Simple stochastic models for glacial dynamics

Glacial-interglacial events have several nonlinear and stochastic characteristics. Recent studies suggested additional stochastic nonlinear features ( not necessarily related to 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 well as (2) a wide multifractal spectrum. Realistic climate models should reproduce these properties of the natural system. We first study several previously proposed stochastic models for glacial-interglacial dynamics and demonstrate that they do not reproduce some of the nonlinear properties of the paleoclimate proxy data. We then suggest two nonlinear stochastic models for glacial-interglacial dynamics that exhibit similar stochastic nonlinear properties to those seen in the natural data. We conjecture that interaction between fast random fluctuations ( representing atmospheric variability) and slowly varying fluctuations ( representing oceanic variability) may underlie the observed stochastic nonlinearity of time series for glacial-interglacial oscillations.