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. Specifically, the last glacial period is characterised by Dansgaard-Oeschger events, with rapid and frequent transitions between stadial and interstadial regimes, and it was suggested that climate changes were then exhibiting multi-fractal dynamics. The present contribution clarifies the interpretation of detrended fluctuation analysis and of power spectra during the last glacial period. We use two simple models exhibiting regime behaviour reminiscent of Dansgaard-Oeshger dynamics: the random telegraph process with additive white Gaussian noise, and Stommel-Cessi’s box model of thermohaline circulation (a study of the Lorenz model is also proposed in the appendix). This analysis then provides a support for interpreting the generalized Hurst exponent h(q) and power-spectrum estimates of two NGRIP (Greenland) ice core records: the oxygen isotope ratio and the calcium ion concentration. We also analyse simulations with a stochastic dynamical system model with ice and astronmical forcings, which we recently proposed to simulate Dansgaard-Oeschger events. Multifractal detrended fluctuation analyses of time series generated by the toy models reveal that their generalized fluctuation functions have a local scaling regime. The generalized Hurst exponent h(q) is lower for q<<0 than for q>0. This dependency of h(q) is named here “apparent multifractality”. It occurs because the behaviour of the autocorrelation function of small fluctuations (within a regime) differs from that of large fluctuations (regime shifts). The generalized Hurst exponents of NGRIP records exhibit a form of apparent multifractality similar to that described in the toy models. The stochastic dynamical system model also captures both the power spectrum of the observations, and the behaviour of h(q). The apparent multifractality of the Dansgaard-Oeschger events records is a consequence of regime switching between stadial and interstadial climates. 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.