The Mid-Pleistocene Transition from Budyko's Energy Balance Model

Here we revisit the long-standing question of which dynamical processes were responsible for a change in the dominant periodicity of glacial cycles from ∼41 to ∼100 thousand years that occurred roughly 1 million years ago. We investigate this phenomenon, the so-called Mid-Pleistocene Transition (MPT), using an Energy Balance Model (EBM) framework. EBMs are the simplest form of global climate models, allowing for a deeper mathematical analysis to complement the physical understanding gained from more complex higher-dimensional models. We argue that a low-order flip-flop model based on a latitudinally averaged EBM provides new insights into the fundamental dynamics. A recent extension of this EBM adds equations of latitudinally averaged quantities, one for the snow/albedo line, and one for the maximum ice extent. This system of three ordinary differential equations admits glacial cycles with similar spectral characteristics as the proxy records. The period and amplitude of the cycles are controlled by a critical bifurcation parameter. When we include orbital forcing to the model and tune the evolution of the bifurcation parameter to a stack of benthic δ¹⁸O records, we observe a transition with similar features to the MPT. The transition follows a mechanism that was recently suggested in the literature: the slow ramping of the internal period via regimes of frequency locking. We demonstrate this clearly by means of a bifurcation analysis using continuation software, which reveals a bifurcation structure primarily organized by Arnold tongues and grazing bifurcations. This work strengthens the case for ramping with frequency locking as a mechanism for the MPT by providing a clear demonstration of the mechanism in a physically-derived model and providing a candidate bifurcation parameter that guides the dynamics through different frequency locking regimes.