On the nonstationarity of the decadal periodicities of the length of day

The Earth's rotation rate is not constant, but changes on all observable timescales, from subdaily to decadal and longer. These variations are usually discussed in terms of variations in the length of the day (LoD) and are caused by processes acting within the interior, at the surface and outside of the Earth. Here, we investigate the presence of long-standing decadal variations in yearly LoD data covering the period from 1832 to 2009 by applying the Hilbert–Huang transform (HHT). The HHT has been slightly modified here to take into account the uncertainty of LoD values that has changed greatly in time due to the use of different LoD measurement techniques. The LoD time series has been completely decomposed into five intrinsic mode functions (IMF) and a residual trend. The estimation of instantaneous frequencies and related amplitudes of the obtained IMFs has allowed us to compute the Hilbert spectrum that has been used as the starting point for studying and discussing the stationarity of typical LoD timescale stationarity. The obtained results while showing the presence of multiple periodicities also indicate the absence of really stationary periodicities. Therefore, rather than considering the processes taking place in the Earth's core as the result of a superposition of oscillations (i.e. stationary mechanisms) occurring on a discrete number of different timescales, it would be better to think of a superposition of fluctuations that are intermittent in both frequency and amplitude.