A fast-slow model for glacial cycles since the Mid-Pleistocene Transition

<p>A new simple approach inspired by MacAyeal (1979) to explain the time-asymmetric &#8216;saw-toothed&#8217; shape and 100,000-year quasi-period of glacial-interglacial cycles since the Middle Pleistocene Transition, is presented. Using a simple model with fast-slow dynamics, the global ice volume is taken to be a function of two independently varying parameters, the solar insolation and &#8216;alpha&#8217;, a secondary control parameter, the study of which is the focus this research. The steady state of the model is a partially folded surface in three-dimensional space where insolation, &#8216;alpha&#8217;, and global ice volume are orthogonal axes. The pleated surface allows for the gradual increase and sudden decrease in ice volume that is observed in the paleoclimate record. To derive a time series of global ice volume, the Euler integration method is used, producing a time series which replicates the &#8216;saw-toothed&#8217; pattern of glacial cycles in the late Pleistocene. The second control parameter, &#8216;alpha&#8217;, is proposed to be related to internal dynamics of the climate system, such as ice sheet dynamics.</p><p>&#160;</p><p>Reference</p><p>D. R. &#160;MacAyeal, &#8216;A Catastrophe Model of the Paleoclimate Record&#8217; , Journal of Glaciology , Volume 24 , Issue 90 , 1979 , pp. 245 &#8211; 257.</p>