Rate-Induced Tipping of the Compost Bomb: Sizzling Summers, Heteroclinic Canards and Metastable Zombie Fires

The Arctic is the fastest warming region on Earth. Understanding how a rapidly changing climate change impacts Arctic systems is therefore an important challenge. This is the basis of the `Compost-Bomb' instability, a theorized runaway heating of northern latitude peat soils when atmospheric temperature rises faster than some critical rate, first proposed in [Luke & Cox, European Journal of Soil Science (2011), 62.1] and analysed in [Wieczorek et al, Proceedings of the Royal Society A (2011), 467.2129]. The Compost Bomb instability was one of the first examples of what is known as Rate-induced tipping or R-tipping.

The key trigger for the compost bomb instability is heat produced by microbial respiration. Here, the original soil carbon and temperature model of Luke & Cox is augmented with a non-monotone microbial respiration function, for a more realistic representation of the process. This gives rise to a meta-stable state, reproducing the results of [Khvorostyanov et al, Tellus (2008), 60B] where a complex PDE model is used. Two non-autonomous climate forcings are examined: (i) a rise in mean air temperature over decades (ii) a short-lived extreme weather event, with the rate-induced compost bomb observed in each. Using techniques of compactification, singular perturbation theory and desingularisation, we reduce the R-tipping problem to one of heteroclinic orbits, uncovering the tipping mechanism for each climate change scenario.