The compost bomb instability in the continuum limit

The ‘Compost Bomb’ instability refers to a proposed uncontrolled increase in soil temperature. This instability is caused when sufficiently rapid atmospheric warming increases soil heterotrophic respiration which, in turn, heats the soil further. This generates a runaway effect in which soil temperatures rise rapidly. We investigate this process, neglected in Earth system models, but which has thus far been analysed with a conceptual model using ordinary differential equations. That model is deliberately idealised without any representation of the spatial structure of soils. We confirm using a partial differential equation framework, this runaway effect still occurs when accounting for soil depth. Using this newer representation we investigate the forcing parameters that make soils vulnerable to this instability. In particular, we discover that the effect of dangerously large seasonal cycle variations in air temperature can create plausible conditions for a ‘compost bomb’ thermal instability.