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Analysis: “The content of carbon dioxide in the atmosphere is accelerating super-exponentially.”

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"Analysis: “The content of carbon dioxide in the atmosphere is accelerating super-exponentially.”"


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UPDATE 2: Thanks to this post, the deniers finally conceded that “the rate of atmospheric CO2 growth has been increasing” — but in a callous, error-riddled post, WattsUpWithThat cheers on the preventable calamity.

UPDATE 1:  I had a good conversation with the co-author Didier Sornette.  This was a draft analysis:  They made a numerical mistake in one of the footnotes and used some inapt wording in a couple of places, none of which changes the main conclusion about CO2 concentrations.  They will be revising the paper and I will make some changes below.

Recent climate science is unequivocal that human civilization is on the precipice.   Climate science also finds that we are pouring carbon dioxide pollution into the atmosphere at an unsustainable rate.  A 2008 Nature Geoscience study found that humans were boosting CO2 levels 14,000 times faster than nature, overwhelming slow negative feedbacks.

That study found, “the mean long-term trend of atmospheric CO2 levels is no more than 22 p.p.m.v. over the past 610,000 years.”  Humans have run up CO2 levels 100 ppm over the last two centuries!  The author of that study noted, “Right now we have put the system entirely out of equilibrium”

It turns out that a purely mathematical analysis, “Evidence for super-exponentially accelerating atmospheric carbon dioxide growth,” comes to a similar conclusion.

The paper itself is mostly mathematically and essentially agnostic on climate science.  But the conclusions are as stark as any in the climate literature:

Overall, the evidence presented here does not augur well for the future….

  • Notwithstanding a lot of discussions, international meetings, prevalence in the media, atmospheric CO2 content growth continues unabated with a clear faster-than-exponential behavior. On the face of this evidence using data until 2009, stabilizing atmospheric carbon dioxide emissions at levels reached in 1990 for instance seems very ambitious, if not utterly unrealistic. We are not pessimistic. We think that only evidence-based decision making can lead to progress. The present evidence gives some measure of the enormous challenges to control our CO2 emissions to acceptable levels.

NOTE:  I left out the ellipsis, so one denier who didn’t read the whole revised post was confused into thinking the authors removed their population conclusions.  No, they are just changing the wording slightly.  In my revision, I moved the population discussion, which is tangential to the climate conclusion, to the end — as anyone can see!


Of course, exponential growth is more than worrisome enough.

That said, we appear to have amplifying feedbacks in overabundance (see “NSIDC bombshell: Thawing permafrost feedback will turn Arctic from carbon sink to source in the 2020s, releasing 100 billion tons of carbon by 2100“).

The solution certainly isn’t easy, but it is, at the same time, straightforward — with benefits that vastly exceed its low net-cost (see “The full global warming solution: How the world can stabilize at 350 to 450 ppm“).

As for “prevalence in the media,” that certainly hasn’t been super-exponential or even exponential or even growing — heck, it’s been shrinking (see “Silence of the Lambs: Media herd’s coverage of climate change “fell off the map” in 2010“).

It is high time for people outside of the climate science community to speak out about how unsustainable our emissions are (see Lonnie Thompson on why climatologists are speaking out: “Virtually all of us are now convinced that global warming poses a clear and present danger to civilization”).

You can read the fascinating bio of one of the authors, Didier Sornette, an expert on risk analysis, here.


The study states in the abstract:

Our empirical calibrations con firm that human population has decelerated from its previous super-exponential growth until 1960 to “just” an exponential growth, but with no sign of more deceleration.

And its population conclusion is:

The human population is still growing at an exponential rate and there is no sign in the data that the growth rate is decreasing. Many argue that economic developments and education of women will lead to a decreased growth rate and an eventual stabilization of human population. This is not yet observed in the population dynamics, when integrated worldwide. Let us hope that the stabilization of the human population will occur endogenously by self-regulation, rather than by more stringent finite carrying capacity constraintsthat can be expected to lead to severe strains on a significant fraction of the population.

Those statements are at odds with the study’s own chart on population and this statement in the text:

… the growth rate of the World population was a strongly increasing function of time till the late 1950s. A sharp decrease of the growth rate occurred, then followed by a resumed acceleration till its peak in 1964, from which a slow decrease can be observed.

I asked Sornette about the inconsistency, and he realized that their use of language was inapt and needed to be changed slightly.  He was referring to the seeming slowdown very recently in the rate of decrease of population growth:


I don’t write much on population here — see “Consumption dwarfs population as main global warming threat” for the reasons — so I didn’t look at the statements on population closely enough in Sornette’s draft paper.  My bad.

It is, of course, widely believed world population will stabilize by mid-century:

World population from 1800 to 2100, based on UN 2004 projections (red, orange, green) and US Census Bureau historical estimates (black).

Sornette’s point on population was primarily that the very recent trend is not consistent with the rosier population projections — and we’re already well past the planet’s carry-capacity.  Hard to argue with that last point.

There’s also a dumb mathematical error in a footnote that is transparently at odds with the data (including the data in the study), which the anti-science crowd (aka WattsUpWithThat — they get upset if you don’t mention them by name) has naturally pounced on.  It isn’t germane to the study’s main conclusions.

Sornette is now working on a revision.

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27 Responses to Analysis: “The content of carbon dioxide in the atmosphere is accelerating super-exponentially.”

  1. Ominous Clouds Overhead says:

    Sornette: Known for prediction of crises and extreme events in complex systems, physics of complex systems and pattern formation in spatio-temporal structures.

    An expert in both economics and geophysics. Interesting couplet of subjects. He can presumably forecast the disaster and then tell you its effect on the economy.

    Maybe he’s agnostic about climate science because he deems it irrelevant, his “stringent finite carrying capacity constraints” will see us all extinct before climate becomes a problem.

  2. Gestur says:

    Quoting the authors, “In summary, we find a very robust FTS behavior for CO2 over a broad and realistic range of parameters, which makes it difficult to constrain the impact of the advance of technology on production efficiency.”

    I’d say that a fair translation of the authors’ conclusion is that the Fat Lady has indeed begun her song. It’s early in the song and so it’s not entirely clear how its lyrics will end. But she’s singing, oh yes, she’s singing.

  3. Gord says:

    Good paper.

  4. David F. says:

    I just saw an interesting chart in the USA Today… it showed the sources of current U.S. power and all of the renewable, green energy sources were less than 1% of the total power generation. The accompanying article stated it would take decades for those power sources to reach even the 9% currently generated by nuclear.

    This is disconcerting. As you have stated, we need to immediately commence a WWII-type effort at making renewable energy sources a much larger proportion of the total power generation. The rig explosion and oil spill in the Gulf and this nuclear crisis should be a strong enough incentive, even if we weren’t heading towards catastrophic climate change. Yet, I don’t see Obama (and certainly not Congress) doing much to change this. Rome is burning, and our leaders are playing the fiddle!

  5. Merrelyn Emery says:

    The word ‘civilization’ is inappropriate. It is neither civil or civilized to breed ourselves out of existence, continue to pour CO2 into the atmosphere or produce nuclear waste for a future we cannot control, ME

  6. elvinator says:

    at times like this we must remind ourselves that rome wasn’t burned in a day.

  7. Bob Lang says:

    My prediction of the future of humanity is depicted here:


  8. Joan Savage says:

    Seven billion people, weighing on average 70 kg each, collectively store about 112 million metric tons of carbon in our personal biomass. That’s roughly one-thousandth the permafrost storage of carbon.
    It seems like one place to start a conversation with a public audience about the magnitude of the carbon releases.

  9. Chris (from Vancouver) says:

    I don’t see the problem. Once we get to 1000 ppm, and we run out of oil we’ll just find a new source of energy.

    Roll my eyes. And resign myself to the fate of our climate.

  10. Rob Jones says:

    Merrelyn Emery

    Indeed you have succinctly summarised humanities failings.

  11. Eric Thurston says:

    “The human population is still growing at an exponential rate and there is no sign in the data that the growth rate is decreasing. Many argue that economic developments and education of women will lead to a decreased growth rate and an eventual stabilization of human population. This is not yet observed in the population dynamics, when integrated worldwide.”

    Joe, from the EarthTrends database http://earthtrends.wri.org/# I have noted the worldwide drop in total fertility rate and the worldwide drop in raw birthrates of the human population, affecting virtually every country on the planet. I believe these trends are what the UN agencies use to predict the leveling off of population sometime around the middle of the century.

    The statistical signs (of a population peak and decline) are definitely there. The question remains as to whether it is too little, too late or not.

  12. Roger says:

    Good Lord! Katy, bar the door.

  13. Mulga Mumblebrain says:

    The really sickening truth is that humanity is being destroyed by the psychopathic behaviour of a tiny, ruling, capitalist elite who have mobilised a rabble of mostly geriatric obscurants and ignoramuses to destroy their own grandchildren’s future. The vast majority are still too apathetic, uninterested, or frightened to appear ‘radical’, to act, or too obese to lurch from their lounges to do anything. The young here in Australia are getting enraged, a very good sign, as this boil will not burst of its own accord, but will need to be lanced, and soon(God, how long have people been saying that!)and then there will need to be a ‘healing crisis’ if we are lucky, lasting a few hundred years, or a rapid collapse of global homeostasis and a quick decline to death.

  14. pete best says:

    Even if you point out the obvious it wont stop it happening. This is why every optimistic soul on the planet keeps on talkng about mitigation by 2050 and then it will be 2060 when we have not done a lot by 2020.

    Same old same old for the time being.

  15. nen says:

    Jon Jermey:

    Willis admits he didn’t read the paper. If he had bothered to read it he would have found:

    “Figure 7 shows that the growth rate of the World population was a strongly
    increasing function of time till the late 1950s. A sharp decrease of the growth
    rate occurred, then followed by a resumed acceleration till its peak in 1964,
    from which a slow decrease can be observed.”

  16. Dodgy Geezer says:

    “..The human population is still growing at an exponential rate and there is no sign in the data that the growth rate is decreasing..”

    This comment seems to be completely wrong…

    The world population figures clearly show that we have a spurt of growth which is currently decreasing. WHO and most others assume that it will continue to fall – this paper just assumes it will stay at the figure it is today. And I can see no consideration of death rates, which are essential if you are considering population growth….

  17. Dan Olner says:

    Gotta say, my hackles went up a bit with the phrase “faster-than-exponential.” While it’s mathematically possible to define a faster-than-exponential function, I can’t see why you’d want to apply that to growth of something like CO2. You should just be able to define it in terms of a certain growth rate just using e and defining the timesteps, surely?

  18. Raul M. says:

    Call to redefine the current
    Exponential pace to more in
    Keeping with actual exponential

  19. with the doves says:

    there is evidence of world pop growth slowing.


    compare pyramids for 1990, 2000, and 2010 – note that the base of the pyramid becomes more vertical 2010.

  20. Leif says:

    While the population growth is in fact a problem I continue to feel that the real problem is consumption and the Carbon Stomp of large numbers of the populations of the world. They are the ones that are inflicting the most damage to the Earth’s Life support systems. The world has many millions with a carbon stomp of a thousand third world folks and a goodly number with a carbon stomp of tens of thousands. Now that Corporations have been classified as people? It is anyones guess.

  21. Tim says:

    I don’t see that the meat of this article article accomplishes more than curve fitting. Here’s an exponential function that does a very good job on all the Mauna Loa data and extrapolates backward to the correct pre-industrial value (X(CO₂) is the atmospheric mole fraction of CO₂ in ppm, y = year):

    X(CO₂) = 285 + 2.3•exp{(y – 1850)/42}

    Heck, if you want the seasonal variation thrown in, add 3.2•sin{2πy) – 1.4•cos[4π(y – 0.66)]

    [JR: I tend to agree that "exponential" is plenty worrisome by itself.]

  22. Dan Olner #18,

    “Faster than exponential” just means “more than log-linear” to a mathematician.

  23. Jane Doe says:

    Good paper.

    Mankind is surely in deep trouble. I note that the recent tsunami was probably caused by GW, so maybe there is a feedback system that will even things out in time.

  24. Jon Jermey says:

    Zot! Suddenly I’m a non-person! But I KNOW I was here because somebody replied to me.

    This never would have happened at WUWT.

    Wonder how long before I disappear again…

  25. Matt Bergin says:

    The world isn’t that populated. The entire 6.5 billion people would fit into the state of Texas. I have done the calculation myself. I admit there wouldn’t be much room left but they would fit. I remember reading The Population Bomb back in the seventies and none of the authors predictions have come true, and only time will tell with this paper but I not holding my breath. Windmills and solar cells will never supply enough energy even if we covered every square inch of the land surface on this planet with them.

  26. Mulga Mumblebrain says:

    Matt #26, when you have squeezed your 6 billion into Taxas, will you be in any way annoyed when someone defecates on your feet? I rather admire pan-denialism, that lumpen Panglossian so beloved of the more hyperactive Dunning Krugerites out to impress their peers. Nothing’s going wrong, nothing can go wrong because either ‘the Holy Market, ‘the Invisible Hand’, ‘God Almighty’ or ‘technology’ will come to our rescue in the nick of time. Dream on.