There’s been a bit of a discussion on Twitter about what it would take to stabilise atmospheric concentrations, or to stabilise global average temperatures (there seemed to be some confusion as to which was being stabilised). The bottom line seems to be that if we want to stabilise atmospheric concentrations, then we’d need to reduce emissions by something like 80%. If we were to halt them altogether, then concentrations would drop and would do so almost exponentially, with an equilibration timescale of around 200 years (see Archer 2009, Figure 2).
However, the atmospheric concentration will asymptote towards a long-term concentration in which atmospheric CO2 is enhanced, relative to pre-industry, by an amount that is equivalent to 20-30% of our total emissions (possibly more if we were to emit a total of a few 1000 PgC). So, it turns out that even though atmospheric concentrations will drop, temperatures will approximately stablise, since the reduction in atmospheric CO2 is matched by the fact that the system was not yet in equilibrium when emissions were stopped (see Steve Easterbrook’s post, this Realclimate post, or Solomon et al. (2008)).
What I wanted to do hear was try to roughly illustrate this.
At the moment, atmospheric concentrations are enhanced by an amount roughly equivalent to 45% of our total emissions. The resulting change in forcing is:
where is our total emissions in ppm. At any instant in time, the transient warming () will be
where is the transient response after a doubling of atmospheric CO2 and is the change in forcing due to a doubling of atmospheric CO2.
If we halted all emissions, then atmospheric concentrations would decay and eventually settle (after hundreds of years) to a long-term concentration which is enhanced (relative to pre-industry) by an amount equivalent to about 25% of our total emissions. In that case, the long-term change in forcing would be:
and the eventual warming would be:
where we’ve used the , rather than the because it would warm to the equilibrium response to the long-term concentration, rather than to the transient response.
Now, imagine we halt all emissions after emitting a total – in ppm – of . The temperature change at that instant would be:
Once atmospheric concentrations reach their long-term value, the warming would be
If you take the ratio, you get
For reasonable values of , the final term on the right-hand-side varies from 1.8 ( ppm) to about 1.6 ( ppm). Hence, if the TCR-to-ECS ratio is around 0.6 (1.0/1.7), the final warming will be similar to the initial (the final equilibrium temperature change will be about the same as the transient response at the instant at which we halt all emissions). A TCR-to-ECS ratio of around 0.6 is what climate models suggest. Hence, technically, there is probably no future commited warming, since zero emissions would roughly stabilise temperatures.
In reality, of course, we can’t simply halt all emissions, so there will be future warming that will depend on how much we emit between now and when net emissions get to zero. However, what seems pretty clear is that stabilising temperatures will probably require halting emissions (net). I should add that if we were to emit a lot more, we would expect the airborne fraction to increase. However, we would also expect the fraction that remains for millenia to also increase. The TCR-to-ECS ratio may also be such that it could continue to warm slightly were we to get emissions to zero, or cool slightly. However, unless I’ve made some kind of silly mistake (I did do this rather quickly) as a rough estimate, our committed warming is about the same as the transient warming at the time when we get emissions to zero.