Wednesday, July 29, 2015

Does climate change break carbon dating?

No, we will just need a bit more complicated equations, and nuclear tests "broke" it 50 years ago, anyway
Windows 10: Off-topic. The last and best Windows, Windows 10, were released today. I have been offered to download the 3 GB file. But can some people tell me what are the threats? Will e.g. Mathematica work? Is it compatible with switchable graphics drivers? Omega 14.12 LeshCat? Will all the non-system folders that you created be preserved? Will the Windows gadgets that I could still preserve in Windows 7 disappear? Have any other apps gotten broken? Thanks for your answers.
According to the mythology, thousands of bad things are being caused by global warming. Some media have announced the 8200th victim of climate change. Let me borrow the titles from the Smithsonian Magazine and PBS:
Climate Change Might Break Carbon Dating

Fossil Fuels Are Destroying Our Ability to Study the Past
Terrible. Radiocarbon dating is becoming impossible! ExxonMobil has apparently destroyed archaeology. The Smithsonian subtitle is more fair: "Fossil fuel emissions mess with the ratio of carbon isotopes in the atmosphere." OK, what's going on? Is the era of radiocarbon dating really over?

First of all, it's important to realize that radiocarbon dating doesn't care about the temperature, humidity, and tons of other things that define the "weather" or its long-term average, the "climate", so the effect of CO2 on the radiocarbon dating has nothing whatever to do with the climate, the climate change, or the global warming!

Carbon dioxide has an effect but this effect is direct, much like the direct effect of CO2 on rising crop yields, and not through the climate.

Second, all these news stories are based on a playful article in PNAS written by a babe from the Imperial College named Dr Heather Graven:
Impact of fossil fuel emissions on atmospheric radiocarbon and various applications of radiocarbon over this century
The paper is nice, the topic is appropriate for an undergraduate term paper, and I would give her an A for that work if it were a term paper, except that it also has some omissions and mistakes we will get to.

Third, how does it actually work and what is getting broken and why?

Radiocarbon dating is an important method to determine the age of objects that contain carbon as long as the age is between centuries (to be sure that the concentrations have changed sufficiently) and tens of thousands of years (to be sure that a detectable amount of carbon-14 is left). How does it work? It's simple. It measures the fraction of the carbon atoms in the sample that contain the unstable carbon-14 nucleus and urges you to make a calculation reflecting the fact that the number of unstable carbon-14 atoms is exponentially decaying with time.

To actually use the method, we must know the initial fraction of carbon-14 atoms, the reason why it's nonzero to start with, and the rate at which the carbon-14 nuclei decay.


There are 15 isotopes of carbon. The totally stable ones are carbon-12 (99% of any macroscopic pile with carbon around you: this isotope defines the unit of mass for all atoms: its mass is 12.00000 units) and carbon-13 (about 1% of any pile).

The only unstable isotope of carbon that is not "hopelessly unstable" is carbon-14 whose lifetime is 8,200 years. After 8,200 years, plus minus half a percent or so, the number of these nuclei that haven't decayed drops \(e=2.718\dots\)-fold. Equivalently, 5,730 years is the half-life of carbon-14.

The remaining 12 isotopes of carbon are hopelessly unstable. All of the lifetimes are shorter than an hour, all but one are shorter than a minute, and all but three are shorter than a second, usually much shorter. We won't need them because they disappear before a carbon dater prepares her paperwork.

Excellent. So we will only deal with carbon-12/13 and carbon-14. Carbon-12 and carbon-13 have an almost fixed ratio and we won't distinguish them, calling them just carbon-12. (Their ratio isn't quite fixed and may be a useful extra tool to determine other quantities but I won't discuss those.) By carbon-12, I will mean the 99%-1% mixture of carbon-12 and carbon-13. Carbon-14 is unstable but does appear in trace amounts around us. Its concentration in the atmosphere remains nonzero even though the atmosphere is billions of years old.

Why is it so and what the percentage of carbon-14 atoms is?

In 1963, the graph showed almost "1,000 parts per thousand" which means that the percentage of carbon-14 in 1963 was 100% higher – doubled – relatively to what it was in 1950.

Well, here you have the money graph. The percentage of carbon-14 went up dramatically between 1955 and 1963 – when most of the nuclear bombs were tested. The nuclear tests have simply produced lots of unstable isotopes including carbon-14.

Since 1963, the concentration has been dropping back towards something that looks like a natural constant. The fast decrease occurred not because carbon-14 was decaying this quickly but because it was being diluted due to the carbon circulation. When a dead plant decays, the – mostly stable – carbon in it gets to the atmosphere while some of the atmospheric carbon – with a higher fraction of carbon-14 – gets incorporated into the currently growing plants.

We won't really need to know the absolute percentage of carbon-14 in the atmosphere but it has been really tiny – about 1.5 parts per trillion (\(10^{12})\). It's still large enough for us to be able to detect the carbon-14. Why is the percentage of carbon-14 nonzero after the billions of years (million of half-lives)? Because in the atmosphere, carbon-14 is being constantly produced from nitrogen:\[

{}^{14}_{\,7}{\rm N} + n \to {}^{14}_{\,6} {\rm C} + p

\] A cosmogenic neutron hits an ordinary stable nucleus of nitrogen, the most abundant element in the atmosphere, kicks one proton out from the nucleus, and sits instead of this proton, thus changing the nitrogen to carbon. Note that this "refreshing" of carbon-14 only occurs if there is nitrogen around – basically only in the atmosphere. The atmosphere with its bombardment by neutrons keeps the carbon "young" – keeps the carbon-14 percentage at a safely nonzero (albeit small) level.

Now, all this carbon (mostly carbon-12/13 but with the trace amounts of carbon-14) gets incorporated to plants. Note that the mass of plants is mostly water and the non-water content of the plants is mostly carbon. It is not extracted from the soil. Instead, it is taken from the atmosphere. The plants' food, CO2, is flying in the air. (In Czech, we have an idiom about the baked pigeons flying directly to [lazy] people's mouths. Plants actually enjoy this luxury!) So if a 10-ton tree suddenly emerges somewhere, it doesn't mean that 10 tons of solid soil was stolen from the ground! Most of the solid mass was taken from the air.

The plants contain much less nitrogen so the cosmogenic production of carbon-14 no longer occurs (or occurs much more slowly). Therefore, the carbon-14 percentage in the plants decays thanks to the reaction\[

{}^{14}_{\,6}{\rm C} \to {}^{14}_{\,7} {\rm N} + e^- + \bar \nu_e

\] This \(\beta\)-decay is basically the previous equation reversed (but the neutron-minus-proton is replaced by an electron-plus-antineutrino). As you can see, the percentage of carbon-14 in plants – but also in animals etc., all solid matter – is exponentially decaying with the lifetime of 8,200 years, as we said.

OK. To find the radiocarbon age of a solid piece of matter with carbon, you measure the percentage of carbon-14 in its carbon, compare it with the percentage of carbon-14 in the atmosphere when the solid object was created from the atmosphere. The ratio is written as the exponential of \((T/8200\,{\rm years})\) and you may interpret \(T\) as the radiocarbon age of the object. Simple.

The problem is that, as we have mentioned, the percentage of carbon-14 in the atmospheric carbon – which I stated to be roughly 1.5 parts per trillion – isn't quite stable. It was doubled during the nuclear test era around 1960. And it has been decreasing ever since.

The decrease has been partly caused by the burning of the fossil fuels. As the name indicates, fossil fuels are fuels that are fossils :-). In other words, they are very very old which also means that the carbon-14 in these fossils has had more than enough time to decay away (almost) completely. So if you release the carbon atoms from the coal and oil into the atmosphere, it's just carbon-12 and carbon-13. The percentage of carbon-14 in the atmosphere goes down.

You may see that the percentage of carbon-14 went up during the nuclear tests. If you think that the nuclear tests were a "bad thing", then it follows that "global warming" is causing the opposite i.e. "good thing"! ;-)

OK, at any rate, the percentage of carbon-14 in the atmosphere has been affected by
  1. common carbon cycle (its motion from/to oceans and from/to biosphere)
  2. nuclear tests
  3. burning of fossil fuels
The first set of effects used to keep the percentage at 1.5 parts per trillion. But the second effect – which has largely ended – was making this natural concentration higher for years. And the last one – which will continue for decades or centuries – will keen on pushing the concentration down. I believe that it already has to be below the initial 1.5 parts per trillion.

When you write down the equation\[

\frac{P_{\rm sample}}{P_{\rm air\,at\,birth}} = \exp(-T / 8,200\,{\rm years})

\] and you realize that the percentage \(P_{\rm air\,at\,birth}\) is a complicated function of time, and not necessarily a monotonic one, you may get several solutions for the age \(T\).

If you neglected that the percentage of carbon-14 is variable, you would think that the atmosphere is getting older (well, apparently older, according to the most naive usage of the radiocarbon dating formula) very quickly. Note that "getting older" means "having a decreasing percentage of carbon-14". And the burning of the fossil fuels is reducing the percentage of carbon-14 in the atmosphere, too. So the fossil fuels are making the atmosphere "apparently older"! ;-)

How quickly? Dr Heather Graven is calculating a model and she decides that these days, the atmosphere is getting older by 30 years every year! ;-) So trees in 2050 AD will have the same reduced carbon-14 content as trees from the year 1000 AD or so! You won't be able to distinguish "very old things" from "very new things" by carbon dating.

It's important to know that if you know that an object with carbon was created before the industrial revolution (and before the discovery of radioactivity and nuclear fission), you will still be able to use the most naive formulae for carbon dating that have always worked – you may completely ignore what has been happening with the atmosphere since the discovery of the steam engine. But if your wish is going to be to find the age of things that may have been born since the Industrial Revolution, you simply have to take the complicated evolution of carbon-14 in the atmosphere into account.

If you are a scientist in 2050 AD who is reading this blog post and you have two samples with carbon, and the percentage of carbon-14 is 10% lower in Sample A than in Sample B, it may mean that Sample A is 820 years older than Sample B (the old-fashioned carbon dating conclusion) or it may also mean that both samples are recent and Sample A is some 28 years younger than Sample B. ;-) Well, you will probably have to be careful. Your equations may have many solutions and the nuclear-test era around 1960 may add two more solutions.

Dr Graven's result that the atmosphere is getting older by 30 years per year isn't exactly what I got but it's of the same order, of course. I think that the carbon cycles etc. are complicated enough so that even as a staunch theorist, I would prefer to simply measure the percentage of carbon-14 instead of calculating it. A disadvantage of measurements is that right now, you may only measure the current value (and rate of change) of the quantity and not the value in a distant future, e.g. in 2050 AD. ;-)

But the estimate goes as follows: The concentration of CO2 in the atmosphere is 400 ppm and each year, it increases by about 2 ppm. We add carbon-12/13 and almost no carbon-14. So every year, the percentage of carbon-14 in the atmosphere goes down by 2/400=1/200 i.e. 0.5%, so it's the same relative change as when the atmosphere "gets older" by 0.5% of the lifetime 8,200 years which is about 41 years.

She got 30 years because there are additional subtleties contributing terms of both signs that the previous paragraph ignored. First of all, we are adding more CO2 into the atmosphere than the equivalent of 2 ppm every year. We are adding about 4 ppm and 2 ppm gets reabsorbed by the oceans and the biosphere each year – which means that the total increase of CO2 is just 2 ppm or so. If this fact – the emissions are higher than the equivalent of 2 ppm per year – were incorporated, you would get the aging by even more than 41 years per year.

But there's the other issue, namely that the percentage of carbon-14 is being increased back towards the "more natural levels" by the cosmogenic bombardment by neutrons – even now, as we speak and burn our fossil fuels. This decreases the rate of apparent aging of the atmosphere.


To summarize, the carbon dioxide emissions don't affect the radiocarbon treatment of truly historical or archaeological samples that were produced before the industrial era. They will only make it harder, but not impossible, to determine the age of things that were "born" after the discovery of the steam engine.

But the CO2 emissions aren't the first effect that has made these things harder: the nuclear tests around 1960 did the same thing, and more quickly. It's obvious that the experts doing radiocarbon dating will have to become familiar with all these subtleties if they really become relevant for their work.

In the modern era, people have numerous methods to "fool" the radiocarbon dating methods – to change the percentage of carbon-14 – anyway. And the projections of the percentage of carbon-14 in the atmosphere that Dr Graven did may be cute – but the future users of the radiocarbon method won't need those, anyway, because they will have had all the measured values of the percentage of carbon-14 that they will have need.

And again, none of these subtleties have anything to do with the climate, weather, or air temperatures.

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