Carbon Cycle Instability
A new preprint
I’ve got a new preprint out in ESD. You can read it here if you like.
A Runaway Carbon Cycle #
If you release some carbon dioxide into the atmosphere there are effects in the climate-carbon system that further increase the amount of carbon in the atmosphere. For example, a release of carbon dioxide warms the planet, which increases heterotrophic respiration which adds some more carbon to the atmosphere.
We’ve worked out under what circumstances you could get a ‘runaway’ release of carbon dioxide (and thus a runaway increase in global temperatures) through this effect.
Being Naive #
For this to occur, we must get enough warming from increasing the concentration of carbon dioxide and also the response of heterotrophic respiration must be strong enough.
We can give a very naive (and wrong) estimate of when this will occur
by the following argument. If we increase carbon dioxide by a small
amount, $\Delta \mathrm{CO}^{(0)}_2$ then we get a small increase in
temperature which depends on the fractional change in carbon dioxide
$$\Delta T = \frac{\mathrm{ECS}}{\log 2} \frac{\Delta
\mathrm{CO}^{(0)}_2}{\mathrm{CO}_2}.$$
This increase in temperature leads to a release of carbon from the
soils through enhanced heterotrophic respiration $$\Delta
\mathrm{CO}^{(1)}_2 = C_L \alpha \Delta T$$ where $C_L$ is the land
carbon store and $\alpha$ is the sensitivity of respiration to
warming. This means that overall we have
$$\Delta \mathrm{CO}^{(1)}_2 = C_L \alpha \frac{\mathrm{ECS}}{\log 2} \frac{\Delta\mathrm{CO}^{(0)}_2}{\mathrm{CO}_2}.$$
However $\Delta \mathrm{CO}^{(1)}_2$ will also lead to warming, causing this process to repeat.
The $n$th iteration will lead to an increase of
$$\Delta \mathrm{CO}^{(n)}_2 = \left( \frac{\mathrm{ECS} C_L \alpha}{\mathrm{CO}_2 \log 2}\right)^n\Delta\mathrm{CO}_2^{(0)}.$$
Remembering some basic facts about geometric series tells us that for the perturbation to remain finite we must have $$\alpha \mathrm{ECS} \frac{C_L}{\mathrm{CO}_2} < \log 2.$$
We assume 1500PgC of carbon on the land, 280ppm of carbon dioxide in the atmosphere and that respiration doubles for every 10K of warming. When this perturbation is not finite, we get a runaway. Taking reasonable parameter estimates gives us that an ECS of 4K leads to a runaway state. Given that the reasonable estimates of ECS have it around 3K, this is a bit close for comfort. Luckily for us, we have ignored important facts about the carbon cycle, such as the fact that the land takes up carbon through the fertilisation of photosynthesis.
The paper #
This argument is right in spirit if wrong in detail. In the paper we perform a more sophisticated version of the above calculation to get the critical ECS threshold and find it agrees with the output of a more complex model. The exact threshold depends on how much carbon is in the atmosphere to begin with and how strong you think the fertilisation effect is. You’ll have to read the paper to find out more!