The USNO combined solution for Earth rotation parameters, commonly known as CORE has recently been made more sensitive to high-frequency signals in the various types of input data. This is particularly important in the estimation of the variation in UT1—UTC which has recently been shown to have real fluctuations over time intervals of less than a week. A second modification was introduced to tailor the data smoothing to the particular noise characteristics of the individual techniques. This has resulted in a redistribution of the weights of these techniques, and in improved time-resolution and accuracy of the CORE solution.

Polar motion data for the period 1981–1985 are used to obtain a combined solution from Doppler, Satellite Laser Ranging, and Astrometric observations. The combined solution is a weighted average of the three series, with weights determined from reported errors which are scaled so that they agree with errors estimated from differences among the various series. The combined solution is effective in removing spurious deviations in the pole path which appear in a single series. However, we also show that estimated errors can be unreliable when derived from short time series, when one series is much less noisy than the others. Thus, a combined solution where weights depend upon estimated errors can yield poor results, and we demonstrate this effect by comparing a combined solution for 1984–85 with the independent IRIS series.

The orientation of the earth in space changes unpredictably in a rapid and irregular manner, in addition to the uniform rotation of the earth. Observations of extra-terrestrial objects from the surface of the earth are affected by these variations, and knowledge of these changes is required for a variety of geodetic and astrometric purposes as well as being of interest in its own right. The orientation of the earth (specified by a three dimensional rotation vector) is measured by a variety of techniques; combination of these data sets is complicated by irregular changes in the spacing and accuracy of the various time series, and also by the existence of lower dimensional measurements of different linear combinations of the rotation vector components. A Kalman filter has been developed at JPL to smooth and predict earth orientation changes for application to spacecraft navigation by the NASA Deep Space Network. The filter, which provides estimates of the earth orientation changes (and of the excitation of these changes) based on whatever measurements are available, has been used for a number of research applications, both in the reduction of geodetic and astrometric data, and in research into the geophysical causes of earth orientation changes. The JPL Kalman filter uses stochastic models to account statistically for otherwise unpredictable changes in earth orientation; these models make it possible to provide reasonable estimates of the error in the smoothed time series, and to automatically vary the amount of smoothing according to the accuracy and density of the data. The derivation of the stochastic models used by the filter, the implementation of the models into the filter, a statistical description of what the filter does, and the results of filtering specific data sets will be discussed.

Autoregressive prediction filters are tested on stationarised time series of UT1–TAI and of accumulated values of the duration of the day derived from the axial atmospheric angular momentum.

Predictions of Earth orientation parameters are affected by the accuracy of the input data, the quality of the statistical models, and the delay between the last observed data and the date of the first prediction. The accuracy of the prediction of polar motion is adequate to meet most user needs, but the prediction of UT1-UTC is more difficult. Extended forecasts of polar motion and the rotational time can also be made with useful accuracies.

The most important factor in getting accurate predictions of Earth orientation parameters (EOP) is choosing suitable input data. Also, we must choose a proper statistical model for the noise in these data. The weights of the data are determined on the basis of these models. Finally, we must determine suitable values of parameters in the computation of EOP predictions.

A new approach to forecasting changes in length-of-day (δl.o.d) with lead times from one to ten days is examined. The approach is based on the high correlation that has been shown to exist between high frequency changes in l.o.d. and those in the atmosphere's angular momentum (M). Because forecasts of tropospheric values of M can be calculated from the zonal wind fields produced by operational numerical weather prediction models, it seems worth investigating whether these forecasts are sufficiently skillful to use to infer the evolution of δl.o.d. Here, we examine the quality of M forecasts made by the Medium Range Forecast (MRF) model of the U.S. National Meteorological Center (NMC). By comparing these forecasts against those based on a simple model of persistence, we find that skillful forecasts of M are being achieved on average by the MRF, although there has been much month-to-month variability in forecast quality. Overall, our results indicate that for prediction lead times of 1–10 days, dynamically-based forecasts of δl.o.d. represent a viable alternative to the empirical approaches currently in use.

It has long been appreciated that atmospheric motions must contribute to the excitation of fluctuations in the Earth's rotation (Munk and MacDonald 1960, Lambeck 1980, Rochester 1984) but the exploitation of modern meteorological data, collected largely to meet the demands of daily global weather forecasting, in the routine evaluation of angular momentum exchange between the atmosphere and the solid Earth was not initiated until comparatively recently (Hide et al. 1980). This procedure constitutes a necessary step towards the accurate separation of these features of the observed non-tidal changes in the length of day and polar motion and that are of meteorological origin from those that must be attributed to other geophysical processes, such as angular momentum transfer between the solid Earth and other fluid regions of the Earth (liquid metallic core, oceans, etc.), and to changes in the inertia tensor of the solid Earth associated with earthquakes, melting of ice, etc.

The U.S. Naval Observatory is responsible for the determination and prediction of UT1-UTC. An investigation was begun to determine if atmospheric angular momentum (AAM) data could be useful in the National Earth Orientation Service (NEOS) combined solution and in the prediction of UT1-UTC. The investigation found AAM data to be useful possibly in the combined solution, but predictions of UT1-UTC were adversely affected when predictions of AAM data were introduced.

We analyzed six years of very–long–baseline interferometry (VLBI) data and determined corrections to the coefficients of the seven terms with the largest amplitudes in the IAU 1980 nutation series. Our analysis yields results consistent with earlier analyses of smaller sets of VLBI data, within the uncertainties of the latter. Here, we restrict discussion to the freely excited core–nutation or “free core–nutation” (FCN). Our analysis yields an estimate of 0.33 ± 0.12 mas for an assumed constant amplitude of the FCN, which allows us to place an upper bound on it of 0.6 mas (99.5% confidence limit). We also studied possible temporal variations of the complex amplitude of the FCN by modeling it as a stochastic process with a white noise excitation. We detected no statistically significant variations of this amplitude for the six–year interval spanned by the VLBI data. However, in the neighborhood of one cycle per day, the power spectral density of the atmospheric surface loading is estimated from global weather data to be 0.24 (g cm−2)2 day, about five times larger than the largest such power spectral density that would be consistent with the upper bound on the amplitude of the FCN placed by the VLBI data. Thus, we conclude that this estimate is too high and that, if the FCN were excited by surface loads with frequencies near one cycle per day, then the power spectral density of these loads must be <0.06 (g cm−2)2 day (99.9% confidence limit).

Previous analyses of nutation angle errors from Mark III VLBI data have been made by estimating offset corrections to the instantaneous nutation angles from single-day observing sessions. Adjustments to the coefficients of the nutation model were then estimated from the time series of offset corrections. In this paper we estimate the corrections to the nutation series coefficients directly from the multi-year ensemble of data. The resulting corrections have smaller uncertainties than corrections estimated from the daily offsets because the direct solution has many fewer degrees of freedom. We have forced the corrections to occur at the periods of the dominant terms of the IAU 1980 nutation series instead of allowing the pole orientation to vary freely on each day. Results from daily offset adjustment and direct nutation series adjustment from nearly seven years of data agree at the level of the combined one-sigma uncertainties, 0.1 milliarcseconds. The amplitude of the free core nutation was also estimated from the daily offset data; no significant amplitude was observed.

A continuous three year series of observations with the model TT40 superconducting gravimeter has been analysed for all frequency domains. The frequency of the nearly diurnal free wobble (NDFW) (1 + 1/(431.2 ± 3.2) cycles/sid.d.) and a damping factor (6208.5 days) are derived from this dataset. These results are not in agreement with the values predicted by the theoretical model presented by Wahr but match very closely the values derived from VLBI observations. A similar study of long period effects suggests furthermore that there is a strog correlation with the polar motion observed by other techniques. By comparing different drift models with respect to the ultra-long period of the gravity variations it is shown that the observed Chandler effect is not principally subjected to this type of instrumentally dependent parameter.

A change in the core free nutation period from its hydrostatic value of 466d to about 433d has been inferred from analysis of both earth's annual nutation amplitude from Polaris VLBI data (Herring et al., 1986) and surface gravity in the diurnal tidal band (Zürn et al., 1986; Neuberg et al., 1986). Gwinn et al. (1986) interpret this shift as due to an excess nonhydrostatic ellipticity ed, equivalent to a change in the equatorial minus polar radius of 0.5 km. In this paper, the effect of a layer at the core-mantle boundary (CMB) on σf (and hence ed) is examined. Although the potential effect of this layer on σf is found to be large, constraints imposed from gravimetry limit changes in ed to 10%. In addition, the annual nutation has a significant out-of-phase component. Mantle solid friction accounts for a large fraction of the out-of-phase nutation.

The adopted nutation series correspond to an elliptical uniformly rotating Earth with an elastic inner core, a liquid core and an elastic mantle. There exist nowadays a difference between the theoretical results and this theory. In this paper, we introduce the mantle inelasticity in the equations in order to give an idea of its contribution to the nutations.

A numerical solution for the luni-solar precession and nutation of the rigid Earth is obtained and compared with the result from the analytical theories which are the basis of the current IAU precession and nutation formulas. We have developed a new scheme of numerical calculation by modifying the equations of motion, which enables us to avoid the numerical integration with a small step. Some errors are found in the long periodic region of nutation in the current IAU theory.

The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.

In the long run, the tidal interaction between the Moon and the solid Earth is mediated by the oceans. It produces the retardation of the Earth's rotation known as ‘tidal friction’. Due to the changing configuration of the continents, it is a non-monotonic function of time. Tides of the solid Earth dominate the short-periodic tidal effects while the exchange with the atmosphere is preponderant in climatic changes, especially with an annual signature. It is shown that the influences of the oceans within such short time-scales must be taken into account for tidal and for non-tidal variations as well if one wants to model the Earth's rotation at the cm-level corresponding to the most advanced observational techniques.

In 1980, Feissel et al. identified a quasi–cyclic variation of 55 days in the irregularities of the Earth Rotation (ER) later detected in the Atmospheric Angular Momentum (AAM) (Langley et al., 1981). The purpose of this work is to analyse whether the causes of this cycle could lie in the physical processes of the Sun. The Wolf Numbers (WN) are used as parameters of the solar activity. Their spectral analysis over the period 1967–1985 shows such a component at 51 days. Analysis of three other periods, among which is the MERIT campaign, confirms it as well as during low or increasing solar activity periods.

The observed polar motion in the period 1860–1985 is analyzed in order to decide whether Chandler frequency was constant. It is shown that while the phase of annual wobble was very stable throughout the interval in question, Chandler wobble phase was subject to sometimes very rapid changes. The most pronounced negative phase changes were always accompanied by extremely low amplitudes, and a significant correlation was found between Chandler wobble phase and its integrated amplitude. The most probable explanation is that the frequency of Chandler wobble is variable and amplitude-dependent, which might be caused by non-equilibrium response of the ocean.

Analysis of data from new, highly accurate, geodetic techniques reveals rapid polar motions. Comparison of the new geodetic data and meteorological excitation estimates shows that the observed rapid polar motions are correlated with atmospheric pressure changes, and that these changes are related to atmospheric normal modes.