I ended up in quite an interesting Twitter discussion about methane and CO2. I got involved when someone mentioned this thread from Ken Caldeira. The point being made is that because CO2 has a long atmospheric lifetime, and because methane oxidises into CO2, the time integrated forcing due to a pulse of methane is dominated by the contribution once its oxidises to CO2, rather than by the contribution when it’s methane.
The point I tried to make in the discussion was that this is only really true for fossil methane emissions, because biogenic methane (from cows, for example) isn’t really adding a “new” carbon into the system. However, although I don’t dispute the original calculation, I also don’t think the comparison is all that reasonable, which I’ll try to explain using a related, but slightly different, comparison.
In a 2015 paper, Ken Caldeira and a colleage (Xiaochun Zhang) showed that the cumulative radiative forcing from CO2 released in fossil fuel combustion exceeds the thermal energy released by a factor of about 100000. They did this in a reasonably detailed way, but I think I can do a ballpark estimate in much simpler way.
If we just consider coal, then 9.46 x 1010 kg of CO2 is released for every EJ (1018 J) of thermal energy. Therefore, if we consider a scenario where we release 1000 GtC = 3600 GtCO2 from burning coal, then this would provide 3.6 x 1015/9.46 x 1010 = 38054 EJ = 3.8 x 1022 J of thermal energy.
If we do emit 1000 GtC, not all will remain in the atmosphere. Once ocean invasion is complete (which would take a few centuries) we’d expect about 25% to remain in the atmosphere. This means atmospheric CO2 would increase by ~250 GtC, which is about 120 ppm. So, it would roughly settle at about 400 ppm. An increase from 280 ppm to 400 ppm produces a change in forcing of about 1.9 W/m2, which will – on average – persist for 10 thousand to 100 thousand years. If you integrate this forcing over those timescales, and multiply by the surface area of the Earth, you get 3.1 x 1026 to 3.1 x 1027 J. So, yes, about 10000 to 100000 times greater than the thermal energy released (remember, this is just a ballpark estimate).
However, what actually happens is that this energy accrues in the climate system, which warms until a new equilibrium is reached. If we assume an ECS of ~ 3K, then a change in forcing of ~1.9 W/m2 would produce an equilibrium warming of about 1.54K. Most of this goes into the oceans, which has a heat capacity of ~4000 J/kg/K. The oceans have a total mass of about 1.4 x 1021 kg, which means a warming of 1.54 K would increase the total energy by 1.4 x 1021 x 4000 x 1.54 = 8.6 x 1024 J.
This is still bigger than the thermal energy released, but only by a factor of ~220, rather than by a factor of 10000 to 100000. If we were to consider gas, rather than coal, then it would be bigger by a factor of ~130, rather than ~220. So, I think that considering the time integrated forcing over-estimates the relative impact by quite a large margin, and I think the same is true for the comparison between the impact of methane and the impact of the CO2 to which it will oxidise.
As far as I’m aware, for any reasonable scenario, the dominant waming impact of methane emissions will occur when it’s methane, rather than when it has oxidised to CO2. In GtC, annual methane emissions are about 5% of CO2 emissions (~0.5 GtC versus ~10 GtC) yet more than 5% of the warming can be attributed to methane emissions. So, even though fossil methane emissions will oxidise to “new” CO2 that will have a long atmospheric lifetime, it is still a small fraction of the direct CO2 emissions from fossil fuel burning and from land-use change.
Ultimately, I think that all this really illustrates is that it’s tricky to compare methane and CO2 emissions. CO2 has a long atmospheric lifetime and, hence, is key to determining how much we eventually warm. Methane, on the other hand, can have a very large impact on shorter timescales, and becomes important if we want to avoid crossing some kind of threshold. Personally, I think we should just consider them separately, rather than doing comparisons. Others may, of course, disagree.