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     

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.     

The contribution of Very Long Baseline Interferometry to ITRF2005

The contribution of the International VLBI Service for Geodesy and Astrometry (IVS) to the ITRF2005 (International Terrestrial Reference Frame 2005) has been computed by the IVS Analysis Coordinator’s office at the Geodetic Institute of the University of Bonn, Germany. For this purpose the IVS Analysis Centres (ACs) provided datum-free normal equation matrices in Solution INdependent EXchange (SINEX) format for each 24 h observing session to be combined on a session-by-session basis by a stacking procedure. In this process, common sets of parameters, transformed to identical reference epochs and a prioris, and especially representative relative weights have been taken into account for each session. In order to assess the quality of the combined IVS files, Earth orientation parameters (EOPs) and scaling factors have been derived from the combined normal equation matrices. The agreement of the EOPs of the combined normal equation matrices with those of the individual ACs in terms of weighted root mean square (WRMS) is in the range of 50–60 μas for the two polar motion components and about 3 μs for UT1−UTC. External comparisons with International GNSS Serive (IGS) polar motion components is at the level of 130–170 μas and 21 μs/day for length of day (LOD). The scale of the terrestrial reference frame realized through the IVS SINEX files agrees with ITRF2000 at the level of 0.2 ppb.     

Geodetic surveys in Messina straits area

By using the fit of theoretical displacements on a fault according toMindlin andCheng (1950) dislocation theory, the vertical deformation field (maximum subsidence of 70 cm) associated to the Dec. 28 1908 MessinaM=7.0 earthquake is compared to the results of a spirit levelling survey that we performed in the Messina Straits area in 1981–1982. The differences in level from the last levelling campaign in the area, completed in 1970, show that the coastlines have undergone a moderate differential subsidence of about1 mm/year in the last decade. This is in agreement with the trend observed around 1908 and with the data of the Messina tide-gauge relative to the period 1897–1908 and 1910–1918. The lack of data in the period 1918–1970 does not allow definite conclusions about the vertical tectonic deformations in the area. Recent data on planimetric deformations have shown a South-North relative motion of Sicily. A comparison with the theoretical displacements indicates that a pure dip-slip of4 cm on the 1908 fault system does explain the observed vertical deformation, but not the horizontal.     

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%.     

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     

Analysis of secular polar motion and continental drift

The secular latitude variations of the five ILS stations of Mizusawa, Kitab, Carloforte, Gaithersburg and Ukiah were analyzed taking into account the recent continental drift theory. Using Le Pichon's 1968 reconstruction, the rate of rotation was computed from the astronomical data, fixing the pole of rotation by Le Pichon's determination. The most reasonable solution was obtained considering Mizusawa, Kitab and Carloforte lying on the Eurasia plate, the two American stations as one on the American plate (Gaithersburg) and the other on the North—East Pacific plate (Ukiah). The resulting relative rate between the Euro-American plates is found to be 0".0028/year and between the American—Pacific plates 0".0032/ years, or about 1°,3/10⁶ years and in excellent agreement with the plate tectonic theory. Luxembourg Meeting of the “Journées Luxembourgeoises de Géodynamique”, 1972.     

Comparison of a GPS-defined global reference frame with ITRF2000

The Global Positioning System is a constellation of 24–28 satellites, which can be used to define a global terrestrial reference frame. Daily offsets between a GPS defined frame and ITRF2000 have been estimated using more than a decade of GPS observations from 1990–2001. A linear fit to the full span of data shows agreement between the two frames at the level of –1 ppb and –0.1 ppb/year for scale, 5 mm and 0 mm/year for the X component of center of mass, –2 mm and –3 mm/year for the Y component, and 4 mm and 6 mm/year for the Z component. GPS is a viable tool for defining the global reference frame either alone, or in combination with other geodetic techniques. Electronic Publication     

Using home buyers’ revealed preferences to define the urban–rural fringe

The location of new homes defines the urban–rural fringe and determines many facets of the urban–rural interaction set in motion by construction of new homes in previously rural areas. Home, neighborhood and school district characteristics play a crucial role in determining the spatial location of new residential construction, which in turn defines the boundary and spatial extent of the urban–rural fringe. We develop and apply a spatial hedonic variant of the Blinder (J Hum Resour 8:436–455, 1973) and Oaxaca (Int Econ Rev 9:693–709, 1973) price decomposition to newer versus older home sales in the Columbus, Ohio metropolitan area during the year 2000. The preferences of buyers of newer homes are compared to those who purchased the nearest neighboring older home located in the same census block group, during the same year. Use of the nearest older home purchased in the same location represents a methodology to control for various neighborhood, social–economic-demographic and school district characteristics that influence home prices. Since newer homes reflect current preferences for home characteristics while older homes reflect past preferences for these characteristics, we use the price differentials between newer and older home sales in the Blinder–Oaxaca decomposition to assess the relative significance of various house characteristics to home buyers.

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.     

Geodetic measurement of horizontal strain across the Red River fault near Thac Ba, Vietnam, 1963–1994

Geodetic measurements from 1963 through 1994 are used to estimate horizontal strain rates across the Red River fault near Thac Ba, Vietnam. Whether or not this fault system is currently active is a subject of some debate. By combining: (1) triangulation from 1963, (2) triangulation in 1983, and (3) Global Positioning System (GPS) observations in 1994, horizontal shear strain rates are estimated without imposing any prior information on fixed stations. The estimated rates of shear strain in ten triangular subnetworks surrounding the fault trace are not significantly different from zero at 95% confidence. The maximum rate of dextral shear is less than 0.3 μrad/year in all but one of the triangles. The estimates help bound the slip rate in a simple elastic dislocation model for a locked, vertical strike-slip fault. By assuming a locking depth of 5–20 km, the most likely values for the deep slip rate are between 1 and 5 mm/year of right-lateral motion. These values delimit the 23% confidence interval. At 95% confidence, the slip rate estimate falls between 7 mm/year of left-lateral motion and 15 mm/year of right-lateral motion. Received: 18 November 1997 / Accepted: 28 January 1999     

Improving strain rate estimation from velocity data of non-permanent GPS stations: the Central Apennine study case (Italy)

An efficient procedure is proposed to define realistic lower limits of velocity errors of a non-permanent GPS station (NPS), i.e., a station where the antenna is installed and operates for short time periods, typically 10–20 days per year. Moreover, the proposed method is aimed at being independent of standard GPS data processing. The key is to subsample appropriately the coordinate time series of several continuous GPS stations situated nearby or inside the considered NPS network, in order to simulate the NPS behavior and to estimate the velocity errors associated with the subsampling procedure. The obtained data are used as lower limits to accept or correct the error estimates provided by standard data processing. The proposed approach is applied to data from the dense, non-permanent network in the Central Apennine of Italy based on a sequence of solutions for the overlapping time spans 1999–2003, 1999–2004, 1999–2005 and 1999–2007. Both the original and error-corrected velocity patterns are used to compute the strain rate fields. The comparison between the corresponding results reveals large differences that could lead to divergent interpretations about the kinematics of the study area.     

Evidence and cause of climate cycles in polar motion

 The long-term variation of polar motion contains a number of periods similar to climate cycles. Two possible causes for these long-term variations are mass redistributions produced by variations of atmospheric and oceanic circulation, and mass exchanges between the cryosphere and hydrosphere. Inner-core wobble, which can be inferred from the observed motion of the geomagnetic pole, is another phenomenon with periods similar to climate cycles. Only observations relating to mass redistributions caused by atmosphere dynamics and inner-core wobble are available for sufficiently long periods of time to investigate their influence on climate cycles in polar motion. Both processes contribute to climate cycles in polar motion, but they cannot completely explain these cycles. Possible sources of climate cycles are discussed. Received: 20 December 1999 / Accepted: 28 August 2000     

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.     

Is there utility in rigorous combinations of VLBI and GPS Earth orientation parameters?

Combinations of station coordinates and velocities from independent space-geodetic techniques have long been the standard method to realize robust global terrestrial reference frames (TRFs). In principle, the particular strengths of one observing method can compensate for weaknesses in others if the combination is properly constructed, suitable weights are found, and accurate co-location ties are available. More recently, the methodology has been extended to combine time-series of results at the normal equation level. This allows Earth orientation parameters (EOPs) to be included and aligned in a fully consistent way with the TRF. While the utility of such multi-technique combinations is generally recognized for the reference frame, the benefits for the EOPs are yet to be quantitatively assessed. In this contribution, which is a sequel to a recent paper on co-location ties (Ray and Altamimi in J Geod 79(4–5): 189–195, 2005), we have studied test combinations of very long baseline interferometry (VLBI) and Global Positioning System (GPS) time-series solutions to evaluate the effects on combined EOP measurements compared with geophysical excitations. One expects any effect to be small, considering that GPS dominates the polar motion estimates due to its relatively dense and uniform global network coverage, high precision, continuous daily sampling, and homogeneity, while VLBI alone observes UT1-UTC. Presently, although clearly desirable, we see no practical method to rigorously include the GPS estimates of length-of-day variations due to significant time-varying biases. Nevertheless, our results, which are the first of this type, indicate that more accurate polar motion from GPS contributes to improved UT1-UTC results from VLBI. The situation with combined polar motion is more complex. The VLBI data contribute directly only very slightly, if at all, with an impact that is probably affected by the weakness of the current VLBI networks (small size and sparseness) and the quality of local ties relating the VLBI and GPS frames. Instead, the VLBI polar motion information is used primarily in rotationally aligning the VLBI and GPS frames, thereby reducing the dependence on co-location tie information. Further research is needed to determine an optimal VLBI-GPS combination strategy that yields the highest quality EOP estimates. Improved local ties (including internal systematic effects within the techniques) will be critically important in such an effort.     

The US Gravimetric Geoid of 2009 (USGG2009): model development and evaluation

A new gravimetric geoid model, USGG2009 (see Abbreviations), has been developed for the United States and its territories including the Conterminous US (CONUS), Alaska, Hawaii, Guam, the Commonwealth of the Northern Mariana Islands, American Samoa, Puerto Rico and the US Virgin Islands. USGG2009 is based on a 1′ × 1′ gravity grid derived from the NGS surface gravity data and the DNSC08 altimetry-derived anomalies, the SRTM-DTED1 3′′ DEM for its topographic reductions, and the global geopotential model EGM08 as a reference model. USGG2009 geoid heights are compared with control values determined at 18,398 Bench Marks over CONUS, where both the ellipsoidal height above NAD 83 and the Helmert orthometric height above NAVD 88 are known. Correcting for the ellipsoidal datum difference, this permits a comparison of the geoid heights to independent data. The standard deviation of the differences is 6.3 cm in contrast to 8.4 cm for its immediate predecessor— USGG2003. To minimize the effect of long-wavelength errors that are known to exist in NAVD88, these comparisons were made on a state-by-state basis. The standard deviations of the differences range from 3–5 cm in eastern states to about 6–9 cm in the more mountainous western states. If the GPS/Bench Marks-derived geoid heights are corrected by removing a GRACE-derived estimate of the long-wavelength NAVD88 errors before the comparison, the standard deviation of their differences from USGG2009 drops to 4.3 cm nationally and 2–4 cm in eastern states and 4–8 in states with a maximum error of 26.4 cm in California and minimum of −32.1 cm in Washington. USGG2009 is also compared with geoid heights derived from 40 tide-gauges and a physical dynamic ocean topography model in the Gulf of Mexico; the mean of the differences is 3.3 cm and their standard deviation is 5.0 cm. When USGG2009-derived deflections of the vertical are compared with 3,415 observed surface astro-geodetic deflections, the standard deviation of the differences in the N–S and E–W components are 0.87′′ and 0.94′′, respectively.     

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.     

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.     

Precision real-time navigation of LEO satellites using global positioning system measurements

Continued advancements in remote sensing technology along with a trend towards highly autonomous spacecraft provide a strong motivation for accurate real-time navigation of satellites in low Earth orbit (LEO). Global Navigation Satellite System (GNSS) sensors nowadays enable a continuous tracking and provide low-noise radiometric measurements onboard a user spacecraft. Following the deactivation of Selective Availability a representative real-time positioning accuracy of 10 m is presently achieved by spaceborne global positioning system (GPS) receivers on LEO satellites. This accuracy can notably be improved by use of dynamic orbit determination techniques. Besides a filtering of measurement noise and other short-term errors, these techniques enable the processing of ambiguous measurements such as carrier phase or code-carrier combinations. In this paper a reference algorithm for real-time onboard orbit determination is described and tested with GPS measurements from various ongoing space missions covering an altitude range of 400–800 km. A trade-off between modeling effort and achievable accuracy is performed, which takes into account the limitations of available onboard processors and the restricted upload capabilities. Furthermore, the benefits of different measurements types and the available real-time ephemeris products are assessed. Using GPS broadcast ephemerides a real-time position accuracy of about 0.5 m (3D rms) is feasible with dual-frequency carrier phase measurements. Slightly inferior results (0.6–1 m) are achieved with single-frequency code-carrier combinations or dual-frequency code. For further performance improvements the use of more accurate real-time GPS ephemeris products is mandatory. By way of example, it is shown that the TDRSS Augmentation Service for Satellites (TASS) offers the potential for 0.1–0.2 m real-time navigation accuracies onboard LEO satellites.