The role of astronomical forcing on stochastically induced climate dynamics

This study is concerned with the influence of astronomical forcing and stochastic disturbances on non-linear dynamics of the Earth’s climate. As a starting point, we take the system of climate equations derived by Saltzman and Maasch for late Cenozoic climate changes. This system contains variations of three prognostic variables: the global ice mass, carbon dioxide concentration, and deep ocean temperature. The bifurcation diagram of deterministic system shows possible existence/coexistence of stable equilibria and limit cycle leading either to monostability or bistability. Fitting the astronomical forcing by an oscillatory function and representing the deep ocean temperature deviations by means of white Gaussian noise of various intensities, we analyze the corresponding stochastic system of Saltzman and Maasch equations for the deviations of prognostic variables from their average values (equilibrium state). The main conclusions of our study are as follows: (i) astronomical forcing causes the climate system transitions from large-amplitude oscillations to small-amplitude ones and vice versa; (ii) astronomical and stochastic forcings together cause the mixed-mode climate oscillations with intermittent large and small amplitudes. In this case, the Earth’s climate would be shifting from one stable equilibrium with a warmer climate to another stable equilibrium with a colder climate and back again.