Earth Rotation Variations Research Articles

Atmospheric angular momentum fluctuations and their excitations of earth rotation variations at seasonal scale

We discuss the atmospheric contributions, especially wind contribution, to seasonal variations in the polar wobble and length of day during the period 1985–1995. The atmospheric angular momentum functions, calculated from the output data of GSM9603 GCM of Japan Meteorological Agency (JMA) are compared with those calculated from the reanalysis data of NCEP / NCAR, and from the operational objective analysis data of JMA. The results show that two different vertical wind integration methods lead to different wind contributions to seasonal polar wobble, especially for the component along Greenwich meridian direction in annual variation. However the inter-annual variations of wind contributions estimated by these two methods are almost the same with each other in the two equatorial components. The simulated axial relative AAM function agrees well with the other two as regards the seasonal variation. In addition, its inter-annual amplitude fluctuation of axial relative AAM function at semi-annual scale shows the main characteristics of ENSO evolution better than that estimated from the NCEP reanalysis data, that is, the semi-annual axial relative AAM oscillation becomes weaker during ENSO periods.

Allan Variance in earth rotation time series analysis

Allan Variance is currently used in Time frequency metrology for estimation of the stability of primary frequency standards. It is also applied in the time domain for characterization of the stability of atomic clocks or atomic time scales. More recently, the Allan Variance analysis was applied to the field of Earth Orientation metrology. At first it can be used to characterize at various time scales, the internal noise of the time series describing the Earth Rotation variations that are derived from the different geodetic techniques like Laser Ranging to artificial Satellites (SLR), Very Large Baseline Interferometry (VLBI) and GPS. In these series much of the noise is white phase noise or flicker phase noise. The uncertainties given for the various series are derived from the data analysis and generally do not correspond to the “true” precision. A second application of the Allan Variance as a statistical tool is to intercompare these series and their internal precision in order to give them a proper weight for their general combination.

Combination procedure for length-of-day time series according to the noise frequency behavior

Length-of-day (LOD) estimates from seven Global Positioning System (GPS) and three satellite laser ranging (SLR) analysis centers were combined into an even-spaced time series for a 27-month period (1996–1998). This time series was compared to the multi-technique Earth-orientation-parameter (EOP) combined solution (C04) derived at the Central Bureau of the International Earth Rotation Service (IERS/CB). Due to inhomogeneities in the different series derived from the various techniques (time, length, quality, and spatial resolution), the concept of a combined solution is justified. The noise behavior in LOD for different techniques varies with frequency; the data series were divided into frequency windows after removing both biases and trends. Different weight factors were assigned in each window, discriminating by technique, and produced one-technique combined solutions. Finally, these one-technique combined solutions were combined to obtain the final multi-technique solution. The LOD combined time series obtained by the present method based on the frequency windows combined series (FWCS) is very close to the IERS C04 solution. It could be useful to generate a new LOD reference time series to be used in the study of high-frequency variations of Earth rotation.

High‐frequency variations in Earth rotation from Global Positioning System data

Using the data of the global, dense Global Positioning System (GPS) network established by the International GPS Service a continuous, uninterrupted series of subdaily Earth rotation parameters (ERPs) with a time resolution of 2 hours has been generated at the Center for Orbit Determination in Europe. The series starts in January 1995 and has a length of more than 3 years. Starting from the 2‐hour ERP values of this, to our knowledge, unique time series, the high‐frequency variations in Universal Time (UT1) and polar motion (PM) due to ocean tides are studied and a set of sine and cosine coefficients is estimated for all the major tidal terms at nearly diurnal and semidiurnal frequencies. The GPS series is not very homogeneous (various processing changes during the 3 years) and still short compared to the length of very long baseline interferometry (VLBI) and satellite laser ranging (SLR) data sets. However, the results derived from this series are already of the same quality as the results from VLBI and SLR. A comparison of the tidal coefficients stemming from all three space‐geodetic techniques shows an agreement on the 1 μs level for UT1 and 10 microarc seconds (μas) for PM, respectively. The RMS difference between the ocean tide amplitudes estimated from GPS data and from TOPEX/Poseidon altimeter data amounts to 0.7–0.9 μs in UT1 and 9–13 μas in PM. The residual spectrum that remains after the removal of all tidal terms has a noise level of ∼5–10 μas in PM and 0.5–1 μs in UT1 and contains nontidal signals (up to 55 μas in PM and 3 μs in UT1) that might be due to the impact of the satellite orbit modeling (12‐hour revolution period of the satellites) or, alternatively, due to atmospheric or oceanic normal modes.

Earth Rotation and El Niño—Theory of Air‐Sea Coupling

AbstractApplying the shallow water equations with air‐sea interaction in low latitudes, the influences of the earth's variable rotation on air‐sea coupled system are discussed in this paper by means of normal mode and special functions. It is shown that the variation of the earth's rotation rate on the one hand affects the propagation and stability of Kelvin and Rossby waves and on the other hand can cause the changes of zonal wind, current and sea surface temperature. Particularly, when the earth's rotation rate is decelerated, the anomaly of zonal wind and current is caused and SST in the east part of low‐latitude oceans is increased through the air‐sea interaction, and thus the El Niño events is created which bring about the global climate changes.

Interannual variations in the length of day and ENSO events in 1982–1983 and 1997–1998

The length of day series during the period of 1962.0–2000.0, the atmospheric angular momentum and the Southern Oscillation Index are adopted to analyze the relationships among the ENSO events that have occurred since 1960, the changes in the length of day and the atmospheric angular momentum. Attention is particularly given to the different effects of the 1982–1983 and 1997–1998 ENSO events on the variations of Earth rotation. The synthetic excitation effects of multi-scale atmospheric oscillations on the anomalous variations of the interannual rates of Earth rotation are revealed by means of the time-frequency spectrum of the wavelet transform.

Very Long Baseline Interferometry — a high precision tool for geodesy and astrometry

Very Long Baseline Interferometry is able to provide a direct geometrical tie to the extragalactic radio sources which represent the best possible realization of an inertial system. By this token, VLBI can measure Earth rotation and orientation as well as precise station positions and their velocities without involving the gravity field of the Earth. In the broader context of Earth observation and the monitoring of geodynamic processes, this one and many more unique features have allowed the VLBI technique to achieve pioneering feats such as the determination of present-day plate tectonic motions, post glacial rebound, sub-daily Earth rotation variations and parameters of general relativity. In this contribution, a brief outline of the VLBI technique and the models used in geodetic data analysis will be given before some of the most important achievements to date will be passed in review and future developments will be indicated.

Hydrological and oceanic excitations to polar motion andlength-of-day variation

SUMMARY Water mass redistributions in the global hydrosphere, including continental water storage change and non-steric sea level change, introduce variations in the hydrological angular momentum (HAM) and the oceanic angular momentum (OAM). Under the conservation of angular momentum, HAM and OAM variations are signi¢cant excitation sources of the Earth rotational variations at a wide range of timescales. In this paper, we estimate HAM and OAM variations and their excitations to polar motion and length-of-day variation using soil moisture and snow estimates and non-steric sea level change determined by TOPEX/Poseidon satellite radar altimeter observations and a simpli¢ed steric sea level change model. The results are compared with the variations of polar motion and LOD that are not accounted for by the atmosphere. This study indicates that seasonal continental water storage change provides signi¢cant contributions to both polar motion and LOD variation, especially to polar motion X, and the non-steric sea level change is responsible for a major part of the remaining excitations at both seasonal scale and high frequencies, particularly in polar motion Y and LOD. The good correlation between OAM contributions and the remaining excitations shows that large-scale non-tidal mass variation exists in the oceans and can be detected by TOPEX/Poseidon altimeter observations.

The C-II ring laser project

The intensive use of Very Long Baseline Interferometry (VLBI), as well as Satellite and Lunar Laser Ranging (SLR, LLR) and the GPS-System allows for a precise monitoring of the current variations in earth rotation. The precision for the VLBI-system is as high as one part in 109 for a 24 hour measurement campaign. Since all these techniques are based on external reference frames, it is desirable to develop inertial sensors to the same resolution. Ring laser gyroscopes have the potential to be used for that purpose. The basic idea is to scale up the area surrounded by the two counter-rotating laser beams in order to gain higher sensitivity for the instrument with respect to the rotation rate. The Canterbury Ring Laser (C-I) consisting of a square of area 0.755 m2 has shown that ring lasers with a perimeter more than 60 cm are possible, in that the occurrence of more than one longitudinal mode of operation could be avoided by reducing the power of the circulating beams (Bilger et al., 1993). The next instrument C-II with an area of 1 m2 demonstrated many of the mechanical requirements for a stable instrument. It was constructed from a monolithic block of Zerodur, so that the size of the area does not change under temperature variations. A successfully built prototype for a large ring (G0) finally proved that it is possible to build a ring laser gyroscope with at least 14 m length of cavity (Rowe et al., 1999). This means that most of the demands for a highly sensitive inertial earth rotation sensor are met. On this basis a high resolution and highly stable instrument, suitable for geophysical applications, can be constructed.

SHORT PERIOD VARIATIONS IN EARTH ROTATION AS SEEN BY VLBI

An overview of the abilities of Very Long Baseline Interferometry (VLBI) to measure the variable Earth rotation and of the international VLBI collaboration is given. The paper concentrates on the short-period, i.e. subseasonal variations of Earth rotation which can be seen in VLBI measurements of length of day (lod) and polar motion between 1981 and 1999. The wavelet transform allows the time localisation of an irregular quasi-harmonic signal within a given data set. The wavelet analysis of lod series yields in the high-frequency range periods of ∼28 days, ∼14 days down to 6.86 days caused by the lunisolar tides and irregular quasi-periodic variations between 40 and 130 days. These are mainly associated with global zonal wind changes which can be seen when looking on the wavelet cross-scalogram between the lod series and the atmospheric angular momentum (AAM) time series. In polar motion variable periods between two and five months and even down to 7–10 days can be made visible by the wavelet scalograms.Today it is possible by VLBI to determine polar motion and UT1-UTC with a temporal resolution of as short as 3–7 minutes. The results of parallel VLBI sessions which took place since 1998 using two independent VLBI networks were analyzed in the subdiurnal period range and compared by computing the wavelet cross-scalograms, the covariance spectrum and the normed coherency. Periods between 5 and 7 hours can be seen in many of the UT1-UTC data sets besides the well-known diurnal and semi-diurnal periods. The wavelet analyses reveal interesting patterns in the subdiurnal range in polar motion, too.

Coseismic Excitation of the Earth’s Polar Motion

AbstractApart from the “shaking” near the epicenter that is the earthquake, a seismic event creates a permanent field of dislocation in the entire Earth. This redistribution of mass changes (slightly) the Earth’s inertia tensor; and the Earth’s rotation will change in accordance with the conservation of angular momentum. Similar to this seismic excitation of Earth rotation variations, the same mass redistribution causes (slight) changes in the Earth’s gravitational field expressible in terms of changes in the Stokes coefficients of its harmonic expansion. In this paper, we give a historical background of the subject and discuss the related physics. We then compute the geodynamic effects caused by earthquakes using Chao and Gross’ (1987) formulas based on Gilbert’s (1970) normal-mode summation scheme. The effects are computed using the centroid moment tensor (CMT) solutions for 15,814 major earthquakes from Jan., 1977, through Feb., 1999, as provided in the Harvard CMT catalog. The computational results update those of Chao and Gross (1987) and Chao et al. (1996), further strengthening their findings and conclusions: (i) the strong tendency for earthquakes to make the Earth rounder and more compact (however slightly) continues; (ii) so does the trend in the seismic “nudging” of the rotation pole toward the general direction of ~ 140°E, roughly opposite to that of the observed polar drift, but two orders of magnitude smaller in drift speed.

Lunar and solar torques on the oceanic tides

A general framework for calculating lunar and solar torques on the oceanic tides is developed in terms of harmonic constituents. Axial torques and their associated angular momentum and Earth rotation variations are deduced from recent satellite‐altimeter and satellite‐tracking tide solutions. Torques on the prograde components of the tide produce the familiar secular braking of the rotation rate. The estimated secular acceleration is approximately −1300 arcseconds/century2 (less 4% after including atmospheric tides); the implied rate of change in the length of day is 2.28 milliseconds/century. Torques on the retrograde components of the tide produce periodic rotation variations at twice the tidal frequency. Interaction torques (for example, solar torques on lunar tides) generate a large suite of rotation‐rate variations at sums and differences of the original tidal frequencies. These are estimated for periods from 18.6 years to 6 hours. At subdaily periods the angular momentum variations are 5 to 6 orders of magnitude smaller than the variations caused by ocean tidal currents.

THE DETERMINATION OF GRAVITATIONAL POTENTIAL DIFFERENCES FROM SATELLITE-TO-SATELLITE TRACKING

A new, rigorous model is developed for the difference of gravitational potential between two close earth-orbiting satellites in terms of measured range-rates, velocities and velocity differ- ences, and specific forces. It is particularly suited to regional geopotential determination from a satellite-to-satellite tracking mission. Based on energy considerations, the model specifically ac- counts for the time variability of the potential in inertial space, principally due to earth's rotation. Analysis shows the latter to be a significant ( 1m 2 /s 2 ) effect that overshadows by many orders of magnitude other time dependencies caused by solar and lunar tidal potentials. Also, variations in earth rotation with respect to terrestrial and celestial coordinate frames are inconsequential. Results of simulations contrast the new model to the simplified linear model (relating potential difference to range-rate) and delineate accuracy requirements in velocity vector measurements needed to supple- ment the range-rate measurements. The numerical analysis is oriented toward the scheduled Gravity Recovery and Climate Experiment (GRACE) mission and shows that an accuracy in the velocity difference vector of 2 10 5 m/s would be commensurate within the model to the anticipated accuracy of 10 6 m/s in range-rate.

On Subdiurnal Effects in Earth Rotation

More than two years of almost continuous polar motion data (obtained by reprocessing GPS-Observations) have been used to analyse the daily/subdaily variations in Earth rotation based on the complex Wavelet-Technique. Systematic and spectral analytical investigations of the degree of variability of periods including tidal have been carried out. Relevant indications of oceanic effects, besides atmospheric components, have been observed.

Effect of subductions and trends in seismically induced Earth rotational variations

In the past, the influences of large earthquakes on Earth rotation and on changes of the gravity field have been the subject of extensive investigations. Though it is now recognized that earthquakes cannot excite the Chandler wobble and that they only drive a very modest secular drift of the Earth's spin axis, their rotational signatures present some intriguing peculiarities. In fact, they preferentially drive the rotation axis toward a well‐defined direction (i.e., ∼ 140°E) and systematically induce negative variations of the Earth's oblateness. In the first part of this work the static dislocation theory is employed to ascertain the origin of these two remarkable trends. This task is accomplished by considering the effects of seismicity on Earth rotation during the last two decades. We find that the above tendencies are operating even on a yearly time scale, and we explain their nature by means of simple geometrical and physical arguments. We also find that the trend of the pole toward 140°E is essentially due to the seismicity which characterizes the western Pacific subduction zones. The seismic excitation function takes for shallow thrust earthquakes a direction roughly opposite to the excitation function associated with mass injection along active subduction zones; this point highlights the potential effects of aseismic mass rearrangement at subduction zones on the secular drift of the pole. Our findings, based on a simple model of steady state subduction, show that in the last two decades this process substantially acts to counterbalance the polar drift due to global seismic activity. We verify that this balance between earthquake‐and subduction‐induced rotational signatures also characterizes the time variations of the dynamic oblateness, which is intrinsically independent of the inertia changes that drive polar motion. From these results, which may potentially have some impact on the interpretation of long‐term polar motion, we conclude that the pole of rotation cannot be significantly perturbed by tectonic motions on a decade time scale.

An interpretation of the non-tidal secular variation in the earth rotation: The interaction between the solar wind and the earth's magnetosphere

The long period variation of the earth rotation is generally explained by the tidal friction. The tidal friction, however, is not the only source to influence the earth rotation in long term. In this paper, by means of the interaction between the solar wind and the magnetosphere of the earth, the additional magnetic pressure will exist in the magnetic tail due to the crowding and sparseness of the magnetic lines in the consideration of the earth rotation, which could be considered as a source of effecting the long term variation of the earth rotation. It is shown in this paper that this mechanism can produce angular deceleration of the Earth rotation in the magnitude of ω = −1.7 × 10-22 s-2. This result might be a prompt to search for other sources in the secular variation of the rate of the Earth rotation variation further in order to regulate the observed result with the theoretical one.

Tidally induced Sagnac signal in a ring laser

The Earth rotation vector is an integral dynamical quantity of the Earth system, with Earth rotation variations depending on the overall dynamics of the Earth system at all time scales. New observations of Earth rotation variations with a precision better than 10−9 of the Earth rotation would contribute to the understanding of many geophysical phenomena. High precision short‐term observations of the projection of the Earth rotation vector ΩE on the area vector A of a ring laser are now possible. Tidally induced Sagnac effects are due to changes in the ring geometry (areal strain and perimeter variations), changes in the normal vector of the ring laser plane (tilt), and the vorticity of the Earth's tidal deformations. Here we estimate the latitude‐dependent effect of the Earth's body tide deformations due to vorticity and tilt. At mid‐latitudes, the vorticity δΩ is of the order 8 · 10−8ΩE, but because it is in the local horizontal plane, it is not detectable by a horizontal ring. The Sagnac effect due to tidal tilt for a horizontal ring at mid‐latitudes is of the order of 4 · 10−8 of the Earth rotation effect. Thus, the tidal signal is of an order of magnitude where it may be used for validation of existing and future ring lasers.

Sensitivity of UT1 determined by single-baseline VLBI to atmospheric delay model, terrestrial and celestial reference frames

At the present time, the daily VLBI observations on the Westford-Wettzell baseline is the only continually running VLBI project for studies of high-frequency Earth rotation variations. An analysis of this experiment with regard to the potential errors in the atmospheric delay model and in adopted celestial and terrestrial reference frames is presented in the paper. A new VLBI geometric delay model is applied and an algorithm for global adjustment for this specific single-baseline VLBI developed. The results over three years show discrepancies at the milliarcsecond level between the daily observations and the adopted atmospheric model as well as the combined celestial reference frame. A significant number of these discrepancies are removed by the global adjustment.

Oceanic tidal angular momentum and Earth's rotation variations

Luni-solar tides affect Earth's rotation in a variety of ways. We give an overview of the physics and focus on the excitation of Earth rotational variations by ocean tides under the conservation of angular momentum. Various models for diurnal and semidiurnal tidal height and tidal current fields have been derived, following a legacy of a number of theoretical tide models, from the Topex/Poseidon (T/P) ocean altimetry data. We review the oceanic tidal angular momenta (OTAM) predicted by these T/P models for the eight major tides (Q 1, O 1, P 1, K 1, N 2, M 2, S 2, K 2), and their excitations on both Earth's rotational speed variation (in terms of length-of-day or UT1) and polar motion (prograde diurnal/semidiurnal components and retrograde semidiurnal components). These small, high-frequency effects have been unambiguously observed in recent years by precise Earth rotation measurements via space geodetic techniques. Here we review the comparison of the very-long-baseline-interferometry (VLBI) data with the T/P OTAM predictions. The agreement is good with discrepancies typically within 1 – 2 microseconds for UT1 and 10 – 30 microarcseconds for polar motion. The eight tides collectively explain the majority of subdaily Earth rotation variance during the intensive VLBI campaign Cont94. This establishes the dominant role of OTAM in exciting the diurnal/semidiurnal polar motion and paves the way for detailed studies of short-period non-OTAM excitations, such as atmospheric and oceanic angular momentum variations, earthquakes, the atmospheric thermal tides, Earth librations, and the response of the mantle lateral inhomogeneities to tidal forcing. These studies await further improvements in tide models and Earth rotation measurements.

Earth rotation and global change

Variations in the rotation of the Earth include changes in the rate of rotation (altering the Length of the Day, LOD), in orientation of the rotation axis relative to a terrestrial frame (Polar Motion, PM) and in orientation relative to a celestial frame due to external torques (Nutation and Precession). Variations occur over a wide range of time scales, from hours to the age of the Earth. Scientific interest in and understanding of Earth rotation variations have proceeded rapidly over the last several decades due, in large part, to enormous improvements in observations by space geodetic means, including satellite laser ranging (SLR), very long baseline interferometry (VLBI), lunar laser ranging (LLR), and satellite positioning methods, especially the global positioning system (GPS). The study of the Earth's rotation is a mature interdisciplinary field, and extensive reviews of many aspects of the field are contained in the AGU monographs ‘Contributions of Space Geodesy to Geodynamics’ (Smith and Turcotte, 1993). Articles by Eubanks (1993), Dickey (1993), Hide and Dickey (1991), and monographs by Lambeck (1988,1980) and Munk and Mac Donald (1960) provide excellent background material on these problems, as well. The reader may also wish to review other IUGG Report articles in this series on related subjects, specifically those on the global gravity field, VLBI technology, satellite orbit dynamics, and GPS.