Inherent characteristics of sawtooth cycles can explain different glacial periodicities

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 (Formula presented.) 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.