From Princeton:
What happens to fossil fuel CO2 added to air?
By burning coal, oil, and natural gas, man is adding fossil fuel CO2 to the atmosphere at a rate sufficient to increase its concentration in air by about 4 ppm/year. For reference, a ppm is a part per million. The pre-industrial CO2 concentration, measured in air from around 1800, was 280 ppm. Man’s activities have since increased that concentration to today’s value of about 400 ppm. Thus for every million molecules of air, there are 400 molecules of CO2.
While the rate of fossil fuel combustion is sufficient to increase CO2 annually by 4 ppm, the observed increase is only about 2 ppm. What happens to the rest? Two things. Some dissolves in seawater. In pre-industrial times, the CO2 concentration of air was in equilibrium with the CO2 concentration of surface seawater. As atmospheric CO2 has risen, the equilibrium has been perturbed, such that the “excess” of CO2 in air now drives a flux of CO2 into the sea in an effort to reestablish equilibrium.
The second process removing CO2 from the atmosphere is the growth of forests and grasslands worldwide. This conclusion may seem counter-intuitive, since we recognize that large masses of vegetation (mostly forests) are converted to CO2 in deforestation, which goes into the atmosphere. Globally, however, the growth of existing and new forests outweighs the effect of deforestation. The causes of this growth remain controversial, but at least two factors are likely to be important. The first is the regrowth of forests on abandoned farmland. The second is the fertilizing affect of higher atmospheric CO2 concentrations, which allow CO2 to enter leaves and be transformed into tissue more rapidly by photosynthesis.
To a first approximation, about half the CO2 emitted by combustion remains in the atmosphere, about 35% dissolves in the oceans, and 15% is taken up by the increase in the biomass of forests. How do we know these numbers? The fraction remaining in air is easy: we just divide the atmospheric increase by the combustion rate. There are various ways scientists estimate ocean versus land uptake. Conceptually, the most straightforward is to make repeat measurements of the concentration of inorganic carbon in the oceans. This concentration is increasing because of the transfer of fossil CO2 from the atmosphere. Knowing the emission rate, the rate of atmospheric increase, and the rate of ocean uptake, we can calculate forest uptake.