Saturday, January 06, 2007

Carbon in the Sky.

The figures for carbon dioxide released from burning fossil fuel and the corresponding atmospheric levels of CO2 suggest that the Earth is absorbing 40% of what is emitted, leaving the 60% remainder to accumulate in the atmosphere. It might be concluded therefore that a reduction in CO2 emissions worldwide to 40% of their current levels would result in a steady-state situation, at the current "concentration" of 381 parts per million (p.p.m.). I now show how I have arrived at this potentially reassuring conclusion, and begin by a recapitulation of a few essential points about the nature of the Earth's atmosphere. The air pressure is the atmospheric force per unit area, and assuming a purely spherical planet, may be written as:

P = M x g/4 x pi x r*2.

Here, p is the pressure in Pascals (Newtons per square metre; N/m*2), M is the atmospheric mass in kilograms, g is the acceleration due to gravity at the planet's surface, and r is the radius of the planet in metres. If we rearrange this formula, the atmospheric mass M may be obtained:

M = p x 4 x pi x r*2/g = 101325 N/m*2 x 4 x pi x (6378 x 1000)*2 m*2/9.78 m/s*2
= 5.296 x 10*18 kg.
(The units cancel if it is recalled that 1 Newton N = 1 kg x m/s*2; hence, dividing by g in m/s*2 leaves just kg).

A similar value may be obtained from noting that the atmospheric force is equal to the "weight" of a column of mercury (Hg, from the Latin word for mercury, hydrargyrum) 760 millimetres in height. Since the density of Hg is 13.6 grams/cubic centimetre, a 760 mm column of Hg, covering an area of one square metre would have a mass of:

76 cm x 100 x 100 x 13.6 = 10,336,000 g = 10,336 kg.
Thus, the mass of air pressing on each square metre of the Earth's surface is 10.3 tonnes! Multiplying by the Earth's surface gives an atmospheric mass of 10,336 x (6378 x 1000)*2
= 5.28 x 10*18 kg. The agreement with the above figure is exact for a column ("pressure") of 762 mm.

However, let's reasonably define the atmospheric mass as 5.3 x 10*18 kg.

Current levels of carbon dioxide stand at 381 ppm. This is erroneously referred to as a "concentration", when it is really a "mixing ratio", i.e. meaning that 381 molecules out of every million molecules of air are CO2. A mean mass for air molecules can be obtained assuming that 78% is nitrogen, 21% is oxygen and the rest (assumed a molecular mass of 40) is argon plus CO2. Hence, this is: (.78 x 28) + (.21 x 32) + (0.01 x 40) = 28.96. The molecular masses of N2, O2, Ar and CO2 are 28, 32, 40 and 44 respectively.

The 381 ppm is in terms of volume but on a mass basis, this becomes (44/28.96) x 381 = 579 ppm, meaning that 579/1,000,000 of the mass of air is from CO2.

Thus, the total mass of CO2 in the atmosphere is: 579 x 10*-6 x 5.3 x 10*18 = 3.07 x 10*15 kg
= 3.07 x 10*12 tonnes. (In terms of "carbon", this is (12/44) x 3.07 x 10*12 = 8.37 x 10*11 tonnes, or 1/3.7 the amount of CO2, about one quarter of it).

Hence, one p.p.m. (equivalent) of carbon = 8.37 x 10*11/381 = 2.20 x 10*9 tonnes. Figures from the Earth Policy Institute indicate that there were 224 x 10*9 tonnes of carbon emitted in the form of CO2 by burning fossil fuels between 1950 and 2001 (inclusive years), and so we might expect an increase in the atmospheric level of CO2 of 224 x 10*9/2.20 x 10*9 = 102 p.p.m.

However, the actual level increased by 60 p.p.m. from 311 p.p.m to 371 p.p.m. This shows that there are "removal mechanisms" operative, but that emissions are exceeding their capacity by around 150%. However, 40% of the emitted CO2 is being absorbed from the atmosphere, and so one might conclude that if we were to reduce world CO2 emissions to 40% of their present levels, the CO2 would remain static at the present 381 p.p.m.
The absorptive capability appears to be functioning at the same level since 2001 too. In the past 5 years, there has been an average of 7 billion tonnes of carbon emitted annually, making a total of 35 billion tonnes. Dividing by 2.20 billion tonnes gives an expected increase of 16 p.p.m.; however, the actual increase is by 10 p.p.m. from the 2001 level. Thus, 6 p.p.m. has been taken up, making 6/16 x 100 = 38% (40% near enough) as the absorptive capacity of the planet for CO2, which is the same as the mean level estimated from the 1950 to 2001 data.

The figures for carbon emissions (that's not CO2 in the atmosphere, which has risen inexorably, but the amount of fossil fuel burned reckoned in terms of its carbon) show two striking "blips" - falls to lower values - first at around the early 1980's, when there was a switch certainly in Europe and the U.K. (we didn't belong to the European EC/Union then) from coal to natural gas, and the latter produces less CO2 per unit of heat, and then in the early 1990's following the collapse of the former Soviet Union, with less manufacture and operative social infrastructure meaning less fuel being burned.

Since we are burning 7 billion tonnes of carbon per year, this amounts to 7/2.2 = 3.18 p.p.m. of carbon (as CO2) being added to the atmosphere annually. If 40% of that continues to be absorbed (presuming the world does not cut its CO2 emissions to the 40% level that my calculations indicate would keep the level constant at the present 381 p.p.m.), that leaves an increase of 1.91 p.p.m. per year. Thus, by 2050 (44 years), we might predict that the level would have climbed to 381 + 44 x 1.91 = 465 p.p.m., and by the end of the century (2100) it would be 561 p.p.m.

There are, however, a number of variables that might potentially be tuned during this period. For a start, peak oil and peak gas will probably kick-in and so the annual emissions of carbon (CO2) over the world will fall. Also, there may well be an urging of growth of plants, forests and ocean phytoplankton by increased CO2 in the atmosphere, which will increase the size of the 40% sink for CO2. The current clearing of rainforest mainly for slash-and-burn farming, will reduce the Earth's lung-capacity, but by how much it is hard to say. It is thought that the oceans' "lawns" of phytoplankton are responsible for around 50% of photosynthesis on the planet, leaving half of the remaining land-based photosynthesis being done by rainforests. Thus, we might conclude that a quarter of the Earth's CO2 "sink" capacity rests there, or 10% of the amount presently emitted is absorbed by forests. I doubt that all of them will ever be cleared, but we could add another 30 p.p.m. to the total if they were to be, which doesn't change the total much. If the phytoplankton were to be killed-off by higher sea temperatures, then we would really be in trouble, but since we need photosynthesis not just to absorb CO2 but to produce oxygen to breathe, it would be the least of our worries!


Anonymous said...

I'd guess, the missing CO2 was simply dissolved in water. What is the concentration of (bi-)carbonates in ocean water, by how much has it risen and what storage capacity does that give the oceans? Presumable the carbonate concentration in rain water is in equilibrium with the CO2 concentration in air.

If that's true, then there may not be a removal mechanism and 40% emissions is just 2.5 times less bad as 100%.

Professor Chris Rhodes said...

You mean that it might just be sitting there waiting for the seas to warm so it will be released again? Mmm, maybe - I've assumed the happy situation that it is all taken up by plant life (including ocean based phytoplankton) through photosynthesis. There's not enough hard data to say about worldwide CO3,2-/HCO3- for sure... but I certainly take your point. The storage capacity of the oceans is HUGE, and they contain 60x as much CO2 as the atmosphere does, and could hold a lot more still. I was reading a few days ago that there was apparently a big jump in atmospheric CO2 last year. No one knows why? Chris.