Quasi-1500-Year-Cycle Signal in Length-of-Day Change

Length-of-day (LOD) change, i.e., variations in Earth’s rotation rate, includes the long-term slowdown trend, as well as periodic and irregular fluctuations. The current continuous sequence of the LOD change covers a time span of <400 years. Using astronomical records in ancient historical documents, combined with a modern astronomical ephemeris, it is possible to obtain ancient LOD change. Some scholars have given a discontinuous LOD data series for the past 4000 years. In this paper, the author uses the Lomb–Scargle periodogram to study the LOD series and finds a significant quasi-1500-year-cycle signal. Furthermore, with weighted wavelet Z-transform, time-varying characteristics of the cycle in the LOD change are obtained.

On the ~ 7 year periodic signal in length of day from a frequency domain stepwise regression method

The intradecadal variations in length-of-day (LOD) and their time-varying characteristics still need to be further studied. Given that the corresponding signal periods on the intradecadal scales are quite close to each other and the span of currently observed ΔLOD data (i.e., 1962–2019, only 57 years) is not long enough, accurate detection of these signals depends on using effective mathematical method. On the basis of the traditional harmonic retrieval model, this work proposes a frequency domain stepwise regression method, which can well identify the periodic components with close periods and recognize the weaker signals to estimate the relevant harmonic parameters (i.e., amplitude, frequency and phase). Furthermore, we apply this method to detection of the actual LOD intradecadal variations, the result of which shows that there are three components (i.e., the ~ 5.9 years, ~ 8.3 years and ~ 7.3 years) existing in LOD intradecadal variations. Here, we firstly give the time-domain harmonic expression of the ~ 7.3 years signal, i.e., $$y\left(t\right)=A\mathrm{cos}\left(\frac{2\pi }{T}\left(t-1962+\psi \right)\right)$$ y t = A cos 2 π T t - 1962 + ψ , where the period $$T=7.33$$ T = 7.33 years, amplitude $$A=0.0413(\pm 0.0099)$$ A = 0.0413 ( ± 0.0099 ) ms, phase $$\psi =-1.58(\pm 0.30)$$ ψ = - 1.58 ( ± 0.30 ) years. The mechanism of this ~ 7.3 years signal needs to be further studied.