Going with your calculation, I think that you can safely conclude that ~85% of the CO2 emitted has been absorbed in sinks and removed from the atmosphere. The problem is we can't quantify where it all goes. This means we don't know at what point the sinks will stop working, or if they will become a source in the future - the 85% is not a constant but a point estimate. Identifying the sinks (and sources) was the focus of some scientists who sent up satellites to find the missing sinks, but issues with rockets exploding sort of messed some of that effort up.
About half of the anthropogenic CO2 emitted into the atmosphere stays in the atmosphere. The other half goes into the oceans and the terrestrial biosphere. The ocean sink is roughly 2 Gt carbon per year, which you would have to convert into Gt CO2 per year for yourself. I think it works out to roughly half of the net CO2 uptake of anthropogenic CO2 per year goes into the oceans.
My hunch is what you are "doing wrong" is calculating ppm on a per mass basis. That is incorrect since ppm is calculated on a per volume basis for gases, which for the atmosphere, since it's nearly an ideal gas, is the same as on a per mole basis. So divide the total mass of CO2 by 2 to get the amount staying in the atmosphere, then divide it by 44 g/mole which is the molar amount, then divide the mass of the atmosphere by the molecular weight of air (which is a little over 28 g/mole) and you should get around the 2 ppm/year figure.
That's just a hunch on my part because the order of magnitudes look right to get you into the range you need. But I didn't do the arithmetic.
Sorry, I don't know the figures but I expect you can work a search engine just as well as I can.
However, you are some figures missing. The CO2 rise will be the total rise from all sources, I suspect. The 31Gt will be from man-made sources only. Nature puts much more into the atmosphere than man does.
The other figures you will need are the ones that say where the CO2 goes. For instance, most of it goes into the ocean. This is complicated by the fact that if the ocean warms then it give some of it back.
Some of it will go into the planet's plant life. This includes more than land plants. For instance, algae can be found in huge quantities in the oceans. This consumes CO2 as well.
The representation of the Carbon Cycle below is from NOAA.
More than 1/3 of the CO2 goes into the oceans. That is was is causing ocean acidification. Much of it goes back to the earth through the natural carbon cycle, mostly through plants.
I can't help with your calcs, but in total atmospheric CO2 is increasing by a little more than 2 ppm per year which is roughly double the rate of the increase in the 1960s.
http://www.esrl.noaa.gov/gmd/ccgg/trends...
You should be sure you are looking at CO2 and not carbon emissions. They can be converted as a ratio of 44 to 12.
Also, the amount of CO2 emitted does not all go into the atmosphere. Perhaps 5gT goes back into the oceans and land.
You are confusing CO2 with Carbon. CO2 is comprised of 1 Carbon atom and 2 Oxygen atoms. The mass of CO2 is 44 g/mol and the mass of Carbon is 12 g/mol. Hence the mass of CO2 is 3.67 times heavier than Carbon. So you need to times 2.13 gigatonnes of Carbon by 3.67 to convert it into CO2. That works out at 7.8 gigatonnes of CO2 per 1ppmv. Therefore if humans are putting 31 gigatonnes of CO2 into the atmosphere annually that works out at 31 divided by 7.8 = about 4ppmv. CO2 is currently increasing at the rate of 2ppmv every year which means natural sources are taking up about 2ppmv (i.e. 50%) every year (according to the IPCC's data). Hope that helps somewhat.
Natural processes that capture CO2 are partially keeping up with the added load. This is good news, because it means we don't have to completely stop all emissions, just get them below the level that Earth can manage.
I'm trying to extrapolate CO2 parts per million in the atmosphere into the future. According to http://en.wikipedia.org/wiki/List_of_countries_by_carbon_dioxide_emissions, the world produces 31 billion tonnes of CO2 annually. Also, 2.13 billion tonnes of CO2 equal one ppm in the atmosphere, according to http://cdiac.ornl.gov/pns/convert.html.
This calculates to 14.7 ppm per year of CO2 added to the atmosphere.
However, according to http://www.wolframalpha.com/input/?i=carbon+dioxide+concentration, CO2 is only rising at about 2 ppm per year.
Is there something wrong with my sources or calculations? Are there better sources I should use instead?
