UT1 Variations Research Articles

Mechanism of error propagation from the subdaily Universal Time model into the celestial pole offsets estimated by VLBI

Within the analysis of space geodetic observations, errors of the applied subdaily Earth rotation model can induce systematic effects in different estimated parameters. In this paper, we focus on the impact of the subdaily Universal Time (UT1) model on the celestial pole offsets (CPO) estimated from very long baseline interferometry (VLBI) observations. We provide a mechanism that describes the error propagation from the subdaily UT1 into the daily CPO.In typical 24-h VLBI sessions the observed quasars are well distributed over the sky. But the observations, if looked at from the Earth-fixed frame, are not homogeneously distributed. The amount of observations performed in different terrestrial directions shows an irregularity which can be roughly compared to the case where the observations are collected in only one Earth-fixed direction. This peculiarity leads to artefacts in VLBI solutions, producing a correlation between the subdaily variations in UT1 and the position of the celestial pole. As a result errors in diurnal terms of the subdaily UT1 model are partly compensated by the estimated CPO. We compute for each 24-h VLBI session from 1990 until 2011 the theoretical response of the CPO to an error in the subdaily UT1 by setting up a least-squares adjustment model and using as input the coordinates of the observed quasars and observation epochs. Then real observed response of the estimated CPO derived from the VLBI session solutions is compared to the predicted one. A very good agreement between the CPO values estimated from VLBI and the predicted values was achieved. The presented model of error propagation from the subdaily UT1 into the daily CPO allows to predict and explain the behaviour of CPO estimates of VLBI solutions computed with different subdaily Earth rotation models, what can be helpful for testing the accuracy of different subdaily tidal models.

Use of atmospheric angular momentum forecasts for UT1 predictions: analyses over CONT08

Real-time orbit determination and interplanetary navigation require accurate predictions of the orientation of the Earth in the celestial reference frame and in particular that for Universal Time UT1. Much of the UT1 variations over periods ranging from hours to a couple of years are due to the global atmospheric circulation. Therefore, the axial atmospheric angular momentum (AAM) forecast series may be used as a proxy index to predict UT1. Our approach taking advantage of this fact is based on an adaptive procedure. It involves incorporating integrations of AAM estimates into UT1 series. The procedure runs on a routine basis using AAM forecasts that are based on the two meteorological series, from the US National Centers for Environmental Prediction and the Japan Meteorological Agency. It is pertinent to test the prediction method for the period that includes the special CONT08 campaign over which we expect a significant improvement in UT1 accuracy. The studies we carried out were aimed both to compare atmospheric forecasts and analyses, as well as to compare the skills of the UT1 forecasts based on the method with atmospheric forecasts and that using current statistical processes, as applied to the C04 Earth orientation parameters series derived by the International Earth rotation and Reference Systems service (IERS). Here we neglect the oceanic sub-diurnal and diurnal variations, as these signals are expected to be smaller than the UT1-equivalent of 100 μs, when averaged over a few days. The prediction performances for a 2-day forecast are similar, but at a forecast horizon of a week, the AAM-based forecast is roughly twice as skillful as the statistically based one.

Status and Prospects for Combined GPS LOD and VLBI UT1 Measurements

Status and Prospects for Combined GPS LOD and VLBI UT1 Measurements A Kalman filter was developed to combine VLBI estimates of UT1-TAI with biased length of day (LOD) estimates from GPS. The VLBI results are the analyses of the NASA Goddard Space Flight Center group from 24-hr multi-station observing sessions several times per week and the nearly daily 1-hr single-baseline sessions. Daily GPS LOD estimates from the International GNSS Service (IGS) are combined with the VLBI UT1-TAI by modeling the natural excitation of LOD as the integral of a white noise process (i.e., as a random walk) and the UT1 variations as the integration of LOD, similar to the method described by Morabito et al. (1988). To account for GPS technique errors, which express themselves mostly as temporally correlated biases in the LOD measurements, a Gauss-Markov model has been added to assimilate the IGS data, together with a fortnightly sinusoidal term to capture errors in the IGS treatments of tidal effects. Evaluated against independent atmospheric and oceanic axial angular momentum (AAM + OAM) excitations and compared to other UT1/LOD combinations, ours performs best overall in terms of lowest RMS residual and highest correlation with (AAM + OAM) over sliding intervals down to 3 d. The IERS 05C04 and Bulletin A combinations show strong high-frequency smoothing and other problems. Until modified, the JPL SPACE series suffered in the high frequencies from not including any GPS-based LODs. We find, surprisingly, that further improvements are possible in the Kalman filter combination by selective rejection of some VLBI data. The best combined results are obtained by excluding all the 1-hr single-baseline UT1 data as well as those 24-hr UT1 measurements with formal errors greater than 5 μs (about 18% of the multi-baseline sessions). A rescaling of the VLBI formal errors, rather than rejection, was not an effective strategy. These results suggest that the UT1 errors of the 1-hr and weaker 24-hr VLBI sessions are non-Gaussian and more heterogeneous than expected, possibly due to the diversity of observing geometries used, other neglected systematic effects, or to the much shorter observational averaging interval of the single-baseline sessions. UT1 prediction services could benefit from better handling of VLBI inputs together with proper assimilation of IGS LOD products, including using the Ultra-rapid series that is updated four times daily with 15 hr delay.

Short-term tidal variations in UT1: compliance between modelling and observation

AbstractThe Earth rotation rate and consequently universal time (UT1) and length of day (LOD) are periodically affected by solid Earth tides and oceanic tides. Solid Earth tides induce changes with periods from around 5 days to 18.6 years, with the largest amplitudes occurring at fortnightly, monthly, semi-annual and annual periods, and at 18.6 years. The principal variations caused by oceanic tides have diurnal and semi-diurnal periods. For the investigation of the tidal effects with periods of up to 35 days, UT1 series are estimated from VLBI observation data of the time interval 1984–2008. The amplitudes and phases of the terms of interest are calculated and the results for diurnal and sub-diurnal periods are compared and evaluated with tidal variations derived from a GNSS-based LOD time series of 8 months. The observed tidal signals are finally compared to the predicted tidal variations according to recent geophysical models.

Common 22-year cycles of Earth rotation and solar activity

AbstractThe 22-year oscillations of the Earth rotation due to several geophysical processes in the core-mantle system, oceans, atmosphere and geomagnetic field are excited mainly by 22-year cycles of the solar activity. These geophysical processes produce their own oscillations of the Earth rotation with different periods around 22 years. The direct and indirect influence of the solar activity on 22-year cycles of the Earth rotation are separated from the core effects and corresponding amplitudes are estimated by means of two approaches. The first, direct approach uses extended time series of Wolf's numbers with 22-year cycles, determined by sign alternation of even sunspot cycles. A linear regression between 22-year cycles of UT1 and solar activity is determined and this regression model is used to calculate the UT1 response to the 22-year cycles of the solar activity. The second, indirect approach uses 22-year oscillation of the mean sea level, caused by water evaporation due to variations of the total solar irradiance. The influence of the mean sea level variations on the Earth rotation is calculated by means of an empirical model of global water redistribution. The core-mantle effects on the 22-year UT1 variations are determined by excluding the UT1 response to the solar activity and core angular momentum due to the geomagnetic field variations, according to the solutions from the Special Bureau of the Core (SBC).

Improved near-term Earth rotation predictions using atmospheric angular momentum analysis and forecasts

Abstract Predicted values of atmospheric angular momentum (AAM) from the U.S. National Centers for Environmental Prediction (NCEP) were introduced into the International Earth Rotation and Reference Systems Service (IERS) Bulletin A (rapid service/prediction of Earth orientation) combination during 2000 in an effort to improve the near-term universal time–coordinated universal time (UT1–UTC) predictions. In this approach, only the atmospheric contributions to the excitation of UT1 variations were included and contributions from other sources, such as the oceans, were neglected. However, we observed that using this approach the AAM inputs sometimes degraded the UT1 predictions as much as they helped and suspended their use in early 2001 for re-evaluation. This re-evaluation resulted in a greater appreciation of the systematic differences between the AAM and UT1R series as well as suggests that, in the actual Earth system, the oceans balance some of the atmospheric variability on specific time scales between 2 and 15 days. Since near-real time oceanic angular momentum information is currently not available, an improved approach for assimilating AAM data products was developed. These improvements include the use of both pressure and wind AAM terms, use of the previously unavailable AAM analysis data at the 24-h epoch for the latest AAM analysis file, smoothing of the AAM-based Length of day (LOD) to reduce sub-diurnal variability before integrating to UT1R, and removal of a best-fit sinusoid from the AAM UT1R time series. The new procedure reduces the effects of systematic trends (both periodic and linear) that do not appear to be present in actual UT1R variability. Retrospective studies indicate that including this new AAM-derived series may reduce UT1R prediction errors by ∼41% at 5 days into the future. Consequently, AAM-derived estimates of UT1R were restored to IERS Bulletin A starting in the 7 August 2001 issue. Comparisons made after the addition of UTAAM into the Bulletin A UT1–UTC combination solution indicate a better than 50% reduction in prediction errors at 5 and 10 days into the future and an ∼1 ms improvement at 30 days into the future.

Polar motions equivalent to high frequency nutations for a nonrigid Earth with anelastic mantle

The coefficients of polar motions of the rigid/nonrigid Earth in frequency bands other than the retrograde diurnal one are systematically computed using general expressions, derived here for the first time, for the prograde and retrograde torques exerted on the Earth by lunisolar potentials of arbitrary spherical harmonic type. Taken together with the already known coefficients of low frequency nutations and UT1 variations, they provide a complete characterization, with high precision, of the motions of the pole of the terrestrial reference frame in space; this is needed for high precision studies in astronomy and space geodesy. The inputs used for our computations are a table of tidal amplitudes, and values of the geopotential coefficients of degrees up to 4 and of other relevant basic Earth parameters. General relations which connect the coefficients of high frequency nutations to those of the equivalent polar motions are established and used for deducing the former. The Chandler resonance plays a significant role in low frequency polar motions. In this context, the role of mantle anelasticity and the nature of the Earth's deformational response to zero frequency forcing are given special consideration. The free core nutation (FCN) resonance of low frequency nutations is shown to affect the prograde semidiurnal nutations through the coupling produced between the nutations in the two frequency bands by triaxiality terms in the angular momenta of the whole Earth and of its fluid core. It is shown in a transparent fashion that the effect of the core triaxiality arises almost exclusively from the huge FCN-related resonance in the wobble of the core. The magnitude of the effect is found to be a few times smaller than reported in a recent paper; it is also found, unlike in that paper, that the changes in the eigenfrequencies due to trixiality are only of the second order in the triaxiality parameter. Numerical results for the polar motions of the nonrigid Earth in different frequency bands, as well as for the elliptical nutations of the rigid Earth, are tabulated and compared with available numbers from earlier works.

Monthly and fortnightly tidal variations of the Earth's rotation rate predicted by a TOPEX/POSEIDON Empirical Ocean Tide Model

Empirical models of the two largest constituents of the long‐period ocean tides, the monthly and the fortnightly constituents, are estimated from repeat cycles 10 to 210 of the TOPEX/POSEIDON (T/P) mission. These models are first validated with tide gauge observations which show residual variances with the T/P‐derived models that are of the order of 2–3 mm² for both the monthly and fortnightly constituents, and which are smaller than residual variances from respective equilibrium models of these long‐period ocean tides. These empirical models are used to predict the contribution that they each have on tidal variations of the Earth's rotation rate. For tidal variations in UT1 these contributions are predicted to be of the order of 0.1 ms with a scatter of the order of 8 and 3 µs for the monthly and fortnightly ocean tides, respectively.

Measurements of length of day using the Global Positioning System

Length‐of‐day (LOD) estimates from the seven Global Positioning System (GPS) analysis centers of the International GPS Service for Geodynamics have been compared to values derived from very long baseline interferometry (VLBI) for a recent 16‐month period. All GPS time series show significant LOD biases which vary widely among the centers. Within individual series the LOD errors show time‐dependent correlations which are sometimes large and periodic. Clear correlations between ostensibly independent analyses are also evident. In the best case the GPS LOD errors, after bias removal, approach Gaussian with an intrinsic scatter estimated to be as small as ∼21 µ/d and a correlation time constant of perhaps 0.75 day. Integration of such data to determine variations in UT1 will have approximately random walk errors which grow as the square root of the integration time. For the current best GPS performance, UT1 errors exceed those of daily 1‐hour VLBI observations after integration for ∼3 days. Assuming the stability of LOD biases can be reliably controlled, GPS‐derived UT1 can be useful for near real time applications where otherwise extrapolations for several days from the most current VLBI data can be inaccurate by up to ∼1 ms.

Measuring rapid variations in Earth orientation, geocenter and crust with satellite laser ranging

This analysis was performed with the GEOSAT software developed at NDRE for high-precision analysis of satellite tracking and VLBI data for geodetic and geodynamic applications. To determine the amplitudes of the tidally coherent daily and sub-daily variations in the Earth's orientation, geocenter, and crust, we have analyzed twelve months of SLR tracking data from the LAGEOS I & II and ETALON I & II satellites, obtained between October 1992 and September 1993. Station coordinates and mean geocenter are determined with an accuracy of 1 to 2 cm. Amplitudes of diurnal and semidiurnal variations in UT1, polar motion, and geocenter are determined with a precision of ~2µts, ~20µas, and 1–3 mm in each component. It is demonstrated that it is possible to determine a one-year continuous high-precision series in UT1 using multi-satellite laser ranging.

Subdaily Earth rotation during the Epoch ‘92 campaign

Global Positioning System (GPS) data were used to estimate Earth rotation variations over an 11‐day period during the Epoch ‘92 campaign in the summer of 1992. Earth orientation was measured simultaneously by several very long baseline interferometry (VLBI) networks. GPS and VLBI estimates of UT1 with 3‐hour time resolution were then compared and analyzed. The high frequency behavior of both data sets is similar, although drifts between the two series of ∼0.1 ms over 2‐5 days are evident. The geodetic results were also compared with models for UT1 fluctuations at tidal periods and with estimates of atmospheric angular momentum made at 6‐hour intervals. Most of the geodetic signal in the diurnal and semidiurnal frequency bands can be attributed to tidal processes, whereas UT1 variations over a few days are mostly atmospheric in origin.

Tidal variations in UT1 observed with very long baseline interferometry

Nine years of very long baseline interferometry (VLBI) observations have been analyzed to determine the magnitudes of the tidal variations in UTl for periods between 5 and 35 days. Corrections for variations in atmospheric angular momentum (AAM) significantly reduce the scatter of the measured amplitudes across both time and frequency. The AAM corrections are found to reduce the scatter in the observed tidal amplitudes by as much as 60% for periods as short as 5.6 days; in contrast, earlier studies have shown a loss of coherence between AAM and length‐of‐day (LOD) for periods shorter than about 10 days. The tidal amplitude measurements place bounds on both the nonequilibrium ocean and mantle anelasticity effects. The in‐phase k/C determination is found to agree to better than 0.5% with the value of 0.944 from Yoder et al. (1981). The out‐of‐phase values are found to have a frequency dependence that can only be explained by nonequilibrium ocean effects. The observed slope is larger than the theoretical by about 3 times the expected error. This result may indicate that the ocean is farther out of equilibrium for the higher frequencies than present models permit. Significant improvements are needed in both ocean and atmosphere modeling to exploit the full capability of the VLBI observations.

Earth Rotation from the IRIS Project

Project IRIS (International Radio Interferometric Surveying) was set up under the IAG and COSPAR to provide an operational system that would employ Very-Long-Baseline Interferometry (VLBI) techniques to monitor variations in the rotation of the Earth. Currently the IRIS-A network, with stations at Westford, MA, Ft. Davis, TX, Richmond, FL, and Wettzell, FRG, conducts 24-hour observing sessions every five days to produce determinations of pole position, UT1, and nutation in addition to other parameters of geophysical and astrometric interest. The resulting Earth orientation parameters (EOP) have been shown to have an accuracy of 1 to 2 milliseconds of arc in pole position, and 0.05 to 0.1 milliseconds of time in UT1. In order to observe the relatively large higher frequency variations in UT1, daily 45-minute observing sessions are conducted using the single baseline between Westford and Wettzell. Intercomparison of the UT1 values from the daily and the 5-day series indicates that the accuracy of the daily values is better than 0.1 millisecond of time.The longer term objectives of the IRIS project include improving the monitoring of Earth orientation by increasing the sampling rate and accuracy of the observations. In April, 1987, the IRIS-P network, with stations in Kashima, Japan, Fairbanks, AK, Ft, Davis, TX, and Richmond, FL began monthly 24-hour observing sessions, and a second series of daily UT1 observing sessions was begun using the stations in Richmond and Bologna, Italy. The additional networks will provide redundancy that will improve the reliability of the system and allow the accuracy of the EOP values to be estimated.The IRIS UT1 time series provides, for the first time, sufficient accuracy and temporal resolution to look for the few percent increase in k/C caused by the anelastic response of the mantle. Initial results presented here suggest that improved methods of accounting for the dynamics of the oceans and atmosphere may be required before the intertwined variations in UT1 can be fully separated.

First VLBI experiments between Kashima and Wettzell for monitoring UT1

During 14 days UT1 was monitored by daily VLBI short experiments between Kashima and Wettzell (GJRO, G erman J apanese Earth R otation O bservations) in order to investigate short-term UT1 variations and to compare the results with those of another independent network, Wettzell and Westford (USA). Both UT1-series agree within 0.2msec if the regular IRIS pole positions are used, but there is still a remaining offset of 0.1 msec. The fortnightly period (13.66d) induced by earth tides was detected in the GJRO results with an increase of the theoretical amplitude by 5–10%. Using the data of the long experiment the baseline vector was also determined. The baseline length coincides with the Crustal Dynamics Project VLBI-campaign solution to within 1cm.

Determination of high frequency variations in earth's rotation from Doppler satellite observations

The determination of high frequency variations in UT-1 and a component of pole position from a single pass of Doppler observations of a Navy Navigation Satellite is affected by instrument errors and uncertainties in the gravity field and atmospheric drag forces used in computing the satellite orbit. For elevation angles above20°, instrument errors contribute about2 msec to the determination of UT-1 and “.03 to the determination of pole position. Gravity and drag errors contribute about 0“.03 of correlated error. But gravity errors may be inferred by statistical analysis of residuuls after drag errors are reduced by drag-compensating devices aboard future Navy Navigation Satellites. Since20 Doppler stations nominally acquire about100 passes each day, daily observations of UT-1 and pole position could achieve precisions of0.2 msec and “.005, respectively, assuming half the passes contribute to the determination of each component of pole position. The current accuracy of Doppler results for two day solutions is about50 cm for pole position and1 msec for high frequency variations in UT-1.

Low Cost Lageos Ranging System

This paper describes a Lageos laser ranging station design based on single photoelectron detection which could be used to monitor polar motion at all periods, and short-period UT1 variations with high accuracy and at moderately low cost. No comparison has been made with the costs of long baseline radio interferometry (LBI) stations, since the establishment and operation of basic international networks using both approaches seems scientifically well justified. Both LBI and lunar laser ranging results will determine intermediate and long-period UT1 variations and nutation. The LAGEOS laser ranging station design suggested here is similar to the design used in the high-mobility LAGEOS ranging station now being constructed by the University of Texas. It has been shown that 30 cm diameter transmit/receive optics with 10 arc second pointing accuracy and 50 milliwatt average laser power output are usually sufficient to give 70 signal counts in a three minute averaging time, even at 20° elevation angle. Lasers having the desired power at 530 nm wavelength with 10 pps repetition rate and 3 ns pulse length are now reported to be commercially available at moderate cost. The resulting range accuracy for normal points corresponding to the three minute averaging time is three cm, including allowances for absolute calibration of the system, atmospheric refraction correction uncertainties, and Earth tide uncertainties. Much of the pulse-timing electronics needed is commercially available, and many time and latitude stations already have good epoch determination systems. The ten arc second pointing requirement for a 30 cm diameter beam seems considerably easier to meet than the optical requirements for classical observing techniques. A simple beam director with flat mirrors appears quite feasible, with inexpensive encoders on each axis for minicomputer control if desired. A number of special features of the University of Texas high-mobility station would not be needed for a fixed station.

Geodetic and Astrometric Results of Very Long-Baseline Interferometric Measurements of Natural Radio Sources

AbstractThe technique of very long-baseline interferometry, initially developed in 1967 to study the angular structure of compact radio sources on the order of a thousandth of a second of arc, has been used to measure to great accuracy geometric quantities of geodetic and geophysical importance. The baseline vector between various radio telescopes has been measured to an accuracy of about 1 m (the accuracy of the measurement of the length of the baseline vector is better than 50 cm). Variations in UT1 have been measured to an accuracy of 1 msec, polar motion to 500 cm, and the coordinates of radio sources to about 0.1 ardsec. Improvement of about 1 order of magnitude is expected in the next 5 years. The major work has been done by three groups: the Massachusetts Institute of Technology/National Aeronautics and Space Administration group; the Jet Propulsion Laboratory group; and the National Radio Astronomy Observatory/California Institute of Technology group. The results available in June 1974, the factors limiting their accuracy, and the prospects for the future are discussed in this paper.