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Where is that extra Carbon Dioxide coming from?

There was a recent video which downplayed global warming and claimed (among other things) that most of the rise in carbon dioxide in the atmosphere was from volcanos. That statement is quite false.

Here's a semi-technical argument that explains why. (Note that I'm not a real expert in this field, though a lot of the statements are basic physics, and I was a real expert in physics not too long ago.)

My discussion here depends on several assumptions where I haven't gone out and checked the primary sources, but I would be vastly surprised if they were seriously wrong:

Now, there are three isotopes of carbon (carbon-12, -13, and -14) which differ in the number of neutrons they have in their nuclei. Despite the difference in weight, they have the same number of electrons, so they make identical bonds to other atoms. All physical and chemical processes we care about will treat C14, C13, and C12 essentially equally. Specifically the ocean will absorb all varieties of CO2 at the same rate.

The interesting isotope here is carbon-14. C14 is produced in the upper atmosphere as cosmic rays collide with Nitrogen atoms. It is radioactive, with a half-life of 5000 years or so. That means, in 5000 years half of it will have radioactively decayed into something else; in about 20,000 years almost all of a sample of C14 will be gone.

Now, CO2 from fossil fuel (and from volcanoes) will have essentially no C14. That is because C14 is radioactive and any C14 that has been held underground for a million years will have long since decayed away. So, as we burn oil and coal (and as volcanoes produce CO2), the isotope ratio in the atmosphere will shift. All varieties of CO2 will dissolve in the ocean or be taken up by plants, but no C14 is being added due to humans. The atmosphere will thus have a smaller fraction of C14 as we burn fossil fuels.

Consequently, unless the sun is producing a much smaller solar wind than previously (which would allow more cosmic rays in to Earth, and would thus make more C14 in the upper atmosphere), there ought to be a nice relationship between the rise in the total atmospheric CO2 and a decrease in the C14 fraction in the atmosphere.

The technology exists to measure these isotope ratios precisely. It's an obvious experiment and I suspect that they have been measured.

Now, what about the ocean? Waves, foam, and other ocean surface effects are not intrinsically dependent on CO2 concentration (except to the extent that CO2 changes the ecology which then produces surfactant molecules). Thus, EMPH whatever the details of the CO2 transport into the ocean, it should follow a first order linear differential equation:

Rate_into_ocean = alpha * (P_CO2_air - P_CO2_ocean).

In this equation, P_CO2 is the pressure (i.e. amount) of CO2; alpha is a number that says how fast it dissoves in the oceans; and Rate_into_ocean would be measured in metric tons per second.

All the messy unknowns are in alpha, which might be temperature-dependent and perhaps time-dependent. More generally, alpha is climate dependent, because it depends on wind speeds and ocean currents. Mathematically, this is a nicely simple model. (Note that the same arguments apply if there are other mechanisms for removing CO2 from the atmosphere, and a similar equation results. All we are really assuming is that the various isotopes travel together, a fact that was solidly established more than 50 years ago.)

From this, you can compute how the isotope ratios change in the atmosphere, given isotope ratios in the ocean and a specified amount of fossil CO2 added to the atmosphere. (Again, even if there are other mechanisms for removing CO2, they will behave similarly with respect to isotope ratios.)

Now, we have an an estimate for the human-generated (fossil) CO2 production, we can estimate for the volcanic CO2 production. (You do that by taking air samples near volcanos and water samples near undersea volcanos, an experiment that geologists do on a regular basis.) From these, and measurement of P_CO2, you can compute an average value alpha (averaged across the world's oceans).

Now, suppose someone has done that (and I'm darn sure they have). Suppose that the effective value of alpha agrees more-or-less with detailed models. (Which it does.) This is the scientific consensus, and is basically consistent with global warming models. It states that most of the CO2 increase in the last century is human-generated from fossil fuels, that alpha = 1/(100 years), and that about half of the CO2 we have generated has gone into the ocean. The other half remains in the atmosphere.

Note that there is no new research so far in this argument. Nothing is controversial, everything is either accounting or science that your parent's generation knew. So no one can argue that people are forced to believe this because of politics or money or research grants. People believed all of this 50 years ago, long before anyone worried about global warming.

Now, what if you believe that human-generated CO2 is not an important contribution to the observed increase in CO2? What could be done that's consistent with all the available data?

Well, you can't reduce the amount of human-generated CO2 from fossil fuels. That's pretty well known -- remember, governments tax it. What you would have to believe is that the volcanic contribution is larger. Suppose we wanted human-generated fossil-fuel CO2 to be only 10% of the total change. That means we need to have volcanoes producing 10 times the human component.

OK. Let's imagine that the geologists are wrong. It would be a coincidence that those volcanoes turned on during the industrial revolution, but coincidences do happen. BUT with volcanos producing 10 times as much CO2, we would need to make alpha 10 times larger in order to get that extra CO2 out of the air. If we wanted the human effect to be only 1% of the volcanoes, we'd need to make alpha 100 times (!) larger.

I suspect our understanding of the ocean surface is good enough to solidly exclude a 100 times increase in alpha. (If alpha were so far off, then you could probably see the difference in a bottle of seltzer water or soda. After all, the physics of CO2 going into and out of the ocean is the same as that of soda fizzing and going flat.) So, let's stick with making humans a 10% effect with a 10 times increase in alpha.

With the larger alpha, the time constant for moving CO2 from the air into the ocean would be only 10 years. With such a short time constant, we now would need to assume that the volcanic CO2 output is roughly tracking the human-generated fossil CO2 output (and always stays about 10x bigger). So, not only did the volcanoes turn on at the start of the industrial revolution, but that they are increasing their output at about the same rate as we humans do. That's getting a bit implausible.

Now, here's where the isotope ratios come into the picture. With the larger alpha and thus faster transfer of CO2 into the ocean, one finds that most of the C14 has moved out of the atmosphere into the ocean. Instead of about half of the C14 moving into the ocean, 90% would have to dissolve. (Remember, all isotopes behave the same, so if 90% of the total CO2 dissolves, then 90% of the C14 must also dissolve.)

If you've followed the logic so far, you see that if volcanos produced lots of CO2, the atmosphere would have very little C14 in it. It would have much less than we actually observe. This is the fatal problem. And, again, it is knowledge from your parent's generation. People have been watching the C14 concentration of the atmosphere because it is important for carbon-dating of archaeological artifacts.

To summarize, if humans aren't important CO2 producers, then we would need to assume that volcanoes are. But, the human contribution is about the right amount, so we would need to believe that the excess CO2 from volcanoes goes into the ocean. If the CO2 goes into the ocean more rapidly, the C14 would also, so you would have to make more of it to maintain the correct concentration in the atmosphere. So, we'd need to believe that somehow, the rate of C14 production in the upper atmosphere would have to be 10x larger than reality. Right?

Now, as we mentioned before, C14 is produced in the upper atmosphere as the result of cosmic rays hitting nitrogen atoms. Unfortunately for the volcanic-CO2 theory, that's old physics that we've known for decades. The amount of nitrogen in the atmosphere has been known since probably 1820, the number of cosmic rays has been known since the 1950s (Dr. James van Allen), and so has the reaction rate. All the relevant scientists are dead or retired, so you can't possibly accuse them of fudging their results in order to get more publicity or research money out of global warming. So, you cannot ask for more C14 to balance the hypothetical increase in volcanic C12 and C13 production. Thus, the entire volcanic CO2 theory falls apart.

In short, you can look at the isotope ratios to figure out how much fossil CO2 is being produced, relative to the production rate of C14. C14 production is known from space research and nuclear physics. Ergo, the rate of fossil CO2 production is known. Since the rate at which we burn fossil fuels is approximately known, whatever is left over is the volcanic contribution.

All that stuff is known, and known fairly accurately. Therefore there really isn't any way for the scientific consensus to be wrong on the subject of CO2 concentration. Certainly not grossly wrong. Therefore, the volcanic option is a red herring. Vulcanism isn't dramatically increasing.

Therefore, we humans are indeed the main cause of the rise in atmospheric carbon dioxide. We are more important than volcanoes, methane clathrates, CO2 from carbonate rocks, anything where the carbon was locked away from the atmosphere. (It may not apply to CO2 from soils and bogs; that's a topic for another day.)

This doesn't mean that the global warming scenario is nailed down completely. The magnitude of the temperature rise is somewhat uncertain, and the economic and political effects are very uncertain. However, anyone who tells you that we're not doubling the amount of CO2 in the atmosphere is, plain and simple, wrong. They are either ignorant, misinformed, unwilling to believe reality, or have such a strong axe to grind that they are lying. Any one of those reasons means that they are probably not to be trusted as a source of information on global warming.

[ Papers | | Phonetics Lab | Oxford ] Last Modified Fri Jul 24 20:42:08 2009 Greg Kochanski: [ ]