Drawing down atmospheric CO2 – part 2

I’ve finally got some time to write up my second post on drawing down atmospheric CO2. In the first post I was trying to get across two basic things. One was that it’s important to distinguish between the residence time for a single CO2 molecule (short), and the time over which an enhancement in atmospheric CO2 would decay back to equilibrium (long, by comparison). The other was that there is more than one carbon cycle; a fast one that cycles CO2 between the ocean, atmosphere and biosphere, and a slow one that sequesters CO2 into the deep ocean and lithosphere, and returns it via volcanic activity. The long-term, quasi-steady atmospheric CO2 concentration is largely set by the slow cycle, and hence returning to quasi-equilibrium – after an enhancement – can take a very long time (10s of thousand of years).

It is in fact, even more complicated than I indicated earlier. There are really more like three carbon cycles. There is a fast cycle that involves CO2 being taken up by the biosphere and being dissolved in the ocean. This reduces the ocean pH, changes the saturation state of the ocean with respect to calcium carbonate (CaCO3) and results in a slower cycle involving chemical reactions between CO2 and CaCO3. The slowest cycle is associated with weathering, in which atmospheric CO2 reacts with carbonates and silicates in rocks.

That the drawdown of atmospheric CO2 is initially quite fast should be evident from the fact that more than 50% of what we’ve emitted to date has already been taken up by the biosphere and the oceans; only about 45% remains in the atmosphere. Now, I want to clarify something here. When I say about 45% remains in the atmosphere I don’t mean that 45% of the specific molecules we emitted are in the atmosphere; I mean that the enhancement in atmospheric CO2 (relative to pre-industrial times) is equivalent to 45% of what we’ve emitted in total.

You can actually use this to try and estimate an atmospheric residence time for anthropogenic CO2. You can assume that there are quasi-steady fluxes into and out of the atmosphere and that any enhancement in atmospheric CO2 increases the flux out of the atmosphere, and that this increase depends linearly on CO2 concentration. If you do this, you essentially get that the concentration decays according to

C(t) = C_{\rm eq} + C_{\rm inj} \exp^{-t/\tau},

where C_{\rm eq} is the equilibrium concentration, C_{\rm inj} is the amount injected into the atmosphere, and \tau is the e-folding time (or adjustment time). This type of analysis leads to estimates for \tau of between 50 and 200 years. This is where – I think – one of the first problems comes in. If \tau \sim 100 years, then that would imply that 37% of the amount injected into the atmosphere would remain in the atmosphere after about 100 years. If you carry on, then you might conclude that there would only by 13% remaining after 200 years, and after 500 years, less than 1%.

Credit : Archer (2005)

Credit : Archer (2005)

This, however, is wrong. Why? Because injecting more CO2 into the system changes the equilibrium concentration associated with the fast cycle. Dissolving CO2 in the ocean increases the partial pressure of CO2 in the ocean and – consequently – increases the corresponding CO2 concentration in the atmosphere. This is illustrated quite nicely in the figure on the right, taken from Archer (2005).

It shows initial injections of 4 different amounts of CO2 and – in each case – three different calculations. One considers only the dissolution of CO2 in the oceans, and runs to 10000 years. The next considers this plus the calcium carbonate cycle, and runs to 30000 years. The final one consider all 3 cycles, and goes all the way to 100000 years. As should be clear, if you consider only the dissolution of CO2 in the ocean, then an injection of CO2 results in a stable atmospheric concentration that is higher than it was initially; the difference depending on the amount injected. For example, adding 1000 GtC will increase atmospheric concentrations from 280ppm to 350ppm. As you add the extra carbon cycles, the concentration eventually returns to what it was prior to the injection of the extra CO2. However, the overall time it takes is longer than 100000 years.

Credit : Archer et al. (2009)

Credit : Archer et al. (2009)

The figure on the left, from Archer et al. (2009), shows what happens on timescales of 1000 years (left-hand side), and 10000 years (right-hand-side). It also shows initial injections of 1000 GtC (top-panel) and 5000 GtC (bottom panel). The different curves are for different models. As can be seen, the initial decay is quite rapid (Archer et al. estimate an adjustment time of ~ 250 years) followed by a much slower decay over the next 10000 years. For an initial pulse of 1000 GtC, about 20-25% of the CO2 injected into the atmosphere remains after about 500 years, and 10-20% after 1000 years. For an initial pulse of 5000 GtC, typically more than 30% remains after 1000 years.

This post is getting rather long, so I’m going to leave the rest of what I was going to say for a third post. The main point I was trying to get across here is that by injecting new CO2 into the atmosphere, the concentration to which the fast cycle will tend is higher than it was before the injection of the new CO2. If we continue as we are, our cumulative emissions could exceed 1000 GtC by about 2050, 20-25% of which will remain in the atmosphere for almost 1000 years, and it will take 10s of thousands for it to return to levels similar to that before the extra CO2 was injected.

Update: Eli’s post explains what I was getting at here very well. The animation at the end is particularly good.

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33 Responses to Drawing down atmospheric CO2 – part 2

  1. Actually I forgot to put something into the post, that I’ll add here. The reason that we don’t quickly tend back to an atmospheric concentration similar to what it was before the injection of new CO2 is essentially because there is now more CO2 in the system. The fraction that remains in the atmosphere for a long time, depends on how much was injected. To give some context, prior to the industrial revolution, the atmosphere contained about 750GtC. We’ve emitted about 550GtC, almost as much as was in the atmosphere prior to us starting to emit CO2. If we carry on as we are we can reach 1000GtC by about 2050. Hence, it is not insubstantial.

  2. Tom Curtis says:

    Rather than three cycles, I would say the carbon cycle is made up of several processes with different time scales. The two most rapid processes are uptake into the surface ocean, and uptake by the biosphere (CO2 fertilization effect) which are responsible for the greater part of the reduction of CO2 relative to the emitted volume on a time scale of about a year or less. There are then three slow processes, the equalization pCO2 with the deep ocean, the restoration of the CaCO3 buffering system (which also restores ocean Ph levels to near initial values, ie, preindustrial values for the modern case), and rock weathering. David Archer includes the following graphic in his book, The Long Thaw (and also here), to illustrate the three slow processes:

    Also of interest is this equation showing a function for each of four of the processes, excluding rock weathering. For background, see discussion here. It is an approximation only, tuned to one model only, and will seriously underestimate remaining CO2 for scenarios with large cumulative anthropogenic emissions (see Hansen and Sato), but provides a convenient approximation to work with.

  3. Tom Curtis says:

    That first image should be:

  4. Tom,

    Rather than three cycles, I would say the carbon cycle is made up of several processes with different time scales.

    Okay, I’ll go with that.

    The figure above is great, really illustrates it very well.

  5. Your link also says it very clearly

    although almost half of newly added carbon dioxide molecules remain for only a decade or two,
    roughly a third stay for a century or more, and fully one fifth for a millennium

  6. Paul Williams says:

    These values cannot be correct. In the last 60 years, the oceans, plants and soils have been absorbing about 1.7% of the excess CO2 out of the atmosphere each year. For example, in 2014 humans emitted 4.4 ppm of CO2 but only 2.3 ppm stayed in the atmosphere. 2.08 ppm was absorbed into the oceans, plants and soils or 1.73% of the excess above 280 ppm.

    This amount getting absorbed each year has consistently been about 1.7% of the excess above 280 ppm over the last 60 years although the drawdown rate might actually be increasing somewhat over the period, starting at 1.5% and now up to 1.7%.

    Draw the excess CO2 down by 1.7% per year and for 400 ppm, it only takes 145 years to get below 290 ppm. For 700 ppm, it only takes 220 years.

  7. Paul,

    These values cannot be correct…….

    Draw the excess CO2 down by 1.7% per year and for 400 ppm, it only takes 145 years to get below 290 ppm. For 700 ppm, it only takes 220 years.

    They are correct, and you’re illustrating the issue. In a standard linear kinetic approach you would solve

    C = C_{\rm eq} + C_{\rm inj} \exp^{-t/\tau}.

    If you did so and assumed that C_{\rm eq} = 280 ppm, then you would get the kind of answer that you’ve got. The problem is that if you inject 1000 GtC of new CO2 into the atmosphere (i.e., more than was in the atmosphere prior to the industrial revolution) then C_{\rm eq} \ne 280 ppm, since the amount of CO2 in the system is higher than it was, and the equilibrium (based on the fast cycle) is now higher (> 280 ppm).

    That’s why we about 20% of what we’ve emitted will still be in the atmosphere 1000 years from now (well, unless we find some way to draw this down ourselves).

  8. Paul, if you only look at the carbon cycle over a timescale as short as 60 years, all you will see is the effects of the most rapid components of the carbon cycle. This is especially true if the observations are made at a time when we are vigorously forcing the carbon cycle by land use change and fossil fuel emissions. The point of this article is to explain why you also need to consider the slower components of the carbon cycle in order to understand how atmospheric CO2 levels will fall if we stop anthropogenic emissions. The point is that the fast carbon cycle will not continue to rapidly absorb CO2 indefinitely, and they won’t get us back down to pre-industrial levels. The science of why this is the case is unfortunately fairly complex, which is why simple models are misleading (see the caveats given about the model in my paper).

  9. Tom Curtis says:

    Paul Williams, there are three reservoirs relevant to the rapid processes regarding CO2 concentration. They are the biosphere, the surface ocean, and the atmosphere. The CO2 emitted to the atmosphere is reduced by movement of CO2 into either the biosphere or the surface ocean, so that we have increased carbon in all three reservoirs. To return to preindustrial conditions, you need to return to preindustrial conditions in all three reservoirs as well. That is, if CO2 in the atmosphere is to reduce by 1.73% of the excess per annum, then we also need excess Dissolved Inorganic Carbon (DIC) in the upper ocean to reduce at the same rate and excess carbon in plant and soil matter to also reduce at 1.73% per annum.

    That begs the question as to where all of this excess carbon from all three reservoirs is going to go.

    Put another way (and ignoring the biosphere), your formula assumes that the relative pCO2 in the atmosphere and ocean can evolve to a massive disequilibrium without any issues. Indeed, you expect the pCO2 of the ocean to massively increase while that in the atmosphere decreases while the ocean is warming at the same time (thereby reducing the amount of DIC it can retain).

    Once you recognize that the excess carbon has to actually go somewhere, it becomes evident that after the ocean invasion (approx 300 years), the CO2 in atmosphere and ocean will only reduce at the slow rate of the restoration of the CaCO3 buffer, and the still slower rate of rock weathering.

  10. bill shockley says:

    Is anyone following the comment exchange in the review process of Hansen’s Storms & Sea Level paper?

    I found the comment remarkable that this snippet comes from:

    We conclude, based on a huge body of research by the scientific community, that
    the Southern Ocean is the key regulator of atmospheric CO2 and CO2 is the control
    knob for global climate. Furthermore, the system is quite sensitive on millennial time
    scales: weak persistent paleo forcings are able to elicit a substantial CO2 change via
    variations of the upwelling of deep ocean carbon.

    Kind of on-topic, I thought… maybe more pertinent to a climate sensitivity discussion.

    Anyway, the Anthropocene began with a little nudge. And ended with a kick in the butt.

  11. izen says:

    The extra carbon we put into the atmosphere is rapidly shared between the oceans, land and biota.

    If we stop adding carbon the extra already added will remain shared in about the same proportions. There is NO automatic process that will continue to take the extra out of the atmosphere and into the oceans, land and biota.

    Once you increase the amount of carbon in circulation then the airbourne fraction will remian elevated. there is an upper limit to how much the oceans and biota can absorb before the ph partial pressure and fire/decay processes constrain it.

    It takes the slow (geological) processes to reduce the amount in the fast carbon cycle and the rate of that is a few orders of magnitude longer than the fast cycle.


  12. izen,
    That’s a great little animation. Thanks.

  13. Eli Rabett says:

    A more complete model of the carbon cycle

  14. Ethan Allen says:


    Hey, that looks like David Evens territory, turn that into a EE diagram even, add a Solar Notch pathway to space (the CO2 thingie does not go into the ocean/ground thingie but instead goes directly into the space Time Lords thingie).

  15. JCH says:

    Leave it to Izen to make succinct explanations. He communicates.

  16. Thanks, izen, for putting that in a nutshell in such an understandable way.

  17. izen says:

    Thanks for those compliments!

    While I am not involved in education, my work has involved trying to get people to understand how complex dynamic systems are likely to impact their lives and what changes may be effective.

    Graphs and equations are convincing to people with a regular familiarity with charts and formula and are used to deriving an understanding, the answer or what can be called epistemic closure from that form of information.

    But for most of the general population such forms of information are of limited influence.
    Constructing simple narratives and analogies that do match the sort of informational structure that people not used to technical jargon or mathematical processes use is required to achieve understanding.

    I suspect this is one reason the deficit model of increasing understanding of AGW is considered to have failed by some. The full understanding of a subject is not acknowledged unless people appear to understand the graphs and formula in the same way they are grasped by those with a scientific/technical background.

  18. anoilman says:

    I wonder if any of the so called ‘economic models’ include the costs of artificially drawing down CO2 to achieve an unbearably hot planet of +2C? Last I heard, it would cost $120 a ton to extract from the atmosphere.

    I suspect that if that adaptation was modeled our economies would quite simply blow up.

  19. Joshua says:

    TE –

    =>> ” ATTP exhibits his own biases when he censors my posts here.”

    Self-victimization is one of the sure signs of confirmation bias.

    Just sayin[g]

  20. Pingback: A few thoughts | …and Then There's Physics

  21. Pingback: Drawing down atmospheric CO2 – part 3 | …and Then There's Physics

  22. Pingback: Henry’s Law | …and Then There's Physics

  23. executor55 says:

    What is your opinion on Michel van Biezen (with 520k subscribed) courses:

  24. executor,
    The response is indeed logarithmic, and the correct equation from our current state is

    \Delta F = 5.35 \ln \frac{C}{280},

    where C is the new atmospheric CO2 concentration, and 280 is the pre-industrial concentration. So, it is true that doubling atmospheric CO2 today (i.e., increasing it by 280 ppm) will have a much smaller effect than the overall greenhouse effect (typically quantified as increasing surface temperatures by 33K). However, this is well known and the general expectation is that each doubling atmospheric CO2 will increase surface temperatures by about 3K.

    You could do a ballpark estimate similar to what van Biezen implies in his video. If we start at 1ppm, how many doubling to get to 280ppm? It’s about 8 doublings. If it warms by 3K per doubling, that would be about 24K. Not quite right, but this is a rough estimate. How many doublings to get to 20ppm. It’s about 4 doublings, so would contribute about 12K of the warming. So, yes, it does look like it might be about half. However, this doesn’t change that if we double atmospheric CO2 from a pre-industrial level of 280ppm to 560ppm, the surface will probably warm by about 3K.

  25. dikranmarsupial says:

    The preceding lecture is rather more questionable (and explains some of the odd statements in the first)

    I think he has been getting some of his information from skeptic blogs. His diagram of the model-observation comparison looks rather like a cartoon of Christies’ nonsense.

  26. dikranmarsupial says:

    Some climate skeptics seem to think it is an inconvenient truth that the temperature dependence on CO2 is logarithmic, but ironically climatologists point that out every time they give a figure for climate sensitivity in terms of a constant increase per doubling of CO2. And they do that a lot. That is essentially saying that the rise is logarithmic in a way that would be understood even if you didn’t know what a logarithm was! ;o)

  27. verytallguy says:

    It’s worth noting that the logarithmic relationship is purely an empirical correlation from heart transfer calculations, does not necessarily apply beyond the modelled range and indeed would not be expected to apply to very low CO2 concentrations.

    It’s always amazing when “sceptics” point to it, as if it was not already taken into account, and not acknowledging that it comes from model calculations they dispute the other outputs of.

  28. verytallguy says:

    For those interested, here’s the paper

    Click to access myhre_grl98.pdf

    CO2 is presented as a logarithmic fit, other GHGs with various other correlations eg CFCs as linear. The CO2 range considered is preindustrial (280ppm) to 1000ppm.

  29. dikranmarsupial says:

    Thanks VTG.

  30. David B. Benson says:

    contains links and comments on removing carbon dioxide from the atmosphere via aggressive tree planting.

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