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We analyse phase lags between the 11-year variations of three records: the semi-annual oscillation of the
length of day (LOD), the solar activity (SA) and the cosmic ray intensity (CRI). The analysis was done for solar cycles 20–23. Observed relationships between LOD, CRI and SA are discussed separately for even and odd solar cycles. Phase lags were calculated using different methods (comparison of maximal points of cycles, maximal correlation coefficient, line of synchronization of cross-recurrence plots). We have found different phase lags between SA and CRI for even and odd solar cycles, confirming previous studies. The evolution
of phase lags between SA and LOD as well as between CRI and LOD shows a positive trend with additional variations of phase lag values. For solar cycle 20, phase lags between SA and CRI, between SA and LOD, and between CRI and LOD were found to be negative. Overall, our study suggests that, if anything, the length of day could be influenced by solar irradiance rather than by cosmic rays.

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... The nature of irregular or aperiodic oscillations is still not clear. It is believed that they can be caused by currents in the liquid core of the Earth [3] [4] or variations of the Solar Wind [5]. ...

The extreme acceleration of the Earth rotation observed in the summer of 2020 is considered. It is concluded that this phenomenon is a consequence of two factors: the longterm acceleration of the Earth rotation, which has been observed since the 1970s, and the extremely strong meteorological excitation of the LOD, which took place in the summer of 2020. The coincidence of the anomaly of the AAM and the geomagnetic Dst index, as well as the correlation between the LOD on the one hand and the solar wind speed and the Gaussian coefficients of the expansion of the Earth’s magnetic field, on the other, are noted. The problem of negative leap second is considered. Preliminary estimates have been made of introduction of a negative leap second, if the current trends in the behavior of UT1-UTC continue. The conclusion is made about the low probability of such an event.

... On the other hand, when we see that the yearly change of the Sun's magnetic field is noticeable, then we can deduce a direct relation between the solar cyclical activity and cosmic radiation. Of course, the correlation of the solar activity and cosmic ray has been revealed by scientists before and we may refer to the Balasubrahmanyan (1969) and a newly analysis by Barlyaeva et al. (2014). Strongly, emissions of the matter and electromagnetic fields from the Sun increase during high solar activity, making it harder for Galactic cosmic rays to reach Earth. ...

We report phenomenological inevitable correlation between the Sun’s magnetic field oscillation through the Earth and the Jupiter, with sinusoidal geomagnetic jerks observed at the Earth, additionally aligned with the gravity and length of day sinusoidal variations and we observe too that the Sun and Jovian planets alignments with Jupiter are origin of the observable abrupt geomagnetic jerks whether historical or new, and experimental results demonstrate a possible explanation on the base of the planetary induced currents upon the metallic liquid cores of the planets upon the varying external magnetic fields as the source of heat flows continued by frictional turbulent and convectional fluid fluxes, amplified and expanding by the Earth magnetic field and observations are showing too that it should be an electric coupling effect between metallic cores of the planets, under the magnetic field oscillation so that Jupiter conductive metallic region interacts with Earth metallic core while the Sun’s magnetic field is oscillating through the Jupiter and we see a relation between secular variation of the Earth’s magnetic field and long term trend of 5.9-years signals as a new method to measure geomagnetic secular variation by LOD signals.

... Recently paper [26] discussed the quasi-periodicity in connection with solar activity and CR. ...

Cosmic rays (CR) play an important role in space weather-related studies. Their temporal variability, both of a quasi-periodic character as well as an irregular one, has been studied from ground-based direct measurements, as well as from cosmogenic nuclides, over a long time. We attempt to describe the current knowledge of selected quasi-periodicities in CR flux in the energy range above the atmospheric threshold, from direct measurements. The power spectrum density (PSD) of the CR time series as measured by neutron monitors (NMs) and by muon detectors has a rather complicated character. Along with the shape (slope) of the PSD, knowledge of the contribution of quasi-periodic variations (q-per) to the CR signal is of importance for the modulation, as well as for checking the links of CR to space weather, and/or to space climate effects. The rotation of the Earth and solar rotation cause two types of mechanisms behind the certain q-per observed in secondary CR on the Earth’s surface. Solar activity and solar magnetic field cyclicities contribute to the q-per signals in CR if studied over a longer time. The complexity of the spatial structure of the interplanetary magnetic field (IMF) and its evolution within the heliosphere, in addition to the changes in the geomagnetic field, cause variability in contributions of the q-per in CR. Wavelet spectra are useful tools for checking the fine structure of q-per and their temporal behaviour. Over a long time NMs and muon telescopes provide information about q-per in CR. © 2015 Science China Press and Springer-Verlag Berlin Heidelberg

The correlation between the solar activity cycles and the Earth rotation is investigated by means of UT1 series from the solution C04 of the IERS. The different oscillations of the Earth rotation are separated by an approximation of the difference UT1-TAI for the period 1962-2006, which includes power polynomials of degree up to 3, main oscillations with periods 22a, 18.6a, 12a, 6.75a, 1a and their harmonics. The UT1-TAI oscillations at solar activity frequencies are approximated with step-variable periods as follow: 11.1a for UT1 data before 1977.5; 10.3a for data between 1977.5 and 1987.8; 9.7a for data between 1987.8 and 1997.5; and 10.0a for data after 1997.5. The step-variable periods yield better approximation of the Earth rotation response to different solar activity cycles. The estimated UT1-TAI oscillations at solar activity frequencies are highly-correlated with the smoothed values of the Wolf's numbers with mean delay of about 1.5a.

The annual and semiannual residuals derived in the axial angular momentum budget of the solid Earth-atmosphere system reflect significant signals. They must be caused by further excitation sources. Since, in particular, the contribution for the wind term from the atmospheric layer between the 10 and 0.3 hPa levels to the seasonal variations in length of day (LOD) is still missing, it is necessary to extend the top level into the upper stratosphere up to 0.3 hPa. Under the conservation of the total angular momentum of the entire Earth, variations in the oceanic angular momentum (OAM) and the hydrological angular momentum (HAM) are further significant excitation sources at seasonal time scales. Focusing on other contributions to the Earth's axial angular momentum budget, the following data are used in this study: axial atmospheric angular momentum (AAM) data derived for the 10-0.3 hPa layer from 1991 to 1997 for computing the missing wind effects; axial OAM functions as generated by oceanic general circulation models (GCMs), namely for the ECHAM3 and the MICOM models, available from 1975 to 1994 and from 1992 to 1994, respectively, for computing the oceanic contributions to LOD changes, and, concerning the HAM variations, the seasonal estimates of the hydrological contribution as derived by Chao and O'Connor [(1988) Geophys J 94: 263-270]. Using vector representation, it is shown that the vectors achieve a close balance in the global axial angular momentum budget within the estimated uncertainties of the momentum quantities on seasonal time scales.

The Earth does not rotate uniformly. Not only does its rate of rotation vary, but it wobbles as it rotates. These variations in the Earth's rotation, which occur on all observable timescales from subdaily to decadal and longer, are caused by a wide variety of processes, from external tidal forces to surficial processes involving the atmosphere, oceans, and hydrosphere to internal processes acting both at the core-mantle boundary as well as within the solid body of the Earth. In this chapter, the equations governing small variations in the Earth's rotation are derived, the techniques used to measure the variations are described, and the processes causing the variations are discussed.

A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El NiñoSouthem Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmöller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of changes in ENSO variance on interdecadal timescales. Using new datasets that extend back to 1871, the Niño3 sea surface temperature and the Southern Oscillation index show significantly higher power during 1880-1920 and 1960-90, and lower power during 1920-60, as well as a possible 15-yr modulation of variance. The power Hovmöller of sea level pressure shows significant variations in 2-8-yr wavelet power in both longitude and time.

Historical to up‐to‐date data of the minute variations in the solid Earth's rotation are subjected to a comprehensive time‐frequency wavelet analysis. The length‐of‐day for the period 1962–2012 confirms the presence of a prominent, robust 6‐year periodicity and reveals an anomalously strong 18.6‐year tidal oscillation as well as a ~13‐year quasi‐periodic signal. The polar‐motion excitation for the period 1900–2012 validates the existence of the ~26‐year Markowitz wobble and shows an ~8‐year quasi‐periodic signal, but no appreciable 18.6‐year periodicity. Although it is known that exchanges of angular momentum with the geophysical fluids are responsible for the rotational variations of the solid Earth, the exact physical mechanisms involved on interannual‐to‐decadal timescales are still far from understood.

The solar “constant” varies over time scales from minutes to years and decades. For the influence on the atmospheric energy budget time scales longer than a few days become important, for climate research information over years to decades is needed. From direct measurements of the solar “constant” during the last 10 years, by e.g. the ACRIM experiment on the Solar Maximum Mission satellite (SMM), one indeed becomes aware of substantial changes on time scales longer than days. The most important influences seem to be related to solar activity.

In the processing of the data obtained by the "prototype" little astrolabe and later by the OPL astrolabe, A. Danjon found large anomalies he attributed to solar activity. Over the following years his results were strongly controversed. In the present paper, the author first briefly presents the method used by A. Danjon and secondly the analyses he has performed over the same interval using OPL astrolabe and Ottawa PZT data. Although his results partly agree with Danjon ones, his explanation is different. Like all variations ranging from one day to about two years, this large oscillation can be attributed with certainty to atmospheric circulation.