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Two main features define a sunspot as an object: a strong magnetic field and a low umbra temperature. The same can be said about a facular knot, in the center of which there is a dark micropore, and the magnetic field is several hundred Gauss (which noticeably exceeds the level of equipartition of about 200–250 G), sometimes reaching 1000 or 1200 G. The temperature decrease in these activity elements is explained by the suppression of circulation (overturning) convection by a strong vertical magnetic field. The first to express this idea was Biermann (1941). Within the framework of this conception, a saturation effect should be expected: when the magnetic field completely suppresses convection, its further growth should not lead to a decrease in temperature. There is still no clear answer to the question of the saturation effect. We will try to answer it in the first part of the work according to the Solar Dynamics Observatory. We show that saturation occurs at B = 2300–2400 G. A further increase in the magnetic field of the spot no longer leads to a decrease in the brightness of its umbra. The relationship of the magnetic field and intensity is also manifested in long-period oscillations of the magnetic field of spots. In this case, the brightness of the spot umbra changes in antiphase with its magnetic field (Efremov et al., 2020) in accordance with the theoretical model of a shallow sun spot (Solov’ev and Kirichek, 2014, 2016). A similar effect was established by us in the second part of this work for facular knots: during slow facular oscillations with periods of more than 1 h, its brightness changes in antiphase with a magnetic field. The obtained results convincingly confirm the Birman hypothesis.

The relationships between different manifestations of solar and geomagnetic activity and the structural peculiarities of the dynamics of the pole wobble and irregularities in the Earth’s rotation are studied using singular spectrum analysis. There are two close major peaks and several lower ones in the same frequency range (1.1–1.3 years) in the Chandler wobble (CW) spectrum. Components in the geomagnetic activity were distinguished in the same frequency band (by the Dst and Ap indices). Six- to seven-year oscillations in the Earth’s rotation rate with a complex dynamics of amplitude variations are shown in variations in geomagnetic activity. It is revealed that secular (decade) variations in the Earth’s rotation rate on average repeat global variations in the secular trend of the Earth’s geomagnetic field with a delay of eight years during the whole observation period.

The work studies the Chandler component of polar motion, obtained from variations in the Pulkovo latitude over 170 years (1840–2009). To extend the time series of variations in the Pulkovo latitude back into the past until 1840, we used the first Pulkov observations on the basis of the Reynolds transit instrument in the prime vertical and on the basis of large vertical Ertel circle. We employed different methods of analysis of nonstationary time series, such as wavelet analysis, methods of bandpass filtering, singular spectral analysis, and Fourier and Hilbert transforms. Changes in the Pulkovo latitude from 1904–2006, as inferred from ZTF-135 observations and as calculated from international data, were compared. It was shown that time changes in the amplitude and phase of Chandler polar motion can be studied based on long-term observation time series of latitude at a single observatory, even if these observation records have gaps. We were the first to study the changes in the Chandler wobble for that long time series of variations in the Pulkovo latitude with the help of different methods. The long observation record and the methods of analysis of nonstationary time series had allowed us to identify two similar structures, both well apparent during the periods of 1845–1925 and 1925–2005 in the time variations of phase and amplitude. The presence of this structure indicates that low-frequency regularities may be present in the Chandler polar motion, and one of the manifestations of this may be the well known feature in the region of 1925. The superimposed epoch method was used to estimate the period of variations in the amplitude with a simultaneous change of phase of this oscillation, which was found to be 80 years. In addition, advantages of singular spectral analysis for studying the long-period time series with involved structure are demonstrated.

Pulkovo astrometric observations began in the 1840s using the Repsold transit instrument in the prime vertical and Ertel vertical circle. The first observers on these instruments were W.I. Struve, 1840–1856, and Kh.I. Peters, 1842–1849. In the present work, we collected and analyzed different series of latitude variations from observations made by M.O. Nuren, B. Wanach, A.A. Ivanov, I.N. Bonsdorf, and A.Ya. Orlov. In addition, results are given of investigations of a specific behavior of the Chandler polar motion in this interval, obtained by C. Chandler, Ivanov, Kh. Kimura, Orlov, and N. Sekiguchi. The aim of this paper is to search for and analyze the earliest series of Pulkovo latitudes, in order to evaluate the possibility of their use to study the motion of the pole at the maximum available range of observations. Different methods were used to isolate and analyze the sum of Chandler and annual latitude variations. The annex provides a series of Pulkovo latitude variations for 1840–1848, which may be used to extend latitude variation back to 1840.

The paper presents the possibilities of the Singular Spectrum Analyses on the examples of its application to several astrometric and geodynamic time series. The comparisons of results obtained by other often used methods (Fourier transform, Wavelet Transform, different filter methods) are given. The Singular Spectrum Analyses method was used for the investigation of the Chandler wobble (CW), which was extracted from the IERS Pole coordinates and latitude variations at Pulkovo. The CW amplitude and phase variations were examined by means of the Hilbert transform. The main conclusion which can be made from this study is: we have found two epochs of deep CW amplitude decreases near 1850 and 2005, which are also accompanied by a large phase jump, similar to well known event in 1920s. The investigation of first latitude observations at Pulkovo (1840–1855) was executed with the aim to gain and analyse the sum of Chandler and annual components from very small quantity of very noisy observations. The SSA is applied for investigation of the zenith troposphere delay time‐series derived from observations of several VLBI stations. Combined IVS time‐series of the zenith wet and total troposphere delays obtained in IGG were used for analysis. For all stations under consideration the non‐linear trends and the seasonal components with annual and semiannual periods were found. Some interesting peculiarities were found to be individual for every stations. Comparison of the trends with meteorological parameters is also presented.