A while ago, there was an excellent question posted as a comment. The Stern Review and other sources say that the world can absorb about five billion tonnes of carbon dioxide equivalent per year. If emissions are above that, atmospheric concentrations rise. If they are below that, they fall. Does that mean that, in the absence of human activity, concentrations would be falling, year-on-year? Are our first five gigatonnes of emissions stabilizing?
To answer this, you need to remember that there are two big kinds of carbon sinks out there. The first is embodied in forests, but consists of all biomass. A world where all the forests of North America and Europe were intact would have less carbon dioxide in the air because more would be in wood, leaves, etc. That being said, for any level of forest cover and atmospheric greenhouse gas, the biosphere will eventually reach an equilibrium point where it emits as much carbon dioxide (from decaying plants, etc) as it absorbs from the air. The biosphere is thus more like a cushion than like an eternal allowance.
The other kind of sink consists primarily of the deep sea. It’s like a great big sponge that absorbs carbon dioxide. At present, it can absorb about five billion tonnes of carbon dioxide equivalent per year (the source of the Stern number). Like a sponge, however, it can only carry on absorbing for some time. As the deep sea becomes saturated with carbon dioxide, a higher and higher proportion of what we emit will remain in the atmosphere causing climate change.
In the long run, then, we don’t have a perpetual allowance of five gigatonnes per year. We have some big sinks that can absorb about that much at present. We need to rapidly cut human emissions below this level. Then, over a longer period of time, we will need to phase them down to virtually nothing. Otherwise, we will always have to contend with rising atmospheric concentrations of greenhouse gasses and the environmental consequences thereof.