Saturday, October 17, 2015

Carbon 14: Reservoir Concentration

Our study of carbon-14, which began with Carbon-14: Origins and Reservoir, reveals that the atmosphere is exchanging carbon dioxide with a reservoir that contains over a hundred times as much carbon dioxide as the atmosphere itself. This exchange must be taking place, because it is the only means by which carbon-14 can be transported out of the atmosphere. The concentration of carbon-14 in the reservoir must be less than in the atmosphere, or else the carbon dioxide exchange would be unable to generate a net flow of carbon-14 into the reservoir.

We guessed that the reservoir was the deep ocean, which does have an adequate capacity to hold the reservoir CO2 in solution. If the deep ocean is the reservoir, its carbon-14 concentration has been measured to be 0.8 ppt, which is indeed less than the atmosphere's 1.0 ppt. Assuming the concentration of the reservoir is 0.8 ppt, we conclude that the carbon dioxide exchange rate in our natural, equilibrium atmosphere is 140 Pg/yr of CO2 (or 37 Pg/yr of carbon), while the reservoir holds 280,000 Pg of CO2 (or 77,000 Pg of carbon). Because our equilibrium atmosphere itself holds 2,400 Pg of CO2 (or 650 Pg of carbon), we see that 5.6% of the CO2 in the atmosphere enters the reservoir every year and is replaced by a like amount emerging from the reservoir. Furthermore, the reservoir holds 120 times as much CO2 as the atmosphere.

In future posts, we will find that the vast size of the reservoir, combined with the ready exchange of carbon dioxide between it and the atmosphere, imply that continuing to burn fossil fuels at the rate we are today will take thousands of years to cause a doubling in the carbon dioxide concentration of the atmosphere. Before we proceed, however, let us consider how our estimate of the size of the reservoir and the magnitude of the exchange are affected by uncertainty in the one parameter that we have guessed at: the concentration of carbon-14 in the reservoir. This concentration must be less than 1.0 ppt, and we guessed it is 0.8 ppt. But perhaps it is 0.7 ppt or 0.9 ppt. Using the equations we derived last time, we re-calculate the carbon exchange rate and the reservoir size for these concentrations.

(Pg/yr of Carbon)
(Pg of Carbon)
0.7 24 88,000
0.8 37 77,000
0.9 74 69,000
Table: Effect of Reservoir Concentration. We have reservoir concentration of carbon-14 in ppt, CR, carbon mass exchange rate in Pg/yr, me, and reservoir carbon mass in Pg, MR. Multiply carbon masses by 44/12 to get CO2 masses.

In Arnold et al., the authors present measurements of carbon-14 concentration in various layers of the ocean, in vegetation, and in soil, relative to the carbon-14 concentration in the atmosphere. These vary from 80% to 96% of the atmospheric concentration, with the deep oceans having the lowest concentration. The concentration in our reservoir must lie somewhere in the range 0.8-1.0 ppt. If the concentration is higher than 0.8 ppt, the reservoir will be slightly smaller, but the exchange rate will be much higher. At 0.9 ppt, for example, the exchange rate will be double what it is for 0.8 ppt. We see that our estimate of the exchange rate, being based upon a reservoir concentration of 0.8 ppt, is a conservative one, while our estimate of the reservoir size is bound to be close. We can now proceed with confidence in our analysis, knowing that we are certain not to over-estimate the exchange of carbon dioxide between the atmosphere and the reservoir.


  1. One our readers writes, "If the ^14C is well-mixed, why is there a 20% difference between the atmosphere/reservoir PPTs? I can see why it would be slightly less in the reservoir (seeing that it is produced in the atmosphere), but I can’t see why the difference is so much."

    1. When the reservoir is large, the difference between the atmospheric concentration and the reservoir concentration is determined by two properties of the carbon cycle: the carbon-14 creation rate (7.5 kg/yr) and the carbon mass exchange rate (m_e). We figure we already know the reservoir concentration, because we are assuming the reservoir is the deep ocean, where we have measured the carbon-14 concentration to be 0.8 ppt. So we can calculate what m_e must be, and we get 37 Pg/yr.

      But let's look at it another way: the way it's determined in nature, where we have an equilibrium atmosphere in which 37 Pg/yr of carbon moves into the ocean reservoir and 37 Pg/yr comes out. This exchange must result in a net transport of almost 7.5 kg/yr or carbon-14 into the reservoir each year. Thus each Pg or carbon exchanged must result in 0.2 kg of carbon-14 exchanged, which means the difference in the concentration in the atmosphere and reservoir must be 0.2 ppt.

  2. The following I copied from an e-mail I received from Peter, who has been checking our calculations.

    1. About 7.5 kg of 14C is created annually by cosmic rays colliding with the nitrogen in the atmosphere.
    2. This 7.5 kg per annum has been consistent for at least 1 million years.
    3. The half-life of 14C is 5,730 years.
    4. 14C decays at the rate (per annum) of 0.012%
    5. Therefore there must be equilibrium between the production and decay of 14C (otherwise the amount of atmospheric 14C would be either accumulating or declining)
    6. During the atmospheric nuclear testing in the 1960s the increase in atmospheric 14C nearly doubled, but
    7. In the 40 years since atmospheric testing ceased, the amount of atmospheric 14C has almost returned to pre-nuclear testing levels.
    8. Atmospheric 14C binds with oxygen to become CO2
    9. The ration of atmospheric 14CO2 to 12CO2 is 1 : 1 trillion.
    10. The ratio of 14C to 12C in the deep ocean (according to G.S. Bien “Radiocarbon Concentration in Pacific Ocean Water”) in 0.8 ppt.
    11. That the atmospheric 14CO2 and 12CO2 are well-mixed
    We also know that early last century the amount of atmospheric CO2 was about 300ppm. We know that the atmospheric CO2 ppm has increased from about 300 to 400 during the last 100 years. We don’t know how much of that 100 additional ppm is due to fossil fuel emissions. We know there that there is a CO2 exchange process between the atmospheric and the various reservoirs on the planet (the oceans, flora, etc), but we don’t know how much CO2 is exchanged annually. Knowing that atmospheric 14C is not increasing and that 7.5 kg is created each year, it is assumed that 7.5 kg is decaying each year (i.e. there is equilibrium between 14C creation and decay), it is possible to determine the size of the reservoir.

    The amount of carbon in the atmosphere can be calculated through knowing how many ppm of CO2 there are; it means that the mass of atmospheric carbon can be determined. Knowing that there is equilibrium between the 14C created and decayed it can be determined how much carbon there is on the planet.

    Taking the 2nd point first: 7.5 kg 14C * 1 trillion / 0.012% = 62,500 Pg (petagrams) if the ratio between the 14C and 12C in the reservoir is the same as in the atmosphere. If it is 0.9 then the reservoir holds 69.5 Pg, and if the ratio is 0.8 to 1 trillion then the reservoir holds 78,125 Pg of carbon.

    The mass of atmospheric carbon is calculated as follows (from “Atmospheric Science: An Introductory Survey”)... Replacing 380ppm with 300ppm comes to about 645 gigatons (petagrams) of atmospheric carbon.

    There is a total of 78,125 Pg of carbon on the planet and 645 Pg of that in the atmosphere, therefore there is about 77,480 Pg in the reservoirs.

    645 Pg of carbon comprises 645 kg of 14C, which decays at the rate of 0.012% per year.

    Therefore about 0.075 Kg per year decays.

    So atmospheric 14C to remain constant, 7.5 - .075 (7.43 Kg).

    Atmospheric 14C is going into the reservoir at 1.0 ppt to 12C and is coming out of the reservoir at 0.8 ppt to 12C.

    The amount of carbon that has to be exchanged between the atmosphere and reservoirs for atmospheric 14C to remain constant will be 7.43 / 0.2 * 1 Pg -> 37.15 Pg.

  3. Also from Peter, looking ahead in the story we are telling:

    · The CO2 reservoirs (excluding the atmosphere) are larger than generally accepted.

    · The availability to readily exchange CO2 between the atmosphere and the other reservoirs is greater than generally accepted.

    · The amount of CO2 from fossil fuel emissions per annum is a much smaller %age contribution to the reservoirs than generally accepted.

    · The increase in atmospheric CO2 since the early 1900s (from 300 to 400 ppm) is about half due to fossil fuel emissions; the other half is due to natural causes.

    · It will take over 1,000 years for fossil fuel emissions (at the current rate) to increase the total reservoir size by 10%.

    1. That's what I claim. We will transfer our equations for carbon-14 to the system of carbon dioxide exchange. We will note that the rate at which CO2 is absorbed by the ocean is proportional to the number of CO2 molecules above the ocean, while the rate at which CO2 is emitted by the ocean is proportional to the amount of CO2 in the ocean. These two observations allow us to calculate how CO2 concentration in the atmosphere will evolve if, for example, human beings started emitting 10 Pg/yr of carbon into our 300 ppmv equilibrium atmosphere.