I’ve written a number of posts about warming commitments, in particular the zero emission commitment (ZEC). In other words, how much additional warming will there be after emissions get to zero. The answer is that on multi-decadal timescales [the ZEC] is close to zero. A common response to this is what about permafrost? It is true that the estimates typically don’t include the potential impact of release from permafrost, so it is a reasonable question.
However, the lead author (Andrew MacDougall) of the recent paper that estimated the ZEC has used one of the models to try and assess the effect of the permafrost carbon feedback on the zero emissions commitment. They carried out a perturbed parameter experiment (i.e., run the same model many times, but vary the parameters), and considered scenarios where 1000 PgC is emitted before emissions go to zero, and another where 2000 PgC is emitted (for context, total emissions to date is about 600 PgC).

There were quite a lot of details that I won’t go into, but the main result is presented in the above figure, which shows how permafrost infuences the ZEC in the 1000 PgC runs (left-hand panel) and 2000 PgC runs (right-hand panel). In other words, how much extra warming is there after emissions go to zero when compared to equivalent runs that don’t consider permafrost.
The basic result (see Table below) is that on multi-decade timescales, the effect is small (probably less than 0.1oC) but that it will increase with time, possibly adding a few tenths of a oC after 500 years. For reference, the temperature increase in the 1000 PgC run when emissions go to zero is about 1.5oC, so after a few hundred years we could have warmed by ~2oC. This isn’t great, but this additional warming would be relatively slow and it’s still considerably smaller than the baseline warming (i.e., most of the warming we’re likely to experience is due to our emissions, not due to these feedbacks).

The analysis also suggests that the impact doesn’t depend strongly on cumulative emissions; the effect is similar for the 1000 PgC and 2000 PgC runs. This is mostly because the linear relationship between emissions and warming breaks down in these models when cumulative emissions are high. There are, however, indications that this may not be a robust results and, hence, it is possible that the effect will continue to increase with increasing emissions.
Also, even this study doesn’t consider abrupt thaw, which could accelerate permafrost processes over the next few centuries. This could further increase the permafrost, but probably by 10s of percent. This probably won’t change the basic result. The effect of permafrost on the zero emission commitment (ZEC) is probably small on multi-decade timescales. Hence, this doesn’t change that the ZEC is probably close to zero on these timescales.
On longer timescales (centuries) the effect of permafrost will probably increase, but is probably still going to be much smaller than the warming due to direct anthropogenic emissions. It could increase warming from 1.5oC to ~2oC over a period of a few centuries, but it seems unlikely that it will commit us to much more than 2oC if we are able to get emissions to zero well before we cross that warming threshold. This isn’t necessarily great news, but it still indicates that the dominant factor in determining how much we will warm is how much we end up emitting.
Links:
Warming commitments – Posts I’ve written about our warming commitments.
Is there warming in the pipeline? A multi-model analysis of the Zero Emissions Commitment from CO2 – MacDougall et al. (2020) paper that discusses the zero emission commitment (ZEC).
Estimated effect of the permafrost carbon feedback on the zero emissions commitment to climate change – MacDougall (2021) paper that estimates how permafrost effects the ZEC.