The middle Pleistocene transition by frequency locking and slow ramping of internal period

Abstract

The increase in glacial cycle length from approximately 41 to on average 100 thousand years around 1 million years ago, called the Middle Pleistocene Transition (MPT), lacks a conclusive explanation. We describe a dynamical mechanism which we call Ramping with Frequency Locking (RFL), that explains the transition by an interaction between the internal period of a self-sustained oscillator and forcing that contains periodic components. This mechanism naturally explains the abrupt increase in cycle length from approximately 40 to 80 thousand years observed in proxy data, unlike some previously proposed mechanisms for the MPT. A rapid increase in durations can be produced by a rapid change in an external parameter, but this assumes rather than explains the abruptness. In contrast, models relying on frequency locking can produce a rapid change in durations assuming only a slow change in an external parameter. We propose a scheme for detecting RFL in complex, computationally expensive models, and motivate the search for climate variables that can gradually increase the internal period of the glacial cycles.

On the Cause of the Mid‐Pleistocene Transition

“…The difference between the larger amplitude of the longer glacial cycles of the Late Pleistocene, and the smaller, shorter (41-kyr) cycles of the Early Pleistocene is clearly visible. The exact timing of the transition is not obvious; different studies have proposed both abrupt and gradual changes, occurring between 1,500 and 600 kyr ago (e.g., Clark et al, 2006;Dyez et al, 2018;Elderfield et al, 2012;Konijnendijk et al, 2015;Liu et al, 2008;Mc-Clymont et al, 2013;Nyman & Ditlevsen, 2019;Rutherford & D'Hondt, 2000;Schulz & Zeebe, 2006;Snyder, 2016). Clark et al (2006) showed that the large spread in proposed timings can be explained, at least partly, by the variety of statistical tools that have been used to analyze the data (e.g., wavelet analysis, moving window Fourier transforms, change-point analysis) and the choice of timing criterion (δ 18 O threshold, time between interglacials, peaks in wavelet spectrograms) as well as by the variety of data that are analyzed (e.g., different individual benthic δ 18 O records from different locations, different stacks).…”

“…The difference between the larger amplitude of the longer glacial cycles of the Late Pleistocene, and the smaller, shorter (41‐kyr) cycles of the Early Pleistocene is clearly visible. The exact timing of the transition is not obvious; different studies have proposed both abrupt and gradual changes, occurring between 1,500 and 600 kyr ago (e.g., Clark et al., 2006; Dyez et al., 2018; Elderfield et al., 2012; Konijnendijk et al., 2015; Liu et al., 2008; McClymont et al., 2013; Nyman & Ditlevsen, 2019; Rutherford & D'Hondt, 2000; Schulz & Zeebe, 2006; Snyder, 2016). Clark et al.…”

Quantification and interpretation of the climate variability record

“…frequency locking between the internal oscillator frequency and the external forcing frequency (Gildor and Tziperman, 2001). The MPT would then be a manifestation of a change from a 1:1 over a 2:1 to a 3:1 frequency locking perhaps triggered by a slow change in an external parameter, such as the CO 2 concentration, (Nyman and Ditlevsen, 2019). An alternative suggestion is that the MPT reflects a change in the structure of the slow manifold in the fast-slow system in such a way that a new branch, the deep glacial state, becomes accessible, (Paillard, 1998).…”

“…Over larger timescales, stationarity may return: for example there may be regular "relaxation" oscillations between the parts of the slow manifold (Crucifix, 2012). The structure of these oscillations may gradually or abruptly change over longer timescales (Ashwin and Ditlevsen, 2015;Ditlevsen and Ashwin, 2018;Nyman and Ditlevsen, 2019).…”

Crossover and peaks in the Pleistocene climate spectrum; understanding from simple ice age models

“…To summarize, for the threshold models the crossover time scale is either set by a diffusion time scale, or given by a linear drift, which in the low noise limit corresponds to the time needed for establishing a glacial maximum. When assuming that the astronomical forcing governs the threshold, the spectrum shows peaks at multiples of the forcing frequencies in accordance with a frequency locking scenario (Nyman and Ditlevsen 2019). Three models, where left panels are the realizations, right panels the power spectra of the realization (blue) and the mean spectra are obtained from 1000 realizations of the model (orange): Top row is a random walk with reflecting boundaries at x max = ± 0.9 .…”