Characteristic disruptions of an excitable carbon cycle

Abstract

The history of the carbon cycle is punctuated by enigmatic transient changes in the ocean’s store of carbon. Mass extinction is always accompanied by such a disruption, but most disruptions are relatively benign. The less calamitous group exhibits a characteristic rate of change whereas greater surges accompany mass extinctions. To better understand these observations, I formulate and analyze a mathematical model that suggests that disruptions are initiated by perturbation of a permanently stable steady state beyond a threshold. The ensuing excitation exhibits the characteristic surge of real disruptions. In this view, the magnitude and timescale of the disruption are properties of the carbon cycle itself rather than its perturbation. Surges associated with mass extinction, however, require additional inputs from external sources such as massive volcanism. Surges are excited when CO2 enters the oceans at a flux that exceeds a threshold. The threshold depends on the duration of the injection. For injections lasting a time ti & 10, 000 y in the modern carbon cycle, the threshold flux is constant; for smaller ti, the threshold scales like ti−1. Consequently the unusually strong but geologically brief duration of modern anthropogenic oceanic CO2 uptake is roughly equivalent, in terms of its potential to excite a major disruption, to relatively weak but longer-lived perturbations associated with massive volcanism in the geologic past.