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.