# The residence time of CO2 in the atmosphere is …. 33 years?

By Roger Andrews

An important consideration in estimating future greenhouse warming risks is how long CO2 remains in the atmosphere. Here I present the results of a simple mass balance model that provides a near-perfect fit between CO2 emissions and observed atmospheric CO2 using a CO2 residence time of 33 years. This, however, is significantly longer than 36 peer reviewed estimates that cluster between 5 and 15 years and much shorter than IPCC’s estimates of 100 years or longer, hence the question mark in the title.

Figure 1: CO2 Residence Time Estimates (data: Jennifer Marohasy )

I developed the mass balance model using the following deductions and assumptions:

1. Between 1750 and 2010 fossil fuel burning and deforestation released approximately 1.85 trillion tons of CO2 into the atmosphere. If all of it had stayed there the CO2 content of the atmosphere would have risen by ~220 ppm, but it rose by only 110 ppm. We can therefore assume, all other things being equal, that about half of the CO2 emitted between 1750 and 2010 has remained in the atmosphere and that the other half has been absorbed, either by vegetation or by the oceans.

2. The half of the CO2 that was absorbed was absorbed over time in accordance with an exponential decay curve of the form:

Fraction remaining = e^(-t/T)

Where t is the elapsed time and T is the “e-folding time”, or the time it takes for the concentration to decrease to 1/e, or 36.8%, of its initial value.

3. “Residence time” is defined as as the time it takes for the fiftieth molecule in a pulse of 100 emitted CO2 molecules to be absorbed (in other words the half-life). Mathematically it works out to 0.69 times the e-folding time.

4. The residence time remains constant. It does not change with time.

5. “Synthetic” CO2 curves can be constructed from emissions data using different residence time values. The value that gives the best fit to observed CO2 concentrations provides the best estimate of residence time.

I constructed CO2 curves using a spreadsheet algorithm that begins in 1760 and works as follows. It takes 1760 CO2 emissions, calculates how much CO2 (in ppm) they added to the atmosphere in 1760 and then reduces the ppm value in each following year in accordance with the decay curve, which will vary with the residence time. The process is then repeated for 1761 and the 1760 and 1761 results are summed, ditto for 1760, 1761 and 1762 and so on for each year through 2010. The procedure, which is analogous to estimating production and depletion rates in an oil or gas field, is summarized graphically in Figure 2, The case shown begins in 1990 (emissions from earlier year are ignored for simplicity) and uses a residence time of 10 years (for illustration purposes only):

Figure 2: Graphical example of operation of spreadsheet algorithm

The data sources used were:

* Atmospheric CO2 concentrations from Mauna Loa

* Emissions data for fossil fuel burning and cement production from CDIAC

* Land use change emission estimates based on forest cover data from forest cover data from Euan Mearns which were added to the fossil fuel emissions. (I used changes in forest cover percentage to calculate the annual tonnage of carbon emitted from deforestation, based on the  current estimate of 638 billion tones of carbon contained in the world’s forests.)

The emissions data used in the analysis are shown in Figure 3:

Figure 3: Annual global carbon emissions since 1760

Now to the results. Figure 4 shows the CO2 curves generated using a) the IPCC’s residence time of 100 years and b) a residence time of 10 years, which is the approximate average of the non-IPCC estimates shown in Figure 1. The 100-year curve gives far too much CO2, implying that CO2 doesn’t stay in the atmosphere for anything like as long as the IPCC’s 100-year residence time would suggest. On the other hand the 10-year curve gives far too little CO2, implying that CO2 stays in the atmosphere much longer than a 10-year residence time would suggest:

Figure 4: CO2 model/observed matches, 10 and 100 year residence times

With a 33-year residence time, however, we get a match which I submit is about as good a model/observed fit as you are ever going to see:

Figure 5: CO2 model/observed match, 33 year residence time

The fit is also quite sensitive to small changes in residence time. With a 31 year residence time the CO2 curve is clearly off on the low side and with a 35 year residence time it’s clearly off on the high side:

Figure 6: CO2 model/observed match, 31 and 35 year residence times

In summary, here we have what appears to be a robust 33-year estimate of residence time derived from a simple mass-balance model. The problem is that the estimate matches no one else’s. I don’t have much doubt that it invalidates the IPCC’s estimates, but why is it so much higher than the numerous estimates obtained from the carbon 14 and radon 222 analyses? Is there a flaw in my logic? Or do radioactive isotopes have a higher sequestration rate than carbon 12? Open for comments.

A couple of closing observations. First, someone is going to ask why I didn’t take the carbon cycle into account, given that the amount of carbon that cycles each year between the atmosphere and land-ocean sinks overwhelms man-made carbon emissions. The simple reason is that to take the carbon cycle into account I need to know how the tonnages of emitted and sequestered CO2 have changed over time, and there are no good numbers available. However, the fact that I get an excellent model-observed fit using a constant residence time suggests that the carbon cycle hasn’t changed much, if at all, since 1959.

Second, it’s not widely recognized, but the IPCC & Co. in fact agree that the residence time of CO2 in the atmosphere is short. SkepticalScience puts it thus: “Individual carbon dioxide molecules have a short life time of around 5 years in the atmosphere.”

So where do the IPCC’s ~100 year residence time estimates come from? SkepticalScience goes on to offer this explanation: “However, when they (the CO2 molecules) leave the atmosphere, they’re simply swapping places with carbon dioxide in the ocean. The final amount of extra CO2 that remains in the atmosphere stays there on a time scale of centuries.”

I’ve been trying to make sense of this statement but haven’t been having much success. Maybe someone can make sense of it for me.

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### 81 Responses to The residence time of CO2 in the atmosphere is …. 33 years?

1. Roger,

I think the answer lies in the authors expertise in ‘post-modern’ science – and lack of understanding of the physics and chemistry of mass balance between the oceans and the atmosphere. If they understood it they would not have written that howler. Actually I can’t make sense of it either, it’s one convoluted non sequitur but an excellent example of PC thinking. Blame the common core education system for producing this scientific nonsense.

• Louis: If you take the authors at their word and assume that every CO2 molecule sequestered in the ocean swaps places with a CO2 molecule released from the ocean – and that the same goes for vegetation – then every molecule of anthropogenic CO2 ever emitted is either still in the atmosphere or still there by proxy, in which case atmospheric CO2 now exceeds 500ppm, the residence time of CO2 is infinity and cutting atmospheric CO2 is possible only by physically sucking it out of the air. Science marches on. 😉

• Stuart says:

A more interesting question is why does the IPCC use a figure of 100 years?

Especially when there are dozens of papers available which seem to coalesce around a figure of 5-15 years, perhaps with the range being explained by geography and chronology.

The IPCC are an entire order of magnitude out.

The most important aspect of the climate change debate is not about being on the correct side of the debate, or about shocking the whole world into action, it is about maintaining credibility so that whatever conclusion is drawn and however that conclusion is quantified it is able to be broadly accepted by all parties.

Anything that risks damaging the credibility of any party in the debate simply reduces the power of that party to elicit any broad action from wider society. This was evident in recent years with the University of East Anglia scandal, which has set public opinion back by a decade.

The IPCC should be beyond reproach. Yet figure 1 significantly debases their credibility.

My own personal view of anthropological climate change is that it is real, but that CO2 emission are now almost entirely in the hands of the Chinese who now emit more CO2 than all of Europe and North America combined.

Their emission growth continues unabated.

Why are Chinese emissions growing at an explosive rate? Because 1.2 billion people are working their way out of abject poverty. India is not far behind them. If the world is to cap CO2 emissions in a bid to avoid a potentially perilous climate, then that means leaving billions of people in poverty.

In my mind climate change is not the big problem facing humanity in the 21st Century. Poverty is. Climate change and spiralling CO2 emissions are simply a symptom of a world still rife with poverty.

No amount of scientific evidence no matter how well researched or how irrefutable will convince 2 billion people to shut down their coal power stations give up their middle income aspirations and return quietly to the paddy fields.

It is impossible. It’s politically undeliverable and morally abhorrent. The only morally acceptable way to avoid climate change is for the developed world to donate all of our accumulated wealth to the worlds poor and to completely flatten global poverty and inequality, thus eliminating the need/desire for anyone to catch up.

After 40 years of listening to the science of climate change, the debate has shifted.

During the 1990’s Climate Change was all about the rich countries decimating any aspirations of the worlds poorer countries, about the rich destroying the environment and forever locking out the poor.

20 years later the tables have completely turned, today it is the world’s poorer countries which dominate CO2 emissions and by some margin. On what basis do we tell these countries to stop their emissions? To shut down their cheap power stations? To stay poor? We have no such right and no such moral authority.

The sad reality is that anthropological climate change is no longer about proving whether or not it is real, today the debate has matured. Now it is a political issue, a moral issue.

We in the West are comparatively enormously wealthy and we have curbed our emissions (we met Kyoto the requirements and more) although we can always do more. But the rich are no longer the source of the problem. It is the world’s poor who are now burning coal in volumes never before witnessed. They don’t care about climate change because they have a bigger and more immediate problem to overcome, their own poverty.

The world cannot tackle climate change unless first we tackle poverty. It’s probably going to be another 10-15 years before people realise this.

2. Rui N Rosa says:

Dear Roger:

The nuclear tests carried out 1955 and 1964 dramatically increased the amount of Carbon-14 in the atmosphere. After the tests ended, the atmospheric concentration of the isotope began to decrease steadily.
This has enabled for instance dating the crop production of a wine from the actual Carbon-14 proportation in its alcohol carbon content (bomb-pulse dating)
The atmospheric half-life for removal of Carbon-14 marked CO2 has been measured and found to be roughly 12 to 16 years. One realizes that the transfer between the ocean shallow layer and the much larger reservoir of bicarbonate in the deeper ocean takes place at a limited but not negligible rate. More important but very difficult to estimate is the exchange of CO2 between the atmosphere and the soil and the rocky crust, by far the larger Carbon reservoir.
So that, although unwillingly, one has a direct experimental assessment of the atmospheric CO2 residence time and removal rate to the remaining planetary reservoirs, that yields about 15 years life-time. Not centuries.

Rui Rosa .

• I’ll get back to this later. Going to bed now:

3. Apparently, comments don’t get into this site easily, so let’s try again…

The dominant return of Carbon to ‘permanent’ storage is achieved by calcifying sea life, which dies and sinks, and whose shells & skeletons thus become components of seafloor limestone,. This amount is under 300 million tonnes of C per year. AAAS Science, Canfield & Kump, vol 339, p533, 2/1/2013

We now emit about 30 times that. Thus we fall ~30 years behind each year, and are now >1500 years behind form historical carbon combustion.

Land and rocks are essentially neutral, or even net CO2 emitters, especially as farming and grazing have expanded.

So, the pH of oceans now is lower than at any time in many 10s of millions of years, already causing loss of sea life, and threatening extinctions of both sea food chains and the dominant sequestration to limestone. We have only years, not decades, to get cracking on protecting sea chemistry and even stopping all emissions today will have little effect…

• Euan Mearns says:

Comments should 1) be on topic, 2) provide supporting evidence for claims made, 3) be polite and 4) not be overly repetitive. Shouting the same thing over and over does not make the thing right and it does get in the way of those who want to have a sensible discussion.

Dr Cannara says:

So, the pH of oceans now is lower than at any time in many 10s of millions of years

Given that we only have two ocean surface sites with pH records going back a few decades I’m intrigued to see your evidence for ocean pH going back 10s of millions of years. Without that evidence this is nothing more than an empty alarmist claim. Below is Roger’s chart of ocean pH.

Dr Canara says:

The dominant return of Carbon to ‘permanent’ storage is achieved by calcifying sea life, which dies and sinks,

There are a number of gigantic carbon sinks / stores that dwarf manmade CO2 emissions. For example, soils and organic matter with 1580 Gt C compared with annual emissions of about 6 Gt, and this is only a small part of a big complex story.

The GRID Arendal Carbon Cycle

http://www.grida.no/graphicslib/detail/carbon-cycle_9d44#

4. Clive Best says:

delta C13 measurements show that only about 6% of CO2 in the atmosphere originates from fossil fuels. The Seuss effect would support a lifetime of about 7 years for an individual CO2 molecule. The decay of C14 measurements following nuclear bomb tests give a residence time of around 10 -14 years. In both cases the fraction of ‘fossil fuel’ CO2 molecules in the atmosphere for current emission levels reaches a limit of < 10% of today’s atmosphere.

IPCC use the BERN carbon model. This is based on all of the apparent 30% increase in CO2 concentrations since pre-industrial times is due to human activity. They are assuming effective CO2 lifetimes of over 100 years in order to explain these levels, plus their models include positive feedbacks to match the data. However direct measurements with C14 and indirect measurements through delta C13 data show that the lifetime of individual CO2 molecules is much less – only about 10 years. This leads to a maximum of 10% increase in CO2 directly, or less than a third of the observed 30% increase. So how can this be ?

I think here are only two possible answers to this apparent mystery.

A) The consensus answer. The addition of anthropogenc CO2 has disrupted the overall carbon cycle. The sink of CO2 in the oceans is so large that it is releasing more natural CO2 to replace absorbed “Fossil” CO2. The end result is the same but the argument is different. The lifetime for CO2 is small but the carbon cycle is itself rebalancing. The is the origin of the ~ 100 year effective lifetime. Geological sinks and deep ocean sinks only react very slowly. The carbon cycle is the earth's long term thermostat. Too warm and rock weathering increases removing CO2, and too cold and rock weathering decreases increasing CO2 levels.

B) Salby is actually right! The Earth has gone through a period of natural warming after the Little Ice Age with a consequent outgassing of CO2 from the oceans as surface temperatures have risen. CO2 levels would have risen anyway. Human activity has added an extra 10% rise to this and increased the warming slightly. In this scenario, temperatures will eventually start falling and CO2 levels should then decrease.

5. Euan Mearns says:

Roger, I think this is a great analysis but clearly someone is wrong. Let me start by clarifying again for the non-geochemistry types that the residence time is the time required to remove ~50% of an input and is effectively equivalent to a half life. As a rule of thumb, 5*half lifes are required to reduce the input to zero. Hence your analysis suggests that 33*5 = 165 years would be required to remove all emissions to date. All emissions made prior to 1850 are already gone.

Reconciling these numbers with the IPCC. Is it possible that these poor souls do not fully understand the technical meaning of residence time and are instead talking about the time required to reduce emissions to zero?

But the real issue is trying to reconcile your analysis with the bomb 14C data. The chart below is from Phil Chapman and shows how bomb 14C is removed from the atmosphere in about 20 years.

Following the rule of thumb detailed above this would imply a residence time of about 4 years that is materially different to your estimate of 33 years. This suggests one of two possibilities 1) bomb 14C is somehow removed more quickly than other emissions or 2) there is something wrong with your model / reasoning (more on that in a separate comment).

As a totally wild card idea (which I reserve the right to delete 😉 I wonder if bomb 14C is atomically identical to “normal” 14C that is made by the capture of thermal neutrons produced by cosmic rays in the stratosphere by 14N. I’m wondering out loud if bomb 14C has the same half life as “normal” 14C?

Another wild possibility might be that 14C does not like being in CO2 as much as 12C and has a different sequestration route. In other words, part of the decay in bomb 14C would be down to preferential diss-association of 14C from O2. Or that 14CO2 is somehow sequestered more rapidly than 12CO2. As a rule of thumb, in geochemistry, the lighter carbon isotopes tend to be preferentially sequestered by plants and animals, so this option flies in the face of conventional understanding.

• Euan: Apologies for the delay, but I had to build another spreadsheet model to get the numbers I needed.

Here’s the problem:

The CO2 concentration in 1760 was 280ppm (I’m rounding the numbers off here).

500 gigatonnes of carbon was emitted between 1760 and 2010, enough to increase atmospheric CO2 from 280 to 500 ppm, i.e. by 220ppm, if all of it had remained in the atmosphere.

But atmospheric CO2 increased by only 110ppm, to 390ppm.

So only half of the carbon emitted between 1760 and 2010, i.e. 250 gigatonnes, remained in the atmosphere.

And 250 gigatonnes remaining is what a 33-year CO2 residence time gives.

The ~10-year “bomb test” CO2 residence time, however, gives only 120 gigatonnes remaining, enough to increase atmospheric CO2 by only about 50 ppm, i.e. to about 330 ppm.

But atmospheric CO2 in 2010 wasn’t 330 ppm. It was 390 ppm. So if we accept the 10-year bomb test residence time as correct for CO2 then the extra 60 ppm of CO2, equivalent to 120 gigatonnes of carbon, must have been released into the atmosphere from natural carbon sinks (nowhere else it could have come from).

While at the same time these sinks absorbed 380 gigatonnes of carbon (nowhere else it could have gone)

Assuming there are no fatal flaws with my model – and so far I haven’t found any – I see three ways of explaining these numbers:

1. Carbon sinks are somehow capable of absorbing and emitting carbon at the same time.

2. The atmospheric residence time of CO2 is significantly longer than the residence time of bomb-test carbon 14.

3. The Bern model, which uses both short-term and long-term carbon residence times, is substantially correct. I plan to look into this next.

• Euan Mearns says:

Roger, relax and take your time. I like posts like this where no one is quite sure where the truth lies and shared information helps everyone understand a bit more.

My gut feel at the moment is that Phil is barking up the right tree:

Carbon sinks are somehow capable of absorbing and emitting carbon at the same time.

Warming means that oceans should be exhaling CO2 but they are being forced to absorb it. Biodetritus is the biggest fast sink and we know that CO2 fertilisation results in more rapid plant growth. But we are chopping down forests. Land biomass + biodetritus together represent 51% of the fast sink. 2050 GtC sink with 6 Gt C annual emissions.

I’ve come back to look a Phil’s table a few times today trying to understand its implications. The point I’ve reached is that Phil’s analysis is based upon an equilibrium while in fact we have a dynamic equilibrium where the size of the sinks may change with time.

I think the starting point to understand what is actually going on is to ask where has the 50% of sequestered emissions gone?

6. Phil Chapman says:

Atmosphere Land biomass Biodetritus Shallow ocean
Store GtC 800 550 1500 1000
Store % 21% 12% 39% 26%
Flows GtC/yr:
Atmosphere 60 60 90
Land biomass 120
Biodetritus 60
Shallow ocean 90
The Fast Carbon Cycle
Source: http://earthobservatory.nasa.gov/Features/CarbonCycle/

Rui Rosa is correct that the time constant for depletion of atmospheric 14C produced by the Soviet nuclear tests was c. 15 years. However photosynthesis (by land plants and oceanic phytoplankton) preferentially consumes the light isotope 12C, which makes up 98.9% of atmospheric carbon. Thus the sub-decadal time constants shown in Roger’s
Fig 1 are probably valid for depletion of a slug of normal CO2 injected into the atmosphere.

What Roger’s analysis neglects is the distribution of carbon among natural reservoirs. The table above shows the estimated carbon stored in “fast” reservoirs – i.e., those that can exchange carbon within a few decades, The figures are in gigatonnes carbon (there is 1 GtC in 3.67 gigatonnes CO2). The total in the 4 reservoirs shown is 3850 GtC.

Also shown are the annual flows from the column-heading reservoirs to the row-heading reservoirs – e.g., the atmosphere transfers 120 GTC/yr via photosynthesis to land biomass, which returns 60 GtC/yr to the atmosphere as plant respiration and delivers 60 GtC/yr to biodetritus (decaying plant matter), and decay then transfers 60 GtC/yr back to the atmosphere. The books balance, and the reservoirs are in equilibrium.

If now we add a one-time slug of carbon to the atmosphere, it will be transferred to (land and shallow ocean) biomass with sub-decadal time constants – but the resulting increase in biomass creates an increase in transfers back to the atmosphere. When equilibrium is restored, each reservoir will end up with the same percentages of the total as before (assuming the processes are linear). Thus the carbon content of the atmosphere will end up with 21% of the carbon slug.

There are several slow reservoirs in addition to the fast ones shown. A small percentage of the carbon in the shallow ocean sinks each year (mostly as calcium carbonate shells of small marine creatures), where it remains until the marine plate subducts and creates volcanoes; some of the atmospheric CO2 becomes carbonic acid (H2CO3) which weathers rocks, and rainfall and rivers then return the products to the sea, where it joins that slow recycling; and some of the biodetritus gets buried as fossil carbon (coal, oil and gas). These processes take thousands to millions of years, but eventually equilibrium will be restored and the stores in the reservoirs will return to the values before we added the slug (which was of course not an external input but a transfer from the fossil carbon reservoir).

(Incidentally, the total carbon in all reservoirs increases each year by a tiny amount (a few thousand tonnes) due to the carbon contained in the annual 50,000 tonnes of incoming meteors.)

The bottom line is that the IPCC is partly correct: something like 21% of the carbon we add will remain in the atmosphere for thousands of years, until removed to the slow reservoirs.

• Phil Chapman says:

My table did not survive. Euan, how do I post tables or figures?

• Euan Mearns says:

Phil, I’m afraid that ordinary commenters cannot post images. Its a major limitation of WordPress. If you mail it to me I’ll post it for you.

• Euan Mearns says:

Phil, this is a simple screen capture from your Word file.

• The bottom line is that the IPCC is partly correct: something like 21% of the carbon we add will remain in the atmosphere for thousands of years, until removed to the slow reservoirs.

The longest CO2 time constant (or e-folding time) used by the IPCC that I’m aware of is 371.6 years (in the SAR) and it applies to only 13% of the CO2 in the atmosphere. With these numbers only 5% of the carbon we add will remain after ~350 years, only 2% after ~700 years and less than 1% after ~1000 years.

http://unfccc.int/resource/brazil/carbon.html

7. Euan Mearns says:

Roger, a further two points which I feel are likely real world processes that need to be incorporated in your analysis:

1) part of the rise in CO2 is natural
2) the residence time is not constant

Natural rise in CO2

We know that in the period of your analysis Earth was recovering from The Little Ice Age cooling event. There is evidence from Law Dome ice core that CO2 was already rising (see chart). Hence, assuming that all of the rise in CO2 is down to manmade emissions will result in over-estimation of residence time (this is the same point made by Clive)

Variable residence time

Deforestation alone suggests that sequestration capacity will decline with time. Deforestation is a double whammy. It adds CO2 to atmosphere AND it can reduce the biospehere’s ability to remove CO2 though I’ve been told that certain agricultural practices may actually enhance CO2 sequestration rates. I dare say the same may be said of the oceans where over exploitation is reducing ability to sequester CO2. And of course rising ocean temperature will reduce sequestration rate, and increasing the amount of dissolved CO2 in the upper ocean layer reduces its ability to absorb more. Combine, all these processes may result in an increase of residence time of CO2 in the atmosphere from the time of the bomb tests to today.

How significant these processes are requires some additional analysis. Will be interested to see if you can replicate the excellent fit of your model to observations with a different set of inputs?

• Euan Mearns says:

@ Rui Rosa, that is a rather excellent WUWT article you link to. Their chart presents a slightly different picture to the one from Phil Chapman.

And you say:

The atmospheric half-life for removal of Carbon-14 marked CO2 has been measured and found to be roughly 12 to 16 years.

This is now much less different to Roger’s estimate and I’d feel more confident that accounting for some natural increase in atmospheric CO2 combined with an increase in residence time with time may bridge the gap between 15 and 33 years.

8. Euan, Phil et al. I’m not ignoring you, it’s just that your comments need some complicated responses. Back ASAP.

9. Dave Rutledge says:

Hi Roger,

Until fossil-fuel production falls by quite a bit, we would not be able to distinguish the difference between your one-time constant model and the conventional one with multiple time constants.

Phil Chapman explains the physics of the conventional thinking well. I found working with Roger Schmitz’ model helpful for understanding the conventional approach. Schmitz’ paper is at

http://ufdcimages.uflib.ufl.edu/AA/00/00/03/83/00156/AA00000383_00156_00296.pdf

Schmitz used Matlab, but it works fine in Excel with a 6-month time step. I assign it to my students for homework. If anyone would like a copy of the Excel model the students use please send me an email at

rutledge AT caltech.edu

Dave

• It is a fair observation that until fossil fuel production falls by quite a bit, we would not be able to distinguish the difference between your one-time constant model and the conventional one with multiple time constants.

I mentioned to Euan a short while ago that I was going to check what happened when I used the “conventional” multiple-time-constant Bern model decay curve instead of my single-time-constant model decay curve. I found that the Bern model also fits observed CO2 almost exactly after 1959:

So your observation was more than “fair”. It hit the nail right on the head. We can’t distinguish numerically between single- and multiple-time-constant models. I’ll have to sit back and think for a while about what this might mean.

• Euan Mearns says:

Roger, math is not my strong point, but I like pictures. I think one lesson is that model output that fits observations does not prove the model is correct. The second lesson might be that the BERN model applies different time constants with time, very fast to begin with and very slow later on. I’m flying on vapour here, but I suspect that model errs by having the wrong distribution of time constants with time. Phil says that at “equilibrium”, 21% of emissions will remain in atmosphere which is one third of the way between your exponential and Bern curves.

The correct answer needs to incorporate the very fast decline in bomb 14C and an understanding of where the 50% of emissions that have been sequestered have gone. And an understanding of how the residence time of CO2 has varied with time as a result of rising CO2 ppmV, warming oceans, deforestation etc. Your estimate of 33 years may be correct but only for 1 day.

• Euan:

The interesting point here is that my crude model and the vastly more complicated Bern model both give a CO2 half-life of around 30 years even though the decay curves are quite different. I think this makes it reasonable to assume a) that the key variable is the half-life and b) that the “average” half-life, or residence time, of atmospheric CO2 is indeed around 30 years.

The questions that remain are a) how many different half-lives contribute to the 30-year “average”, and b) why should there be different half lives anyway? According to the Bern model it’s because different carbon sinks have different time constants, but I haven’t quite come to grips with that concept yet. (As I understand it the time constants defined by the Bern model don’t change with time, incidentally.)

Regarding where the 250 gigatonnes of sequestered carbon sequestered between 1760 and 2010 went, as I mentioned earlier there are only two places they could have gone – into the sea or into the terrestrial biosphere, and putting them there doesn’t pose insuperable problems. According to the Takahashi air-sea flux model the oceans sequestered 1.37 gigatonnes of carbon in 2000, and according to McGuire et al the terrestrial biosphere has been a net carbon sink since 1958, sequestering between 0.3 and 1.5 gigatonnes/year during the 1980s because of CO2-enhanced growth.

On another issue you mentioned elsewhere, I don’t think temperature has much impact on CO2. I don’t have the results in front of me but as I remember the Vostok data show a rise of only about 8ppm for each 1C increase in temperature. This plot of more recent CO2 measurements from Mauna Loa and Law Dome, on which the impact of the LIA is clearly visible, gives a similar relationship.

10. Euan Mearns says:

Roger, I am going salmon fishing today 🙂 I leave you in charge 🙂 I told you that I spent quite a bit of time trying to understand the C cycle a few months back before hitting a brick wall. Applying different time constants to a single slug of CO2 is an invalid approach IMO. But applying different time constants to successive slugs is valid based on observation that deforestation reduces Earth’s ability to sequester emissions. Or that greater partial P of CO2 leads to enhanced sequestration rates. A couple of charts:

In 2011, Earth managed to sequester 20 Gt CO2 while back in the early 60s it was only managing less than 5 Gt CO2.

11. Euan Mearns says:

The odd thing is that Earth has always been managing to sequester about 50% of emissions even though there has been enormous emissions growth. El Ninos clearly reduce Earth’s ability to do so.

One final observation, absent from all the C cycle models I’ve seen is the burial of bio-detritus. That is the burial of organic matter on flood planes and in lakes, deltas and continental slopes.

12. Euan Mearns says:

I think maybe I have it. The residence time for CO2 is about 15 years (Rui Rosa) and is fairly constant. If you re-plot this chart with 15 years then the residual between model and observed is the natural rise in CO2.

In his article Phil says this:

http://www.pkchapman.com/2010/01/global-temperature-records.html

This result proves beyond any reasonable doubt that the residence time of CO­2 in the atmosphere is much shorter than assumed by the IPCC. This has profound implications for the theory of anthropogenic global warming (AGW), as it indicates that most of the CO2 emitted due to human activities has been absorbed long ago. Calculation shows that the quantity remaining in the atmosphere is less than 300 GT, or 40% of the measured increase in the atmospheric load.

The inescapable conclusion is that some 60% of the observed increase is from natural sources. The most probable cause is warming of the surface layer of the oceans (which reduces the solubility of CO2).

• Roger Andrews says:

Hi Euan:

“This result proves beyond any reasonable doubt that the residence time of CO2 in the atmosphere is much shorter than assumed by the IPCC.”

That’s what I thought to begin with, but now that I’ve found that my short-residence-time exponential curve and the long-residence time Bern curve give effectively identical results (see my response to Dave Rutledge above) I realize that it actually doesn’t prove it.

I think maybe I have it. The residence time for CO2 is about 15 years (Rui Rosa) and is fairly constant. If you re-plot this chart with 15 years then the residual between model and observed is the natural rise in CO2.

I don’t think this is what’s happening, but here’s a mechanism that might explain how the ocean absorbs three parts of “anthropogenic” carbon at the same time as it emits one part of “natural” carbon. The distinction between “anthropogenic” and “natural” is a little shaky because neither the atmosphere nor the ocean can tell the difference, but we’ll let it pass: 😉

Could you tell me where you got the data for your “sequestered emissions” plots from? Thanks.

• Euan Mearns says:

The sequestered emissions plots are based on BP emissions data and Mauna Loa, comparing annual changes in mass of atmospheric CO2 with mass of Co2 added.

• Phil Chapman says:

I now think I was wrong when I wrote that passage, back in 2010. It is true that the atmospheric concentration from a slug of tagged CO2 molecules (like the 14C from bomb tests) declines exponentially to zero with a time constant <15 years, being absorbed by land and sea biomass. At the same time, creating more biomass increases the CO2 release to the atmosphere through plant respiration and decay. The result is that a slug of anonymous CO2 declines with a short time constant — but to the new equilibrium concentration, not the original concentration (before the slug was added). At equilibrium, the atmosphere will have the same fraction of the total C in all fast-acting reservoirs (somewhere between 20% and 30%) that it had before the slug was added. An amount equal to that fraction of the slug (but not the same molecules) will therefore remain in the atmosphere until slow geological processes remove it. The carbon stored in deep-sea sediments (17,000 GtC) and buried fossil fuels (10,000 GtC) is large compared to that in the atmosphere (800 GtC) so the small amount we transfer from fossil fuels to the atmosphere (9 GtC/yr) will not make much difference when the final equilibrium is eventually reached.

13. roberto says:

Hello:

According to this paper, often referenced in the field of climatology…

Archer, David (2005), “Fate of fossil fuel CO2 in geologic time” (PDF),
Journal of Geophysical Research Vol. 110 , C09S05, doi:10.1029/2004JC002625

… the fate of CO2 is this:

“A mean atmospheric lifetime of order 104 years is in
start contrast with the ‘‘popular’’ perception of several
hundred year lifetime for atmospheric CO2. In fairness, if
the fate of anthropogenic carbon must be boiled down into a
single number for popular discussion, then 300 years is a
sensible number to choose, because it captures the behavior
of the majority of the carbon. A single exponential decay of
300 years is arguably a better approximation than a single
exponential decay of 30,000 years, if one is forced to
choose. However, the 300 year simplification misses the
immense longevity of the tail on the CO2 lifetime, and
hence its interaction with major ice sheets, ocean methane
clathrate deposits, and future glacial/interglacial cycles. One
could sensibly argue that public discussion should focus on
a time frame within which we live our lives, rather than
concern ourselves with climate impacts tens of thousands of
years in the future. On the other hand, the 10 kyr lifetime of
nuclear waste seems quite relevant to public perception
of nuclear energy decisions today.

—> A better approximation of the lifetime of fossil fuel CO2 for public discussion might be ‘‘300 years, plus 25% that lasts forever.’’” <—

Cheers,

R.

• roberto says:

First line of the text…

“of order 104 years”

should be understood as “of the order of 10^4 years”… the copy-paste didn’t work well, sorry.

R.

• Roberto:

Archer considers the fate of fossil fuel CO2 in “geologic time”. He claims that FF CO2 will create an excess of CO2 in the oceans that will continue to filter back into the atmosphere until the CaCO3 weathering and burial cycle re-equilibrates, which according to his model runs will take thousands of years. This claim isn’t incompatible with my results, which cover only a brief time interval. As to whether it’s correct, there’s only one way to find out. Come back in a few thousand years.

• Euan Mearns says:

Roberto, the bomb 14C data are quite clear, the residence time for CO2 is of the order 10 to 15 years. Phil Chapman provides a useful additional perspective with 21% of emissions may hang around for a long time.

14. jmurray1946 says:

See Sarmiento and Gruber (2002) Physics Today, August, p.30-36
The pre-industrial residence time of atmospheric CO2 was 4.5 years and as the mass balance is no longer at steady state is now about 5.6 years. These values may change slightly in different studies but are close to correct.

residence time equals inventory divided by total source or sink

15. itzman says:

There’s another metric somewhere – volcanism emits CO2 spikes and these are singular enough to result in a predictable and measurable decay curve. I cannot offhand remember the numbers, but they were short – under ten years IIRC.

They are particularly useful because they represent the nearest source similar to burning fossil fuels.

Many other things – like deforestation and farming, affect sources and sinks in complex ways.
Its all very well to look at C14, but after a while, C14 is being emitted by the decaying plants that took it up.

As with all things climate, devils lurk in every detail.

• Volcanic eruptions usually don’t emit measurable CO2 spikes. Pinatubo didn’t.

• Rui N Rosa says:

CO2 emission by volcanic activity and diffuse CO2 geological emission go on permanently. Presently an upper estimate might approach 1 Gt/yr – rather smaller than anthropogenic emmission, but not negligible. Volcanic crisis can set in, for weeks or years, as has happen along ages, with spectacular consequencies. It would be nice to use data from past episodes to model the pulse impact. But there are several variables at play, and ash in the atmosphere has led to cooling rather than to heating, prevailing over CO2 GHG effect. Mass extinction is a extreme impact in the historic record.

Rui

• Rui N Rosa says:

I would say that the the planetary cycle of CO2 includes the weathering of silicate rocks (mostly mafic and ultramafic rocks, rich in MgO, CaO, and FeO), by way of which CO2 is drawn from the atmosphere and fixed as carbonates. The rate is rather slow, but the reacting surface is enormous (fractal). These carbonates are partly washed down the rivers in solution to the sea, from where they feed the growth of carbonate shells and bones etc of the acquatic biosphere. It is the deposition of organic and inorganic carbon componds in lakes, deltas and open seas, that gives rise to very many (not all) sedimentary rocks (and eventually oil and gas). Subduction of sea plates’, driven by plate tectonics, carries those sedimentary rocks to the upper mantle under the continents. Hight temperature and pressure breaks up the carbonate bonds and eventually CO2 is relesed through volcanic activity, and also, more widely and silently, by magmatic intrusions and metamorphism (and sparkling spring water…). So that CO2, as well as other gases such methane, helium, etc. show up in the atmosphere, that is continuously replenished from the crust (and the mantle too – promordial volatiles left over in solution there): Helium is slowly lost to the outer space, Methane is chemicallyy dossociated relatively fast. Atmospheric CO2 is partly removed by photosynthesis, partly consumed in weathering crust rocks, and also slowly dissolving into the ocean. The crust is by far the larger reservoir of carbon, and carbon flows in and out, being relatively slow, are huge, and driven by an engine of its own – plate tectonis, fuelled by fossil heat in Earth’s mantle and core.
I guess that modeling the carbon cycle with two or three reservoirs (hidrosphere, atmosphere, biosphere plus detrictus/soil) might approach reality fairly enough – but cannot be accurate if the crust is ignored. There two engines at work – the sun and earth’s mantle/core. Carbon is moved around by both, reflecting their own evolutions and cycles.
Rui

16. Euan Mearns says:

Roger, recall in email 2 days ago I had 3 comments and could not recall the third one. I’ve remembered what point 3 was. You make an assumption that there is no natural increase in atmospheric CO2 and go on to deduce a residence time that is at odds with the quite clear bomb data.

If you do this the other way around and accept the bomb data residence time you are then left with the conclusion that a significant part of the rise in atmospheric CO2 is natural.

The “residence time” in any given year is a constant equalling the sum (average) of all sequestration modes from fast to slow acting at that time. It seems that the Bern model applies different rates of sequestration to different time slices throughout the residence. This I believe is invalid methodology. They have massaged the methodology to create a fit between model and observations – I think it is just made up! It is very hard to make the 100+ year Bern residence time compatible with the bomb data.

I’d like to do a second post on this, would be really handy to have a chart showing the difference between observations and a 15 year residence model and another showing the residual between the two continuing from the law Dome record!

• You make an assumption that there is no natural increase in atmospheric CO2 and go on to deduce a residence time that is at odds with the quite clear bomb data. If you do this the other way around and accept the bomb data residence time you are then left with the conclusion that a significant part of the rise in atmospheric CO2 is natural.

You said earlier you liked pictures, Euan, so here are some more, this time going back all the way to 1760.

First the “best fit”, which now occurs with a residence time of 32 years, not 33, but close enough. It ignores pre-1760 emissions but that won’t make much difference. The Law Dome CO2 numbers aren’t that good anyway.

The fit is very similar to the Schmitz fit in the link Dave Rutledge posted earlier:

Now here’s what I get with an 8-year bomb test residence time (8 years is the rounded-off average of the 36 estimates shown in Figure 1 with the outlier Suess & Lal estimate removed):

How do carbon sinks sequester anthropogenic carbon at the same time as they emit “natural” carbon?

Incidentally, here’s my best attempt to explain the natural component as a result of increasing SST (using HadSST3). It didn’t work out too well.

• Euan Mearns says:

How do carbon sinks sequester anthropogenic carbon at the same time as they emit “natural” carbon?

Oceans – imagine upwelling deep water adding CO2 to atmosphere that is removed in surface waters else where with time lags. That flux is not in yours or anyone else’s model.

Forests – one bit being cut down and burned emits CO2 (you have that in your model) which may then be removed by the forest that is not burned. Not in your model is the emissions from forest soils.

In fact it’s not necessary for the sinks to be the source. The observation is simply that with an 8 year residence time about 50% of the rise in atmospheric CO2 is from sources other than those emissions accounted for in your model. These could be unmetered manmade emissions or rising natural emissions. An example of the latter could be melting permafrost. We are in an interglacial and within that cycle, still recovering from The Little Ice Age.

The paradox (Roger’s Paradox) here is that with an 8 year residence time atmospheric CO2 should not be rising as fast as it is doing with the current set of known knowns. Hence we have a known unknown in the form of an unmetered rising CO2 flux.

You have to either accept the 8 y time constant and that there is an unmetered flux. Or you can argue that we know all there is to know about the carbon cycle, everything is accounted for and the time constant is 33 y. In this case the bomb data is somehow wrong.

17. Roger Andrews says:

Euan:

I see no paradox here. The cause of the CO2 increase is obvious:

Why look for complex explanations when such a simple one is to hand?

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

• Clive Best says:

The BERN model has 3 ‘lifetime’ terms. The decay of a pulse of CO2 with time t is given by:

a0 + sum(i=1,3)(ai.exp(-t/Taui)) , Where a0 = 0.217, a1 = 0.259, a2 = 0.338, a3 = 0.186, Tau1 = 172.9 years, Tau2 = 18.51 years, and Tau3 = 1.186 years.

This is like having a bucket with 3 holes in it. One very big hole, one small hole and one tiny hole. The net effect seems to be approximately a single hole with an overall lifetime of 33 years.

I think the very long lifetime is rock weathering, 180 year term is sequestration in the deep ocean, and 18.5 years is net land biota/surface ocean.

• Clive: Thanks for the Bern curve equation. Here’s a plot that compares the sum of the four component Bern curves (which fits the CO2 data) with my exponential curve (which also fits the data) and with the 8-year bomb test curve (which doesn’t). However, the sum of the two low-tau (1.186 and 18.51 year) Bern curves tracks the bomb test curve quite closely:

• Euan Mearns says:

Roger, I think this zeroes in on the answer. The long time constant reservoir (which seems to be given enormous weight) only becomes relevant when the 1.2y and 18.5y reservoirs become saturated.

• Euan Mearns says:

Roger, its a nice chart but poorly labelled. The bomb test curve is also exponential but with a much shorter time constant.

• Euan Mearns says:

Clive, you have 3 time constants here:

173 y
18.5 y
1.2 y

I can’t connect your comment to these constants. Can you say how each of the constants are weighted. Its the weighting that represents the size of the holes in the bucket.

• clivebest says:

Each year a pulse of CO2 enters the atmosphere. A percentage decays through the 3 lifetime routes

26% 173y
34%. 18.5y
18%. 1.2y

Plus 22% leaves the atmosphere immediately.

The Bern model has of course been tuned to agree with the M-L data. So these numbers are not empirical.

• Euan Mearns says:

Thanks Clive, the weighted average T half for that lot is 52 years which is clearly “rubbish” since we know that at least 50% of emissions are sequestered – it needs a rapid process. Removing the 173 y slice gives a weighted average T half of 9 years which is getting into “our” ball park. Perhaps the 173 y slice is equivalent to Phil’s 21% that remains for a very long time?

• Euan Mearns says:

1. Between 1750 and 2010 fossil fuel burning and deforestation released approximately 1.85 trillion tons of CO2 into the atmosphere. If all of it had stayed there the CO2 content of the atmosphere would have risen by ~220 ppm, but it rose by only 110 ppm. We can therefore assume, all other things being equal, that about half of the CO2 emitted between 1750 and 2010 has remained in the atmosphere and that the other half has been absorbed, either by vegetation or by the oceans.

This statement also needs to be qualified with the assumption that the net natural flux is zero even though the size of the natural flux is huge. With a net positive natural flux even more than 50% of emissions will have been sequestered. Ice cores give proxy CO2 data that smooth out short term natural variations because of diffusion within firn and exchange between firn and atmosphere.

18. Euan Mearns says:

d13C in the atmosphere has hardly changed 1991 to 2006. For example the drop in d13C is about 0.3 per mil but the annual cycle is about 0.2 per mil. FF comes in at about -28 per mil so the drift is in the right direction, but we know that a significant amount of the CO2 increase is for FF.

I’m supposed to know and be able to do this stuff so I’ll try and get back with some mass / isotope balance mixing calculations. If all the of the increase in CO2 ppm from 1991 is from FF then the book should balance. A complicating factor is that flux from terrestrial biomass -26 and from the oceans -9.5, all will drag the atmosphere d13C down.

http://www.esrl.noaa.gov/gmd/outreach/isotopes/c13tellsus.html

• Euan Mearns says:

From my spread sheet I have:

atmosphere 1991 2667 Gt CO2
atmosphere 2006 2864 Gt CO2
delta 1991 to 2006 = 197 Gt CO2

Roger’s theory is that all of this increase is due to emissions. I’m taking;

d13C atmosphere 1991 = -7.8
d13C atmosphere 2006 = -8.2
d13C emissions = -28 per mill

Using Gt CO2 to weight is the same as using GtC, we get..

((2667 Gt atmosphere * -7.8) + (197 Gt accumulated emissions * -28))/2864 = -9.2 per mil expected in 2006. The actual is -8.2 per mill. Hence the atmosphere in 2006 is way off being a simple mixture of atmosphere 1991 + emissions.

I’m nervous I may have done something wrong here and have my hand hovering on the delete comment button. I’m not prepared to do this calculation in reverse to work out what % of atmosphere CO2 is from emissions since I view this as a multi-component system with poorly constrained fluxes.

• Euan Mearns says:

I unapproved this and approved it again. I’m nervous this is oversimplified since the Earth is breathing in and out CO2 every year. I’ll leave it up as an end point discussion comment.

• Euan: I checked your calculations and they’re correct (I pulled my own numbers from the Scripps data and came up with -9.8 versus -8.3).

However, they are dependent on your d13C emissions = -28 per mill figure. Could you explain to this “isodope” what this number represents? Thanks.

• Euan Mearns says:

I took the number from here;

Same NOAA source as before.

http://www.esrl.noaa.gov/gmd/outreach/isotopes/c13tellsus.html

d13C in FF is very different to the atmosphere and so adding lots of FF C to the atmosphere should change the atmosphere’s isotope ratio significantly.

• Euan: Thanks for the link. Forgive me for quoting it back at you, but it seems to reach a different conclusion to the one you reach:

“The relative proportion of 13C in our atmosphere is steadily decreasing over time ….. (This) is explained by the addition of carbon dioxide to the atmosphere that must come from the terrestrial biosphere and/or fossil fuels. In fact, we know from Δ14C measurements, inventories, and other sources, that this decrease is from fossil fuel emissions ….”

I don’t know whether it has any impact on the applicability of the bomb test results, but the link also states that “fossil fuel emissions do not contain 14C”.

• Euan Mearns says:

Roger, I agree with the statement you quote. But my back of envelope calculation suggests that only 21% of the increase in CO2 1991 to 2006 comes from FF. The rest comes from somewhere else. All I need to do now is check how this fits with an 8 year time constant.

19. Euan Mearns says:

This is a great source..

http://funwithkrill.blogspot.co.uk/2012/09/seawater-chemistry-north-atlantic-vs.html

pH is much lower and CO2 is much higher deep in the oceans. The Pacific and Atlantic are totally different. Where deep water upwells to surface (where the blue bands upwell and turn to red bands) will bring low pH and CO2 rich water to surface.

20. Euan Mearns says:

Last one for tonight. Showing same as previous but this is a tremendous resource:

http://www.gly.uga.edu/railsback/Fundamentals/FundamentalsCarbs.html

But I disagree with the statement: “because the Pacific deepwater has had more time to accumulate CO2 from oxidation of organic matter”. The ocean mixing time is normally viewed to be about 1000 years which makes a nonsense of this statement. It seems more likely to me that higher CO2 in the deep Pacific is due to higher organic productivity in the upper oceanic layers. But that is another story.

21. Euan Mearns says:

Roger, and some bad news, I have replicated your model and adjusted decline rate so that 50% of emissions are sequestered. For this time series I get T half ~ 6 years and so I’m really struggling to see how you could fit emissions to observations with T half = 33 years. I’m away to make a full time series model.

• Roger Andrews says:

No, not bad news, Euan. If you can show that I’ve screwed up and that a ~6 year half life fits CO2 observations, well, that’s blog science in action. The ? after the 33 years in the title is there for a reason, after all 🙂

• Euan, the removal of extra CO2 above the (temperature dictated) equilibrium is from the total extra pressure of all extra CO2 in the atmosphere, not from the short-term emissions over some period (but which are adding to the total). The current extra pressure is ~110 ppmv above the 290 ppmv equilibrium at the current temperature. That gives an extra uptake of ~2.15 ppmv/year or a e-fold decay rate of slightly over 50 years. See e.g. the paper of Peter Dietze of already 17 years ago:
http://www.john-daly.com/carbon.htm

• A new global Carbon Cycle Model with a realistic CO2 e-fold lifetime of 55 years (half-life time: 38 years) ….

Off by only 5 years. Not bad for 17 years ago. 😉

22. Sorry that I am late at the game here, didn’t know this was on…

The problem with the 14C/12C ratio and the 13C/12C ratio is that their decline/upgrade is a lot faster than the decay rate of an excess amount of 12CO2 in the atmosphere above equilibrium.

About 20% of all CO2 in the atmosphere is exchanged with CO2 from other reservoirs over the seasons. That gives a residence time of ~5 years. Everybody agrees on that, IPCC as well as skeptics. But that is only throughput, and doesn’t change the total amount of CO2 in the atmosphere as long as inputs and outputs are equal.

It is the difference between inputs and outputs which gives how much the mass of CO2 changes in the atmosphere.

The seasonal fluxes are ~90 GtC/year as CO2 in and out the oceans and ~60/120 GtC in/out vegetation. These are largely temperature driven and in this case, the NH land vegetation is dominant, as the CO2 and the δ13C changes in the NH are opposite to each other. If the main exchange was from the oceans, the CO2 and δ13C changes would be far less and parallel each other:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_CO2_d13C_MLO_BRW.jpg

The ocean-atmosphere exchanges must be split in two parts: the exchange with the ocean surface (the “mixed layer”) which is very fast: 1-3 years and the exchanges with the deep oceans which are a lot slower and with a huge delay between sinks (near the poles) and sources (near the equator): some 500-1500 years.

How does that translate to the 14C/13C/12C exchanges? Most exchange with the biosphere is coming back the next season/years, that is the case for all isotopes (with some small changes in ratio, not of much interest at this point). The same for the ocean surface.

Not so for the deep oceans. What goes into the deep oceans is the current 13C/12C and 14C/12C ratio of the atmosphere (minus the isotopic shift at the air-water border). But what comes out is the ratio of ~1000 years ago, modified with deep ocean exchanges (and the shift at the water-air border).

If you look at the decay rate of extra 12CO2, that is caused by the extra CO2 pressure in the atmosphere: more uptake by plants (~1 GtC/year) and more uptake and less release by the oceans (~3.5 GtC/year). The other isotopes follow the same mass transfer in the deep oceans, but the extra 14C from the 1960 peak doesn’t return within the next centuries, what returns is the composition of long before the bomb tests.
That gives that the 14C rate is not only declining in “mass” identical to the decline of 12C mass. but also declines in ratio compared to the 12C return, here for the 1960 bomb 14C peak:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/14co2_distri_1960.jpg
and here for the year 2000:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/14co2_distri_2000.jpg

That makes that the 14 years decay rate deduced from the 14C bomb test peak is much faster than the real 12C decay rate which presents near all CO2 mass in the atmosphere…

Something similar, but opposite happens to the 13C/12C ratio. Humans emit low 13C fossil fuels. These are mixed with the rest of the atmosphere and sink with all CO2 near the poles, while what gets out of the deep has the composition of the atmosphere / deep oceans of centuries ago. That can be used to calculate the deep oceans-atmosphere CO2 throughput:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
If all human emissions still would reside in the atmosphere, the drop in 13C/12C ratio would be much faster than measured. For different deep ocean exchanges, on can calculate the influence on the 13C/12C drop. That makes that the deep ocean-atmosphere exchanges are around 40 GtC/year, which is a quite continuous flow of CO2 in the atmosphere from the equator to the poles and back via the deep oceans.
The discrepancy in the earlier years is from vegetation, which changes from a slight emitter to a slight absorber over time, which also changes the 13C/12C ratio…

From the 14C decay rate a similar 40 GtC/year exchange rate between deep oceans and atmosphere was deduced…

• Hi Ferdinand, and welcome to Energy Matters (Ferdinand and I have fought the CO2 fight on other blogs in the past).

It will take me a little time to go through everything you’ve written, but your conclusion that 14C in the atmosphere decays much faster than 12C is of the highest importance. If it’s correct then the question is answered; the residence time of 12C in the atmosphere really is on the order of 30 years.

I’d also be interested in your views on the 21.7% of atmospheric CO2 which according to the Bern model has an effectively infinite residence time. I’m having some problems with the concept.

Euan, you might care to add a comment or two here.

• Hello Roger,

The Bern model has some merits, but also some problems. If we take the three decay rates for the three main reservoirs for granted, then we have:
– a fast decay rate for the ocean surface
– a slower decay rate for the deep oceans
– a much slower decay rate for vegetation.

For each of them, the Bern model gives a maximum uptake and there it is where the problems start.

For the ocean surface, the Bern model is right: at about 10% of the change in the atmosphere, the ocean surface gets saturated, due to the Revelle/buffer factor. That is a matter of chemical equilibrium which give extra uptake of CO2 in seawater compared to the uptake in fresh water which is very limited, but that also limits the uptake in seawater when in equilibrium.

For the deep oceans, that is questionable. The pCO2 of seawater at the sink places is largely undersaturated compared to the pCO2 in the atmosphere, thus there is no reason for less CO2 uptake now and in the far future. Because of the huge C mass in the deep oceans, the total emissions of all human CO2 until now would give an increase of 1% in the deep oceans, or a 1% increase in pCO2 of the oceans at equilibrium or some 3 ppmv extra in the atmosphere…

The fact that the average uptake remained at the same ratio (even slightly increased) with the increase in the atmosphere over time shows that there is no saturation in sight for the deep oceans.

Then for vegetation, there is simply no saturation at all: for every increase in CO2, more CO2 will be incorporated in more permanent carbon storage (peat, browncoal, coal), be it at a very slow rate…

So, there is no way that large quantities of CO2 will remain in the atmosphere forever. Except if you burn all available oil and lost of coal in short time. That is at 3,000 and 5,000 GtC emissions, 10 and more times the total emissions of the past 160 years… That is where the Bern model was based on, but they didn’t adjust the remaining fractions for smaller total emissions…

• So, there is no way that large quantities of CO2 will remain in the atmosphere forever

I played around with my model to see how much I had to adjust reservoir uptakes to make it fit observed CO2 with the 21.7% “infinite” component deleted and with the time constants for the other three reservoirs kept the same as before. I got a near-perfect fit with 50% vegetation, 30% deep oceans and 20% ocean surface compared to 25.9%, 33.8% and 18.6% in the current Bern model. Are these numbers plausible?

• Euan Mearns says:

Ferdinand, I read your posts here. I think I understand and probably agree with most of what you say. It seems like you’ve been thinking about this a long time and I’ve only been thinking about this specific problem for a week or so – a lot of catching up to do. I’m writing a follow up to Roger’s post with 2, maybe 3 parts. I think I understand quite a bit but no all of what is going on. I hope to post the first part on Friday. Can we pick up the discussion then since its impossible for me to engage in a lengthy discussion here, even though I’m sure it would be fruitful, and write a post at the same time.

Chart is my rendering of Bern, that I know nothing about, but it makes quite a bit of sense, and the fit makes me believe I’m not doing everything wrong. One bit of the puzzle I’ve not begun to look at in detail is reconciling the bomb 14C with the d13C data.

• clivebest says:

Ferdinand,

You are the blogosphere expert on the carbon cycle ! So Let me ask you the following question.

Burning coal consumes two oxygen molecules in the atmosphere for each carbon molecule. Since 1990 Schripps measurements show O2 levels have fallen by about 4 parts in 10000 so a tiny fraction of a percent. Molecule for molecule that would equate to just 20% of the observed increase in CO2 concentrations.

can you explain this ?

• “The global O2 depletion rate inferred from the La Jolla data agrees well with the trend expected from the buning of fossil fuels”.

http://bluemoon.ucsd.edu/publications/ralph/3_Seasonal.pdf

• Clivebest, Roger has given you the measurements of La Jolla.

But in short: for every C atom one O2 molecule is used that forms CO2. But that is only for coal. If you burn oil, it is about 1.5:1 O2:C as the hydrogen in oil also binds with oxygen and for natural gas it is 2:1 because CH4 gives CO2 + 2 H2O with two molecules O2.

There are more recent measurements of the oxygen use by burning fossil fuels. These were used to measure the uptake or release of CO2 by the biosphere. If the sink rate of O2 was more than calculated from fossil fuel use, that would show that there was more decay than uptake of the biosphere, as vegetation decay (microbes, molds, feed/food) also uses oxygen. The opposite was true: less oxygen was used than calculated, thus the whole biosphere was a net source of oxygen, thus a net sink for CO2:
http://www.sciencemag.org/content/287/5462/2467.short
and up to 2002:
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf

The IPCC used that to show the distribution between atmosphere, oceans and vegetation of the human emissions:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif

Sometimes even the IPCC gets things right…

• Euan Mearns says:

Ferdinand, on this chart

http://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif

What is it that constrains the proportion of land and ocean uptake?

• The main constraint for the oceans is the pressure difference between pCO2 atmosphere and pCO2 oceans the influxes and outfluxes are directly proportional to the pCO2 difference. The pCO2 of the oceans depends of temperature and biolife, but that influence is smaller (~ 8 μatm/K where μatm = ~ppmv in the atmosphere) than of a few years emissions…

For vegetation it is a lot more complicated, as CO2 is not the only limiting factor. In ideal circumstances of nutrients, fertilizers, water, temperature the average extra growth of plants is ~50% for a CO2 doubling. In the real world many of the other constraints play a larger role than the extra CO2.

Since the 1990’s, the biosphere evolved from a small net emitter to a small net absorber of CO2. The difference is about 1.5 GtC/year (~2.5% of the seasonal cycle) extra uptake for an increase of ~8% CO2 in the same time frame.

• clivebest says:

The current 13/12 C rate implies that only about 5% of the CO2 molecules in the atmosphere are from fossil fuels. The growing excess of CO2 in the atmosphere is mainly ‘natural’ CO2 caused by long term imbalances of sources and sinks.

If I light a charcoal barbecue in my garden it emits CO2. The mean lifetime for one of those individual molecules to be absorbed by the biosphere is about 5 years. However, for every 2 molecules absorbed 1 natural molecule is added.

There is a fundamental geological effect which is not mentioned by IPCC nor by Fernand. That is the sequestration of CO2 by rock weathering and formation of sedimentary rocks by ocean life. This removes CO2 from the atmosphere for millions of years but luckily not quite for ever.

First some interesting facts about photosynthesis that need to be explained :

– Current levels of photosynthesis on earth would deplete all CO2 in the atmosphere in just 9 years.
– Photosynthesis in the Oceans depletes all available phosphorous needed by aquatic plants and algae in just 86 years.
– Most of the CO2 absorbed by plants is soon liberated to the atmosphere when they die or are eaten by animals, while only a tiny amount of carbon is buried in sediments. Even by including this recycling effect we still find CO2 depletion of the atmosphere takes a mere 13,000 years while phosphorous depletion takes only 29,000 years.

So what are we doing wrong?

The incredible story is that these trapped sediments are not lost from the environment for ever because plate tectonics recycles material over very long timescales even today. Subduction, mountain building and sea level change continuously re-exposes the raw materials for life through weathering. Plate tectonics is essential to re-cycle the raw materials for life to be able to continue on earth !

CO2 re-enters the atmosphere from the mantle through out-gassing of Volcanoes and also through deep ocean vents near mid ocean ridges. CO2 is removed from the atmosphere by weathering due to the abundance of water on the earth. Such weathering does not happen for example on Venus. The ‘natural’ carbon cycle essentially controls the temperature on earth because weathering by liquid water is a temperature dependent phenomenon.

The total content of Oxygen in the atmosphere is equal to the total buried carbon in the sediments. This results in the current 21% oxygen content. The total CO2 content in the atmosphere is instead fine tuned to the temperature of the earth.

That is why there is no long term damage being done by humans to the climate. Even if temperatures rise by 2 or 3 degrees, the CO2 thermostats would stabilize temperatures again by pumping down CO2 levels through increased rock weathering. Human impacts may however offset the next ice age.

The real mystery is why CO2 levels are naturally so low. Why should 290 ppm be the natural level? During Ice ages there is barely enough CO2 for plants to survive! I think the answer lies in thermodynamics. Cooling of the atmosphere through radiation to space is maximised with CO2 levels around 300ppm. More CO2 and radiation to space from the atmosphere decreases. Less CO2 and the radiation also decreases from the atmosphere itself.

• Euan Mearns says:

Clive, i think we have to be very careful in the interpretation of the 14C and 13C data. Others on the thread allude to the correct process. The large annual flux between biosphere and ocean water and atmosphere strips 14C and 13C out more rapidly than simple mass balance suggests. The CO2 that comes out of the ocean annually is not the same CO2 that goes in, some of it will be, but not all of it.

There are of course natural sources of CO2 that should not be ignored. What about weathering of limestones? And absent from the debate so far is Redox. Organic rich sediments quickly become anoxic. Does this ever happen in the Oceans? It certainly happens periodically in shelf seas and rift basins.

• clivebest says:

Euan,

These are mostly details. The big picture is that while water born life on earth continues to flourish CO2 levels will remain small. Humans are a tiny blip in the earth’s history.

• Rui N Rosa says:

Thanks for clarifying. The depletion of 14C from the atmosphere measures the gross flow rate of CO2 from the atmoshere OK. But not the rate of change in CO2 from equilibrium to equilibrium state, because the latter must take into accunt the direct and the reverse flows. In the case of 14C the other reservoirs are “empty” so that there is no reverse flow to damp the observed rate. Any way, the removal of 14C offers integrated rate of actually acting flows, emphasizing that actual CO2 concetrations are the result of multiple exchanges among several reservoirs in a complex system – isolating a part doesn’t allow to understand the whole.
Some people don’t know or don’t want to know. That is why you can read articles like the one today in the Financial Times:
«Last updated: September 9, 2014 8:04 pm, Level of carbon dioxide in the atmosphere surges, By Pilita Clark in London»