Abstract
The power spectrum provides a compact representation of the scale dependence of the variability in time series. At multi-millennial time scales the spectrum of the Pleistocene climate is composed of a set of narrow band spectral modes attributed to the regularly varying changes in insolation from the astronomical change in Earth’s orbit and rotation superimposed on a continuous background generally attributed to stochastic variations. Quantitative analyses of paleoclimatic records indicate that the continuous part comprises a dominant part of the variance. It exhibits a power-law dependency typical of stochastic, self-similar processes, but with a scale break at the frequency of glacial-interglacial cycles. Here we discuss possible origins of this scale break, the connection between the continuous background and the narrow bands, and the apparently modest spectral power above the continuum at these scales. We demonstrate that the observed scale break around 100 ka can have a variety of different origins and does not imply an internal time scale of correlation as implied by the simplest linear stochastic model.
Highlights
The schematic picture of the climate spectrum proposed by Mitchell (1976), reproduced in Fig. 1, provides a classical, standard view of climate variability
Spectrum estimates of paleoclimate records tend to show weak astronomical modes over a dominant continuous stochastic background. While this has been noted since the seventies, it still challenges the widespread conception that glacial cycles are generated by changes in Earth’s orbit and inclination
Any satisfactory theory of Quaternary variability must explain both the weakness of astronomical modes in the power spectrum, and the existence of a crossover around 100 ka, yet be compatible with the fact that deglaciations and glacial inceptions are paced by the orbital forcing
Summary
The schematic picture of the climate spectrum proposed by Mitchell (1976), reproduced in Fig. 1, provides a classical, standard view of climate variability. The observed spectrum strongly suggests that the dynamics implies a broad band response to the narrow band forcing To approach this problem, we will illustrate the interplay between scale breaks in the continuous spectrum and spectral peaks by focusing on the range of scales imprinting the Pleistocene glacial cycles using the simplest available models of the glacial climate. After briefly reviewing some basic relations for power spectra and stochastic models, we perform simple numerical experiments with the Saltzman and Maasch (1990) limit cycle glacial model (SM90) to show that even moderate dating uncertainties, realistic for paleoclimatic records, result in substantial spectral broadening of a discrete spectrum This broadening leads to a spectrum with a scale break similar to what is seen in the estimated spectra for the paleoclimatic observations. In these stochastic models the spectrum shows a crossover at a time scale determined by a characteristic transit time
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