CO2 Increase

CO2 in our atmosphere is still increasing. In fact this year the annual average amount has passed 400 ppmv (part per million by volume) for the first time in a long time — at least a million years. The reason: we’re burning fossil fuels like oil, coal, natural gas. When we do, it turns that long-buried carbon into carbon dioxide, which ends up in the atmosphere. It’s as simple as that.

Lately, though, more and more are talking about reducing our emissions of CO2. So, how is planet earth doing? We haven’t stopped increasing atmospheric CO2, but is there any sign that at least we’ve slowed down?

Here’s CO2 concentration from the Mauna Loa atmospheric observatory:


Clearly there’s an annual cycle; we can see the planet “breathe” in and out each year. During spring and summer in the northern hemisphere (where most of the land is), plants grow, absorbing CO2 from the atmosphere. During fall and winter they decay, releasing CO2 back into the air.

So, the first thing I’ll do is remove the annual cycle to give a clearer picture of the changes which are not part of that annual cycle of plant growth and decay. Then I’ll compute yearly averages of such “de-seasonalized” data. We get this:


Yes, it’s still going up. But how fast? I’ll estimate it in two ways. For one, I’ll fit a smooth curve, and a piecewise-linear fit with changepoint analysis, and use those to estimate when and how the growth rate has changed. For an even simpler method, I’ll just take the difference in the amount from one year to the next. Both will give me estimates of how much CO2 is increasing each year, which we can examine for growth rate changes.

Change-point analysis suggests three moments of rate change, at all of which the rate increased:


The changes are a lot easier to see if we first subtract a straight line from the data, showing “linearly de-trended” data and its changes. That gives us this:


This suggests that there’s no change in the growth rate after 2000 — at least, none we can confirm with confidence. We do note, however, that the growth rate has increased over time. This models it as sudden changes from one time span to another, but that’s not necessarily the way it’s really happening.

Here are the year-to-year rates, with a straight-line fit:


The increase from each year to the next, a.k.a. the growth rate, is itself increasing. It fluctuates from year to year, but the overall increase is evident (and “statistically significant”). The present rate of increase is a smidgen over 2 ppmv/year.

Let’s add the rate determined by a “smooth fit” to the data:


Nothing new here. As we saw with year-on-year data, the rate of increase itself is itself increasing. There are variations, but overall the rise in the growth rate has been consistent, and there’s no real evidence that the growth rate has stopped increasing, let along started to decline.

It seems that we know this much: CO2 in the atmosphere is still increasing, and the rate of increase has itself been increasing. But it’s not yet clear whether that rate has changed since 2000.

My best estimate of the present rate comes from taking the monthly data since 2000, and doing a simultaneous fit of an annual cycle and a linear increase.


That estimates the current growth rate is 2.07 ppmv/year (+/- 0.04 ppmv/year).

The world is finally waking up to the fact that to avoid climate disaster, we need to reduce CO2 emissions. But it seems not yet to have realized that what we really need to do is stop CO2 increase. The frightening truth is that not only have we failed to stop CO2 growth, we haven’t even slowed it down.

The more frightening truth is that as warming increases, we run the risk of triggering feedbacks in the carbon cycle. If the warming we’ve already brought about, or that soon to come, releases yet more CO2 from sources other than fossil fuels, well then … the phrase that comes to mind is, “We’re fucked.”

37 responses to “CO2 Increase

  1. excuse my lack of knowledge but carbon banks such as the oceans and increased vegetation are filling up- rather like the bath overflow constricting as the tap continues to drip into the full bath, so are these carbon sinks capable of absorbing at the same rate- will they expand or will they contract? and leading from that is the rate of emission actually growing at a faster rate?

    How does global consumption rates of growth in burning fossil fuels compare with atmospheric content?

    btw I realise that China may over play coal consumption and other growth indicators to give the impression their economic growth rate is healthier than it really is. And there is other areas of growth in CO2 like flaring in the US, forest fires of carbon sinks etc that will not be accounted for.

  2. Tamino: the phrase that comes to mind is, “We’re fucked.”

    Jason Box should have (c)’d that :)

    [Response: I got it from him.]

  3. Thank you, very nice, your posts can be both informative and educational…

    And as to your conclusion that “we’re fucked” (WF = “we’re fucked” ) I concur, but can data alone tell us we are in WF overshoot? So if humans stopped all CO2 emissions, yet Mauna Loa CO2 rates continue to climb, then we would see compelling data of a WF condition. Yes? Is this linear or will it turn to a WF hockey stick? (call it a WFHS!)

    The WF world is nicely commented in song by Broad Commedienne Katie Goodman

    And in poetry by Benjamin the Donkey and his clever limericks at

    His latest:

    Benjamin TheDonkey

    Fuck It

    Fuck It to getting Ahead,
    And fuck getting up out of Bed;
    Fuck crowd-pleasing Cred,
    Fuck me till I’m Dead,
    And fuck teaching doom special Ed.

    Fuck all the bullshit I’m Fed,
    Fuck G, and repeat rhymes I’ve said;
    Fuck the shit in my Head,
    Fuck J up ahead,
    And fuck what I should say Instead.

    Fuck meeting the next Knucklehead,
    And fuck my whole life that I’ve Led;
    M, N, O, and ahead,
    The Q watch me shed,
    And fuck those who think they’re Purebred.

    Fuck all the bullshit I’ve Read,
    And fuck every wrong thing I’ve Said;
    Fuck this whole stupid Thread,
    Fuck zombies Undead,
    And fuck all the suffering Widespread.

    Fuck mistakes, and the words I retread,
    Fuck V, and more Fuck Its ahead:
    Fuku’s X-rays now shed,
    You and me, walking dead—
    Fuck it all, from A down to Zed.

  4. At least a million years, huh? Well, that doesn’t seem so bad, although if the rate of increase is higher it might cause some problems. It takes more that a million years for plants and animals to fully adapt to changes, so they should have the genetics to quickly adapt to the higher levels.

    But wait, you say “at least”. How long has it really been since we were above current levels? Wikipedia ('s_atmosphere) says it has probably been 20 million years. That’s very bad.

    It’s unlike you to understate a problem by so much.

    • The Wikipedia quote you reference is based on rather old data. If you note it is reliant on IPCC TAR data which is (goodness) from the last century. (While the graphed data from that time may not have been so robust, the general finding was robust and may perhaps give pause for thought given where CO2 levels are presently headed. Pearson & Palmer (2000) tell us “Since the early Miocene (about 24 Myr ago), atmospheric CO2 concentrations appear to have remained below 500 p.p.m. and were more stable than before, although transient intervals of CO2 reduction may have occurred during periods of rapid cooling approximately 15 and 3 Myr ago.”)

      The “more than a million years” statement is based on the well-known 800,000 year ice core data which shows CO2 rising to maximums of high-200s ppm during interglacials. Of course, back in 2001 the TAR only had 400,000 years of such data.
      There is also more recent evidence (2009) from the pretty sea shells found in ocean ooze which suggests CO2 was likely entirely below 300ppm for the past 2.1million years.
      Prior to that (paleo-climatically speaking), there was a little peak in CO2 at about 3My bp (due to the processes caused by the creation of the Panama isthmus and leading to the onset of Arctic glaciation) during which CO2 may have topped 400ppm. I see this as unlikely (although there are those who will insist it was then +400ppm). Before 3My bp, CO2 was probably only above 400ppm back 15My bp or so, as per Figure 5 of Zhang et al (2013).
      The general dropping of CO2 levels over the past tens of millions of years is seen as the result of the Himalayas being warn down, which is an infernally slow process for some reason or other. Me, I don’t think those mountains are really trying hard enough:-).

  5. Thanks Tamino. I’m a bit surprised that changepoint analysis didn’t report anything about the fall of the Soviet Union. But my attention was most drawn the more recent years (perhaps focusing on time periods that are too short). I’m actually glad that the growth rate hasn’t recently shown a detectable increase. I was thinking about coal in China, economic recovery elsewhere, and warm Pacific SST perhaps slowing absorption. You make a very good point regarding possible positive feedback tipping points, but I’m encouraged that at least we don’t seem to be accelerating toward them in the short term. Hopefully we can put a downward dent in that growth curve in the near future!

    • Timothy (likes zebras)

      You can see it in some of the graphs (In particular numbers 4 and 6), but I guess that since it was a one-off adjustment, rather than a sustained change in direction, it doesn’t have a lasting impact on the rate of growth.

    • Steve,

      “I’m actually glad that the growth rate hasn’t recently shown a detectable increase.”

      Your relief at that result may have caused you to quit reading too soon. For CPA that’s true but that wasn’t the end of the story. Note this about the CPA:

      We do note, however, that the growth rate has increased over time. This models it as sudden changes from one time span to another, but that’s not necessarily the way it’s really happening.

      then this:

      Nothing new here. As we saw with year-on-year data, the rate of increase itself is itself increasing.

  6. Those that battle disinformation on blogs and in comments section know.
    We will win eventually.
    The laws of physics are on our side.
    The only problem being we also know we will not have satisfaction in the victory.
    All of humanity will lose.

  7. It is rather disappointing, isn’t it?

    A technical question on change point analysis: if one was to do a change point analysis on a quadratic curve (perhaps one resembling the CO2 time series) would it find change points? I.e. could the assumption of a piecewise linear trend with change points force change points to be found on what is actually a smoothly curved time series?

    [Response: Definitely yes. Any continuous curve can be approximated as a piecewise linear function, and changepoint analysis (in this version) will find such an approximation, the one which fits best without including changes which can’t be confirmed statistically.

    That’s one of the possible tricky aspects of this kind of analysis; it forces a model which is piecewise linear, but may be only an approximation to a different curve. As long as we regard it as a useful approximation, and confirmation of reliable slope changes, we’re fine. But it doesn’t prove the actual behavior is a sequence of linear slopes.]

  8. And as a conclusion, we need the bloody price on ghg emissions, and fast. Is this so difficult to get? (to whom it concerns) Be it Hansens carbon tax with redistributing the money, or be it a world wide cap and trade system. Anyone of it will do. But we need it.

  9. Actually, while stopping the increase of emissions is a first step, what we need to do is zero emissions. Reasons?



    Nice curve for the “smooth fit”, BTW. What did you use? Splines? I wanted to do a study like this to illustrate various models in a Kalman smoother.

    Incidentally, an impressive trick that can be done to show technical modeling is really on top of the CO2 curve is to delete some of the monthly points and then use a technique like SSA to reconstruct them. See

    and then

    with reference

    and discussion

    I believe reconstruction can be done with a Kalman RTS approach, too, but I have not done it. I did use the SSA for the two traces linked above.

  10. Considering the fact that the ice age cycle is triggered by a relatively minor force, i.e. the change in solar insolation Milankovitch identified, but driven by feedbacks, GHG and albedo change, it is very hard to imagine that feedbacks are not on the way at this moment. It seems ludicrous to imagine that civilization could drive CO2 from 280 to 400 ppm and well beyond, then stabilize concentration and get away with it. Hansen has been stressing this for years: its an extremely sensitive system being struck with a hammer. You are describing how, decades after it became clear what was going on, that civilization appears to be continuing to increase the rate at which the size of the hammer increases….

  11. Interestingly enough, I was doing similar analysis on CO2 concentration in atmosphere vs global CO2 emissions, using data from NOAA ( and BP (

    And the conclusions seem to be the same: No statistical evidence change in CO2 increase rate a function of global CO2 emissions. For change point analysis I applied the R-code that Tamino used for a paper on “hiatus” last summer (thanks!). Naturally I may have made mistakes in application of that.

    Anyway, in case you are interested, the graphs are here

    1) “big picture” visualizing changes in CO2 emissions, atmosphric CO2 and temperature anomalies!116533&authkey=!AMQuIIRZO3EbSDI&v=3&ithint=photo%2cpng

    2 a) CO2 change trend as function of time (linear fit with error estimates) and emissions on the same graph!116534&authkey=!AONySG89ln2yUgE&v=3&ithint=photo%2cpng

    2 b) Trying to identify a change point with Tamino’s two-piece code (not even close)!116536&authkey=!AHAZx1OnLF7WJqg&v=3&ithint=photo%2cpng

    3 a) CO2 change trend as function of global emissions (showing tiny dots around data points correspponding to NOAA’s estimate of error)!116535&authkey=!AKq2IHhuUvBHwPY&v=3&ithint=photo%2cpng

    3 b) Trying to find change point CO2 increase vs emissions – nothing found again

    Just wondering, if there can be some issues in the reporting of global emissions as they are not as “easily” measurable as CO2 concentration of temperature..?

    • One can plot many things against many things, and it’s not necessarily clear that one choice is necessarily better than another, but I like to get time out of things whenever i can and, so, obtained the following plot of CO2 increase against fossil fuel emissions:

      A linear fit shows the relationship even a bit more starkly, even if the notion that fossil fuel emissions are pretty much monotonically increasing is important to interpret it:

  12. The record is shown in a much less seasonal way by the Baring Head measurement record, second only to Mauna Loa in length.

    Not incidentally, Baring Head is also a site for recording CH4 concentrations, and these have shown the same precipitous increase that we are seeing in the Northern Hemisphere. A few years ago the large increase was being described as nothing to worry about. That didn’t seem credible then and it seems even less credible now.

  13. Emissions per year are about 33 Gtn of CO2. This is equivalent to about 6 ppm. The growth rate in the atmosphere is about 2 ppm. Where does the rest go? Oceans? They should be warming and emitting CO2. Greening the planet?

  14. Sorry, the growth rate in the atmosphere is 3ppm per mass. But anyway, half is missing

  15. Timothy (likes zebras)

    ENSO plays a pretty big role in some of the interannual variation. I forget whether this is because of changes in the ocean circulation/temperature, or because of the impacts on vegetation of the rainfall effects from ENSO.

    This reminded me immediately of your analysis on the global surface temperature record where you performed a multivariate correlation with ENSO, volcanoes, etc, so that you could remove the effects of those factors on the temperature record.

    I wonder whether anyone has done that for the CO2 record, and if that makes the picture at all different.

  16. +Esa-Matti Lilius Yes, about 40% goes into the oceans. There is some slight increase in northern forests productivity, but it is tough to tease out. See:

  17. Esa-Matti Lilius: “Where does the rest [of emitted CO2] go?”

    1) The oceans and 2) terrestrial biomass, particularly northern boreal forests. The portion that remains in the atmosphere is called the “airborne fraction.”

    E-M L: “The [oceans] should be warming and emitting CO2.”

    No, not for a very long time yet. 1) Partial pressure currently overwhelmingly drives CO2 from the atmosphere into ocean surface water and will for a long time to come. That is why ocean surface layer pH is declining. 2) Ocean mass and heat capacity is vastly larger than that of the atmosphere, and ocean heat propagation is very slow, with equilibrium warming on the order of 800-1000 years (the much abused “lag” in the ice core record). Net ocean absorption of CO2 will first need to drop to zero before the ocean can become a net emitter, and so far no decline and corresponding rise in the airborne fraction has been observed.

    • Indeed, while increased oceanic temperature decreases the capacity of oceans to take up additional free CO2, we’re a long way from a “soda pop defizz” due to temperature. This is partly because of the scales and capacities, as Jim said, and partly because CO2 in oceans dissociates and becomes carbonic acid. Indeed, the limitation on ability of oceans to take up additional CO2 in a short time is constrained by the availability of carbonate ions. See Ray Pierrehumbert, PoPC, section 8.4, Zeebe’s notes on dissolved CO2 in oceans at SOEST from Hawaii at, Omta, Dutkiewicz, and Follows (“Dependence of the ocean‐atmosphere partitioning of carbon on temperature and alkalinity“) in GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 25, GB1003, doi:10.1029/2010GB003839, 2011, a detailed exposition from a Stanford oceanography course, and a presentation by Omte, et al of the “Dependence” paper cited above.

      Defizzing isn’t the problem. There is another problem, shown in the 11th slide of the work just cited, Omte, et al, reproduced here. Essentially, once cumulative emissions exceeds 5000 GtC, the ability of oceans to take up CO2 decreases as the Revelle factor decreases. Moreover, quoting Professor RayP (page 520, PoPC):

      Although nearly 80% of the first trillion tonnes of carbon we add to the atmosphere will eventually work its way into the ocean, transforming the environmental problem from one of global warming to one of ocean acidification, it will take 500 years or more for this equilibrium to be achieved. The time scale is set by the time required to mix dissolved carbon species into the deep ocean, since one needs the full mass of the ocean in order to deal with such a large amount of carbon. The deep ocean time scale becomes important because the exhaustion of carbonate ion keeps the upper ocean alone from being able to take up much additional carbon (see Problem 8.13). The important role of the carbonate ion in limiting ocean carbon uptake, and its consequences for the magnitude of the global warming problem, was first recognized by Bolin and Eri[k]sson. This breakthrough is commonly misattributed to Revelle and Suess (see Chapter 1), who in fact completely misinterpreted the effect and thought the ocean could handily take care of any likely amount of carbon humankind could throw at it. It will take about another 10[,]000 years for carbonate ion to be resupplied by dissolution, allowing the pH to rise gradually and the icean to take up additional carbon over that span of time.

      And see for where we stand.

      • Scholarship related to a later discussion begun by Esa-Matti Lilius let to a paper showing the following graph which, although not a shiny new result, confirms the deterioration in the ability of oceans to deal with fossil fuel emissions.

        I dunno about anyone else, but, to me, that’s a pretty scary result, even if it’s just an empirical confirmation of Professor RayP’s explanation.

  18. JE: it is probably not that simple depending only on the partial pressure of CO2. Lot of CO2 goes into the oceans via rain water and I guess also by rivers. CO2 has equilibrium reactions with CO3= and HCO3- Part of these ions are precipitated with metal ions CO2 leaving the circulation. I wonder whether there is any one able to tell exactly what is currently happening to CO2 between earth surface, oceans and atmosphere.

  19. I’ve always regarded the CO2 increase as exponential , C=C0(exp(rt)-1), in line with the emissions increase of about 2% per year (doubling every 35 years) as it has been for the past 200 years. Why would you fit straight lines to something that is clearly better modelled as exponential. Isn’t change point analysis just showing that sooner or later a straight line must fail for an exponential trend.

  20. hypergeometric: thak you very much for the interesting article. So, it seems that I was initially at least half way right. Taken the year 2011: human emissions were 10.4±1.0 PgC. Growth in the atmosphere was 3.6±0.2 PgC (only 35% from the emissions) Oceans got 2.7±0.5 PgC (26%) and land 4,1±0.9 PgC (39%). The earth must be greening efficiently.

  21. Over a short term, CH4 is ~80 times more powerful greenhouse gas than CO2, so considering methane increases over the short term (e.g., ) this year’s rise in equivalent CO2 is more like ~4 ppme.

    Very little above is related to carbon feedback, and while Mother Nature does not post here, she always has the last word.
    ( )

    While I like Dr. Box, and respect his language skills, we need to start looking for a stronger phrase.

  22. Apologies: a typo in my comment. I meant an equation like C = C0 + A(exp(r t) – 1) where r is about 0.02