekeepers. Pop in there to discuss the matter, and see how far you get.

  6. Nicely done (as usual). Love your work. I find it annoying that sea ice extent is always the one people refer to – it is so damn two dimensional. Each winter the sun sets for a few months and the surface freezes. So why not look more at sea ice volume. But how much melts and how much freezes each year – surely that 3 dimensional question is better than the 2 dimensional one. Rate is -1000 cubic kilometres per decade. OUCH.
    http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/

  7. Pingback: Facts About the Arctic in October 2021 | The Great White Con

  8. michael Sweet

    I think you also need to consider that as the sea ice retreats the remaining area is smaller. Then if the same area of sea ice is lost it is a greater percentage of the area that was lost. In addition, the remaining ice is that much further north. As the sea ice retreats the remaining ice is in the more cold areas and melts slower. Of course Tamino knows all that and just left it out so the post would not be too long.

    Thanks for another good analysis.

  9. The latest denier “hiatus”.

    Why is it denial blogs/bloggers have never seen a statistical trough (or peak) that they cannot finagle into a “hiatus”, a “stabilization”, or even a “recovery”???

    It’s almost as if they are looking for ripe cherries.

  10. A heads up that Paul Homewood published another post today about the UKMO’s Arctic article:

    https://GreatWhiteCon.info/2021/09/arctic-sea-ice-disinformation-and-cop26/#Oct-02

    It still contains no statistics, although it does mention a practitioner thereof once:

    “The Met Office justify their claim by including data from 1979 to 2007, when ice extent did fall. But as any scientist/statistician knows, the past is no guide to the future. What happened twenty or more years ago is of no relevance to what is happening now.”

    • What happened twenty or more years ago is of no relevance to what is happening now

      Not your statement, I know, but it is remarkable. “What is happening now” is unasserted to be independent of what is happening in future. Yet, the same sources criticized projections of what soon might happen because they were so inconsistent with what has happened in the 50 years lagging past.

  11. How annoyingly distracting indeed. One wonders if Paul and Anthony realize that Earth’s surface is accumulating 4 Hiroshima atomic bombs worth of heat every second. Energy going in, not out into space, thanks to the growing blanket of CO2, CH4, NO2, H2O. Why do humans think *any* internal process is able to mitigate the heat energy buildup that entails? Ice melt is just one tiny representation of what happens when you have a heat-energy surplus that has nowhere left to go. Please..

  12. The hype and hysteria around so called manmade climate change is truly pathetic.

    Anyone who has statistical understanding can see that the confidence intervals for CO2 causing climate change are just not there. No climate ‘scientist’ can ever point in the direction of evidence which shows these confidence intervals being statistically sound. All their glorified models are way outside acceptable p values and they want to treat this junk as science.

    Thank goodness for the real scientists at WUWT who can poke holes through the nonsense that is manmade global warming.

    • Uh, I’m curious. By what criterion do you judge tamino–plus many of us here as well–to have to have no “statistical understanding? How many papers on stats have you gotten published?

    • Mr. West, the evidence for global warming does not rest on statistics. It rests on radiation physics which have been developed for 200 years. When Svante Arrhenius predicted global warming back in 1896, he did not use statistics, nor did he use a computer. In short, you are criticizing a field you have not studied and do not understand. Please open a book on climate science and read through it. I can recommend some good ones if you are interested.

  13. If tamino and others have any statistical understanding then they would be able to show how climate change can be linked to CO2 to a point of statistical significance. All of the farcical models do not show any kind of correlation between CO2 and temperature, yet the ‘scientists’ keep claiming that warming is occurring. We cannot with the statistical certainties we have.

    • It’s been done:

      Saltzman, E. S., J. R. Petit, J. Jouzel, D. Raynaud, N. I. Barkov, J. M. Barnola, I. Basile et al. “420,000 years of climate and atmospheric history revealed by the Vostok deep Antarctic ice core.” Nature 399, no. 6735 (1999): 429-436.

      Even a causal analysis:

      Van Nes, Egbert H., Marten Scheffer, Victor Brovkin, Timothy M. Lenton, Hao Ye, Ethan Deyle, and George Sugihara. “Causal feedbacks in climate change.” Nature Climate Change 5, no. 5 (2015): 445-448.

      The trouble with WUWT-style statistical analyses of CO2, temperature, and other series are that (a) they are superficial, (b) generally use linear time series analysis, and (c) don’t treat changepoints properly. The latter introduce non-stationarity across stationary regimes punctuated by the changepoints.

      Tamino uses broken line changepoint analysis all the time.

      If you really want to understand the causation, couldn’t do better than Van Nes, Scheffer, Brovkin, Lenton, Ye, Deyle, and Sugihara.

      [Response: A word, to the wise.]

  14. The likes of Paul Homewood, Anthony Watts and their baying gullible followers like Mark West are self-deluded bitter-enders who probably will never become cognizant of their own wilful ignorance about science or climate change.

    • At least Toony and other denier “leaders” have the excuse of enriching themselves monetarily, Jim. Prostitution/charlatanism is not very smart money in the long run, to be sure, but at least it’s an understandable motive. And there is a lot of money on the table for such activities as has been documented repeatedly. Kinda’ like raising money by touting “stop the steal”, “stop pizza parlor basement pedos”, “anti-vaxxing/anti-public health” etc., etc., etc. Charlatans–from “professors” selling elixirs/trombones to “rain men”, to what have you–have always made a fine living in the US. It’s part of the culture. Only the specifics change, never the strategies.

      Followers, on the hand, are simply as you describe. I would only add “fleeced” to your other descriptors. Trust me here, the prostitutes/charlatans do too.

  15. Here’s the relationship between CO2 and temperature demonstrated to very high significance. No doubt this will immediately convince Mark West, as it’s just what he’s been asking for:

    https://bartonlevenson.com/CO218502019.html