Nonlinear comparative analysis of Greenland and Antarctica ice cores data.

We analyze the temperature time series of the EPICA Dome C ice cores in Antarctica and of the Greenland project, Summit, with durations of 800 000 and 248 000 years, respectively, with a recent mathematical tool defined through the Fourier phases of the series, known as the J-index. This data driven index can differentiate between purely random dynamics and dynamics with a deterministic component. It is sensitive to nonlinear components and robust to the presence of noise. Our J-index data analysis shows that both Greenland and Antarctica climatic fluctuations possess deterministic traits and suggests the presence of an underlying nonlinear dynamics. Furthermore, in both regions, it reveals the simultaneous occurrence of an important global event known as the "Pelukian transgression." For Antarctica, it also detects the marine isotopic stage 11. Additionally, our calculation of the time series Hurst exponents and our detrended fluctuation analysis show the presence of long-range persistent correlations for Antarctica and anti-persistent correlations for Greenland. For the latter case, our fractal dimension determinations are indicative of a more complex climatic dynamics in Greenland with respect to Antarctica. Our results are encouraging for further development of climate variability deterministic models for these regions.