Data-driven stochastic model for the Pleistocene global temperature: Dynamical mechanism of the Middle Pleistocene transition

The pronounce change in the glacial-interglacial regime that occurred about 1 million years ago - the so-called Middle Pleistocene transition (MPT) - is widely thought as an apparent manifestation of climate system's nonlinearity. The MPT is observed as a shift in glaciation periodicity (from 41 kyrs to approximately 100 kyrs) accompanied by both increasing of the ice/temperature oscillation amplitude and changing of the characteristic shape of the oscillations. Currently, there are ongoing debates about mechanisms of the MPT and the roles of different orbital parameters and the natural climate variability in it.

The empirical study presented here is aimed to derive a dynamical model from direct data analysis, which provides maximal probability to produce the records we have in hands. We use stochastic nonlinear evolution operator for the global temperature proxy (dO¹⁸) parameterized by a universal approximator (artificial neural network) and forced by the insolation signals at different latitudes. The model also contains adjusting explicit dependence on time reflecting the slow cooling (and decreasing CO₂) trend that was permanent during the Pleistocene. The model includes deterministic as well stochastic state-dependent terms. The deterministic term describes internal system dynamics with tens to hundred kyr time scales. The stochastic one reflects shorter-scale (millennial and centennial) processes which are under temporal resolution of data we use.

We obtained that strong nonlinearity, stochastic and insolation (obliquity) forcings are all important for the MPT. In fact, the MPT was occurred due to noise-induced transitions in the deterministic phase space of strongly nonlinear system possessing relaxation oscillations. So, the millennial and centennial processes (parameterized by the random term of the model) appear to have crucial role in the MPT. Regarding the external forcing, the Earth's obliquity 41 kyr oscillations dominate. This forcing provides the phase locking of temperature and 41 kyr insolation signal in the post-MPT glacial-interglacial cycles.

The study was supported by the Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS).