A preliminary nonlinear analysis of the earth's chandler wobble

The Chandler wobble (CW) is a resonant response of the Earth rotational pole wandering around its figure axis whose excitation mechanism is still uncertain. It appears as polar motion oscillations with an average period of about 433 days and a slowly varying amplitude in the range (0–300) milliarcsec (mas). We here perform a nonlinear analysis of the CW via a time-delay coordinate embedding of its measured X and Y components and show that the CW can be interpreted as a low dimensional unstable deterministic process. In a first step the trend, annual wobble and CW are separated from the raw polar motion data time series spanning the period 1846–1997. The optimal delays as deduced from the average mutual information function are 105 and 115 days for the X and Y components respectively. Then from the global statistics of the false neighbours, the embedding dimension D E = 4 is estimated for both series. The local dimension D L can also be extracted from the time series by testing the predictive skill of local mappings fitted to the embedded data vectors. The result D L = 3 is quite robust and corroborate the idea that the CW behaves like a dissipative oscillator driven by a deterministic process. Indeed the orbit reconstructions in pseudo-phase space both draw the figure of a perturbated 1-torus. The computation of the Lyapunov spectra further shows that this torus-like figure is an attractor with a 1D unstable manifold. The theoretical horizons of prediction deduced from the (positive) principal exponents are about 367 and 276 days for the X and Y Chandler components respectively. Moreover the local Lyapunov exponents exhibit significant variations with maxima (and corresponding losses of predictibility) in the decades 1860–1870 and 1940–1950.