Nonlinear climate dynamics: From deterministic behaviour to stochastic excitability and chaos

Glacial–interglacial cycles are global climatic changes which have characterized the last 3 million years. The eight latest glacial–interglacial cycles represent changes in sea level over 100 m, and their average duration was around 100,000 years. There is a long tradition of modelling glacial–interglacialcycles with low-order dynamical systems. In some of these models, the cyclic phenomenon is caused by non-linear interactions between components of the climate system, which generate a limit cycle. Other models incorporate the established Milankovitch theory according to which changes in Earth's orbit and obliquity force variations in ice volume and ice sheet extent along with, either directly or indirectly, variations in other variables of the climate system. One then distinguishes the strong interpretation, in which the astronomical forcing is necessary to generate glacial–interglacial cycles, from the weak interpretation, in which the astronomical forcing synchronizes a limit cycle. The purpose of the present contribution is to consider specifically the effects of stochastic forcings. Indeed, the trajectories obtained in presence of stochastic fluctuations are not necessarily noised-up versions of the deterministic trajectories. They may follow pathways which have no analogue in the deterministic version of the model. Our purpose is to demonstrate the mechanisms by which stochastic excitation may generate such large-scale oscillations, sometimes with an intermittent character. To this end, we consider a series of models previously introduced in the literature, starting with autonomous models with two variables, and then three variables. The properties of stochastic trajectories are understood by reference to the bifurcation diagrams, the vector field, and a method called stochastic sensitivity analysis. We then introduce models accounting for the Milankovitch forcing, and distinguish forced and synchronized ice-age scenarios. We show again how noise may generate trajectories which have no immediate analogue in the deterministic model. We conclude on a general reflection on the interest of this research and its potential applications on a wide range of climatic phenomena.