OA not OK part 11: Did we do it? Yes we did!

This post is number #11 in a series about ocean acidification. Other posts: Introduction, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, Summary 1 of 2, Summary 2 of 2.

Welcome to the 11th post in our ocean acidification series. This time we step through the calculation for how much CO2 is ‘missing’ from the atmosphere. That is, how do we work out how much CO2, that we know was released to the atmosphere, is just not there? The post is the most mathematically intensive of all the posts in the series.

As noted in previous posts, The International Energy Annual reports that globally, 603 billion tons of CO2 were released from the 'consumption and flaring of fossil fuels' between 1980 and 2006 (the most recent year they have published full data for). Over the same time atmospheric CO2 increased by 43 ppm from 339 ppm to 382 ppm (i.e. 2006 = 13% more than 1980).

For historical reasons atmospheric concentrations of gases are expressed as parts per million (ppm). So we need to convert the tons of CO2 to ppm. To do this we need to know the mass of the atmosphere.  Calculations by Trenberth give 5.148 ×1018 kg, which we will round to 5.1 ×1018 kg. (You can roughly check this yourself by taking sea level air pressure and multiplying by the area of the Earth).

1 part per million (ppm) of this atmospheric mass is 5.1 ×1012 kg (5.1 billion tons), but this does not take into account the fact that CO2 molecules are heavier than other molecules in the atmosphere. Most of the atmosphere is nitrogen (78%) and oxygen (21%). Nitrogen (N2) has an atomic mass of 28 and oxygen (O2) has a mass of 32. Thus, we can say the 'average' molecule in air has a relative mass of about 29. CO2 however has a mass of 44.

So, 1 ppm of CO2 thus has a mass of (44/29) × (5.1 x1012) kg = 7.7 ×1012 kg = 7.7 billion tons. If the calculation is done more carefully then the answer is 7.8 billion tons of CO2. (The FAQ at the US government Carbon Dioxide Information Analysis Center says 1 ppm CO2 = 2.13 Gt C, but we recall from post 5 that we can convert that to Gt CO2 by multiplying by 3.67: 2.13 × 3.67 = 7.8)

Using the more accurate value, we can see that the 603 billion tons of fossil fuel CO2 released in the last 30 years gives an expected change of 77 ppm (= 603/7.8) CO2 in the atmosphere.

But, CO2 has increased by only 43 ppm. That is, about half (44%) of the fossil fuel CO2 released between 1980 and 2006 by humans – some 270 billion tons! – is missing. (To say nothing of CO2 missing from pre-1980 emissions).

Where has it gone? Could it have been taken up by soils and plants? No, not all of it. The total global masses of carbon in land plants and soil are about 500 billion and 1500 billion tons, respectively (see Table 3-2 from the IPCC 3rd Assessment Report of 2001).  That is, the collective 'standing crop' of soils and plants is 6 to 7 times the mass of the missing CO2. If soil and plants had taken up all or most of the fossil fuel CO2 it means they must have increased by about 1/6th (15-20%) since 1980. There is simply no evidence to support the idea that soils and/or plant mass has increased by this amount. So where has the CO2 gone?

We know from Henry's law that there is a strong drive for the CO2 to be absorbed by water. If the CO2 has been absorbed then we would expect to have seen a decrease in ocean pH. Has this happened? We discuss observations of ocean pH in the next post.

Written by Doug Mackie, Christina McGraw, and Keith Hunter. This post is number 11 in a series about ocean acidification. Other posts: Introduction, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, Summary 1 of 2, Summary 2 of 2.

Posted by Doug Mackie on Saturday, 30 July, 2011