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Rate-dependent tipping points: the example of the compost bomb instability

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This paper discusses rate-dependent tipping points related to a novel excitability type where a (globally) stable equilibrium exists for all different fixed settings of a system’s parameter but catastrophic excitable bursts appear when the parameter is increased slowly, or ramped, from one setting to another. Such excitable systems form a singularly perturbed problem with at least two slow variables, and we focus on the case with locally folded critical manifold. Our analysis based on desingularisation relates the rate-dependent tipping point to a canard trajectory through a folded saddle and gives the general equation for the critical rate of ramping. The general analysis is motivated by a need to understand the response of peatlands to global warming. It is estimated that peatland soils contain 400 to 1000 billion tonnes of carbon, which is of the same order of magnitude of the carbon content of the atmosphere. Recent work suggests that biochemical heat release could destabilize peatland above some critical rate of global warming, leading to a catastrophic release of soil carbon into the atmosphere termed the ``compost bomb instability’’. This instability is identified as a rate-dependent tipping point in the response of the climate system to anthropogenic forcing (atmospheric temperature ramping).

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