Reference Frames for Applications in Geosciences

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.

This paper reports on the activities of the IAG Working Group 1.1.1 on combination and comparison of precise orbits based on different space geodetic techniques. It will focus on the Dancer project which implements a distributed parameter estimation process that is scalable in the number of GPS receivers, so that an arbitrarily large number of receivers can be processed in a single reference frame realization. The background of this project will be summarized and its mathematical principles will be explained, as well as the essential aspects of the involved internet communication. It will show that the workload for data processing at a single participating receiver remains independent of the network size, while the data traffic only grows as a logarithmic function of the network size.

The Earth’s center of mass (CM) is defined in the satellite orbit dynamics as the center of mass of the entire Earth system, including the solid earth, oceans, cryosphere and atmosphere. Satellite Laser Ranging (SLR) provides accurate and unambiguous range measurements to geodetic satellites to determine variations in the vector from the origin of the ITRF to the CM. Estimates of the Global mass redistribution induced geocenter variations at seasonal scales from SLR are in good agreement with the results from the global inversion from the displacements of the dense network of GPS sites and from ocean bottom pressure model and GRACE-derived geoid changes.

The International Terrestrial Reference Frame (ITRF) datum definition is of primary importance for many Earth Science Applications. While accurate origin information (Earth Center of Mass) is required for any precise satellite orbit determination, an accurate scale is indispensable for various calibrations (altimeter absolute bias, GNSS satellite antenna phase center offsets). Studies involving vertical motion determination, such as mean sea level and Glacial Isostatic Adjustment (GIA) are also affected by the choice of the underlying Terrestrial Reference Frame. ITRF datum accuracy evaluation has been traditionally performed by comparing independent space geodetic technique performances and successive ITRF solutions. While the ITRF2005 to ITRF2000 comparison may lead to pessimistic evaluation of the ITRF datum accuracy, the question is raised whether the error budget deduced from the ITRF2008 to ITRF2005 comparison would be optimistic, especially for the time evolution of the origin. It is fundamental to explore external ways to evaluate the ITRF frame parameters and especially their time evolution which impacts the results of many climatic studies. The state of art of available methods is reviewed by stressing their advantages and drawbacks. Most of them have been already implemented and show that the ITRF2005 origin rate is probably reliable at the millimeter per year level. However these methods have been applied on different velocity field with different models and required assumptions which make their mutual comparison difficult. Thus, new analyses are required in the future.

As an ILRS Analysis Center (AC), we report further the official (final) ITRF2008 solution delivered by the ITRS product center. Following the operational analysis scheme of SLR data, that we perform over the period 1995–2010, we compute for the Lageos-1 and Lageos-2 satellites weekly arcs with ITRF2005 and ITRF2008. Then, we evaluate the sets of orbital parameters, of Earth Orientation Parameters (EOPs), and of Station Coordinates (SSCs). We also compare our results to those obtained by other ACs, in terms of SSCs, EOPs, translations and scale factors.

The International Terrestrial Reference System (ITRS) is defined by the IERS Conventions as a geocentric system with the origin in the Earth’s centre of mass. It is realized by a crust-fixed frame of reference stations (ITRF). The paper deals with alternative realizations of these specifications with the high accuracy needed in geosciences research.

A geocentric frame fixes the origin permanently in the Earth’s centre of mass, while a crust-fixed frame moves with the Earth’s crust, and the origin of the coordinate system may depart from the geocentre (“geocentre motion”). The characteristics and realizations of both definitions are discussed along with their advantages and shortcomings.

The computation of the reference frame is highly correlated with the observed network. In a global reference frame, the network stations should be distributed homogeneously over the Earth. Clusters of stations affect the frame by possible systematic (e.g. climatic) effects, in particular when applying similarity (Helmert) transformations. Densifications of the global frame in sparsely occupied regions of the network suffer from eventual distortions created by inhomogeneous station distributions.

The time evolution of the reference frames is at present done by linear station coordinate changes (constant velocities) over long time intervals only. Seasonal variations are not considered. Experiences with the Chile 2010 earthquake demonstrate the necessity of successive reference frames with short time lag. Alternatives are discussed in the paper.

We report on an evaluation of the stability of four different GNSS monuments that was conducted in the summer of 2010. The monuments were monitored by forward intersections using a survey system consisting of two robotic total stations and a set of retro reflecting prisms. The system was operated for almost 3 months, performing observations in two faces with a repetition cycle of 5min. Movements in excess of 6 mm were detected. The results show clear evidence that the detected deformations are related to variations in temperature and solar radiation and can be suppressed by simple shielding of the monument. Furthermore, our project is a step towards the realization of continuous cartesian connections at geodetic fundamental stations.

IGN and DGFI both generated realizations of the terrestrial reference frame under the auspices of the IERS from combination of the same space geodetic data. We compared the IGN and DGFI TRFs with a GSFC CALC/SOLVE TRF. WRMS position and velocity differences for the 40 most frequently observed sites were 2–3mm and 0.3–0.4mm/year. There was a scale difference of −0.39/−0.09ppb between the IGN/DGFI realizations and the GSFC solution. When we fixed positions and velocities to either the IGN or DGFI values in CALC/SOLVE solutions, the resulting EOP estimates were not significantly different from the estimates from a standard TRF solution.

This paper presents the IERS Conventions (2010) the new reference edition replacing the Conventions (2003) and describes their most significant features: new realizations of the celestial and terrestrial reference systems; a new conventional geopotential model along with updated model and implementation for the ocean tides; updated models for several components of the station displacement; new models for all aspects of atmospheric propagation.

Throughout its nearly two decades, the International GNSS (Global Navigation Satellite Systems) Service (IGS) has sought to align its products closely to successive realizations of the International Terrestrial Reference Frame (ITRF). This has been disruptive for IGS users at times, especially during the 1990s when some radical ITRF datum choices were adopted. During the past decade, IGS impacts due to ITRF updates have been smaller and mostly caused by errors in the results from the contributing space geodetic techniques.

Frame orientations (rotations) are purely conventional, so the IGS relies on the ITRF via a subset of reliable, globally distributed stations. Except for the period when ITRF93 was used, this procedure has worked well. The IGS origin in principle could be self-reliant or contributory to ITRF by direct observation of a frame origin aligned to the long-term center of mass of the entire Earth system. In practice, however, GNSS-based results have been less reliable than those from satellite laser ranging (SLR). So the ITRF origin, based on SLR only, has been adopted historically. Until the transition from ITRF2005 to ITRF2008, there have sometimes been significant origin shifts as SLR results have evolved. However, the present stability of the ITRF origin may finally have reached the few-mm level.

In many respects, the IGS dependence on the ITRF scale is most subtle and problematic. In addition to an overall Helmert alignment of the IGS frame to match the ITRF scale (and other datum parameters), since 2006 the IGS calibration values for the GNSS satellite antenna

z

-offsets depend directly on the same ITRF scale (due to high correlations if the IGS frame scale is not fixed). We therefore face a non-linear situation to maintain full consistency between all IGS products and the ITRF scale: each IGS frame contribution to ITRF based on one set of antenna calibrations must be used, together with frames from other techniques, to determine an updated ITRF and new antenna calibrations, which are then no longer strictly consistent with the starting IGS frame. One can hope that the process will iteratively converge eventually. But large shifts in the ITRF scale, such as the −1ppb change from ITRF2005 to ITRF2008, are highly disturbing, much more so than the associated rotational or translational shifts.

Only SLR and very long baseline interferometry (VLBI) have been considered reliable and accurate enough to be used for the ITRF scale. But experience and theoretical studies have shown that neither is accurate to better than about 1ppb. Note in particular that a 1ppb uncertainty in the GM constant fundamentally limits the possible scale agreement between SLR and VLBI to no better. Consequently, the authors strongly urge that the ITRF scale hereafter be fixed conventionally to the ITRF2008 scale indefinitely until it is convincingly shown that VLBI and/or SLR can determine the ITRF scale within 0.5ppb. If this is not done, the IGS might maintain its own ITRF2008 scaled frame to minimize future operational dislocations.

Since February 2010, the Institut Géographique National (IGN) has replaced Natural Resources Canada as the terrestrial frame coordinator of the International GNSS Service (IGS). One important task of this coordination consists in weekly combinations of the solutions provided by nine IGS Analysis Centres into weekly IGS solutions which include station positions, Earth rotation parameters and coordinates of the geocenter.

These combinations enable inter-comparisons of the AC solutions. We show that such comparisons reveal systematic distortions between the AC solutions and that relating them to analysis specificities can be a way to improve the quality of both the AC and combined solutions.

Because the geocenter determination by GNSS still suffers from mismodeling issues, a rigorous combination of the AC geocenter estimates is not feasible yet. The comparison of recently reprocessed geocenter time series from GNSS and SLR is however encouraging.

Tie vectors (TVs) measured at co-location sites carry fundamental information for the computation of the International Terrestrial Reference Frame (ITRF). The combination of the different frames stemming from each space geodetic (SG) technique relies on the availability and accuracy of the relative positions between reference points of co-located SG instruments, i.e. TV. If, on the one hand, TVs accurate at 1mm level are sought to preserve the accuracy of the global frame and fulfill the requirements of the global geodetic observing system (GGOS), on the other hand, the assessment of TVs accuracy is not easy. Their accuracies are often questioned on the base of their agreement within the combination of SG solutions and the combination residuals. Though, the final discrepancies highlighted by the combination residuals do not depend uniquely on the accuracy of the TVs but are influenced by several factors of different origin. In this paper, we identify some of these factors and investigate their possible origin adopting different perspectives: local ties and terrestrial surveying, SG techniques and frames combination. Our purpose is to highlight some of the possible systematic errors in terrestrial and SG data analysis as well as to identify actions to be taken in the near future to mitigate the biases highlighted by the residuals of the combination. In contrast to what is commonly assumed, we show that the residuals are potentially influenced by a combination of biases affecting the TVs, their alignment and the SG solutions. Therefore, an objective evaluation of the error sources is necessary for each SG technique in order to improve their results as well as the combined SG products.

The new realization of the International Terrestrial Reference System, ITRF2008, follows the same strategy of ITRF2005 and is based on an inter-technique combination of geodetic solutions, in turn obtained from an intra-technique combination strategy performed at the Technique Centre (ILRS, IGS, IVS, IDS) level. In Summer 2009, ILRS has provided IERS with its official contribution to the ITRF2008: a homogeneous set of coordinate time series for the period 1983–2008, obtained by ASI/CGS ILRS Primary Combination Center combining time series sets of solutions provided by seven official ILRS Analysis Centers.

A detailed analysis of the ILRS solution origin and scale parameters is presented looking at the time series of the translations and scale with respect to newly released ITRF2008. The analysis is made both for combined and individual solutions, to highlight especially their non-linear behavior; these tiny, non-linear, residual effects must be investigated and possibly minimized.

The DTRF2008 is a realization of the ITRS computed by the ITRS Combination Centre at DGFI. It is based on the same input data as the ITRF2008. In order to assess the internal and external accuracy of DTRF2008 several validation procedures are applied which are based on comparisons with technique-only multi-year solutions (for assessing the internal accuracy) and comparisons with ITRF2008 and ITRF2005 (for assessing the external accuracy). The analysis is done separately for the four space-geodetic techniques GPS, VLBI, SLR and DORIS. The internal accuracy for station positions is between 0.6 and 3.3mm and the external accuracy between 7 and 10mm depending on the space technique. For the velocities the internal accuracy is between 0.25 and 1.0mm/a and the external between 0.2 and 2.0mm/a.

Deformations at the local site level will directly introduce errors both into site coordinates that are determined from individual geodetic techniques and the measured site ties that link those techniques at co-located sites. Such errors will be present in individual-technique solutions and affect their combination in the formation of an International Terrestrial Reference Frame (ITRF). The NERC Space Geodesy Facility at Herstmonceux, UK, operates a highly precise and prolific International Laser Ranging Service satellite laser ranging (SLR) station, two International Global Navigational Satellite Systems Service (IGS) receivers and a permanently-installed absolute gravimeter. As a result, the site remains an important contributor to the maintenance of the ITRF. Site deformation is monitored using a recently-instigated programme of precise digital levelling and by short-baseline GPS analyses using data from on-site and regional GNSS receivers. The stability of the Herstmonceux site will impact on the validity of future comparisons of site height changes observed using the three independent techniques, SLR, GPS and absolute gravimetry.

We introduce a static a priori gradient model (APG) based on a spherical harmonic expansion up to degree and order nine to describe the azimuthal asymmetry of tropospheric delays. APG is determined from climatology data of the European Centre for Medium-Range Weather Forecasts (ECMWF), and the refined model can be used in the analysis of observations from Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI). Comparisons reveal that gradients estimated in GNSS analysis are mostly smaller than those provided by APG. This difference is also confirmed by station and source coordinate changes if APG is used in GNSS and VLBI analysis.

Space geodetic techniques have different strengths and weaknesses for recovering geodetic parameters which makes their combination useful. However they may have some systematic behaviour which can be detected and removed at the observation level. In order to review the interest in combining techniques at this level, a Working Group was set up in the course of 2009 in the frame of the International Earth Rotation and Reference Systems Service (IERS). A major task of the WG COL is to study methods and advantages of combining space geodetic techniques (DORIS, GNSS, SLR, VLBI), searching for an optimal strategy to solve for geodetic parameters. The first action of the Working Group was to organize an inter-comparison benchmark campaign to serve as a test. The period chosen is from August 10 to August 30, 2008. It includes the intensive CONT08 VLBI period.

The combination analyses are based on weekly (or daily for VLBI) combined SINEX files which contain normal equations of station coordinates, Earth Orientation Parameters from all space geodetic techniques, quasar coordinates for the VLBI technique and troposphere parameters for all techniques except SLR. The objectives of the present paper are twofold: first give an overview of the method, present the objectives and strategy of the newly born working group COL; second to present some preliminary results obtained by the Groupe de Recherche en Géodésie Spatiale (GRGS) for Earth orientation parameters.

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.

However, time-correlated noise amplitude is not constant in long time series, but depends on the time period of the time series data. Older time series data contain larger time-correlated noise amplitudes than newer time series data. This way, shorter time series with older data time period exhibit time-correlated noise amplitudes similar to the whole time series. This paper focuses on the source of the time-correlated noise amplitude decrease from older to newer time series period data. The results of several tested sources are presented. Neither the increasing ambiguity fixation rate, nor the increasing number of tracking stations, nor the increasing number of observed satellites are likely the source of the noise reduction. The quality improvement of the equipment of both tracking network and constellation is likely the main source of the correlated noise evolution.

Global Navigation Satellite Systems (GNSS) are important contributors to the realization of the International Terrestrial Reference System (ITRS). For the combination of different space geodetic techniques, terrestrial measurements between the corresponding reference points are necessary. Discrepancies between these so-called local ties on the one hand and the coordinate differences derived from space techniques on the other hand are a major limitation for the realization of the ITRS nowadays. In the past, these discrepancies have often been attributed to inaccurate terrestrial measurements. This paper shows that a major part of the differences can be explained by systematic GNSS-specific errors, if a global data analysis is simulated. One of the most important error sources for GNSS are interactions of the antenna with its immediate vicinity, primarily multipath.

At the Geodetic Observatory Wettzell (Germany), up to six GNSS permanent sites are operated in parallel at a distance of only a few meters. This antenna array is ideal to study the impact of local effects on the various GNSS observables and linear combinations. Comparisons of solutions obtained from different GNSS observables reveal cm-level discrepancies. Individual receiver antenna calibrations have an impact on the estimated station positions on the level of several millimeters. As other error sources dominate, their application does not lead to an improvement in all cases.

The paper presents preliminary results of coordinate time series analysis in Serbian network of permanent GNSS stations. Analysis methodology is outlined and resulting station velocities are briefly commented. Despite the short time span used, the crustal deformation trend was clearly identified, confirming the potential of the network of permanent stations for local and regional geodynamical studies.

The Working Group on “Regional Dense Velocity Fields” (see

http://epncb.oma.be/IAG

) of the International Association of Geodesy (IAG) aims at densifying the International Terrestrial Reference Frame and creating a dense velocity field based on regional and global GNSS networks. With the goal to generate a high-quality solution for a core network, several newly reprocessed global and regional cumulative position and velocity solutions were submitted to the Working Group. In order to find a consensus on discontinuity epochs for stations common to several networks (an issue which was problematic in previous submissions), the new submissions were restricted to contain only the core networks over which the analyst has full control so that ITRF2008 discontinuities could be applied. The 3D-RMS of the agreement of the new solutions with the ITRF2008 (after outlier rejection) varies between 0.6 and 1.1mm/year; it is extremely good for some solutions, while others still require more iteration to reach the required level of agreement. A part of these disagreements has been identified and often originates in the use of different data time spans within the ITRF2008 and submitted solution.

In the upcoming year, the Working Group expects to generate and use a discontinuity database complementing the ITRF2008 set and identify/solve the sources of disagreements. In addition, several of the regional solutions will be reprocessed to embed the regional network in a global network and reduce the error induced by the network effect.

In this article we discuss and give an example of three different methods to measure the local tie between the IGS GPS antenna reference point (ARP) and the VLBI antenna reference point at the Metsähovi fundamental station. First we introduce traditional survey approach combined with a space intersection technique and then local tie based on kinematic GPS during geo-VLBI campaigns and finally local ties with static GPS measurements. We discuss the measurements and computations, problems and error sources encountered between the planning of the measurements and the end product, the local tie vector. Although millimetre precision can be achieved, our experience during tests at Metsähovi fundamental station shows that some techniques are very time consuming and impractical for a routine use. We aim for a more automated process in local tie measurement.

Based on our experiments and results, we propose that in the future, the VLBI antenna tie could be tracked permanently during geo-VLBI campaigns with attached GPS antennas.

The western part of the SIRGAS region is an extremely active seismic area because it is located in the plate boundary zone of six tectonic plates, namely the Pacific, Cocos, Nazca, North American, Caribbean, and South American plates. The frequent occurrence of earthquakes causes episodic station movements, which affect the long-term stability of the SIRGAS reference frame. Normally, these episodic events are taken into account in the frame realisation by introducing new position and, optionally, velocity parameters for the affected stations. However, this is not enough to guarantee the high precision required in a reference frame such as SIRGAS. Additional analyses about the post-seismic behaviour of the reference stations are necessary to allow the precise transformation between pre-seismic and post-seismic (deformed) frames. According to this, the paper presents an evaluation of the long-term stability of the SIRGAS reference frame including the comparison of the different SIRGAS realisations and the analysis of station displacements caused by earthquakes in the SIRGAS region. Special care is given to the events happened in Arequipa (on 2001-06-23, M=8.4) and Chile (on 2010-02-27, M=8.8). The analysis is based on the SIRGAS Continuously Operating Network (SIRGAS-CON). Beside analysing the station position time series and estimating the displacement vectors of the SIRGAS reference stations, some recommendations to mitigate the impact of this kind of events in the use of SIRGAS as a reference frame are formulated.

Following the adoption of the International Celestial Reference System and Frame (ICRS and ICRF) by the IAU in 1997, several resolutions on reference systems have been passed by the IAU in 2000 and 2006 and endorsed by the IUGG in 2003 and 2007, respectively. These resolutions concern especially the transformation between the International Terrestrial Reference System (ITRS) and the Geocentric Celestial Reference System (GCRS) that is essential for realizing the ICRS from directions of extragalactic radio sources observed from the Earth by VLBI.

First, the IAU 2000 resolutions have refined the concepts and definition of the astronomical reference systems and parameters for Earth’s rotation, and adopted the IAU 2000 precession-nutation. Then, the IAU 2006 resolutions have adopted a new precession model that is consistent with dynamical theories and have addressed definition, terminology or orientation issues relative to reference systems and time scales that needed to be specified after the adoption of the IAU 2000 resolutions. These in particular provide a refined definition of the pole and the origin on the equator as well as a rigorous definition of sidereal rotation of the Earth. These also allow an accurate realization of the celestial intermediate system that replaces the classical celestial system based on the true equator and equinox of date. There was an additional IUGG 2007 resolution for the terrestrial reference system. Finally, the IAU 2009. Transactions of the IAU XXVIIB. Rio de Janeiro, Corbett I (ed) vol 6. Cambridge University Press, pp 55–70) resolutions have adopted a new system of astronomical constants – including conventional values of the IAU 2000/2006 resolutions – and adopted the Second Realization, ICRF2, of the International Celestial Reference Frame.

This paper recalls the main aspects of these recent IAU resolutions as well as their consequences on the concepts, definitions, nomenclature and models that are suitable for modern realizations of reference systems. The impact of these resolutions on the definition and realization of the International Celestial Reference Frame (ICRF) is described.

The ICRF2 became official on Jan 1, 2010. It includes positions of 3414 compact radio astronomical sources observed with VLBI, a fivefold increase over the first ICRF. ICRF2 was aligned with the ICRS using 138 stable sources common to both ICRF2 and ICRF-Ext2. Maintenance of ICRF2 is to be made using 295 defining sources chosen for their historical positional stability, minimal source structure, and sky distribution. The switchover to ICRF2 has had some small effects on the terrestrial reference frame (TRF), celestial reference frame (CRF) and Earth orientation parameter (EOP) solutions from VLBI. A CRF based on ICRF2 shows a relative rotation of ~40μas with respect to ICRF, mostly about the Y-axis. Small shifts are also seen in the EOP, the largest being ~11μas in X

pole

. Some small but insignificant differences are also seen in the TRF.

We assess the systematics between Very Long Baseline Interferometry (VLBI) terrestrial and celestial reference frames (TRF and CRF) solutions caused by different analysis options. Comparisons are achieved by sequential variation of options relative to a reference solution, which fulfills the requirements of the International VLBI Service for Geodesy and Astrometry (IVS) analysis coordination. Neglecting the total NASA/GSFC Data Assimilation Office (DAO) a priori gradients causes the largest effects: Mean source declinations differ up to 0.2mas, station positions are shifted southwards, and heights are systematically larger by up to 3mm, if no a priori gradients are applied. The effect is explained with the application of gradient constraints. Antenna thermal deformations, atmospheric pressure loading, and the atmosphere pressure used for hydrostatic delay modeling still exhibit significant effects on the TRF, but corresponding CRF differences (about 10μas) are insignificant. The application of NMF atmosphere mapping functions can systematically affect source declinations up to 30μas, which is between the estimated axes stability (10μas) and the mean positional accuracy (40μas) specified for the ICRF2. Further significant systematic effects are seasonal variations of the terrestrial network scale (±1mm) neglecting antenna thermal deformations, and seasonal variations of station positions, primarily of the vertical component up to 5mm, neglecting atmospheric loading. The application of NMF instead of VMF1 can result in differences of station heights up to 6mm, but no overall global systematic can be found. Using constant atmosphere pressure values for the determination of hydrostatic zenith delays systematically deforms the TRF: station height differences mostly show the same sign with absolute values exceeding 1mm.

A celestial reference frame at X/Ka-band (8.4/32GHz) has been constructed using fifty-one 24-h sessions with the Deep Space Network. We report on observations which have detected 436 sources covering the full 24 h of right ascension and declinations down to −45°. Comparison of this X/Ka-band frame to the S/X-band (2.3/8.4 GHz) ICRF2 shows wRMS agreement of 200 micro-arcsec (μas) in

$$ \alpha cos\delta $$

and 290 μas in δ. There is evidence for zonal errors at the 100 μas level. Known errors include limited SNR, lack of phase calibration, troposphere mismodelling, and limited southern geometry. The motivations for extending the ICRF to frequencies above 8 GHz are to access more compact source morphology for improved frame stability, to provide calibrators for phase referencing, and to support spacecraft navigation at Ka-band.

In this study, we investigate the influence of different analysis setup options for the processing of VLBI measurement data from 2002 until 2010 to derive the terrestrial reference frame (TRF). For estimating the consequent changes of the TRF, the simulation tool of the Vienna VLBI Software (VieVS) is used by applying different a priori models. We show that neglecting atmosphere loading causes a systematic annual scale variation of±0.3 mm, and that the application of the cubic model recommended in the most recent IERS Conventions for the mean pole introduces a scale change of −0.6mm over 8.5years. The effects of antenna thermal deformation on the TRF are±0.5 to 1mm/year in translation and±2 mm/year in scale. No systematic effects are found for the different troposphere mapping functions tested. Besides systematic, annual, and episodic impacts on the coordinates, we focus on possible changes in the scale of the reference frames.

Precise gravity field modelling is essential for a unification of local vertical datums (LVDs) and realization of the World Height System. The quality of terrestrial gravimetric measurements has substantial impact on the accuracy of detailed geoid/quasigeoid models. The precision of their positions, especially their vertical components, is of the same importance as precision of gravity itself. Therefore inconsistencies due to shifts and tilts of LVDs can distort precise solutions.

In this paper we present how inconsistencies of vertical positions of input terrestrial gravity data can influence numerical solutions obtained by the finite element method and finite volume method. Considering information from satellite missions, we solve the geodetic BVP with mixed boundary conditions (BCs) in the 3D domain above the Earth’s surface. This space domain is bounded by the Earth’s surface at the bottom, one spherical artificial boundary outside the Earth at altitude of a satellite mission and four side artificial boundaries. All numerical solutions are fixed to the satellite only geopotential model on all artificial boundaries, where the Dirichlet BCs are imposed. On the Earth surface the oblique derivative BC in the form of surface, gravity disturbances is prescribed. In our numerical experiments we compare numerical solutions with and without considering the corrections from the shifts and tilts of LVDs in the input surface gravity disturbances. We study how the corrected solutions backward-influence estimations of the shifts and tilts of LVDs. Our experiments are performed in areas of Australia, New Zealand and Great Britain.

A conventional transformation between different realizations of a vertical reference system is an important tool for geodetic studies on precise vertical positioning and physical height determination. Its main role is the evaluation of the consistency for co-located vertical reference frames (VRFs) on the basis of some fundamental ‘datum perturbation’ parameters. Our scope herein is to discuss a number of key issues related to the formulation of such a VRF transformation model and to present a few examples from its practical implementation in the comparison of various existing vertical frames over Europe.

The success of the dedicated gravity satellite missions CHAMP and GRACE has enabled global geoid determination at unprecedented accuracy and has stimulated study on geoid modeling at a very high-resolution on a global scale as well as for local improvement. The paper first describes the latest determination of a gravimetric geoid model for Japan, obtained by combining a GRACE-derived global geopotential model, altimetry-derived ocean gravity model and local surface gravity measurements on land and at sea. Then, a comparison of the model is made with EGM2008 and GPS/leveling geoidal undulations over four main islands of Japan. Third, we determine sea surface dynamic heights around Japan from a combination of a regional geoid model, tidal records and GPS/leveling data at the coast and on isolated islands and compare them with an oceanographic model.

The creation of vertical reference surfaces at sea, related to a reference ellipsoid, is a necessary step to enable the use of GPS (Global Positioning System) for referencing depth measurements at sea. Several projects exist for specific parts of the oceans, resulting in surfaces that partly overlap. As an example, we will present the French BATHYELLI project in detail, followed by a comparison of results for the North Sea area.

We combine GRACE-derived rates of vertical crustal motion, joint water gauge and satellite altimetry and GPS vertical velocities in the Great Lakes region. The combined vertical motion model is realized via a least-squares adjustment procedure, including variance-component estimation and robust outlier detection. This is necessary to ensure reliable estimates of the relative errors in the least-squares adjustment (via re-scaling of data variance-covariance matrices) and to ensure that the vertical motion model is not distorted by erroneous data. The combined vertical motion model shows a subsidence of 1–2 mm/year along the southern shores and an uplift of 3–4 mm/year along the northern shores generally consistent with the models of postglacial rebound in North America.

The values of

$$ \Delta g $$

corrections for vertical component of gravity produced by TOPEX/POSEIDON sea level variations were estimated. With this aim, the M. Molodensky boundary problem for deformation of elastic gravitating compressible sphere was solved. An equation connecting boundary conditions on the mantle surface and bottom was obtained. The values of load Love numbers for several models of upper layers of the Earth were calculated. We demonstrate that magnitude of

$$ \Delta g $$

corrections appreciably depend from used models of the upper mantle and lithosphere structure.

The United States adopted the North American Vertical Datum of 1988 (NAVD 88) for its official vertical datum in the 1990s. Canada has been using the Canadian Geodetic Vertical Datum (CGVD28) for its height applications since the 1930s. The use of the different datums causes inconsistent heights across the border between the two countries, and the topographic height data from the two countries are not compatible. Both datums rely on passive control and significant pre-modern survey data, yielding not only misalignment of the datums to the best known global geoid at approximately 1–2 m, but also local uplift and subsidence issues which may significantly exceed 1–2 m in extreme cases.

Today, the GNSS provides the geometric (ellipsoidal) height to an accuracy of 1–2 cm globally. The use of current inaccurate vertical datums no longer serves the purpose it once did. Because of this, users have begun to demand a physical height system that is closely related to the Earth’s gravity field to a comparable accuracy. To address this need, government agencies of both countries are preparing the next generation of vertical datums. Even if the new datums are based on the same concepts and parameters, it is possible to have inconsistent heights along the borders due to the differences in the realization of the datums. To avoid inconsistency, it is in the interest of both countries to have a united, seamless, highly accurate vertical datum. The proposed replacements for CGVD28 and NAVD88 shall be based on GNSS positioning and a high accuracy gravimetric geoid that covers the territories of the United States, Canada, Mexico and the surrounding waters (to include all of Alaska, Hawaii, the Caribbean and Central America). To account for the effect of the sea level change, postglacial rebound, earthquakes and subsidence, this datum will also provide information on these changes. Detailed description of the definition, realization and maintenance of the datum is proposed. The challenges in realization and maintaining the datum are also discussed.

The IAG Sub-Commission 1.3b, SIRGAS (Sistema de Referencia Geocéntrico para las Américas), operates a service for computing regional ionospheric maps based on GNSS observations from its Continuously Operating Network (SIRGAS-CON). The ionospheric model used by SIRGAS (named La Plata Ionopsheric Model, LPIM), has continuously evolved from a “thin layer” simplification for computing the vTEC distribution to a formulation that approximates the electron density (ED) distributions of the E, F1, F2 and top-side ionospheric layers.

This contribution presents the newest improvements in the model formulation and validates the obtained results by comparing the computed vTEC to experimental values provided by the ocean altimetry Jason 1 mission. Comparisons showed a small underestimation of the Jason 1 vTEC by about 1.3 TECu on average and rather small differences ranging from −0.5 to −3.4 TECu (at 95 % probability level). The results are encouraging given that comparisons were made in the open ocean regions (far away from the SIRGAS-CON stations).

Navigation of interplanetary spacecraft is typically based on range, Doppler, and differential interferometric measurements made by ground-based telescopes. Successful tracking requires knowledge of the telescope positions in the terrestrial reference frame. Spacecraft move against a background of extra-galactic radio sources and navigation depends upon precise knowledge of those background radio source positions in the celestial reference frame. Work is underway at JPL to reprocess historical VLBI and GPS data to improve realizations of the terrestrial and celestial frames. The purpose of this brief paper is to provide a snapshot of reference frame results.

Allan Variance (AVAR) was introduced more than 40 years ago as an estimator of the stability of frequency standards. Now it is also used for investigations of time series in astronomy and geodesy. However, there are several issues with this method that need special consideration. First, unlike frequency measurements, astronomical and geodetic time series usually consist of data points with unequal uncertainties. Thus one needs to apply data weighting during statistical analysis. Second, some sets of scalar time series naturally form multidimensional vector series. For example, Cartesian station coordinates form the 3D station position vector. The original AVAR definition does not allow one to process unevenly weighted and/or multidimensional data. To overcome these deficiencies, AVAR modifications were proposed in Malkin (2008. On the accuracy assessment of celestial reference frame realizations. J Geodesy 82: 325–329). In this paper, we give some examples of processing geodetic and astrometric time series using the classical and the modified AVAR approaches, and compare the results.

For Precise Agriculture purposes, several steps of a maize crop-system were recorded by the use of a GPS receiver with EGNOS and RTK capabilities. The field is about 35 km far from two GNSS CORS, one from RENEP, operated by IGS, and the other from SERVIR, operated by IGEoE. Both networks disseminate real-time GNSS data streams over the Internet using the NTRIP protocol. The GNSS data streams from RENEP reference stations (including validated station coordinates) provide the user with a real-time access to the ETRS89 and, those same streams from IGEoE, a military institution, are in ITRS, allowing large scale scientific applications. The validation of the EGNOS and the RTK solutions, obtained in the two TRS systems, was achieved by the results from post-processed measurements. RTK solutions, when compared to the post-processed values in the same TRS, show sub-decimeter accuracy what is enough for many of the Precision Agriculture studies. However, the two RTK solutions have a translation with a magnitude of the order of 0.5 m that can be explained by the independence of the ETRS89 on the continental drift. Indeed, at the zone where the field is located, while the ETRFyy Cartesian coordinates have velocities less than 1 mm/year, the ITRFyy Cartesian coordinates have velocities greater than 1 cm/year, what give rise to a point position variation with a magnitude of 2.5 cm/year.

In order to correlate the tractor velocity, during a pre-emergence herbicide application, to the terrain slope, the field orthometric heights were obtained by the use of GRS80 ondulations, on a 1.5′ × 1.5′grid, in the local Portuguese geoid model GeodPT08. The global precision of this model is estimated in 4 cm, which is within the error for the real time solutions obtained.