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Data presentation: A trend lesson

I just came across an interesting way to eliminate the impression of a global warming. A trick used to argue that the global warming had stopped, and the simple recipe is as follows:

  • Cut off parts of the measurements and only keep the last 17 years.
  • Plot all the months of these 17 years to get plenty of data points.
  • A good idea is to show a streched plot with longer time axis.
  • I’ve tried to reproduce the plot below (here is the R-script):

    Plotting the monthly anomalies of the global mean temperature.

    At least, many different global analyses were shown – not just the one which indicates weakest trends since year 2000. The data presented in this case included both surface analyses (GISTEMP, NCDC, and HadCRUT3) in addition to satellite products for the lower troposphere (Microwave Sounding Unit – MSU). The MSU data tend to describe more pronounced peaks associated with the El Nino Southern Oscillation.

    A comparison between the original version of this plot and my reproduction (based on the same data sources) is presented below (here is a link to a PDF-version). Note, my attempt is very close to the original version, but not identical.

    One should note that plotting the same data over the their entire length (e.g. from the starting date of the satellites in 1979) will make global warming trends more visible (see figure below). Hence, the curves must be cropped to give the impression that the global warming has disappeared.

    The real trick, however, is to show all the short-term variations. Hourly and daily values would be an over-kill, but showing monthly values works. Climate change involves time scales of many years, and hence if emphasis is given to much shorter time scales, the trends will drown in noisy variations. This can be seen if we show annual mean anomalies (as shown below for exactly the same data), rather than the monthly anomalies (again, done with the same R-script)

    A linear trend fit to the annual mean anomalies the last 17 years suggest similar warming rates as reported by Grant Foster and Stefan Rahmstorf. These trends are derived from exactly the same data as those used in the original figure, that was used to argue that the global warming had stopped – by two professors and a statistician, the very same who performed curve-fitting and removed data not fitting their conclusion.


    1. G. Foster, and S. Rahmstorf, "Global temperature evolution 1979–2010", Environmental Research Letters, vol. 6, pp. 044022, 2011.

    119 Responses to “Data presentation: A trend lesson”

    1. 1

      It would be even more fun if you reverse the x or y axis. People don’t look at the numbers on the side anyway :)

    2. 2

      The real trick is deciding on the end points.

      Since global average surface temperature exhibits a long-term sinusoidal trend, one can display either a positive or negative trend with careful start and end point choices.

      Your mileage may vary depending on your destination.

    3. 3
      Utahn says:

      “by two professors and a statistician…” So which one is Inferno?

    4. 4
      Salamano says:

      This is another great example why archiving/providing as much of the data (and any manipulations to it) as possible is useful for science.

    5. 5
      Ron Manley says:

      Since 30-year trends are the new ‘meme’ I’ve been looking at running 30-year trends. For example, the rate of increase from 1850 to 1880, from 1851 to 1881, and so on.Using three long-term global data sets it shows an underlying increase but clear fluctuation in the rate. There were maxima in the 30 years up to 1882, 1941 and 2004, and minima in the years 1907 and 1967.

    6. 6
      P.E. McDaniel says:

      When I was a student studying chemistry I would frequently see a text for a class I regret not taking. Class was an upper division statistics class, the text was “How to Lie with Statistics”.

      Whenever I see graphs or data provided by politicians, advertising agencies or climate deniers, I think of that book.

      I think look for the visual ‘flaw’ in the graph …

    7. 7

      #5 Ron Manley,

      Fascinating plot. The model ensemble should average out internal variability of the climate/weather system and leave only the forced response. This is seen in Johanessen et al 2009, “Arctic climate change: observed and modelled temperature and sea-ice variability.” They find that the recent warming appears in all model runs, whereas the 1940s event does not appear in model runs, although similar warming events appear at different times. See fig 1 and text.

    8. 8
      Hank Roberts says:

      > Since global average surface temperature
      Since when?

      > exhibits

      > a long-term

      > sinusoidal

      > trend
      Why do you think any of the above is true?

      You refer on your blog to “possible future climate change over which we have no control” — why do you believe we’re not controlling climate now?

    9. 9
      Kasuha says:

      There’s something I don’t understand. When I run linear regression over UAH data between 1994 and 2012 as per both the original graph and your reconstruction, I get the same trend value regardless whether I run it on monthly or annual averages. Of course it’s a positive trend exactly as in your fourth figure. The original graph however does not seem to talk about trends over that period but about “net change relative to average 1979-1988” – which is supposed to be zero particularly for UAH. As I assume you have access to the whole paper rather than just the graph, could you please explain what net change is meant there?

    10. 10
      Hank Roberts says:

      Oh, you’re a WTF guy. The ‘Hayduke’ nickname had me hoping for science, but, no.

    11. 11

      What does “WTF guy” mean and what does it have to do with Hayduke? What does Hayduke have to do with science, for that matter?

      Is this a blog where everyone trashes everyone else based on labels? What about content?

    12. 12

      With regard to “possible future climate change over which we have no control”…

      I hope this is not a site promoting the idea that only human activity influences climate change. This would be an unfortunate position, since it is quite evident that climate did indeed change before humans came on the scene, let alone before humans had any means of influencing climate.

      There are natural factors influencing climate over which we have no control, neh?

    13. 13
      Hank Roberts says:

      > I hope this is not a site promoting the idea that only
      > human activity influences climate change.

      Not remotely. I’d recommend using the ‘Open Thread’ for the month if you want to talk about yourself and what you believe people here think, so we don’t distract from the topic here.

      I’ve put a response to you there.

    14. 14
      Ray Ladbury says:

      Michael Lewis,
      Yes, of course there are natural factors that influence climate. They have very little to do with the rapid warming we are seeing at present, which, if we are not to deny the evidence, is overwhelmingly due to anthropogenic greenhouse gasses.

    15. 15
      dhogaza says:

      Michael A. Lewis, PhD:

      I hope this is not a site promoting the idea that only human activity influences climate change.

      Despite being burdened with a PhD I think it’s reasonable for us to expect you to be capable of exploring the site a bit before making silly statements. Do you see the “start here” link at the top left corner of the home page? Hint: it’s meant to be taken literally.

      OK, so reading your site, you’re a PhD in Anthropology, and a survivalist with an interest in the eco-warrior fantasies of Edward Abbey (who himself was wise enough to make no effort, for the most part, to live them).

      Exactly the credentials that will convince people that we’re seeing a “long-term sinusoidal trend” (odd use of “trend”, BTW, you’re supposed to conclude that there’s *no* trend, maybe you should try copy-pasting denialist talking points directly rather than paraphrasing them?) rather than warming.

      I mean it’s clear that you’re right and all those professionals working in the field of climate science are wrong …

      Oh, this:

      What does “WTF guy” mean

      He’s suggesting you’re a denizen of Watts Up With That, a motely crew of folks who, when it comes to knowledge of science, for the most part fall far short of the blog’s host’s high-school degree.

    16. 16
      Doug H says:

      No, this is a site where all the forcings on climate are investigated, human and natural. The fact that human factors are forcing current warming trends is one outcome of those investigations.

    17. 17
      Thomas says:

      Eyeballing it (I don’t want to figure out how to get the raw numbers), I am convinced I’d get the same result as Kasuha, a significant linear trend if I did a least squares fit to a linear. But of course for the writer interested in disinformation, he can hand draw a flat line, and fool the uninitiated.

    18. 18

      #12 Michael A. Lewis, PhD

      What is your PhD in? Naivete and Ignorance?

      In other words your post displays a tremendous amount of ignorance. You jump straight to a conclusion and obviously have not looked at the tremendous wealth and depth of material discussed on this site.

      It’s funny, people think that just because someone has a PhD behind their name that those individuals will automatically make sense. You have displayed a good example of how that simply is not true.

      Start Here:

    19. 19
      David B. Benson says:

      Michael A. Lewis, PhD — I strongly recommend that you begin with “The Discovery of Global Warming” by Spencer Weart, first link in the science section of the sidebar. Then you might care to listen/watch David Archer’s videotaped lectures, available online from his website. If you then want a solid background in climatology, study Ray Pierrehumbert’s “Principles of Planetary Climate”

    20. 20

      #12 Michael A. Lewis, PhD

      And while we’re on the subject:

      “…let alone before humans had any means of influencing climate.”

      Aren’t you ignoring the unknown unknowns here. Isn’t it possible that some humans may have figured out how to influence pre-human climate by teleporting thought waves through space/time anomalies?

      I mean if we are going to fantasize, hey, why not go big!

    21. 21
      Owl905 says:

      There’s probably no stopping the stats trench warfare anytime soon. The pro-pollutionist put number-crunched honey in the trap, and whistled a short tune. Now everything from climate science to the world’s largest pollution problem is on sabbatical.

      Suggestion (and it won’t force you to fold up your spreadsheet):

      Brag about the size of your graph!

      Brag about your graph respecting all the time series; all the weather-noise; and all the chaos! Brag about how your graph satisfies all the evidene!

      Draw attention to their tiny little graphs! To their short attention span! To their need to compensate for an inability to satisfy the evidence!

    22. 22
      GSW says:


      Is there a link to the original work/paper? Foster & Rahmstorf is referenced but not Solheim et al. Which journal is this from?

      A couple of comments; I’m guessing, without seeing the paper, that the 17yrs is from Santer et al (2011?). Also, I’m struggling to see the “trick” in plotting monthly values rather than year anomalies for such a short time period. The calculated trend should be the same.

      [Response:Yes. The point there I believe is that doing so can give the impression of there being more truly relevant data to the question at hand than there actually are–you really only need the yearly averages to get the longer term trend.–Jim]

    23. 23
      Robert Butler says:

      A quick visit to Wiki and Amazon shows “How to Lie with Statistics” by Darrell Huff is well known, in print, and available.

    24. 24
      Richard Simons says:

      Owl905: I am far from clear what point you are trying to make. Are you trying to criticize the author (Rasmus) without saying anything that could be used against you, while being a smart Aleck?

    25. 25
      Andrew Park says:

      The subject of time series trends using different degrees of discrimination raises an important statistical point. What is the importance of autocorrelation in these series and how should it be accounted for, if at all.

      I am no time series expert, but my understanding is that autocorrelation articifically infaltes type I error rates by diminishing the effective degrees of freedom. Often such data sets are detrended to see the autoregressive structure of the data more clearly. But of course, we want to see any trends that exist in climate data, right? So is there a way to remove the autocorrelation – or at least to allow for it in such a way that you can analyze the trend with appropriate degrees of freedom, in the absence of autocorrelation?

      [Response:Yes there are a number of ways of doing so. Arguably the simplest is to just to compute the (lower) effective sample size based on the actual size and the estimated autocorrelation, and use that value to determine your probability (p). The formula for which escapes me at the moment however.–Jim]

    26. 26

      I’m just geting a feel for the discourse here. I see nothing different from the “denialist” lists.

      Thanks for the demonstration.

      [Response:You can learn a great deal of climate science from the discourse here if you set your mind to doing so. It’s up to you really.–Jim]

    27. 27
      John E Pearson says:

      2 Michael A. Lewis, Ph.D wrote: “sinusoidal trend”.

      Very interesting

    28. 28
      John E Pearson says:

      5 Ron wrote there were maxima and minima:

      I’ve personally examined ALL the temperature data for the lifetime of the planet and I’ve made not one but two great discoveries. Great discovery 1: every pair of temperature maxima are separated by a temperature minimum. Great discovery 2: every pair of temperature minima are separated by a temperature maximum.
      There are as many increases as decreases. THE CONCLUSION IS INESCAPABLE!!! COOLING IS AS LIKELY AS WARMING!!!

    29. 29
      Radge Havers says:

      MAL, PhD @ 26

      “I see nothing different from the “denialist” lists.”

      As my paleontology teacher used to say, there are two kinds of people in the world: lumpers and splitters. Looks like you’re a lumper. Of course you’d expect a scientist to be willing to invest time analyzing the classes in question before making that decision. And you’d especially expect an anthropologist to be nuanced in assessing the social context of a conflict like this.

      OTOH, are you by chance one of those magical Carlos Castaneda type anthropologists? One who thinks any naming is just an arbitrary cultural invention equal in value to all other namings — the only inferior system being that of the mad robot scientists who secretly rule the world?

    30. 30
      Jim Larsen says:

      22 GSW said, ” Also, I’m struggling to see the “trick” in plotting monthly values rather than year anomalies for such a short time period. The calculated trend should be the same.”

      Me too. I google scholared “Solheim 2012” and checked the first few pages of results. Nada of relevance to this post. (or I’m blind. That often happens)

      Who/when/what were the conclusions Rasmus was talking about? Trend line “they” said was ______? Why is it wrong? What caused the unstated difference in trend or significance? I’m sure for many folks this post works, but it’s frustrating for me. It assumes I know stuff I don’t. So, I’ll give my thoughts and hope a kind expert will correct my errors:

      17 data points has less significance than 204. Yearly values has been the standard forever. Going to months is a huge deviation, for which there must be a motive. Perhaps it’s to artificially increase the statistical significance.

      Also, adding in monthly values “pollutes” the data, hiding trends within short term variability. Obviously, this would randomly increase or decrease the trend. In this instance, it happened to decrease(?) the trend, and so the Monoskeptics used that happenstance to make a false point. (I’m real fuzzy as to how this works)

      Woo, a twofer! Both increases statistical significance and decreases the trend, and all done by going monthly instead of the standard yearly.

    31. 31

      #26 Michael A. Lewis, PhD

      Another ‘Pot meet Kettle’ moment… Well, thank you for the hypocrisy.

      Why is it that you think we/I don’t know how to use the internet? Why is it that you think we/I can’t see what you have written already? Why is it that you are inferring that we/I are somehow guilty of pointing out that you are hypocritical in your posting here?

      SInce your one of the writers on

      and have co-written an article with Anthony Watts stating:

      “Global warming hyperbole has been used to discredit free-thinking, independent scientific research, free expression, free thought and free action. The individuals and corporations funding this movement are laying the ground work for society controlled by corporate-government-military oligarchies to maintain the economic and political status quo.”

      using phrasing such as

      – “These activist dolts…”

      – “I love this retarded logic: …”

      – “Idiots.”

      – “…I hope some TV station sues the living crap out of these bozos…”

      Other articles you have written include phrases such as:

      – “The Trenberth article contains so many glaring errors and biased assumptions, it’s hard to know where to start.”


      – “Since we do not yet fully understand the natural geophysical processes that result in observed climate variations over geologic time periods, it is very difficult, if not impossible, for us to fully understand the contribution to global climate variation resulting from anthropogenic greenhouse gases.”


      “Their unceasing drum-beat for Anthropogenic Global Warming will ultimately discredit their otherwise worthwhile and necessary programs to reduce human pollution as a result of unrestricted human population and economic growth.”


      “it is clear from the tone of the article on the NCAR web site that this is ideologically driven publication, not scientific research.”

      You are basically arguing from your own lack of knowledge of the science, you feel justified coming into RC, playing innocent, and indirectly accusing folks (such as myself) of not being nice to you.

      You use tired old non-science arguments to say climate science doesn’t know everything therefore we do not have enough knowledge to make any decisions. That’s simply false.

    32. 32
      Ron Manley says:

      John E Pearson #28
      From your comment its not clear whether or not you have looked at the link I gave. The significance was not that maxima were follwed by minima but the timing which suggests a multidecadal periodicity in the temperature trend. This is very obvious when you follow the link.

    33. 33
      Jim Larsen says:

      27 John said, ” 2 Michael A. Lewis, Ph.D wrote: “sinusoidal trend”. Very interesting”

      English is a wonderful language that way. We can use words to convey thoughts beyond their original intent. He’s talking about the supposed ~60 year natural cycle over a benign recovery from the little ice age, as slightly influenced by mankind’s emissions.

      It all sounds grand, but unfortunately it just ain’t true.

      Michael, if you’re here to learn (they never are, sigh), then go to “Start here”. Skeptical Science has some great resources too. After spending a night digging, come back here to the Unforced Variations thread and give alternative hypotheses or ask questions. This site, used correctly, is an awesome resource.

      [Response:Unfortunately, he isn’t, as his last boreholed comment demonstrates.–Jim]

    34. 34
      R. Gates says:

      Excellent lesson in how to pick data cherries. Seems the skeptics of anthropogenic climate change really don’t need any lessons as they are quite the experts already, and the cherries they pick tend to be of the psychotropic variety, leading to all sort of interesting mental states.

      An of course while studies such as Foster & Rahmstorf and others have shown the underlying warming of the troposphere that is continuing when background noise is eliminated from the longer-term signal that growing greenhouse concentrations are causing, the important message of warming is not found in the troposphere at all, but in the cryosphere and oceans, where the last 10 years (rather than being somewhat flat like the tropopshere has) have been warming at accelerated rates. Given that the cryosphere and oceans are far better long-term indicators of changes in Earth’s energy balance than the much more “noisy” troposphere, for anyone to suggest that the warming of the Earth system has slowed or stopped over the past 10 years, means they are purposely ignoring the far bigger heat sinks of the cryrosphere and oceans, or they simply want to spout nonsense.

    35. 35
      Doug Rusta says:

      #28 John E Pearson

      When all (or most) of the factors that contribute to climate are considered, it is obvious that cyclical patterns will result over long time scales. World climate conditions will change as the oceans and atmosphere seek new equilibrium conditions. Your capitalized conclusion is thus devoid of useful information content. Sure, there will be short term ups and downs in average global temperatures, but what matters is the longer trend toward a new “stable” condition. What will the world look like when this new equilibrium is achieved? That is the issue of concern, and it matters little which side wins the debate since our political system is so badly broken.

    36. 36
      Owl905 says:

      @Richard Simmons – no.

    37. 37
      Brian Dodge says:

      @ Michael Lewis (not that he’s still listening)
      “Ice core records go back thousands of years, but are not helpful in the past 2,000 years.”
      Misinformation like this is what gets you jumped on. Who told you that? – see &

    38. 38
      Owl905 says:

      @Doug Rusta 35 – It is not obvious that cyclical patterns will evolve over long time scales. In fact, cyclical patterns grow and die subject to the physical and chemical evolution of the planet. The most recent big example is the anomaly drainage of the mid-North American ice-age sea (Lake Agassiz) into the Arctic. It may not be a co-incidence that the current long Holocene plateau is a function of that anomaly. Likewise, AGHG is not cyclical – it’s an event disruption that could very well overwhelm some basic natural cyclical patterns.

      JPearson’s remark was an excellent indictment of how to twist a statistical tautology into an agenda.

    39. 39

      Re. #33 Jim Bouldin’s note:

      I took a look at the Michael Lewis boreholed comment out of curiosity. How he is coming to his conclusions is baffling. He says the most recent warming period is the last 1.5 million years, but data indicates that we went form a more stable warmer state with smaller oscillations into deeper oscillations into colder states.

      This indicates a general cooling trend on average for the 1.5 million year period in question. How does he come to the idea that a cooling period is a warming period one can only wonder?

      I would like to know his source for this assessment. Michael, care to share? Or is your source for this data and your assessment of 1.5 million years of warming a secret?

      FYI: Michael, for the past million years the general warming and cooling cycle revolves around 100 kyr cycles

    40. 40
      Neil Fisher says:

      The full graph look more like a step to me – would you be so kind as to re-plot the trends witha break-point analysis?

    41. 41
      John E Pearson says:

      35: Doug: You’ve exemplified a big problem with Real Climate. I found the notion that someone thinks it’s profound that every two maxima are separated by a minimum to be pretty funny and on intellectual par with the vast majority of denialist arguments. I remember quite well one of my earlier attempts at humor here after Texas Rod claimed that a short lived downturn in the temperature record meant that x years of warming had been wiped out. I found Rod’s comment idiotic beyond belief so I wrote something to the effect that “alarmists call them seasons” or some such. I understand that humor is a dicey business for a professional physicist to engage in but still I can’t help myself. I was surprised, though, at the hostility on the part of otherwise intelligent people. I was immediately called an idiot by Hank Roberts and a bunch of other people some of whom made up some fairly silly stuff in order to attack what they perceived as denialism on my part. There is a well-heeled denial machine that in spite of the science operates with great effectiveness. You cannot defeat it with reason. You cannot defeat it in the schools. You can hope to defeat it with humor. Possibly you can defeat it with music. You cannot defeat it with humorlessness no matter how sincere you are.

    42. 42

      #28 John E Pearson

      There are as many increases as decreases. THE CONCLUSION IS INESCAPABLE!!! COOLING IS AS LIKELY AS WARMING!!!

      Of course, you are not accounting for reason in this statement.

      Attribution is critical to understanding. If you ignore the reasons why things happen and focus on the ups and downs, you can conclude much less to very little, if anything at all.

      It is the ‘reason’ that the temperature goes up and down at different times under different circumstances that counts toward understanding.

      As I have said in the past, two different people can dislike you at different times, for entirely different reasons, just as with two whom like you…

      Knowing some like you and some dislike you as data points provides no understanding as to why.

    43. 43
      flxible says:

      John Pearson – FWIW, this non-physicist not only caught your humour but smiled at the targets expense . . . in both cases. ;)

    44. 44

      #28 John E Pearson

      hmmm… or were you just being humorous again?

    45. 45
      Hank Roberts says:

      > John P. Reisman (OSS Foundation) says:… Michael Lewis

      Always possible he’s considering changing his mind, though. People do.
      I suggested going into that in the ‘Open Thread’ …

    46. 46

      #45 Hank Roberts

      I understand your concern. I do not believe I am being unduly harsh though. Reasonable people can learn and I hope he is one that can. But from what I’ve read of his writings on WUWT it seems clear he is not basing his assumptions on science, or science in context. In fact there are leanings indicated toward conspiracy.

      Conspiracy theorists are hard to turn around. I did a talk about a month ago and it was a particularly tough crowd. 61% thought global warming was a conspiracy. After one hour that number was dropped to 33%. If I had two hours I might have done even better. But I think it is much harder to turn a conspiracy theorist around via a blog. If Michael Lewis is actually basing his perspective merely on bad data and is not belief oriented then he has a better chance of learning.

      I for one am very curious how anyone can think Earth has been in a warming period for 1.5 million years? I have never heard that claim before and all the evidence I’ve seen indicates otherwise. I hope he can quote a source for that assumption though. I would like to see it.

    47. 47
      David B. Benson says:

      When attempting humor whilst blogging, plase end with
      as there will always be some who don’t get it otherwise.

    48. 48
      Hank Roberts says:

      Having trouble finding ‘The Bore Hole’?

      here’s how to find stuff.

      1) on this or any other web page: use “find” in your browser; it will find the words you type into the box; often (as here) they’re a link;
      2) on this and many other websites: use a Search box; here, it’s at the top right corner of each page;
      3) use a Site Search:
      4) on this website, look in the right sidebar (you’ll see the same words the “find” command hilights). That’s the last item under Categories. It’s a link; click it.
      5) ask.

      Note: people are people; some will be rude; some will be helpful; some will be both rude and helpful, as explained here: How To Ask Questions The Smart Way; and some will not say a word til they get a feel for whether you’re going to bother learning what’s available.

      Best of luck.

    49. 49
      Erica says:

      So what you’re really saying then, is that a trend over the last 17 years is not enough to establish anything. 30+ is what is needed. Yes?

    50. 50
      Erica says:

      John E Pearson, You speak of a “well-heeled denial machine”. Realistically though, what they spend is peanuts compared to what government spends on – adopting your own terminology style – what one might call an “alarmist machine”.

      [Response:One might call anything one might like, but you completely misunderstand the nature of funding for basic research and data gathering (a few $bn a year). To describe the funding for NPOESS or AURA or MODIS or SCIAMACHY or NCEP or MERRA as part of an ‘alarmist machine’ is simply a nonsense. – gavin]