Orbital Forcing and Endogenous Nonlinearity in the Pleistocene: The Greenland Ice Core

The succession of ice ages and interglacials during the Pleistocene is understood to have been caused primarily by shifts in the earth's orbit. At the same time, there is evidence of high variability in climate at suborbital frequencies. This paper conducts a statistical analysis of Pleistocene climate using the Greenland Ice Core Research Project (GRIP) data. Factoring temperature into the component explained by orbital forcing and a residual demonstrates that variations at suborbital frequencies are nonlinear and aperiodic. There is evidence of a regular cycle at 7.9 kyr, evidently a subharmonic of the orbital frequencies. Apart from this, however, the proximate memory of both the actual data and the residual decays slowly over a period of 15 kyr. Residual variations in temperature show two prominent features, alternating periods of high and low volatility, and states of distance from and proximity to the path implied by orbital forcing. A parametric model incorporating both of these properties is fit to the data, and is found to significantly improve the forecastability of climate. Transitions between states of proximity and distance from the orbital path can be partially predicted using the statistical model.