What’s up with the Bomb Model?

It has become a popular belief among climate sceptics that nuclear bomb test 14CO2 data falsifies the Bern model [1, 2010; 2, 2013]. The Bern model is used to link atmospheric rise in CO2 to manmade emissions and lies at the heart of IPCC projections for the future trajectory of global CO2. What could be more important?

In this post I present a simple ocean surface water mixing model that explains why 14C cannot be used to predict the sequestration rate of CO2. Each year the ocean inhales about 92Gt of carbon from the atmosphere that is tagged with 14C. This inhaled CO2 mixes with the 1020 Gt carbon in surface ocean water before about 90 Gt is exhaled. The CO2 exhaled is not the same CO2 that was inhaled and is depleted in 14C. If the 14C tracer were to work, it would be necessary to assume that the CO2 exhaled had the exact same 14C ratio as that inhaled, the portion of 14C removed from the atmosphere residing in the 2Gt sequestered C. The CO2 exhaled is depleted in 14C and this gives an artificial false picture of rapid CO2 sequestration rates.

The dilution of 14C in the atmosphere by burning fossil fuel that contains zero 14C is a further process that gives rise to artificial rapid decline in the 14C curve that is not related to sequestration rates [3]. The IPCC also recognises that 14C cannot easily be used to describe CO2 sequestration processes and on this occasion I agree with them.

Figure 1 Comparison of 14C decline from atomic bomb tests (red) with the Bern model (blue). The unlabelled Y-axis is 14C and the unlabelled X-axis is years since bomb test (1962). This post explains why 14CO2 cannot be used to model the sequestration rate of CO2 from the atmosphere and hence it cannot be used to falsify Bern. This does not mean that Bern is correct. Chart from WUWT [2].

In late 1962 the Earth was subjected to a gigantic experiment. Retired NASA Astronaut Phil Chapman writes [1]:

Between August 2 and Christmas in 1962, just before the atmospheric test ban went into effect, the Soviet Union detonated no fewer than 36 nuclear weapons at their test site on Novaya Zemlya in the high Arctic, with an incredible total yield of 141.5 megatons of TNT equivalent. The series included, on Christmas Eve, the second-largest bomb ever tested, with a yield of 24.2 megatons.


When a nuclear weapon is detonated in the atmosphere, the neutrons emitted from the blast cause a sudden and quite substantial increase in the 14C content of the atmosphere. The excited carbon immediately combines with oxygen, so the effect of an airburst is to inject a slug of CO2 into the atmosphere that is tagged so that we can watch what happens to it.

14C is naturally radioactive with a half life of 5,700 years. It is formed on Earth by nature by the action of galactic cosmic rays on nitrogen and this provides the foundation for radiocarbon dating and for tracing the impact of galactic cosmic rays on Earth’s climate over time. In 1962, the atomic bomb tests injected a huge slug of additional 14C that spread around the globe and was monitored at a number of sites. This clearly provides a means of tracking the mixing time of the atmosphere but there are problems using this data to define sequestration rate of CO2 from the atmosphere into biosphere and ocean sinks as described below.

Phil Chapman makes some key observations [1]:

The prevailing winds presumably took the cloud of 14CO2 right around the world to the site in Austria, which was 2,000 miles southwest of Novaya Zemlya. It took about two years more to reach New Zealand, in the Southern Hemisphere. At the time of the peak in New Zealand, the concentration was still higher in Austria, indicating that the carbon-14 was not yet evenly distributed in the whole atmosphere. Thus some of the initial decrease in Austria was apparently due to dilution of the cloud as it spread.

Figure 2 Atmospheric 14C following atomic bomb tests in Russia in 1962 [1]. The data are useful for examining atmospheric mixing times but can the exponential decline be used to model natural CO2 sequestration rates?

Some bomb 14C arrived in new Zealand within a year, it took 2 years to reach a peak in New Zealand and about 10 years to fully homogenise between monitoring sites in Austria and New Zealand (Figure 2). This is all valuable insight to atmospheric mixing rates.

The bomb 14C data has been used to model sequestration rates of CO2 from the atmosphere. The exponential decline of bomb 14C from 1969 onwards is not due to radioactive decay since the half life is over 5000 years (Figures 1, 2, 3). It was therefore hypothesised that the decline was due to sequestration of CO2 from the atmosphere by fast sinks and the data could be used to model CO2 sequestration rates.

In Figure 3 I fit an exponential decline to a set of bomb 14C data [2] and deduce very roughly that the decline rate is of the order 7% per annum. This is much more rapid than the decline rates deduced by Roger Andrews and myself as discussed in recent posts [4, 5] and is much more rapid than the mean decline of the Bern Model that is not exponential and is dominated  by slow processes (Figure 1). The consequence of the rapid 7% decline deduced from bomb data is shown in Figure 4. Such rapid decline does not match atmospheric observations and the gap between emissions and atmosphere needs to be filled by a natural CO2 flux.

Figure 3 Background image of bomb 14C from WUWT [2]. The red line represents a 7% per annum exponential decline, equivalent to a half-life ~ 10 years for CO2.

Figure 4 Comparing actual emissions that are declined at 7% per annum with actual atmosphere there is gap that if the bomb 14C decline was correct would need to be filled by a natural CO2 flux.

When I first saw information on the bomb sequestration rates I thought the conclusions had to be bomb proof. The ramifications were profound. Natural sequestration rates were very fast and would pump away manmade emissions within a few decades and a major component of the rise in atmospheric CO2 was natural in origin.

We had a really good discussion on Roger’s post a few weeks ago [5] attempting to reconcile the various lines of evidence and Roger said:

What’s out of whack here is the 8-year bomb test residence time. It’s telling us only part of the story.

And that got me thinking. What processes may be in action that might lead to the bomb 14C data giving a false result? I used to make my living offering isotope analyses and data interpretations to the oil industry much of this based on understanding the distribution of isotope ratios in seawater and formation water systems. It didn’t take long to come up with the answer which is in fact the answer articulated by the IPCC.

The starting point is to have some understanding of the carbon cycle. For the purpose of this illustration I will focus on the ocean carbon cycle (Figure 5) although the argument may be applied equally to the land biomass side of the story.

Figure 5 The ocean carbon cycle according to  IPCC Grid Arendal.

Every year the oceans exchange approximately 90 Gt C with the atmosphere. 92 Gt go in and 90 Gt comes out again. Surface ocean waters contain about 1020 Gt C and so what happens is that 92 Gt goes in, mixes with 1000 Gt and what comes out again is not the same CO2 molecules that went in. What we are trying to measure using the bomb 14C data is the rate at which that notional 2 Gt difference is sequestered. The bomb 14C data can only be used to measure that if the CO2 exhaled had the exact same 14C composition (14C/12C) as that inhaled and this will clearly not be the case.

For those who require convincing I have created a model to illustrate the process (Figure 6). At t1 the atmosphere is greatly enriched in 14C relative to the ocean. The ocean does contain some natural radiogenic 14C. The ocean inhales CO2 with the 14C signature of the atmosphere (t1.4). This then mixes with the carbon resident in the upper ocean layer (t1.6). And then finally the ocean exhales CO2 that will have a very different d14C ratio than the CO2 that was inhaled. In this simple model the ocean exhales the exact same amount of CO2 that is inhaled but the mixing and 14C dilution process that takes place in the shallow ocean results in a significant reduction in the amount of 14C in the atmosphere without any CO2 being sequestered. It should therefore be obvious that 14C in the atmosphere cannot be used to measure the rate of CO2 sequestration. 14C gets pumped down at an artificial high rate giving the false impression of rapid CO2 sequestration. Roger was right.

Figure 6 14C in red and 12C in yellow. It is not necessary to show 13C for the purpose of this exercise. In this simple model the amount of CO2 in the atmosphere and ocean at t2 is the same as at t1. No Co2 is sequestered but the concentration of 14C in the atmosphere is reduced from 50% at t1 to 41% at t2. Clearly 14CO2 cannot be used to measure CO2 sequestration rate.

d13C compositions will be affected by the same effect and should not be used to model atmosphere processes without taking this shallow ocean mixing process into account.

I recognise that many readers of Energy Matters may prefer energy based posts and so we will try to get back on that theme for a couple of weeks. “What’s up with the weathering sink” to follow in a few weeks.

[1] Phil Chapman 2010: Are we Responsible for the CO2 in the Atmosphere?
[2] WUWT Gösta Pettersson 2013: The bombtest curve and its implications for atmospheric carbon dioxide residency time
[3] WotsUp 2013: Watt about the bombtest?
[4] Energy Matters Euan Mearns 2014: What’s up with the Bern Model?
[5] Energy Matters Roger Andrews 2014: The residence time of CO2 in the atmosphere is …. 33 years?

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36 Responses to What’s up with the Bomb Model?

  1. After getting a sneak preview of this excellent post I began to wonder if would be possible to model the prefential decay of 14C on a spreadsheet using the mechanism Euan describes. So I gave it a shot.

    First I added the terrestrial biosphere sink to the ocean sink that Euan bases his estimates on. This roughly doubles the amount of carbon cycled each year between the atmosphere and land/ocean sinks to ~200 Gt carbon a year.

    Then I assumed that the carbon absorbed in the sinks after the bomb test would be enriched in 14C while the carbon released from the sinks would not. This is not completely true of the land sinks, which would release a proportion of the enriched carbon back into the atmosphere from the same vegetation that absorbed it earlier in the year, but it should be true of the ocean sinks, which absorb carbon dominantly in temperate latitudes and release it several thousand miles away in the Tropics.

    Further assumptions were:

    * Weight of carbon in atmosphere is 860Gt.
    * The bomb test 14C is regularly distributed through the atmosphere
    * Concentration of 14C immediately after bomb test is 200 pMC/percent. Background concentration is 100 pMC/percent (data from graphic below):

    The model is anothe simple mass balance model which calculates how much 14C is contained in the 200Gt of atmospheric carbon (concentration 200) that’s absorbed into the land and ocean sinks during the annual carbon cycle in year zero and how much is contained in the 200Gt of carbon (concentration 100) released from the sinks. It then calculates what the atmospheric concentration of 14C is at the end of year zero and repeats the process for succeeding years. Here are the results (note, not yet peer-reviewed):

    The decay curve is very similar to the bomb test decay curves, and with an even shorter time constant. However, the time constant would have been longer if I’d allowed for release of bomb test 14C from decaying vegetation.

    Over to you, Euan. 🙂

    • Euan Mearns says:

      Roger, a very useful and interesting exercise for illustrative purposes. I think you show that the kind of process I propose will produce the kind of result observed in the 14C bomb test data.

      Moving on to the quantitative stage is a different story. To use isotope data quantitatively in two component mixing models you have 4 variables. The isotope ratio and element concentrations in each end member. If you know three of these you can make a stab at estimating the fourth.

      In this case we do not have two components but at least two very different Earth system processes, one the land based bio mass cycle and the other the oceanic solution based cycle. It becomes a vey difficult problem to untangle these.

      So as an illustration of how this type of process might work full marks, but at the quantitative level I think this modelling is extreme complex. E

  2. Phil Chapman says:

    I basically agree with you, Euan.

    If we assume that the rate of transfer from the atmosphere to the sinks is proportional to the mass M of carbon in the atmosphere, and if we ignore the carbon released by the sinks, the rate of change of atmospheric carbon is

    dM/dt = -kM +f(t)

    where f(t) is the anthropogenic release. Using Roger’s numbers (M(0) = 860 GTC, dM/dt = 200 GTC/year at t = 0), k = 200/860.

    If f(t) is an impulse of size m at t = 0, this equation is easily solved to give

    M= M(0) + m exp(-kt)

    so the e-folding time constant is only 1/k = 860/200 = 4.3 years, much shorter than that indicated by the bomb test.

    Photosynthesis prefers C-12 to C-14, but this is a small effect. About half the sugars produced by photosynthesis are quickly oxidized to make the energy needed for plant growth, movement, etc , releasing CO2 back into the air (this is called plant respiration). The other half of the sugars are used to build plant material (leaves, stems, etc). Deciduous trees and annual plants drop litter that rots within a year or two, but the C-14 that gets incorporated in tree trunks, etc., may be locked up for centuries. Working out the delays in releasing C-14 would require a major study, but I think Roger is right that quite a lot of the C-14 absorbed by terrestrial biomass is quickly returned to the atmosphere, which probably explains why the bomb data gives a time constant more like 16 years than 4 or 5.

    • Phil: My graph gives an e-folding time of ~4 years, very close to your 4.3 years. So I’m going to assume my model is now peer-reviewed 😉

    • Euan Mearns says:

      I basically agree with you, Euan.

      Phil, I’m happy to hear that. I hope that the majority of sceptical scientists are equally easy to convince. Of course what I present here is not supposed to be the truth but steps on the road to discovering that truth.

      The land bio mass part of the cycle is extreme complex and the “stable isotope” fractionation processes such as photosynthesis are non-trivial. For d14C, 2 amus / 12 amus for carbon is a large differential. d13C is heavily depleted in bio mass 1 amu difference /12.

      I think Roger is right that quite a lot of the C-14 absorbed by terrestrial biomass is quickly returned to the atmosphere

      I agree with that, but some of it goes down tree trunks into the soil as organic acids to dissolve mineral grains to provide nutrients to the trees. In a previous life I did some amazing 87Sr/86Sr analyses on tree rings, extremely challenging work to do, but then I went and set up a company.

    • Yvan: There are lots of curves in the reference you cite. Which one should it fit?

    • Euan Mearns says:

      Hi Yvan, thanks for your continued engagement here that is valued. I’ve had a look at the paper and as you said before this is non-trivial stuff. I’d point out that in comments, which on blogs = peer review, Dennis Coyne who is I believe on the opposite side of the climate argument to me (but I have blogged with him for many years) came up with these two amazing charts.

      The top chart being the Bern Model. The bottom chart being a modified version of the 2 Tau model I had presented in that post. The latter has taken a few days of my time and bloggers time to iterate towards. The key fact is that thanks to Phil Chapman (commenting here) I think I understand the physical science basis of the 2 Tau model. But I don’t understand the physical science basis of the Bern Model that tries to unify different processes 1) atmosphere to surface water and 2) surface water into deep water (see excerpt up top) , into a single equation. They are two separate processes that need to be treated separately. And as a part of the Bern model we are supposed to have 22% of emissions that stay in the atmosphere forever – its impossible.

      If Joos is still alive and anyone knows him (her) you should ask him (her) to call by 😉

      • dennis coyne says:

        Hi Euan,

        I am indeed on a different page than most here on the climate science.

        Note that the Bern model is an approximation of reality, and like most models of complex processes will not be perfect. Note that your criticism of the 21.7% component of the AR4 Bern approximation is easily addressed by substituting a long Tau on the order of 1000 years for that portion of the process. I played around a little more with the two tier model in comparison with the modified Bern model above (Tau409, Tau49.5, Tau12, and Tau1) by creating a futures emissions scenario (including estimated land use change.)

        The futures emmision scenario is based on a URR of 3300 Gb for C+C+NGL, 16,400 TCF natural gas, and 940 Gt of coal (all estimates for 1751 to 2200), future land use change is assumed to decrease by 3.5% per year, cement is assumed to follow its past relationship to total fossil fuel emissions, and natural gas flaring follows the past relationship with natural gas output. Webhubbletelescope’s oil shock model is used to model future oil, natural gas, and coal output and the CO2 emissions is shown in Gt/year on the right axis.

        For the two tier model I matched estimated CO2 emissions with the model over the 1895 to 2013 period (land use change was included) and used least squares and solver in Excel to come up with the best fit.

        Many different models can be devised( an infinite number) so I constrained the slow processes to have a Tau equal to the modified Bern model above (409 years) and the fast processes to have Tau between 4 and 50 years, I was also trying to bracket the Bern model with two variations of the two tier model.

        The result was model 1 with 75% of CO2 emissions sequestered by fast processes where Tau slow is 409 years and Tau fast is 14.5 years and model 2 with 70% of CO2 emissions sequestered by fast processes where Tau slow is 409 years and Tau fast is 11 years. The fit through 2070 is excellent (if the Bern model is roughly correct) for model 2.

        The 70% of CO2 sequestered by fast processes is somewhat higher than Euan and Phil Chapman’s assumed 81% sequestered by fast processes, but over the 1965 to 2013 period 55% of CO2 emissions were sequestered based on data, the modified Bern model underestimates atmospheric CO2 in 2013 by 50 Gt (1.5% error) and overestimates atmospheric CO2 in 1965 by 30 Gt (1.2% error) and consequently overestimates CO2 sequestration at 61% for this period.

        The 70% result for fast sequestration is midway between the 80% estimate favored by Euan and the 60% sequestration which matches the data.

        Interesting paper by David Archer on ocean chemistry and how it is affected by CO2 emissions is at link below:


        Chart with modified Bern, model 1 and model 2 and emissions (right axis) at link below:


        • dennis coyne says:

          Upon reading the Joos paper, it seems “the Bern Model” is a misnomer, Joos calls this a pulse response model and its structure is quite different from what we are calling a “Bern” model.

          I have also been reading the AR5 and this “Bern” model is quite outdated and is not really used by climate scientists any longer, so it is not worth putting any more effort into it.

          Better models take account of the buffering capacity of the ocean and long term changes of carbonate in the ocean through the formation and dissolution of calcium carbonate. (See work by David Archer) as well as the terrestrial carbon cycle to model carbon fluxes in the earth system.

  3. Euan: You might check out Figure 1 in the link Yvan posted above. It shows a large difference between the rates of CO2 and 14C decay. Based on a 20-year old model, so FWIW.

  4. Euan Mearns says:

    Roger, I was wondering if you spotted the errors in the equations 😉 None of the curves in Figure 1 look like exponentials to me and bomb 14C does more or less follow an exponential. I the explanation of bomb 14C depletion may be similar to mine but they fail to recognise that falsifying bomb 14C data does not prove that the other curves are correct.

    The bomb 14C data is not fit for purpose – what is?

    • On a somewhat unrelated issue, do the biomass-burners realize that half of the CO2 they emit remains in the atmosphere for hundreds of years and over 20% of it stays there for ever? 😉

      • Dennis Coyne says:

        Hi Roger,

        The 20% forever criticism really doesn’t hold much water, the model is changed very little by a long decay for the slow processes that remove carbon from the surface of the ocean to deeper waters. Also the rational behind biomass burning is that much of the CO2 would be emitted due to decomposition anyway, though the rates would be very different (slower in the case of decomposition relative to burning).

        • the rational behind biomass burning is that much of the CO2 would be emitted due to decomposition anyway

          Hi Dennis. Yes, that’s the way it’s supposed to work. But some people are beginning to have second thoughts:


          • dennis coyne says:

            Hi Roger,

            Interesting piece, I am surprised that burning logs would be worse than burning coal. Most people that burn wood in a wood stove are using locally sourced wood where inputs for cutting the wood and transporting are low. Typically power plants use wood waste, or that was my assumption, I would think while logs would be expensive.

            When people burn wood in the US, it is because it is cheaper.

  5. Geoff Sherrington says:

    Hi from Down Under,
    There are attempts to calculate the portion of atmospheric anthropogenic CO2 today from carbon isotopes. If one assumes that combustion of fossil fuels is a short-time shock, it can be modelled similarly to the bomb test method. Only it is not, because the burning process continues each subsequent year while the bombs do not.
    Which is a round-about way of asking if modelling of combustion CO2 uses the same observation of annual recycling through the oceans as you illustrate for the bomb CO2.
    Sorry the Q is so vague, I’m away from my data base. Do you get what I’m driving at?
    While we are here, I find Net searches for items like % of anthropogenic C in the atmosphere today to be unusually hard because the engine returns a motley collection of barely relevant proselytising. What is a summary of the present state of understanding, reconciled with measurements from fossil combustion, cement making, etc., with sources and sinks identified?

    p.s. Years ago I also set up a lab and did a lot of radioactivity work, including buying my own fast neutron generator for NAA. Much work was for uranium exploration/ore grade control.

    • Euan Mearns says:

      Geoff, d13C data on atmosphere will be affected by same process as bomb data and as you point out it is not a single pulse but continuous addition. d13C will show that there is FF CO2 in the atmosphere – what a shock! But to use this in any quantitative way will be fraught with uncertainty – I wouldn’t try to do it.

      I had two micromass 354 thermal ionisation mass specs and a stable isotope machine. It became too much effort keeping the whole show going.


      In an earlier post someone posted this link to emissions – is this what your are looking for? It doesn’t include forests.

  6. Euan,
    Your Figure 4 is extremely close to the answer. We just need to do a sensitivity analysis on the decline rate. What decline rate of each year’s atmospheric additions would allow the stacked decline curves to most closely match the growth in total Atmospheric CO2? Visually, it looks like a 3-4% decline rate ought to be close to the match sought.

    Beyond that point, are we assuming that the CO2 account balance of the land (soil+plants+animals) and the ocean (CO2, BiCarbonate, CaCO3) each remain constant? This is quite dubious.

    As to your main point, you are correct. The 14C decline curve is a measure of short term mixing rates, not sequestration. It is easily an upper bound on the sequestration rate (lower bound on half-life residence time).

    Logically invalidating the 14C curve does nothing to add support to the Bern model. Indeed, by explicitly investigating how atmospheric CO2 mixes with a gargantuan carbon sink that is the ocean, it makes one believe the Bern model less.

  7. Euan,
    Your figure 4 is to me the approach one should take to solve the puzzle. Clearly, a 7% decline rate from the 14C data is too high, as you well show by the problem with mixing with the ocean (14C in, 12C out). But it also seem clear that a 0.2% decline rate is far too low. A simple sensitivity of What decline rate most closely matches the observed increase in the balance? By eyeball, a 2.5-4% decline rate ought to be a good match.

    It make one wonder, however, if any 14C ocean content data has been measured over time.

    Finally, are we making assumptions that the CO2 balance on land (soil+plants+animals) and the ocean (CO2, carbonate-ions, CaCO3) are constant. That is a most dubious assumption, especially for the ocean.

    • Euan Mearns says:

      About 4.5% applied to about 78% (Tau 14.7 above) of emissions and a long tau of a few hundred years applied to the rest. You need to read the concept Phil Chapman introduced which I think is valid physical science. Basically more CO2 circulating in the fast sinks will leave more CO2 in the atmosphere until the slow sinks pump the fast sinks down.

  8. Hans Erren says:

    Peter Dietze already critised the Bern model years ago. Simply using emissions and concentrations a halving time of 55 years can be derived for a co2 pulse injection.
    In graph:

  9. Martin A says:

    I may be missing a point of understanding here. If so, please pardon me and if you’d care to point out where I am going wrong I’d be grateful.

    First, I think the system is linear – which means that we can analyse what happens to an injected dollop of CO₂ separately from what is already happening.

    We can assume that, prior to injection of man-made CO₂, the system is in equilibrium with (say) 90Gt leaving the ocean for the atmosphere each year, and 90Gt going in the other direction.

    I think you are looking at that situation where the system is in equilibrium, except for an unbalance in the isotopic mix. I think you are then discussing how long it takes for the isotopic mix to become equal in the ocean and the atmosphere. Have I got that right?

    We are interested in the question: If we inject an *additional * dollop of CO₂, into the atmosphere, how long does it take for 50% of the injected dollop to disappear from the atmosphere? (Or some alternative measure such as the so-called e-folding time). I am not sure that that is the same as your question. (Nor am I sure that it is different from your question so clearly there is something I have not understood.)

    The question is complicated slightly because the ocean is not infinite, so things will eventually reach a new equilibrium with the injected dollop shared between the atmosphere and ocean (most of it finishing in the ocean but a small but finite quantity of the additional dollop remaining in the atmosphere because the final equilibrium is different from the equilibrium before the injection of the dollop.

    The point I have not yet grasped is why (because of linearity) we can’t simply calculate (or observe) the time for the injected dollop to disappear from the atmosphere, separately from what is going on with the continuing ocean/atmosphere equilibrium exchange.

    If the injected dollop happened to be 14C flavour, I don’t see that that changes anything. So, I have not yet grasped why the rate of disappearance of atmospheric 14C does not also tell us the rate of disappearance of an injected dollop of any flavour of CO₂.

    Because of linearity, if the next year we then inject another dollop, the disappearance of this new dollop can be calculated independently of the other dollop. And so on.

    Does this make any sense? What am I missing? Perhaps it’s obvious but I have not yet got my head around it.

    • Euan Mearns says:

      Have I got that right?

      Martin, with respect, up to that point you hadn’t got much right. If you look at Figure 6. In very simple terms, the bomb model tries to predict how much bomb carbon is removed from the atmosphere by looking at the shade of orange of the carbon left in the atmosphere. In Figure 6 I show that the shade of orange in the atmosphere changes without removing any bomb carbon hence the methodology fails.

      This is a minor blow. Bomb 14C cannot be used to falsify Bern. This does not mean that Bern is correct. There are a number of other reasons that explain why Bern is false.

      • Martin A says:

        Euan – thank you. In that case, I’ll go back and try to better understand your Fig 6 reasoning.

        Yes, I think there are a number of things that don’t add up with the Bern model. I believe it is a linear ‘box model’. Linear box models are equivalent in their dynamic behaviour to electrical networks consisting solely of resistors (with positive resistance) and capacitors (with positive capacitance) (ie only passive components). The Bern model’s impulse response as I remember consists of a sum of exponentials. I think that its impulse response was obtained by approximating the simulated impulse response by a sum of exponentials – despite the fact that such a function cannot in reality be the impulse response of a passive RC network.

        • Euan Mearns says:

          Martin, I think you are venturing out on to virgin territory here since I don’t understand electrical systems and suspect there may be nomenclature confusion surrounding the concept of “impulse response”. In isotope geochemistry two component mixing is non-linear and is controlled by the element concentrations and isotope ratios of the end members. The more components you have the more complex it becomes. The system is dominated by the component with the highest concentration (or mass) of the element of interest, in this case C.

          For some reason your comments are not being posted automatically, I don’t know why. I am not knowingly doing anything to block them. Building bridges of understanding is important, and so if needs be I can call on Prof Dave Rutledge from Call Tech (electrical engineering) who may be able to help explain.

          • Martin A says:

            Euan, Thank you for putting me right.

            Thanks to your help, I now see what your Fig 6 model is saying: If you have a situation where there is equilibrium between atmospheric and ocean CO2 (same mass transferred in each direction per year) then, if the atmospheric CO2 is initially rich in 14C, the atmospheric 14C will diminish, even though the total atmospheric CO2 remains constant.

            If the dynamics of the exchanges between reservoirs are significantly nonlinear, then the analogy with linear resistor capacitor networks does not hold. That is too bad, because there is a wealth of understanding of the properties of such networks – what they can and cannot do etc.

            Furthermore, if the dynamics are nonlinear, then the notion of impulse response is of essentially no use. If the system is linear, the impulse response can be used to compute the response to an arbitrary function of time.

            But if the system is nonlinear, the superposition principle does not hold, and the response of the system to an arbitrary input cannot be computed by considering the input as a summation of impulses and the response of the system as the corresponding summation of impulse responses.

      • Euan Mearns says:

        Correction: that should read “without removing any CO2”. Bomb 14C is removed without changing the amount of CO2 in the atmosphere.

  10. Geoff Sherrington says:

    Thanks for your reply Euan.
    Used to visit ORNL in the 1980s.
    They did some good science then.

  11. DocMartyn says:

    Think of the simplest two box model, you have two reservoirs A and B.
    You add 14C to reservoir A and you have a first order rate of transfer from A to B and also a first order rate from B to A; the overall rate is the difference in the rates.
    So far, so good. However, you can get more information out of the 14C disappearance from the atmosphere. If there was initially no 14C in either A or B, after a detonation series you had 100 units of radioactivity in A, you can work out the ratio of the size of the two reservoirs; if A and B were equally size, the end point would be 50 units; it B>A by a factor of 10, then the end point is 10 units, and so on.
    With the actual data we have two problems; firstly we have increased the amount of carbon in reservoir A and B, and if we don’t know the ratio of sizes, the the relative dilution of CO2 in the two reservoirs is tricky. Secondly we have a steady state level of 14C anyway, due to the zeroish order rate of cosmic ray radiation acting on nitrogen.
    Overall we can state that A, the atmosphere is at least 25 times smaller than the pool of carbon it is talking to on an annual basis, B. in a decade or so we shall be able to smooth the various monitoring stations data and show that the endpoint is less than 1% of the pre-1945 level; the biggest challenge is to know how small the pre-atomic 14C level actually was, so we don’t know what the endpoint would be if reservoir B was infinite.
    You can work out the ratio of the the atmosphere to the pools it is talking to by the data you have posted, not taking account of the dilution, and the answer is far larger than the BERN model suggests.
    That the BERN model is wrong is not that surprising given, the surface of the ocean is denuded of CO2/Inorganic carbon and the very rapid rate of marine snow and sinking to the bottom of the ocean is ignored.

    • Euan Mearns says:

      I think imagining an ocean with zero C14 at the start is helpful. If the atmosphere contains 14C and If the ocean breathes in XCO2 and breathes XCO2 out again the ocean will be enriched in 14C and the atmosphere depleted. Hence depletion of 14C in the atmosphere cannot be used to measure sequestration rate since in this case no sequestration takes place.

      The other processes are complications. We think we know there is roughly 1000 Gt C in the upper ocean. But on an annual cycle, we do not know how much of that mixes with the CO2 inhaled. And I also suspect that the notion of a static upper ocean layer is totally false with a far greater rate of exchange between it and deeper water than currently projected (see next post on Gulf Stream for example).

      The rate of removal by the biological pump is another good question. I think I read yesterday that the oceans account for about 50% of photosynthesis on Earth and yet the Grid Arendal C cycle I refer to has only 3 Gt of C in marine organisms and 4 Gt of C sequestered per annum by the biological pump. And yet the deep oceans are far more acid than surface layers because of all that rotting phytoplankton.

  12. itzman says:

    The bomb curves show how fast CO2 is removed from the atmosphere. What they don’t show, is how fast CO2 is re emitted.

    Re-emitted C-14 of course will show up. So what the other curves show is that there is a massive amount of NON (short term) organic CO2 being emitted all the time.

    Which could be fossil fuels or it could be…..a response to a warming climate causing oceanic carbon to outgas?

    a proposition slightly supported by the lag between geological temperature rises and CO2 content of the atmosphere.

    the problem is the carbon cycle is not understood in any detail, and rushing in to use a small part of it to prove any point is loaded with caveats.

    But climate pundits rush in where angels…

    …in the end its probably irrelevant because the CO2 content of the air is rising, and overall temperatures are not.

    Which means it interesting, but not important .

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