Yes, I remember I looked it up and it seemed that the increased CO2 matched the decreased O2. Which was interesting to me because it meant that increased CO2 could not be explained as, for example, outgassing from the sea.

I'll try to dig out what I found.

OK - I found my notes. I hope this is of interest.

Warning: This was done entirely for my own interest without any intention of making it public and has not been checked, so may very well contain errors. I recommend not using any of this information without carefully re-doing the calculations and checking that I correctly understood the data sources - and forming a judgement about their dependibility. I'll be grateful for any errors to be pointed out.

Question: Does the CO2 added to the atmosphere each year match the O2 disappearing from the atmosphere each year?

Answer: Yes if you count only the CO2 added from fossil fuel burning and ignore or assume negligible CO2 coming from other sources.

Molecules of CO2 released per year
Ref 1: Annual carbon burn (in 2008) 8749 Mt carbon - ["Mt" = "million metric tonnes"]

This gives the mass of CO2 released per year as 8749 * 44/12 = 32.1 Gt [giga tonnes]

One molecule of CO2 has mass 7.31E-38 Gt
- [notation: "7.31E-38" = "7.31 times 10 to the power minus 38"]

So annual burn of C results in 32.1/7.31E-38 = 4.39E38 CO2 molecules

Molecules of O2 disappearing from atmosphere each year
Ref 2:

"Atmospheric Oxygen Levels are Decreasing
Oxygen levels are decreasing globally due to fossil-fuel burning. The changes are too small to have an impact on human health, but are of interest to the study of climate change and carbon dioxide. These plots show the atmospheric O2 concentration relative to the level around 1985. The observed downward trend amounts to 19 'per meg' per year. This corresponds to losing 19 O2 molecules out of every 1 million O2 molecules in the atmosphere each year."

Mass of O2 in atmosphere = 1.2E18 kg = 1.18E6 Gt (ref. 3)
So mass disappearing annually = 1.18E6*19/1,000,000 = 22.4 Gt

One molecule of O2 has mass = 5.35 E-26 kg = 5.35E-38 Gt
So 4.19E+038 O2 molecules disappear from the atmosphere per year

This matches the number of CO2 molecules released per year to within about 5 per cent.

References:

Ref 1. Mass of CO2 released from fossil fuel use per year, Tom Boden, Gregg Marland, Bob Andres
Carbon Dioxide Information Analysis Center
Oak Ridge National Laboratory
Oak Ridge, Tennessee 37831-6290
http://cdiac.ornl.gov/ftp/ndp030/global.1751_2008.ems
http://www.webcitation.org/67MiWaatO

Ref 2. Mass of oxygen subtracted from atmosphere per year
http://scrippso2.ucsd.edu/
http://www.webcitation.org/67MiaSKPW

Ref 3. Total mass of oxygen in atmosphere
http://www.globalchange.umich.edu/gctext/Inquiries/Inquiries_by_Unit/Unit_10c.htm
http://www.webcitation.org/67Mihmigg

http://members.shaw.ca/tfrisen/is_there_enough_oxygen.htm
http://www.webcitation.org/67MiduQrs

Thanks for checking.

I don't know anything about the fertilisation effect - I assume it means that, as atmospheric CO2 goes up, the rate of absorption (and conversion of CO2 back to O2) by plant growth also goes up.

I just don't know. One thing to remember is that CO2 does not only come from burning fossil fuel. It can, in principle, also come from:
- outgassing from the sea
- volcanoes
- change of land use

The last one is new to me but apparently a source of 1/3 of cumulative CO2 emissions (presumably anthropogenic) and the dominant source until 1965 http://www.ecd.bnl.gov/steve/pres/WellKnownAGU10vgphs.pdf

Yes, it's not obvious what's what. Even if vanished O2 does seem to match CO2 produced, it's not a proof that the O2 was used in burning C. As you point out, you also need O2 to burn H2.

I think a lot of the data needs to be regarded as potentially dodgy and, even if figures match, that could be just a fluke.

A topic I know just about zero about is the "missing CO2". http://www.c3headlines.com/2011/06/the-ipccs-missing-co2-remains-a-major-embarassment-of-its-consensus-science-its-still-awol-maybe.html
If it's true that NASA cannot account for 50% of released CO2, then I don't think you or I should get too concerned if we can't get the figures to match up.

(My own guess would be that CO2 is absorbed far more rapidly by the ocean and/or biosphere than they reckon.)