I was quite intrigued by a recent Watts Up With That (WUWT) post called the bombtest curve and its implications for atmospheric carbon dioxide residency time. It includes the following figure which shows the change in carbon-14 to carbon-12 ratio with time (black data points with red curve) and an estimate of how it should have changed based on the residency time estimated using what is called the Bern model.
Change in carbon-14 to carbon-12 ratio (black data points, red curve) and estimate from the Bern model (credit : Gosta Petterson, WUWT).
If I understand the figure correctly, the y-axis is the percentage increase in carbon-14 to carbon-12 over what it was prior to the start of nuclear testing in the 1950s. Above ground nuclear tests in the 1950s and 1960s essentially doubled the carbon-14 concentration in the atmosphere.
What this WUWT post seems to be claiming is that the model for how CO2 concentration should change with time (assuming we were to stop adding more) has a residency time that is much greater than is estimated based on the change in the carbon-14 to carbon-12 ratio since nuclear testing stopped. At first I thought that maybe the author of this post had a point, but I think there are two fundamental problems with his analysis. One is that our use of fossil fuels has increased the concentration of carbon-12 by about 25% since about 1960 (there is no carbon-14 in fossil fuels because it decays with a half-life of 5700 years). This alone – if I’ve done my calculation correctly – would change the carbon-14 to carbon-12 ratio by about 40%.
The other problem is that there are, in a sense, two residence times for CO2. One is the amount of time an individual CO2 molecule spends in the atmosphere before being absorbed by the oceans or used by a plant. However, in this case, it will be replaced by a different CO2 molecule and so the net atmospheric concentration doesn’t change. This residence time is a few years. The other timescale is the time it would take for the atmospheric concentrations to drop by some factor. This timescale is much longer than the residence time of an individual molecule – hundreds of years. Because there is very little carbon-14 in the carbon cycle, when a carbon dioxide molecule comprising carbon-14 is absorbed by the ocean or by a plant, it is more likely to be replaced by a molecule containing carbon-12 than one containing carbon-14.
So, as far as I can tell, the decay of the carbon-14 to carbon-12 ratio in the figure above is more representative of the residence time of an individual molecule than representative of the decay timescale of the atmospheric CO2 concentration. The mismatch between what is observed and what is predicted by the Bern model seems, therefore, to be entirely consistent with how one would expect the process to work. Admittedly, I’m no expert, so happy to be corrected by those who know more.
...and Then There's Physics 
I think your first explanation is spot on. As for residence times, you need to take into account that when 14C is absorbed by other C reservoirs (sea, plants), the amount of 14C going from those to the atmosphere increases.
Here is a post in Swedish explaining Gösta’s error. There are two figures: Fig 1 is based on measuring 14C as fraction of all C in the atmosphere, and Fig 2 is based on 14C as fraction of dry air. As the amount of air doesn’t change much, the latter is a good measure of how 14C changes in absolute terms. As you can see in Fig 2, a considerable amount of atom bomb 14C still remains.
Thanks. So if I understand the two plots, the first includes the change in CO2 concentration through our use of fossil fuels and hence (in a sense) overestimates the reduction in carbon-14 concentration. The second is relative to the air so is a better representation of the change in the absolute concentration of carbon-14. Interesting.
Yes, that is correct. The first graph (as well as the one in your post) includes the effect of 14C-free fossil CO2 being added to the atmosphere.
The biggest problem with the WUWT article is that the Bern model does not distinguish between various forms of Carbon. Therefore it cannot calculate the change in isotope ratios over time. More exactly, the blue line represents the Bern model calculation of the reduction in total atmospheric CO2 given an initial doubling of atmospheric CO2 and no further net emissions. Presenting that as a model of change of isotope ratios shows either a complete incompetence on the subject matter, or a complete disregard for truth.
Graven et al, 2012 present a model of change of C14/C ratios in CO2 including such factors as cosmogenic production, production from the nuclear industry, the slow return of excess CO2 from the biosphere to the atmosphere, and of course, ocean absorption and dilution by fossil fuel emissions. The results match closely with observations.
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