ITRF2008: an improved solution of the international terrestrial reference frame

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, Y and 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.

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.

Highly accurate Terrestrial Reference Frames (TRF) – based on the combination of the four space-geodetic techniques Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Navigation Satellite Systems (GNSS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) – are the fundamental backbone for a broad range of applications like land surveying, the geodetic monitoring of geophysical processes within the Earth system or navigation on and near the Earth’s surface. Recent efforts at the Geodetic Observatory Wettzell (GOW), Germany, aim at a transition from the purely geometric link between space-geodetic techniques via local ties as the current standard to an innovative quasi-error-free combination based on a common clock (CC) and a common target (CT).Once the CC/CT-based infrastructure at GOW is fully developed and operational, it will be possible to uncover systematics between the space-geodetic techniques as well as individual instruments. However, to guarantee the long-term accuracy and stability of the TRF, it is indispensable to know and, if possible, to eliminate the systematics over the entire observation period of the techniques. A prerequisite for this is to compile an inventory of the existing discrepancies between the techniques and their possible causes.The DFG research unit ‘Clock Metrology: Time as a New Variable in Geodesy’ features a joint project by DGFI-TUM and Uni Bonn with focus on developing a new CC-/CT-based approach to combine the space-geodetic techniques. As a basis, we develop an approach to analyse and cross-compare station position time series from different instruments/techniques observed over several decades. Based on the example of GOW co-locating all four space-geodetic techniques, we investigate absolute station position time series consistently aligned to the datum of the DTRF2020, DGFI-TUM’s most-recent realisation of the International Terrestrial Reference System (ITRS), as well as differential time series eliminating datum-realisation-related variations in the time series of one technique. Finally, we prepare a pool of metadata (log files, data time series from meteorological sensors and weather models, estimated clock and tropospheric parameters, etc.) and include these data in the analysis to identify causes of systematics. From the analyses, discontinuities, time-variable drifts and the spectra of intra- and inter-technique position difference time series between individual instruments at GOW can be identified and interpreted. The result of the work is an inventory which lists both, known and previously unmodelled systematics, and, as far as possible, their causes, thus providing the basis for the consistent combination of techniques in a common space-time.

Refined approaches for terrestrial reference frame computations

To better describe the shape of the constantly deforming Earth’s surface, the ITRF2020 is provided as an augmented terrestrial reference frame that precisely models nonlinear station motions for both seasonal (annual and semi-annual) signals present in the station position time series and Post-Seismic Deformation (PSD) for sites impacted by major earthquakes. Reprocessed solutions in the form of station position time series and Earth Orientation Parameters using the full observation history provided by the four space geodetic techniques (DORIS, GNSS, SLR and VLBI) were used as input data, spanning 28, 27, 38 and 41 years of observations, respectively. The ITRF2020 long-term origin follows linearly with time the Earth’s Center of Mass (CM) as sensed by SLR, based on observations collected over the time span 1993.0–2021.0. We evaluate the accuracy of the ITRF2020 long-term origin position and time evolution by comparison to previous solutions, namely ITRF2014, ITRF2008 and ITRF2005, to be at the level of or better than 5 mm and 0.5 mm/yr, respectively. The ITRF2020 long-term scale is defined by a rigorous weighted average of selected VLBI sessions up to 2013.75 and SLR weekly solutions covering the 1997.75–2021.0 time span. For the first time of the ITRF history, the scale agreement between SLR and VLBI long-term solutions is at the level of 0.15 ppb (1 mm at the equator) at epoch 2015.0, with no drift. To accommodate most of ITRF2020 users, the seasonal station coordinate variations are provided in the CM as well as in the Center of Figure frames, together with a seasonal geocenter motion model. While the PSD parametric models were determined by fitting GNSS data only, they also fit the station position time series of the three other techniques that are colocated with GNSS, demonstrating their high performance in describing site post-seismic trajectories.

The Celestial Reference System (CRS) is currently realized only by Very Long Baseline Interferometry (VLBI) because it is the space geodetic technique that enables observations in that frame. In contrast, the Terrestrial Reference System (TRS) is realized by means of the combination of four space geodetic techniques: Global Navigation Satellite System (GNSS), VLBI, Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite. The Earth orientation parameters (EOP) are the link between the two types of systems, CRS and TRS. The EOP series of the International Earth Rotation and Reference Systems Service were combined of specifically selected series from various analysis centers. Other EOP series were generated by a simultaneous estimation together with the TRF while the CRF was fixed. Those computation approaches entail inherent inconsistencies between TRF, EOP, and CRF, also because the input data sets are different. A combined normal equation (NEQ) system, which consists of all the parameters, i.e., TRF, EOP, and CRF, would overcome such an inconsistency. In this paper, we simultaneously estimate TRF, EOP, and CRF from an inter-technique combined NEQ using the latest GNSS, VLBI, and SLR data (2005–2015). The results show that the selection of local ties is most critical to the TRF. The combination of pole coordinates is beneficial for the CRF, whereas the combination of $$\varDelta \hbox {UT1}$$ results in clear rotations of the estimated CRF. However, the standard deviations of the EOP and the CRF improve by the inter-technique combination which indicates the benefits of a common estimation of all parameters. It became evident that the common determination of TRF, EOP, and CRF systematically influences future ICRF computations at the level of several $$\upmu $$ as. Moreover, the CRF is influenced by up to $$50~\upmu $$ as if the station coordinates and EOP are dominated by the satellite techniques.

We examine the contribution of the International GNSS Service (IGS) to the International Terrestrial Reference Frame (ITRF) by evaluating the quality of the incorporated solutions as well as their major role in the ITRF formation. Starting with the ITRF2005, the ITRF 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. Analysis of time series of station positions is a fundamental first step in the ITRF elaboration, allowing to assess not only the stations behavior, but also the frame parameters and in particular the physical ones, namely the origin and the scale. As it will be seen, given the poor number and distribution of SLR and VLBI co-location sites, the IGS GPS network plays a major role by connecting these two techniques together, given their relevance for the definition of the origin and the scale of the ITRF. Time series analysis of the IGS weekly combined and other individual Analysis Center solutions indicates an internal precision (or repeatability) <2 mm in the horizontal component and <5 mm in the vertical component. Analysis of three AC weekly solutions shows generally poor agreement in origin and scale, with some indication of better agreement when the IGS started to use the absolute model of antenna phase center variations after the GPS week 1400 (November 2006).

Constructing and maintaining a stable terrestrial reference frame (TRF) is one of the key objectives of fundamental astronomy and geodesy. The datumrealization for all the global TRF versions, such as ITRF2014 and its predecessor ITRF2008, assumes linear time evolution for transformation parameters and then imposes some conditions on these Helmert transformation parameters. In this paper, we investigate a new approach, which is based on weekly estimation of station positions and Helmert transformation parameters from a combination of the solutions of four space-geodetic techniques, i.e., Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), Global Positioning System (GPS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS). For this study, an interval of one week is chosen because the arc length of the SLR solutions is seven days. The major advantage of this weekly estimated reference frame is that both the non-linear station motions and the non-linear origin motion are implicitly taken into account. In order to study the non-linear behavior of station motions and physical parameters, ITRF2008 is used as a reference. As for datum definition of weekly reference frame, on one hand SLR is the unique technique to realize the origin and determine the scale together with VLBI, and on the other hand the orientation is realized via no net rotation with respect to ITRF2005 on a subset of core stations. Given the fact that without enough collocations an inter-technique combined TRF could not exist, the selection and relative weight of local ties surveyed at co-location sites are critical issues. To get stable results, we first assume that, if there were no events such as equipment changes between the measurement epoch of the local tie and that of the space-geodetic solution, the relative position between the two co-located stations should be invariant and this local tie could be used for computing the inter-technique combined reference frame in those weeks during the stable period of this tie. The resulting time series of both station positions and transformation parameters are studied in detail and are compared with ITRF2008. The residual station positions in the weekly combined reference frame are usually in the range of two millimeters without any periodic characteristic, but the residual station positions, when subtracting the regularized station position in ITRF2008, may reach a magnitude of a few centimeters and seem to have a significant annual signal. The physical parameter series between the weekly reference frame and ITRF2008 also show the obvious existence of an annual signal and reach a magnitude of one centimeter for origin motion and two parts per billion (ppb) for scale.

This report is divided into two parts: the first part gives an overview of the combination studies performed by the Forschungseinrichtung Satellitengeodasie TU Munchen (FESG) and the Deutsches Geodatisches Forschungsinstitut (DGFI) based on the data of the continuous IVS campaign CONT02. The close cooperation of the two institutions established the basis for a detailed adaption of the GPS and the VLBI software concerning models and parameterization to avoid systematic differences between the technique contributions. Special attention was payed to parameters with a high temporal resolution; in this study tropospheric parameters and Earth rotation parameters (ERP) are considered. Including the troposphere parameters offered a good possibility to study the correlation between troposphere parameters and station coordinates. It was found that this interaction can deliver a very important contribution to validate the available local tie information. For comparison of the troposphere results derived for the 14-days campaign CONT02, long time series for VLBI and GPS were used as well, and it turned out that the results are in good agreement. Regarding the sub-daily Earth rotation parameters it can be shown that a combination of the space techniques improves the results compared to single-technique solutions. Furthermore, it is illustrated that UT1-UTC can be combined from VLBI together with the satellite techniques. All in all, the presented results demonstrate the high potential of a combination of VLBI, GPS and SLR data. The second part is devoted to the combination of long sub-daily EOP time series from VLBI and GPS. Space geodetic techniques like the Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI) can provide Earth Orientation Parameter (EOP) time series with very high sampling rates. This offers the opportunity to study sub-daily tidal excitations and the influences of high-frequency or episodic geophysical effects on Earth rotation. Therefore we need sub-daily time series as consistent and homogeneous as possible. Based on the Combined Smoothing method of Vondrak and Cepek (2000), we developed a new combination scheme for sub-daily EOPs to obtain a new sub-daily time series which benefits from the longterm stability of VLBI and the continuity of GPS. Furthermore we can remove the weakness of UT1 estimations of the satellite techniques. We analysed the combination using spectral imaging methods and the results from sub-daily tidal harmonic estimation.

For the first time, the ITRF2005 input data are in the form of time series of station positions and Earth orientation parameters, together with full variance‐covariance information. The first step of the ITRF2005 analysis consists of rigorously stacking each time series to yield a long‐term solution per technique. As a by‐product, time series of position residuals contain the nonlinear motion of points over the Earth's surface. In this paper, the height residual time series of very long baseline interferometry (VLBI), Global Positioning System (GPS), and satellite laser ranging (SLR) solutions submitted to ITRF2005 are compared. We note that the interpretation of the ITRF2005 position residual time series as observed physical motions at the various stations is delicate due to the inhomogeneous site distribution. We estimate that the network effect may introduce an averaged scatter of 3 and 2 mm in the VLBI and SLR height residuals, respectively. Although noise levels are different among these three techniques, a common 1.0 cycles per year (cpy) frequency is clearly detected. The GPS height annual signal exhibits significant regional correlations that are confirmed by VLBI and SLR measurements in some colocated sites. Significant power near frequencies 2.00, 3.12, and 4.16 cpy is also detected in the individual GPS height residuals time series as mentioned by Ray et al. (2007). However, neither VLBI nor SLR show any significant signals at these frequencies for colocated sites. The agreement between detrended height time series at colocated sites is quantified using a novel method based on Kalman filtering and on maximum likelihood estimation. The GPS and VLBI measurements are shown to agree fairly well for most of the colocated sites. However, agreement is not generally observed in the GPS and SLR comparisons. A study of the interannual signal at colocated sites indicates that the good correlation cannot be completely attributed to the annual harmonic.

Unlike the previous versions of the International Terrestrial Reference Frame (ITRF), the ITRF2005 will be constructed with input data under the form of time series of station positions and Earth Orientation Parameters (EOP’s). This paper presents some preliminary results of the analysis of the time series submitted to the ITRF2005, focusing on the frame parameters and in particular the origin and the scale, as well as the EOP alignment to the combined frame. Quality assessment of the preliminary combinations is addressed in view of the ITRF2005 official solution.

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.

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.

The publicly available Earth Orientation Parameter (EOP) time series provided by the Earth Orientation Centre of the IERS (e.g., IERS Bulletin A, IERS 14 C04) result from the combination of individual space-geodetic solutions on a daily basis, i.e., a parameter-level combination. Current activities of the Federal Agency for Cartography and Geodesy (BKG) focus on the development of a combination strategy, the main objective of which is to improve the consistency between the space-geodetic techniques through common parameters, i.e., mainly EOP, but also station coordinates and tropospheric parameters using local ties and atmospheric ties, respectively. In this study, we present our combination strategy and the results of the combination of VLBI data available within approximately two weeks (i.e., Intensive and R1/R4 sessions) with data from the global GNSS network. The combination is done at the normal equation (NEQ) level on a daily and multi-day basis. We compare our EOP solutions with the respective daily and multi-day single-technique EOP solutions as well as with the low-latency inter-technique EOP time series (COMBI RAP) examined in previous studies, which is based on the combination of GNSS and VLBI Intensive data only. We found regarding the dUT1 solution, that the addition of the VLBI R1/R4 sessions to the VLBI Intensives and GNSS data has a positive impact on the entire 7-day solution, and especially stabilizes the dUT1 estimates of the boundary days of the multi-day continuous polygon. The dUT1 estimates of the left and right boundary day compared to IERS Bulletin A and COMBI RAP reveal an improvement in terms of WRMS of the residuals by 2.3 μs and 1.4 μs, respectively. For the pole coordinates, the consistency of the estimates with external reference series is almost at the same level as for the COMBI RAP solution.

Variations in Earth orientation parameters (EOP) are related to mass redistribution, gravitational, and geodynamic processes in the Earth system and have gained a great deal of attention in Earth science, astronomy, and climate change studies. In addition, real-time EOP information is needed for many space geodetic applications, including satellite navigation from the ground and low-Earth orbit, like tracking interplanetary spacecraft and forecasting the weather. Currently, the EOP can be estimated at the best possible accuracy with modern high-precision space geodetic techniques like Very Long Baseline Interferometry (VLBI), Global Navigation Satellite Systems (GNSS), and Satellite Laser Ranging (SLR). However, the complex nature of data processing and the time it takes to process it always lead to delays. Consequently, predicting EOP is of great scientific and practical importance. Accordingly, several methods have been developed and applied to EOP prediction. In spite of this, the accuracy of EOP still needs to meet our expectations, even for forecasts of a few days into the future. We will therefore have to face two major challenges in order to provide the best prediction data: which input data to use and which prediction methods are superior to others. In order to answer these two questions, new methods or a combination of existing approaches are investigated to improve the accuracy of the predicted EOP time seires. Such in-depth investigations are currently conducted within the &amp;#8220;Second EOP Prediction Comparison Campaign (EOP-PCC)&amp;#8221; organized by IAG and IERS. In this study, we investigate a redesigned prediction package (input data and method) to improve the possibility of bridging the existing gap between the observation and the final estimated product.We will briefly present our contribution to EOP-PCC and illustrate the result of EOP data obtained from single space geodetic techniques provided by the department of geodesy at BKG. Then, we run our prediction algorithm with the official IERS EOP series and our BKG&amp;#8217;s single-technique analysis products for VLBI and SLR using the combination of a deterministic and a stochastic method and compare it with different prediction techniques. Finally, we will show the potential of using a combination of VLBI and GNSS techniques to obtain real-time EOP estimates.