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 std.dev. 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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