Detectability of deterministic non-linear processes in Earth rotation time-series - I. Embedding

Atmospheric and oceanic flows generate the main perturbations in the Earth's rotation for periods shorter than about 100 days. Both their own dynamics and the Earth's response being non-linear, we expect to find non-linear low-dimensional deterministic signatures in filtered time-series of Earth orientation parameters (EOP). Starting from daily observations of the length of day (LOD) and polar motion components (PMX, PMY) spanning more than 27 years, we apply non-linear time-series analysis techniques based on the embedding theory in order to determine the dimensional (this paper) and dynamic (Paper TT) characteristics of the sought signal source. Estimates of the time delays required to embed the scalar data time-series in a pseudophase space E* are obtained from the average mutual information function. They are of 10 days for LOD, 15 days for PMX and 18 days for PMY, The dimension D-E* Of the embedding space E* then has to be determined to unfold the expected source attractor. We try two independent determinations, based on the percentage of global false neighbours and on the correlation integrals. We obtain embedding dimensions between 5 and 7 for the three EOP time-series. The robustness of the results with regard to various data contaminations and series degradations is checked throughout. Finally, 3-D projections of delayed coordinate data vectors are drawn. They are clearly different from stochastic power-law noise and seem to issue from a smooth dynamical system whose dynamical characteristics are investigated in Paper II.