Simple stochastic models for glacial dynamics

Glacial-interglacial events have several nonlinear and stochastic characteristics.Recent studies suggested additional stochastic nonlinear features (not necessarily relatedto the large-scale dynamics of the glacial cycle) in the timescale of 1–100 kyr including(1) strong long-range correlations in the magnitude of climate variable increments as wellas (2) a wide multifractal spectrum. Realistic climate models should reproduce theseproperties of the natural system. We first study several previously proposed stochasticmodels for glacial-interglacial dynamics and demonstrate that they do not reproduce someof the nonlinear properties of the paleoclimate proxy data. We then suggest two nonlinearstochastic models for glacial-interglacial dynamics that exhibit similar stochastic nonlinearproperties to those seen in the natural data. We conjecture that interaction between fastrandom fluctuations (representing atmospheric variability) and slowly varying fluctuations(representing oceanic variability) may underlie the observed stochastic nonlinearity oftime series for glacial-interglacial oscillations