Is the glacial climate scale invariant?

Previous estimates of the power spectrum and of the scaling exponent of the detrended fluctuation analysis of palaeoclimate time series yielded the suggestion that climate fluctuations are scale invariant over a wide range of time scales. The present contribution clarifies the implications of these findings, with focus on the last glacial period. The last glacial period is characterised by Dansgaard-Oeschger events, with rapid and frequent transitions between stadial and interstadial regimes. We therefore consider three simple models known to display regime switching dynamics. Multifractal detrended fluctuation analyses of time series generated by these models reveal that their generalized fluctuation functions have a local scaling regime, with generalized Hurst exponent h(q) being lower for q 0. Such dependency of $h(q)$ is qualified here as apparent multifractality. It occurs because the behaviour of the autocorrelation function of small fluctuations (within a regime) differ from that of large fluctuations (regime shifts). It turns out that the generalized Hurst exponent of the oxygen isotope ratio and that of the calcium ion concentration in the NGRIP (Greenland) record exhibit a similar form of apparent multifractality. We then verify that a stochastic model previously used to simulate Dansgaard-Oeschger events, and which also displays regime switching dynamics, generates a generalized Hurst exponent and a power spectrum consistent with the observations. We therefore conclude that the apparent multifractality of these records is a consequence of regime switching between stadial and interstadial climates, and that neither the local scaling in the power spectrum, nor the output of the multifractal detrended fluctuation analysis implies that the underlying process is scale invariant