Another “Pause” Claim

There’s a new “pause” claim, but it’s not a pause in temperature, it’s a pause in the rate of CO2 growth. Not a pause in growth, of course, but a pause in the rate of growth.

It wasn’t long ago I posted about how I don’t see any evidence that CO2 has stopped accelerating, i.e. that the growth rate has stopped increasing. But a new paper by Keenan et al. concludes that acceleration has stopped, reverting to CO2 increase at a constant rate. I’m skeptical.

Here’s the data they use for the CO2 growth rate (from here):


The dashed line shows when they believe a “pause” began. The analysis on which they base the claim of a “pause” in the growth rate seems to be this:


Figure 1 | Changes in the airborne fraction and the CO2 growth rate. (a) Observed (solid black line) and modelled (DGVM ensemble—mean (dashed black line) and s.d. (orange area)) changes in the atmospheric CO2 growth rate from 1960 to 2012. The vertical grey line (2002) indicates the point of structural change identified using a linear modelling analysis. The red lines indicate a significant increasing trend from 1959 to 1990 (solid red) and 1959 to 2002 (dashed red) (P < 0.1), with no trend evident between 2002 and 2014 (blue). All trends are estimated using the non-parametric Mann–Kendall Tau trend test with Sen’s method. The grey area represents the underlying 5-year dynamic (mean±1 s.d.), estimated using SSA.

I estimated the trend lines using the Theil-Sen method (as they did) myself, for the time intervals they quote. I get this:


My calculated trend lines differ from theirs, just a little, but noticeably. I wrote my own program for Theil-Sen, so this made me question whether I’d made a mistake. To find out, I downloaded the “zyp” package for R to calculate it independently, and confirmed that I got it right.

Why the difference? I can’t be sure, but it’s possible that the data have changed slightly (only slightly) since they downloaded it.

I also computed the linear trend using least squares; the results are statistically indistinguishable from the Theil-Sen estimates:


They didn’t really need to use the Sen slope estimate, least squares would have been fine, and the residuals show no sign of any autocorrelation (Box-Ljung and Box-Pierce tests) or departure from normality (Shapiro-Wilk). But Theil-Sen is also just fine.

The interesting thing is that they seem to base their claim of a pause (not a claim of a possible pause, but an outright assertion) on the linear fits. But here are the estimated rates for the entire time span and the three time spans they display, together with 95% confidence intervals:


I know the simple comparison of confidence intervals can be misleading, but it actually increases the chance of a false conclusion of trend change, so genuine evidence for a trend change in CO2 growth rate is simply not there. The same conclusion follows from doing it right — by fitting a trend-change model without jump discontinuity, and by fitting a trend-change model with jump discontinuity (and using the Chow test).

That doesn’t mean there was definitely no such change — this is statistics, we don’t get to do that. But the evidence for it is so weak, so not even close, that to assert it rather than suggest it as a possibility seems to me to be very bad practice.

The real kicker is that another year’s data is available since they captured theirs for this analysis. When we add the final year, suddenly the graph looks like this:


I know it’s enhanced by the recent el Niño, but so will be 2016 (for which CO2 growth has yet to be determined) … and it’s still higher than preceding el Niño years.

All in all, the statistically best model for the CO2 annual growth data is a straight line, with no slope change, plus Gaussian noise with no autocorrelation:


Dr. Keenan suggests that the real evidence for a “pause” is in the singular spectrum analysis (SSA); it’s represented by the gray area in their graph. First, their +/- 1 range is, it seems to me, way too small. I know from experience how theoretial calculations of same can be extraordinarily difficult, so I ran some Monte Carlo tests to find out. According to my results, the uncertainty is way bigger than is plotted on that graph. My suggestion to Dr. Keenan: generate some time series with the same slope and residual standard deviation as the observations. Run exactly the same SSA you used, on those linear-trend-plus-white-noise series. Find out how many of them give just as much or more “evidence” of a “pause” somewhere. I expect you’ll be surprised.

Is a “pause” in the growth rate possible? Of course, it always is. Is it demonstrated? In my opinion, there’s not just a lack of statistical proof, there’s a lack of evidence at all.

The only thing I see in this entire work which makes the claim even plausible as a possibility (but by no means established), is comparison of the CO2 growth data to what they expect based on their carbon cycle model. This is illustrated in their figure S1 from the supplementary information:


Supplementary Figure 1 | Divergence of the atmospheric CO2 growth rate from a linear model of atmospheric CO2. (a) Observed (black dashed line) and modeled (solid red line) growth rate, and (b) residuals between the observed and predicted atmospheric CO2 growth rate from the linear model. A clear divergence is visible during this century, which is significant from 2002 (at p < 0.05, vertical orange dashed line on panel b), indicating a change in the efficiency of global CO2 sinks.

I do think the research is very interesting and addresses questions well worth knowing about. I also think they may be on to something about changes in how the biosphere is taking up CO2 and in the airborne fraction (how much of our emissions remain in the atmosphere). But I dearly wish they hadn’t been so assertive of a change, let alone a “pause,” in the CO2 growth rate (i.e., acceleration of CO2 concentration) when I see absolutely no basis for it.

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17 responses to “Another “Pause” Claim

  1. Thanks for that…

  2. Blimey, for a minute there I thought *Doug* Keenan had got into Nature Communications.

  3. This is a measurement for which it seems reasonable to suggest an ‘instantaneous’ change in growth rate, and a discontinuity – down, at the time the Soviet bloc and their economies collapsed, so around 1990. The countries’ emissions, calculated by fossil fuel use, are well documented as dropping sharply at that time.

    You might argue whether that ought to be used as ‘start to 1990’ and ‘1991 onwards’, or ‘start to 1990’ and ‘1992 onwards’ or similar. That would, I suppose, give a slightly higher growth rate both before and after the discontinuity.

  4. I have been seeing some day on day CO2 sat numbers that suggest the rate is dropping from the 3.5 ppm range back into the under 3 ppm range. This is expected as EN passes into rear view mirror so that the year on year comparison looks at a current non-EN number against the EN number from the previous year. I have been waiting to see that increase number go flat and maybe that has started. Daily and weekly averages are very noisy so I think they should be considered anecdotal.


    November 9, 2016: 402.94 ppm
    November 9, 2015: 400.29 ppm
    2.65 ppm increase.

    As always cherrypicking the time frame for comparison and then extrapolating a pause, change in trend, etc is an indication that the presenter may be acting in good faith or best practice.

  5. Tamino, since you mention above that atmospheric CO2 levels are affected bu El Nino (and I would assume other factors like volcanoes (maybe)), do you think it would be worthwhile to do a similar analysis for CO2 levels (or acceleration) vs confounding factors like ENSO, volcanoes, and anything else you can think of (like global economic activity, for example)? I wonder if that would smooth out the long term trend for CO2 fluctuations like your analysis has done for the global average temperature trend. It’s nice to be able to get rid of the noise long enough to focus on the trend a little better, and it’s also interesting to quantify the effects of various inputs as you have done for temperature.

    Thanks foe all you do, from someone who has been reading your blog for a long time even though I rarely make comments.

    [Response: Yes, I think it would be worthwhile. Might also be fun. But it’s also a fair amount of work. Given the result of the recent presidential election, I might turn my efforts in another direction. I’m considering doing less of the detailed technical science and more of the “outreach” and “education” stuff. Some readers may be disappointed — me too — but my own satisfaction is less important than informing the voting public at large just how bad of a mess we’re in, and how bad it’s going to get, soon.]

    • Argh, Tamino, the dilemma! We need two of you!

      The least peeps could do it to slip some appreciation into Peaseblossom’s Closet.

    • Tamino:

      my own satisfaction is less important than informing the voting public at large just how bad of a mess we’re in, and how bad it’s going to get, soon.

      As a strictly amateur scientist, I’ve long suspected my own “outreach” and “education” efforts are only for my own satisfaction. I may get a few upvotes on comment threads in public fora, but the election of a truculent AGW-denier as POTUS at best fails to confirm I’ve educated anyone. Lost in the noise, no doubt 8^}.

      Thankfully, Tamino’s track record allow me to hope his results will be better than mine.

  6. We published a prediction of the CO2 growth rate for 2016 – a record rate, above 3ppm/yr, higher than recent years due to El Niño, but also higher than 1997/98 because of course emissions have increased by 20% since then

  7. I have a question not sure if you are the right kind of person to ask. But you would know who or where is I hope.
    The world is warming, net energy is going into the oceans. If at some future time net energy was coming out (a lot as water vapor) id expect that to both possibly push up water vapor feedback, and storm intensity.
    Similarly: When we even get to a stable temp for our new Co2 level, might water vapor feedback be even higher than it is now? if that is significant is it in the GCMs underlying physics model?

  8. I suppose I might be a bit mean to suggest this, but maybe Keenan et al wanted to get published, and had they waited for a change in trend to be statistically significant, they may well have never been able to publish.

    But watching the CO2 levels in the atmosphere and how they are changing is definitely something worth doing. How else do we know if any of our efforts to reduce CO2 emissions are working?

    • …had they waited for a change in trend to be statistically significant…

      Indeed John – I wondered the same thing.

      Of course at some point in the next decade or two ‘pausing’ and thence plateauing will occur, simply because we live on a finite planet (and Sprengel and Leibig are relevant with respect to things other than CO₂), but perhaps the wisdom of waiting to publish at that time and with respect to the story then did not overwhelm the desire to churn out this effort and its particular claim…

  9. We sure could use some good news right now, but realistically I can’t see how this could be possible without some well understood mechanism driving that rate change.
    But argument from incredulity is not good reasoning either.

  10. Wondering what you make of this paper and the one that precedes it:


  11. Greetings, It’s been a while since I’ve spent any time here, good to see you again!
    I’ve been looking at this paper for a few days, still trying to break everything down. That said I did notice that your graphs are labelled as dealing with global temps, and their graph is dealing with terrestrial data (data gathered only over continental land masses, Could this be where and why the two graphs diverge?

  12. excuse me, “global CO2 data” instead of “global temps”