Application of spectra-temporal analysis methods to detect common signals in length of day, global sea level rise, global temperature data, and ENSO indices

It is already well known that intra-seasonal oscillations in the Earth’s global temperature are driven by ENSO (El Niño Southern Oscillation) events. ENSO signal is also present in length of day and global sea level rise, because during El Niño the increase of the length of day and global sea level rise can be noticed. To detect common oscillations in length of day, global sea level rise, global temperature data and ENSO indices the wavelet-based semblance filtering method was used. This method, however, seeks the signals with a good phase agreement of oscillations in two time series thus, no phase agreement results in very small amplitudes of the common signals. The spectra-temporal semblance functions allow detecting the similarity of two time series in spectral bands in which the amplitudes and phases of the oscillations are consistent with each other. The amplitudes of oscillations in the considered data vary in time and in order to detect the signals with similar amplitude variations between pairs of time series the normalized Morlet wavelet transform (NMWT) and the combination of the Fourier transform bandpass filter with the Hilbert transform (FTBPF+HT) were used. These two methods enable computation of the instantaneous amplitudes and phases of oscillations in two real-valued time series. In order to detect oscillations with similar amplitude variations in two time series correlation coefficients between the amplitude variations as a function of oscillation frequencies were computed.