Scale invariance in long-term time series. In: M. Novak, (Ed.) Fractal Reviews in the Natural and Applied Sciences

The 15 SPECMAP records of reconstructed paleotemperatures, the GRIP isotopic oxygen record, and the extended Vostok ice-core temperature and air composition records are analysed in terms of structure functions. The range of analysed time scales is 100-200,000 years. It is shown that the characteristic fluctuations of temperature, CO2 and CH4 concentrations follow a scale invariant law up to time scales of about 10,000 years; the parameters of structure functions depend upon site location. Although different sites yield different slopes, there is a clear evidence for a break in the scaling at time scales of about 10,000--19,000 years at high latitudes and of about 6,000 years in the equatorial belt. At timescales longer than the upper scaling limit and up to 200,000 years the characteristic temperature variations are quasi-stationary. In this regime, the temperature fluctuations at different latitudes are determined by orbital cyclicity.

The scaling regime of the structure functions describes the random part of climate variability: in the range of time scales where the scale invariant law holds, the climatic system has no characteristic time scale, and the climate changes result from the accumulation of random fluctuations. The break of scaling signifies the appearence of the basic periods in climate system and identifies the boundary between the random and deterministic regimes in the scale space. In the equatorial sites, the earlier break of scaling and the scaling exponent lower than 0.5 (antipersistence), together a relatively small range of characteristic temperature fluctuations, indicate a governing role of stabilizing mechanisms (negative feedbacks) in tropical climate.