Posted on 30 July 2011 by Doug Mackie

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 11^th 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 3^rd 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 1/6^th (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.