Detectability of deterministic non-linear processes in Earth rotation time-series—II. Dynamics

We investigate the possibility of detecting non-linear low-dimensional deterministic processes in the time-series of the length of day (LOD) and polar motion components (PMX, PMY), filtered to keep the period range [ ≈ 1 day–100 days]. After each time-series has been embedded in a pseudo-phase space with dimension DE*=5 or 6 (see Frede & Mazzega 1999, hereafter referred to as Paper I) we extract the geometric and dynamical characteristics of the reconstructed orbit. Using a local false neighbours algorithm and an analysis of the data local covariance matrix eigenspectrum, we find a local dimension DL=5 for the three EOP series. The principal Lyapunov exponents averaged over the ≈ 27 years of observation (1970–1997) are positive. This result unambiguously indicates the chaotic nature of the Earth’s rotational dynamical regime in this period range of fluctuations. As a consequence, some theoretical prediction horizons cannot be exceeded by any tentative forecast of the EOP evolution. Horizons of 11.3 days for LOD, 8.7 days for PMX and 8.1 days for PMY are found, beyond which prediction errors will be of the order of the s of the filtered EOP series, say 0.12 ms, 2.30 mas (milliarcsecond) and 1.57 mas respectively. From the Lyapunov spectra we estimate the Lyapunov dimension DLyap, which is an upper bound for the corresponding attractor dimension DA. We find DLyap(LOD)=4.48, DLyap(PMX)=4.90 and DLyap(PMY)=4.97. These determinations are in broad agreement with those of the attractor dimensions obtained from correlation integrals, i.e. DA(LOD)=4.5–5.5, DA(PMX)=3.5–4.5, DA(PMY)=4–5. We finally show that the Earth’s rotational state experiences large changes in stability. Indeed, the local prediction horizons, as deduced from the local Lyapunov exponents, occasionally drop to about 3.3 days for LOD in the years 1982–1984, 2.6 days for PMX in 1972–1973 and 2.6 days for PMY in 1996–1997. Some of these momentary stability perturbations of the Earth’s rotation are clearly related to El Niño events, although others lack an obvious source mechanism.