PLIOTOCENE PLEISTOCENE CLIMATE MODELING BASED ON OXYGEN-ISOTOPE TIME-SERIES FROM DEEP-SEA SEDIMENT CORES - THE GRASSBERGER-PROCACCIA ALGORITHM AND CHAOTIC CLIMATE SYSTEMS

The question whether paleoclimatic systems are governed by a small num ber of significant variables (low-dimensional systems) is of importanc e for modeling such systems. As indicators for global Plio-/Pleistocen e climate variability, four marine, sedimentary oxygen isotope time se ries are analyzed with regard to their dimensionality using a modified Grassberger-Procaccia algorithm. An artificial, low-dimensional chaot ic time series (Henon map) is included for the validation of the metho d. In order to extract equidistant data the raw data are interpolated with the Akima-subspline method since this method minimizes the change in variance due to the interpolation. The nonlinear least-squares Gau ss-Marquardt regression method is used instead of the linear least-squ ares fit to the logarithmically transformed points, in order to acquir e an unbiased estimate of the correlation dimension. The dependences o f the estimated correlation dimension on the embedding dimension do no t indicate a small number (i.e., less than 5) of influencing variables on the investigated paleoclimatic system, whereas the low dimension f or the Henon map is verified (dimension 1.22-1.28). Because of the lim ited amount of data in the oxygen isotope records, dimensions greater than about 5 cannot be examined.