# Inherent characteristics of sawtooth cycles can explain different glacial periodicities

A.W. Omta, B.W. Kooi, G.A.K. van Voorn, R.E.M Rickaby, M.J. Follows

### Abstract

At the Mid-Pleistocene Transition about 1 Ma, the dominant periodicity of the glacial-interglacial cycles shifted from ~40 to ~100 kyr. Here, we use a previously developed mathematical model to investigate the possible dynamical origin of these different periodicities. The model has two variables, one of which exhibits sawtooth oscillations, resembling the glacial-interglacial cycles, whereas the other variable exhibits spikes at the rapid transitions. When applying a sinusoidal forcing with a fixed period, there emerges a rich variety of cycles with different periodicities, each being a multiple of the forcing period. Furthermore, the dominant periodicity of the system can change, while the forcing periodicity remains fixed, due to either random variations or different frequency components of the orbital forcing. Two key relationships stand out as predictions to be tested against observations: (1) the amplitude and the periodicity of the cycles are approximately linearly proportional to each other, a relationship that is also found in the $$\delta ^{18}\hbox {O}$$δ18O temperature proxy. (2) The magnitude of the spikes increases with increasing periodicity and amplitude of the sawtooth. This prediction could be used to identify one or more currently hidden spiking variables driving the glacial-interglacial transitions. Essentially, the quest would be for any proxy record, concurrent with a dynamical model prediction, that exhibits deglacial spikes which increase at times when the amplitude/periodicity of the glacial cycles increases. In the specific context of our calcifier-alkalinity mechanism, the records of interest would be calcifier productivity and calcite accumulation. We believe that such a falsifiable hypothesis should provide a strong motivation for the collection of further records.
Original language English 557-569 Climate Dynamics 46 16 Apr 2015 https://doi.org/10.1007/s00382-015-2598-x Published - 2016

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periodicity
glacial-interglacial cycle
prediction
orbital forcing
interglacial
alkalinity
calcite
oscillation
Pleistocene
productivity
temperature

### Cite this

Omta, A.W. ; Kooi, B.W. ; van Voorn, G.A.K. ; Rickaby, R.E.M ; Follows, M.J. / Inherent characteristics of sawtooth cycles can explain different glacial periodicities. In: Climate Dynamics. 2016 ; Vol. 46. pp. 557-569.
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title = "Inherent characteristics of sawtooth cycles can explain different glacial periodicities",
abstract = "At the Mid-Pleistocene Transition about 1 Ma, the dominant periodicity of the glacial-interglacial cycles shifted from ~40 to ~100 kyr. Here, we use a previously developed mathematical model to investigate the possible dynamical origin of these different periodicities. The model has two variables, one of which exhibits sawtooth oscillations, resembling the glacial-interglacial cycles, whereas the other variable exhibits spikes at the rapid transitions. When applying a sinusoidal forcing with a fixed period, there emerges a rich variety of cycles with different periodicities, each being a multiple of the forcing period. Furthermore, the dominant periodicity of the system can change, while the forcing periodicity remains fixed, due to either random variations or different frequency components of the orbital forcing. Two key relationships stand out as predictions to be tested against observations: (1) the amplitude and the periodicity of the cycles are approximately linearly proportional to each other, a relationship that is also found in the $$\delta ^{18}\hbox {O}$$δ18O temperature proxy. (2) The magnitude of the spikes increases with increasing periodicity and amplitude of the sawtooth. This prediction could be used to identify one or more currently hidden spiking variables driving the glacial-interglacial transitions. Essentially, the quest would be for any proxy record, concurrent with a dynamical model prediction, that exhibits deglacial spikes which increase at times when the amplitude/periodicity of the glacial cycles increases. In the specific context of our calcifier-alkalinity mechanism, the records of interest would be calcifier productivity and calcite accumulation. We believe that such a falsifiable hypothesis should provide a strong motivation for the collection of further records.",
author = "A.W. Omta and B.W. Kooi and {van Voorn}, G.A.K. and R.E.M Rickaby and M.J. Follows",
year = "2016",
doi = "10.1007/s00382-015-2598-x",
language = "English",
volume = "46",
pages = "557--569",
journal = "Climate Dynamics",
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}

Inherent characteristics of sawtooth cycles can explain different glacial periodicities. / Omta, A.W.; Kooi, B.W.; van Voorn, G.A.K.; Rickaby, R.E.M; Follows, M.J.

In: Climate Dynamics, Vol. 46, 2016, p. 557-569.

TY - JOUR

T1 - Inherent characteristics of sawtooth cycles can explain different glacial periodicities

AU - Omta, A.W.

AU - Kooi, B.W.

AU - van Voorn, G.A.K.

AU - Rickaby, R.E.M

AU - Follows, M.J.

PY - 2016

Y1 - 2016

N2 - At the Mid-Pleistocene Transition about 1 Ma, the dominant periodicity of the glacial-interglacial cycles shifted from ~40 to ~100 kyr. Here, we use a previously developed mathematical model to investigate the possible dynamical origin of these different periodicities. The model has two variables, one of which exhibits sawtooth oscillations, resembling the glacial-interglacial cycles, whereas the other variable exhibits spikes at the rapid transitions. When applying a sinusoidal forcing with a fixed period, there emerges a rich variety of cycles with different periodicities, each being a multiple of the forcing period. Furthermore, the dominant periodicity of the system can change, while the forcing periodicity remains fixed, due to either random variations or different frequency components of the orbital forcing. Two key relationships stand out as predictions to be tested against observations: (1) the amplitude and the periodicity of the cycles are approximately linearly proportional to each other, a relationship that is also found in the $$\delta ^{18}\hbox {O}$$δ18O temperature proxy. (2) The magnitude of the spikes increases with increasing periodicity and amplitude of the sawtooth. This prediction could be used to identify one or more currently hidden spiking variables driving the glacial-interglacial transitions. Essentially, the quest would be for any proxy record, concurrent with a dynamical model prediction, that exhibits deglacial spikes which increase at times when the amplitude/periodicity of the glacial cycles increases. In the specific context of our calcifier-alkalinity mechanism, the records of interest would be calcifier productivity and calcite accumulation. We believe that such a falsifiable hypothesis should provide a strong motivation for the collection of further records.

AB - At the Mid-Pleistocene Transition about 1 Ma, the dominant periodicity of the glacial-interglacial cycles shifted from ~40 to ~100 kyr. Here, we use a previously developed mathematical model to investigate the possible dynamical origin of these different periodicities. The model has two variables, one of which exhibits sawtooth oscillations, resembling the glacial-interglacial cycles, whereas the other variable exhibits spikes at the rapid transitions. When applying a sinusoidal forcing with a fixed period, there emerges a rich variety of cycles with different periodicities, each being a multiple of the forcing period. Furthermore, the dominant periodicity of the system can change, while the forcing periodicity remains fixed, due to either random variations or different frequency components of the orbital forcing. Two key relationships stand out as predictions to be tested against observations: (1) the amplitude and the periodicity of the cycles are approximately linearly proportional to each other, a relationship that is also found in the $$\delta ^{18}\hbox {O}$$δ18O temperature proxy. (2) The magnitude of the spikes increases with increasing periodicity and amplitude of the sawtooth. This prediction could be used to identify one or more currently hidden spiking variables driving the glacial-interglacial transitions. Essentially, the quest would be for any proxy record, concurrent with a dynamical model prediction, that exhibits deglacial spikes which increase at times when the amplitude/periodicity of the glacial cycles increases. In the specific context of our calcifier-alkalinity mechanism, the records of interest would be calcifier productivity and calcite accumulation. We believe that such a falsifiable hypothesis should provide a strong motivation for the collection of further records.

U2 - 10.1007/s00382-015-2598-x

DO - 10.1007/s00382-015-2598-x

M3 - Article

VL - 46

SP - 557

EP - 569

JO - Climate Dynamics

JF - Climate Dynamics

SN - 0930-7575

ER -