Orbital forcing and endogenous interactions: Non-linearity, persistence and convergence in late Pleistocene climate

Abstract

The succession of ice ages and interglacials during the late Pleistocene has been linked with changes in the eccentricity, obliquity and precession of the earth's orbit. The combined effect of orbital cycles with different periodicities argues that climate should exhibit both persistence — significant dependence between observations at distant intervals — and non-linearity. At the same time, a significant component of climatic variation derives from endogenous interactions which exhibit non-linear properties at both higher and lower frequencies than the orbital variations. In order to analyze the effect of orbital shifts and endogenous interactions, climate is factored into an orbitally forced and a residual component. The component explained by orbital forcing shows some evidence of non-linearity, strong dependence between observations over the first 10 ka, and additional dependence between observations at frequencies corresponding to the orbital cycles. The residual component shows greater dependence between observations over the first 20 ka, some evidence of dependence at the orbital cycles, and significantly greater degrees of non-linearity. Neither shows evidence of actual chaoticity. The climatic residual generally moves in the same direction as the path implied by orbital forcing, meaning that endogenous interactions reinforce and accentuate changes in climate implied by orbital shifts. Despite the high variability of the residual, orbital forcing acts as a long-run attractor both for temperature and for atmospheric CO 2. Actual temperatures converge to the path implied by orbital forcing, on average within a period of 7.14 ka. Because orbital forcing is a long-term attractor for temperature but short-term movements show strong serial dependence, the best forecasts for Pleistocene climate are obtained from a model including distributed lags of both orbital shifts and temperature.