Carbon Recycling

The carbon cycle can be rather confusing as there are at least 3 totally separate processes at play, each occurring on different time scales. Here we show that it is just geological processes that result in a ‘long tail’ as the atmosphere recovers from a doubling of CO2. This long tail is very small and has little long term consequences. Glacial variations are much larger.

To understand the carbon cycle means understanding the difference between CO2 residence time and turnover time. The residence time for an individual CO2 molecule emitted by man is only about 5-10 years (C14 measurements). Every CO2 molecule in the atmosphere is rather quickly absorbed either by photosynthesis or by the ocean. However on average most of them are simply replaced by another CO2 molecule entering the atmosphere through evaporation from the ocean or by respiration. The turnover time is the e-folding time needed for a sudden net increase in CO2 to decay back to normal. At equilibrium the total CO2 content of the atmosphere remains constant over decadal time scales. Currently though, as a result of our emissions, slightly more CO2 molecules are being absorbed than are being returned to the atmosphere. The atmosphere is therefore not quite in equilibrium with ‘natural’ life and the oceans.

Estimate of current carbon flows between the atmosphere and the oceans. Figures are in Gtons of carbon. Graph originally from Grid Arendal

Estimates of the current imbalance of carbon flows between the atmosphere and the oceans. All figures are in Gtons of carbon based on a total atmospheric carbon at 750 Gtons (CO2: 390ppm). Plot made by Grid Arendal

If you sum up all the sources and sinks then you find that about half man-made emissions are being absorbed each year. That means that only about half of the CO2 emitted by humans remains in the atmosphere. The strange thing is that this ratio hasn’t changed at all in 50 years, despite rapid increases in emissions.

AR4 plot: The fraction of Anthropogenic CO2 retained in the atmosphere is unchanged in over 50 years, despite increasing emissions.

AR4 plot: The fraction of Anthropogenic CO2 retained in the atmosphere (b) is unchanged in  50 years, despite increasing emissions (a).

Today we are emitting about twice as much carbon dioxide as we did 30 years ago, yet only half of it survives a full year. That means that currently, an amount of carbon dioxide equal to the total annual emissions of 30 years ago is being absorbed each year. Why is this and what does it mean? Part of the answer lies with the greening of the earth, but far more importantly the answer lies in how the oceans are responding.

There is a ‘concentration effect’ acting on ocean sinks due to the increasing partial pressure of CO2 in the atmosphere.  While we are still increasing emissions then levels will continue to rise. If instead we can stabilise emissions at some number of Gtons/year then CO2 levels would also stabilise, albeit at a higher level in the future. If we could cut emissions completely then levels would stabilise at a much lower level over a few hundred years. However, they would still not fall to pre-industrial levels for 100s of thousands of years. This is because of the so-called ‘long tail’ effect. So what exactly is going on and can we estimate what future levels will be?

There are 3 independent Carbon cycles which in total must balance.
1. Dissolution/Absorption of CO2 at  Ocean surfaces.
2. Biological re-cycling of CO2
3. Geological re-cycling of CO2

  1. Dissolution/Absorption of CO2 at  Ocean surfaces.

In stability there is a balance of CO2 Partial Pressures between the surface of the ocean and the atmosphere. At any given temperature the exchange of carbon dioxide molecules between the atmosphere and the ocean surface always reaches an equilibrium. This equilibrium is controlled by the partial pressure of CO2 in the atmosphere equalising to the partial pressure of CO2 in the surface of the ocean. Then the number of carbon dioxide molecules that escape from the sea surface is  balanced by the number that enter the sea from the atmosphere.

If the temperature of the ocean rises then the kinetic energy of the carbon dioxide molecules in the seawater increases and more carbon dioxide molecules will leave the ocean than would enter the ocean. This continues until the partial pressure of carbon dioxide in the atmosphere increases to balance the new pressure at the sea surface.

If instead the ocean were to cool then the reverse of the above would happen, and CO2 levels would fall. Consequently carbon dioxide is more soluble in cold water than in warm water. This is Henry’s law. One consequence of this effect is that the oceans “inhale” carbon dioxide from the atmosphere into cold sea surfaces at high latitudes and “exhale” it from warm sea surfaces at low latitudes.

Increasing the carbon dioxide concentration of the atmosphere therefore causes the oceans to take up (inhale) more carbon dioxide. Because the oceans surface layer mixes slowly with the deep ocean (hundreds of years) the increased carbon dioxide content of the surface ocean will be mixed very slowly into the large carbon reservoir of the deep ocean. The rate of our adding carbon dioxide to the atmosphere is too fast for the deep ocean to be a significant reservoir. So as the carbon dioxide content of the atmosphere rises, so too does the concentration in the ocean surface.

2. Biological cycle of CO2

Cyanobacteria were the first organisms to develop photosynthesis. They evolved 2.5 billion years ago and quickly spread across the oceans, because they depend only on CO2, H2O and sunlight. They absorb CO2 and exhale oxygen. As they died and were fossilised into rocks so the oxygen levels in the atmosphere built up by an amount exactly equal to the organic carbon buried in rocks. Plants and trees depend on chloroplasts for photosynthesis, which evolved from symbiosis with Cyanobacteria. Animals could only  evolve to eat plants and breath once oxygen levels became sufficiently high. Biogenic CO2 from dead organisms, mainly calcium carbonate shells, slowly gets buried over eons into sedimentary rocks, a tiny percentage of which ends up as fossil fuels. Peat deposition in wetlands also buries carbon vegetation which eventually ends up as coal. All these processes removes CO2 from the atmosphere and form the biological component of the geological cycle.

The total mass of living plants and animals and carbon in soil, at any given time represents a temporary store of carbon. This is comparable to the mass of CO2 in the atmosphere. Life thrives in warmer climates with high CO2 levels and suffers during colder more arid glacial periods with  low CO2 levels.

3. Geological cycle.

Carbon dioxide in the atmosphere combines with water to produce weakly acidic rain. This acidic rain reacts with Igneous rocks to produce a set of ions and a weak acid. This is washed through soils down rivers to the sea where they react to produce opaline silicate and calcium carbonate. As a result CO2 is removed from the atmosphere.


SiO2 and CaCO3 are insoluble and will settle to the ocean floor where they are moved by plate tectonics to subduction zones, carried deep into the Earth and heated converting them back into metamorphic rocks and releasing carbon dioxide. When these rocks and their associated carbon encounter Volcanic eruptions or Mid Ocean vents they return the CO2 to the atmosphere, thus ending the cycle.

The Geological thermostat

The rate of tectonic plate motions set the rate at which CO2 is released from the Earth’s interior to the atmosphere. If release from the earth’s interior exceeds the rate at which CO2 is removed from the ocean by the formation of calcium carbonate shells by oceanic biological processes, then carbon dioxide will accumulate in the atmosphere and visa versa. More CO2 leads to a warmer and wetter world which increases rock weathering, removing CO2 from the atmosphere and cooling down the planet  again.

This process has been proposed as the natural thermostat which  kept the climate habitable for 4 billion years apart from a couple of excursions. It sounds like a good theory, but is it actually true? Why is it that 280ppm seems to be the set point for the thermostat? Just how confident  are climate scientists that they really understand the carbon cycle? Can they, for example, explain why lower levels of CO2 occurred during ice ages? This is what AR5 says on the matter.

AR5: All of the major drivers of the glacial-to-interglacial atmospheric CO2 changes (Figure 6.5) are likely to have already been identified. However, Earth System Models have been unable to reproduce the full magnitude of the glacial-to-interglacial CO2 changes. Significant uncertainties exist in glacial boundary conditions and on some of the primary controls on carbon storage in the ocean and in the land. These uncertainties prevent an unambiguous attribution of individual mechanisms as controllers of the low glacial CO2 concentrations.

So the simple answer is no they don’t really understand the carbon cycle. Nor can they determine why CO2 levels in the atmosphere are naturally so low at <0.03%. A proper understanding of the carbon cycle should at least be able to determine why 280ppm is the natural level for today’s climate. I think this is the fundamental challenge for Carbon Cycle modellers.

Anthropogenic CO2

A stable CO2 level in the atmosphere is achieved once  an equilibrium is reached between the ocean and the atmosphere, and this depends on temperature. Anthropogenic emissions must eventually reach such an equilibrium with the ocean and CO2 levels stop rising. This will result in some DT rise in global temperatures. The rock weathering thermostat presumably would then  kick in to reduce CO2 levels back to ‘normal’ over several 100 thousands of years. However before then we would anyway have entered another series of ice ages with lower CO2 settings. Lets see if we can estimate what will happen in the future.

My Simple Model.

We take two Carbon reservoirs of mass Y(Ocean) and and mass X(Atmosphere).

We emit 2DX per year into the atmosphere X, of which half is retained and half is absorbed into the Ocean. Now consider a time when atmospheric levels have exactly doubled, after which all emissions stop.

Then Atmosphere partial pressure = 2P(X), where P(X) is initial atmospheric pressure.
Ocean Partial Pressure = P(Y+X), the new pressure of the Ocean with  X more CO2 added

We know that at time zero P(Y) = P(X), and that at equilibrium the partial pressures will again equalise.  So putting in some numbers

Case 1: Using full Ocean (after mixing)

Y= 40,000 GtC while X = 610 GtC  (in 1750)

So P(Y+X) = P(Y)40610/40000 = 1.015 P(Y)

Therefore at equilibrium we find that the final atmospheric pressure will be 285ppm. ( a rise of just 5ppm)

Case 2: Shallow ocean mixing only (fast response)

If instead we consider only the surface mixed zone then we should use Y=1000 GtC. Then the answer would be

P(Y+X) =P(Y)1610/1000 = 1.61 P(Y) = 450 ppm.

All this means is that levels would quickly fall within ~10 years to 450ppm and then drop more slowly  over the next ~300 years to 285ppm.

Fall in atmospheric CO2 levels following a doubling of pre-industrial values. Assumes zero emissions thereafter.

Fall in atmospheric CO2 levels following a doubling of pre-industrial values. Assumes zero emissions thereafter. The gap between the blue curve and the dashed line at pre-industrial levels is the ‘long tail’

This simple calculation is complicated slightly if the  climate also warms by say  3C as a direct result of a doubling of  CO2, but you can allow for that using Henry’s law. Since we are using CO2 levels rather than temperature, Henry’s law actually helps us. Taking a mean ocean temperature value of 13 C the solubility of CO2 actually increases by about 10% as temperatures falls. So levels actually fall slightly faster.

My results totally disagree with the BERN model. The BERN model as described in AR4 predicts instead the following decay.

Bern Model calculation of CO2 levels following a doubling of CO2 in the atmosphere.

Bern Model calculation of CO2 levels following a doubling of CO2 in the atmosphere.

In my opinion the BERN model has a logical flaw. It assumes that a fixed 22% of the Anthropogenic increase in CO2 will remain in the atmosphere for hundreds of thousands of years, waiting for  geological weathering – but why would it?  What possible justification is there to image that  it is a fixed percentage,  independent of amplitude?

To illustrate my point, here is an analogy: Suppose I have a bath full of water with 3 holes in the bottom. The first hole is 10 cm wide, the second is 1cm wide, and the third is 1 micron wide. The water will all empty quickly, mostly through the large hole, some through the small hole and essentially ignore the 1 micron wide hole. However the BERN model says no this is wrong. More than  20% of the excess CO2 will sit around waiting hundreds of thousands of years to pass through the 1 micron hole, while ignoring the option of dissolving in the ocean!

It is only when the partial pressures of carbon dioxide between the atmosphere and the ocean re-balances that a new ‘geological’ balance of CO2 can be reached. That happens rather fast and the net increase is small compared to glacial cycle variations, which as we have seen, climate scientists don’t yet understand.


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