Some comment replies require more than just a few brief lines.

Richard Mallett | May 19, 2015 at 4:28 pm |

I see that somebody has been posting replies in italics and within square brackets that do not appear in my email client.

One claims that we can prove that warming has accelerated over time. Since we have had warming and cooling periods as shown below, I would be interested to see how one can prove from such varying data that the warming has accelerated over time. identifies the following warming and cooling periods in GISS since 1880 :-
1880-1912 cooling 32 years
1912-1940 warming 28 years
1940-1970 cooling 30 years
1970-2014 warming 34 years

Response: It appears that you don’t know the definition of “acceleration.” When velocity (generally, the rate of change which in this case means warming rate) itself changes, that’s acceleration. When it decreases one often distinguishes deceleration from acceleration, but mathematically they’re both still acceleration.

Then you want proof — after yourself posting numbers suggesting that yes indeed, the warming rate has changed.

Quite apart from arguing the technical definition of acceleration, the actual point is that you have entirely missed the point. Which is: when velocity has so clearly, provably, and sizeably changed, attempts to extrapolate a linear trend far into the future are a fool’s errand. Put more succinctly, that’s stupid.

But you sure did it. Not just with global temperature but with sea level as well.

It’s something I’ve been trying to get across for a while (read this), especially to the deniers of the danger of sea level rise, who seem the most likely to resort to this idiocy. They also have such blinders on that the only kind of “acceleration” they accept as worth paying attention to is constantly increasing, never reversing, always got to be going faster every minute of every day or — their inevitable conlusion — there’s not a thing to worry about.

The second asks me for statistical evidence that the trend from 1998 to 2014 is different from the trend from 1970 to 1998.

So, since these two comments are related, let’s examine the linear trend from 1970 to 1998 and from 1998 to 2014 on the three main data sets :-

NASA GISS 1970-1998 +1.67 C 1998-2014 +0.83 C per century.
HadCRUT4 1970-1998 +1.73 C 1998-2014 +0.62 C per century.
NOAA NCDC 1970-1998 +1.65 C 1998-2014 +0.56 C per century.

Response: Evidently you don’t know the meaning of the phrase “statistical evidence.”

But you still feel qualified to post what you think constitutes evidence, so soon after having referred to the same post on RealClimate by Rahmstorf which demonstrates the lack of such evidence. But then, I’ve done that myself, not just applying a suite of tests besides change-point analysis, but looking at 8 major data sets.

Perhaps you suffer from that disease where, if something you don’t want to accept involves a bit of complication beyond the simplistic, you’re unwilling to do the work required actually to know what you’re talking about.

The longer you persist in posting nonsense with an air of confidence, the harder it will be when the truth finally dawns on you.


38 responses to “Response:

  1. joeldshore

    “The longer you persist in posting nonsense with an air of confidence, the harder it will be when the truth finally dawns on you.”

    This statement assumes that the truth will ever dawn on him. In my experience with such people, they seem to be able to successfully avoid the truth forever.

    [Response: Don’t be too pessimistic.]

    • arch stanton

      There is indeed some hope:

      A follow-up study, reported in the same paper, suggests that grossly incompetent students improved their ability to estimate their rank after minimal tutoring in the skills they had previously lacked, regardless of the negligible improvement in actual skills.

  2. Earlier today Richard Betts of the Met Office tweeted: “The “pause/hiatus” in global mean surface temperature doesn’t mean global warming has stopped. But it is worth investigating & understanding”.

    Though he’s correct, of course, I responded: “I’d rather refer to it as the “intermittent rise in global mean surface temp”. The variability goes both ways. ;-)”

    I guess I was correct, Katherine Hayhoe ‘favorited’ it.

  3. Richard Mallett

    I have deliberately avoided extrapolating a linear trend far into the future, either with temperatures or with sea level, so that criticism doesn’t apply..

    [Response: From your comment:

    “If we want to use linear trends, since 1850 the linear trend has been +0.49 C per century, so 2.0 C warming would take 408 years from 1850 = AD 2258.

    Regarding sea level, gives the rate as 3.3 +/- 0.4 mm. per year since 1992, so a 4 metre rise would take 4000 / 3.3 = 1212 years.”

    Did I quote you correctly?


    If you don’t accept the evidence of linear trends from 1970-1998 and from 1998-2014 as evidence that those linear trends are different, there is nothing else that I can say to try to convince you that 1.67, 1.73 and 1.65 are statistically different from 0.83, 0.62 and 0.56. It’s as simple as that.

    [Response: Take any time series, of anything at all, one which follows any trend whatever — maybe just a straight line, maybe something else — but does have some noise in it.

    Separate it into two intervals at some moment. Compute the linear trend (by least squares) for each interval separately. Will they be identical?

    No. Never. That different time spans give different numbers isn’t evidence of a trend change. Not at all. None.

    That different data sets (NASA, NOAA, HadCRU) give similar results isn’t evidence either. It just shows that they’re estimating about the same thing, so they see about the same trend *and noise*.

    The real question: when you look at the variations in detail, is the difference in the rates you get big enough that it actually amounts to something meaningful (trend-wise)? That’s the question addressed directly by Rahmstorf, and by me. The answer we both got: no.

    All you did was show that the trend estimates come out different. That’s not evidence, it’s the inevitable consequence of the existence of noise.

    Very fundamental.]

  4. Reblogged this on Hypergeometric and commented:
    Denialist tripe, swatted by Tamino. Now, I know I am learning via the Denial101x course by John Cook that the reason why Deniers are Deniers is because the notion of global warming itself challenges their values or the solutions they imagine are needed to curtail warming are unacceptable. Nevertheless, it is amazing to me that people will repeatedly trot out the same old crap and somehow believe if they do they are advancing understanding. Either they don’t really understand, or they are just parrots of a few key spigots of climate denial. I don’t know the degree to which this is true, but I have read, but have not (yet) investigated that some comments at online news sites are not posted by people but by bots. Now, in Tamino’s case, it’s improbable Mallett is a bot, but this might go some of the way explaining my dismay on why the same old-same old gets trotted out, including the “warming stopped in 1998” thing.

    • Richard Mallett

      You certainly won’t ever get ‘the “warming stopped in 1998” thing’ from me. As I have demonstrated, the warming from 1998 to 2014 is between 0.56 and 0.83 C per century.

      [Response: No, you haven’t. This might be the stupidest thing you’ve said yet.]

      • Richard Mallet.



        Really, just stop. You’re embarrassing yourself, even if you don’t know it yet. Even a competent first year university student would bury your nonsense.

        How can you not see this?

  5. @Hypergeometric:
    “…people will repeatedly trot out the same old crap and somehow believe if they do they are advancing understanding.”

    I doubt any hard core deniers believe that. They believe they are advancing doubt, and care nothing for understanding.

  6. You can’t expect most people to have any math IQ at all. Most stop reading when they see an “=” sign or any other mathematical thing.

    • Richard Mallett

      I have a BSc degree in mathematics, so please use as many equals signs or other mathematical things as you like.

      • And yet you don’t understand basic statistical tests or the concept of statistical significance? Must have been a really “interesting” maths degree you did. I hope they give refunds.

      • I have a BSc degree in mathematics…

        Ask for your money back.

      • Nobody round here is impressed by claims of having a degree, I suspect most of us here have a degree in one field or another (Me? Electronics, 30 years ago.). So, yeah, just another graduate, so much for that. The degree is just the start, what matters is when you are doing the job how you can actually implement the basic knowledge of a degree. In that sense Richard, you are not doing well.

  7. @ R. Mallett — If you are assuming linear trends and are doing linear regression, your software package should be able to provide you with 95% confidence intervals of the slopes. I don’t claim any particular statistical expertise, but this seems like a pretty simple approach to deciding (at least as a first approximation) whether two slopes are different (if I’m wrong, I’m sure Tamino will point that out). In this case, I have done that with the NASA GISS data and find that the 95% confidence intervals of the slopes of the linear regression lines are overlapping for the two time domains you have selected. Thus, I think it is not possible to make a statistically robust case for a pause at this point, or even for a difference in slopes between the two time domains. Also, bear in mind that one of the time series is 28 years and the other only 16. Given the year-to-year variability, I don’t think you have proved anything with your analysis.

    I have not done the analysis with the other two datasets.

    [Response: If one uses monthly data, the autocorrelation is so strong that it effectively invalidates the confidence interval you get from standard statistical software (which assumes a white noise model). If you use annual rather than monthly data, that ameliorates most (but not all!) of the autocorrelation problem, and it will at least get you in the ballpark. That’s for global temperature data, other types will show different autocorrelation structures.]

  8. Tamino — I used annual data. And the data were global temperatures. Not really sure how to deal with autocorrelation issues — as I mentioned, I’m not a statistical expert. Advice would be appreciated.

    FWIW — a plot of the residuals vs. year from the 1970-1998 regression gives a slope of 8.37e-6, and a plot of the residuals from the 1998-2014 regression gives a slope of 7.94e-7, both of which are pretty close to 0. So no apparent trend vs. time in the noise. R^2 values for these plots were 5.3e-11 and 3.15e-13, respectively. No obvious visual patterns in the scatter plots of the residuals. Not sure how relevant that is relative to concerns about autocorrelation.

    • Since linear regression extracts out all possible variation that is, well, linear–that is both true linear signal and chance linear noise–residuals will by definition be as near zero in trend as is mathematically possible. This is what is known as “capitalizing on chance” and is most basically why you tend to see regression to the mean in the first place.

      There are many kinds of patterns in residuals that are problematic but not readily apparent to the eye. For example, a pattern in which every other observation is above and then below zero may look OK given lots of points, but in fact exhibits a negative autocorrelation. Time series distributions very often do exhibit residuals which do not meet OLS assumptions and this is impt to control for in estimating the CIs (estimates of the mean are still unbiased, CIs may be greatly affected, however).

      Most of my work never involved such distributions so I won’t comment further.

      • Regarding “both true linear signal and chance linear noise–residuals will by definition be as near zero in trend as is mathematically possible.” — Yeah, I knew that (or should have). But it was late and I was tired (I know — lame excuse). A plot of the squared residuals vs. year also shows no trend.
        But I think if I want to continue playing with the data, I’ll probably have to dive into the weeds and try to learn how to deal with this autocorrelation issue. I’ve ignored it up to now, although I was aware of it as a potential issue. The software package I’m using is pretty basic.

      • R is cheap. As in free.

  9. I find it funny that instead of understanding the underlying physics involved which would certainly tell us what to expect – a lot of contrarians just look blindy at data as if it’s a crystal ball that is trying to tell them something. You don’t have to jump out of a window in the 10th floor to learn how gravity works. The way the earth absorbs and re-radiates the suns energy is plain physics and arguing whether its real or not is like arguing that gravity doesn’t exist.

    • Well, there are two basic choices, aren’t there? One is to try to rationalize away the physical mechanisms, which the the Path Of The Slayer–down that road lies the argument that back radiation can’t warm the surface because Second Law of Thermodynamics, the argument that surface temps are set by lapse rate and nothing else, because Ideal Gas Law, and other memes which are richly productive of confusion and wasted time.

      The second–convenient for those who are just a little less inclined to imagine themselves ‘the next Galileo’–is to simply look away. Ignore the physics completely, make sure ever and always to pose climate change as a problem existing only in the statistical realm. As the Doobie Brothers sang, “It ain’t so hard to do if you know how.” And boy howdy, some sure do know how.

    • Of course, you should look at the data blindly, because it is very easy to get the physics wrong. The data gives you clues as to where your physics might be wrong. Over time, you’ll improve your physics, and gain confidence in it.
      But as Tamino is fond of pointing out, you should only expect the physics to explain what the data actually shows. The data shows no “pause”, so there is no need to explain it.

      • arch stanton

        “…you should only expect the physics to explain what the data actually shows…”

        That puts it pretty well.

      • Indeed, my point being that the physics is rather solid on what to expect when you rise the amount of CO2 in the atmosphere by over 40% in 150 years time. Most contrarians just throw out all knowledge gained about the physics involved in their quest to seek ways to deceive people with cherry picking and their “look, no warming” nonsense. Surely the more data we get, the more confident we get at the total forcing that the added CO2 affects the planet. But a lot of data can be collected through experiments to shorten the timeframe needed in order to understand the properties of the universe. We don’t have to wait another 100 years for more data about the properties of CO2, they are already very solid and we pretty much know where we will be in 100 years time with regards to global warming.

      • “…it is very easy to get the physics wrong.”

        Sure. But that isn’t a permanent condition, at least, not with respect to specific bits of physics–like radiative transfer, say. It’s not as if thee or me has to reinvent the wheel.

  10. RM,

    Regress temperature anomalies 1850-2014 (or 1880-2014, whatever you have available) on elapsed time, using dT = f(year). Then regress it as dT = f(year, year^2). Do a partial-F test to see if adding the quadratic term is justified. If it is, then warming is accelerating.

  11. Nothing about AGW is a smooth ride. The primary heat sink (water/ice) has a discontinuity as it warms through the interval of 0C. And, another heat content discontinuity as it partitions into the vapor phase.

    Heat transfer processes have oscillations such as El Nino/La Nina. And, as the relative concentrations of CO2, H2O vapor, and other greenhouse gases change, the rate of heat collection changes., For example, a doubling of CO2 significantly increases warming, but does not double it. And, a PULSE of CH4, produces a pulse of warming.

    Thus, the theory of AGW predicts that the rate of atmospheric warming will vary significantly as different time periods are considered.

    In fact, if i saw a linear increase in atmospheric temperatures, I would have to seriously question AGW, and go looking for an alternative explanation.

  12. If you believe in 60-year cycles, the following curve is a proof of acceleration:

  13. The way Mallet shows his sequence of roughly equivalent cooling and warming periods (his first “data set” on top of the article), I wonder why we’re so much warmer now than in 1880.

  14. Hmm, Why does Mallet remind me of “sack of hammers”?

  15. Pete Dunkelberg

    OT Another day another cycle. This may interest Tamino as astronomer.

  16. I love Tamino. Though until now I’ve been a lurker, this has been my favorite blog for some time. And I love the intelligence and humor of many of the commenters as well. “Fractally wrong” and “Steve Goddard” cracked me up. On a more serious note, I’ve made a plot of my own, inspired by Tamino’s “Post-1998 Surprise”, which you can see here:

    • arch stanton

      “Fractally wrong” was indeed a good one.

      Tamino is cool too.

      I guess I just lost interest in (Steve) Goddard a long time ago.

      Beware of “proving” anything on the internet. Jus’ sayin’