From a comparison between the ILS interannual polar motion and that calculated from the ILS latitude data but with different combinations of the ILS stations, the ILS polar motion has been studied at interannual time scales. It has been concluded that the interannual polar motion reduced from the ILS observations is influenced by an unknown phenomenon of the Earth; the obtained polar motion is reflecting, at interannual time scales, the real motion of the pole at certain epochs only.

This is a special demonstration of the polar motion over the last century. Our figures represent the (xp, yp) coordinates of Earth’s axis, and the elapsed time along the z-axis. The figures remind us of a spiral spring. For the sake of illustration we used the so-called anaglif projection. Red and green glasses must be used to see the figures. The whole century (1899–1999) is too long for one diagram. So we divided the database into ten parts and present ten figures. The historic data was taken from IERS EOP C01 database and the new data from the IERS Bulletin B (1997,1998). The EOP C01 database contains only twenty (xp, yp) pairs per year. This is not sufficient for the refined representation, therefore we used the cubic spline interpolation for densification. The ten figures presented provide a quick review of the history of the polar motion over the last century: small amplitude in the twenties and thirties, with powerful fluctuation in the fifties. It is remarkable how the spiral leaves the Conventional International Origin (CIO) westwards due to the secular polar motion.

Remark: a series of figures is available upon request from the author (e-mail: [email protected]).

Conceptual models of polar motion have evolved over the past century, as improved data revealed signals over progressively wider frequency bands. In the 1890s, Chandler represented polar motion as a sum of discrete components, 14 month and annual terms, and this component model effectively summarized the observations, but did not provide a physical explanation for them. Over time both the search for a physical understanding of polar motion, and the ability to observe the broad band continuum outside the Chandler and annual bands have led to an understanding of polar motion as a continuum of variations, not adequately described by a few discrete components. The continuum concept is now the working model in most studies of polar motion. The transition from component to continuum conceptual models preceded the arrival of high quality data by several decades, and reflected significant contributions from Harold Jeffreys. With modern space geodetic observations and good global numerical models of the atmosphere, oceans, and other climate processes, it is clear that air and water motion and redistribution are the dominant contributors to the excitation continuum.

I had originally planned to focus this talk on two novel sources of Chandler wobble excitation: tectonic, associated with aseismic processes occurring for example at subduction zones; and cryospheric, associated with the transient oceanic responses to episodes of ice-cap melting. I was also asked by the conference convenors to present a brief historical review of the secular motion of Earth’s rotation pole. In the course of preparing that review, I was struck by the exceedingly controversial nature of the topic, from beginning to end; as a result, the review will be somewhat lengthy, and I will not have time to discuss cryospheric excitation of wobble.

Variations in the angular momentum of the atmosphere in the equatorial plane due to shifts in air mass distribution and changing winds impact the orientation of Earth so that motions of the pole occur on a broad range of time scales. The wind terms have notable diurnal fluctuations, which appear as a tidal signature. Subseasonal fluctuations of the pole are shown to be related to the atmospheric signal on scales as short as at least a week, according to a coherency analysis. Atmospheric mass fluctuations over certain regions, such as Eurasia and North America, appear to be more responsible for rapid polar motions than are those elsewhere, and may be related to known climate modes. On the other hand, atmospheric pressure fluctuations over the ocean are counteracted in large measure by a sea level response, due to an inverted barometer relationship. Ocean forcing from model results assist in narrowing the differences in the geodetic and atmospheric budgets. Efforts to assess dynamic forecasts of the atmospheric polar motion excitations have demonstrated positive skill out to at least 10 days for the mass term.

The analytical studies of the Chandler motion of the Earth’s pole on the basis of the special approach to the problem, using the canonical and noncanonical equations in the Andoyer elastic variables (Barkin, et al. 1995; Barkin, 1996; in press) have been fulfilled. The Earth is considered as an isolated celestial body with the anelastic (in general case) external envelope (the mantle) and an invariant central part (the core).

The interpretation of the Chandler motion of the body, deformed by its own rotation, was given in the case of an elastic envelope. It was shown that the body rotates as a fictitious rigid body with different moments of inertia. The analytical solution of the problem let us explain the next properties of the motion of the deformable bodies: 1) observed period of the Earth’s polar motion; 2) ellipticity of the pole trajectory and difference of the eccentricities of the Chandler and Euler motions; 3) nonuniform velocity of the counter-clockwise polar motion along the Chandler ellipse; 4) orientation of this ellipse (its minor axis is located in the meridian plane, at 14.5 W degrees).

The influence of the dissipation on the damping of the Chandler polar motion was studied. The analytical solution of the problem was obtained for the simplest treatment of the delay of the tides caused by the Earth’s rotation (Getino & Ferrándiz 1991; Kubo, 1991). This model explains the characteristic behaviour of the amplitude of the Chandler motion in the periods 1905–1920, 1943–1960 (Vondrák, & Cyril, 1966). The excitation of the Chandler motion can be explained by the upper and lower envelope displacements (Barkin, 1999) with Moon-Sun forced attraction with a period of 412 days, close to the Chandler period.

The redistribution of air and water masses between the Pacific and Indian oceans during the El Niño/Southern oscillation (ENSO) changes the components of the Earth’s inertia tensor and shifts the position of the pole of the Earth’s rotation. The spectrum of the ENSO has components with periods of about 6, 3.6, 2.8, and 2.4 years. These periods are all the multiples of the Chandler period T = 1.2 yr. and the principal period of nutation 18.6 yr. A nonlinear model for the Chandler polar motion has been constructed based on this empirical fact. In this model, the ENSO excites the Chandler polar motion by acting on the Earth at the frequencies of combinative resonance. At the same time, the Chandler polar motion induces a polar tide in the atmosphere and the World Ocean, which orders the ENSO. As a result, the dominant components in the noise spectrum of the ENSO are those with the periods indicated above.

Atmospheric and oceanic variability have been shown to play a role in the excitation of polar motion. Regional patterns of atmospheric and oceanic excitation are analysed and compared. The equatorial excitation functions, χ1 an χ2, for the ocean are computed using velocity and mass fields from a near-global ocean model, driven by observed surface winds stresses, surface heat and freshwater fluxes, for the period from January 1985 to June 1997. To understand the relative role of the ocean versus the atmosphere, we used atmospheric excitation functions computed from the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalyses. We consider regional mass terms [bottom pressure and atmospheric surface pressure with the inverted barometer (IB) correction] and regional motion terms as well (currents and winds). Results here confirm recent findings that oceans supplement the atmosphere as an important source for polar motion excitation. Regional signals in the oceanic bottom pressure terms have comparable amplitudes to those in the atmospheric pressure-IB terms. The regional wind term amplitudes, however, are several times larger than the values for both regional oceanic currents term and atmospheric pressure-IB term. Power in regional oceanic excitation is distributed between seasonal and subseasonal timescales while in the case of atmospheric excitation it is concentrated rather at seasonal timescales.

The Chandler wobble, one of the main feature of the Earth’s polar motion, is related to the properties of the mantle and liquid core as well as the mobility of the oceans. The equilibrium pole tide and mantle anelasticity both lengthen the Chandler period, moreover, the former imposes a slight ellipticity on the pole path, and the latter is responsible for the wobble energy dissipation. On the basis of the perturbation principles, we derive the theoretical Qω of the Chandler wobble, assuming that the wobble energy is totally dissipated within the mantle. The theoretical ellipticity and orientation of the semimajor axis of the Chandler wobble path for an anelastic Earth are given. Compared with the results for the elastic Earth, the effect of mantle anelasticity does not change the wobble ellipticity significantly, but slightly changes the orientation of the semimajor axis in the opposite direction. This paper has also proved that the effect of the Earth’s 3-axis feature on the wobble ellipticity is only about 19% of that of the equilibrium pole tide. Analysis of the polar motion data obtained by using modern geodetic techniques shows that the observed ellipticity and orientation of the semimajor axis agree with the theoretical results. We can deduce that the pole tide in the globe should be close to equilibrium.

The Hamiltonian formalism is applied to the treatment of the free motion of a three layered Earth model, where the effects of the pressure coupling, centrifugal deformation as well as gravitational and viscous-electromagnetic torques, are considered. Analytical expressions of the four normal modes of this dynamical system are derived.

Analysis of the spectral power-density function and the Poincaré method are used to identify the type of motion exhibited by the Earth’s pole from 1900–1990. The former method allows identification of a quasi-periodic regime with two main frequencies — annual and Chandler. The existence of combinational frequencies in this spectrum and the broadening of the spectral peaks suggest a quasi-periodic regime making a transition to chaos. It is concluded that the identification of the polar motion regime over the time interval considered is insufficient to predict the further evolution of the system over arbitrarily long times.

Internal links in the Earth-Moon system are determined by gravitational interaction. According to the least compulsion principle of Gauss, the deviation of “free motion” of heliocentric orbits of two material points with Earth and Moon masses is determined by the sum of the products of each material points’ deviation from its free motion and its mass.

By solving the minimization problem using the Lagrange multiplier method, Lagrange equations of the first kind were obtained in vector form. With acceptable assumptions (introduction of non-dimensional time τ = nt, where n is the sidereal rotation of the Moon, and the lunar orbit is considered to be circular) the linkage coefficient (Lagrange multiplier) is:

where v1and v2 are proper frequencies of the Earth and the Moon and μ is the Moon/Earth mass ratio.

In this paper, we introduce a nonlinear dynamical model for Chandler wobble including resonance excitation, bifurcation dissipation, frequency modulation, parameter resonance and visco-elastic long-time attenuation.

To estimate the real accuracy of EOP predictions, real-time predictions made by the IERS Subbureau for Rapid Service and Prediction (USNO) and at the IAA EOP Service are analyzed. Methods of estimating prediction accuracy are discussed.

Since 1992 the IGS ACs (International GPS Service Analysis Centers) have delivered daily estimates of polar motion (PM) and length of day (LOD) to the IERS (International Earth Rotation Service). The IGS combined PM and LOD series are available since January 1, 1995. Since June 1996 the IGS rapid and the final combined orbits are accompanied with two distinct IGS combined PM series with the same time resolution of one day. Both, the IGS final and rapid combined PM series also include combined PM rate data as well as LOD, starting in March 1997.

Since 1995 the CODE Analysis Center of the IGS has produced PM and LOD estimates with a two-hour time resolution on a routine basis. A study of the time series with sub-daily time resolution clearly shows the half-daily and daily tidal signals. The results correspond very well to those obtained from satellite altimetry.

These sub-daily time series are based on the same observational data from the IGS tracking network as those time series with a one-day time resolution. It would thus be possible with a minor analysis effort, without additional observational effort, to come up with a long and consistent series of PM and LOD with a time resolution of about 1 to 2 hours.

Since June 1992 the International GPS Service (IGS) has provided time series of its products comprising, among others, very accurate polar motion estimates. While the products of the pilot phase were based on data from about 30 permanent stations, the network now consists of about 140 globally distributed tracking sites (Neilan, 1998).

Several efforts have been undertaken at the CODE Analysis Center of the IGS aiming at the optimization of the global processing strategy, including satellite orbit and troposphere modeling. In addition, the time resolution of the ERP series has been increased to two hours or even one hour. This paper deals with sub-daily polar motion and LOD series of four months in late 1996, which have been calculated in a reprocessing step very recently. The investigations performed allow for comparisons of the new series with results stemming from intensive VLBI tracking campaigns and for the detailed study of the influence of the processing strategy and parametrization on the ERP series.

Sub-seasonal variations and especially sub-seasonal oscillations with periods of about 120, 60, 50, 40 days in polar motion and of about 120, 60–90, and 50 days in LOD are presented. Variations of amplitudes of these sub-seasonal oscillations of polar motion are shown. Maxima of these amplitudes are of the order of 2–4 mas. These oscillations are elliptical ones. The correlation coefficients between geodetic and atmospheric excitation functions in this range of the spectrum are variable and have annual variations. Maxima of correlation coefficients are of the order of 0.6–0.8.

Modern geodetic VLBI experiments provide very accurate results in polar motion and UT1–UTC with a temporal resolution of 3–7 minutes. Several irregular, quasi-periodic variations were found. In many UT1–UTC data sets, oscillations with periods around 8 hours and between 5 and 7 hours can be seen.

The 0.042-day Earth rotation data (diurnal and semidiurnal) computed by the International GPS Service were used to analyze the daily/sub-daily variations of polar motion (PM) and length of day (LOD). Systematic and advanced spectral analytical investigations of the degree of periodic variability have been carried out. They show that the prominent periodical components can be found at the tidal frequencies of zonal, tesseral and sectorial waves. These investigations should give better insight into the physical processes, which influence Earth orientation (i.e. due to the atmospheric and oceanic motions, tidal forces etc.). It should be the basis for the detailed modeling of excitation functions in the sub-diurnal range of the high-frequency spectrum.

The atmospheric effective angular momentum functions were used to study the excitation of the diurnal polar motion and nutation. The main effect on polar motion at the frequency of the S1 tide is up to 10 µas, and on the annual prograde nutation term is up to 0.1 mas. The atmosphere and viscosity of the outer core of the Earth were taken into account in calculating the transfer function.

The atmosphere treated as a thin rotating layer gives two new eigen-modes or two new resonance frequencies in the Earth’s transfer function, and one of them is in the diurnal frequency band. Viscosity of the fluid outer core and choice of the Earth’s model change the nearly diurnal frequencies of the normal modes.

The equations for the rotation of a weakly deformable celestial body in non canonical Andoyer variables have been used to study the perturbation of Earth rotation due to tidal deformation raised by the Moon and Sun. A theory of the perturbed rotational motion of an isolated weakly deformable body in Andoyer variables and in components of the angular velocity has been developed. Mantle tidal deformations due to lunar and solar influences were analytically described and taken into account. Perturbations of the first order in the Earth’s polar motion were determined.