Multi-reference evaluation of uncertainty in earth orientation parameter measurements

Uncertainties in polar motion and length-of-day measurements are evaluated empirically using several data series from the space-geodetic techniques of the global positioning system (GPS), satellite laser ranging (SLR), and very long baseline interferometry (VLBI) during 1997–2002. In the evaluation procedure employed here, known as the three-corner hat (TCH) technique, the signal common to each series is eliminated by forming pair-wise differences between the series, thus requiring no assumed values for the “truth” signal. From the variances of the differenced series, the uncertainty of each series can be recovered when reasonable assumptions are made about the correlations between the series. In order to form the pair-wise differences, the series data must be given at the same epoch. All measurement data sets studied here were sampled at noon (UTC); except for the VLBI series, whose data are interpolated to noon and whose UT1 values are also numerically differentiated to obtain LOD. The numerical error introduced to the VLBI values by the interpolation and differentiation is shown to be comparable in magnitude to the values determined by the TCH method for the uncertainties of the VLBI series. The TCH estimates for the VLBI series are corrupted by such numerical errors mostly as a result of the relatively large data intervals. Of the remaining data sets studied here, it is found that the IGS Final combined series has the smallest polar motion and length-of-day uncertainties.     

ITRF2008: an improved solution of the international terrestrial reference frame

ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16?years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010?ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: ?0.5, ?0.9 and ?4.7?mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3?mm/yr. The estimated formal errors of these parameters are 0.2?mm and 0.2?mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8?mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1?cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2?ppb (8?mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.     

DORIS Contribution to ITRF2005

We examine the contribution of the Doppler Orbit determination and Radiopositioning Integrated by Satellite (DORIS) technique to the International Terrestrial Reference Frame (ITRF2005) by evaluating the quality of the submitted solutions as well as that of the frame parameters, especially the origin and the scale. Unlike the previous versions of the ITRF, ITRF2005 is constructed with input data in the form of time-series of station positions (weekly for satellite techniques and daily for VLBI) and daily Earth orientation parameters (EOPs), including full variance–covariance information. Analysis of the DORIS station positions’ time-series indicates an internal precision reaching 15 mm or better, at a weekly sampling. A cumulative solution using 12 years of weekly time-series was obtained and compared to a similar International GNSS Service (IGS) GPS solution (at 37 co-located sites) yielding a weighted root mean scatter (WRMS) of the order of 8 mm in position (at the epoch of minimum variance) and about 2.5 mm/year in velocity. The quality of this cumulative solution resulting from the combination of two individual DORIS solutions is better than any individual solution. A quality assessment of polar motion embedded in the contributed DORIS solutions is performed by comparison with the results of other space-geodetic techniques and in particular GPS. The inferred WRMS of polar motion varies significantly from one DORIS solution to another and is between 0.5 and 2 mas, depending on the strategy used and in particular estimating or not polar motion rate by the analysis centers. This particular aspect certainly needs more investigation by the DORIS Analysis Centers.     

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.     

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.     

Global plate tectonics and the secular motion of the Pole

Astronomical data compiled during the last 70 years by the international organizations (ILS/IPMS, BIH) providing the coordinates of the instantaneous pole, clearly shows a continuous drift of the “mean pole” (≡barycenter of the wobble cycle with respect to the Conventional International Origin (CIO). This study was undertaken to investigate the possibility of an actual secular motion of the barycenter (approximated by the earth's maximum principal moment of inertia axis or axis of figure) due to differential mass displacements from lithospheric plate rotations. The method assumes the earth's crust modeled as a mosaic of 1°×1° blocks, each one moving independently with their corresponding absolute plate velocities. The differential contributions to the earth's second-order tensor of inertia were computed, resulting in no significant displacement of the earth's axis of figure. In view of the above, the possibleapparent displacement of the “mean pole” as a consequence of station drifting due to absolute plate motions was also analyzed, again without great success. As a further step the old speculation of the whole crust possibly sliding over the upper mantle is revived and the usefulness of the CIO is questioned. Presented at the IAU Symposium No. 78, “Nutation and the Earth Rotation”, Kiev, 22–29, May, 1977.     

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     

信噪比的GNSS宽巷模糊度单历元固定算法

针对常规GNSS解算模糊度存在的问题,该文提出了一种新的GNSS宽巷模糊度单历元求解算法。利用单历元双频码伪距观测值和载波相位观测值得到双差宽巷模糊度浮点解,将所有浮点宽巷模糊度分别向上、向下取整建立模糊度搜索空间;将模糊度空间中的所有备选组合代入双差宽巷观测方程中进行最小二乘解算,其中单位权中误差最小的组合就是最优的宽巷模糊度组合;然后对最优组合进行正确性检验以确定宽巷模糊度。确定宽巷模糊度后,可以利用宽巷观测值和载波观测值求出基础模糊度整周解。实验表明,该文提出的模糊度固定方法具有较高的成功率和可靠性,静态数据中模糊度固定成功率达到98.84%,动态数据中模糊度固定成功率达到了99.60%。     

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     

Non-linear station motions in epoch and multi-year reference frames

In the conventions of the International Earth Rotation and Reference Systems Service (e.g. IERS Conventions 2010), it is recommended that the instantaneous station position, which is fixed to the Earth’s crust, is described by a regularized station position and conventional correction models. Current realizations of the International Terrestrial Reference Frame use a station position at a reference epoch and a constant velocity to describe the motion of the regularized station position in time. An advantage of this parameterization is the possibility to provide station coordinates of high accuracy over a long time span. Various publications have shown that residual non-linear station motions can reach a magnitude of a few centimeters due to not considered loading effects. Consistently estimated parameters like the Earth Orientation Parameters (EOP) may be affected if these non-linear station motions are neglected. In this paper, we investigate a new approach, which is based on a frequent (e.g. weekly) estimation of station positions and EOP from a combination of epoch normal equations of the space geodetic techniques Global Positioning System (GPS), Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI). The resulting time series of epoch reference frames are studied in detail and are compared with the conventional secular approach. It is shown that both approaches have specific advantages and disadvantages, which are discussed in the paper. A major advantage of the frequently estimated epoch reference frames is that the non-linear station motions are implicitly taken into account, which is a major limiting factor for the accuracy of the secular frames. Various test computations and comparisons between the epoch and secular approach are performed. The authors found that the consistently estimated EOP are systematically affected by the two different combination approaches. The differences between the epoch and secular frames reach magnitudes of $23.6~\upmu \hbox {as}$ (0.73 mm) and $39.8~\upmu \hbox {as}$ (1.23 mm) for the x-pole and y-pole, respectively, in case of the combined solutions. For the SLR-only solutions, significant differences with amplitudes of $77.3~\upmu \hbox {as}$ (2.39 mm) can be found.     

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.     

Combined GPS/GLONASS data processing

To obtain the GLONASS satellite position at an epoch other than reference time, the satellite's equation of motion has to be integrated with broadcasting ephemerides. The iterative detecting and repairing method of cycle slips based on triple difference residuals for combined GPS/GLONASS positioning and the iterative ambiguity resolution approach suitable for combined post processing positioning are discussed systematically. Experiments show that millimeter accuracy can be achieved in short baselines with a few hours' dual frequency or even single frequency GPS/GLONASS carrier phase observations, and the precision of dual frequency observations is distinctly higher than that of single frequency observations.     

利用窗口小波去噪的高精度动态单历元定位算法

为提高动态单历元定位的精度和实现实时处理,提出了一种利用窗口小波去噪的高精度动态单历元算法。该算法首先利用常规单历元方法获得观测值残差,在当前历元右侧通过数据延拓来改善端部效应的影响,然后利用窗口小波对当前历元观测值残差去噪,通过交叉证认实现小波去噪分解层数的自适应选取,最后利用去噪后得到的较为干净的观测值实现最终定位。实验结果表明,与常规单历元定位相比,在不同的运动情况下,该方法的定位精度均有较大的提高,与小波后处理结果一致。     

Rotational evaluation of a long-period spherical harmonic ocean tide model

By exchanging angular momentum with the solid earth, tidal variations in ocean currents and sea level cause the rotation of the solid earth to change. Observations of earth rotation variations can therefore be used to evaluate ocean tide models. The rotational predictions of a spherical harmonic ocean tide model that is not constrained by any type of data are compared here to the predictions of numerical ocean tide models and to earth rotation observations from which atmospheric and non-tidal oceanic effects have been removed. The spherical harmonic ocean tide model is shown to account for the observed variations at the fortnightly tidal period in polar motion excitation but not in length-of-day. Overall, its long-period polar motion excitation predictions fit the observed tidal signals better than do the predictions of the numerical ocean tide models studied here. It may be possible to improve its agreement with length-of-day observations by tuning certain model parameters, as was done to obtain the close agreement reported here between the modeled and observed polar motion excitation; alternatively, the discrepancy in length-of-day may point to the need to revise current models of mantle anelasticity and/or models of the oceanic response to atmospheric pressure variations.     

A study of gravity variations caused by polar motion using superconducting gravimeter data from the GGP network

Long-term continuous gravity observations, recorded at five superconducting gravimeter (SG) stations in the Global Geodynamic Project (GGP) network, as well as data on orientation variations in the Earths rotation axis (i.e. polar motion), have been used to investigate the characteristics of gravity variations on the Earths surface caused by polar motion. All the SG gravity data sets were pre-processed using identical techniques to remove the luni-solar gravity tides, the long-term trends of the instrumental drift, and the effects of atmospheric pressure. The analysis indicates that the spectral peaks, related to the Chandler and annual wobbles, were identified in both the power and product spectral density estimates. The magnitude of gravity variations, as well as the gravimetric amplitude factor associated with the Chandler wobble, changed significantly at different SG stations and during different observation periods. However, when all the SG observations at these five sites were combined, the gravimetric parameters of the Chandler wobble were retrieved accurately: 1.1613 ± 0.0737 for the amplitude factor and –1°.30 ± 1°.33 for the phase difference. The value of the estimated amplitude factor is in agreement with that predicted theoretically for the zonal tides of an elastic Earth model.     

Polar motion modeling,analysis, and prediction with time dependent harmonic coefficients

A time dependent amplitude model was proposed for the analysis and prediction of polar motion time series. The formulation was implemented to analyze part of the new combined solution, EOP (IERS) C 04, daily polar motion time series of 14 years length using a statistical model with first order autoregressive disturbances. A new solution approach, where the serial correlations of the disturbances are eliminated by sequentially differencing the measurements, was used to estimate the model parameters using weighted least squares. The new model parsimoniously represents the 14-year time series with 0.5 mas rms fit, close to the reported 0.1 mas observed pole position precisions for the x and y components. The model can also predict 6 months into the future with less than 4 mas rms prediction error for both polar motion components, and down to sub mas for one-step ahead prediction as validated using a set of daily time series data that are not used in the estimation. This study is dedicated to the memory of Prof. Urho Uotila (1923–2006) whose teaching of “Adjustment Computations” over the years influenced so much, so many of us who had the privilege of being his students.     

Geodetic and geophysical implications of the homogeneous reduction of pole coordinates (1899–1979)

The new series ILS (H) of pole coordinates (1899.9–1979.0) computed in a homogeneous system has been employed for the determination of the period of Chandler's component of polar motion. The comparison with a value derived from a previous series ILS (VY) shows there is no significant variation in the period in spite of the known systematic errors affecting the ILS (VY) series. Any high precision geodetic network adjustment has to take account of the pole coordinates defined by the ILS (H) series. Such long series permitted the identification of another component of polar motion with a period of about 30 years. The polhode derived from the ILS (H) series shows greater regularity than previously deduced polhodes and, therefore, we can conclude that past investigations in geodesy and geophysics trying to correlated the irregularities of the polhode with different geophysical phenomena, for instance, earthquakes, may have to be revised.     

Four dimensional studies in Earth space

Summary A system of reference which is directly related to observations, is proposed for four dimensional studies in Earth space. The requisite data is used to define both global control network and also polar wandering. The determination of variations of the Earth’s gravitational field with time also forms part of such a system. Techniques are outlined for the unique definition of the motion of the geocenter, and the changes in the location of the axis of rotation of an instantaneous Earth model, in relation to values at some epoch of reference. The instantaneous system referred to is directly related to a fundamental equation in geodynamics. The reference system defined would provide an unambiguous frame for long period studies in Earth space, provided the scale of the space were specified. Presented at the I.A.G./A.G.U. Symposium on Earth Gravity Models related problems, St Louis, Missouri, U.S.A., 16–18 August 1972.     

Period variations of the Chandler wobble

Variations in the period of the Chandler wobble have been discussed since its discovery by Chandler in 1892. Various authors engaged in the investigation of polar motion time series suggest both a variable and an invariable period. It cannot be resolved by the analysis of time series whether the Chandler period is variable. By studying the influence of mass redistributions on the Chandler period it has been found that it is in fact variable, but the magnitude of such variation is much smaller than that found by polar motion time series analysis. For the currently available time series of polar motion, it is sufficient to assume an invariable Chandler period. AcknowledgmentsUseful discussions with Dr. F. Barthelmes and Dr. K. Fleming are gratefully appreciated.     

Comparison of length of day with oceanic and atmospheric angular momentum series

This is a companion paper to earlier comparisons and study of operational polar motion series, published recently in the same journal. In this contribution, four operational, publicly available, length-of-day (LOD) time series have been compared to the atmospheric angular momentum (AAM) augmented with recent oceanic angular momentum (OAM) data during September 1997–July 2000, using several intervals ranging from 3 days to almost 3 years. Additionally, the LOD of the International GNSS Service (IGS) historical series and a new LOD combination (CMB) were also analyzed. All the six LOD series showed an overall correlation exceeding 0.99 for the complete interval of almost 3 years. Even for the shortest interval of only 3 days, the correlation was still higher than 0.60. The combined AAM + OAM series with inverted barometer corrections always gave the best correlation. The Rapid Service LOD of the International Earth Rotation and Reference Systems Service (IERS) compared the best at all intervals but the shortest one, where the CMB LOD was the best with a correlation of 0.73, followed by both IGS series with a correlation of about 0.71. Prior to all the correlation analyses, in addition to the removal of all the known (conventional) LOD tidal variations with periods ranging from 5.6 days to 18.6 years and lunar fortnightly and monthly oceanic tides, small corrections of lunar fortnightly and monthly tides, semi-annual, annual periodical signals, drift and scale had to be estimated with respect to the combined AAM + OAM series.