Of course, this is an old argument. Eli prettified it up a bit at Bishop Hill and repeats the argument here in polite company (You, yes you in the back. Stop laughing). Apologies to the original source
Postscript: Dikran with the algebra at QuantPaleo
Δ - is the change in atmospheric CO2, over any period of a year or greater
He - is the emission of CO2 due to humans burning fossil fuel,
Ne - is the natural emissions of CO2 from all sources. Here, Eli is using the word nature to stand for everything except CO2 generated by burning fossil fuels.
Na - is the total natural absorption of CO2,We can simply write
Δ = He + Ne - NaThis is an accounting identity. Rearrange the equation by subtracting He from both sides of the equation
Δ - He = Ne - NaWe know that emissions from humans burning fossil fuel He are greater that the change in atmospheric CO2 by about a factor of 2, so He > Δ and (Δ - He) is negative.
0 > Δ - He = Ne - NaThis means that Ne - Na must be negative, so the natural emissions must be less than the natural absorption or, Ne < Na, and nature is not the source of the observed increase in CO2 since the amount of CO2 emitted into the atmosphere by everything except burning fossil fuels is less than the amount of CO2 absorbed from the atmosphere by both physical and biological processes.
See how easy it is. It is only necessary to know two things.
First that the change in CO2 atmospheric concentration, Δ, is positive. That comes from the Mauna Loa observations, ice cores, you name it. Second that emissions due to burning of fossil fuel would increase the amount of CO2 in the atmosphere more than the observed increase (Δ-He < 0).
That is known both from the source term, the amounts of fossil fuels mined (coal and tar sands), pumped (oil and gas) and a sink term, the amounts burned to generate electricity, run cars and trucks, etc. I f anything the measures of He are underestimates.