The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.
When we see records being broken and unprecedented events such as this, the onus is on those who deny any connection to climate change to prove their case. Global warming has fundamentally altered the background conditions that give rise to all weather. In the strictest sense, all weather is now connected to climate change. Kevin Trenberth HIT THE PAGE DOWN KEY TO SEE THE POSTS Now at 8,800+ articles. HIT THE PAGE DOWN KEY TO SEE THE POSTS
Monday, December 6, 2010
Excitability in ramped systems: the compost-bomb instability
Excitability in ramped systems: the compost-bomb instability
The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.
The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.
Somebody has got to get a copy of this.
ReplyDeleteWell, you know, this is not only true for methane, although it may be the most near-term problem, much nearer than sea-level rise or ocean acidification, or well, you name it.
ReplyDeleteAnyway, this is not the first paper on catastrophic tipping points.
Hope you find a copy.