Atmospheric carbon dioxide – a tale of two timescales

Guest Post by David Ellard

Executive Summary

One of the most controversial topics in understanding the build-up of carbon dioxide in the atmosphere is the question of timescales – the effect of the build-up depends not only on the amounts being released by human(-related) activities but also on how long the gas stays in the atmosphere.

In fact much of the controversy/confusion stems from the fact that there are two relevant timescales, one which determines how the amount of carbon dioxide in the atmosphere equilibrates with other reservoirs (notably physical exchange with the oceans, and biological exchange via photosynthesis and respiration), and another which determines the exchange of carbon atoms.

By analysing the amounts of a marker carbon isotope (carbon-13) it is possible to calculate these two timescales. The timescale for the amount of carbon dioxide is approximately twenty years, a significantly shorter timescale than often claimed (e.g. by the IPCC). From these figures, we can also deduce that the increased carbon dioxide in the atmosphere since the industrial revolution has led to a noticeable increase in the photosynthetic rate of the Earth’s plants and green algae (about 8%). This has clear implications for the on-going discussions on the costs, and indeed benefits, of increasing carbon dioxide levels.

The reasons why the IPCC’s (and others’) estimates of carbon dioxide timescales in the atmosphere are overestimated are analysed – notably because no account is taken of changes in net respiration rates (ever more people, and domesticated animals, and animal pests that depend on them), because hydrocarbon usage by UN member states is underreported (quite possibly for reasons of political prestige), and finally because the models ignore the key empirical evidence (the carbon-13 isotope measurements).

Bio – David Ellard

David Ellard studied Natural Sciences at Kings College Cambridge with specialisations in mathematical and atmospheric chemistry.

Since then he has worked over twenty years in the European Commission in Brussels in various science/technology/law-related areas, notably responsible for the Commission’s proposed directive on the patentability of computer-implemented inventions.

Begins: Atmospheric carbon dioxide – a tale of two timescales

Once upon a time, when the world (and this author) was young, students of atmospheric chemistry were taught about an entirely straightforward and uncontroversial concept.

This was the residence timescale of a given (gaseous) component of the atmosphere such as nitrogen, oxygen and argon, or the trace gases such as carbon dioxide, sulphur dioxide and methane. The atmospheric timescale was easily calculated given the amount of the gas present and the known sources and sinks:

tr = (atmospheric mass of component) / (average of sources and sinks)

Strangely, amid all the current scientific controversy about atmospheric carbon dioxide, there is very little debate about the scale of the most important flows in the carbon cycle illustrated by the following diagram (other versions of the same diagram, including those of the IPCC, show numbers which do not differ significantly):

[fig.1 Carbon cycle according to NASA]

It is not a great mathematical achievement to plug in the flows (note that the sources are slightly greater than the sinks – carbon dioxide is increasing in the atmosphere of course) and calculate the residence timescale. The answer is:

And yet, this simple result is now the subject of intense controversy. The IPCC has claimed that the relevant timescale for CO2 in the atmosphere is actually 50 years, figures of ‘hundreds of years’ are routinely quoted by “alarmist” websites. This blog itself has estimated the timescale at 33 years.

So what gives? How do we reconcile these apparently contradictory claims?

The simple answer is that there are two relevant timescales, one of which is the above-calculated atmospheric residence timescale, which really is of the order of 4 years. The other one, which is often – in fact almost invariably – also referred to as the atmospheric residence timescale, isn’t. And, furthermore, estimates of it – however it should be referred to – vary wildly.

The purpose of this post is to try and explain the nature of the two timescales, and pin down using actual physical measurements (rather than computer games) the size of both.

If you look at fig. 1, you will see that there are actually only two processes that count when it comes to calculating the atmospheric residence timescale of carbon dioxide. One is the flux between the atmosphere and the biota – the source being the respiration (and, indeed, combustion) of carbon-containing molecules by living creatures and the sink being photosynthesis. The second is the process of diffusion of CO2 across the boundary between the surface waters of the Earth (i.e. the oceans) and the atmosphere. Note that these fluxes overlap in space – an important part of photosynthesis takes place in the surface waters of the oceans by phytoplankton. Nonetheless they are quite distinct.

I am going to start by looking at the latter – the physical (as opposed to biological) process of exchange of CO2 between the atmosphere and oceans.

The key principle which determines the equilibrium between a substance in gaseous form and dissolved in a solvent is Henry’s Law. But I am going to illustrate the Law, which in fact derives from the deeper principles of thermodynamics, which are inherently statistical in nature, using a different example.

The porter’s lodge of St. Henry’s College Oxbridge contains two sets of pigeon holes on opposite walls – the east wall and the west wall. One day the porter, who has a keen amateur interest in theoretical thermodynamics, releases an infinitesimal number of pigeons inside the lodge and observes what happens.

Each pigeon alights in a given pigeon hole at random, on either wall of the lodge. The pigeon decides how much it likes the given pigeon hole it is in and, depending on that liking – which we shall shortly quantify as its utility function – spends a proportional amount of time in that hole before flying off and realighting in a random pigeon hole, just as before.

These pigeons are a mite anti-social. If they sense another pigeon in a nearby pigeon hole, they will spend less time in that hole. All the pigeon holes on each wall are identical and therefore have an identical utility function as follows:

U(either wall) = k x N + k2 x N2

where k and k2 are constants and N is the number of pigeons. If pigeons are anti-social, as gas molecules generally are, then k2 will be negative.

The utility function is defined such that the ratio of time spent by pigeons on the east wall to the west wall will be given by the ratio of the utility of their respective pigeon holes. The porter immediately intuits that this ratio will, over the long term, be one, regardless of the number of pigeons, because the east wall utility function is identical to that of the west wall.

One can well imagine the porter’s shock, on arriving for work one Sunday morning, to discover that some unruly students have come into the lodge during the previous night and painted all the pigeon holes of the east wall, and only the east wall, an unappealing shade of lime green.

While the porter contemplates this new situation, (s)he is immediately struck by the consequences for the theoretical pigeons. Pigeons may or may not prefer the lime green pigeon holes, but there must undoubtedly now be a difference in the utility function for the two walls:

U(east wall) = kE x N + k2 x N2

U(west wall) = kW x N + k2 x N2

So we now have two different first order utility constants kE and kW, but nonetheless the second order utility constant k2 remains the same (because this is based on dislike of pigeons of the proximity of other pigeons and the pigeon holes are the same size, and therefore have the same separation, on both walls).

Disregarding the term in N2, we can see that the average ratio of pigeons on the east wall to the west wall is now given by the fixed expression kE/kW ≠ 1.

Disregarding? What kind of science is that? The answer is, that is a reasonable approximation as long as N is small. It will indeed be an exact answer when N is infinitesimal – in other words when no pigeons are actually present (which is, one would hope, the normal state of the porter’s lodge). If N starts to grow though, the constant k2, the anti-sociability of pigeons, will become an increasingly important factor, and the ratio of east wall to west wall pigeons will change.

And so we arrive at Henry’s Law which states that, ‘at infinite dilution’, the ratio of a given molecule in a gaseous phase which is in contact with a given solvent (so in a liquid phase) will be fixed, providing the two phases (the gas and the solvent) are in equilibrium.

The gas phase and the solvent are like the (repainted) east and west walls. They have in principle a different attraction for the molecule (pigeon) in question. But as long as the assumption of ‘infinite dilution’ holds, the ratio of molecules in equilibrium between the two phases will be fixed.

Hold on, infinite dilution? Henry’s Law only applies exactly when the molecule in question is not actually physically present! What use is that? The answer is, very useful, because Henry’s Law applies approximately to real situations where the molecule in question is present in significant, but non-infinite, dilution.

What Henry’s Law is telling us, then, is that when we add molecules of carbon dioxide to the atmosphere, these molecules will ultimately partition themselves (leaving aside the effects of the biota) in an approximately fixed ratio between atmosphere and ocean (the solvent).

Three questions arise: what is the dilution of carbon dioxide in the oceans? what does ‘ultimately’ mean? and what actually is the value of the fixed ratio?

In order of asking: very dilute (the oceans are approximately 500 times undersaturated in molecular carbon dioxide), it depends on the mixing processes both within and between the atmosphere and ocean (discussed further on), and:

This is, in my view, a rather startling result but, like the rather short atmospheric residence timescale, is extremely difficult to track down in current scientific literature. It is not actually absent so much as simply hidden in plain sight by only ever being quoted indirectly (as the product of other factors, see below).

To rephrase then, for every six molecules of CO2 that are introduced into the atmosphere, five of the six (again ignoring biological processes) will end up in the oceans, only one of them will hang around in the air.

Not only that but, as noted above, molecular CO2 is a very dilute solute in the oceans. At current rates, it would take tens of thousands of years for mankind to achieve saturation. The partition ratio 1:5 will continue to apply for the foreseeable future!

The interested reader who attempts some research on this will be immediately confused. They will no doubt encounter the fact that the actual ratio of atmospheric carbon dioxide to that dissolved in the oceans (so-called Dissolved Inorganic Carbon, or DIC) is:

The scientific literature will further confuse the unsuspecting amateur researcher by insisting that this ratio will change as further CO2 is added to the atmosphere, in apparent contradiction to Henry’s Law.

Oh dear. Fortunately help is at hand. The answer lies in chemistry.

Here’s a thought (or even real) experiment for you. Take a bucket of normal water, add some ordinary table salt (sodium chloride) until the water is distinctly salty. Sit back and watch. What doesn’t happen?

Lots of things, obviously. One of the things that doesn’t happen is that a highly poisonous green gas, used as a weapon in the First World War, exits the solution in the bucket and drifts across to our unsuspecting (thought) experimenter.

Why not? After all we just put pots of the element chlorine into the bucket in the table salt, and chlorine gas is made out of – the name gives it away really – chlorine. Why doesn’t the chlorine present in solution in the bucket equilibrate with that in the air around our intrepid experimenter, as Henry’s Law would seemingly predict?

We can put this supposed equilibrium in a form beloved of chemistry teachers:

[reaction 1: Air-gas equilibrium of chlorine/chloride: warning this is not a real chemical reaction!]

2 Cl (aq) ⇌ Cl2 (g)

where (aq) denotes aqueous phase i.e. dissolved in the bucket, (g) denotes gaseous phase i.e. in the air and Cl denotes chloride, the ion present in table salt solution.

Any chemists, however, reading this post will by now be experiencing severe heart palpitations, if they have not already undergone full cardiac arrest.

In fact the chemical reaction given above is nonsense. No chlorine gas is emitted by table salt solution.

Why not?

The reason is that the reaction books don’t balance. It is Enron chemistry. The left hand side has two more electrons (the negative sign on the chloride ions) than the right hand side. Since (valence) electrons are more or less the entire point of chemistry, this is a major flaw. Chloride ions cannot equilibrate with chlorine molecules because they are fundamentally different things. Pigeons cannot equilibrate with badgers.

On the other hand, if one visits a swimming pool, one is indeed very likely to smell the characteristic odour of chlorine molecules – which are also present, in accordance with Henry’s Law, in the water of the pool itself (which is the whole point, of course). The water contains chlorine molecules in solution, which are chemically different from chloride ions in solution. Swimming pool water does not normally taste salty.

However there are also saltwater swimming pools out there. Chlorine molecules can also be added to the salty water to guard against infection. In principle there would be a Henry’s Law equilibrium between the chlorine molecules dissolved in the saltwater and those smellable in the gas phase above the pool. As good and careful chemists, we would differentiate between the chlorine molecules in solution in the water, participating in the Henry’s Law equilibrium, and the chloride ions in the same solution which don’t.

If we were dealing with carbon dioxide, instead of chlorine, we would naturally take the same care. Sadly this is overwhelmingly not the case with the scientific literature on the question. There is a whole bunch of Enron carbon dioxide ocean chemistry out there which fails to make this crucial distinction. You have been warned.

Like chlorine, carbon dioxide can also exist in ionic as well as molecular form in solution. These ions are referred to as carbonates. We will examine the exact chemistry in more detail shortly (it is more complicated than for chloride).

The basic take home fact is that the ‘dissolved inorganic carbon’ or DIC in the world’s oceans is, in principle, a mixture of molecular carbon dioxide and dissolved carbonates. What is the ratio of molecular to ionic carbon dioxide? The smart among you will already have guessed: there is approximately 9 times as much ionic CO2 dissolved in the oceans as molecular. Only the latter is in Henry’s Law equilibrium with CO2 in the atmosphere. Hence the different ratios of 1:5 (atmospheric:molecular dissolved CO2) and 1:50 (atmospheric:molecular plus ionic dissolved CO2 i.e. DIC).

In principle we can understand the difference by carrying out the thought experiment of boiling the world’s oceans dry (don’t do this for real please readers). After we have done this, 90% of the CO2 originally dissolved will end up in the form of carbonate salts precipitated out on the ocean floors. If you ever needed a top up of bath salts, this is the place to look. The other 10% – the fraction of dissolved molecular carbon dioxide – will have escaped into the atmosphere as CO2 gas (thus increasing the concentration there by a factor of 6, causing no doubt heart attacks to the folks at the IPCC, again please don’t do this at home readers).

The ratio of DIC to dissolved molecular carbon dioxide (which is 10:1 since the former also includes the latter) is often referred to in the scientific literature as the Revelle factor. This factor actually varies with the surface temperature and salinity of the world’s oceans (as indeed does the Henry’s Law constant of carbon dioxide, but the implications of that would need to be covered by a whole other post).

Thus, as we (both theoretically and actually) add carbon dioxide to the atmosphere, the ratio of atmospheric to dissolved molecular carbon dioxide (at equilibrium) will stay the same, in accordance with Henry’s law. The oft-repeated claim that the ratio of atmospheric to total dissolved CO2 or DIC (i.e. molecular plus ionic, the latter of which is fixed) will rise is therefore perfectly correct, and perfectly irrelevant. The ratio of atmospheric to dissolved molecular CO2 plus elephants will also rise. Most readers can readily see that elephants are not comparable to carbon dioxide molecules. Only the most chemically sophisticated, however, will appreciate that the comparison of molecular to ionic dissolved CO2 is, in the context of the Henry’s Law equilibrium, also specious.

DIC is nonetheless important in one very significant respect. For at this point, it is time to look in more detail at what happens at the ocean-atmosphere interface. We are going to assume that someone (humankind you know who I am talking about) has added some carbon dioxide to an atmosphere that was previously in perfect Henry’s Law equilibrium with the oceans. Not only that, but they have added special CO2 molecules containing an atomic marker – a form, or isotope, of carbon which can be readily identified. In the following explanations, these molecules will be marked with a green dot.

In a given time period, these ten surplus molecules from the atmosphere, all with atomic markers, will meet ten unremarkable, unmarked CO2-containing molecules from the ocean at the interface between the two – the surface. We now know that nine of these molecules will (in principle) be ionic – carbonates. Only one of the ten will be dissolved molecular carbon dioxide, capable of participating in the Henry’s Law equilibrium.

[fig.2 Schematic of ocean-atmosphere physical exchange]

As the atmosphere is now out of equilibrium, all ten surplus molecules will participate in forward reactions with their ocean counterparts. What reactions?

When a gaseous neutral carbon dioxide meets a dissolved ionic counterpart, no Henry’s Law equilibration can take place. Nonetheless, the marker atom can be exchanged as follows:

[reaction 2: Air-ocean carbon atom exchange]

If you associate chemical reactions with things exploding in the front of chemistry labs at school, you are going to be sorely disappointed by this one. The reaction starts with one gaseous and one dissolved molecule. It ends exactly the same way. From the point of view of Henry’s Law, nothing has happened. But something has happened – something we can measure. Isotope exchange has taken place between the atmosphere and ocean.
What about our lone molecule of dissolved neutral CO2? It meets its atmospheric counterpart and undergoes the following ‘reaction’:
[reaction 3: Air-ocean carbon dioxide molecular exchange]

This is the Henry’s Law equilibration. Our marked gaseous carbon dioxide molecule has dissolved in the oceans.

So we can now recap. Before the exchange the atmosphere contained ten surplus marked molecules of carbon dioxide. After the exchange, there were still nine surplus molecules in the atmosphere, but none of them contained the marker! The ocean gained a single extra molecule of carbon dioxide but gained an extra nine atoms of marked carbon (and lost nine unmarked ones).

At this point, I am hoping that you are experiencing an ‘a ha!’ moment. Do you begin to see why there are two relevant timescales to exchange of CO2 between atmosphere and ocean?

We have to distinguish between the timescale for exchange of carbon isotopes (the marked molecules) which corresponds to the arrows in fig.1 showing diffusional exchange between atmosphere and ocean surface and the atmosphere. The flux is given as 92 Gt (gigatonnes = 109 tonnes) of carbon/year which corresponds to a timescale (relative to the atmospheric inventory) of about 8 years.

But we now know that the timescale for exchange of carbon dioxide molecules is ten times slower! This timescale is thus 80 years.

Having now explained the principle of what is known as ‘isotopic disequilibrium’, one of the most difficult and least intuitive of the principles of oceanic carbon chemistry, I must unfortunately now draw your attention to a further complication.

When reading the scientific literature, you will doubtless come across a third ratio that will confuse you. You will read that:

Nothing is simple in life, and neither is it in ocean carbon chemistry. The further complication for carbon dioxide and its aqueous ions, which is not the case for chlorine/chlorides, is that molecular carbon dioxide which has just reached the oceans from the atmosphere undergoes a further reaction. For each ten molecules which dissolve, nine of them react with a dissolved carbonate ion to produce an intermediate ion called bicarbonate (you may remember the name of the sodium salt which is used for baking – bicarbonate of soda):

[reaction 4: Dissolution of gaseous CO2 in seawater]

10 CO2 (aq) + 9 H2O + 9 CO32- → 1 CO2 (aq) + 18 HCO3

This reaction is important from the point of view of ocean chemistry but it is, again, irrelevant to the Henry’s Law equilibrium which determines the ratio of atmospheric to dissolved molecular CO2 – only part of which (10%) consists of ‘free-floating’ aqueous CO2 molecules. Furthermore, if you consult the constants of equilibration between air and ocean, you will invariably be quoted the ratio between atmospheric and aqueous CO2 which is not the same as the Henry’s Law partition ratio!

The ratio of atmospheric partial pressure of CO2 to aqueous CO2 in the oceans is treated as a Henry’s Law constant in the literature, but it isn’t because atmospheric CO2 is not in Henry’s Law equilibrium with aqueous CO2! The reason this is done is because, in practice, it is hard to measure the precise concentration of molecular carbon dioxide dissolved in water (not only because it exists in two forms, as aqueous CO2 and combined in a bicarbonate complex, but because bicarbonate ions themselves can be created as a result of interactions between water molecules and carbonate ions). We must nevertheless be extremely vigilant not to be confused by such ‘pseudo-Henry’s Law constants’ into thinking the partition ratio of CO2 between atmosphere and ocean is ten times greater than it actually is.

A further confusion/deception in the scientific literature is that humanity’s tendency to pump CO2 into the atmosphere and hence into the oceans will change the ‘pseudo-Henry’s Law’ constant applying to gaseous versus aqueous CO2. The reason is because the ratio of aqueous to molecular dissolved CO2 will also change due to the complex chemical equilibrium in the oceans. But this is all irrelevant/deliberate misdirection because Henry’s Law must continue to apply! The partition ratio of 1:5 cannot change (or only very slightly as the CO2 in the oceans becomes less dilute).

Having delved into ocean carbon chemistry in some depth, we are now ready to turn our attention back to the carbon cycle as a whole, have a look in particular at how the living world interacts with CO2 in the atmosphere, and introduce the four-box model.

[fig.3 Ocean-surface-atmosphere-biosphere carbon exchange model]

In principle we will need to make the same distinction for exchange of carbon isotopes vs. CO2 molecules when it comes to exchange between atmosphere and biota as we previously made with the ocean (the exact reasons for which we will examine later).

In addition, there is a fifth timescale relevant which corresponds to how water is exchanged between the deep oceans and the surface waters (which is where the exchange with the atmosphere takes place, of course). In an effort to try to keep the mathematics as simple as possible, I am going to initially assume that this timescale is actually zero. This means that the ocean and surface are instantaneously well mixed and the concentrations of both carbon isotopes and CO2 molecules are always the same in both. Needless to say, this is highly unphysical. Do not fear, I will relax this assumption after completing the initial calculations!

In the following calculations, we will use X to denote ‘concentration’, both for atoms/molecules in the atmosphere but also in the ocean and biota. In the atmosphere this will have a direct physical meaning (for CO2, I will generally quote in ppmv which means parts per million by volume), in the ocean it will denote a concentration that would be in Henry’s Law equilibrium with the corresponding concentration in the atmosphere. In the biota it means nothing physical at all, it is just a notional figure that allows us to calculate the flow of CO2 between biota and atmosphere.

We now arrive at more or less the entire point of this article. We know three of the relevant four timescales from fig. 1 and our analysis of ocean carbon chemistry. The fifth timescale (the deep ocean-surface exchange) we are currently ignoring. These are then:

toi – the timescale for exchange of carbon atoms/isotopes between atmosphere and oceans = 8 years (from fig. 1)

toc – the timescale for exchange of carbon dioxide molecules between atmosphere and oceans = 80 years (multiply toi by the Revelle factor)

tbi – the timescale for exchange of carbon atoms/isotopes between atmosphere and biota = 6 years (from fig.1)

tbc – the timescale for exchange of carbon dioxide molecules between atmosphere and biota = ???

tos – the timescale for exchange of water between the deep oceans and the surface waters (which we are currently assuming is zero)

We therefore now have two equations for the atmospheric residence timescale and a timescale that corresponds to how long it takes for additional CO2 molecules to dissipate from the atmosphere. This is the crucial missing timescale that I mentioned in the introduction. For want of a better name, I am going to call it the carbon dioxide atmospheric adjustment timescale or just ‘adjustment timescale’. These equations are (ignoring tos for the time being as discussed above):

1/tr (residence) = 1/toi + 1/tbi

1/ta (adjustment) = 1/toc + 1/tbc

Whatever we do, nomenclature wise, does not alter the fact that we have an equation for the adjustment timescale with one unknown – the timescale for exchange of CO2 molecules (as opposed to carbon atoms) between atmosphere and biota.

We badly need to constrain this equation if we want to solve it. And indeed we can, and we can.

It is a simple consequence of the elementary laws of thermodynamics that increasing the amount of carbon dioxide in the air must, all things being equal, increase the rate of photosynthesis by the biota. This is known to chemists as Le Chetalier’s Principle and applies equally well to living/biochemical systems as it does to non-living/inorganic systems.

Le Chetalier’s Principle tells us that the biota will try to reduce the ‘excess’ CO2 in the air by increasing their rate of photosynthesis, but it does not tell us by how much. In order to find out the rate order for photosynthesis, the increase in reaction rate with respect to the increase in concentration of the reactant CO2, we need to understand a bit of biochemistry.

Plants fix carbon (convert it from gaseous to solid form) by absorbing CO2 via their leaves through microscopic openings called stomata. The process is entirely passive – CO2 enters plants because the effective concentration in plant tissues (yes this is another Henry’s Law equilibrium in principle) is lower than in the air – i.e. it takes place via molecular diffusion, through the stomata.

This means that the rate order cannot be greater than one. Le Chetalier tells us it must be at least zero. The effective rate order will be given by the percentage of the biota (in terms of photosynthetic production) whose photosynthetic rate will be constrained by the rate of diffusion of CO2 into plant tissue.

A detailed description of the various constraints on photosynthesis is beyond the scope of this post, but suffice to say that we can express the rate order as the ratio of the biotic equivalent of the two timescales we just explored for the ocean-atmosphere exchange i.e. tbi/tbc.

So how to constrain the equation for the adjustment timescale of CO2? Remember that the timescales for elimination of carbon atoms from the atmosphere are much faster than for carbon dioxide molecules. Remember also, our discussion about marker atoms when we were looking at ocean-atmosphere exchange. I hope you can see where this is going?

Carbon exists in three isotopes in nature. By far the most common isotope is carbon-12. A rare, but very useful, isotope is carbon-14 which is radioactive and decays with a half-life of about 6,000 years, and is hence especially prized by archaeologists to date ancient objects.

But here we are going to look at the other carbon isotope – carbon-13. Unlike its heavier analogue, carbon-13 is stable (not radioactive). It constitutes approximately 1.1% of naturally occurring carbon on Earth. Approximately, because the ratio of carbon-13 varies very slightly depending on its origin. And therein lies the key.

Carbon dioxide which is formed by the combustion of hydrocarbon fuels is depleted in carbon-13 relative to the carbon in the atmosphere. The measurement is referred to as d13C (pronounced ‘delta thirteen C’) and the typical signature of hydrocarbon-derived carbon is -25‰ (‘per mil’, so parts per thousand, relative to a fixed standard).

This means that as mankind has been busy pumping carbon dioxide into the atmosphere, the carbon-13 ratio has been falling, from a pre-industrial estimate of -6.5‰ to a current figure of -8‰.

But before we analyse these figures, we should calculate what we would expect to see based on the timescales discussed previously. If we assume that the pre-industrial concentration of carbon dioxide in the atmosphere is X0 and that the rate of addition of (anthropogenic) carbon dioxide is (dX/dt)anth, then it follows that the actual concentration of carbon dioxide will tend to:

X0 + ta x (dX/dt)anth, where ta is the adjustment timescale for atmospheric CO2.

But the concentration of marked CO2 (i.e. carbon dioxide with the isotope ratios of hydrocarbon fuels) will tend to a different concentration of:

X0 + tr x (dX/dt)anth, where tr is the atmospheric residence timescale of CO2.

We can now see that the ratio of total ‘excess’ carbon dioxide to ‘excess’ marked carbon dioxide is simply, lo and behold, the ratio of the two timescales ta / tr. In other words, the carbon-13 ratio in current atmospheric carbon dioxide allows us, since we started off this article stating the known atmospheric residence timescale, to calculate the adjustment timescale.


You are all, I hope, holding your breaths at this point. The proportion of atmospheric carbon dioxide which has a hydrocarbon fuel origin is given by:

(d13C(atmosphere, present day) – d13C(atmosphere, pre-industrial)) / (d13C(hydrocarbon) – d13C(atmosphere, pre-industrial))

which gives:

This is already very striking, because it is clearly much smaller than the proportion of ‘excess’ carbon dioxide in the atmosphere (i.e. the difference between current levels and those prevailing before the industrial revolution).

What actually is (was) the pre-industrial concentration of carbon dioxide in the atmosphere? Conventional (including the IPCC’s) wisdom is 280 ppmv. However, accurate measurements have only been available since the Mauna Loa atmospheric observatory was set up in 1960. The level then was 315 ppmv, and that has been increasing since (at a steadily increasing rate) to just over 400 ppmv presently. If we take estimated hydrocarbon combustion figures from 1900-1960 and compare with 1960-present day, we arrive instead at a figure of 300 ppmv. I would need a whole other post to explain this in detail but I like the 300 ppmv figure not only because I think it is nearer the truth but also because it is a round number.

Those who prefer to defer to scientific authority are of course welcome to carry out the calculation using the classic 280 ppmv figure. It will not make much difference. Of course, if you really defer to scientific authority, you probably shouldn’t be reading this post (or blog) in the first place.

This gives us then the result that the ‘excess’ carbon dioxide is 100 ppmv and the ‘excess’ marked hydrocarbon-derived carbon is 30 ppmv (8% times 400 ppmv). This allows us our first estimate of the carbon dioxide adjustment timescale which is 12 years.

This is already a surprising result! However, before we proceed further, there are two modifications to this number that we need to take into account. The first is the effect, as already briefly mentioned, of any delay in mixing between the deep ocean water and the surface. This will cause the surface waters to be more similar to the atmosphere in composition and will have the effect of making the equilibration timescales between atmosphere and ocean longer.

Before we look into this, there is another implicit assumption I have made that needs to be examined more closely. I have assumed in the foregoing that all of the ‘excess’ (i.e. anthropogenic) carbon dioxide in the atmosphere derives from the combustion of hydrocarbon fuels, and hence has the characteristic carbon-13 profile.

But does it?

There is another (bio)chemical process, remarkably similar to combustion, which does the same job of converting solid (‘fixed’) carbon compounds to carbon dioxide gas. It is called respiration and the results of this (bio)chemical reaction come out of our noses and mouths every time we breathe.

Since the industrial revolution, the human population of this planet has exploded. Not just humans though. We also have caused an explosion in the number of domestic animals, sheep, pigs, cows and chickens and the like. And not just the intended results of human food production. There are a myriad rats, cockroaches, potato blight funguses and the like out there which depend for their existence on our (unintended) generosity. They are also all busy respiring carbon dioxide into the atmosphere, thanks to us.

We have to take this into account, as well as any changes in photosynthetic fluxes (which have the opposite tendency, to reduce atmospheric carbon dioxide). I would need a whole other post to discuss this in detail, but I am simply going to assume that one third of the ‘excess’ carbon dioxide is not of hydrocarbon origin. The crucial point is that this excess CO2 will not have the distinctive carbon-13 marking. Its carbon-13 profile will be almost identical to (well, pretty similar to, we will ignore the difference for simplicity) that already in the atmosphere.

So we are going to calculate the carbon dioxide adjustment timescale as a function of the deep ocean-surface mixing timescale but reduce the result by a third to take into account non-hydrocarbon anthropogenic CO2 emissions. If you object to this piece of fudging, by all means feel free to do the calculation without it.

Do we actually know what the deep ocean-surface mixing timescale is? There are estimates of the ocean overturning timescale of 300-1,000 years. This means in effect how long in the past the average drop of water in the oceans was last in contact with the atmosphere. To obtain the deep ocean-surface mixing timescale we need to multiply this timescale by the ratio of the mass of the well-mixed surface layer to that of the oceans as a whole. If we assume the well-mixed surface layer is 40 metres deep and the ocean is 4,000 metres deep (you can see how approximate all these estimates are) then a ballpark answer is 3-10 years, but basically no one really knows, as oceanographers (fairly) freely admit.

At steady state, the concentration of isotopes and carbon dioxide molecules at the ocean surface will be given by:

Xsi = (Xoitoi + Xaitos) / (toi + tos)

Xsc = (Xoctoc + Xactos) / (toc + tos)

We can now correct the equations linking the atmospheric residence and adjustment timescales (you may want to take my word for this):

1/ta = (1/tr + 1/(toi + tos) – 1/toi) x 30/100 x 3/2 + 1/toc – 1/(toc + tos)

If you plot a graph of this using values of the deep ocean-surface mixing timescale of between, say, 0 and 100 years (which really should cover all eventualities), the value of the adjustment timescale varies between 16 and 23 years. Let’s take a happy median, thus:

At this point, we can start to see why the adjustment timescale of CO2 is so important. We can derive a number of important results about the build-up (or not) of carbon dioxide in the atmosphere based on our best estimate (guess? a bit harsh if you don’t mind me saying so) above.

To start with, we can now estimate the changes in global photosynthesis which have resulted from the increase in carbon dioxide in the atmosphere which is the rate order of photosynthesis as a function of atmospheric concentration, or tbi/tbc, multiplied by the proportionate increase in CO2 in the atmosphere, which gives:

This tells us that the rate order of photosynthesis by the biota is in the region of 20-25%. To put it another way, it implies that 20-25% of photosynthetic production of the biota is drought constrained (why this is so would need another post). Considering that drought is not a problem for marine phytoplankton, nor for wet climes like northwestern Europe, that strikes me as a very reasonable result.

We can now draw up a rough schematic of the excess flows of carbon dioxide into and out of the atmosphere i.e. the changes in the natural flows as a result of mankind’s activities.

The current concentration of carbon dioxide in the atmosphere is 400 ppmv and is increasing by 2 ppmv/year. If the atmospheric adjustment timescale is 20 years then it means the oceans and biota are together absorbing 5 ppmv/year of the excess. Three quarters of this absorption is due to the increase in productivity of the biota and one quarter to the Henry’s Law re-equilibration in the oceans.

So we can say that for every seven molecules of CO2 put into the air by mankind, of which just under five are from burning hydrocarbons, two accumulate there, one and a bit is dissolved into the oceans and just under four are reabsorbed by the biota via increased photosynthetic productivity.

How does all this compare with the estimates of carbon dioxide timescales I introduced at the start of this piece? First off, I should point out that, if we take out my assumption that a third of anthropogenic CO2 comes from non-hydrocarbon sources (increase in respiration by the biota) then Euan’s timescale, bar a little terminological inexactitude, is spot on the money – the carbon-13 isotope results would then imply about 30 years.

The IPCC’s estimate of 50 years is difficult to sustain. Even if we take the pre-industrial CO2 concentration as 280 ppmv instead of 300 ppmv and adjust the surface-deep ocean mixing timescale as generously as we dare, we cannot get a timescale larger than about 40 years. What is wrong with their estimate?

Two things really. Firstly, the IPCC model ignores the carbon-13 isotope evidence and relies instead on submissions of hydrocarbon combustion rates by UN member states. To take a drastic analogy, it’s as if Sherlock Holmes stumbled on a man with a drawn blood-stained knife and a fresh corpse. Our hero has a choice of methods for deducing the identity of the murderer: he can test the blood on the knife blade for DNA matching the corpse, or he can ask the murderer if he is guilty i.e. rely on hearsay.

The IPCC method is essentially the latter. The analogy is somewhat exact because, in considerable part because of political pressures brought to bear on countries as a result of the IPCC’s alarmist messages about CO2 emissions, there is a tendency of UN member states to underreport their emissions, figures that the IPCC then duly regards as gospel truth.

Secondly, they ignore the obvious logic that increased human (and human-dependent) populations have led to increases in global respiration rates. Indeed the IPCC’s figures seem to assume that both photosynthetic production and net respiration by the biota have remained unchanged since the industrial revolution. In the light of facts such as the doubling of biological nitrogen throughput – thanks to the invention by humans of the Haber process – and the drastic alterations made by mankind to surface vegetation, those seem like heroic assumptions (Freeman Dyson has made a similar observation).

The combination means that the IPCC has probably underestimated anthropogenic CO2 contributions. Hence it has overestimated the adjustment timescale. Models trump measurements indeed. And this, of course, has the effect of further exaggerating alarm at such CO2 contributions.

But to my mind the most striking result, if we bring the carbon-13 isotope evidence fully to bear, is the increase in photosynthesis that must have taken place over the course of the twentieth century. The Henry’s Law equilibration between atmosphere and oceans is simply too slow to get rid of much of mankind’s excess CO2. The fact that there is not a lot more of this CO2 still lingering in the atmosphere (and therefore that the proportion which is hydrocarbon-derived is not even smaller) shows us that the donkey work of mopping up (most of) the excess has been carried out by the biota – all the phytoplankton, trees, grasses and algae that give wide areas of our planet’s surface its distinctive green colour.

There is, then, some good news amid all the gloom and alarmism. There have been vast increases in human agricultural productivity throughout the twentieth and early twenty-first century. Most of this is of course due to improvements in plant strains, fertilisers, mechanisation etc; But nonetheless a (significant) part must also be down to the fact that it is easier for plants (including the ones we cultivate) to grow when there is more carbon dioxide in the air.

© David Ellard 2016

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61 Responses to Atmospheric carbon dioxide – a tale of two timescales

    • Willem Post says:


      How can the tale of two timescales be resolved?

      The IPCC used its logic to arrive at its timescale.

      Others use their logic to arrive at other timescales.

      Is there some way to show which timescale is more correct, i.e., more logical, and show which timescales, that are floating around, are obviously incorrect?

      A comparison of methodologies and assumptions is needed, with the IPCC approach on one side, versus the approaches of others on the other side.

      A case needs to be built.

      Without it, article writing will go nowhere.

      • David Ellard says:

        Hi Willem, the key difference is that I account for the carbon-13 isotope measurements in the current atmosphere. The IPCC, as far as I know, takes no account of this. Their model would not be compatible with the actual measurements.

  1. Joe Public says:

    That’s one massive chemistry lesson for so early on a Monday morning. Thank you David.

  2. brianrlcatt says:

    I ha ahevother work to do and sh kimmed this, but looked for the evidence based points. So there is C-13 based evidence for the rather obvious but not well documented with fact hypothesis that the other non anthropogenic life forms on the planet are happy to mop up a lot of the CO2 Humans produce, indeed will be grateful for it, as I also read plants developed photosynthesis when CO2 levels were much higher that today, so are happeir working at higher levels of atmospheric CO2 ?

  3. Jim Brough says:

    In biology we learned about the buffers which make our life possible.
    The oceans are like that, contain most of the world’s CO2 and absorb CO2 or release it according to temperature of the ocean.

    • John ONeill says:

      Actually there is far more carbon in the lithosphere – the rocks – than in the biosphere, the atmosphere or the oceans. If all the limestone and coal on Earth released its CO2, we’d be Venus II. Mountain building, volcanoes and weathering change CO2 levels on very long timescales. By that standard, ice ages and interglacials are like seasonal changes.

  4. Willem Post says:


    I just happen to have made some calculations regarding emissions of cows, sheep and goats and compared that with the emissions of light duty vehicles and wind turbines.

    World CO2 Equivalent Emissions: The EPA and IPCC determined the emissions of agriculture, forestry and other land use were 13.200 billion Mt of CO2 eq. in 2015, or about 24% of the world’s manmade CO2 eq. emissions. See below table. emissions.png/view

    LDV Emissions:

    One LDV emits about 10,647 lb, or about 4.830 metric ton of CO2/y, based on CO2 emission/gal = 19.4 lb, combustion + 5 lb upstream = 24.4 lb; travel = 12,000 miles/y, assumption; MPG = 27.5, assumption. The world has about 1 billion LDVs.

    World LDV emission is about 1.0 billion x 4.830 = 4.830 billion Mt of CO2/y

    Ruminant CO2 and Methane (CH4) Emissions:

    The world has about 1.5 billion cattle (dairy and beef cows, buffalo, etc.), 2.1 billion sheep and goats, 1.0 billion pigs, and 21 billion chickens.

    One dairy cow emits about 6000 liter CO2/d and 600 liter CH4/d, about 2 times a beef cow, about 14 times a sheep, about 22 times a goat, about 74 times a pig. Assumption for calculations:

    – 3000 liter CO2/cow/d, 300 liter CH4/cow/d
    – 333 liter CO2/sheep or goat/d, 33 liter CH4/sheep or goat/d

    One cow emits about 2.150 Mt of CO2/y, based on 3000 liter CO2/d, and 1.9631 g CO2/l.
    One cow emits about 2.781 Mt of CO2 eq./y, based on 300 liter CH4/d; 1 cubic meter CH4 = 0.01693 Mt CO2 eq.
    World cow emission is about 1.5 billion x (2.150 + 2.781) = 6.005 billion Mt CO2 eq./y

    One goat or sheep emits about 0.239 Mt of CO2/y, based on 333 liter CO2/d, and 1.9631 g CO2/l.
    One goat or sheep emits about 0.206 Mt of CO2 eq./y, based on 33 liter CH4/d; 1 cubic meter CH4 = 0.01693 Mt CO2 eq.
    World goat and sheep emission is about 2.1 billion x (0.239 + 0.206) = 0.934 billion Mt CO2 eq./y

    World ruminant emission is about 6.005 + 0.934 = 6.939 billion Mt of CO2 eq./y, or about 6.939/13.200 = 52.6% of agriculture, forestry, and other land use CO2 eq. emissions.

    Additional ruminant-related emissions are due to pasturing, feeding, processing, packaging, selling, etc. of meat and dairy products. For example, in the US, the life cycle CO2 eq. emission is about 8.377 kg per one kg of cheddar cheese, equivalent to travelling 9.44 miles at 27.5 miles per gallon.

    NOTE: The world’s 1.5 billion cows and 2.1 billion sheep, goats, etc., emit various gases, including methane, CH4, a greenhouse gas about 25 times more potent than CO2. Two-thirds of all ammonia, NH3, is emitted by cows. World ruminants eat about 50% of world’s food crops. See COWSPIRACY movie on Netflix.

    NOTE: Some experts say 100 – 200 liters of methane/cow/d (or about 26 – 53 gallons), others say it’s up to 500 liters (about 132 gallons)/cow/d.

    NOTE: 1 cubic meter CH4 x (35.31466 cf CH4 / 1 cubic meter CH4) x (1 lb-mole / 379.48 cf) x (16.0426 lb. CH4 / 1 lb-mole) x (1 metric ton / 2,204.62 lb.) x (25 CO2 eq. / 1 CH4) = 0.01693 metric ton CO2 eq.

    NOTE: The proposed 28 turbine, 96.6 MW, $250 million, Windham/Grafton wind turbine power plant in Vermont would produce about 280,000 MWh/y, which would reduce CO2 emissions by about 92,104 Mt/y, based on 0.3296 Mt of CO2/MWh on the New England grid. The CO2 reduction is:

    – Equivalent to the exhaust of about 92,104/4.830 = 19,069 LDVs.
    – Equivalent to the emission of about 92,104/4.931 = 18,679 cows.

    • Joe Public says:

      Hi Willem

      Re: Ruminants & CH4 – in perspective:

      Termite farts are estimated to be about 20 million tonnes each year.

      And rice paddies are possibly the biggest man-made atmospheric methane sources, creating between 50m – 100m tonnes of CH4 a year.

      • Willem Post says:


        The magnitude of the CO2 eq./y numbers is astounding.

        Termites at 20 million Mt CO2 eq./y is small potatoes compared to mankind’s ruminants.

        The EPA and IPCC determined the emissions of agriculture, forestry and other land use were 13.200 billion Mt CO2 eq. in 2015, or about 24% of the world’s manmade CO2 eq. emissions/y.

  5. depriv says:

    I have a headache, some more tons of work to do today and still few hours in job, so just in nutshell:

    – “a (significant) part (of agricultural productivity) must also be down to the fact that it is easier for plants (including the ones we cultivate) to grow when there is more carbon dioxide in the air” — between the supposed pre-industrial and actual CO2 level it gives around 25% increase (general results about CO2 fertilization). It’s indeed significant, but… well, even just for the last ~ 60 years the sum increase is over 200% as I recall.

    – “The fact that there is not a lot more of this CO2 still lingering in the atmosphere (and therefore that the proportion which is hydrocarbon-derived is not even smaller) shows us that the donkey work of mopping up (most of) the excess has been carried out by the biota” I’m still to chew myself through most of the stuff up there, but mind you: just to disprove something does not means that the next convenient option is proven. There might be holes in the ‘official’ reasoning, but that does not means, that it can be accounted on something without maaany further work to support the idea.

    – “increased human (and human-dependent) populations have led to increases in global respiration rates. ” Human-depended agriculture has a tendency to be represented in (human and animal) food stock. Maybe worth a check how much impact should we expect from the stocked carbon compared to the freely available?

    • Willem Post says:


      World Population: The above comparison of LDV to ruminant emissions is a consequence of the world’s population being in out-of-control growth mode for at least 200 years. That growth and the abundant availability of fossil fuels since 1800, have greatly increased electricity and heat generation, agriculture, industry, transportation, etc., which in turn increased the world’s CO2 equivalent emissions.

      Since 1800, CO2 and methane emissions have increased from:

      – The human population.
      – Domestic animals; cows, sheep, goats, pigs, chickens, pets, etc.
      – Rats, cockroaches, potato blight funguses, etc., which depend for their existence on our (unintended) generosity.

      There is no solution to this trend, except to very significantly reduce the world’s population and have the remaining people reduce their energy consumption per capita by at least 4 times (the level of 1800) and consumption of other resources by at least 15 times (the level of 1800). This should not significantly affect living standards, because, at present, energy and other resources are used much more efficiently than in 1800.

      Those measures would enable maintaining at least 50% of the world in pristine condition, so the world’s fauna and flora could re-establish itself to a semblance of its former glory. The present, locust-type devouring of the world by humans, their animals and other support systems, is a major aberration, and clearly should not continue. See below table.

      • depriv says:

        I did not address those parts, and I think it would be a mistake to go that general way under an article with such a stricht focus.

        It’s without the ‘e’ at the end. No problem, just take care next time, please 🙂

        • Willem Post says:



          My iPad has a mind of its own regarding spelling.

          The article did mention it:

          “Since the industrial revolution, the human population of this planet has exploded. Not just humans though. We also have caused an explosion in the number of domestic animals, sheep, pigs, cows and chickens and the like. And not just the intended results of human food production. There are a myriad rats, cockroaches, potato blight funguses and the like out there which depend for their existence on our (unintended) generosity. They are also all busy respiring carbon dioxide into the atmosphere, thanks to us.”

          • depriv says:

            OK, I see. Thanks. So the last of my points is a misunderstanding as it were put.

            – I can’t take as sure that the sum of biomass what’s respiring is any more after the industrial revolution than before. More of it has been noticed by us and more of it depends on us, but to prove that in general it’s more … it is kind of hard I think.
            – I can’t take as sure that it has any importance at all apart from the carbon detained in the biomass – a more or less constant amount of biomass supposed to has ~the same carbon output as input.
            – the same for the effects of CO2 fertilization. It seems to stand for anything what lives on land, but as a sum…

          • Willem Post says:


            The author mentioned it as being important, and I agree with him.

            Much of the CO2-emitting wild animals, such as buffalo, have been killed, as part of the human population exploding.

          • depriv says:

            “Much of the CO2-emitting wild animals, such as buffalo, have been killed, as part of the human population exploding.”

            Exactly that’s why I can’t take as sure that in sum the amount of biomass what’s respiring increased at all.

            It’s a kind of ironic to find such things hinted in an article which is about finding baseless claims in the ‘official’ reasoning.

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  7. Roger Andrews says:

    David: Thanks for your thought-provoking article.

    I have a couple of observations. First I should perhaps point out that I’ve done a lot of work on the CO2 records and am satisfied that the 280ppm “pre-industrial” and the current 400ppm values are correct. (The 280ppm value is supported by the Law Dome ice core data, which merge seamlessly into the South Pole CO2 flask measurements, and by chemical measurements documented by Callendar in 1957.) Proceeding from here I come up with the following round numbers:

    Weight of CO2 in atmosphere at 280 ppm = 2,200 gigatonnes

    CO2 added to the atmosphere by anthropogenic emissions since 1800 = 1,800 gigatonnes

    CO2 concentration if all these emissions had remained in the atmosphere = 510ppm

    Actual CO2 concentration = 400ppm

    These results indicate that approximately half of the anthropogenic CO2 emitted since 1800 has been re-absorbed by land and ocean sinks.

    On the question of the size of the land/vegetation sink, the “terrestrial biosphere” post that Euan linked to in his earlier comment concludes that the size of this sink increased by more than 20% between 1978 and 2006.

    I’m wondering how these observations dovetail with your conclusions.

    • David Ellard says:

      Dear Roger,

      First of all, on pre-industrial levels of CO2 in the atmosphere, that’s a big topic in itself, I will only scratch the surface, also I have not yet been able to look at the data you quote, however:

      (1) The advection timescale (winds) of the atmosphere is about 5 years, compared to the residence time of CO2 (mentioned in the post) of 3.5 years. This means that CO2 is fairly well mixed but by no means perfectly. Generally CO2 levels are higher nearer human settlement (because we are net emitters). Levels over the Antarctic are typically lower than in the tropics (Mauna Loa). Is it not therefore perfectly possible that in, say 1900, levels were 280 ppmv near the South Pole but would have been measured at 300 ppmv at Mauna Loa if the observatory had existed at that time?

      (2) Furthermore, assuming that cumulative hydrocarbon combustion statistics are a good proxy for excess (anthropogenic) CO2 in the atmosphere, the ratio of pre-Mauna Loa (1960) hydrocarbon combustion to post-1960 would be 35:85 in your reckoning, but only 15:85 if we assume a pre-industrial figure of 300 ppmv. On my rough calculations, at least, the 15:85 ratio is much nearer the mark. Otherwise you would need to explain that anomaly.

      (3) Furthermore 300 ppmv is a nice round number, as I point out, and:

      (4) Whether you choose 280 ppmv or 300 ppmv doesn’t make much difference to the calculations, the point I the IPCC model is inconsistent with the carbon-13 isotope measurements whichever way round you take it

      Secondly, according to my ‘model’: ‘we can say that for every seven molecules of CO2 put into the air by mankind, of which just under five are from burning hydrocarbons, two accumulate there, one and a bit is dissolved into the oceans and just under four are reabsorbed by the biota via increased photosynthetic productivity.’

      So I calculate that something like 70%, not half, of anthropogenic CO2 has been reabsorbed by ocean and land sinks. The 50% figure you quote I think comes from the IPCC model. But this predicts a long timescale for CO2 adjustment compared to the residence time, which implies a figure of 3-4% for the proportion of hydrocarbon-derived CO2 in the current atmosphere. But the carbon-13 measurements show this is 8%. So the IPCC’s model, and the 50% reabsorption result, must be wrong.

      As I mention, I calculate photosynthetic uptake has increased by about 8% since the industrial revolution.

      • Stuart says:

        The difference here is that Roger is saying anthropogenic emissions are 1,800 GTe and David is saying anthropogenic emissions were actually greater than this.

        The Carbon 13 signature suggests there should be a lot more CO2 in the atmosphere today than 400ppm. But there isn’t.

        So where did it all go? Plants photosynthesised it. Well plants photosynthesised 4/7ths of it (and not 3/14ths as IPCC assume).

        As CO2 concentrations increase photosynthesis becomes more efficient and removes more of the CO2. This also suggests that a runaway greenhouse effect is not possible on a planet with green plants. Even if there is a planetary CO2 event that outruns photosynthesis (e.g. hydrocarbon combustion) eventually the event will end (it’s a finite store) and photosynthesis will remain.

        As a geological event event anthropological climate change is far far less dramatic than the glaciation or melt that accompanies an ice age.

        The take away from David’s work is that the system/carbon cycle is much more “active” than the IPCC model. That the earth has an incredible ability of self regulation and that no matter what we do about climate change over the next 30 years, 250 years from now the outcome will be exactly the same.

        David is suggesting that CO2 equilibrium can be achieved if we can reduce anthropogenic CO2 emissions globally by 28% (2/7ths).

        Indeed if we were to reduce our CO2 emissions to near zero as some ambitions this could induce a period of rapid cooling (-5ppm CO2) much more dramatic than the anthropogenic warming (+2ppm CO2).

        • depriv says:


          Photosynthesis is not a CO2 sink. It’s just the entry point for the biomass.

          A ‘mature’ biological system has ~ a constant amount of biomass => it can only detain some CO2, but cannot ‘sink’ it, especially not indefinitely.

          • Stuart says:

            But isn’t that the point?

            There isn’t a constant amount of biomass. The climate has always been changing and the anthropocene is an accelerated change.

            More CO2 means photosynthetic life (plant life) grows faster.

            I know some people will point to deforestation etc, but the earth is blue.

        • depriv says:

          @ Stuart,

          It does not matter if the photosynthetic life grows faster. That only feeds a complex ecosystem with energy, and at the very end of the food chain every piece of that ecosystem ends up dead -> what the photosynthesis could catch goes back to the atmosphere as CO2 as it goes down on the food chain.

          What matters is only:
          – the amount of biomass
          – the amount of carbon which goes to inorganic reservoirs from the biomass.

          The letter process is slow and as things goes, it is almost negligible on the human timescale.

          The former – by the best estimates I coud see so far it’s ~ constant or slowly shrinking, but not even one paper I could see so far dared to suggest that its increase keeps up or even: would be able to keep up on long run with the human related emission.

          • Stuart says:

            Nobody is suggesting biomass keeps up with emissions. The point I was making is that emissions are temporary (a few hundred years) so one day equilibrium will be restored.

            If you read the article it says of 7 parts emissions ~4 are captured by photosynthesis. 1 is absorbed into oceans and 2 remain in the atmosphere.

            What you are saying is that 4 parts are captured by photosynthesis and then later the same 4 are respired into the atmosphere. Constant biomass.

            Except the accumulated atmospheric CO2 has less C-13 than hydrocarbon emissions. Therefore C-13 is dropping out of the atmosphere faster than expected.

            More CO2 is passing through plants than expected so are plants holding onto C-13 and releasing C-12 and C-14 in it’s place? Are plants scrubbing the atmosphere of C-13?

          • depriv says:


            Of course there will be some kind of equilibrium given enough time. Trivial. That’s so trivial that it has no real relevance for us.

            “the article says of 7 parts emissions ~4 are captured by photosynthesis. 1 is absorbed into oceans and 2 remain in the atmosphere.

            …t 4 parts are captured by photosynthesis and then later the same 4 are respired into the atmosphere.

            … C-13 is dropping out of the atmosphere faster than expected.”

            Good sum. So we now has a question, and a mere hint that ‘it can go nowhere else so we’ll be OK to blame it to the photosynthesis’ won’t do. It just don’t met up with the depth aimed.

            Ps.: actually it does not really has to be an equilibrium. As the history of Earth and the complexity of this system goes a (stable) equilibrium might be the less probable outcome – however it’s just as irrelevant for our timescale as an equilibrium would be.

        • John ONeill says:

          ‘..this could induce a period of rapid cooling..’
          For an example from Earth ( pre ) history, the Azolla Event is named after the Azolla plant, which thrived in the warm, fresh waters of what is now the Arctic Ocean, 49 million years ago. The plant could supposedly pull 6 tonnes of carbon per acre, per year, out of the air. In 20 hour daylight and warm conditions it could double its mass in a few days.It reduced CO2 from 3,500 ppm to 650 – still well above today’s level – but it took 800,000 years to do it.
          So we’ve about doubled CO2 once in 200 years, when this supposedly ‘catastrophic ‘event took about 2,000 times as long to halve it.
          Incidentally, the Azolla deposits may contain oil, so if the ice gets out of the way, parts of the oil industry are keen to get some of that carbon back into circulation.

      • Stuart says:

        I’ve had another very simple idea about what might be behind the difference in anthropogenic CO2 absorption (50% v’s 70%).

        Is it as simple as:

        1). Land based photosynthesis removes CO2 from the atmosphere and stores it in biomass until it is respired or the biomass dies at which point the CO2 is released back into the atmosphere.

        2) Ocean based photosynthesis removes CO2 from the atmosphere and stores it in biomass until it is respired or the biomass dies at which point the CO2 sinks to the bottom of the Ocean or is suspended in the water column.

        In this scenario the four buckets model is missing a pathway as the biota can deposit CO2 directly into the deep ocean. Perhaps this is where the C-13 is heading?

      • David: Thanks for your response. I’ll comment on just a couple of your statements:

        This means that CO2 is fairly well mixed but by no means perfectly. Generally CO2 levels are higher nearer human settlement (because we are net emitters). Levels over the Antarctic are typically lower than in the tropics (Mauna Loa). Is it not therefore perfectly possible that in, say 1900, levels were 280 ppmv near the South Pole but would have been measured at 300 ppmv at Mauna Loa if the observatory had existed at that time?

        CO2 mixes rapidly in the Northern Hemisphere and also in the Southern but takes a couple of years to make its way across the ITCZ, which is why CO2 at the South Pole runs consistently 4-5ppm lower than CO2 at Alert (81 degrees N). This is illustrated in the graphic below, which shows 12-month averages of Scripps flask CO2 data. CO2 levels in fact increase progressively as we go north. These results make it appear unlikely that CO2 at the South Pole in 1900 could have been 280ppm while CO2 at Mauna Loa was 300ppm. In 1958, which takes us half way back to 1900, CO2 levels at the two stations were the same.

        What makes it appear even less likely is the next graphic, which plots CO2 estimates from three sets of Antarctic ice core records (South Pole, Dronning Maud and Siple) against two sets of chemical measurements (South Pole after 1958 and Callendar’s 1957 data for Baltic stations) and a set of CO2 measurements from plant stomata. As I mentioned earlier, the Law Dome ice core CO2 runs virtually seamlessly into the South Pole flask CO2, and the three sets of ice core measurements match each other closely before 1958, flattening out at around 280ppm. The Callendar chemical measurements show a lot of scatter but their average is comparable to the other data sets. The plant stomata data, however, track the other data sets quite closely. These results make a good case for accepting 280ppm as the best estimate of the “pre-industrial” CO2 level.

        So I calculate that something like 70%, not half, of anthropogenic CO2 has been reabsorbed by ocean and land sinks. The 50% figure you quote I think comes from the IPCC model ….. So the IPCC’s model, and the 50% reabsorption result, must be wrong.

        The 50% estimate comes from my own research, not the IPCC (it’s one of the few things I think the IPCC has got right). But if 70% of anthropogenic CO2 has indeed been reabsorbed by land and ocean sinks then a simple mass balance calculation based on 280ppm pre-industrial CO2 shows that CO2 levels should now be around 350ppm, not 400ppm.

        • David Ellard says:


          There is a major problem with the idea that pre-industrial CO2 levels in the atmosphere were 280 ppmv. It is not consistent with what we know about hydrocarbon combustion figures, or indeed basic notions of economic development in the 20th century.


          2015 population: 7 billion, per capita hydrocarbon combustion 70 GJ/yr
          1960 population: 3 billion, per capita hydrocarbon combustion 55 GJ/yr
          1900 population: 1.5 billion, per capita hydrocarbon combustion 20 GJ/yr


          A rough estimate is therefore that total accumulated hydrocarbon combustion from the dawn of history to 1960 was about 4 x 10E21 J
          Total hydrocarbon combustion from 1960 to the present day is about 20 x 10E21 J, so five times as great

          If we assume that the ratio of accumulated CO2 to emitted CO2 (50% in your model, 30% in mine) has remained constant (and ignore non-hydrocarbon sources of CO2 i.e. respiration) then it follows that:

          (present day CO2 – CO2 in 1960) / (CO2 in 1960 – pre-industrial CO2) = 5

          which implies that pre-industrial CO2 levels were 300 ppmv or thereabouts

          The only way round this is to assume:

          (1) That the accumulation ratio has DECREASED over time. No one believes this. The alarmists want us to believe that the accumulation ratio is increasing (because the oceans are getting ‘saturated’ in CO2 and plants are unable to absorb the excess). This article tends to the view that the ratio should be broadly stable (partly because of Henry’s Law). But no one is suggesting the opposite. For the 280 ppmv figure to be correct, the ratio of accumulation would have to have more than halved over the course of the 20th century – the more CO2 we pump into the atmosphere, the less proportionately accumulates i.e. the system eliminates the excess in an ever more efficient fashion.

          (2) That per capita hydrocarbon combustion DECREASED up to 1960. That flies in the face of all (historical) economic logic.

          Any other explanations?

          The simplest remaining one, I would suggest, is that there is a problem in the measurement/sampling methodology for the pre-1960 CO2 measurements (either the measurements are in error e.g. through disenclathrisation of the ice cores, or the measurements are correct but not representative of the atmosphere as a whole).

  8. Ron Clutz says:

    Reblogged this on Science Matters and added:

    David Ellard provides a thorough and timely explanation of the carbon cycle from first principles. His essay meets the standard for all speeches or papers: “A presentation should be like a woman’s dress–long enough to cover the subject but short enough to be interesting.” (OK I’m dated and not PC: the long enough part is passé).

    Since the subject is to describe the carbon dioxide fluxes and atmospheric residence timescales, the essay is necessarily long. It is made more lengthy by the need to untangle confusions, deceptions and obfuscations of CO2 science by IPCC partisans pushing CO2 alarms. To completely remove the wool from your eyes takes a full reading and pondering. I will attempt a synopsis here to encourage interested parties to take the lesson for themselves. The experience reminded me of college classes I took majoring in Organic Chemistry, though in those days CO2 was anything but contentious.

    Several posts here (links below) have danced around Ellard’s subject, but his exposition is the real deal. Getting to the bottom of this issue, he explains how Henry’s law works regarding CO2 in the real world, makes an important distinction between CO2 molecules and ions and factors in an accounting of the CO2 output from rising populations of humans and animals.

  9. Jan Ebenholtz says:

    At main page there is a recent study of CO2 and plantgrowth that I found contradictory to your findings. Please make a comment on this.

  10. Javier says:

    Thanks David and Euan for such a thorough and well explained article that joins Roger contributions to pinpoint a residence time for CO2 around 30 years.

    I was already very suspicious about those claims that it would take many thousands of years to get rid of humankind’s CO2, because evidence from stomata proxies of CO2 changes during the Younger Dryas indicate pretty drastic reductions in CO2 levels in just about 200 years.

    However from a practical point of view of an alarmist, the shorter the residence time of CO2, the more efforts should be put into curtailing CO2 emissions, because the sooner we will benefit from the effect of those cuts.

    Already some uber-alarmists were saying that we were doomed even if we reduce our emissions due to accumulated warming in the pipeline.

    Of course if one takes the view that CO2 is beneficial and offers protection against cooling, then the shorter the residence time the worse. We will have to start burning limestone once we run out of fossil fuels.

  11. donb says:

    I think I agree with the author’s explanation. However, it is so round-about and simplified that it is hard to say for sure. I would prefer to briefly explain the CO2 issue as follows. (I spent a career as an isotope geochemist working with volatiles.)
    Carbon in the environment, as with most substances, maintains some equilibrium concentration between each interacting phase pair, so long as other factors do not change. This equilibrium may be between two physical states such as in air or dissolved in water, or it may be between two chemical states, such as dissolved CO2 and one of the (mostly ionic) chemical states such as bicarbonate. At equilibrium the C concentration in the two phases tends to remain constant.

    IF extra CO2 is introduced into the atmosphere, that tends to alter the various phase equilibria and drives more atmos. CO2 into the other C-bearing phases. But some of these equilibria exist in linear sequences, and equilibria further down the sequence do not respond until equilibria earlier in the sequence have responded. Thus, the equilibrium between atmos and dissolved CO2 must increase dissolved CO2 concentration before the equilibrium between dissolved CO2 and various C-salt phases in the ocean can respond. That is, the total equilibrium of the entire system is partially delayed by each equilibrium step.

    The comments above apply to carbon concentration, as present in each phase. But C is made of three isotopes, 12C, 13, & 14C, where 12C is much more abundant and 14C is radioactive. (Isotopes have identical chemical properties, but different masses, and the mass differences change the rate at which various equilibrium steps occur and thus final isotopic concentrations.) So, IF extra 14C is introduce into atmos CO2 (as occurred with nuclear explosions after 1945), that extra 14C will slowly transfer via isotope exchanges to other C reservoirs, such as ocean phases or living materials. Note that this transfer of extra 14C into other phase occurs even IF the C concentration of the various reservoirs involved do NOT change. That is atmos CO2 need not increase for that extra 14C to transfer to other C reservoirs. This is called isotopic exchange, as opposed to phase equilibrium discussed above.

    Because 14C decays away, the 13C/12C ratio is commonly used to monitor such isotopic exchanges. Measurement techniques are quite sensitive. However, the 13C/12C ratio varies among various materials. For example living things prefer 12C over 13C and lower the 13C/12C ratio by about 2.5% compared to 13C/12C in the oceans. Biogenic methane lowers the 13C/12C by twice this amount. So, various reservoirs of C in the living and geochemical cycles have different 13C/12C ratios, which complicates efforts to use this 13C/12C ratio to accurately monitor relative sources and sinks of C in the various cycles.
    For example, using measured 13C/12C in atmos CO2 and that in fossil fuels (about 1.5% lower) it has been estimated that atmospheric CO2 only contains a few percent of fossil fuel CO2. This is true on an instantaneous basis. However, it ignores the isotopic exchange that has previous occurred between atmos. CO2 and other C reservoirs, whereby most of that deficiency in fossil fuel 13C has been transferred to other reservoirs. And variations in 13C/12C among reservoirs makes even these estimates more uncertain.

    Carbon is an amazing atom and fully understanding its many phases and interactions is not simple.

    • Stuart Brown says:


      You said ‘Isotopes have identical chemical properties…’ yep, that’s what I understood, and then said ‘living things prefer 12C over 13C’. Why is that? Genuinely interested, not arguing.


      • donb says:

        Because the rate (speed) at which a chemical reaction occurs depends to some degree on the mass of the C atom. 12C diffuses and reacts faster in photosynthesis and related reactions compared to 12C. So, plants concentrate 12C over 13C.
        The opposite effect occurs in shallow oceans and lakes. Evaporation of water prefers 12C over 13C (because 12C “moves” faster), so surface water is enriched in 13C — about 1% compared to atmospheric CO2

        • Stuart Brown says:

          Size (mass) matters! Thank you

          • donb says:

            Yes. And size does vary slightly between 12C and 13C because of the extra neutron in the 13C nucleus.
            In chemical reactions, the ability for different atoms to approach close matters. And slight size differences can also subtly alter the reaction rates. Mass and size may not always work in the same direction.
            All this of course is only indicative and greatly over-simplified relative to the Coulomb-Quantum forces involved.

    • Willem Post says:


      Would your understanding of the physical chemistry yield similar results as David’s approach?

    • John ONeill says:

      Very surprised when you say isotopes differ in size as well as mass. Could you supply a link for that? I couldn’t find anything.

  12. Euan Mearns says:

    David, a couple of years ago we had a lot of discussion here about the carbon cycle, if you see the links I have posted. Then, Phil Chapman (our resident Apollo astronaut) came up with an idea that that went towards explaining different time scales.

    Put simply, Phil suggested that Man is adding to the total size of the C reservoir resident in atmosphere, oceans and life. One thing is to look at the rate of removal. But another thing is the equilibrium point between atmosphere and the other reservoirs that moves as a consequence of total C increasing. In other words, most of the CO2 gets pumped down quickly but there is a tail that lingers waiting on long time scale sequestration of C in sediments.

    Any thoughts?

    • depriv says:

      Euan Mearns,

      From the wiewpoint of an engineer: you can calculate how long will one marked atom usually stay in one place and you can calculate the time constant/delay for the interaction between reservoirs (like for complex control loop stages). These are two different things, with different consequences and meanings.

    • David Ellard says:

      Hi Euan,

      My article only dealt with the shortest term fluxes i.e. diffusion between ocean and atmosphere and respiration/photosynthesis.

      To look at the carbon cycle at longer timescales you would indeed need to look at ocean sedimentation, volcanism, tectonics, carbon burial on land etc; etc;

      I think the idea that Man is increasing the ‘active’ C reservoir is fundamentally correct, though.

  13. robertok06 says:


    interesting article indeed… but how to make any agreement/interpretation with respect to papers like this?

    “The mean lifetime of anthropogenic CO2 is dominated by the long tail, resulting in a range of 30 35 kyr.
    The long lifetime of fossil fuel carbon release implies that the anthropogenic climate perturbation may have time to interact with ice sheets, methane clathrate deposits, and glacial/interglacial climate dynamics.”

    Looks like we are all doomed! 🙂

  14. ristvan says:

    I know this post omits the deep ocean and only consider pCO2 in the mixed surface layer. Bit you shouldn’t. Briny surface water sinks as seasonal polar sea ice forms. This takes the dissovled CO2 deep. The thermohaline circulation in total is about 800 years. Not coincidentally, the ‘Henry’s law’ lag of delta CO2 behind delta T on polar ice cores is also about 800 years. Other than carbonate formation by marine organisms (a quasi permanent sink but for subduction zone Volcanism) the deep oceans are the other major long term sink. Its time comstant is ~800 years.

    • Euan Mearns says:

      Figure 4 Comparison of pH and C content of the Pacific and Atlantic Oceans [2]. The deep Pacific has much lower pH and higher carbon content than the Atlantic.

      Bbbbbut, deep ocean water has a lot more CO2 than surface water. So sinking cold salty surface water reduces the total CO2 in the oceans. Phytoplankton snow, photosynthetic rate and gravity are the key drivers here.

  15. Oliver K. Manuel says:


    Thank you for this post. I am not a climatologist, but I am convinced that an error in logic (sloping baseline across the top of Figure 2) isolated humanity from reality eighty years ago (1936-2016):–social-costs-from-overlooking-this-power/

    My research mentor, the late Professor P.K. Kuroda (1917-2001), noticed this error in the first question to Nobel Laureate F.W. Aston after his lecture at the Imperial University of Tokyo on 13 June 1936.

  16. Blackburn's with Darwin says:

    A lot of good stuff posted on this subject … but let’s take a little time out to remember why this little molecule is ‘soooo’ important …

  17. Pingback: Fear Not CO2: The Real Chemistry – Newsfeed

  18. John Stephenson says:

    I have two comments to make on David Ellard’s paper:

    1) 405 ppm of Carbon dioxide (CO2) in air means that 405 cubic centimeters of pure CO2 are mixed into each cubic meter of air. From this I calculate that there are approximately 10,000 trillion molecules of CO2 in each cubic centimeter of air. This is not a small number.

    2) I think that the exchange of 13C atoms with 12C atoms, as described, is not correct.
    Many years ago I developed a method for measuring the concentration of tritiated water (symbol = HTO) vapour in air, based on diffusion principles. A small volume of nominally HTO free water (a ‘sink’) was placed into a container fitted with an orifice which can be opened and closed at will. HTO molecules diffusing through the orifice will be adsorbed by the sink, quantitatively, relative to the concentration of HTO in air and the collection time.
    I explained the process as follows:
    a) the HTO molecule is as distinct from the HOH molecule as oxygen is from nitrogen.
    b) the number of HTO molecules relative to the number of HOH molecules is very small
    c) assume we have an open barrel filled with peas which is vigorously vibrated. Some of the peas at the surface of the barrel will jump into the air, and a few will actually jump out of the barrel. If we add a stream of peas to the barrel then this process will simulate the process of water evaporation from a pool, and the exchange of water molecules between air and the surface of the pool,
    Now drop a bean into the barrel. It will rapidly disapear into the volume of peas, and the probability that it will be thrown out of the barrel is small. However as the number of beans in the barrel increases, the probability that a bean will be thrown out of the barrel increases. This effect was quantitatively observed when developing the HTO measuring device.

    My point is that the 13CO2 molecule can be considered to be similarly distinct from the 12CO2 molecule. Because the concentration of 13CO2 molecules in the ocean is small, the 13CO2 molecules in the thin layer of air above the ocean will diffuse to, and be absorbed into the surface layer of the ocean (which acts as a ‘sink’). The probability that such molecules will be re emitted from the ocean surface is low. Eventually equilibrium between the concentration of 13CO2 in air and the ocean will be reached, but because the ocean is effectively an infinite sink, it will take a very long time.

  19. oldfossil says:

    Although the article is titled “Atmospheric carbon dioxide” it is really about the residence time of CO2 in the biosphere. Exclude the oceans and biomass and you get a short residence time. Add the oceans and you get closer to 200 years. So…. while we’re talking about the oceans we should also be discussing the carbon cycle there. Shoot me if I’m wrong, but this is my understanding:

    Almost all oceanic life starts out with the plankton. Most plankton (singular and plural forms of the noun are the same) reside near the surface as they require light to perform photosynthesis, or the conversion of light and inorganic carbon to organic carbon. Some deep-dwelling plankton achieve the carbon conversion via chemosynthesis instead. Plankton get their inorganic carbon from carbonates, chemical compounds formed when carbon is dissolved in water. It is thought that plankton are adversely sensitive to higher carbonate levels, which could lead to a reduction in the carbon-absorbing capacity of the oceans, but because the life-cycle of the plankton is so short it is capable of rapid evolution and this is probably just another false alarm.

    Two factors govern the nett of CO2 absorption and outgassing by the oceans. One is the partial pressure of CO2 in the atmosphere and the other is the temperature of the air in contact with the ocean surface. Absorption and outgassing occur simultaneously. I can understand that CO2 absorption might step up faster than outgassing, leading to ocean acidification. But there’s another claim that increased atmospheric temperatures, global warming, will result in nett outgassing, acting as a positive feedback.

    At which point you might exclaim, wottheheck, make up your mind, is it more absorption or more outgassing?

    For both claims to be true, the residence time of CO2 in the oceans has to be in sharp decline. In other words, the velocity of the cycle has to be accelerating. This is the area that needs serious research.

  20. polarscientist says:

    When we see back of the envelope calculations like Ellard’s diverging from what we understand from the scientific literature, and summaries of that literature like those made by the IPCC, we should sit up and take notice. Our starting point should be not that the experts are wrong, but that the back of the envelope calculation may have missed some critical factor. Reading chapter 6 of the 5th assessment report of the IPCC, it is plain that the multiple authors of that review were well aware of the use of 13C to ascertain the behaviour of CO2 in the carbon cycle, and the chapter refers the reader to several papers that did use 13C to ascertain rates of exchange across the ocean-atmosphere interface. So, I doubt the veracity of Ellard’s assertion that the experts have neglected the evidence as to how the carbon cycle works and the use of 13C to explain it. One of the key papers along these lines is by David Archer et al in the Annual Reviews of Earth and Planetary Science 37, for 2009, pages 117-134, on the “Atmospheric lifetime of fossil fuel carbon dioxide”. I would be willing to bet that Archer and his team know a great deal more about the carbon cycle that Ellard, and it is groups like theirs whose science is reviewed by the IPCC. Now, if Ellard was prepared to publish his stuff in a peer-reviewed journal, rather than on a blog site uncriticised by experts, perhaps we might all have occasion to pay serious attention to it. Of course, I could be wrong.

    • Euan Mearns says:

      Colin, why don’t you simply be specific in pointing out where David has gone wrong?

      Roger Andrews kicked this ball rolling a couple of years by pointing out that it was not possible to match emissions to atmosphere using the Taus used by Bern and IPCC. I followed up by replicating Roger’s findings. When the model does not match reality, the model is wrong. That’s how it works everywhere else at any rate apart from in climate science.

  21. John Stephenson says:

    I have been reading the discussion related to Roger Andrews estimate of a carbon dioxide residence time in the atmosphere of 33 years. Part of that discussion relates to the residence time of approximately 14 years for 14CO2, which is at odds with Roger’s estimate. The following information may lead to an explanation of the short residence time:

    Back in 1970 I was told by a colleague that if a beaker of water was left on a shelf in the health physics lab (at Rolphton nuclear generating station) for several days, it collected tritiated water vapour (HTO) even though the concentration of HTO in the air was very low. This initiated my interest in using the phenomenon as a means of measuring the concentration of HTO in the air. In my previous comment on this topic I said that I believed that the HTO molecule behaved as a distinct molecular species that was as different from the HOH molecule as oxygen is from nitrogen. I then used the concept of a vibrating barrel of peas to explain how a bean dropped into the barrel would quickly disappear below the surface, and the probability that it would be caused to jump out of the barrel would be very small. I suggest that the same process applies to the 14CO2 molecule in a thin layer of air above the ocean. The 14CO2 molecUles are relatively few in number, so the probability that they would be re-emitted from the surface of the ocean is small. Normal diffusion processes will replace the 14CO2 molecules in the thin layer of air over the ocean, enabling continuous removal of the 14CO2 molecules from the atmosphere. Because the ocean is effectively an infinite sink the 14CO2 molecules will be removed from the atmosphere faster than the 13CO2 and 12CO2 molecules, leading to the apparent short residence time in the atmosphere.

  22. polarscientist says:

    John Stephenson is right. We do have to take into consideration the isotopic fractionation that occurs across interfaces. There’s a nice article on that at Clearly CO2 containing the heavy and rare 14C isotope does in effect ‘disappear’ into the ocean, making it seem that the turn over time for CO2 is about 4 years, a gross underestimate. Equally, CO2 containing the slightly less heavy 13C isotope, which represents only about 1% of the carbon in CO2, experiences some fractionation across boundaries. It is particularly discriminated against by plants, which prefer to use CO2 containing the much more abundant and lighter isotope 12C. The balance between 13C and 12C across the ocean-atmosphere boundary is less extreme. Hence one must take great care in using carbon isotopes to calculate the residence time of CO2 in the atmosphere, not least because the concentrations of both 14C and 13C are so low, such that tiny variations can easily distort the results.

  23. Macha says:

    I regard work focussing on CO2 / carbon cycle, as a sideshow. Paraphrasing S.Wilde, The atmosphere stabilises surface temperature at a level proportional to the density of the atmosphere, leaving the main variation in temperature dependent on variations in the energy coming in from the sun. Ie. It is the density of the atmosphere, not composition, so CO2 is an irrelevance due to its affect on overall density being such a small proportion of our atmosphere.
    For me, the mainshow is the water cycle, oceans and clouds.

  24. David, are you familiar with the work of Dr. Murray Salby? I think you might enjoy his take on isotopes.

  25. A few months ago, and in fact much before that, Ferdinand Engelbeen posted on WUWT about the residual CO2 in the atmosphere being mostly due to human fossil fuel use. He also referred to d13C values (from coralline sponge data – Bohm et al) and how there is a marked drop off in the curve signifying that CO2 levels were going up.

    Now, people can argue about what nature emits and how much human effects there are but the most interesting takeaway from the argument (and one I believe Ferdinand makes note of himself) is that before mankind was emitting more CO2 in the atmosphere, CO2 was a good proxy for varying temperatures.

    The argument is simple: if you believe the same gas processes and carbon isotope ratio variations are adequate to explain how to attribute CO2 in today’s atmosphere, then when there weren’t large man made emissions of CO2, variations in CO2 levels must still follow the same physical processes. The main one being Henry’s Law.
    So when you see variations of 8 to 10 ppm in sponge data and also in ice core data (Law Dome is one) it suggests that there were decadal temperature fluctuations of around 1 degrees C before any significant human input.

    I posted about this on Bishop Hill last year. It’s another case of taking the AGW arguments and following the logic. People like to argue that CO2 rise is natural. However if it’s man made which I believe it is and you can apply the ideas that have been posted here, it doesn’t look that good for AGW.

  26. John Reid says:

    I am surprised that only the 13C:12C ratio is discussed. The important one – the 14C:12C ratio gives a much clearer picture of what is going on. There was a massive injection of bomb-test 14C over a short period of time in the late 1960s then production of 14C returned to background. It was a completely accidental, serendiptous experiment which, shows unequivocally that:

    1. The atmosphere exchanges carbon with a much larger reservoir
    2. The half time of CO2 in the atmosphere is 10 years.

    The only suitably large candidate reservoir is the deep ocean.

    There is some discussion of 14C at .

    Both treatments assume that CO2 diffuses between the various reservoirs; the existence of deep ocean upwellings is completely ignored. These upwellings deliver nutrients from the deep ocean and can be either net sources or net sinks of atmospheric carbon depending on the Redfield ratios of the deep nutrients. In this way deep ocean carbon is effectively pumped into the atmosphere.

    The carbon chemistry Ellard discusses is complex but Henry’s law becomes irrelevant once deep ocean pumping is taken into account.

  27. Ike Kiefer says:

    A couple of contributions.

    1. While it is based on a computer model and was intended to foment climate alarmism by depicting CO2 as a blood red plague, this NASA animation actually is a powerful demonstration of how CO2-hungry the Earth’s biosphere is . In the summer during peak growing season, anthropogenic CO2 is devoured as fast as it is produced. And the lengthened growing seasons from a warming planet continue to increase photosynthetic sequestration of carbon. The animation also argues against the assumption that CO2 is well-mixed in the atmosphere. It clearly shows CO2 “weather” in the horizontal plane. However, the lack of mixing is even more pronounced in the vertical, where heavier-than-air CO2 boils up from the surface during the day and settles toward the ground at night. It is important to note that the full-spectrum color range from blue to red is only 5 ppm.

    2. In one of your Henry’s Law examples you speak of smelling chlorine at a pool. Chlorine is not what one smells at a pool or from a faucet. When dissolved in water, chlorine converts to an equilibrium mixture of chlorine (Cl2), hydrochloric acid (HCl), hypochlorous acid (HOCl), and the hypochlorite anion (OCl-). None of these species evolves from tap water or pool water dilutions fast enough into air to produce a detectable odor. Rather, what is smelled is the much more volatile compound chloramine, which, in one of its three forms, is the product of chlorine reacting with organic materials in the water and tearing them down into their constituent amino acids. It is really more an ammonia smell than a chlorine smell, and it is strongest when the water is “dirty” and the chlorine is doing its disinfecting work. I only point this out because you seem to be fastidious about facts.

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