Understanding nonlinear responses of the climate system to orbital forcing

We have recently introduced the working hypothesis that frequency modulation (FM) of the orbital eccentricity forcing may be one important source of the nonlinearities observed in delta O-18 time series from deep-sea sediment cores (J.A. Rial (1999a) Pacemaking the Ice Ages by frequency modulation of Earth's orbital eccentricity. Science 285, 564-568.) In this paper we shall discuss further evidence of frequency modulation found in data from the Vostok ice core. Analyses of the 430,000-year long, orbitally untuned, time series of CO2, deuterium, aerosol and methane, suggest frequency modulation of the 41 kyr (0.0244 kyr(-1)) obliquity forcing by the 413 kyr-eccentricity signal and its harmonics. Conventional and higher-order spectral analyses show that two distinct spectral peaks at similar to 29 kyr (0.034 kyr(-1)) and similar to 69 kyr (0.014 kyr(-1)) and other, smaller peaks surrounding the 41 kyr obliquity peak are harmonically (nonlinearly) related and likely to be FM-generated sidebands of the obliquity signal. All peaks can be closely matched by the spectrum of an appropriately built theoretical FM signal. A preliminary model, based on the classic logistic growth delay differential equation, reproduces the longer period FM effect and the familiar multiply peaked spectra of the eccentricity band. Since the FM effect appears to be a common feature in climate response, finding out its cause may help understand climate dynamics and global climate change. (C) 2000 Elsevier Science Ltd. All rights reserved.