How Sheldon Walker Views Global Warming

Sheldon Walker recently posted at WUWT his view of global warming, in which he objects to the Skeptical Science view of global warming. He takes particular exception to their graphical display of same:


Sheldon Walker prefers what he calls a “contour map.” He takes all possible time intervals, estimates the warming rate for each by linear regression, then produces a graph in which the estimated rate at a particular time, of a particular duration, is indicated by color.

Here’s Sheldon Walker’s view (of the NASA GISS data used in the Skeptical Science graph):


I produced a similar graph:


The colors I’ve used aren’t exactly the same as his, but they’re close, and it’s clear the differences are only cosmetic.

He elaborates on his disbelief thus:

Note that the SkepticalScience view of the warming rate agrees with what the warming rate actually did, when the trend length is greater than 26 years. However, when the trend length is less than 26 years, the SkepticalScience view of the warming rate looks completely bland, and is definitely wrong. Where are the El Nino’s and La Nina’s? Where are the slowdowns and speedups. Do they expect us to believe that global warming proceeds at a uniform constant rate?

To answer your question, Sheldon: we don’t expect you to believe it.

Here are three more contour maps, for three other global temperature data sets:




How would Sheldon Walker interpret these? Do they show “slowdown” episodes? He states explicity:

You now have all of the information that you need to find a Slowdown. Find a contour map with yellow or orange at the top point of the triangular contour map. Now look for any green colour on the map. If you can find any green, then you have found a Slowdown. If you need any help, most 8 year olds are very good at this.

According to which, all three graphs show slowdown episodes. The second one, in particular, shows a slowdown episode which lasts over 20 years.

I wonder whether Sheldon Walker would believe me if I told him I’m quite certain that none of them shows a slowdown.

I wonder what Sheldon Walker will think when I inform him that these “global temperature” graphs aren’t for real global temperature data, they’re for artificial data. The artificial data sets are made from a straight line with the same slope as the NASA data, plus random noise with the same standard deviation as the residuals of the NASA data departures from a straight line.

I repeat: those three graphs are for straight-line-plus-random-noise. The straight line has the same slope as the NASA data. The noise has the same size (standard deviation) and autocorrelation structure as the NASA residuals.

And now to the most important thing.

Climate is the “rules of the game” — weather is the “rolls of the dice.” For the artificial data sets, the rules of the game are straight line increase. That’s the climate. The rolls of the dice are autocorrelated random numbers. That’s the weather. Because the climate — the rules of the game — is straight-line-increase, it’s absolutely certain, no denying it, that these data show no trend change.

But of course the rolls of the dice lead to fluctuations. That’s what weather is all about. It’s not what climate is all about. Those fluctuations cause trend estimates to fluctuate, and sometimes — especially when the time span is short — the estimate can be quite different from the actual trend. The actual trend is the climate, which we know, for certain, no denying it, did not change.

Global warming is about the climate, not about the weather. Except, of course, insofar as weather is influenced by climate.

Sheldon Walker’s method, and his view, include taking any fluctuation of a trend estimate as a slowdown of global warming. It means taking every fluctuation of weather and calling it a change of the climate trend. Most 8 year olds are very good at this.

If you apply some actual statistics to the trend estimates, you’ll find that none of the departures from constant-warming are significant. The statistics can be pretty tricky because the noise isn’t the simplest kind (referred to as “white noise”), it’s autocorrelated noise, and there are other statistical issues too (like “broken trends” and the “multiple testing problem”). But when done right, one finds that (to repeat myself) none of the departures from constant-warming are significant.

Walker’s graphs are an application of the technique which Nicola Scafetta called “multi-scale dynamical analysis” when he applied it to tide gauge data, in an attempt to link sea level changes to lots of stuff other than global warming (in particular, ocean oscillations). Scafetta too failed to do any actual statistics, relying instead on the visual inspection of colored graphs, an “analysis” (actually, lack of analysis) which was rather effectively refuted.

Sheldon Walker has been posting here frequently of late. I’m curious to know what he has learned from this.

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72 responses to “How Sheldon Walker Views Global Warming

  1. Sheldon was of course showing off his bright graphical triangles of temperature OLS trends on an earlier thread. What he has failed to address in that thread is criticism concerning the description of what his pretty triangles actually mean. Sheldon is correct in his understanding of eight-year-olds in that they can recognise green. The pertenant question, however, is ‘What is that green bit?’ I have a feeling that Sheldon doesn’t really grasp what it is he is graphing out. Although he has been playing with these pretty triangles for a while, I assume he is too stupid to see the lies he is creating.

    The tip (using the longest set of data) of Sheldon’s primary evidence for the existance of his “slowdown” is the 14-year period 2001-2014 for which he is using GISTEMP data. Feed that data into the SkS trend calculator (2001.0 to 2014.99) and yes the result is a trend below 1ºC/century (It comes to +0.79ºC/century), but the confidence intervals are +/- 1.4ºC/century.
    I believe Nick Stokes was the first to start producing these colourful triangles. A criticism at the time was that the confidence intervals of much of the data presented were far broader than the representation would have you believe. That is, for trends calculated using the shorter sets of data the graphs were a lie. The trend calculations cannot be sorted into the bands displayed if the confidence intervals are larger than the bands. In the case of Sheldon’s primary evidence, the best that can be achieved is to use the longest period of trend in his green bit. That is that 14-year period 2001-14 when the confidence interval is still three times broader than Sheldon’s representation. For him to ignore that mismatch makes him stupid or a liar.

    • Al, these graphs have been around since before Scafetta used them in 2014, but frustratingly I can find the paper/text where I first saw something like this. I actually knocked up a similar graph to Sheldon Walker’s a few years ago myself, although I started with an orientation more like Nick Stokes’, from using the end points rather than a midpoints as the values for the abscissa. Once these are plotted a similar pattern emerges, and then it becomes rapidly obvious that using a midpoint makes for easier interpretation: I can’t help but wonder if Sheldon Walker followed this path himself.

      The next obvious question is that which realfacepalm asks directly below – what would the plot look like is confidence intervals were included? At this point I gave up because of the autocorrelation issue (I couldn’t justify the time figuring out how to do it) but it remains an interesting question.

      The fascinating thing though is that even without the actual 95% confidence threshold values being included on the graph, one can very easily see the effect of short-term noise on the ability to discern the underlying global warming signal. The dark blues and reds at the bottom of the triangle show the insignificance of considering very short intervals of time when searching for a signal, but once one arrives at using around a decade or more of data it’s apparent that the only trajectories that are returned are warming ones.

      What Sheldon Walker has done is to ignore the fact that these graphs are effectly implying that short intervals return statistically-insignificant results (blue or red in equal measure along the bottom of the triangle), and that the warming signal emerges with spans greater than about a decade. His ‘find yellow or orange and go down to green’ ploy is in fact no different to saying “ignore the longer-term signal and focus on short-term noise, and only on short-term noise that has the negative slope which appears to support a ‘cooling’ trend” – even when that ‘trend’ is only noise.

      If the 95% confidence intervals were superimposed on the plot they’d look a little (though not exactly) like this, but with autocorrelation accounted for, and with midpoint values for minimum period rather than the endpoint values that I used. I suspect that the line would track around the ordinal location of the orange colouring on the graphs.

      • “…but frustratingly I can‘t find the paper/text …”

      • Bernard J.
        Scarfetta could be an earlier culprit. My memory was I saw such graphs and the hoo-haa over the lack of statistical significance quite some time ago. The Nick Stokes graphics are what I remember, but they don’t seem so old.
        Whoever started the rot, using ridiculously small amounts of data to calculate trends makes the confidence intervals mushroom and making the results very quickly nonsensical.

        From the maths, for similar data sets, the size of OLS trend confidence intervals are inversely-proportional to the amount of data to the power 1.5. So compared with a 30-year regression, the CI will grow to 180% for a 20-year regression and to 420% for a 10-year regression. And that isn’t far off what happens using the GISS LOTI data. Accounting for autocorrelatation (a few sample calcs from the SkS trend tool), the average CI (+/-2sd) through this GISS LOTI data is +/-0.55ºC/century for 30-year, +/-0.94ºC/century for 20-year and +/-2.44ºC/century for 10-year.
        This means that if you try to explain these pretty triangles as showing actual real phenomenon, you are taking the piss. These jokers are suggesting it is like a contour map of say a field, measuring actual humps and bumps. But visit the field and it is pretty-much flat. The humps and bumps are created from a flat field because the field is soft and squidgy, as fields usually are. All Sheldon is measuring is mired in statistical squidginess.

        The question of whether the pretty-pretty can be adapted to show when the trend is statistically valid isn’t the best question. It is of course the usual ding-dong – whether there is a statistically-significant trend at all. You can imagine Lindzen bashing on about this back in the 1980s. But today that isn’t the issue. Today there is no question there is a trend and that it is statistically significant. If there isn’t a statistically-significant trend, this could be because there is no significance in the data. Or it could be because the trend is too small to register. Using a shorter set of data to find a change-in-trend isn’t the same problem. Mind, if it was, for the 10-year trends using GISS, it manages a statistically-significance trend for 19.8% of the time. So not a lot, becuse the CIs are so big.
        But the pretty-pretty isn’t trying to show the absense of a trend. a la 1980s.

        What perhaps best illustrates the nonsense of the nonsense in Sheldon’s graphic is to plot the wobbly short-length trend Confidence Intervals in all their glory. The short-period trends CIs extend entirely beyond the CIs of longer-period regressions for almost all the time. So the difference between Sheldon’s 10-year data and his 20-year data is statistically significant for just 29% of the time. The 20-year to 30-year difference is 13% and the 10-year to 30-year difference is 0.8%. I have uploaded a graphic of this here (usually 2 clicks to ‘download your attachment’)

  2. I do find this triangles a very informing and interesting way of displaying the data – but with the caveat of not showing / expressing confidence.

    Is it possible to calculate the confidence intervals, and to, e.g., blight out in lighter colour the not significant results?

    • Yes, but the bottom part of the triangle would be as white as a sheet for some height.

      • Timothy (likes zebras)

        I agree that it’s an interesting way of presenting the data and I think showing the full triangle, and then one with statistically insignificant trends masked out, would be interesting.

        This masking of insignificant data is frequently used when presenting latitude-longitude maps of certain data, such as correlation with ENSO of 500hPa height, to give just one of many examples.

  3. presumably if you can concoct a graphical display of rising temp data that does not actually show a rising temp data trend line, all you have proved is that you pretty good at graphical sophistry

  4. Stephen B Baines

    Actually, I think any trend that is not significant should be replaced by white. That would show how dependent the statistical significance is on length of record. This is a clear case of amplifying the noise to drown out the signal.

    But Sheldon’s interpretation that a focus on the longer time scales in his graph implies monotonic increase is batcrap crazy.

    Also, in a larger scheme, I see this as an attempt to move away from the obvious imagery of the times series, which is indisputable in it’s implication of increasing temps, to something much more complex.

    Keep it simple! Don’t follow that rabbit down that hole!

  5. Bernard from Aus

    You know, I actually like that graph. It clearly shows how there are short-term fluctuations in temperature (associated with ENSO & other factors), but the higher up the chart you go, the less fluctuations you see, until all you’re left with is the steady increase of anthropogenic global warming.

    • Right. That’s what I thought. It’s a nice illustration of where the ’30 years’ rule of thumb comes from. Turns out that 20 years is enough most of the time.

  6. Seems to me the graphs confirm that the long term trend is “increase.” There is not a single point below ten years of “trend length” that shows a decline, and the further up you go (longer trend length), the more the area is covered by greater increases. The bottom of the graph where all the declines are located are showing short term ‘trends.’ What am I missing?

    • louploup2, you’re probably not missing very much at all. As the others above also demosntrate, a considered deconstruction of the graph shows that a warming signal emerges from the short-term noise over about a decades’ worth of data. Sheldon Walker’s strategy is to point to the negative ‘trend’ trajectories in the short term noise and hope that he can fool people into believing that there’s actually no consistent underlying global warming.

  7. I had the same thought as realfacepalm. Maybe adjust the color saturation according to the level of confidence.

  8. I am happy to discuss all aspects of my global warming contour maps.

    [Response: No, you’re not. You will not discuss the effect of noise on those graphs. You really don’t get the difference between climate and weather, so you continue to take all the impact of noise and think of it as climate change. Until you recognize the error of your ways, you will be stuck in your fantasy world. We have tried to reason with you, but your mind is closed.]


    I will discuss other issues about global warming contour maps in other posts.

    [Response: Not here you won’t. As I’ve said before, this site is not for deniers.]

  9. Tamino said, “Climate is the “rules of the game” — weather is the “rolls of the dice.””

    Tamino has seriously confused “climate simulation” with “the real climate”.

    Climate is an emergent property of weather. It is NOT independent of weather.

    You might specify a rule like, “you need to look at 30 years of weather to determine climate”.

    But in the real world, you can NOT set the climate that you want, and then add “rolls of the dice” to make weather.


    Tamino said, “I repeat: those three graphs are for straight-line-plus-random-noise. The straight line has the same slope as the NASA data. The noise has the same size (standard deviation) and autocorrelation structure as the NASA residuals.”

    Congratulations Tamino, you made some simulated climate, which includes simulated slowdowns.

    Note how your simulated climate also includes simulated speedups. Because your “straight line climate” is only an average. And we would expect to have some below the average (slowdowns), and some above the average (speedups).

    YOUR global warming contour graphs show YOUR simulated climate perfectly.

    [Response: Congratulations, Sheldon. You steadfastly refuse to recognize the difference between climate and weather.]

    • “Climate is an emergent property of weather. It is NOT independent of weather.”
      The second sentence is basically true, but you’ve got the first one essentially backwards. Climate determines what weather you can possibly have. I understand how you might have heard the expression “climate is the average of weather” and think that means that weather makes climate, but that’s not how it works. Climate sets the bounds of the possible and then various cycles, psuedo-cycles and plain old randomness determine the weather you get within the bounds of the possible. The way we *measure* climate is to average the weather, but climate is a more fundamental physical reality.

    • Climate is an emergent property of weather. It is NOT independent of weather.

      What Greg Wellman says, with the added observation that the very graphs on which you’re relying themselves indicate that what’s emerging from the short-term temperature noise (in both* directions) is a global warming signal.

      It takes a particularly robust self-deluding obstinacy to be able to refuse to acknowledge this, however you have it down pat.

      [* I note for the record that you didn’t ever talk about looking for “yellow or orange” and finding red below…]

    • Sheldon – At the risk of repeating myself repeating myself, I wonder what your views are on the points raised by Dr. Darren Schreiber in the video at:

      What are your views on the points I raised for that matter?

    • Significant+meaningful: A reduction of climate data into lines and fluctuations about those lines that “looks” meaningful.

      Insignificant+nonmeaningful: A reduction of simulated climate data into lines and fluctuations about those lines that even if it looks meaningful is not because…well, er, because. If something “looks” meaningful it is not because…well, er, because.

    • Please take a book on turbulence and learn about energy cascade and forcing. Look at how energy is transferred in the mean (very clear in spectral space) from large to small scales, about energy backscatter. The differences when doing this analysis for 2D and 3D flows. Learn about the turbulent production term in the kinetic energy budget equations, having a different sign in the mean and turbulent kinetic energy budget showing you how energy is transferred between the mean and fluctuating field. Then you will realise, that what you say is wrong.

  10. Harry Twinotter

    I think Sheldon Walker is knowingly promoting a fraud with these diagrams, he is engaging in willful deception. This means that NO amount of discussion will get him to admit his diagrams are nothing more than cherry-picking short term trends, because he know that fact already!

    The diagrams are actually evidence for global warming.

  11. This the effect of reducing the colour and brightness to equal values at 0 and increasing to maximum difference around 35 to indicate uncertainty.

    But with this sort of plot I would take the horizontal width of the triangle as a rough measure of the uncertainty.

    • Thank you for doing the work there! The overwhelming impression of the image is “Yellow!” ;)

      Of course, to enable proper “by-eye” analysis, you need to use a colormap that doesn’t fool the eye, which rainbow type colormaps are known for doing – maybe something like matplotlib’s “coolwarm” with it’s centre value of white is more appropriate?

  12. It’s all fine to argue that “Climate is an emergent property of weather”, when you want to make out that climate on the scale of decades is somehow accidental, but for the argument to work, the same logic must be applied to any other kind of climate.

    Why is the climate in the Bahamas consistently different from that in Ontario? Why is the climate in summer consistently different from that of winter everywhere on Earth? All places have weather, and weather is notoriously hard to predict in all places, yet there are (politically uncontroversial) examples of climate all over.

    The point is that there are persistent, stable, structural differences present in the background of every single unique, random, instance of weather. Climate simply cannot be an emergent property of weather -if it was, we’d have no reason to bet against snow in Nassau this Christmas.

    The climates, and seasonal climate changes, we observe routinely all over the world only exist because there are physical mechanisms which exert cumulative effects in addition to the random effects of weather. We know that greenhouse gases are one such physical mechanism; they are to yearly weather variations as the tilt of the Earth’s axis is to weekly weather variations.

    If we created a pyramid graph of the temperature trend between June and January in any city, we would expect the bottom of the graph to vary from the middle and upper sections. This is not even slightly challenging to our understanding of the seasons, because we know there is one major forcing on seasonal change -we know a lot about the mechanism, and we know it will work independently of short term weather variations. We also know a lot about greenhouse gases, and it is not even slightly challenging to our understanding of global warming that the bottom of the pyramid graph varies from the middle and upper sections.

    • Well-said, IMO.

      FWIW, I’d say that both “climate” and “weather” are abstractions, not basic realities. The realities are the physical conditions which may be measured. “Weather” is generalization of those conditions, a recognition of patterns that recur. We can give them names, and that’s extremely helpful in understanding them; we can model them, and that’s helpful in actually predicting them, albeit imperfectly. “Climate” is a generalization, too; originally, the concept was spatially differentiated, but static over time. It was an intellectual shock when geologists began to recognize evidence of Ice Ages, and it was a shock that took a long time to damp out. (Indeed, I’m not sure it has quite finished yet.)

      So, if both “climate” and “weather” are higher-order human abstractions of the physical reality, it’s quite clear that neither ’causes’ the other. Rather, both are founded upon the dynamic physical reality we observe in the realms we call “meteorology” and “climatology”.

  13. Sheldon Walker’s method, and his view, include taking any fluctuation of a trend estimate as a slowdown of global warming. It means taking every fluctuation of weather and calling it a change of the climate trend.

    One of the commonest misconceptions is calling “long” term weather events such as el Nino and la Nina variations in the climate. Then there are things like the annual “State of the Climate” reports by various agencies (,, that reinforce the mistaken notion that climate varies significantly from one year to the next. All these misconceptions help feed into the global warming/climate science denialist meme that climate has always changed therefore what is happening is just more of the same old climate change.

    Weather is not just something that changes from one day to the next as most people seem to think. It changes from one year to the next too. It is disappointing that official agencies actually reinforce the mistaken notion that it isn’t.

  14. Thanks Sheldon Walker! I find these triangles really interesting as a visual of averages of different lengths. But they tell us nothing new. He asks “Where are the El Nino’s, La Nina’s?” Well, these are short time fluctuations so you’d expect to find them along the bottom of the triangles, and …. THERE THEY ARE. Is he not bright enough to understand his own graphs? What was he looking for?

  15. This means Sheldon needs to enroll in Stats -101

  16. IMO, this is much ado about not much. Sheldon is desperate to have ‘slowdowns’, Tamino quite insistent that there is no such beast.

    Absent, though, is any agreed definition of a “slowdown” or of what it means (or would mean). Tamino is implying that a real “slowdown” would mean a change in trend–a sensible position, IMO, since there’s good physical reason to think that planetary heat content, unlike mean surface temperature, can’t be highly variable. Not sure what Sheldon thinks a “slowdown” is, or what it means, or why he thinks its important. But there are those who find GMST variability an interesting topic of study, and it may turn out to be important in some way not yet obvious.

    All fine–the problem comes in when someone tries to abuse variability to sow doubt about trend. That’s something we’ve seen a lot of:

    • That’s just it. I’ve asked Sheldon repeatedly to define what he means by “slowdown”. Hell, we could have a slowdown of warming and cooling on a daily cycle based on Sheldon’s analysis. The dude is stupidity sent to college with a big dollop of narcissism as well.

      • “…we could have a slowdown of warming and cooling on a daily cycle based on Sheldon’s analysis.”

        Yes, and in fact that was a point I made satirically in the “When Did Global Warming Stop” article I linked.

  17. I asked once what is the point of SW’s pursuit. No answer. So I’ll just guess. What people out there are selling is the concept the planet is on the cusp of a prolonged cooling/hiatus from warming based upon ocean dynamics. Wyatt et al’s stadium wave is one rendition of the sales product. What often comes with that is the notion that climate models are wrong because they do not properly account for the ~60-year cycle, and that makes prediction of the climate at 2100 impossible until every crackpot theory about natural variation is included in the models.

    Meanwhile, this recently from Issac Held:

    The evolution of GMT is controlled by a combination of climate sensitivity, radiative forcing, and internal variability. I don’t know of any way to robustly increase or decrease a model’s internal variability on decadal and longer time scales. …

    The slowdown that never happened spawned a large number of studies explaining with observations and scientific speculations what the authors think caused the slowdown that never happened. Maybe you have to deal with it.

    I don’t really think a statistics-based argument is working. It’s certainly not working on SW. If the GMST can go flat for ~17 years, why couldn’t it go flat for 30 years, or better yet, cool for 30 years? Twain, channeling Desraeli, is asking, and you’re answering with “statistics”.

  18. Some more idiocy from WUWT, just cited to me by a ‘skeptic’:

    There’s quite a bit in there that I can dismantle, but perhaps the misuse of statistics from “Bevan Dockery, B.Sc.(Hons), Grad. Dip. Computing, retired geophysicist” may be of interest.

    • A bit of googling and oh dear, has Watts allowed the Dragon Slayers back in? Dockery has an entry at PSI, and is of the opinion that the CO2 increase is due to temperature.

      • Googled it up, and yeah, it’s pretty much the same piece. PSI apparently came first, and now it’s been recycled to WUWT.

        Linear regression analysis applied to the historic data has revealed that both the monthly and annual changes in each of the CO2 concentration and the satellite lower tropospheric temperature generate insignificant correlation coefficients with a high probability that the coefficients are zero. An example is the Scripps Institute data from the Mauna Loa Observatory, Hawaii [1].

        The data shows two very clear and inescapable facts:

        (1) The correlation between the monthly CO2 change and the monthly temperature change was 0.02 with 64% probability that the value could be zero.

        A shock, given that NH trends dominate and that the annual CO2 cycle trends upward in fall and downward in spring.

        (2) The correlation between the annual CO2 change and the annual temperature change was 0.11 with 2% probability that the value could be zero.

        Another shocker, given that we know that the warming trend is much smaller on annual time scales than the variability.

        The Tropics Land satellite lower tropospheric temperature data from University of Alabama, Huntsville [2], was used for these calculations.

        A curious choice, no? Why investigate a global phenomenon with “Tropics Land” data? What, I wonder, would happen if you redid his analysis with some other data set?

        Hence there is no causal relationship between changes in both CO2 concentration and satellite lower tropospheric temperature. CO2 does not cause global warming.

        However, regression analysis has revealed that there is a high correlation between the annual average temperature and the annual increment in CO2. At Mauna Loa this correlation coefficient was 0.69 with negligible probability that the correlation is zero….Clearly the temperature level drives the rate of change in CO2 concentration for reasons which may have been discovered long ago if the UN Intergovernmental Panel on Climate Change (IPCC) had not restricted itself to studying only “human-induced climate change”.

        So “correlation is causation”, apparently. (I don’t think that’s the way I’ve heard that adage quoted in the past.) And it apparently only runs in the direction favorable to the author’s thesis.

        I do spot one difference between the two pieces at this point, though; there’s nothing about correcting for auto-correlation in the PSI piece, whereas he did apply a correction in the WUWT version. Maybe someone dropped him a hint, or maybe he’s been doing some reading on stats.

      • In my view, the fatal error by this Bevan Dockery character occurs in the third sentence. He says “The obvious correlation between the two (CO2 & RSS TLT) raises the possibility that there may be some common causal factor whereby the temperature drives the rate of change of CO2 concentration.” He somehow failed to complete the rest of what that sentence should say ‘…or more likely the “common causal factor” could be the ENSO cycle.’ Then, being into slaying Sky Dragons, perhaps he can also argue that there is some temporal shift in the space-time continuum that allows the months-earlier ENSO wobble to be driven by the months-later global temperature wobble.

      • Or perhaps, Al, the “shift” you speak of somehow gives all the new CO2 the isotopic signature appertaining to FF sourced carbon? That is, after all, a new mystery posed by the “Dockery effect.”

  19. It seems to me that the triangle is saying exactly the same thing as the Sceptical Science plot – the shorter the time interval, the more noise and the easier to draw false conclusions. D’oh!

    For long term trends, look towards the top of the triangle. For the short term trends influenced by El Nino and La Nina, look towards the bottom.

    The Skeptical Science plot has much more clarity, though.

  20. Incidentally, the triangle shows that if there was a “slowdown” around the year 2010, it is well and truly over, and had no affect on the long term trend.

  21. Sheldon, let’s play poker sometime. I look forward to your “analysis” of trends in the cards (and to the money I’ll take from you).

  22. I’m probably one of the less educated and least informed people to post here but even I can see the wrongness and nonsense of the statement that “Climate is an emergent property of weather”. It’s back to front.

    When we talk about weather, what are we talking about; aren’t we talking about events and conditions related to temperature such as humidity, and winds and storms which are the interactions of air masses of different temperatures? Is Sheldon Walker saying that weather patterns just happen magically and through some unknown process create the underlying temperature, rather than the other way around, which is that it’s the temperature which affects the weather, and then averaging it to call it climate?

    People like that can’t be taught and can’t be reasoned with. They would rather resort to any conspiratorial and/or scientific nonsense than admit the planet is warming and we are the cause.

    [Response: I suspect you’re better educated and informed than you give yourself credit for.]

  23. Am I wrong in thinking that the physics of greenhouse gasses is pretty well understood, and that that isn’t even disputed by climate scientists who are on the ‘skeptical’ side? I don’t know of any valid arguments against the idea that more of these gases in the atmosphere will cause increased warming of the planet. Most (but not all) of the arguments seem to focus on surface temperatures (where we live), but isn’t that just 30% of the picture?
    My view is that more energy is being let in to the system than is going out, and that includes the vast ocean where 90% of that excess is going. The system is a complicated dynamic exchange back and forth between the atmosphere and ocean, which is nearly impossible to model but the effects of which can be observed in the long term trend.
    Unless the ‘skeptics’ can show us any mechanism whereby that excess energy isn’t being retained, and explain the melting of ice worldwide, then what are we really arguing about other than the actual rate of (not the fact of) heat increase?

    • The system is a complicated dynamic exchange back and forth between the atmosphere and ocean, which is nearly impossible to model

      The ocean was the source of the so called “pause” (statistically insignificant that it was), so in one sense it’s the ocean (which is not the cause of global warming) that makes it difficult to model the outcome.

  24. There is a small granule of truth in Mr. Walker’s belief that noise is an emergent property of the signal: the more the warming signal emerges from the background of variation, the more the amount denial noise that emerges.

  25. When I read the notification email for thsi post, I immediately thought it referred to Sheldon from Big Bang Theory, who I now see is Sheldon Cooper. What a let-down! I would be much more interested in his views.

  26. I found this interesting enought to give it a try. Using HadCrut4 monthly temperature data this is what I get:

    Which looks fine. But lets map an alpha channel to the inverse of the standard deviation of the estimate:

    and we get a representation of what we talk when we talk about global warming.

    • The ‘de-colouring’ of Shedlon’s pretty graphic is probably not the way to account for the widening error bars that grow so large at the bottom of the triangle.
      I would suggest the colours are adjusted such that, at each level of the triangle, the colour-bands are chosen that match the level of confidence within the data. Thus, by the 20-year trend, the yellow colour would have spread from representing +1ºC to +2ºC to represent +0.5ºC to +2.5ºC. That is by 20 years,half the colour bands would be replaced by their neighbours. By 15 years two-thirds of the original bands would be gone, by 10 year four-fifths, and so on. This would get a bit extreme as the trend lengths reduce. For instance, at 3 years ‘yellow’ would be representing trends of -9ºC to +11ºC but the Confidence Intervals are very very wide when calculating a 3-year trend subjected to autocorrelation..
      And if Sheldon’s pretty graphic was thus adjusted, would there be any colour other than yellow on the entire triangle? If there was, it wouldn’t amount to much.

      • “I would suggest the colours are adjusted such that, at each level of the triangle, the colour-bands are chosen that match the level of confidence within the data.”
        IMO, that’s asking colors to do too many things. My plots offer the option of fading trends that are not significantly different from zero (95%, Ar(1) model uncertainty). Here is an example – you can check a wide variety of datasets at the site:

      • Nick Stokes.
        I don’t think it is I who is ” asking colors to do too many things.” I’m just saying you should adjust the number of colours you use to prevent people reading into your graphs that which is not there. Indeed, is it not you yourself who is asking too much of the colours; bright and shiny one moment, pale and dull the next.
        I would also question your CIs. They do seem to be far smaller than the SkS calculator CIs (about 60% of the SkS value). Indeed, the couple of tests I made showed your CIs to be equal to 4sd from an OLS with no adjustment for autcorrelation. How do you calculate your CIs?

      • ” How do you calculate your CIs?”
        I did a detailed accounting (and comparison with SkS) here, with earlier posts linked there. There is a follow-up in the next post.

        I use an AR(1) model, implemented by a Quenouille correction (more on that here). SkS follows Tamino, I think, in using ARMA(1,1), which generally gives less confidence, but not usually much less. I explain in the first link why I stuck with AR(1), which is the more common choice.

      • Concerning AR(1) & ARMA(1,1), you seem to be less attracted to the latter. For instance, as neither capture that 45-month periodicity, your comment (in your linked account) that AR(1)’s ‘undeshooting’ looks better with longer lags, does that really stand up to scrutiny? And invoking the use of AR(1) elsewhere is not well presented with the Phil Jones/Harrabin Q&A which pre-dates F&R(2011). AR(1) may have been the common method in 2010 but does it remain so? (I suppose IPCC AR5 provides an excuse of sorts.)

        And on the colours: here is a thought. Your fading out of trends that are not significantly different from zero is surely anachronistic. Evey the most hardened denialist shouts about ‘hiatus’ which logically suggests they agree there must have been warming prior to this ‘event’. Surely then, the point of interest is not a demonstration of regions with/without statistically zero warming, but instead regions that are/aren’t statistically equal to the long-term trend. (You will of course note this is a call for my yellow triangle, again.)

      • “instead regions that are/aren’t statistically equal to the long-term trend”
        Yes, I don’t attach much importance to affirming absence of statistical significance. So there are also plots (buttons just below) which show upper and lower CI. And on all plots I have used a special color for 1.7°C/Cen, which was my estimate of expected long term trend. So I would regard the following plot as more useful. The grey shows where the CI equals 1.7; the green inside is below. That is a test of significance in the right direction; the trend was significantly below expected. Of course, since there is a 5% chance of that happening in any given place, the fact that such areas do crop up to some extent is actually overall not significant.

      • Sorry, lost the plot:

      • Nick Stokes,
        Thanks for the pointer to the usefulness of the Upper CI option on your trend viewer.
        As for my yellow triangle, the red/orange in the Upper CI plot will almost all turn yellow as, bar a few points (as shown red & orange on the Lower CI option) which don’t have their Lower CIs below the long-term mean. Thus the triangle is predominantly yellow. If ARMA(1,1) were used to adjust for autocorrelation, much of what is left un-yellow would prersumably also disappear.
        I would post my version of the yellow AR(1) triangle but I note a point of concern.
        Examining the bits that remain significantly-different-to-the-long-term-mean, within the period 2002 to 2013, the flatest bit of the GISS wobble-way, I was surprised at the depth of the dip below the ‘yellow’. Now this is presented with CIs (using AR(1) as you do) which appear rather deflated in size. Looking a bit more carefully, specific to 12-year periods, there is a dip in the size of your CIs (by 75%) that is not present using unadjusted annual or monthly OLS or in the SkS trend calculator output.
        Could there be a reason for this 75% deflation of CIs?

      • Al,
        If I look near the centre of the dip, I have Dec 2001 to Aug 2013, the actual trend is low, at 0.191 C/Cen (GISS). It seems to me that the dip in the CI pretty much tracks the dip in the actual trend, and would probably do so in any other model (eg ARMA(1,1).

      • Indeed, the GISS slope for Dec01-Aug13 is 0.1912(deg C/century) with your Viewer giving the Upper CI at 1.075, the latter bing the quamtity of interest.
        To allow a comparison with an OLS using Annual rather than Monthly data, I have added 3 months to your period to complete 144 months=12 full years. In the table below, the middle row represents the ‘dip’ period with the two other rows ‘before’ and ‘after’ periods.
        (The SkS data uses the shortest autocorrelation assessment period the calculator will allow roughly centred on the regression period. The Annual figure uses 2.2sd for the CI to account for the low DoF.)

        Upper-CI ….. Monthly .. Annual .. NS-Viewer .. SkS Cal’or
        Sep1996-08 …. 2.14 ….. 3.27 …….. 2.69 ………. 3.37
        Sep2001-13 …. 0.76 ….. 1.36 …….. 1.06 ………. 1.45
        Dec2005-16 …. 3.00 ….. 4.18 …….. 3.82 ………. 4.10

        This table does rather show the Annual & SkS-Calculator in remarkably good agreement while the NS-Viewer value provides an outlying deeper dip.

      • Al,
        I ran Sep 2001-Aug 2013 in R Arima, monthly data. I get

        	trend  CI
        NS         0.219  1.061
        Ar(1)      0.243  1.061
        arma(1,1)  0.256  1.19
        OLS		   0.219  0.748

        I was a little surprised that the trend varied so much. But I think the agreement with Ar(1) is good. I quote 95% CI = 1.96*σ.

      • Nick Stokes,
        I think I am also surprised by variation you present in those the central trends. If you are using monthly data each time, shouldn’t the trend be identical?
        Mind, I do have some variation to report myself. Firstly, the 75% (remaining,25% dropped) decribed up thead (Dec 23rd am) is partly fat finger syndrom while running your Viewer.
        More of interest, the trend variations using annual data (with different start-months for the year) are quite marked. This wobble led to my comment that annual data matched the SkS ARMA(1,1) numbers. The wobble actually sits sweetly between your Viewer CIs and the SkS CIs (with short autocorrelation period calcs) and data I calculated coincided with the tops of those annual-data wobbles. Presumably the wobbliness is because when outlying months move from one year-bucket to the next, they shift temporaly by a whole year. You given exemplar of upper CI was 1.19ºC/century, SkS gives 1.45C/c & with 30-year autocorrelation calcs 1.99ºC/c.
        All that aside, taking Your Viewer figures as given, my take on converting your colourful triangle to my yellow triange yeilds the following:-

        Specific to this, the question it raises is how significant is the existance of the two points X & Y on the 12-year trend line, Apr92-Mar04 (0.55ºC above upper CI) and Sep01-Aug13 (0.64ºC below lower CI). With 37-11 years, should we not expect a year outside the 95% CIs? These two X & Y do total more than a year – about 3 years between them. But they do share data so they are not independent of each other.
        In conclusion, I don’t think these trend maps will “end up just being eye candy” (to quote Sheldon Walker on a different whizzy set of graphics he forged). I would argue that these triangles are measuring a rate of change resulting from the variously sized & variously timed ENSO and are far too sensitive to that cycle to show anything of climatological interest.
        An alternative does come to mind, so I shall be back on how that works out.

      • It seems I also lost the plot. The link is here but I will also attempt a second time to paste the image in-thread:-

      • Al,
        “I would argue that these triangles are measuring a rate of change resulting from the variously sized & variously timed ENSO and are far too sensitive to that cycle to show anything of climatological interest.”
        I think they are ENSO dominated in the short term. But they do show an interesting way of looking at it. Each ENSO up or down, very visible on the hypotenuse, casts two shadows, one into the future and one of opposite sign into the past. These show as horizontal or vertical bars. They intersect other bars, and “pauses” are likely to be at an intersection. This is just a fancy way of saying that a pause is likely to have a peak at the start and a dip at the end. But it does show it rather quantitatively.

        “If you are using monthly data each time, shouldn’t the trend be identical?”
        These are the ARMA(?) models, so the trend can vary. I use the Quenouille correction for AR(1), which leaves the OLS trend and just changes the CIs. The general view is that the model shouldn’t affect the trend much; in those cases the effect is more than I expected.

  27. This debate is just incredibly silly. Of course the temperature data goes up and down. You don’t need fancy colored pyramids to see that – just look at the original data.
    There is also no need for fancy statistical methods to see that the long term trend is up.
    What exactly is Sheldon trying to say ?

  28. Regarding Sheldon’s wrong comment “Climate is an emergent property of weather”, it seems to me things would be clearer if the concept of “earth’s energy budget” was more frequently and directly used in climate science communication. Just trying to argue that climate is a separate thing entwined with but different from weather-over-time tends to be a grey and semantic argument, helping enable the (willfully embraced) sort of confusion Sheldon expresses. I think the clearer physical thing to say is that earth’s energy budget, rooted in conservation of energy i.e. first law of thermodynamics, drives the range of warmth for the climate, within which weather can fluctuate (essentially by dynamically swirling heat from here to there, including deeper into the ocean to slow surface warming etc.)

    • Perhaps it is more accurate to say that weather is a deviation from the climate. Neil De Grassse Tyson used a good analogy in the remake of Cosmos. A man walking their dog along the beach on a lead. Man walks in a straight line along the beach. But the dog meanders chaotically around the man, out to the limit of the lead. The man is climate, the dog is weather.

      Essentially energy balance determines where the man is. And energy conservation means that the closer to the limits of the lead the dog s, the more likely it will be pulled back.

      If Climate changes that is the man walking higher or lower on the beach. Or the length of the lead changing giving greater variability.

  29. So, based on Sheldon’s statement “If you can find any green, then you have found a Slowdown,” he’s basically *confirming* the statement being made by the SkepticalClimate animation – that really is how contrarians view global warming. They willfully ignore the long-term warming trend and hyperfocus on the < 10 year time periods that can be made to show a decline, never bothering to explain why the average annual temperature anomalies for the last few years have been higher than those in the 1970s.

    Just in case Sheldon's reading this comment – no, nobody expects you to believe that the *actual* warming trend is a straight line. However, the straight-line *model* is a decent enough approximation of the actual trend to make useful predictions.

    For example, take the time period from 1968 to 1997 and compute the linear trend, then project that trend forward to 2015. *Except for 1998*, the anomlies for all of the following years are within 1 standard deviation of that trend line (i.e., no more than 1/2 std dev above or below that line). 2014 was *bang on* that trend line. 1998 fell outside of that 1 standard deviation.

    So *what* if the actual trend briefly slowed down over a 5- or 10-year period? What difference does it make in any meaningful way? What if it sped up by an equivalent amount over the next 5 years? The *long-term* trend is what matters, and the *long-term* trend is increased warming (which is *what your own contour graphs show*), and by an alarming rate relative to past "natural" warming events.

    • also never bothering to explain that so each and every slow down has been predictive that what will happen next according to them as it happened all the other times) is it will get warmer.. quite suddenly.
      and what do you mean what if it sped up, at the end of every slow down since 1980 that is exactly what happened after their slowdowns.
      Its true statisticians have been describing that well known phenomena as regression to the mean(in this case a mean trend) for along long time. But for them its all surprising and new.

  30. I have different and somewhat unusual question. (not really a question, I can see the answer.)
    (please do be careful as the question cheats because I know the underlying trend in the real temp data is actually a linear rise. This works because of that. Its just funny though.)
    So I see the green regions and I know they were computed as having below average linear regression trends, and normally with a trend you linearly extrapolate to make predictions. But as we’ve been making up stats thus far and ignoring things like confidence limits. What happens if we take learning from data approach and find out what blue/green periods actually predict? And we do that by looking at what happens next and if it usually the same thing then the green predicts that the future temperature will? I am pretty sure you will if you do an analysis find out that green periods predict reasonably reliably the imminent arrival of a rapidly warming period. LOL.
    So green stuff predicts AGCC is about to go gang busters. I mean right after the last pause, we had 2014 2015 2016. Right after the slowdown that ended when Pinatubo did shortly after that we had the gang busters 1998…
    So slowdown should make us all panic because they mean temp is about to suddenly rise. And sudden rises mean another pause is coming…
    The green/red periods are >anti predictive< of what follows (slowdowns predict rapid future rises)(and red bits predict future slowdowns) really.
    I have been for some time been predicting that a no warming since 2014 meme will appear within a few years of 2014 for a while now. Originally I was really banking on an ordinary solar max. But I will take no warming since the 2014-15 El Nino as a more than fair replacement. The last fake pause is dead, Long live the next fake pause. sigh…
    I really should not laugh at people, but sometimes they make it hard not to.
    Also while TBMK antilearning from data is possible a bit, but this antilearning is not a case of that is case of BSitis or regression to the known mean linear trend.

  31. Sheldon Walker’s tricks of course work only on the innumerate and the uncertainly numerate. For those folks, I like to just go with averages for calendar decades (1970-79, 1980-89, etc). A lot harder to fool with than fancy colors. I often offered bets on those comparisons, but alas no takers. Actually, Mr Walker, if you’re still reading, any predictions on the next decade that, absent very unusual volcanism, will be cooler than its predecessor? Or, more to the point, cooler than 2, or even 3, decades previous? I’m offering to bet more than my middle-class US salary on such measurements, details available if you believe your own, um, stuff, and are not too much of a coward to go public with a bet. If we agree to terms, I’ll remain polite, and call you wrong, but not a coward. If you *do* think that decadal averages will continue to climb, then why oh why fiddle around with charts that seem to claim otherwise? C’mon, put yer money where yer mouth is.

  32. OK, blighting out or decreasing saturation does not seem to suffice.

    Another way: How about adding a line at 1 sigma, 2 sigma, 3 Sigma with the confidence level (95% at 2sigma, etc.) shown at the side of the triangle?
    So the full range of fluctuations can be shown (thats the beauty of this charts), with corresponding confidence levels* in plain sight.

    *or better non-confidence levels for shorter periods ;-)