Is the apparent recent acceleration in temperature significant?

Reader nzcpe wants to know. At the RealClimate blog, reader Robert McLachlan wants to know. So do a lot of people.

According to the data from NASA, it is:

The graph shows yearly averages since 1979, but we get the same result using higher time resolution (like monthly averages). The red line (with pink shading around it) shows the result of fitting a parabolic trend line (with its uncertainty range). That’s the simplest, most direct way to test for acceleration; not a panacea, but a natural first step. It easily confirms that acceleration is “statistically significant” with the rate of acceleration estimated at 0.0006 ± 0.0005 °C/yr/yr.

According to the data from HadCRU (the Hadley Centre/Climate Research Unit in the U.K.), it is not:

Again, the red line shows a parabolic fit — but now it looks like a straight-line fit because the “quadratic coefficient” is too small to make the curvature visible. That’s because the estimated acceleration is too small to be “statistically significant.”

Those are just two of the best-known global temperature estimates. There are at least three others widely used, from NOAA (National Oceanic and Atmospheric Administration), from Cowtan & Way, and from the Berkeley team. NOAA agrees with NASA, that acceleration is statistically significant; Berkeley and Cowtan & Way agree with HadCRU that it is not.

Does this mean that the data sets disagree wildly, that their results are suspect? Don’t be Willis ridiculous.

They can disagree about the “statistical significance” even when their estimates are essentially in agreement. Let me plot their estimated accelerations, with an “error bar” showing how uncertain each estimate is:

Just for fun I threw in the estimates according to two other temperature data sets, from RSS and UAH, but they’re not for temperature at Earth’s surface (where we live), they’re for temperature in the lower troposphere (the bottom ten miles or so of the atmosphere).

The likely range from every data set overlaps the likely range from every other data set. That’s not a proper statistical comparison, but it is a sign that the different data sets essentially agree. If you do the proper statistical comparison, you get the same result.

If they agree so well, why do they give different answers to the “statistically significant acceleration” question? Suppose you and I had to estimate the height of Shaquille O’Neal just from wathching videos of his career as an NBA superstar. You guessed 7 feet 2.5 inches, I guessed 7 feet 1.5 inches. Essentially we are in excellent agreement! But given that Kareem Abdul-Jabbar was 7 feet 2 inches tall, we disagree on the question “was Shaq taller than Kareem?”

All data sets estimate acceleration as upward, not downward. But only NASA and NOAA put it high enough to cross the “statistically significant” threshhold.

Global temperature is affected by things other than human activity. In particular, we know of three natural factors that influence it: ENSO (the el Niño Southern Oscillation), volcanic eruptions, and changes in the output of the sun. Published research shows the method I use to remove their influence. This helps isolate the part due to humanity — maybe it will help us decide whether or not there’s acceleration due to humanity. Here’s the result for NASA data:

As you can see, the amount of fluctuation — the pervasive wiggling up and down — is much smaller now. But the acceleration is still there, at least according to these data.

We can similarly adjust all data sets, and test for acceleration in the revised data. Here are the rates we find:

The results are more precise — the “error bars” are smaller — but the results are unchanged. NASA and NOAA say acceleration is statistically significant, HadCRU, C&W, and Berkely (as well as RSS and UAH) say it is not.

What’s the bottom line?

I’m not ready to declare “acceleration.” Not yet.

But there sure are signs. NASA data show it, NOAA data show it. Other data sets (like the ERA5 reanalysis data) show it.

But there are caveats. HadCRU data, C&W, Berkeley, RSS, and UAH don’t show it, even after removing the confounding influence of ENSO, volcanoes, and solar variations. When looking for something significant, if you try many data sets you increase the chance of finding it just by accident.

But I repeat: there are signs. I expect that by 2025 we’ll know much better. If acceleration has begun, we’re in far worse shape than we thought. Even if is hasn’t, we’re already in trouble and headed for much more. Let’s not wait to start fixing this — and that means, wean ourselves off fossil fuels.

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30 responses to “Is the apparent recent acceleration in temperature significant?

  1. The answer will depend a lot on the length of the period. Take a shorter period and none of the datasets will show statistically significant acceleration. Make the period 100 years and all observational datasets show accelerated warming.

    [Response: The question was about *recent* acceleration, and I take that to mean since the last “turning point” we can establish with certainty. That’s about 1975 — earlier for some data sets, later for others — but that’s the earliest time we *used to* be able to say “no statistically significant acceleration.” Starting with 1979 includes most of that time span for all data sets, and enables us to include satellite data too.

    I think the point is that for a long time we haven’t been able to contradict “straight-line trend since 1979.” But lately, for some data sets (NASA and NOAA) that has changed.]

    • My comment was more aimed at your readers, than at you. I was trying to add context for people not analysing with climate data regularly and explain who much work the term recent does.

      It would be interesting to see how much acceleration is possible before the change point algorithm sets another breakpoint and make the new recent warming period a straight line without acceleration again.

  2. Thanks Tamino for this job.

    Interesting is here that C&W’s infilling using kriging interpolation doesn’t show accelaration, unlike NASA & NOAA do.

    I therefore would be very surprised if the data provided by the Japanese Met Agency would!

    because JMA is known to be a bit stingy with infilling.

    Tamino, this is clearly off topic here, but the stuff below irritates me to such an extent that I would be grateful if you had time & interest to go a bit into it:


    [Response: That’s about the most crack-pot crackpottery I’ve ever seen — and I’ve seen a lot. Really, I have better things to do with my time. Especially now. Sorry, but I’m going to do the author a favor by not giving free publicity.]

  3. Thanks for the work.
    Kind o’good news, but only kind of: it’s only linearly heading to catastrophic warming, not faster than linearly (to avoid the practically always misused word “exponentially” here).
    To throw in other, albeit microscopic scale news: my cousin refrained fromt flying to India because of climate reasons. I said: “3 x Bravo!”.
    And we need the price on GHG emissions.

  4. The temperature records have seemed remarkably linear until recently, and that back to 1975. So I would have thought testing for acceleration over the entire period will require a bit of movement to overrule that linearity.

    And regarding the ‘movement’ that has appeared to-date, messing around with the NOAA data, the NH Ocean temperatures as well as the SH Land temperatures do seem to have a bit more vaaah-vaaah-vooom in these recent few years relative to the vaaah-vaaah-vooom in NH Land, while the SH Ocean is showing decidedly less.

  5. IIRC, NASA and HadCRU data use distinct methods to measure/infer temperature on the poles. Would that be a factor? It is generally assumed/observed that the poles warm faster, which now shows up already in the NASA data, but not yet in HadCRU.

  6. The answer also depends upon the p-value cutoff chosen. People can claim that cutoff is picked “by convention” but that doesn’t endow it with any special meaning.

    The behavior as datasets vary isn’t surprising either: p-values are random variables.

    [Response: All of which highlights some of the shortcomings of p-values, and makes a Bayesian approach look good. Someday …]

  7. Excellent work and presentation. I think acceleration is happening, but I accept your work and conclusion that we can be sure yet based on the data. I think you are correct that by 2025 we may have enough data to say definitively, yes, acceleration is happening. We could address global warming on something like a global war financial footing and really turn global emissions down by 2025, but I don’t see much sign that we will do that. Grab your fiddles, Rome is burning. Hot time in the old town tonight.

    • There is acceleration, just not statistically significant over this period. The temperature was slowly going down for thousands of years and is now rising fast, so there sure was a clear acceleration.

      • to VV on acceleration: If the acceleration seen is not statistically significant, doesn’t that mean we cannot rule out noise and natural variation as the “acceleration” being seen?

        If yes, then I don’t think we should say there is acceleration (without the caveats about data set and type of analysis being done). From a precision pov, aren’t we limited to saying that there are only signs of acceleration at this point?

      • If you zoom in thing becomes more linear (less acceleration). That is the reason the round Earth looks flat to the eye. The noise makes it harder to see any acceleration or roundness, meaning that you have to zoom in less before it looks flat, straight, without acceleration.

        It is impossible to explain the meaning of “statistically significant” in a few words without a statistician complaining. So let me give you a link to a source of nearly infinite knowledge.

      • @VV,

        The article on “effect size” at the Fountain of Infinite Knowledge ought to be read in tandem with its article regarding Significance.

      • His point is that over a longer time scale there is an undoubted acceleration, since otherwise the observed change of sign in trend would be impossible.

  8. See also Greenland as in:

    Sander Greenland (2019), “Valid P-Values Behave Exactly as They Should:
    Some Misleading Criticisms of P-Values and Their Resolution With S-Values”, The American Statistician, 73:sup1, 106-114,
    DOI: 10.1080/00031305.2018.1529625

  9. Do the datasets that don’t show a significant quadratic term have a marginally higher linear term? It doesn’t take much of a disagreement in the middle of the time period to alter the quad term, but if they agree on the change over the full period then all that does is change acceleration into average speed.

  10. Hey thanks man, what a top quality answer to my question! Love your work!

  11. Nice work. So, a key difference appears to be SST dataset, not surprisingly. The ERSSTv5-based products indicate acceleration whereas HadSST3-based ones do not. Could you try the Cowtan & Way version using HadSST4 instead (only up to 2018 right now)? That’s much more similar to ERSSTv5 in recent years.

    • Yes, I think there is some Cowtan et al paper showing a cool bias in HadSST3 during the recent two decades.
      Regarding HadCRUT, it has a coverage bias, so full coverage in the Arctic and Antarctic probably enhance acceleration globally.

    • paulski0

      ” Could you try the Cowtan & Way version using HadSST4 instead (only up to 2018 right now)? ”

      I’m not sure it would give the result you expect: when you move to Kevin Cowtan’s trend computador

      and compare there HadCRUT4krig v2 (+ HadSST3) with the new HadSST4 variant, you obtain 0.187 ± 0.035 °C/decade (2σ) with HadSST3 and 0.186 with HadSST4.

  12. Have you got your units correct. An acceleration of 0.0005 over 40 years would increase temperature by 0.0005 * 1600 = 0.8 C. I think your value is 0.0005 C/decade/year.

  13. Oops!. I mean 1/2 * 0.0005 * 1600 = 0.4 C

  14. The forcings in IPCC AR5 annex ii show a rapid increase from 1965-75 and then a steady increase perhaps with a little acceleration. I think this backs up Tamino’s suggested start date.

    The CO2 forcing definitely contributes acceleration (approx 0.00016 C/yr² ) to the system since 1960. The predicted temperature response to the acceleration from CO2 is greater than but comparable to the observed acceleration.

    Since the putative observed accleration is smaller and may yet prove to be zero than this suggests that non CO2 forcings offset the acceleration. Unless this offset increases inline with CO2 however an acceleration of 0.00016 C/yr² will eventually become evident in the temperature data. We have 60 years of CO2 data clearly showing forcing acceleration. In 15 years we will have 60 years of temperature data from 1975. This should be enough to see temperature acceleration despite the extra climate noise.

    However if we steadily reduce the rate at which we increase our CO2 emissions to reach peak emissions over the next decade or so then even though CO2 levels continue to accelerate during this period the forcing (F) will not because of the logarithmic relationship. So the CO2 forcing could increase at a constant rate and the acceleration in temperature may never be observed in the data.

    At the present the net athropogenic forcing is just about showing significant acceleration nearly all from CO2. But if you try to mix in solar forcing the acceleration and significance vanish. And volcanic forcing impacts too.

    So the forcing data back up what we observe in the temperature data. A small anthropogenic acceleration of the right order of magnitude is predicted but is currently being masked by natural noise. But acceleration should soon emerge from that noise unless we change our behaviour.

  15. You said:
    “The likely range from every data set overlaps the likely range from every other data set. That’s not a proper statistical comparison, but it is a sign that the different data sets essentially agree. If you do the proper statistical comparison, you get the same result.”

    You may well have explained this before, but this surprised me a little – I was happy that looking at a set of ranges side by side was a valid comparison? Could you expand on this a little and explain what ‘a proper statistical test’ is in this context? (and in what way lining them up on a graph is not).

    Cheers. And I understand that you may well have more important things to do, but I suspect I’m not the only one a bit confused by this :-)

    [Response: See the latest post ]

  16. John Nielsen-Gammon

    Coincidentally, the issue of what it means (or doesn’t mean) when one set of data is statistically significant and another is not came up separately recently in a New York Times op-ed on what makes a lot of research on childhood obesity so unreliable. If you can see it through the paywall,
    The problem is common enough to have a name: “differences in nominal significance (DINS) error”. Google will show many examples.

  17. A lot of denialists like citing tropospheric water vapor trends from the NCEP re-analysis, even though they’re known to be spurious, as Dr. Dessler showed awhile back. A fairly recent example is from Monckton, though David Evans is also notorious for this:

    The NCEP re-analyses were also a favorite of Dr. Pielke, Sr. But after reading Dr. Foster’s blog posts, I’m wondering about the surface warming trends from NCEP and its update NCEP-2. I think OlofR looked into this already as well. Dr. Foster already covered JRA-55 and ERA5. So NCEP/NCEP-2 would complete the trilogy (the MERRA-2 and CFSR re-analyses are deeply flawed for recent surface warming trends, for reasons I won’t go over now).

    Maybe NCEP/NCEP-2 show acceleration, or maybe they don’t (I suspect the latter). But they still show about the same warming trend as the instrumental analyses. I wonder what its advocates will make of that? Their warming trends are, in K per decade:

    NCEP : 0.17
    NCEP-2 : 0.19

  18. Since global warming is a consequence of radiative forcing, which itself is a consequence of GHG atmospheric concentration, wouldn’t it be logical to see an acceleration in global warming since we have ample data showing a (statistically significant) acceleration in the three main GHG concentrations (CO2, CH4 and N2O)?
    See “WMO Greenhouse Gas Bulletin (GHG Bulletin) – No. 15”

    • @Andrew,

      There are lags, although apparently they aren’t as long as was once thought although there is some pushback from a more sophisticated analysis. The lag is at least 10 years, but Zickfield and Herrington calculate the full warming effects are multiple decades to centuries. They say, however:

      Most of the warming, however, will emerge relatively quickly, implying that CO2 emission cuts will not only benefit subsequent generations but also the generation implementing those cuts.

      • at Andrew: I think your suggestion is completely logical and will be shown to be true. We should slam the brakes and try the emission cuts that Zickfield and Herrington are imagining to see if they are correct. I think Z&H are probably correct, but the big problem is that our species has not been able to slow the increase of accumulation of ghg in the atmosphere so far.

        As always, the discussion about what happens when we reduce emissions seems like a red herring to me because the real problem is GHG accumulation in the atmosphere. I am more interested in discussion of what happens when ghg accumulation in the atmosphere starts to fall. It’s very hard to cook the books on the hard numbers we get from MLO et al.

        Also, as time passes and we watch the MLO numbers rise, we have to start thinking about the cost of deploying the technologies to remove CO2 directly from the atmosphere. It makes sense for the early costs of the removal technology to be funded directly from carbon taxes because that technology and funding source are so beautifully linked and make use of market forces. Human beings respond to market forces.

      • Thanks for those references, eq!