Xavier Collilieux

ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters

[1] Unlike the past International Terrestrial Reference Frame (ITRF) versions where global long-term solutions were combined, the ITRF2005 uses as input data time series (weekly from satellite techniques and 24-h session-wise from Very Long Baseline Interferometry) of station positions and daily Earth Orientation Parameters (EOPs). The advantage of using time series of station positions is that it allows to monitor station non-linear motion and discontinuities and to examine the temporal behavior of the frame physical parameters, namely the origin and the scale. The ITRF2005 origin is defined in such a way that it has zero translations and translation rates with respect to the Earth center of mass, averaged by the Satellite Laser Ranging (SLR) time series spanning 13 years of observations. Its scale is defined by nullifying the scale and its rate with respect to the Very Long Baseline Interferometry (VLBI) time series spanning 26 years of observations. The ITRF2005 orientation (at epoch 2000.0) and its rate are aligned to the ITRF2000 using 70 stations of high geodetic quality. The estimated level of consistency of the ITRF2005 origin (at epoch 2000.0) and its rate with respect to the ITRF2000 is respectively 0.1, 0.8, 5.8 mm and 0.2, 0.1, 1.8 mm/yr along the X, Yand Z-axis. We estimate the formal errors on these components to be 0.3 mm and 0.3 mm/yr. We believe that this low level of agreement between the two frame origins is most probably due to the poor SLR network geometry and its degradation over time. The ITRF2005 combination involving 84 co-location sites revealed a scale inconsistency of 1 ppb (6.3 mm at the equator), at epoch 2000.0, and 0.08 ppb/yr between the SLR and VLBI long-term solutions as obtained by the stacking of their respective time series. Possible causes of this inconsistency may include the poor SLR and VLBI networks and their co-locations, local tie uncertainties, systematic effects and possible inconsistent model corrections used in the data analysis of both techniques. For the first time of the ITRF history, the ITRF2005 rigorous combination provides self-consistent series of EOPs, including Polar Motion from VLBI and satellite techniques and Universal Time and Length of Day from VLBI only. A velocity field of 152 sites with an error less than 1.5 mm/yr is used to estimate absolute rotation poles of 15 tectonic plates that are consistent with the ITRF2005 frame. This new absolute plate motion model supersedes and significantly improves that of the ITRF2000 which involved six major tectonic plates. Citation: Altamimi, Z., X. Collilieux, J. Legrand, B. Garayt, and C. Boucher (2007), ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters, J. Geophys. Res., 112, B09401,

Accuracy of the International Terrestrial Reference Frame origin and Earth expansion

The International Terrestrial Reference Frame (ITRF) is a fundamental datum for high?precision orbit tracking, navigation, and global change monitoring. Accurately realizing and maintaining ITRF origin at the mean Earth system center of mass (CM) is critical to surface and spacecraft based geodetic measurements including those of sea level rise and its sources. Although ITRF combines data from satellite laser ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Positioning System (GPS), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), its origin is currently realized by the single technique of SLR. Consequently, it is difficult to independently evaluate the origin accuracy. Also, whether the solid Earth is expanding or shrinking has attracted persistent attention. The expansion rate, if any, has not been accurately determined before, due to insufficient data coverage on the Earths surface and the presence of other geophysical processes. Here, we use multiple precise geodetic data sets and a simultaneous global estimation platform to determine that the ITRF2008 origin is consistent with the mean CM at the level of 0.5 mm yr?1, and the mean radius of the Earth is not changing to within 1? measurement uncertainty of 0.2 mm yr?1.

Hydrological deformation induced by the West African Monsoon: Comparison of GPS, GRACE and loading models

Three-dimensional ground deformation measured with permanent GPS stations in West Africa was used for investigating the hydrological loading deformation associated with Monsoon precipitation. The GPS data were processed within a global network for the 2003–2008 period. Weekly station positions were retrieved with a repeatability (including unmodeled loading effects) of 1–2 mm in the horizontal components and between 2.5 and 6 mm in the vertical component. The annual signal in the vertical component for sites located between 9.6N and 16.7N is in the range 10–15 mm. It is consistent at the 3 mm-level with the annual regional-scale loading deformations estimated from GRACE satellite products and modeled with a combination of hydrological, atmospheric, and nontidal oceanic models. An additional 6 month transient signal was detected in the vertical component of GPS estimates at most of the West African sites. It takes the form of an oscillation occurring between September and March, and reaching a maximum amplitude of 12–16 mm at Ouagadougou (12.5N). The analysis of in situ hydro-geological data revealed a strong coincidence between this transient signal and peak river discharge at three sites located along the Niger River (Timbuktu, Gao, and Niamey). At Ouagadougou, a similar coincidence was found with the seasonal variations of the water table depth. We propose a mechanism to account for this signal that involves a sequence of swelling/shrinking of clays combined with local loading effects associated with flooding of the Niger River.

KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization

The current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at todays millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi-instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.

Accuracy Assessment of the ITRF Datum Definition

One of the main objectives of the International Terrestrial Reference Frame (ITRF) is to provide a standard global reference frame having the most attainable accuracy of its datum definition in terms of its origin, scale and the time evolution of its orientation. This latter should satisfy, by convention, the no net rotation condition. The accuracy of the ITRF datum specifications are obviously dependent on the quality and the internal consistency of the solutions contributing to its elaboration and definition. In this paper, we examine and review the quality of the current ITRF datum definition with an accuracy assessment based on the ITRF2005 results and by consistency evaluation with respect to ITRF2000. The availability of time series of station positions and Earth Orientation Parameters, used now as input for the current ITRF construction, will facilitate the accuracy assessment. When rigorously stacking the time series of a given technique to estimate a long-term frame solution, the 7 transformation parameters of each individual temporal set of station positions are also estimated. By applying dynamically internal constraints (equivalent to minimum constraints approach) over the time series of the 7 parameters, we then preserve some physical “natural” parameters as for instance the scale and the origin from VLBI and SLR, respectively. Our conservative evaluation of the estimated accuracy of the ITRF datum definition is that the origin and its rate are accurate at the level of 5 mm and 2 mm/yr, the scale and its rate are at the level of 1 part per billion (ppb) and 0.1 ppb/yr and the No-Net-Rotation condition implementation is at the level of 2 mm/yr.

ITRF Combination: Theoretical and Practical Considerations and Lessons from ITRF2008

The current ITRF construction is based on a two-step approach, combining input data provided by space geodesy techniques (VLBI, SLR, GPS, DORIS) in the form of time series of station positions and Earth Orientation Parameters. In the first step, the individual technique time series are rigorously stacked (accumulated) yielding long-term secular solutions, while the second step forms the ITRF final combination of the four technique long-term solutions together with local ties at co-location sites. The combination model involves a 7- or 14-parameter similarity transformation formula, for time series stacking and multi-technique combination, respectively. Not all these parameters are necessarily estimated in the combination process, some or all of them could be eliminated from the constructed normal equation, depending on the combination purpose. The paper discusses the relevance of the combination model and its appropriateness for the ITRF combination activities, both from the theoretical and practical point of views, and in particular for the reference frame specifications (origin, scale, orientation and their time evolutions). Selected analysis tests of ITRF2008 input data and results are used to illustrate the discussion as well as to address lessons learned from ITRF2008 experience.

Global coseismic deformations, GNSS time series analysis, and earthquake scaling laws

We investigate how two decades of coseismic deformations affect time series of GPS station coordinates (Global Navigation Satellite System) and what constraints geodetic observations give on earthquake scaling laws. We developed a simple but rapid model for coseismic deformations, assuming different earthquake scaling relations, that we systematically applied on earthquakes with magnitude larger than 4. We found that coseismic displacements accumulated during the last two decades can be larger than 10 m locally and that the cumulative displacement is not only due to large earthquakes but also to the accumulation of many small motions induced by smaller earthquakes. Then, investigating a global network of GPS stations, we demonstrate that a systematic global modeling of coseismic deformations helps greatly to detect discontinuities in GPS coordinate time series, which are still today one of the major sources of error in terrestrial reference frame construction (e.g., the International Terrestrial Reference Frame). We show that numerous discontinuities induced by earthquakes are too small to be visually detected because of seasonal variations and GPS noise that disturb their identification. However, not taking these discontinuities into account has a large impact on the station velocity estimation, considering todays precision requirements. Finally, six groups of earthquake scaling laws were tested. Comparisons with our GPS time series analysis on dedicated earthquakes give insights on the consistency of these scaling laws with geodetic observations and Okada coseismic approach.

Impact of the North Atlantic Oscillation on Southern Europe Water Distribution: Insights from Geodetic Data

AbstractFrom space gravity and station position data over southern Europe from 2002 to 2010, this study investigates the interannual mass redistributions using principal component analysis. The dominant mode, which appears both in gravity and positioning, results from the North Atlantic Oscillation (NAO). This analysis allows us to isolate and characterize the NAO impact on the mass distribution, which appears centered over the Black Sea and its two main catchment basins, the Danube and Dnieper.

Strengthes and Limitations of the ITRF: ITRF2005 and Beyond

As the International Terrestrial Reference Frame (ITRF) is constructed by combination of space geodesy technique solutions together with terrestrial local ties in co-location sites, it then inherits strengths and weaknesses of the combined data. This paper uses the ITRF2005 results in order to illustrate the critical aspects of the combination that impact the ITRF datum definition: the origin, the scale and the No Net Rotation condition. The main ITRF2005 results, using as input data time series of station positions, indicate a drift of 1.8 mm/yr in the origin Z-translation component with respect to ITRF2000, while SLR solutions are used to define the origins of both frames. A scale bias of about 1 ppb between VLBI and SLR solutions is also detected. Possible causes of this inconsistency include the poor SLR and VLBI networks and their co-locations, systematic errors and possible inconsistent model corrections used in the data analysis of both techniques. As conclusion of this paper, some recommendations for improvements of future ITRF solutions are addressed.

Time-Correlated GPS Noise Dependency on Data Time Period

GPS position time series contain time-correlated noise. The estimated parameters using correlated time series data, as station velocities, are then more uncertain than if the time series data were uncorrelated. If the level of the time-correlated noise is not taken into account, the estimated formal uncertainties will be smaller. By estimating the type and amplitude of the noise content in time series, more realistic formal uncertainties can be assessed.