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

dc.creator Esther R. Widiasih
dc.creator Andrew Keane
dc.creator Malte F. Stuecker
dc.date.accessioned 2024-01-16T23:23:38Z
dc.date.available 2024-01-16T23:23:38Z
dc.date.copyright 2023
dc.date.issued 2023-11-15
dc.description.abstract 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 O 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.
dc.format Article
dc.format.extent 11 pages
dc.identifier.citation Widiasih, E. R., Keane, A., & Stuecker, M. F. (2024). The Mid-Pleistocene Transition from Budyko’s Energy Balance Model. <em>Physica. D</em>, 458, 133991-. https://doi.org/10.1016/j.physd.2023.133991
dc.identifier.uri https://hdl.handle.net/10790/42730
dc.language eng
dc.title The Mid-Pleistocene Transition from Budyko’s Energy Balance Model
dcterms.type Text
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