Noise-induced generation of saw-tooth type transitions between climate attractors and stochastic excitability of paleoclimate

Abstract

Motivated by important paleoclimate applications we study a three dimensional model of the Quaternary climatic variations in the presence of stochastic forcing. It is shown that the deterministic system exhibits a limit cycle and two stable system equilibria. We demonstrate that the closer paleoclimate system to its bifurcation points (lying either in its monostable or bistable zone) the smaller noise generates small or large amplitude stochastic oscillations, respectively. In the bistable zone with two stable equilibria, noise induces a complex multimodal stochastic regime with intermittency of small and large amplitude stochastic fluctuations. In the monostable zone, the small amplitude stochastic oscillations localized in the vicinity of unstable equilibrium appear along with the large amplitude oscillations near the stable limit cycle. For the analysis of these noise-induced effects, we develop the stochastic sensitivity technique and use the Mahalanobis metric in the three-dimensional case. To approximate the distribution of random trajectories in Poincare sections, we use a method of confidence ellipses. A spatial configuration of these ellipses is defined by the stochastic sensitivity and noise intensity. The glaciation/deglaciation transitions going between two polar Earth’s states with the warm and cold climate become easier and quicker with increasing the noise intensity. Our stochastic analysis demonstrates a near 100 ky saw-tooth type climate self fluctuations known from paleoclimate records. In addition, the enhancement of noise intensity blurs the sharp climate cycles and reduces the glaciation-deglaciation periods of the Earth’s paleoclimate.