Recent Improvements to IERS Bulletin A Combination and Prediction

Driven by a need for increased accuracy in real-time Earth orientation parameters (EOPs), the Bulletin A (Rapid Servce and Predictions) of the International Earth Rotation Service (IERS) has recently made several major changes to its combination and prediction procedures. Changes to the process ob combining multi-technique results include creation of a daily Bulletin A updata, inclusion of several new data sets, and use of polar motion rantes for the latest epoch. Notably, the contributions from GPS observations have grown steadily in significance, both for polar motion and Universal Time (UT1). The prediction procedure has, in turn, benefited from these changes as well as improvements to the polar motion prediction model. As a result, demanding real-time applications, such as for satellite orbit extrapolations should observe a major improvement in the accuracy of our real-time EOP products. All results, together with supporting and diagnostic information, are available at the website http://maia.usno.navy.mil. The maximum EOP errors (root-mean-squared sense) that a real-time user would experience using the latest available update of Bulletin A are currently estimated to be ∼0.9 milliarcseconds (mas) for polar motion and ∼0.15 milliseconds (ms) for UT1-UTC. The data latency (the lag since the most recent observations) for EOP predictions need not exceed ∼41 hours for users who avail themselves of the daily updates. Over the past four years, the accuracy for real-time applications has improved by nearly a factor of 4 in polar motion and a factor of 10 in UT1. This is primarily due to the large reduction in data latency, which in turn is mostly possible due to the Rapid product delivery of the International GPS Service (IGS) (see Mireault et al, 1999). ? 2001 John Wiley & Sons, Inc.     

Possible improvement of Earth orientation forecast using autocovariance prediction procedures

 Autocovariance prediction has been applied to attempt to improve polar motion and UT1-UTC predictions. The predicted polar motion is the sum of the least-squares extrapolation model based on the Chandler circle, annual and semiannual ellipses, and a bias fit to the past 3 years of observations and the autocovariance prediction of these extrapolation residuals computed after subtraction of this model from pole coordinate data. This prediction method has been applied also to the UT1-UTC data, from which all known predictable effects were removed, but the prediction error has not been reduced with respect to the error of the current prediction model. However, the results show the possibility of decreasing polar motion prediction errors by about 50 for different prediction lengths from 50 to 200 days with respect to the errors of the current prediction model. Because of irregular variations in polar motion and UT1-UTC, the accuracy of the autocovariance prediction does depend on the epoch of the prediction. To explain irregular variations in x, y pole coordinate data, time-variable spectra of the equatorial components of the effective atmospheric angular momentum, determined by the National Center for Environmental Prediction, were computed. These time-variable spectra maxima for oscillations with periods of 100–140 days, which occurred in 1985, 1988, and 1990 could be responsible for excitation of the irregular short-period variations in pole coordinate data. Additionally, time-variable coherence between geodetic and atmospheric excitation function was computed, and the coherence maxima coincide also with the greatest irregular variations in polar motion extrapolation residuals. Received: 22 October 1996 / Accepted: 16 September 1997     

利用LS_AR模型对极移参数的中长期预报

为了满足深空探测器自主导航定位对极移参数中长期预报的需求,阐述了基于LS_AR模型的极移参数中长期预报和精度评定的原理,提出了4种改进方案对LS_AR模型的构建进行优化,并利用IERS提供的1990～1996年的极移参数的时间序列检验4种优化方案,得到了最优的预报模型,在400 d跨度上,其预报结果的平均绝对误差比未优化的模型小3 mas左右。     

Long-term prediction of polar motion using a combined SSA and ARMA model

To meet the need for real-time and high-accuracy predictions of polar motion (PM), the singular spectrum analysis (SSA) and the autoregressive moving average (ARMA) model are combined for short- and long-term PM prediction. According to the SSA results for PM and the SSA prediction algorithm, the principal components of PM were predicted by SSA, and the remaining components were predicted by the ARMA model. In applying this proposed method, multiple sets of PM predictions were made with lead times of two years, based on an IERS 08 C04 series. The observations and predictions of the principal components correlated well, and the SSA \(+\) ARMA model effectively predicted the PM. For 360-day lead time predictions, the root-mean-square errors (RMSEs) of PMx and PMy were 20.67 and 20.42 mas, respectively, which were less than the 24.46 and 24.78 mas predicted by IERS Bulletin A. The RMSEs of PMx and PMy in the 720-day lead time predictions were 28.61 and 27.95 mas, respectively.     

Prediction of polar motion

Based on an analysis of polar motion behavior, we found the possibility of predicting polar motion up to one year in advance. Comparing these predicted polar coordinates with the observed ones (smoothed), the rms of the differences is about 0".02. The differences of the relative polar motion are much smaller. For any time interval of 20–30 days throughout the whole year, the rms of the relative polar motion differences is about 0".01. It appears that 80–90% of the polar motion is composed of the stable, predictable Chandler and annual terms.     

Methodology for the combination of sub-daily Earth rotation from GPS and VLBI observations

A combination procedure of Earth orientation parameters from Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI) observations was developed on the basis of homogeneous normal equation systems. The emphasis and purpose of the combination was the determination of sub-daily polar motion (PM) and universal time (UT1) for a long time-span of 13 years. Time series with an hourly resolution and a model for tidal variations of PM and UT1-TAI (dUT1) were estimated. In both cases, 14-day nutation corrections were estimated simultaneously with the ERPs. Due to the combination procedure, it was warranted that the strengths of both techniques were preserved. At the same time, only a minimum of de-correlating or stabilizing constraints were necessary. Hereby, a PM time series was determined, whose precision is mainly dominated by GPS observations. However, this setup benefits from the fact that VLBI delivered nutation and dUT1 estimates at the same time. An even bigger enhancement can be seen for the dUT1 estimation, where the high-frequency variations are provided by GPS, while the long term trend is defined by VLBI. The estimated combined tidal PM and dUT1 model was predominantly determined from the GPS observations. Overall, the combined tidal model for the first time completely comprises the geometrical benefits of VLBI and GPS observations. In terms of root mean squared (RMS) differences, the tidal amplitudes agree with other empirical single-technique tidal models below 4 μas in PM and 0.25 μs in dUT1. The noise floor of the tidal ERP model was investigated in three ways resulting in about 1 μas for diurnal PM and 0.07 μs for diurnal dUT1 while the semi-diurnal components have a slightly better accuracy.     

Short-term polar motion forecasts from earth system modeling data

Polar motion predictions for up to 10 days into the future are obtained from predicted states of the atmosphere, ocean and continental hydrosphere in a hind-cast experiment covering 2003–2008. High-frequency mass variations within the geophysical fluids are the main cause of wide-band stochastic signals not considered in the presently used statistical prediction approach of IERS bulletin A for polar motion. Taking EAM functions based on forecasted model states, derived from ECMWF medium-range forecasts and corresponding LSDM and OMCT simulations, into account the prediction errors are reduced by 26%. The effective forecast length of the model combination is found to be 7 days, primarily limited by the accuracy of the forecasted atmospheric wind fields. Highest improvements are found for forecast days 4–5 with prediction skill scores of the polar motion excitation functions improved by a factor up to 5. Whereas bulletin A forecasts can explain the observed variance within the first 10 days only by up to 40%, half of the model forecasts reach relative explained variances between 40 and 80%.     

Excitation of non-atmospheric polar motion by the migration of the Pacific Warm Pool

Changes in the annual variation of the Earths polar motion are found to be largely caused by the variation of the atmospheric angular momentum (AAM). Recent simulation results of oceanic general circulation models further suggest global oceanic effects on the annual polar motion in addition to the atmosphere. In comparison with previous model studies of global oceanic effects, this research particularly singles out a large-scale ocean anomaly and investigates its effect on the annual polar motion, determined from satellite observations of the movement of the Western Pacific Warm Pool (WPWP). Although the scale of the warm pool is much smaller than that of the solid Earth, analysis of the non-atmospheric polar motion excitation has shown that the WPWP contributes non-negligibly to the annual polar motion. The analysis consists of over 30 years of WPWP data (1970–2000) and shows values of polar motion excitation for the x-component of (2.5 mas, –79°) and for the y-component of (0.6 mas, 173°). Comparison of this result with the total geodetic non-atmospheric polar motion excitation of (10.3 mas, 59°) for the x-component and (10.6 mas, 62°) for the y-component shows the significance of the WPWP. Changes in the Earths polar motion have attracted significant attention, not only because it is an important geodetic issue, but also because it has significant value as a global measure of variations within the hydrosphere, atmosphere, cryosphere, and solid Earth, and hence global changes.Tel: 86–21–64386191 Fax: 86–21–64384618Acknowledgments. The authors are grateful to Dr. R. Gross (JPL) and two anonymous reviewers for providing invaluable comments. They also thank Dr. J.L. Chen (CSR) for helpful discussions. Y. Zhou, D. Zheng and X. Liao were supported by the National Natural Science Foundation of China (10273018, 10133010) and Key Project of Chinese Academy of Sciences (KJCX2-SW-T1). X-H. Yan was supported by the National Aeronautics and Space Administration (NASA) through Grant NAG5–12745, and by the National Science Foundation (NSF) through the Presidential Faculty Fellow award to X-H. Yan (OCE-9453499). W.T. Liu was supported by the NASA Physical Oceanography Program.     

Combination of modeled short-term angular momentum function forecasts from atmosphere, ocean, and hydrology with 90-day EOP predictions

Angular momentum forecasts for up to 10 days into the future, modeled from predicted states of the atmosphere, ocean and continental hydrosphere, are combined with the operational IERS EOP prediction bulletin A to reduce the prediction error in the very first day and to improve the subsequent 90-day prediction by exploitation of the revised initial state and trend information. EAM functions derived from ECMWF short-range forecasts and corresponding LSDM and OMCT simulations can account for high-frequency mass variations within the geophysical fluids for up to 7 days into the future primarily limited by the accuracy of the forecasted atmospheric wind fields. Including these wide-band stochastic signals into the first days of the 90-day statistical IERS predictions reduces the mean absolute prediction error even for predictions beyond day 10, especially for polar motion, where the presently used prediction approach does not include geophysical fluids data directly. In a hindcast experiment using 1 year of daily predictions from May 2011 till July 2012, the mean prediction error in polar motion, compared to bulletin A, is reduced by 32, 12, and 3 % for prediction days 10, 30, and 90, respectively. In average, the prediction error for medium-range forecasts (30–90 days) is reduced by 1.3–1.7 mas. Even for UT1-UTC, where AAM forecasts are already included in IERS bulletin A, we obtain slight improvements of up to 5 % (up to 0.5 ms) after day 10 due to the additional consideration of oceanic angular momentum forecasts. The improved 90-day predictions can be generated operationally on a daily basis directly after the publication of the related IERS bulletin A product finals2000A.daily.     

Parameter variability of the observed periodic oscillations of polar motion with smaller amplitudes

Compared to the Chandler and annual wobbles, the higher-frequency components of polar motion (PM) have substantially smaller amplitudes. Therefore, their study has had to wait until higher-quality time series with high temporal resolution, as measured by space geodetic techniques, have become available. Based on the combined Earth orientation series SPACE99 computed by the Jet Propulsion Laboratory (JPL) from 1976 to 2000 at daily intervals, the periodic PM terms, in particular at the quasi-biennial, 300-day, semi-Chandler, semi-annual, 4-month, 90-day, 2-month and 1.5-month periods, have been separated by band-pass filtering and it has been found that the persistence of oscillations becomes less with increasing frequency. In order to quantify and better describe the parameter variability of these PM components over time, the radii, direction angles and period lengths were computed from the periodic terms filtered out from the time series. The results clearly show the characteristics and time evolution of the periodic PM components. The largest elliptic oscillation is the semi-annual wobble with a maximum semi-major axis of up to 13 mas (milliarc seconds). The other wobbles are smaller. They have maximum semi-major axes of between 3 and 8 mas. If the oscillations have period lengths of 4 months and less, then they are elapsed not only progradly, but also retrogradly. AcknowledgementsThis paper was presented at the 27th General Assembly of the European Geophysical Society in Nice, France, 22–26 April 2002. Thanks go to Kevin Fleming for his linguistic advice. The author would also like to thank Barbara Koaczek for suggesting some valuable improvements.     

On long-period polar motion

 Five separate polar motion series are examined in order to understand what portion of their variations at periods exceeding several years represents true polar motion. The data since the development of space-geodetic techniques (by themselves insufficient for study of long-period motion), and a variety of historical astrometric data sets, allow the following tentative conclusions: retrograde long-period polar motion below about −0.2 cpy (cycles per year) in pre-space-geodetic data (pre-1976) is dominantly noise. For 1976–1992, there is poor agreement between space-geodetic and astrometric series over the range −0.2 to +0.2 cpy, demonstrating that classical astrometry lacked the precision to monitor polar motion in this frequency range. It is concluded that all the pre-1976 astrometric polar motion data are likely to be dominated by noise at periods exceeding about 10 years. The exception to this is possibly a linear trend found in some astrometric and space geodetic series. At frequencies above prograde +0.2 cpy (periods shorter than about 5 years), historical astrometric data may be of sufficient quality for comparisons with geophysical excitation time series. Even in the era of space geodesy, significant differences are found in long-period variations in published polar motion time series. Received: 27 March 2001 / Accepted: 15 October 2001     

An improved empirical model for the effect of long-period ocean tides on polar motion

Because the tide-raising potential is symmetric about the Earth’s polar axis it can excite polar motion only by acting upon non-axisymmetric features of the Earth like the oceans. In fact, after removing atmospheric and non-tidal oceanic effects, polar motion excitation observations show a strong fortnightly tidal signal that is not completely explained by existing dynamical and empirical ocean tide models. So a new empirical model for the effect of the termensual (Mtm and mtm), fortnightly (Mf and mf), and monthly (Mm) tides on polar motion is derived here by fitting periodic terms at these tidal frequencies to polar motion excitation observations that span 2 January 1980 to 8 September 2006 and from which atmospheric and non-tidal oceanic effects have been removed. While this new empirical tide model can fully explain the observed fortnightly polar motion excitation signal during this time interval it would still be desirable to have a model for the effect of long-period ocean tides on polar motion that is determined from a dynamical ocean tide model and that is therefore independent of polar motion observations.     

7个月周期极移的非线性动力机制

从滞弹性阻尼形变摄动造成CW频率调制假设出发，对CW的共振激发模型加上参数的时变调制，变成了参数共振模型。经正演计算发现，参数共振模型完全符合CW的实际，表明滞弹性阻尼形变摄动造成频率的3％调制，进一步使得CW振幅调制可达70％以上。这一参数共振模型是一个非线性动力系统，在非线性情况下，运动将发生分岔，即多解。     

Harmonic analysis of total electron contents time series: methodology and results

In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation spectra are introduced and estimated for the series to detect the regular and modulated dominant frequencies of the periodic patterns. Two significant periodic patterns are the diurnal and annual signals with periods of 24/n hours and 365.25/n days (n = 1, 2, …), which are the Fourier series decomposition of the regular daily and yearly periodic variations of the ionosphere. The spectrum shows a cluster of periods near 27 days, thereby indicating irregularities at this solar cycle period. A series of peaks, with periods close to the diurnal signal and its harmonics, are evident in the spectrum. In fact, the daily signal harmonics of ω _i  = 2πi are modulated with the annual signal harmonics of ω _j  = 2πj/365.25 as ω _ijM  = 2πi(1 ± j/365.25i). Among them, at low and midlatitudes, the largest variations belong to the diurnal signal modulated to the semiannual signal. Some preliminary results on the modulated part are presented. The maximum ranges of the modulated daily signal are ±15 TECU and ±6 TECU at high and low solar periods, respectively. A model consisting of purely harmonic functions plus modulated ones is capable of studying known regular anomalies of the ionosphere, which is currently in progress.     

利用小波分解改进极移预报模型

为进一步提高极移预报精度，将小波分解引入极移预报中。首先利用小波分解对极移序列进行分解，分离低频分量与高频分量，然后对低频分量建立最小二乘外推模型，获得极移序列的趋势项外推值与残差序列，最后采用自回归（autoregressive，AR）模型对高频分量与残差序列之和进行预报，最终极移的预报值为最小二乘外推值与AR模型预报值之和。结果表明，小波分解可以明显改善最小二乘外推与AR组合模型的极移预报精度，尤其对于中长期预报改善更为明显。     

Modeling and forecast of the polar motion excitation functions for short-term polar motion prediction

Short-term forecast of the polar motion is considered by introducing a prediction model for the excitation function that drives the polar motion dynamics. The excitation function model consists of a slowly varying trend, periodic modes with annual and several sub-annual frequencies (down to the 13.6-day fortnightly tidal period), and a transient decay function with a time constant of 1.5 days. Each periodic mode is stochastically specified using a second-order auto-regression process, allowing its frequency, phase, and amplitude to vary in time within a statistical tolerance. The model is used to time-extrapolate the excitation function series, which is then used to generate a polar motion forecast dynamically. The skills of this forecast method are evaluated by comparison to the C-04 polar motion series. Over the lead-time horizon of four months, the proposed method has performed equally well to some of the state-of-art polar motion prediction methods, none of which specifically features forecasting of the excitation function. The annual mode in the ₂ component is energetically the most dominant periodicity. The modes with longer periods, annual and semi-annual in particular, are found to contribute more significantly to forecast accuracy than those with shorter periods.     

Radio source instability in VLBI analysis

The source position time-series for many of the frequently observed radio sources in the NASA geodetic very long baseline interferometry (VLBI) program show systematic linear and non-linear variations of as much as 0.5 mas (milli-arc-seconds) to 1.0 mas, due mainly to source structure changes. In standard terrestrial reference frame (TRF) geodetic solutions, it is a common practice to only estimate a global source position for each source over the entire history of VLBI observing sessions. If apparent source position variations are not modeled, they produce corresponding systematic variations in estimated Earth orientation parameters (EOPs) at the level of 0.02–0.04 mas in nutation and 0.01–0.02 mas in polar motion. We examine the stability of position time-series of the 107 radio sources in the current NASA geodetic source catalog since these sources have relatively dense observing histories from which it is possible to detect systematic variations. We consider different strategies for handling source instabilities where we (1) estimate the positions of unstable sources for each session they are observed, or (2) estimate spline parameters or rate parameters for sources chosen to fit the specific variation seen in the position-time series. We found that some strategies improve VLBI EOP accuracy by reducing the biases and weighted root mean square differences between measurements from independent VLBI networks operating simultaneously. We discuss the problem of identifying frequently observed unstable sources and how to identify new sources to replace these unstable sources in the NASA VLBI geodetic source catalog.     

Influence of subdaily polar motion model on nutation offsets estimated by very long baseline interferometry

This paper studies the connection between the subdaily model for polar motion used in the processing of very long baseline interferometry (VLBI) observations and the estimated nutation offsets. By convention accepted by the International Earth Rotation Service, the subdaily model for polar motion recommended for routine processing of geodetic observations does not contain any daily retrograde terms due to their one-to-one correlation with the nutation. Nevertheless, for a 24-h VLBI solution a part of the signal contained in the polar motion given by the used subdaily model is numerically mistaken for a retrograde daily sidereal signal. This fictitious retrograde daily signal contributes to the estimated nutation, leading to systematic differences between the nutation offsets from VLBI solutions computed with different subdaily polar motion models. We demonstrate this effect using solutions for all suitable 24-h VLBI sessions over a time span of 11 years (2000–2011). By changing the amplitudes of one tidal term in the underlying subdaily model for polar motion and comparing the estimated parameters to the solutions computed with the unchanged subdaily model, the paper shows and explains theoretically the effects produced by the individual subdaily terms on the VLBI nutation estimates.     

VLBI terrestrial reference frame contributions to ITRF2008

In late 2008, the Product Center for the International Terrestrial Reference Frame (ITRF) of the International Earth Rotation and Reference Systems Service (IERS) issued a call for contributions to the next realization of the International Terrestrial Reference System, ITRF2008. The official contribution of the International VLBI Service for Geodesy and Astrometry (IVS) to ITRF2008 consists of session-wise datum-free normal equations of altogether 4,539 daily Very Long Baseline Interferometry (VLBI) sessions from 1979.7 to 2009.0 including data of 115 different VLBI sites. It is the result of a combination of individual series of session-wise datum-free normal equations provided by seven analysis centers (ACs) of the IVS. All series are completely reprocessed following homogeneous analysis options according to the IERS Conventions 2003 and IVS Analysis Conventions. Altogether, nine IVS ACs analyzed the full history of VLBI observations with four different software packages. Unfortunately, the contributions of two ACs, Institute of Applied Astronomy (IAA) and Geoscience Australia (AUS), had to be excluded from the combination process. This was mostly done because the IAA series exhibits a clear scale offset while the solution computed from normal equations contained in the AUS SINEX files yielded unreliable results. Based on the experience gathered since the combination efforts for ITRF2005, some discrepancies between the individual series were discovered and overcome. Thus, the consistency of the individual VLBI solutions has improved considerably. The agreement in terms of WRMS of the Terrestrial Reference Frame (TRF) horizontal components is 1 mm, of the height component 2 mm. Comparisons between ITRF2005 and the combined TRF solution for ITRF2008 yielded systematic height differences of up to 5 mm with a zonal signature. These differences can be related to a pole tide correction referenced to a zero mean pole used by four of five IVS ACs in the ITRF2005 contribution instead of a linear mean pole path as recommended in the IERS Conventions. Furthermore, these systematics are the reason for an offset in the scale of 0.4 ppb between the IVS’ contribution to ITRF2008 and ITRF2005. The Earth orientation parameters of seven series used as input for the IVS combined series are consistent to a huge amount with about 50 μas WRMS in polar motion and 3 μs in dUT1.