Investigating the dynamics of cusp bifurcations: A conceptual model for glacial-interglacial cycles

An investigation into the dynamics of a two-parameter family of non-linear differential equations inspired by MacAyeal (1979) reveals the utility of simple conceptual models in understanding climate response to forcing. A slow-fast model is used to explain the non-linear response of the climate to insolation forcing after the Mid-Pleistocene Transition (MPT) which produces the saw-toothed glacial cycles in the paleoclimate record. Global ice volume is taken to be a function of two independently varying parameters, the solar insolation and ‘alpha’, a secondary control parameter. The pleated cusp geometry of the model, due to the addition of the second control allows the system to exhibit both smooth changes and sudden discontinuous transitions from one stable solution to another, producing the gradual increase and sudden decrease in global ice volume observed in the paleoclimate record.  The control parameter alpha is suggested to be related to internal dynamics of the climate system, proposed to be a measure of glacial-oceanic interaction, which varies due to glacial isostatic adjustments of the bedrock.  The transition in period of glacial cycles at the MPT is suggested to occur as a result of northern hemisphere glaciers exceeding a critical threshold, which allows alpha to become larger, causing the asymmetric, higher amplitude glacial cycles with quasi-period of 100kyr of the late Pleistocene.

 

Reference

R. MacAyeal, ‘A Catastrophe Model of the Paleoclimate Record’ , Journal of Glaciology , Volume 24 , Issue 90 , 1979 , pp. 245 – 257.