I like it when people do interesting calculations and help me put their results on this blog. Renato Iturriaga has plotted a graph that raises some interesting questions about carbon dioxide in the Earth’s atmosphere. Maybe you can help us out!
The atmospheric CO2 concentration, as measured at Mauna Loa in Hawaii, looks like it’s rising quite smoothly apart from seasonal variations:
However, if you take the annual averages from here:
• NOAA Earth System Laboratory, Global Monitoring Division, Recent Mauna Loa CO2.
and plot how much the average rises each year, the graph is pretty bumpy. You’ll see what I mean in a minute.
In comparison, if you plot the carbon dioxide emissions produced by burning fossil fuels, you get a rather smooth curve, at least according to these numbers:
• U. S. Energy Information Administration Total carbon dioxide emissions from the consumption of energy, 1980-2008.
Renato decided to plot both of these curves and their difference. Here’s his result:
The blue curve shows how much CO2 we put into the atmosphere each year by burning fossil fuels, measured in parts per million.
The red curve shows the observed increase in atmospheric CO2.
The green curve is the difference.
The puzzle is to explain this graph. Why is the red curve roughly 40% lower than the blue one? Why is the red curve so jagged?
Of course, a lot of research has already been done on these issues. There are a lot of subtleties! So if you like, think of our puzzle as an invitation to read the existing literature and tell us how well it does at explaining this graph. You might start here, and then read the references, and then keep digging.
But first, let me explain exactly how Renato Iturriaga created this graph! If he’s making a mistake, maybe you can catch it.
The red curve is straightforward: he took the annual mean growth rate of CO2 from the NOAA website I mentioned above, and graphed it. Let me do a spot check to see if he did it correctly. I see a big spike in the red curve around 1998: it looks like the CO2 went up around 2.75 ppm that year. But then the next year it seems to have gone up just about 1 ppm. On the website it says 2.97 ppm for 1998, and 0.91 for 1999. So that looks roughly right, though I’m not completely happy about 1998.
[Note added later: as you’ll see below, he actually got his data from here; this explains the small discrepancy.]
Renato got the blue curve by taking the US Energy Information Administration numbers and converting them from gigatons of CO2 to parts per million moles. He assumed that that the atmosphere weighs 5 × 1015 tons and that CO2 gets well mixed with the whole atmosphere each year. Given this, we can simply say that one gigaton is 0.2 parts per million of the atmosphere’s mass.
But people usually measure CO2 in parts per million volume. Now, a mole is just a certain large number of molecules. Furthermore, the volume of a gas at fixed pressure is almost exactly proportional to the number of molecules, regardless of its composition. So parts per million volume is essentially the same as parts per million moles.
So we just need to do a little conversion. Remember:
• The molecular mass of N2 is 28, and about 79% of the atmosphere’s volume is nitrogen.
• The molecular mass of O2 is 32, and about 21% of the atmosphere’s volume is oxygen.
• By comparison, there’s very little of the other gases.
So, the average molecular mass of air is
28 × .79 + 32 × .21 = 28.84
On the other hand, the molecular mass of CO2 is 44. So one ppm mass of CO2 is less than one ppm volume: it’s just
28.84/44 = 0.655
parts per million volume. So, a gigaton of CO2 is about 0.2 ppm mass, but only about
0.2 × 0.655 = 0.13
parts per million volume (or moles).
So to get the blue curve, Renato took gigatons of CO2 and multiplied by 0.13 to get ppm volume. Let me do another spot check! The blue curve reaches about 4 ppm in 2008. Dividing 4 by 0.13 we get about 30, and that’s good, because energy consumption put about 30 gigatons of CO2 into the atmosphere in 2008.
And then, of course, the green curve is the blue one minus the red one:
Now, more about the puzzles.
One puzzle is why the red curve is so much lower than the blue one. The atmospheric CO2 concentration is only going up by about 60% of the CO2 emitted, on average — though the fluctuations are huge. So, you might ask, where’s the rest of the CO2 going?
Probably into the ocean, plants, and soil:
But at first glance, the fact that only 60% stays in the atmosphere seems to contract this famous graph:
This shows it taking many years for a dose of CO2 added to the atmosphere to decrease to 60% of its original level!
Is the famous graph wrong? There are other possible explanations!
Here’s a non-explanation. Humans are putting CO2 into the atmosphere in other ways besides burning fossil fuels. For example, deforestation and other changes in land use put somewhere between 0.5 and 2.7 gigatons of carbon into the atmosphere each year. There’s a lot of uncertainty here. But this doesn’t help solve our puzzle: it means there’s more carbon to account for.
Here’s a possible explanation. Maybe my estimate of 5 × 1015 tons for the mass of the atmosphere is too high! That would change everything. I got my estimate off the internet somewhere — does anyone know a really accurate figure?
Renato came up with a more interesting possible explanation. It’s very important, and very well-known, that CO2 doesn’t leave the atmosphere in a simple exponential decay process. Imagine for simplicity that carbon stays in three boxes:
• Box A: the atmosphere.
• Box B: places that exchange carbon with the atmosphere quite rapidly.
• Box C: places that exchange carbon with the atmosphere and box B quite slowly.
As we pump CO2 into box A, a lot of it quickly flows into box B. It then slowly flows from boxes A and B into box C.
The quick flow from box A to box B accounts for the large amounts of ‘missing’ CO2 in Renato’s graph. But if we stop putting CO2 into box A, it will soon come into equilibrium with box B. At that point, we will not see the CO2 level continue to quickly drop. Instead, CO2 will continue to slowly flow from boxes A and B into box C. So, it can take many years for the atmospheric CO2 concentration to drop to 60% of its original level — as the famous graph suggests.
This makes sense to me. It shows that the red curve can be a lot lower than the blue one even if the famous graph is right.
But I’m still puzzled by the dramatic fluctuations in the red curve! That’s the other puzzle.