Drawing down atmospheric CO2 – an illustration

I’ve written a number of post on drawing down atmospheric CO2. Eli has some posts about this too.

One of the key things I was trying to stress is that we expect something like 20% of our total emissions to remain in the atmosphere for millenia. This will, however, depend on how much we do actually emit. The more we emit, the large the fraction that will remain in the atmosphere. It was therefore a little surprising to find a paper for review called a simple model of the anthropogenically forced CO2 cycle (Weber, Lüdecke & Weiss) with the following figure

Credit : Weber, Ludicke & Weiss (2015)

Credit : Weber, Lüdecke & Weiss (2015)

The figure shows the results from their model (blue line) compared to results from 15 other models (Grey band – Joos 2013). The grey band shows that the other models suggest – as expected – 20%, or more, of our total emissions will remain in the atmosphere for millenia. The Weber, Ludicke & Weiss model, however, suggests that it should return to almost zero within centuries.

So, why the difference? Well, this is quite easy to understand. If you go to the section describing their model, you will see that the equation describing the flux between the atmosphere and the ocean is

\dfrac{d n_{s}}{dt} = \dfrac{1}{\tau}(N_a(t) - N_o),

where N_a(t) is the carbon content in the atmosphere at time t, N_o is the carbon content in the atmosphere in 1750, and \tau is the time factor of the process, which they estimate to be about 80 years. So, essentially, their model assumes that there will be a net flux into the oceans, from the atmosphere, as long as atmospheric concentrations are above pre-industrial levels. So, given that \tau \sim 80 years, it’s no great surprise that their model shows atmospheric CO2 returning to pre-industrial levels within a few hundred years.

However, this assumption of theirs is simply wrong. By burning fossil fuels, we’re adding new CO2 into the system (surface ocean, atmosphere, biosphere) and so the atmospheric concentration to which the system will settle is not going to be the same as it was before we started burning fossil fuels. Eli’s animation in this post illustrates this nicely.

Essentially, given how much we are likely to emit, 20% – or maybe more – of our total emissions are likely to remain in the atmosphere for millenia. Of course, if your model assumes that the net flux into the ocean will remain positive until concentrations return to pre-industrial levels, then your model will suggest that concentrations will drop down to pre-industrial levels quite quickly (hundreds of years). This, however, is simply wrong.

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44 Responses to Drawing down atmospheric CO2 – an illustration

  1. christian says:


    Yes, but dont care about this Paper, its from the German Denier-Scence, its called “EIKE” here in Germany, if you want to try and speak a bit German: http://www.eike-klima-energie.eu. Its every Year the same, they produce simplified Papers with a bit of erroneous assumptions to hope that some Referees fall asleep and publish this in their Journal, but for the Auhors in dosent Matter, because on “EIKE” their in peer-review rejected Papers are still in discuss like they would be published in the Journal 🙂

  2. christian,
    Thanks. Yes, I was aware about the origins. I did debate whether or not I should discuss it at all, but I do think it’s a good illustration of how one’s assumptions are crucial; if you assume that the oceans will continue to rapidly take up CO2 until concentrations return to pre-industrial levels, then that’s what your model will show. That assumption, however, is simply wrong.

  3. I note that of English climate ‘debaters’, EIKE chooses to translate Eric Worrall, David Archibald and Tim Ball. That’s just the home page.

  4. john,
    Oh, that’s bizarre. I hadn’t noticed that. If I’d known they were quite that way out, I might have just ignored this paper. I still think it’s a nice illustration of how one’s assumptions can so obviously influence the results, though.

  5. christian says:


    Correct. Its only a Question of, how its the balance between Atmosphere and Ocean pressure of CO2. In current state of climate, the oceans are still uptake CO2, but if we stop emissions, to CO2 is first rapidly falling to a state of equilibrium to the ocean, then the falling slows down and the ocean could become to give CO2 to the Atmosphere. On this state, the CO2-Levels beginns slowly to decline.

    The ocean itself is mixing on higher timescales, but not on this scales we looking for, so the Question is, when we have stoped CO2-Emissions, how is the State of oceans, because that should answer how much CO2 will remains in Atmosphere on a longer Timescale

  6. @aTTP

    I’d agree about assumptions dictating the results. No problem. But I would suggest the word ‘assumption’ lets them off too lightly.

  7. john,
    Yes, possibly. You’re highlighting a problem I have. When dealing with people who have actual expertise in this field, it’s quite hard to attribute these kind of things to ignorance, or some lack of understanding.

  8. @christian

    It would appear that the error they made (if it really is an error) is that CO2, when taken up by the ocean, just vanishes.

  9. john,
    Yes, that’s essentially it. If we add 100s/1000s Gt of new carbon into the system, their model assumes that it enters the oceans and simply disappears. Magic?

  10. christian says:


    Yes. That its whats ATTP said in his Blog-Post 🙂 But my comment was not so direct to the Paper, more a generally comment, which is why the Paper goes wrong.


    Not Magic, but very unlikely, what the Papers say would happen if ocean are mixing fast, very fast, but then, climate change would not be a Problem because the oceans Surface would be like in a fixed State (cant warming much because mixing is to large). Not seen in Reality to now, but how knows, perhaps some deep Water-Monsters are now beginning the Mixing the Oceans on a incredible way 🙂

  11. ‘Skeptics’ seem to have a fondness for simple models that don’t reflect reality. Didn’t a group of them come up with a similarly simple one that was equally erroneous a few months back? If they like simple models why are they so damning of more complex ones that reflect reality? Could it be that they don’t like the reality?

  12. christian,
    Indeed. If the oceans could mix very fast, then atmospheric drawdown would be rapid and we’d return to pre-industrial levels very rapidly. It doesn’t, though. The actual removal/sequestration of the CO2 is a very slow process.

  13. christian says:


    I think thats a point of what the model does, if its mean, that warming is low, that its okay its simpel or complex, but is warming large, then blame the model is to simple or the model is so complex that the results must be wrong.

    Y, they dont like realitiy

  14. christian says:


    Yes, but i want to point out, that this not mean its must be Magic, but must mean the oceans have to mix very very fast. This is not observed, in Paleoclimate there is also no note to this.

    For the Paper it means, they make a Model that results are likley as apple do not fall down to ground but beginn to fly to atmosphere 🙂

  15. christian,

    Yes, but i want to point out, that this not mean its must be Magic

    Yes, I realise. I was being hyperbolic – exaggerating for effect 🙂

  16. christian says:


    You made a mistake on your post, your written: ” The Weber, Ludicke & Weiss model, however..” ans repeat this error..

    But Ludicke have to named to be Lüdecke

  17. bill shockley says:

    I call it trickery. Of course, I accused my calculus and advanced algebra teachers of the same thing, so… FWIW!

  18. Paul Williams says:

    Oceans, Plants and Soils (OPS) are currently net absorbers of about 4.5 gigatons Carbon per year. This rate has risen more-or-less in step with the amount of excess Carbon in the atmosphere.

    The 2015 atmosphere has about 852 gigatons of Carbon in it (locked in CO2) while the pre-industrial was about 596 gigatons.

    852 / 2.13 = 400 ppm CO2 ; 596 / 2.13 = 280 ppm : 400ppm * 2.13 = 852 gigatons Carbon: 560ppm * 2.13 = 1193 gigatons Carbon when CO2 doubles.

    Simple formula is Drawdown Rate = (Excess Carbon above pre-Industrial) * 1.75%

    = (852 – 596) * 1.75% = 4.5 gigatons.

    This simple formula more-or-less describes the actual net Carbon absorption rate that has actually occurred since about the 1940s or lets say 75 straight years now. This is exactly what OPS has been absorbing for 75 years now. (before that, there may not have been enough Excess Carbon for a stable rate to materialize).

    We are currently adding 9.8 gigatons of Carbon to the atmosphere each year right now. 9.8 / 2.13 = 4.6 ppm CO2; 4.5 / 2.13 = 2.1 ppm absorbed ; CO2 in the atmosphere increases by 4.6 – 2.1 = 2.5 ppm increase

    When the atmosphere gets to the doubling level or 1193 gigatons, Oceans, Plants and Soils will then be absorbing about 10.4 gigatons per year.

    So to stabilize Carbon at the doubling level means that human emissions can grow a small amount from 9.8 to 10.4 gigatons per year.

    If you want to stabilize at 450 ppm CO2, then our emissions can only be = ((450*2.13)-596)*0.0175 = 6.34 gigatons per year or about 35% lower than our current emissions.

    Just adding some formulae that people can use to decipher this made-to-be-overly-complex topic.

  19. CaycePryhs says:

    Some 99% of the atmospheric CO2 molecules are 12CO2 molecules containing the stable isotope 12C (Segalstad, 1982). To calculate the RT of the bulk atmospheric CO2 molecule 12CO2, Essenhigh (2009) uses the IPCC data of 1990 with a total mass of carbon of 750 gigatons in the atmospheric CO2 and a natural input/output exchange rate of 150 gigatons of carbon per year (Houghton et al., 1990). The characteristic decay time (denoted by the Greek letter tau) is simply the former value divided by the latter value: 750 / 150 = 5 years. This is a similar value to the ~5 years found from 13C/12C carbon isotope mass balance calculations of measured atmospheric CO2 13C/12C carbon isotope data by Segalstad (1992); the ~5 years obtained from CO2 solubility data by Murray (1992); and the ~5 years derived from CO2 chemical kinetic data by Stumm & Morgan (1970).
    Revelle & Suess (1957) calculated from data for the trace atmospheric molecule 14CO2, containing the radioactive isotope14C, that the amount of atmospheric “CO2 derived from industrial fuel combustion” would be only 1.2% for an atmospheric CO2 lifetime of 5 years, and 1.73% for a CO2 lifetime of 7 years (Segalstad, 1998).
    Essenhigh (2009) reviews measurements of 14C from 1963 up to 1995, and finds that the RT of atmospheric 14CO2 is ~16 (16.3) years. He also uses the 14C data to find that the time value (exchange time) for variation of the concentration difference between the northern and southern hemispheres is ~2 (2.2) years for atmospheric 14CO2. This result compares well with the observed hemispheric transport of volcanic debris leading to “the year without a summer” in 1816 in the northern hemisphere after the 1815 Tambora volcano cataclysmic eruption in Indonesia in 1815.
    Sundquist (1985) compiled a large number of measured RTs of CO2 found by different methods. The list, containing RTs for both 12CO2 and 14CO2, was expanded by Segalstad (1998), showing a total range for all reported RTs from 1 to 15 years, with most RT values ranging from 5 to 15 years.
    Essenhigh (2009) emphasizes that this list of measured values of RT compares well with his calculated RT of 5 years (atmospheric bulk 12CO2) and ~16 years (atmospheric trace 14CO2). Furthermore he points out that the annual oscillations in the measured atmospheric CO2 levels would be impossible without a short atmospheric residence time for the CO2 molecules.

  20. Paul,

    Just adding some formulae that people can use to decipher this made-to-be-overly-complex topic.

    Yes, but a great pity that they’re wrong.

    For example, this isn’t right, and is kind of the point I’m getting at here

    Simple formula is Drawdown Rate = (Excess Carbon above pre-Industrial) * 1.75%

    The formula in the paper I mention here is almost right, but it should really be

    \dfrac{d n_s}{dt} = \dfrac{1}{\tau} (N_a(t) - N_{\rm equil}),

    where N_{\rm equil} is the new equilibrium concentration and is – approximately – the pre-industrial concentration plus 20% of our total emissions to date. So, consider your 450ppm example. At 450ppm, we will probably have emitted a total of about 800 GtC. If we take 20% of this, the new equilibrium concentration will be pre-industrial (596GtC) + 20% of this (200GtC). Therefore the initial net flux into the oceans (assuming \tau = 80 years) will be about 2GtC. So, if we get to 450ppm and stop emitting, the drawdown will start at about 2GtC per year. This is also probably too fast, since more complex models (Archer et al. 2009, for example) suggest that \tau should be around 200 years. If we were still adding 6.34 GtC per year, it would continue to rise, it would not stablise, as you’re suggesting.

    Now, I appreciate that you think you’re right, but you’re not. There’s also so many times that I can explain why you’re wrong about this. You’re essentially making the same mistake as is being made in the paper I’m discussing here. You’re assuming that the drawdown rate depends on the difference between the current concentration and the pre-industrial. It does not. It depends on the current concentration and the new equilibrium concentration, which is higher than pre-industry, because we’ve added new CO2.

    If you don’t believe me, try this Geological carbon cycle model. Set the transition CO2 spike to 415 GtC and see what happens. It’s actually initially slower than what I suggested above, because it’s using a pulse of 415GtC, rather than a slower injection of 800GtC.

  21. Cayce,
    Essenhigh (2009) is even more wrong, than the paper I discuss here. Essenhigh is essentially confusing the residence time for a CO2 molecule, with the decay time for an enhancement of atmospheric CO2. It is indeed true that the residence time for an individual molecule is quite short – a few years. However, there are fluxes into and out of the different carbon reservoirs (oceans, atmosphere, biosphere). Therefore, the time it would take for an enhancement in concentration to decay is much longer than the time it takes for an individual molecule to move from the atmosphere into one of the other reservoirs (ocean or biosphere).

  22. bill shockley says:


    it might be instructive to compare and contrast the carbon cycle with the methane cycle which approximates to a much simpler formula based solely on the decay time of a molecule in the atmosphere. I would be interested in seeing such an exercise including a decay profile graph.

  23. dikranmarsupial says:

    As Einstein said :

    “It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.”

    usually more snappily misquoted as “Everything should be made as simple as possible, but no simpler.”. Sadly, this is exactly what Weber, Ludicke & Weiss have done. The simple model works reasonably well over the last 50 years or so, but this is during a time when anthropogenic emissions have been strongly forcing the carbon cycle, and the response of the carbon cycle is dominated by the faster components. However that doesn’t mean that the slower components won’t come to the fore if the carbon cycle is left to re-equilibriate (which is why their model disagrees with the others).

    While the WLW model can explain the last 50 years, can it explain paleoclimate as well (as the standard models can)? The answer is likely to be “no” as there are plenty of “data of experience” that the “L” ignores, for instance we know the ocean can’t be modeled as a single reservoir as it is strongly stratified, as demonstrated by the existence of a thermocline.

    It is ironic that WLW cite my paper, but ignore the section that explains why such simple models cannot be used to make useful quantative predictions about future atmospheric CO2 levels.

  24. Dikran,
    Thanks. If you have a moment you could expand on why Essenhigh is also wrong – as per CaycePryhs’s comment. And for CaycePryhs’s benefit, the paper responding to Essenhigh was written by Dikran.

    But isn’t methane much more complex, because it is also removed via chemical reactions? It’s not simply removed by being absorbed by one of the other reservoirs – I think.

  25. dikranmarsupial says:

    CaycePryhs might also be interested in my blog post here, which also discusses the confusion between residence time and adjustment time that crops up very commonly on climate skeptic blogs etc., despite the fact the first IPCC report specifically cautions against this confusion.

  26. bill shockley says:

    ATTP, methane sinks are completely dominated by atmospheric hydroxyl radicals where the methane is oxidized. That sink has complicated chemistry, but it reduces to a simple global average CH4 lifetime of 9 or 10 years. The sink is strong near the equator and weak at the poles. Methane sources are a matter of large uncertainty because they are scattered and therefore hard to quantify. It’s become a subject of interest lately because global concentrations had plateaued between ~2000 and 2006, and have since been rising strongly. Much debate over the new source. Most suspected are wetlands, shallow subsea permafrost in the arctic shelves (Shakhova), and the explosion in US fracking where raw methane leaks which, some allege, have been greatly underestimated.

  27. bill,
    I’m still not sure I see the equivalence. With respect to CO2 there is a cycle that rapidly moves CO2 through the different reservoirs (years), but that would draw down an enhancement much more slowly. As I understand it, methane does actually get removed quite quickly through the process you describe.

  28. bill shockley says:

    So, while you’re right that a detailed model would be complex, to allow for variations in the hydroxyl sink, spatially and temporally, and to incorporate all the chemistry leading to that variation, a model wouldn’t have to do all that to simply test theories about which source might be contributing to the new rise in methane levels. You could just construct a simple global average decay profile based on an assumed 10-year lifetime. The model would just give you a guideline for how large an increase you are looking for from the various sources.

  29. bill shockley says:

    Maybe not enough equivalence between the scenarios to be instructive?

  30. bill,
    I’m not sure. It seems that we’re saying slightly different things. I think the source of the rise in atmospheric CO2 is obviously us. It seems that methane is more complex. What you suggsted in your 4:55pm comment seems reasonable, but I don’t know enough about methane specifically to really comment further.

  31. bill shockley says:

    ATTP, I was asking more than I thought. To illustrate it like I suggested for the sake of contrasting with CO2 decay, you’d have to assemble the data and build the model. I’ve got the model, but I did it without a decay profile, because, since the system is near equilibrium, you can do it much more simply without one. But if I wanted to show the case of a halt in emissions, I would have to create a decay model or a somewhat realistic decay profile. My to-do list just took another step towards infinity.

  32. Not having the maths and physics myself to get into the depths of papers like WLW I very much appreciate these kind of posts and the discussions below so that I can understand the climate science in at least a little more depth: thanks ATTP and all.

    Just on the methane vs CO2 point that Bill raises, you probably know David Archer’s page of web browser models at http://climatemodels.uchicago.edu (move your cursor over the model names to get an explanation of each). In particular the ‘Slugulator’ informatively illustrates the difference in ppm and temperature ‘rise decay curves’ for a user-specified ‘slug’ of CO2 vs a slug of CH4 over different time scales and the output gives the energy trapped and also the ‘time integrated warming’ (ºCyears).

    Maybe Dikran or someone could say how big the uncertainty range might be for ‘Deep ocean overturning time’, initialised as 1000 years in the model.

  33. Paul,
    I’m not sure about the uncertainty in the overturning time, but this fact sheet by Stefan Rahmstorf uses the same timescale.

  34. Lüdecke had a dreadful paper in Climate of the Past Discussion last year that fail to satisfy the reviewers. I wonder why they are chosing to publish in these Copernicus journals with open peer review. Are they so dim that they don’t realise that their aphysical models are going to be treated harshly, and publicly by reviewers, or is this the plan so they can claim their visionary ideas were supressed by hostile reviewers?

  35. Richard,
    Yes, I remember you discussing it. Were you thinking of making a comment on the most recent one? I had considered doing so, as it seems pretty obvious what the issue is, but being a simple blogger in this context, I decided against that.

  36. christian says:


    As i first replied here, it dosent matter for the Auhors, if the Paper will then published in the Journal or not, on their Blog or Webside “EIKE” it will always talked about as it is published because readers there are not carefully(amd wont be), they belive them when the said they published a new Paper.

    I think you(or we) should not pay so much Attention to the Papers of them, because it dosent mattter at all

  37. I’ve just read through the paper. For a climate sceptic paper on the carbon cycle, it is not too bad. It doesn’t confuse the residence time of a CO2 molecule with the response time of a pulse of CO2: indeed it is explicit on this point.
    It declares that CO2 concentrations were constant before the industrial revolution, which on long time scales is nonsense, but over the last thousand years is approximately true, certainly much better than Ernst-Georg Beck’s work.
    The mistake the paper makes is to assume that because a simple model fits reasonably well, that a more complex model (and physically plausible) would not fit better.
    I won’t submit a short comment on this paper – others know this stuff much better than I and I have my eye on some other papers in CPD that might need a little attention.

  38. It doesn’t confuse the residence time of a CO2 molecule with the response time of a pulse of CO2

    That’s certainly a plus 🙂

  39. Actually, this is a good way of putting it

    The mistake the paper makes is to assume that because a simple model fits reasonably well, that a more complex model (and physically plausible) would not fit better.

    I’d missed the bit at the very end of the paper where they say

    The difference in the long run may stem from the Revelle effect, included in the elaborate models, a resistance to absorbing atmospheric CO2 by the ocean due to bicarbonate chemistry. However, as Gloor (2010) underlines, there exists so far no evidence for the Revelle effect. Thus, such effects are presently hypothetical.

    I’m no expert, but my understanding is that the statement that there is no evidence for the Revelle effect isn’t correct.

  40. Well, I can’t find any mention of the Revelle effect in Gloor (2010). What it does say is:

    For one thing, the continuous acidification of the ocean will inevitably lead to a decrease in the oceanic uptake capacity for anthropogenic carbon (Sarmiento and Le Quere, 1996).

  41. Eli Rabett says:

    WRT methane, first, adsorption in the oceans and deposition onto the surface are small effects (in the oceans methane does not ionize, so everything is governed by Henry’s Law. On the surface there isn’t much chemistry to decompose it). As was said above everything is dominated by OH attack CH4 + OH –> H2O + CH3

    Once that happens it is all downhill A discussion can be found on Rabett Run (of course)


  42. dikranmarsupial says:

    “The mistake the paper makes is to assume that because a simple model fits reasonably well, that a more complex model (and physically plausible) would not fit better.”

    I’m not sure a better model would necessarily fit the observations any better over the course of the Mauna Loa record, at a time when the carbon cycle is being strongly driven by anthropogenic emissions, the carbon cycle response will be dominated by the fast mechansims and a first order model may be indistinguishable from a better model. The problem is really extrapolation, you can model data as a curve-fitting exercise, but it will only extrapolate well if the model actually represents the causal system, and a good fit to the data is no guarantee of that. As a statistician, I am more convinced by physics.

    I would however agree that it is a much better skeptic paper than most.

  43. Pingback: Oh no, not again | …and Then There's Physics

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