Modeling the response of the marine carbon cycle to extreme CO$_2$ injection events

We explore how the response of a conceptual model of the marine carbon cycle depends on the way in which carbon is injected from the atmosphere.

We find that, for single-injection pulses, the threshold amount required for a large response of the excitable system depends on pulse duration but not on its specific form.

We do, however, see differences in the number of large transient responses in carbon and, correspondingly, the duration of the response for different pulse shapes.

These differences are magnified as the system is pushed towards increased excitability and can be understood in terms of the geometry of an increasingly winding heteroclinic orbit.

Inspired by Large Igneous Provinces (LIPs), we also consider random sequences of injection pulses.

We find a wide range of possible responses for a given overall amount injected and duration, depending on the mean characteristics of the individual pulses.

We also identify a resonance-like "Goldilocks" zone, in which intermediate pulse durations or arrival frequencies produce the largest number of repeated transients, and we test the framework with illustrative scenarios motivated by the Siberian Traps and Columbia River Basalt Group.