Geodesy for Planet Earth

The SIRGAS reference system is at present realized by the SIRGAS Continuously Operating Network (SIRGAS-CON) composed by about 200 stations distributed over Latin America and the Caribbean. SIRGAS member countries are improving their national reference frames by installing continuously operating GPS stations, which have to be consistently integrated into the continental network. As the number of these stations is rapidly increasing, the analysis strategy of the SIRGAS-CON network is based on two hierarchy levels: a) A core network with homogeneous continental coverage and stable site locations ensures the long-term stability of the reference frame. This network is processed by DGFI (Germany) as the IGS RNAAC SIR. b) Several densification sub-networks (corresponding to the national reference networks) improve the accessibility to the reference frame in the individual countries. Currently, the SIRGAS-CON stations are classified in three densification sub-networks (a southern, a middle, and a northern one), which are processed by the SIRGAS Local Processing Centres CIMA (Argentina), IBGE (Brazil), and IGAC (Colombia). These four Processing Centres deliver loosely constrained weekly solutions for the assigned sub-networks, which are integrated in a unified solution by the SIRGAS Combination Centres (DGFI and IBGE). The main SIRGAS products are: loosely constrained weekly solutions in SINEX format for further combinations of the network, weekly positions aligned to the ITRF as reference for GPS positioning in Latin America; and multi-year solutions (positions + velocities) for practical and scientific applications requiring time-dependent coordinates. This paper describes the analysis of the SIRGAS-CON network as the current realization of the SIRGAS reference system, its quality and consistency, as well as the planned activities to continue improving this reference frame.

The University of La Rochelle (ULR) TIGA Analysis Center (TAC) completed a new global reprocessed solution spanning 13 years with more than 300 GPS permanent stations, 216 of them being co-located with tide gauges. A state-of-the-art GPS processing strategy was applied, in particular, the station sub-networks used in the daily processing were optimally built. Station vertical velocities were estimated in the ITRF2005 reference frame by stacking the weekly position estimates. Outliers, offsets and discontinuities in time series were carefully examined. Vertical velocities uncertainties were assessed in a realistic way by analysing the type and amplitude of the noise content in the residual position time series. The comparison shows that the velocity uncertainties have been reduced by a factor of 2 with respect to previous ULR solutions. The analysis of this solution and its by-products shows the high geodetic quality achieved in terms of homogeneity, precision and consistency with respect to other top-level geodetic solutions.

In a collaborative effort with the regional sub-commissions within IAG sub-commission 1.3 “Regional Reference Frames”, the IAG Working Group (WG) on “Regional Dense Velocity Fields” (see http://epncb.oma.be/IAG) has made a first attempt to create a dense global velocity field. GNSS-based velocity solutions for more than 6,000 continuous and episodic GNSS tracking stations, were proposed to the WG in reply to the first call for participation issued in November 2008. The combination of a part of these solutions was done in a two-step approach: first at the regional level, and secondly at the global level. Comparisons between different velocity solutions show an RMS agreement between 0.3 and 0.5 mm/year resp. for the horizontal and vertical velocities. In some cases, significant disagreements between the velocities of some of the networks are seen, but these are primarily caused by the inconsistent handling of discontinuity epochs and solution numbers. In the future, the WG will re-visit the procedures in order to develop a combination process that is efficient, automated, transparent, and not more complex than it needs to be.

This paper describes the EUREF Permanent Network (EPN) and the efforts made to monitor and improve the quality of the EPN products and services. It is shown that the EPN is becoming a multi-GNSS tracking network and that the EPN Central Bureau and the Analysis Centers are preparating to include the new satellite signals in their routine operations.

Thanks to the EPN Special Project on “Reprocessing”, set up early 2009, EPN products with much better quality and homogeneity will be generated. The Special Project on “Real-time analysis” will improve the reliability of the EPN real-time data streams and develop new EPN real-time products.

For the next-generation geodetic VLBI network a 1 mm positioning accuracy is anticipated. The accuracy should be site-independent consistent, reliably controlled, and traceable over long time periods. There are a number of remaining limitations. These include random and systematic components of the delay observable itself, various antenna-related errors, and especially a proper handling of local ties at multi-technique sites.

At the Metsähovi Fundamental Station operated by the Finnish Geodetic Institute there are a CGPS and Glonass receivers, both in IGS network, a SLR (currently under renovation), a DORIS beacon, a superconducting gravimeter, and a 14.5 m radio telescope owned by Metsähovi Radio Observatory of the Helsinki University of Technology. Between five and eight geodetic VLBI sessions are conducted annually.

We tested a method to simultaneously measure the tie of the VLBI antenna to the GPS network by tracking the movement of two GPS antennas attached to the radio telescope during geodetic VLBI sessions. We used kinematic trajectory solutions of the two GPS antennas to calculate the orientation and the reference point of the VLBI antenna.

In this paper we describe the data acquisition, calculation model, some error sources and test results of four campaigns. The position of the reference point is time, temperature, antenna elevation and azimuth dependent. We propose that in the future, the position should be tracked permanently during geo-VLBI campaigns with attached GPS antennas.

In preparation for the computation of ITRF2008, the DORIS IGN analysis center has undertaken the task of a complete reprocessing of all DORIS data from 1993.0 to 2009.0, using all available DORIS data as well as the most recent models and estimation strategies. We provide here a detailed description of the major improvements recently made in the DORIS data processing, mainly in terms of solar radiation pressure, atmospheric drag, gravity field, and tropospheric correction. We address here the impact of the new IGN time series (ignwd08) on geodetic products using comparison to the previous IGN solutions (ignwd04). In particular, previous artifacts, such as 118-day or 1-year periodic errors in the TZ-geocenter solution or in the vertical component of high latitude DORIS tracking stations, have now disappeared, leading to more precise and reliable time series of DORIS station coordinates. Finally, possible future improvements are discussed proposing new investigations for the future.

The International Terrestrial Reference Frame (ITRF), the Earth Orientation Parameter (EOP) time series, and the International Celestial Reference Frame are obtained separately and may thus present inconsistencies. To solve this problem, a first step has been made with the latest ITRF realization (ITRF2005), which has been computed, for the first time, with consistent EOP time series. Another approach to better understand this issue is to directly estimate, in the same process, station positions and EOP time series, from all the space-geodetic measurements.

In the framework of the French Groupe de Recherche de Géodésie Spatiale (GRGS) activities, this latter approach has been studied for several years. For this purpose, the observations of VLBI, SLR, GPS, and DORIS techniques are combined using the same models and software for all the individual data processing.

In this paper, we study methodological issues regarding the definition and the consistency of the weekly combined terrestrial frames.

Traceability is a feature that is required more frequently in local geodetic high-precision measurements. This basic term of metrology, a measurement science, describes the property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty (BIPM International vocabulary of metrology – basic and general concepts and associated terms (VIM). JCGM 200:2008. Joint Committee for Guides in Metrology, 2008b).

GPS measurements are widely used in local geodynamical research. From the viewpoint of metrology, their traceability is uncontrollable because the scale cannot be unambiguously conducted based on the definition of the metre. In particular, atmospheric effects on a GPS signal cannot be modelled or calibrated along the path of the signal.

We are testing a method to bring the traceable scale to small GPS networks using high-precision electronic distance measurement (EDM) instruments, the scales of which have been corrected and validated in calibrations at the Nummela Standard Baseline. The traceable scale of EDM is expected to explain the annual scale variations that have been found in GPS time series and to improve results of episodic GPS campaigns.

The scale of a standard baseline is validated and maintained through regular interference measurements with the Väisälä interference comparator, in which a quartz gauge conveys the traceable scale. The results from the interference measurements in 2005 and 2007 in Nummela are presented here together with a brief description of the present state of the renowned measurement standard. A standard uncertainty of ±0.08 ppm was obtained again for the baseline length of 864 m, and the results confirm the good long-term stability of the baseline. The scale is transferred further to geodetic and geophysical applications by using calibrated high-precision EDM instruments as transfer standards.

Local geodynamical measurements will profit from the reduced and accurately estimated uncertainty of the measurement, and therefore we seek further innovations to improve their traceability. We present here a topical example of calibrations and scale transfer for a baseline and monitoring network around a nuclear power plant. We compare simultaneously measured EDM and GPS results and show a scale bias of approximately 1 ppm between them. By using a traceable length in the network, the bias could be reduced, e.g. by improving the processing strategy of GPS observations. This paper focuses on the metrological part of EDM. Some related results and analysis of GPS measurements are discussed in another paper in this volume (Koivula et al. GPS metrology – bringing traceable scale to local crustal deformation GPS network. IAG Scientific Assembly “Geodesy for Planet Earth”, Buenos Aires, Argentina, 2010).

Geodetic parameters always correspond to a reference system defined by conventions and realized by a reference frame through materialized points with given coordinates. For the coordinate estimation one has to fix the geodetic datum, i.e. the origin and directions of the coordinate axes, and the scale unit. In geosciences applications, e.g. for geodynamics and global change research, the datum has to be fixed over a very long time period in order to refer time-dependent parameters to one and the same reference frame. The paper focuses on the methodology how to fix the datum by parameters independent of the measurements and deformations of the reference frame, and to hold it over a long time span. It is shown that transformations between reference frames at different epochs are not suited to realize the datum parameters because systematic network deformations may affect it. Independent parameters are in particular the first degree and order harmonic coefficients of the gravity field for fixing the origin, and external calibration for fixing the scale. The long-term stability is achieved by the permanent fixing of the datum parameters. Regional reference frames must refer to the global datum by using epoch station coordinates as fiducial values.

The IAG Reference Frame Sub-Commission for Europe (EUREF) created the European Terrestrial Reference System 89 (ETRS89) and fixed it to the Eurasian plate in order to avoid time evolution of the coordinates due to plate motions. However, the Fennoscandian area in Northern Europe is affected by postglacial rebound (PGR), causing intraplate deformations with respect to the stable part of the Eurasian tectonic plate.

The Nordic countries created their national ETRS89 realizations in the 1990s and have adopted them as the basis for geospatial data. As the most accurate GNSS processing is done in ITRS realizations, an accurate connection to national ETRS89 realizations is required. If the official EUREF transformation is used, residuals are up to 10 cm in the Nordic countries. Therefore, the Nordic Geodetic Commission (NKG) has created a 3-D intraplate velocity model NKG_RF03vel over Fennoscandia and a new transformation procedure to correct for the deformations caused by PGR.

This paper evaluates the NKG approach and compares it to the current recommendation given by EUREF with a 100-point ETRS89 realization in Finland. The results show that, by using a high-quality intraplate velocity model, the transformation residuals are reduced to the cm-level.

The GGOS-D terrestrial reference frame has been computed in a common adjustment of station positions and velocities together with the Earth orientation parameters and the quasar coordinates (celestial reference frame). The data were processed as datum-free normal equations from homogeneously generated VLBI, SLR and GPS observation time series using identical standards for the modelling and parameterization. A major focus was on the analysis of the station position time series, investigations regarding seasonal variations in station motions and on the combination methodology for the terrestrial reference frame computation.

More than 10 years (1996–2008) of weekly GPS solutions of 299 globally distributed stations have been used to quantify the impact of the reference frame definition and especially the size of the network on the estimated station positions, velocities, and residual position time series. For that purpose, weekly regional solutions (covering the European region) and global solutions have been respectively stacked to obtain regional and global station positions, velocities, and residual position time series. In both cases, the estimated long-term solutions have been tied to the ITRF2005 under minimal constraints using a selected set of reference stations. This study shows that: (1) regional position and velocity solutions can present biases with respect to each other and to global solutions, while in comparison, global solutions are much more stable; (2) the obtained residual position time series are affected by the size of the network with significantly reduced periodic signals in the regional networks, e.g. a 27% reduction of the annual signals in the height component.

A constant scale difference between GPS solutions and traceable electronic distance measurement (EDM) results was found during semi-annually repeated campaigns performed in Olkiluoto, Finland. Since EDM results are very accurate and uncertainties are well-defined, this leads to an assumption that the GPS solution is biased.

At the Kyviškės test field in Lithuania, the true lengths with traceable uncertainties between observation pillars were measured using a Kern ME5000 Mekometer as a scale transfer standard. GPS observations were processed using individual and type calibrated antenna tables, a local and global ionosphere model, and three different cut-off elevation angles, and several linear combinations and were then compared with the EDM results. The results show that the ambiguity resolution strategy and antenna calibration model play a significant role compared to the cut-off elevation angle and ionosphere model.

Individual antenna calibration is required for the best metrological accuracy by means of the best agreement with traceable EDM results. The best metrological agreement was obtained with an L1 solution and individually calibrated antennas. The rms and maximum difference to the true (EDM) values were 0.3 and 0.7 mm, respectively. However, a clear distance dependency of 0.5 ppm was also evident. In particular, linear combinations with type calibrated tables caused variations up to 4 mm from the true value, even when high quality choke ring antennas were used. With individually calibrated antennas, all solutions were within ±1 mm of the true value.

GPS satellite orbits available from the International GNSS Service (IGS) show a peculiar pattern in the SLR residuals at the few centimeter level that is related to radiation pressure mismodeling. Part of the mismodeling may be attributed to neglecting the solar radiation reflected and reemitted from the Earth, the albedo radiation, as most IGS analysis centers do not yet take into account this radiation pressure component. In this study the relative importance of different albedo model constituents is analyzed. The impact of nine albedo models with increasing complexity is investigated using 1 year of global GPS data from the IGS tracking network. The most important model components are the solar panels of the satellites while different Earth radiation models have a minor impact on orbits at GPS altitudes. Albedo radiation has the potential to remove part of the anomalous SLR residual pattern observed by Urschl et al. (Calibrating GNSS orbits with SLR tracking data. Proceedings of the 15th International Workshop on Laser Ranging, 2008) in a Sun-fixed reference frame.

The determination, monitoring and understanding of sea level change at various spatial and temporal scales has been the focus of many studies during the past decades. The advent of satellite altimetry and the multitude of unprecedented in accuracy and resolution observations that it offers allowed, in combination with tide gauge data, precise determinations of sea level variations. The realization of the GRACE mission and the forthcoming GOCE data offer new opportunities for the estimation of sea level trends at regional and global scales and the identification of seasonal signals. In such studies, even though the data combination and processing strategies have been carried out carefully with proper control, a point that has been given little attention is error propagation and variance component estimation of the data variance-covariance matrices. The latter two are of significant importance in heterogeneous data combination studies, since on one hand error propagation can provide reliable estimates of the output signal error while variance component estimation allows for a rigorous control of the data covariance matrices and subsequent sound decisions on statistical testing of hypotheses involving least-squares residuals and the estimated deterministic parameters. This work presents some new ideas towards the estimation of sea level change through the combination of altimetric, tide gauge, atmospheric, and GRACE- and GOCE-type observables. The combination scheme is based on a hybrid deterministic and stochastic treatment of the data errors and an estimation of sea level changes through least-squares collocation with considerations for glacial isostatic adjustment and continental water outpour effects. The deterministic model parameters treat datum and geophysical correction model inconsistencies in the data used, while the stochastic part allows for a simultaneous determination of stochastic parameters included in the data in terms of residual signals. Within this mixed adjustment scheme with stochastic parameters, variance component estimation is carried out using the iterative almost unbiased estimator method. The analytical equations for the prediction of the adjusted input and output signals are presented along with possible modifications of the observation equation for the determination of solely steric and atmospheric-driven sea level changes.

The L3H phase of operation of ICESat’s laser in the winter of 2007 coincided for about two weeks with the cruise of the British submarine “Tireless” which was equipped with upward-looking sonars. This provided a rare opportunity for a simultaneous determination of the sea ice freeboard and draft in the Arctic Ocean.

Since March 2002 the two GRACE satellites orbit the Earth at relatively low altitude (500 km in 2002, still close to 460 km mid of 2009). GPS-receivers for orbit determination, star cameras and thrusters for attitude control, accelerometers to observe the surface forces, and a very precise microwave link (K-band) to measure the inter-satellite distance with micrometer accuracy are the principal instruments onboard the satellites. Determination of the gravity field of the Earth including its temporal variations from the satellites’ orbits and the inter-satellite measurements is the main goal of the mission.

The accelerometers are needed to separate the gravitational acceleration from the surface forces acting on the satellites. They collect a wealth of information about the atmospheric density at satellite height as a by-product. These accelerations have not yet been analyzed thoroughly, because their interpretation is complicated due to numerous thruster spikes. We outline a method to model the thruster spikes and to clean the time series of the accelerations. The isolated effect of the modeled thruster pulses on the satellite orbits is studied and a first interpretation of the cleaned accelerations is given. A correlation between K-band residuals and regions of high atmospheric fluctuations was not observed, which is probably due to time variable signals of hydrological origin that dominate the residuals.

In standard gravity field processing, short-term mass variations in the atmosphere and the ocean are eliminated in the so-called de-aliasing step. Up to now the background models used for de-aliasing have been assumed to be error-free. As the accuracy assessed prior to launch could not yet be achieved in the analysis of real GRACE data, the de-aliasing process and related geophysical model uncertainties have to be considered as potential error sources in GRACE gravity field determination. The goal of this study is to identify the impact of atmospheric uncertainties on the de-aliasing products and on the resulting GRACE gravity field models. The paper summarizes the standard GRACE de-aliasing process and studies the effect of uncertainties in the atmospheric (temperature, surface pressure, specific humidity, geopotential) input parameters on the gravity field potential coefficients. Finally, the impact of alternative de-aliasing products (with and without atmospheric model errors) on a GRACE gravity field solution is investigated on the level of K-band range-rate residuals. The results indicate that atmospheric model uncertainties are small in terms of the associated spherical harmonic coefficients. The effect in terms of K-band observation residuals is negligible compared to other modeling errors.

The following contribution addresses some of the problems involved with the determination of long-term gravity field variations from GRACE satellite observations. First of all the choice of the time span plays a very important role, especially since it generally is a hard task to derive secular trends from only a few years of satellite data. Another issue, when one is interested in a single trend phenomenon, is the reduction of all other geophysical effects causing long-term gravity field variations. This paper uses the example of trends in continental hydrological water masses for the case of the High Plains aquifer to demonstrate some of the challenges implicated by trend analysis from GRACE.

The gravity field model AIUB-GRACE02S is the second release of a model generated with the Celestial Mechanics Approach using GRACE data. Inter-satellite K-band range-rate measurements and GPS-derived kinematic positions serve as observations to solve for the Earth’s static gravity field in a generalized orbit determination problem. Apart from the normalized spherical harmonic coefficients up to degree 150, arc-specific parameters like initial conditions and pseudo-stochastic parameters are solved for in a rigorous least-squares adjustment based on both types of observations. The quality of AIUB-GRACE02S has significantly improved with respect to the earlier release 01 due to a refined orbit parametrization and the implementation of all relevant background models. AIUB-GRACE02S is based on 2 years of data and was derived in one iteration step from EGM96, which served as a priori gravity field model. Comparisons with levelling data and models from other groups are used to assess the suitability of the Celestial Mechanics Approach for GRACE gravity field determination.

In this study we address the question of whether regional gravity field modeling techniques of GRACE data can offer improved resolution over traditional global spherical harmonic solutions. Earlier studies into large, equatorial river basins such as the Amazon, Zambezi and others showed no obvious distinction between regional and global techniques, but this may have been limited by the fact that these equatorial regions are at the latitudes where GRACE errors are known to be largest (due to the sparse groundtrack coverage). This study will focus on regions of higher latitude, specifically Greenland and Antarctica, where the density of GRACE measurements is much higher. The regional modeling technique employed made use of spherical radial basis functions (SRBF), complete with an optimal filtering algorithm. Comparisons of these regional solutions were made to a range of other publicly available global spherical harmonic solutions, and validated using ICESat laser altimetry. The timeframe considered was a 3 year period spanning from October 2003 to September 2006.

The geometrical point-wise satellite positions of a Low Earth Orbiter (LEO) equipped with a Global Navigation Satellite System (GNSS) receiver can be derived by GNSS analysis techniques based on hl-SST (high-low Satellite to Satellite Tracking) observations. In the geometrically determined LEO orbit, there is no connection between subsequent positions, and consequently, no information about the velocity and the acceleration or in general kinematical information of the satellite is available. If the kinematical parameters which consistently connects positions, velocities and accelerations are determined by a best fitting process based on the observations, we perform a pure Kinematical Precise Orbit Determination (KPOD). In addition, the proposed approach has a capability to use certain dynamical constraints based on the dynamical force function model. In this case, we introduce a Reduced-Kinematical Precise Orbit Determination (RKPOD) of a specific level depending on the strength of the “dynamical constraints”. The various possibilities and the corresponding results of CHAMP orbits based on GNSS observations are presented.

The interest in a precise orbit determination of Low Earth Orbiters (LEOs) especially in pure geometrical mode using Global Navigation Satellite System (GNSS) observations has been rapidly grown. Conventional GNSS-based strategies rely on the GNSS observations from a terrestrial network of ground receivers (IGS network) as well as the GNSS receiver on-board LEO in double difference (DD) or in triple difference (TD) data processing modes. With the advent of precise orbit and clock products at centimeter level accuracy provided by the IGS centers, the two errors associated with broadcast orbits and clocks can be significantly reduced. Therefore, higher positioning accuracy can be expected even when only a single GNSS receiver is used in a zero difference (ZD) procedure. Along with improvements in the International GNSS Services (IGS) products in terms of Global Position System (GPS) satellite orbits and clock offsets, the Precise Point Positioning (PPP) technique based on zero (un-) differenced carrier phase observations has been developed in recent years. In this paper, the zero difference procedure has been applied to the CHAllenging Minisatellite Payload (CHAMP) high–low GPS Satellite to Satellite Tracking (hl-SST) observations, then the solution has been denoted as Geometrical Precise Orbit Determination (GPOD). The estimated GPOD CHAMP results are comparable with results of other groups e.g. Švehla at TUM (Švehla D, Rothacher M (Švehla and Rothacher 2002) and Bock at Bern (Bock 2003) but because of different outliers detection and data processing strategies, the GPOD results presented here are more or less different than the other groups’ results. The estimated geometrical orbit of CHAMP is point-wise and its accuracy relies on the geometrical status of the GNSS satellites and on the number of the tracked GNSS satellites as well as on the GNSS measurement accuracy in the data processing. The position accuracy of 2–5 cm of CHAMP based on high–low GPS carrier phase observations with zero difference procedure has been achieved. These point-wise absolute positions can be used to estimate kinematical orbit of the LEOs.

The purpose of the presentation is to discuss the combination of terrestrial and satellite gravity field data and to show its spectral and space domain interpretation. Potential theory is of key importance in this field. However, the problems discussed are overdetermined by nature. Therefore, methods typical for the solution of boundary-value problems are used together with an optimization concept, target functions and regularization techniques. Two cases are treated. They are motivated by the use of a satellite-only model of the gravity field of the Earth or by data coming from satellite missions (especially GOCE) in common with terrestrial gravity measurements. For the results reached in the spectral domain summation techniques are applied in order to find the interpretation of the results in terms of kernel (Green’s) functions related to the particular combination scheme. This enables to show the tie between the global and the local modelling of the gravity field. In order to demonstrate the efficiency of the procedure results of numerical simulations are added. Differences of the closed loop simulation are very promising.

The GOCE mission, exploiting for the first time the concept of satellite gradiometry, promises to estimate the Earth’s gravitational field from space with unprecedented accuracy and spatial resolution. Also inverse gravimetric problems can get benefit from GOCE observations. In this work the general problem of estimating the discontinuity surface between two layers of different density is investigated. A possible solution based on a local Fourier analysis and Wiener deconvolution of satellite data (such as gravitational potential and its second radial derivative) is proposed. Moreover a numerical method to combine in an efficient way gridded satellite data with sparse ground data, like gravity anomalies, has been implemented. Numerical simulations on different synthetic Moho profiles have been carried out. Finally a two-dimensional simulation on realistic data over the Alps has been set up. The results confirm that GOCE data can significantly contribute to the detection of geophysical structures, leading to a much better determination of the signal long wavelengths (up to about 200 km). The use of local ground data improves the satellite-only estimate, making possible the recovery of higher resolution details.

The electrostatic accelerometers of the CHAMP satellite as well as of the GRACE two ones have provided the necessary information to distinguish the satellite actual trajectories from the pure gravitational orbits. By providing the measurements of the satellite non-gravitational forces, one can distinguish the position or velocity fluctuations of the satellite due to the Earth gravity anomalies from those due to the drag fluctuations. In-orbit calibration and validation of on-board instruments, bandwidth, bias stability and resolution proof the success of the mission scientific geodesic return. The basic principle of these sensors stays on the servo-control of one solid mass, maintained motionless from the instrument highly stable structure. Care is paid for the mass motion detection, down to tenth of Angstrom, and to the fine measurement of the servo-controlled forces applied on the mass through electrostatic pressures. With the same concept and technologies, the GOCE inertial sensors have been designed, produced and tested to reach even better performances in order to deal with the milli-Eötvös gradiometer objectives. The performance of the instrument and the interest of the obtained measurements do not only depend on the sensor accuracy itself but also on the on-board environment (magnetic, thermal, vibrational…), on the satellite attitude motions and on the in-orbit configuration and aliasing aspects. Future missions will have also to consider these aspects, especially when envisaging cryogenic electrostatic sensors which can exhibit better self accuracy or when considering satellite to satellite laser tracking.

Launched on March 17th 2009 from the Plesetsk Cosmodrome (Northern Russia), GOCE maps the Earth’s gravity field with unprecedented accuracy and resolution and will be of benefit for many branches of Earth science. This paper gives an overview of the European Space Agency’s (ESA) recent technical developments and activities going beyond the GOCE mission and its technology. It describes the outcome of the recent Laser SST concept studies, the Laser metrology concept and the objectives of the ongoing parallel Next Generation Gravimetry Mission studies, together with an overview on the latest technology development studies on atomic clocks and atom interferometry for possible future gravity sensing.

Modern satellite gravity field recovery missions use accelerometric, intersatellite tracking or gradiometric observables for deducing gravity field related data. In this study an alternative observable type for gravity field recovery, the relativistic frequency shift, is investigated. As Einstein stated in his general theory of relativity, gravity can be considered as attribute of space-time. In this view mass alters the geometric shape of the metric tensor. Moreover mass, respectively gravity, has effects on electromagnetic wave propagation [Einstein (Annalen der Physik 35:898–908 1911)]. Although these relativistic effects are quite small and difficult to measure, with upcoming atomic clocks which have sufficient accuracy and short-term stability it will be possible to derive meaningful gravity related information. Since relativistic effects are used this method is called Post-Newtonian method. The main target of this paper is to demonstrate the validity of the derived relativistic equations.

The scientific quality of the relativistic frequency shift observed by means of highly accurate atomic clocks is investigated. In our basic scenario a low earth orbit (LEO) sends an electromagnetic wave to a receiver. The reference station determines the frequency shift of the signal, which is connected to the time dilatation between the atomic clock of the satellite and an identical atomic clock nearby the receiver. A simplified, mathematical model for numerical simulations of this configuration is presented. The effect of different error sources are investigated by numerical closed-loop simulations. Thus, the performance requirements of atomic clocks, position and velocity determination and limiting factors for deducing earth’s gravity field can be derived.

A long recognized connection between the gravitational gradients of the Earth’s crust and its magnetic anomalies, known as Poisson’s relationship, is the object of investigation in this paper. We develop the mathematical and theoretical basis of this relationship in both the space and frequency domains. Anomalies of the magnetic field thus implied by the gravitational gradients (or other derivatives of the gravitational potential) are called pseudo-magnetic anomalies; and, they assume a linear relationship between the mass density of the source material and its magnetization induced by the Earth’s main magnetic field. Tests in several regions of the U.S. that compare gravitational gradients derived from the high-resolution model, EGM08, and a continental magnetic anomaly data base reveal that the correlation implied by Poisson’s relationship is not consistent. Some areas exhibit high positive correlation at various frequencies, while others have even strong negative correlation. Therefore, useful applications of Poisson’s relationship depend on the validity of the underlying assumptions that, conversely, may also be investigated and studied using a combination of gradiometric and magnetic data.

The detection of mass anomalies in the near subsurface is an important problem in many areas of interest, such as archeology, construction, and hazard analysis. Assuming that the approximate geometry of an anomaly is known, its possible location can be determined by applying a matched filter to observations of gravity, gravity gradient, and magnetic anomalies, as well as to electro-magnetic data. We analyze the specific combination of gravity, gravity gradient, and magnetic data in order to determine their relative strengths and weaknesses in the detection problem. Poisson’s Relation is used to model the magnetic signals generated by the source to be detected, and the mutual covariances of the background geologic noise that may contaminate the observations. Simulations show that the magnetic data can improve the detection using the matched filter, especially with limited gravity gradients from a typical ground gravity gradiometer. Further analyses using actual data over a known local anomaly illustrate the enhancements as well as limitations of the gravimetry, gradiometry, and magnetic data combinations.

Airborne gravimetry is a cost-effective technique to complement the gravity field information from satellite missions such as GRACE and, in the near future, GOCE. Measurements can be collected over regional areas in a relatively short time. Moreover, it is an especially useful method in remote areas and coastal water zones where terrestrial and ship-borne gravity measurements are difficult.

One drawback of airborne gravimetry is aircraft availability and the associated cost of flight time. If these problems can be reduced or minimised, airborne gravimetry can be made more accessible and cost-effective. A possible option discussed here is based on the use of Unmanned Autonomous Vehicles (UAVs).

The use of UAVs has increased in a large number of fields and is proving to be a viable and cost-effective option. However, the performance of UAVs is considerably different from regular fixed-wing aircraft and will have a significant impact on the performance of a gravimetry system. Also, due to the dimensions and operational requirements of spring gravimeter systems, these systems cannot be used inside UAVs.

This paper discusses how parameters, such as flight speed, endurance, and flight dynamics, can affect the determination of gravity anomalies and definition of the geoid using strapdown gravimetry systems on board of UAVs.

The study is limited to the use of the so-called Light UAVs which have a Maximum Take-Off Mass (MTOM) of less than 150 kg, since those can be relatively inexpensive. Some typical parameters used here for this range of UAVs are a cruise speed of 30 m/s, an endurance of several hours and a payload mass of several tens of kilograms.

First results, based on PSD (Power Spectral Density) analysis, indicate that, for a navigation grade inertial system, the use of UAVs can be an advantage in recovering the short wavelength (<5 km) information of the gravity field.

The goal of maintaining an accurate gravity network at the BIPM headquarters is twofold: firstly to support the International Comparison of Absolute Gravimeters (ICAG), and secondly to support the BIPM watt balance (WB) project, which aims at determining the Planck constant

h

or realizing a future new definition of the kilogram based on a fixed value of

h

. In addition the absolute gravity measurements, Relative Gravity Campaign (RGC) is organized as part of each ICAG.

The BIPM gravity network is characterized by its small size, indoor laboratory conditions, three-dimensional structure, and large number of parallel absolute gravity determinations. Over the last 3 decades, repeated precise horizontal and vertical ties have been measured using relative and absolute gravimeters, and precision leveling has been undertaken regularly to monitor the deformation of the terrain. The ICAG is held every 4 years; the 8th ICAG took place in mid-2009 and for the first time, it was organized as a metrological key comparison as defined by the CIPM MRA. Its results will such constitute a precise and consistent gravity reference system in SI units which can be used as the global basis for geodetic and geophysical observations. Additionally, to support the WB project, the network was extended to the BIPM WB laboratory.

In this paper, we briefly recall the background of the ICAG/RGC2009 and outline the new characteristics of the updated network, the organization and the performance of the measurements. Finally we present preliminary results from the RGC2009.

The A-10 field absolute gravimeter produced by the company Micro-g LaCoste Inc. was found to comply well with the producer specification of an uncertainty of 100 nm s

−2

for the determination of gravity acceleration. Repeated observational checks at a known reference station and careful calibration of instrumental standards demonstrated that the gravity measurements quality could further be enhanced. This opens new applications for precise gravimetry like the establishment of reference networks for monitoring global change processes where uncertainties of a few 10 nm s

−2

are of high value. The results and experiences from two extensive field campaigns using an A-10 gravimeter are presented.

During recent investigations concerning geodetic applications of the torsion balance measurements several problems arose, which required performing new torsion balance measurements. For that reason an Eötvös-Rybár (Auterbal) torsion balance, which has been out of operation for many decades, was reconstructed and modernized. The scale reading has been automated and its accuracy has been improved by using CCD sensors. Calibration and processing of field measurements were computerized to meet today’s requirements. Test measurements have shown that this instrument was able to work according to the expectations of our age.

We describe development of a transportable version of the Superconducting Gravimeter (SG) and its test in a field experiment to monitor storage in a karst (limestone) aquifer in central Texas. The SG is contained within two aluminum enclosures, one holding the SG in its 35 l helium dewar, plus electronics; and the second for refrigerator and power supply. In the field test, the SG was supported on threaded steel rods cemented into limestone, and surrounded by weather-protecting sheds. The steel rod design was not completely satisfactory, and in most field settings a concrete floor will probably be required. Field operation requires wired electric power, but is managed remotely using wireless internet. The experiment south of Austin Texas was designed to monitor ground water level, precipitation, and other variables, and observe mass variations associated with storage changes in the aquifer. Drought conditions prevailed, limiting conclusions about the aquifer, but the experiment demonstrated the feasibility of remote unattended operation for periods of many months.

Hydrological variations of up to some 10 nm/s

2

are significant and broadband signals in temporal gravity observations. On the one hand they need to be eliminated from the data as they interfere with geodynamic signals. On the other hand they can be used to improve the understanding of hydrological process dynamics and to evaluate distributed hydrological models. Compared to satellite observations which are affected by global and regional hydrological variations continuous recordings from superconducting gravimeters (SGs) additionally may contain extractable information on local changes. To compare terrestrial data to satellite observations and to regional/global hydrological models, a local hydrological impact on the observations must be quantified and appropriately reduced first.

To investigate the local hydrological impact on gravity of the hilly and geologically heterogeneous surroundings of the SG at the Geodynamic Observatory Moxa, Germany, interdisciplinary research has been carried out. For an area of about 1.5 × 1.5 km

2

a hydrological catchment model was combined with a gravimetric 3D model, including heterogeneities of the subsoil and topography in detail. A reduction of the local hydrological signal in the SG recordings was developed. About 30% of the local hydrological effect in the SG data originate from an area within a radius of 90 m around the observatory. The contribution of areas above the SG level is about 85% of the total local effect. After the local hydrological signal is separated, the SG data become suitable to be interpreted with regard to changes in continental water storage as found in GRACE satellite observations and in global hydrological models. The evaluation of the local hydrological model basing on the gravimetric modelling and the SG data highlights approaches for further enhancement of the internal hydrological process representations.

The superconducting gravimeter (SG) operating at the South African Geodynamic Observatory Sutherland (SAGOS) is one of the few instruments installed in the southern hemisphere and presently still the only one of its kind on the African continent. SAGOS is located in the Karoo, a semi-arid area with an average annual precipitation of 200–400 mm. The distance to the ocean is approx. 220 km.

A local hydrology-related seasonal effect on gravity is clearly seen in the SG record. Its general order of magnitude is estimated to be about 4–10 nm/s

2

. A large-scale hydrological influence in a similar order of magnitude or even larger (up to 60 nm/s

2

peak-to-peak) is inferred from global hydrological models for the years 2003–2007. Significant contributions are found for the southern coast, the central Cape region, and the basin of the Orange river. Contributing basins with larger distance comprise the areas of Okavango/Sambesi, Congo, and eastern Africa. Between SG data, temporal GRACE gravity field solutions, and the gravity effect derived from global hydrological models clear differences exist. Among others, the deviations between the hydrological models can be traced to deviations in the gravity effect originating from the Okavango basin and the central Cape region.

Gravity residuals reduced for changes in continental water storage are compared to the gravity effect caused by non-tidal oceanic mass changes. A rudimentary correlation between observed variations and modeled effect is found.

The peak-to-peak amplitude of the modeled effects amounts to 15 nm/s

2

for the years 2001–2008. After reducing the SG data for this oceanic effect the variation of the residuals decreases by 9%.

The present findings indicate the suitability of the SG observations at Sutherland for studies on mass transport phenomena in the South African region.

Preparations to establish a new accurate gravity network in Estonia were initiated in 2001. Since then several LCR (LaCoste&Romberg) G-type and Scintrex CG-5 relative gravimeters have been used to determine gravity differences precisely. The calibration functions of those relative instruments have been repeatedly checked at the calibration lines in Estonia and in Finland. Since the beginning of the 1990s absolute gravity values have been determined three times in Estonia: in 1995 at three stations with JILAg-5 by the Finnish Geodetic Institute (FGI), in 2007 at two stations with FG5-220 by the Institut für Erdmessung (IfE), University of Hannover, and a year later at seven stations with FG5-221 again by FGI. On the ground of collected absolute and relative gravity data, a new realization (network GV-EST) of the Estonian gravity system (EGS) is currently being established. However, before the completion of the network, several issues should be solved, including the calibration of relative gravimeters, the corrections of readings and setup of the functional model, the weighting of observation data and selection of statistical tests, the short and long term changes of the gravity field, the choice of the epoch. In the current paper I introduced the concept of EGS as well as the methodology to solve the afore-mentioned issues. Since the estimated uncertainties of gravity values from network adjustment stayed below ±10 μGal (1 μGal = 10

−8

m/s

2

) it was concluded that the selected methods had been efficient.

The new global Earth gravitational model EGM2008 has been evaluated within geopotential space by comparison with its predecessor EGM96 and the GRACE combination model EIGEN-GL04C. The methodology comprises establishing geodetic coordinates of mean sea level (MSL) from GPS observations, tide gauge (TG) time series and levelling. The gravity potential at MSL was estimated at each TG location by utilising the ellipsoidal harmonic coefficients of the adopted gravity field models to their maximum degree and order. This study uses data from 23 TGs around the Baltic Sea, nine in the UK and one in France. Comparison involves testing the agreement between geopotential values for each country as gravity potentials at MSL are supposed to be consistent for regions where mean dynamic topography (MDT) does not differ significantly. Results show significant improvement with the EGM2008 model compared against its counterparts. The study shows the effect of omission errors on the solution by limiting the EGM2008 model to maximum degree and order 360 in the regional study. In addition to the regional study, EGM2008 was also evaluated globally using MSL derived from altimetric data. The global study shows that

W

0

, the potential value on the geoid, is not affected by high degree terms of the EGM2008.

This paper discusses advantages of the fixed gravimetric boundary value problem (FGBVP) for precise gravity field modeling that is necessary for a unification of local vertical datums (LVDs). Our objective is to show how inconsistencies of input gravity data due to shifts and tilts of LVDs can influence precise solutions. Such systematic errors can backward affect estimations of the shifts and tilts of LVDs. This drawback completely vanishes in case of FGBVP. Terrestrial gravimetric measurements accompanied by the precise 3D positioning by GNSS yield globally consistent surface gravity disturbances that are fully independent from any LVD (assuming the same gravity datums). Since terrestrial gravity data from the past are related to LVDs, we try to reconstruct their ellipsoidal heights using available geoid/quasi-geoid models as well as shifts and tilts of LVDs modeled from GPS/Leveling data. In this way we simulate consistent surface gravity disturbances that represent oblique derivative boundary condition for FGBVP. In the numerical experiments we deal with (i) the global gravity field modeling using the boundary element method (BEM), and with (ii) the continental modeling using the finite volume method (FVM). In both cases we compare the numerical solutions obtained with and without taking into account corrections from the shifts and tilts of LVDs in the input data. It shows how an absolute precision of vertical positions of terrestrial gravity data influence precise numerical solutions.

We utilize the geopotential value approach to determine the average offsets of 12 major local vertical datums (LVDs) in New Zealand (NZ) relative to the world height system (WHS). The LVD offsets are estimated using the EGM2008 global geopotential model coefficients complete to degree 2159 of spherical harmonics and the GPS-levelling data. WHS is defined by the adopted geoidal geopotential value W

0

= 62636856 m

2

s

−2

. Our test results reveal that the average offsets of 12 major LVDs situated at the South and North Islands of NZ range from 0.01 m (Wellington 1953 LVD) to 0.37 m (One Tree Point 1964 LVD). The geopotential value of the tide-gauge station used as the origin for the LVD Wellington 1953 is thus almost the same as the geoidal geopotential value W

0

. EGM2008 and GPS-levelling data are further used to compute the differences between the NZGeoid05 regional quasigeoid model and the EGM2008 global quasigeoid model. The same analysis is done for NZGeoid2009 which is the official national quasigeoid model for NZ. The systematic bias of about 0.56 m is found between NZGeoid05 and EGM2008. A similar systematic bias of about 0.51 m is confirmed between NZGeoid2009 and EGM2008.

The recent improvements in satellite tracking data processing, the availability of new surface gravity data sets, and the availability of a new mean sea surface height model from altimetry processing gave rise to the generation of several new global gravity field models. However, to know their potentiality for using in practical situations, we understood that it was necessary their applications in a limited regions. This paper we compare recent geopotential models with gravimetric data over leveling points of Argentinean National Geografhical Institute (ANGI) vertical network in

Santiago del Estero

region, northwestern Argentine. We have highlighted the most important information, we have established the future expectations to continue with such applications. Results of comparisons are presented.

The airborne gravimetry system provides an efficient tool to collect the homogeneous airborne gravity data over large areas. For this purpose Intermap has developed a new Airborne Inertial Gravimetry System (AIGS), based on the GPS/INS components of Intermap’s Interferometric SAR (IFSAR) system and the airborne gravity process software, called StarGrav. The state-of-the art in the acquisition of airborne gravity data at Intermap will be discussed and the process in gravity determination will be described.

The paper presents recent airborne gravity results for different topography and scenarios. The airborne gravity measurements by Intermap’s StarGrav system are compared to the upward continued ground gravity data and to the independent airborne gravity results provided by NGS. The results demonstrate that the accuracy of 2–3 mGal (1σ) for the airborne gravity measurements by Intermap airborne gravity mapping system can be achieved. The geoid determined using the airborne gravity data could have the relative accuracy of 5 cm (1σ) when compared with an independently determined geoid reference.

Between Aug 14, 2006 and Apr 24, 2007, and enjoying a considerable interest from the Danish authorities, the Danish public and the Danish media, the scientific expedition Galathea-3 circumnavigated the globe. Its domestic purpose was to attract the Danish youth to science.

DTU Space, Technical University of Denmark, participated in the expedition with two experiments. From Perth, Western Australia to Copenhagen, Denmark the exact position and movements of the ship were monitored using a combination of GPS, INS and laser measurements. The purpose was to measure the instantaneous sea surface topography.

This paper reports on the second experiment in which a continuous marine gravity profile along the ship’s route was measured. The focus of the paper is on the practical aspects of such large scale world wide operation and on the challenges of the data processing. Furthermore, the processed free-air gravity values are compared to three global models: EGM96, EGM08 and DNSC08. Even though the along-track resolution of marine data is higher than the resolution in any global gravity model (which influences the direct comparison of the collected marine data to the model) the statistics for the residual free-air gravity anomalies show, that EGM08 and DNSC08 are better models than EGM96 for all Galathea-3 legs. Some areas along the ships route are quite challenging for modellers.

The so-called Colombo-Nyquist (Colombo, The global mapping of gravity with two satellites, 1984) rule in satellite geodesy has been revisited. This rule predicts that for a gravimetric satellite flying in a (near-)polar circular repeat orbit, the maximum resolvable geopotential spherical harmonic degree (

l

max

) is equal to half the number of orbital revolutions (

n

r

) the satellite completes in one repeat period. This rule has been tested for different observation types, including geoid values at sea level along the satellite ground track, orbit perturbations (radial, along-track, cross-track), low-low satellite-to-satellite tracking, and satellite gravity gradiometry observations (all three diagonal components). Results show that the Colombo–Nyquist must be reformulated. Simulations indicate that the maximum resolvable degree is in fact equal to

kn

r

+ 1, where

k

can be equal to 1, 2, or even 3 depending on the combination of observation types. However, the original rule is correct to some extent, considering that the quality of recovered gravity field models is homogeneous as a function of geographical longitude as long as

l

max

<

n

r

/2.

We compare the accuracy of local gravity field modelling in rugged mountains using three different discretised integral equations; namely (1) the single layer approach, (2) Poisson’s integral approach, and (3) Green’s integral approach. The study area comprises a rough part of the Canadian Rocky Mountains with adjacent plains. The numerical experiment is conducted for gravity disturbances and for topographically corrected gravity disturbances. The external gravity field is parameterized by gravity disturbances (Poisson’s integral approach) and disturbing potential values (Green’s integral approach), both discretised below the data points at the same depth beneath the Bjerhammar sphere. The point masses in the single layer approach are discretised below the data points on a parallel surface located at the same depth beneath the Earth’s surface. The accuracy of the gravity field modelling is assessed in terms of the STD of the differences between predicted and observed gravity data. For the three chosen discretisation schemes, the most accurate gravity field approximation is attained using Green’s integral approach. However, the solution contains a systematic bias in mountainous regions. This systematic bias is larger if topographically corrected gravity disturbances are used as input data.

We compute globally the topographically corrected and topo-density contrast stripped gravity disturbances and gravity anomalies taking into account the major known density variations within the topography. The topographical and topo-density contrast stripping corrections are applied to the EGM08 gravity field quantities in two successive steps. First, the gravitational contribution of the topography of constant average density 2,670 kg/m

3

is subtracted. Then the ice, sediment, and upper crust topo-density contrast stripping corrections are applied to the topographically corrected gravity field quantities in order to model the gravitational contribution due to anomalous density variations within the topography. The coefficients of the global geopotential model EGM08 complete to degree 180 of spherical harmonics are used to compute the gravity disturbances and gravity anomalies. The 5 × 5 arc-min global elevation data from the ETOPO5 are used to generate the global elevation coefficients. These coefficients are utilized to compute the topographical correction with a spectral resolution complete to degree and order 180. The 2 × 2 arc-deg global data of the ice, sediment, and upper crust from the CRUST 2.0 global crustal model are used to compute the ice, sediment, and upper crust topo-density contrast stripping corrections with a 2 × 2 arc-deg spatial resolution. All data are evaluated globally on a 1 × 1 arc-deg grid at the Earth’s surface.

We analyze the performance of a least-squares approximation of the gravity field using Spherical Radial Basis Functions (SRBFs) in rugged mountains. The numerical experiment is conducted for the gravity disturbances and for the topographically corrected gravity disturbances, both provided on a 5 ×5 arc-min grid located at the Earth’s surface. The target area is a rough part of the Canadian Rocky Mountains with adjacent planes. The data area and the parameterization area extend the target area in all directions by 3 arc-deg. The accuracy of the gravity field approximation is investigated using a SRBF parameterization (Poisson wavelet of order 3) on different spherical equal-angular grids with step sizes varying between 6 and 12 arc-min. For every choice of grid, the optimal depth of SRBFs bellow the Bjerhammar sphere is found using the minimization of the RMS differences between predicted and observed values. The results of the numerical experiment reveal that the application of the topographical correction to the observed gravity data reduces the number of SRBFs by more than 56%, and improves the fit to the data by 12%. Unfortunately, it also introduces a systematic bias in the adjusted gravity disturbances.

The Input–Output System Theory (IOST) method is primarily based on the spectral combination of heterogeneous data taking into account their statistical properties and approximating the Power Spectral Density (PSD) functions of the signals and their errors. In this study a Multiple Input–Multiple Output System (MIMOS) is proposed, where the input measurements as well as the input and output signals are different gravity field observables. The work presents a sensitivity analysis of the IOST method towards the input data noise and the effect of integral kernel modifications to the error prediction estimates. Simulated input noise fields along with the contribution of the input data resolution to the output prediction errors are investigated towards the analysis of the 2D error covariance functions. Special attention is paid to the contribution of different kernels to the error prediction estimates and 2D planar and spherical discrete kernels are tested considering the overall prediction improvement of the spectral procedure. The MIMOS system is finally assessed by a number of numerical tests and conclusions are drawn in terms of the optimal modelling of the input data noise and the significance of the spherical kernels in the improvement of the prediction results.

During the last decade, the realization of the satellite gravity missions of CHAMP and GRACE, the acquisition of new gravity data and the development of novel processing methodologies has led to the determination of more accurate and higher in resolution global geopotential models. The spatial scale of ~110 km that EGM96 could represent has improved today with EGM2008 to the level of ~16 km (full wavelength). This advance in the representation of higher frequencies by the geopotential models may signal the need to reassess the methodologies and techniques traditionally used for local and regional geoid determination. The traditional procedure followed is that of the remove-compute-restore method. The input functionals related to the Earth's gravity field are first reduced to a reference geopotential model, then the topographic effects are taken into account through one of the available reduction methods, computations follow using the reduced observations, and finally the contribution of the global geopotential model and the topographic indirect effects are added back to the computed reduced geoid values. One crucial point to this operation is that the attraction of the masses considered with a topographic reduction scheme is supposed to represent the medium and high frequencies in the gravity field, which still remain in the data, in principle even after they have been reduced to a geopotential model. Given that the best available digital depth models have a resolution of 30 arcsec, which translates to roughly 1 km spatial wavelength, it becomes apparent that the contribution of such a model to the reduction of gravity and geoid data, when a high resolution geopotential model is used as reference, is questionable or should be at least investigated. This final point is the main goal of this paper, i.e., to investigate the contribution of the available digital depth models to the reduction of gravity anomalies and geoid heights when a geopotential model with the resolution of EGM2008 is used. To this extent, marine gravity anomalies and satellite altimetry sea surface heights are used off-shore the Atlantic coast of Argentina. EGM2008 is used as a reference surface to reduce the available gravimetric and altimetric observations, and the latest bathymetry model from the Scripps Institute of Oceanography group (SIOv11.1) is employed in order to compute topographic reductions based on the Residual Terrain Model (RTM) scheme. The results acquired are validated in terms of the reduction they provide to the available input data, both the mean and the standard deviation of the residuals, as well as in terms of the spectral content of the residual signal spectrum. Conclusions and recommendations on the use of topographic reductions and the treatment of topographic effects for geoid modelling in the presence of a high-resolution geopotential model are also drawn so as to ensure the consistency between data used and results acquired.

Geoid computation according to the Stokes-Helmert scheme requires accurate modelling of the variations of mass-density within topography. Current topographical models used in this scheme consider only horizontal variations, although in reality density varies three-dimensionally. Insufficient knowledge of regional three-dimensional density distributions prevents evaluation from real data. In light of this deficiency, we attempt to estimate the order of magnitude of the error in geoidal heights caused by neglecting the depth variations by calculating, for artificial but realistic mass-density distributions, the difference between results from 2D and 3D models.

Our previous work has shown that for simulations involving simple mass-density distributions in the form of planes, discs or wedges, the effect of mass-density variation unaccounted for in 2D models can reach centimeter-level magnitude in areas of high elevation, or where large mass-density contrasts exist. However, real mass-density distributions are more complicated than those we have modeled so far, and involve multiple structures whose effects might mitigate each other. We form a more complex structure by creating an array of discs that individually we expect to have a very significant effect, and show that while the contribution of such an array to the direct topographical effect on geoidal height is sub centimeter (0.85 cm for our simulation), the resulting primary indirect topographical effect may reach several centimeters or more (5 cm for our simulation).

Satellite altimetry in near-coastal marine areas is notoriously problematic, and gravity anomalies derived from various satellite-altimetry-derived gravity models differ significantly near the coast. In this paper, gravity anomalies from the DNSC08 and Sandwell & Smith v18.1 (SS18) models are compared and ‘validated’ against shipborne and airborne gravity anomalies around the Australian coast. Due to the scarcity of high-quality gravity observations just off the coast, a true validation of the models cannot be achieved. However, DNSC08 conforms slightly better to both shipborne and airborne gravity observations closest to the coast in selected test areas, although the standard deviation of differences between the models and the test data barely exceeds the estimated test data accuracy.

The GRAVSOFT suite of Fortran programs enables gravity field modeling using 3D or 2D Least-Squares Collocation and Fourier techniques, the computation of topographic effects, the evaluation of high-degree spherical harmonic series and several other functions. It has been developed since the early 1970s with a line-oriented DOS-interface. Sponsored by the Geodetic Survey of Malaysia a modern graphical interface has been designed using Python (

www.python.org

) and the widget toolkit Tk, following the Apple Design Guidelines.

A prototype was designed and tested at a geoid workshop in Malaysia. An iteration of this was then tested at the International Geoid School, Como and a third iteration during a graduate course at the University of Copenhagen. The result is two main redesigns; the GRAVSOFT Launcher Interface and the browsing Interface.

User evaluation showed high satisfaction with the Interface, but identified the error/help support as dissatisfying. However 1 in 4 found it difficult to learn to use the programs. Difficulties in learning is correlated with participants educational level, showing that when applications – which have been used in research – target other user groups, redesign and user testing is required.

The Antarctic Geoid Project (AntGP) aims at the improvement of terrestrial observations of the gravity field in Antarctica and, eventually, at the improvement of the Antarctic geoid. Until present, vast areas of Antarctica are still unexplored with regard to gravity measurements. The polar data gap due to the deflection from a polar inclination of the respective satellite and the limitation to a certain harmonic degree of resolution prevent a complete, high-resolution data coverage to be obtained from the dedicated gravity satellite missions only. In this context, the International Polar Year (March 2007 to February 2009) provided a framework for broad international and interdisciplinary collaboration, which opened also an excellent opportunity for the realization of new gravity surveys. Especially, there was a focus on airborne gravimetry which provides the most powerful technique to carry out observations in vast and remote areas. The paper will review the present situation and will give an outlook to further activities. The feasibility of the regional geoid improvement in Antarctica will be discussed, utilizing the heterogeneous gravity data available from different surveys and techniques.

We present an improved quasigeoid of the Palmer Land Region, Antarctic Peninsula, derived from recent aerogravimetry profiles provided by the British Antarctic Survey (BAS). Special focus is given to the treatment of the ice layer covering the bedrock topography, the latter one being regarded as the boundary surface. The remove-compute-restore technique (RCR) with least-squares collocation (LSC) and a point mass modeling, respectively, are applied and compared. In addition to previous studies, an alternative strategy regarding downward continuation has been introduced. Furthermore, the Residual Terrain Model (RTM) has been enhanced to incorporate the individual densities of water, ice and bedrock.

In 2004, the French Institut Géographique National (IGN), upon the request of the steering committee of the European Gravity and Geoid Project, prepared a dataset to test geoid computation methods. It consists of a set of about 240,000 gravity points, three digital terrestrial models (an accurate one, a low-resolution one and a filtered one) and 75 GPS/levelling points to evaluate the quality of the computed geoid models (Duquenne, A data set to test geoid computation methods. In: Dergisi H (eds.), Proceedings of the 1st international symposium of the international gravity field service “gravity field of the earth”, pp 61–65, 2006).

In this paper, we compared the following geoid computation methods using the Auvergne dataset: the remove-compute-restore method using the unmodified Stokes’ kernel, the deterministic (Wong and Gore) and stochastic (KTH) modifications of Stokes’ kernel. For each method, we tested different choices of the parameters (radius of integration of Stokes’ anomalies, degree of modification of Stokes’ kernel, radius of integration of terrain effect, etc.). We analysed the results in order to find out which method performs the best and how the geoid modelling method impacts the results, considering the presence of errors in the dataset. The question that this work intends to answer is whether we should put our efforts rather on the theoretical investigations of geoid modelling methodologies, or on the acquisition of gravity measurements.

As part of its strategic plan for 2008–2018 [The NGS Ten Year-Plan, Mission, vision and strategy, 2008–2018], the National Geodetic Survey has resolved to engage in activities which would allow for the development of a 1-cm accurate national gravimetric geoid for the conterminous US. In this regard, the Ohio Department of Transportation has been collaborating with the OSU SPIN Laboratory in height modernization activities for the state of Ohio. Presented in this paper are the results of an investigation used to evaluate the quality of gravity and height data needed to produce a cm-accurate geoid in Ohio.

In this study a local geoid model over Ohio was computed in a remove-restore geoid determination procedure using EGM2008 [Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An earth gravitational model to degree 2160: EGM2008, presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13–18], publicly-available surface gravity data from the PACES website and the GTOPO30 DEM. Terrain corrections (subject to a planar approximation) were evaluated using a 2D FFT algorithm [Forsberg R (1985) Gravity field terrain effect computations by FFT. Bull G odésique 59:342–3601; Forsberg R (1997) Terrain effects in geoid computations. Lecture notes. International School for the Determination and Use of the Geoid, Rio de Janeiro, Sept 1997]. Ohioan terrain being substantially flat (on average about 330 ± 160 m AMSL) produced terrain corrections which were, for the most part, at the sub-mGal level. However, these translated into a geoid contribution of about 0.039 ± 0.038 m in the local model. A 1D FFT technique [Haagmans R, de Min E, von Gelderen M (1993) Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes’ integral. Manuscripta Geodaetica 18:227–241] was used to evaluate the Stokes’ integral [Heiskanen WA, Moritz H (1967) Physical geodesy, W.H. Freeman, San Francisco, CA] over a 5° × 5° region on a 5′ × 5′ grid encompassing the state of Ohio and its environs.

This local geoid model was used as a reference solution for statistical comparisons made to subsequently computed geoid determinations (over the same region) in which the latter had been evaluated using surface gravity and height data sets subjected to simulated zero-mean Gaussian-distributed random errors of homogeneous spatial distribution. While EGM2008 was assumed to be perfect, the standard deviation of the errors applied to the surface gravity ranged from ±0.1 to ±5 mGal while those associated with the height data (of both the gravity and the DEM) ranged from ±0.5 to ±20 m. For each Gaussian dispersion utilized, 100 simulated error-prone data sets were selected and their associated geoid solutions determined using the same Stokes/FFT algorithms which were used to evaluate the aforementioned reference geoid model. Summary statistics were evaluated for each set of the 100 “randomized” geoid models relative to the reference solution, allowing for an evaluation of the potential impact of random errors present in the input height and gravity data on the local geoid solution in Ohio.

It was found that simulated height errors which were ±10 m or less produced a 1 cm (1σ) accurate local geoid while those in excess did not. RMS differences of 1–1.6 cm occurred on application of gravity errors of ±3 to ±5 mGal, prohibiting the possibility of achieving a cm-accurate geoid. Based on the results of this study, it was concluded that minimum requirements for a cm accurate geoid determination in Ohio would be a combination of gravity and height data accurate up to about the ±3 mGal and ±10 m levels, respectively.

Future studies will be conducted using updated gravity and height data sets. In addition the geoid height error analysis would account for (1) the implementation of a spatially-heterogeneous error modeling scheme based on surface gravity data density and (2) simulated random errors in the global geopotential model used in concert with the surface gravity and height data sets.

The combined adjustment of GPS/Levelling observations on benchmarks with gravimetric geoid heights has been the focus of extensive research both from the theoretical and practical point of view. Up until today, with few exceptions, the main blame for the inconsistencies/disagreement between these three types of heights has been put to the geoid heights due mainly to their poorer accuracy. With the advent of the new CHAMP- and GRACE-based global geopotential models and the realization of EGM2008 the achievable cumulative geoid accuracy has improved significantly so that its differences to GPS/Levelling heights reach the few cm level. In Greece, GPS observations on BMs are very scarce and cover only small parts, in terms of spatial scale, of the country. Recently, an effort has been carried out to perform new GPS measurements on levelling BMs, so that reliable GPS/Levelling and gravimetric geoid height adjustment studies can be carried out. This resulted in part of North-Western Greece to be covered with reliable observations within an area extending 3° in longitude and 1° in latitude. Therefore, some new potential for the common adjustment of the available geometric, orthometric and geoid heights, using various parametric surfaces to model and interpret their differences, are offered. These are used to come to some conclusions on the accuracy of the various geoid models used (both global geopotential and local gravimetric models), while an extensive outlook is paid to the questionable behaviour of the orthometric heights. The latter is especially important for the Greek territory since the available benchmarks are delaminated in so-called “map-leaflets” and a common adjustment of the entire vertical network has not been carried out so far. It is concluded that even between neighbouring “map-leaflets” large biases in the adjusted GPS/Levelling and gravimetric geoid heights exist, which indicates distortions in the Greek vertical datum as this is realized by the levelling benchmarks. Given that the latter are commonly used for everyday surveying purposes, conclusions and proposals on the determination of adjusted orthometric heights are finally drawn.

Here we estimate hydrological polar motion excitation functions over land areas regionally from hydrological models and from Gravity and Climate Recovery Experiment (GRACE) gravity fields. The models include equivalent water heights fields determined from groundwater, soil moisture and snow estimates on continents. In this regard, we consider land data from the Climate Prediction Center (CPC) hydrological model and from the surface modelling system Global Land Data Assimilation System (GLDAS), both of which produce monthly estimates. Also we used satellite -gravimetry data, in the form of the GRACE RL04 equivalent water heights from Center for Space Research. The mass effects of the ocean and atmosphere and postglacial rebound are being removed, so in this way hydrological excitation of polar motion can be estimated from the gravimetric data. The monthly step of the data restricts our analysis to seasonal signals only. Large hydrological variability in equivalent water thickness occurs in the lower latitude Southeast Asia, South Asia, and the South American Amazon regions, and remain important in polar excitation even after multiplication by polar motion transfer functions, with the exception of the band very close to the equator. Differences among models and GRACE related values are still considerable, and need to be reconciled to form the best estimates of hydrological variability. Additionally, variations from the atmosphere are determined over land areas from NCEP/NCAR reanalyses; they are noted to be strongly dependent on variability over the high topography regions of Eurasia and North America.

The 14-month Chandler wobble is a free motion of the pole excited by geophysical processes. Several recent studies demonstrated that the combination of atmospheric and oceanic excitations contains enough power at the Chandler frequency and is significantly coherent with the observed free wobble. This paper is an extension of earlier studies by Brzeziński and Nastula (Adv Space Res 30:195–200, 2002), Brzeziński et al. (Oceanic excitation of the Chandler wobble using a 50-year time series of ocean angular momentum. In: Ádám J, Schwarz K-P (eds) Vistas for geodesy in the new millennium. IAG Symposia, vol 125. Springer, Berlin, pp 434–439, 2002) using the same method of analysis but other available estimates of atmospheric and oceanic excitation of polar motion. We also try to assess the role of land hydrology in the excitation balance by taking into account the hydrological angular momentum estimates. Our results generally confirm earlier conclusions concerning the atmospheric and oceanic excitation. Adding the hydrological excitation is found to increase slightly the Chandler wobble excitation power, while the improvement of coherence depends on the geophysical models under consideration.

It is presently believed that the liquid core motions that lead to variations in the geomagnetic field and in the Earth’s rotation rate in scales at and above the bi-decadal originate internally. Although, the length of the day (LOD) variations bears some relationship with solar activity and, therefore, either solar activity is exciting some modes of oscillations in the Earth, or these modes have the same external origin in the two bodies. We have introduced a suitable wavelet base function that allows for splitting the modulation in the Hale solar cycle in the Gleissberg cycle and two quasi-harmonic oscillations. They have periodicities in the lower Gleissberg band, 40–60 years and in the Hale, 20–30 years, bands and are baptized semi-secular (SS), and bi-decadal (BD) oscillations, respectively. Here we find that these two modes of oscillations are also visible in LOD variations. But while the bi-decadal modes in sunspot number (R) and in LOD are synchronic and follow each other linearly, the SS modes are non-linearly related, with a time lag in LOD, of 94 years. We compare the SS mode of oscillations in LOD with oscillations in the angular velocity of precession of the solar orbit in the inertial reference frame (Daxym). The lengths of Daxym and LOD SS oscillations vary slightly with their amplitudes, but the relationship between them is always exactly 3/4. The 178.7 year cycle in the modulations of Daxym oscillations is also followed by the SS oscillation in LOD. The wavelet components that correspond to the semi-secular oscillation are in the upper band of the modes of torsional oscillations in the liquid core as inferred from geomagnetic variations. The large time lag of LOD semi-secular oscillation with respect to the exciting force indicates that the torsional oscillations originate deep inside the core. This is consistent with the fact that torsional oscillations have been found to originate near the surface of a cylinder that is tangent to the equator of the inner core. In view to the above findings we discuss a mechanism by which torsional oscillations in the liquid core might be externally excited but internally powered.

The Earth orientation parameters (EOP) are determined by space geodetic techniques with very high accuracy corresponding to a few millimeters on the Earth’s surface. However, the accuracy of their prediction, even for a few days in the future, is several times lower and still unsatisfactory for certain users. Wavelet decomposition of the EOP data and prediction of their different frequency components reveals that the increase of

x

,

y

pole coordinate and UT1-UTC data prediction errors up to about 100 days in the future are mostly caused by irregular short period oscillations with periods less than half a year. These irregular short period variations in

x

,

y

pole coordinates data are mostly excited by the equatorial components of atmospheric and ocean excitation functions while in UT1-UTC data are excited mostly by axial component of atmospheric excitation function. The main problem of each prediction technique is to predict simultaneously long and short period oscillations of the EOP data. The nature of short period oscillations in EOP data is mostly stochastic and longer period seasonal oscillations can be modeled using deterministic method. It has been shown that the combination of the prediction methods which are different for deterministic and stochastic part of the EOP can provide the best accuracy of prediction. Several prediction techniques, involving the least-squares extrapolation for prediction of the deterministic part and autoregressive method to predict short period stochastic part are good candidates for the prediction algorithms of the EOP data. The main problem of each prediction technique is to predict simultaneously long and short period oscillations of the EOP data and this problem can be solved by the combination of wavelet transform decomposition with the autocovariance prediction method.

It was just July 20, 1969 when the first retro-reflector for Lunar Laser Ranging (LLR) was deployed on the Moon by the Apollo 11 crew. From this day on, LLR is carried out to measure the distance between Earth and Moon. The complete set of observations is analysed and various parameters of the Earth–Moon system are determined by least-squares adjustment. Because of the long time span of data, long-term lunisolar nutation coefficients of the 18.6-year period (and the precession rate) can be determined well. But also other periods (182.62-day, 9.3-year, 365.26-day) can be fitted. The nutation coefficients were determined from LLR based on the models for precession and nutation according to the IAU Resolution 2006 and compared to the MHB2000 model of Mathews et al. (2002). In this paper, the corresponding preliminary results are discussed.

Traditionally, deglaciation-induced polar wander changes are modelled using a saw-tooth-shaped function for the time-history of ice sheets and spherical caps to express their spatial extent. In this contribution we present a set of analytical formulae that allow for a more realistic temporal evolution as well as spatial distribution of current ice masses and the corresponding sea level change when partly or completely melted. Starting with the linearized Liouville equations we develop closed-form time-domain solutions via the Laplace-domain, which are based on the assumption of a piecewise linear time-history of the perturbation of the inertia, which do not require the solution of convolution integrals. As being a central aspect of polar wander modelling we also revisit perturbation of the moment of inertia changes due to arbitrary surface loading due to changes in ice and ocean water masses and compare them with the result of the more simplistic models of spherical ice caps and a uniform sea level change. Finally, the correctness of the developed formulae is checked by various numerical checks based on more simplistic models and numerical integration techniques.

The time variable gravity field of the Earth is determined by GRACE and SLR. Different gravity field solutions reveal some discrepancies in the low degree coefficients, especially

C

20

. The second degree gravity field coefficients are directly related to the Earth’s unknown tensor of inertia as well as the mass terms of the excitation functions, which describe the effects of atmosphere and ocean on Earth rotation. A further relationship exists between the Earth orientation parameters (polar motion and length of day), the motion terms of the excitation functions and the tensor of inertia. Up to now these interdependencies are not used for the calculation of the gravity field coefficients. They can therefore be used to validate the various parameter groups mutually. More reliable second degree gravity field coefficients can possibly be obtained if the Earth orientation parameters and the excitation functions are taken into account. This paper presents a novel method to integrate Earth orientation parameters, excitation functions and gravity field coefficients in a least-squares adjustment model with additional condition equations. This leads to consistent time series.

This paper provides a review on statistical properties of sea level fluctuations, both in global and regional scales. Accurate information on up-to-date dynamics of sea level variability can be obtained from satellite altimetry, in particular from TOPEX/Poseidon and Jason-1 missions. A global-scale analysis is based on a single time series, however a regional-scale investigation employs multiple data sets corresponding to dissimilar geographic locations. The statistical characteristics of long-, medium-, and short-term components of sea level fluctuations computed from TOPEX/Poseidon and Jason-1 altimetric measurements are discussed. The new finding of this paper is that a few statistical measures of sea level variability in central equatorial Pacific reveal similar spatial patterns.

Understanding present-day global sea level rise requires a correct evaluation of past sea level field variability. We use sea level height fields obtained by satellite altimeters between 1992 and 2006, sea level height fields from recent reanalyses of oceanic circulation (SODA) and worldwide tide gauges series for the time interval 1958–2006, to investigate the limitations inherent in reconstructing the past ~50 years of sea level variation using empirical orthogonal function (EOF) decomposition. To understand some of the weaknesses we found, we tested the influence of the spatial distribution of tide gauges as well as the ability to properly reconstruct sea level in certain frequencies bands. The presence of the particularly strong 1997–1998 El Niño event, and the short time span of the base period (1992–2006), limits the determination of other spatial teleconnections and then the reconstruction over preceding epochs. More particularly, during the pre-satellite era and outside the tropics, the non-stationary characteristics of heat transport at interannual time scales and other low frequencies oscillations associated with sea level height fields undermine the methodology.

Relative mean sea level (MSL) trends for nine tide gauges in the Adriatic have been determined with high precision using common inter-annual sea level variability.

Annual MSL values are free from seasonal changes and short-periodic tidal effects. Moreover, one can assume that inter-annual sea level changes, driven by climate variations and long-periodic tidal effects, are very similar for close sites, especially in enclosed seas such as the Adriatic. Accordingly, common inter-annual variation of sea level can be determined for the tide gauges in question from annual means, under assumption that residual variations at each site are close to random.

Through common adjustment of nine tide gauge time series of annual means from PSMSL common inter-annual variability as well as relative MSL trends and MSL for each tide gauge have been determined. For 50-year period relative trends have been determined with standard deviations from 0.1 to 0.3 mm/year (later refers to tide gauges with shorter records). Values of common inter-annual variability are determined with standard deviations of less than 4 mm.

The quantification of the long-term variability of relative sea-level is a fundamental problem in geodesy. In the present study, quantile regression is applied for characterising the long-term variability in relative sea-level at the Gedser and Hornbæk tide gauges, in the North Sea–Baltic Sea transition zone. Quantile regression allows to quantify not only the rate of change in mean sea-level but also in extreme heights, providing a more complete description of long-term variability. At Gedser the lowest relative heights are increasing at a rate approximately 40% higher than the mean rate, while at Hornbæk the relative sea-level slopes are stable across most of the quantiles. A 30-year running window analysis shows that the linear trends display considerable decadal variability over the twentieth century for both stations.

Ocean Tide Loading displacements in the West of France are among the largest in the world. In order to contribute to the improvement of tidal models for GPS processing, we estimate ocean tides in this area with static GPS. Observations recorded over at least 1.5 years are used from ~60 stations with typical separation distances of 50–80 km. Previous studies showed the consistency of the FES2004 model of OTL displacements with GPS estimates of the main semi-diurnal tides in the North of Brittany. We extend this study over a larger spatial scale and investigate the ten main tides. The largest differences between GPS estimates and modeled values are obtained for the M2, K1, and K2 tides. We attribute the discrepancies of K1 and K2 tides to multipath effects. Preliminary results about the impact of using current annual empirical tropospheric models instead of 6 h-period data derived from ECMWF data and provided by TU Vienna are presented.

As a joint project, the Instituto Antártico Argentino (IAA) and TU Dresden (TUD) carried out gravimetric time series recordings at the Argentine Antarctic stations Belgrano II and San Martín. At both stations gravimetric data were recorded for about 1 year, using LaCoste&Romberg gravity meters. At Belgrano II the observations were carried out from February to November 2007, and at San Martín from February 2008 to January 2009. The set-up of the gravimetric stations and the instrumentation utilized are shown. We discuss and compare the data gained at the two stations as well as the analyses in order to solve for the tidal constituents. Generally, tidal gravimetry has the potential to provide independent data to validate and to improve ocean tide models at the Antarctic seas, especially since in-situ data to be used for the establishment of the models are sparse and satellite altimetry has limitations in high latitudes and over ice-covered regions. We discuss the feasibility of the obtained data to pursue this goal of an improvement of ocean tide models. Finally, an outlook for further investigations is given.

In a warming climate, it is critical to accurately estimate ice-sheet mass balance to quantify its contribution to present-day sea-level rise. In this study temporal mass variations in Antarctica are investigated based on monthly GRACE gravity solutions. In order to diminish the effect of large uncertainties in glacial isostatic adjustment (GIA) models, an approach is developed to estimate the acceleration of the ice-sheet mass, assuming the presence of accelerated melt signal in the GRACE data. Though the estimate of accelerated melt does not provide an absolute value for the volume of the melting ice, it is a viable tool for characterizing the present-day ice-sheet mass balance.

After 7 years in orbit, the GRACE satellite mission now facilitates the detection of smaller secular trends of mass variations as well as long-periodic signals. In this study, we focus on changes of the permafrost regime in Siberia, Russia, using GRACE monthly solutions from the three main analysis centres GFZ, CSR and JPL. The results show that observed positive trends of mass changes are related to large Siberian rivers such as Ob, Lena and Yenisei. Two major trends of about 0.7 μGal/a can be clearly identified. The first concerns the upper Ob River. It includes, depending on the specific GRACE solution centre, the Angara River drainage basin, which is part of the Yenisei River system. The second trend is centred on the upper Lena River north-east of Lake Baikal and is also clearly determined, but with different solution-dependent values. All these significant trends seem to be caused by long-term hydrological changes, especially since no other reasonable geophysical explanation is found yet. Similar features can be found in the trend of the GLDAS hydrology model. Removing the hydrological contribution positive mass changes of about 0.8 μGal/a appear in the Central Siberian Plateau and the Kolyma River drainage basin, which may be related to changes in permafrost. However, further investigations are needed to really understand such mass changes and attribute them to the related physical processes.

The objective of the present study is to analyze seasonal variability of land water storage in South America from GRACE data. High precision estimate of temporal variations in the Earth’s gravity are obtained using monthly Release-04 (RL04) gravity field coefficients provided by the Center for Space Research (CSR) of the University of Texas at Austin. Water mass anomalies, as equivalent height of water, are calculated based on the direct relationship between gravity and mass. To remove the effects of the noise observed in the equivalent-water thickness solutions at high harmonic degrees, an optimized smoothing technique is applied. Finally, temporal distributions of land water storage are compared to monthly mean precipitation data extracted from in-situ rain gauge records in order to identify, correlate and understand patterns of water movement at continental scale in South America.

Aquatic environments perform important functions in nature such as the control of climate, floods and nutrients, and they provide goods and services for humanity. To monitor these environments at large spatial scales, the satellite gravity mission GRACE provides time-variable gravity field models that reflect the Earth’s gravity field variations due to mass transport processes like continental water storage variations.

The La Plata Basin is the second largest one in South America and it is a sample of the abundance, variety and quality of natural resources and the possibilities offered in connection with the production of goods and services.

In this work the GRACE capability to monitor the water storage over La Plata Basin will be analyzed, using the solutions provided by the four different GRACE processing centers: CSR, GFZ, JPL and BGI. Afterward the calculated hydrological signal will be used to estimate four mass change models over this hydrographic system’s area using a generalized inversion method on the gravity trends. Also, preliminary results from ENVISAT altimetry data are presented and compared with GRACE solutions.

All the solutions detected the significant mass changes of the area, thought there are some discrepancies between the four GRACE processing centers.

The Global Positioning System (GPS) transmits signals in two frequencies. It allows the correction of the first order ionospheric effect by using the ionosphere free combination. However, the second and third order ionospheric effects, which combined may cause errors of the order of centimeters in the GPS measurements, still remain. In this paper the second and third order ionospheric effects, which were taken into account in the GPS data processing in the Brazilian region, were investigated. The corrected and not corrected GPS data from these effects were processed in the relative and precise point positioning (PPP) approaches, respectively, using Bernese V5.0 software and the PPP software (GPSPPP) from NRCAN (Natural Resources Canada). The second and third order corrections were applied in the GPS data using an in-house software that is capable of reading a RINEX file and applying the corrections to the GPS observables, creating a corrected RINEX file. For the relative processing case, a Brazilian network with long baselines was processed in a daily solution considering a period of approximately one year. For the PPP case, the processing was accomplished using data collected by the IGS FORT station considering the period from 2001 to 2006 and a seasonal analysis was carried out, showing a semi-annual and an annual variation in the vertical component. In addition, a geographical variation analysis in the PPP for the Brazilian region has confirmed that the equatorial regions are more affected by the second and third order ionospheric effects than other regions.

Since the past decade, geodetic techniques are widely used to gain important information for the monitoring and modeling of the deformation of the Earth at different length and time scales. Although the GNSS derived estimates of the Earth crust velocity are becoming more and more reliable, advanced data analysis techniques are needed to recognize geophysical features in the GNSS time-series, e.g., non linear behaviors, discontinuities in the signal and in its derivative, i.e., in the velocity. Unfortunately these phenomena are often hidden in the time-series noise and external information, as seismic events, are not always known. The main focus of this work is the detection of signal discontinuities in GNSS time-series through the use of advanced analysis techniques: the wavelets, the Bayesian and the variational methods. The Mumford and Shah (Commun Pure Appl Math 42:577–685, 1989) and the Blake and Zisserman (Visual reconstruction, 1987) variational models for signal segmentation can detect signal discontinuities in an explicitly way. The Blake and Zisserman (Visual reconstruction, 1987) model can also detect discontinuities of the signal first derivative, i.e., velocity abrupt changes can be detected. At first, to prove and assess the capability to detect discontinuities correctly, the methods have been applied to some Cascadia (North America) time-series, characterized by well known aseismic deformations. A second test area has been taken into account: the Calabrian Arc subduction zone, in southern Italy. The analyzed Italian GNSS time-series are characterized by very weak and noisy signals and the geodynamic of the area is mostly unknown. When present, discontinuities are expected to be very small and compatible with the signal noise. This motivates the use of advanced data analysis techniques to investigate the presence of discontinuities. At the moment, the analysis of the Italian time-series has revealed several discontinuities which nature cannot be labeled easily as geophysical or geodetic.

A network adjustment analysis was derived for a GPS network called TAMDEF (Trans Antarctic Mountains Deformation), located in Victoria Land, Antarctica. The network adjustment strategy involved the careful selection and application of the appropriate approach to process the TAMDEF network. Therefore, for the first part of the presented study, four cases denoted as Cases I–IV were investigated for the TAMDEF network processing with respect to the IGS (International GNSS Service) sites inside and outside the Antarctic continent. Here, the GPS data processing relied on the PAGES (Program for Adjustment of GPS Ephemerides) software, which was set up to run using the Least-Squares adjustment with Stochastic Constraints (SCLESS). The second part of the study focus in considering alternative network adjustment approaches: the Minimum-Norm LESS adjustment (MINOLESS); the Partial Minimum-Norm LESS (Partial-MINOLESS) and the Best LInear Minimum Partial-Bias Estimation (BLIMPBE) to validate results from the SCLESS approach (Case I) for IGS sites inside the Antarctica. Based on the applied network adjustment approaches within the Antarctic tectonic plate, it can be demonstrated that the GPS data used is clean of bias after properly taken care of ionosphere, troposphere and some other sources that affect GPS positioning.

To quantify the present-day tectonic deformation in the Pyrenees mountain range area where the seismic activity is continuous and moderate, different GPS ResPyr campaigns were performed between 1995 and 2008. Considering the expected rate of deformation of about 1 mm/yr, we can wonder what would be the impact of the different loading effects on velocity field computed from GPS campaigns and therefore on the characterization of the deformation.

The data are processed using the GINS software package and we estimated the effect of the loading phenomena on the velocity field resulting from the different campaigns. The final solution uncertainties are of the same order of the expected displacements and we demonstrated the non negligible impact of the various loading phenomena on the velocity field. Indeed, the accumulated loading effect (except tidal ocean load) can reach 0.8 mm/yr on horizontal velocity estimates, which is at the level of the searched signal.

Coordinates solutions are compared between the absolute and the relative phase center variation (PCV) models using the dense regional GPS network data in Japan before 1400 GPS week. In the result for the regional network sites and the western Pacific IGS fiducial network sites during 2005 and 2006 (GPS weeks 1303 through 1399) the coordinates repeatabilities applying the absolute PCV models are better than those adopting the relative PCVs, although the advantages are not significant for the period between 1996 and 1999 (GPS weeks 869 through 1042). The former result indicates the solutions applying the absolute PCV models are more precise than those adopting the relative PCVs even for the weeks when IGS precise orbits are calculated using the relative PCV models. The latter result may be caused by the sparse distribution of the IGS fiducial sites in the region, and the impreciseness of IGS precise orbits caused by the immature regional reference frame.

Station velocities derived from space geodetic measurements in Central and South America were processed by the finite element method using a geophysical model and by a least squares collocation approach with empirical correlation functions for computing a continuous velocity field of the South American and the Caribbean crust. Velocities of the reference frame for the Americas (SIRGAS), and of various geodynamic networks (CASA, SNAPP, CAP, SAGA, and seismic gap projects) are used as input data. In general, the results present good agreement with previous models. Moreover, there are significant improvements, particularly in areas with new data (northern and central Andes, southern Tierra del Fuego).

In this study we present results from a recent re-processing effort that included data from more than 120 continuous Global Positioning System (CGPS) stations in the British Isles for the period from 1997 to 2008. Not only was the CGPS network dramatically densified from previous investigations by the authors, it now also includes, for the first time, stations in Northern Ireland, providing new constraints on glacio-isostatic processes active in the region. In our processing strategy we apply a combination of re-analysed satellite orbit and Earth rotation products together with updated models for absolute satellite and receiver antenna phase centers, and for the computation of atmospheric delays. Our reference frame implementation uses a semi-global network of 37 stations, to align our daily position estimates, using a minimal constraints approach, to ITRF2005. This network uses a combination of current IGS reference frame stations plus additional IGS stations in order to provide similar network geometries throughout the complete time span. The derived horizontal and vertical station velocities are used to investigate present-day crustal/land motions in the British Isles. This first solution provides the basis for our contribution to the Working Group on Regional Dense Velocity Fields, 2007–2011 of the International Association of Geodesy Subcommission 1.3 on Regional Reference Frames.

The Upper Rhine Graben (URG) is a north-northeast trending rift system belonging to the European Cenozoic Rift System. Today, the southern part of the URG is seismically still active. Earthquakes of magnitude five have a recurrence time of approximately a few decades. In order to monitor and to determine recent crustal displacements in the URG area, the transnational cooperation GURN (

G

NSS

U

pper

R

hine Graben

N

etwork) was established in September 2008. Within GURN geo-scientific research is carried out. The focus is on processing and analysing of observation data of continuously operating GNSS (Global Navigation Satellite Systems, e.g. GPS) sites.

The paper describes the determination of horizontal and vertical movements of the Adriatic microplate on the basis of GPS measurements carried out in the period between 1994 and 2005 within the frame of the 21 measuring campaigns organized at the research territory. The role of geodetic measurement methods particularly GPS method is essential in applications that requires high accuracy and precision as in the velocity field estimation of tectonic plates. The processing of GPS data as well as computation of the coordinates of points and their velocities was performed by Bernese GPS Software Ver. 5.0 based on 140 daily solutions. The mean standard deviations of estimated coordinates from repeatability of daily solutions and combined solution are

σ

ϕ

=

2.0 mm,

σ

λ

= 2.2 mm and

σ

h

= 5.6 mm. In purpose to determine and present the trend of height component the comparison of the data obtained by monitoring the change of sea level and the results of GPS measurement data was investigated. On the basis of the computed relative velocities of points as related to the Euro-Asian plate, the parameters of Euler rotation vector and Euler pole of the Adriatic microplate have been calculated and compared with other solutions. Also, the kinematic research area model has been determined on the basis of the combined solution results and compared with global kinematic models NNR-NUVEL-1A and APKIM2000.

The Federal Office of Topography swisstopo is responsible for the maintenance of the coordinate reference frames in Switzerland. Beside the static reference frames, used for national surveying, the development of a kinematic model, mainly used for scientific investigations, is under development since many years. For the determination of vertical movements the analysis of more than 100 years of levelling observations showed a significant alpine uplift of maximally 1.5 mm/year relative to an arbitrarily chosen bench mark in Aarburg (at the south of the Jura mountains). For the determination of horizontal movements the various GPS-campaigns, measured since 1988, are the basis. With the Automated GNSS Network of Switzerland (AGNES), which operates permanently since 1998, valuable information can be extracted for 30 sites. The paper shows that the time series of AGNES nowadays allow statements concerning possible vertical movements. The potential of additional information sources, such as local tie surveys, are discussed. Comparisons of the results of the two independent measuring techniques GNSS and levelling are the main topic of the paper.

The NZGD2000 is the official 3-D semi-dynamic geodetic datum for New Zealand that incorporates a deformation model to correct the horizontal coordinates and survey observations for the effect of regional-scale tectonic movements of the Earth’s crust. These horizontal tectonic deformations are up to a few centimetres per year. Except for the Southern Alps (central South Island) and the Taupo volcanic zone (North Island), the currently available information indicates that the vertical tectonic deformations are an order of magnitude smaller than the horizontal components. In this study we compile a preliminary map of vertical deformations in New Zealand using the GPS time series. The least-squares linear regression analysis is used to estimate the vertical velocities at GPS sites. After applying outlier detection, the vertical deformations are investigated with respect to the tectonic setup of New Zealand. The results reveal that the uplift of the Southern Alps at the currently established GPS sites reaches 6 mm/year. The largest regional-scale tectonic subsidence, at approximately 9 mm/year, is detected in the lower and central part of the North Island. The estimated vertical tectonic deformations are compared with evidence from geochronological data and results of previous studies.

Unambiguous, consistent and homogeneous GPS station coordinates are the fundamental requirement in the appropriate determination of geodetic velocities that are often used for the derivation of geodetic and geophysical models for a variety of applications [Segall and Davis, Ann Rev Earth Planet Sci 23:201–336, 1997]. Because of this, there have been significant efforts to improve the modeling and parameterization of global GPS solutions in order to get stable and homogeneous positions and velocities. This paper presents a study aiming at detecting least-squares spectral peaks present at the best available (at the time) IGS weekly vertical component time series of five permanent stations in Canada. These peaks are the result of short and long term effects of mismodelled and unmodelled geophysical phenomena on the height. The LSSA approach is used. Results show strong periodic constituents in the LSSA spectrum below or at the 1 year window but most notably constituents with periods longer than a year.

GNSS, InSAR and LIDAR are identified as important techniques when it comes to monitoring and remote sensing of our planet Earth and its atmosphere. In fact, these techniques can be considered as key elements of the Global Geodetic Observing System. Examples of applications are: environmental monitoring; volcano monitoring, land slides, tectonic motion, deforming structures, atmosphere modeling, and ocean remote sensing. Hence, it concerns applications at local and regional scales, as well as at global scales. The main issues can be summarized as: need for a better understanding of processes, leading to better models; need for observational material; and adequate modeling techniques.

Rapid developments in engineering, microelectronics and the computer sciences have greatly changed both instrumentation and methodology in

engineering geodesy

. To build higher and longer, on the other hand, have been key challenges for engineers and scientists since ancient times. Now, and for the foreseeable future, engineers confront the limits of size, not merely to set records, but to meet the real needs of society minimizing negative environmental impact. Highly developed engineering geodesy techniques are needed to meet these challenges. The SC will therefore endevour to coordinate research and other activities that address the broad areas of the theory and applications of engineering geodesy tools. The tools range from conventional terrestrial measurement and alignment technology (optical, RF, etc.), Global Navigation Satellite Systems (GNSS), geotechnical instrumentation, to software systems such as GIS, decision support systems, etc. The applications range from construction engineering and structural monitoring, to natural phenomena such as landslides and ground subsidence that have a local effect on structures and community infrastructure. The SC will carry out its work in close cooperation with other IAG Entities, as well as via linkages with relevant scientific and professional organizations such as ISPRS, FIG, IEEE, ION.

The major objectives of the SC are:

To monitor research and development into new technologies that are applicable to the general field of “engineering geodesy”, including hardware, software and analysis techniques.

To study advances in dynamic monitoring and data evaluation systems for buildings and other manmade structures.

To study advances in monitoring and alert systems for local geodynamic processes, such as landslides, ground subsidence, etc.

To study advances in geodetic methods used on large construction sites.

To study advances in the application of artificial intelligence techniques in engineering geodesy.

To document the body of knowledge in this field, and to present this knowledge in a consistent frame work at symposia and workshops.

To promote research into several new technology areas or applications through the SC 4.2 Working Groups.

The achievements of the work of the SC in the past 2 years will be presented and discussed in this paper.

In this paper, “fixed-

σ

” refers to a stochastic process that has a constant standard deviation. “Digital representation” refers to a discrete representation of a stochastic process. A good example of a digital representation of a stochastic process field is the earth’s surface, with elevation as the random scalar, commonly referred to as a digital terrain model (DTM). It is widely know that the roughness of terrain is a factor that inhibits DTM accuracy. This implies that accuracy of DTM varies from pixel to pixel; it is not fixed across the landscape because it varies according to the terrain’s vertical variations. Such a nonfixed

-σ

DTM is not a proper source of topographic data. However, its regular character (pixels are of equal size) is required as a prerequisite for procedures involved in the DTM data acquisition, processing and dissemination. The data acquisition methods may include InSAR and LiDAR technology, and raster techniques for producing a picture on a screen. In this paper, we discuss the possibility of modelling any type of terrain using a DTM which would be characterised by a limiting or fixed standard deviation. A starting point for these considerations is a recently published result of investigations of estimates of the target-induced error of the Shuttle Radar Topography Mission (SRTM) dataset. This target induced-error model connects the standard deviation of the disparities (DTM versus reference data), pixel size and slope of the terrain in an original and straightforward framework. An obvious consequence of such a fixed-

σ

DTM is the variable pixel size. This paper formulates a number of questions regarding the feasibility for such a DTM and potential advantages or disadvantages. For example, it appears that such a pixel-variable but fixed-

σ

arrangement of a DTM would better serve many of its purposes and provide opportunities to increase the efficiency of digital image storing and processing. The discussion includes a potential and required change in the data acquisition strategy and feasibility from systematic sampling to an adaptive sampling of the earth’s surface. A new set of algorithms for such a DTM is required to calculate DTM-derived parameters, including aspect and slope. The proposed fixed-

σ

digital representation of a random scalar field is not restricted in any way to only DTMs. It can be used in many other fields that use digital imagery.

Nowadays, L1 SBAS signals can be used in a combined GPS+SBAS data processing. However, such situation restricts the studies over short baselines. Besides of increasing the satellite availability, SBAS satellites orbit configuration is different from that of GPS. In order to analyze how these characteristics can impact GPS positioning in the southeast area of Brazil, experiments involving GPS-only and combined GPS+SBAS data were performed. Solutions using single point and relative positioning were computed to show the impact over satellite geometry, positioning accuracy and short baseline ambiguity resolution. Results showed that the inclusion of SBAS satellites can improve the accuracy of positioning. Nevertheless, the bad quality of the data broadcasted by these satellites limits their usage.

The precise and accurate determination as well as the usage of individual calibration values of GNSS (Global Navigation Satellite Systems) antennas are of fundamental importance for state-of-the-art GNSS positioning at millimeter accuracy level, especially concerning the precise determination of the height component. Calibration values can be determined in various ways (relative vs. absolute, chamber vs. field). Within the transnational research project “PROBRAL: Precise positioning and height determination by means of GPS – Modeling of errors and transformation into physical heights”, the first relative antenna calibration field of Latin America was established.

One main goal of this cooperation was to establish a relative receiving antenna calibration field for GNSS instrumentations on the roof top of the “Astronomical Laboratory Camil Gemael” called BCAL/UFPR (

http://www.lage.ufpr.br/

), situated on the Polytechnic Campus of the Federal University of Paraná in Curitiba (Brazil).

The status of the calibration field as well as recent results are going to be presented within this paper, e.g. a TRM22020.00+GP antenna was calibrated in three sessions of 24 h, with a data sampling rate of 15 s. The software WaSoft/Kalib was used to process the GPS phase observations. Carrier phase center offset values and carrier phase center variation values were determined relatively with respect to a Leica Choke Ring antenna.

The goal of Network RTK is to provide users with precise ionospheric corrections in order to conduct fast GPS ambiguity resolution and to get cm-level positioning results over medium-distance baselines. In this paper it is shown that a Network RTK user should apply the ratio test with fixed failure rate, having a threshold value that depends on the model at hand, as to test whether the estimated integer solution can be accepted with sufficient more likelihood than the second-best integer solution. Application of the traditional ratio test (with a fixed threshold value) may namely result in too many wrong fixes and consequently severe positioning errors. However, in the paper it is also demonstrated that the ratio test with fixed failure rate should be applied with care, since its correct performance depends on the correctness of the underlying model.

SIRGAS is responsible of the terrestrial reference frame of Latin America and the Caribbean. To fulfil this commitment it manages a continuously operational GNSS network with more than 200 receivers. Although that network was not planed for ionospheric studies, SIRGAS attempted to exploit it by establishing, in early 2008, a regular service for computing regional maps of the vertical Total Electron Content. This paper describes an effort for developing a new SIRGAS product, concretely, a 4-dimensional (space and time) representation of the free electron distribution in the ionosphere. The working methodology is based on the ingestion of dual-frequency GNSS observations into a global electron density model in order to update its parameters. Preliminary results are presented and their quality is assessed by comparing the electron density computed with the methodology here described and the one estimated from totally independent observations. A preliminary analysis reveals that the performance of the electron density model improves by a factor greater than 2 after data ingestion.

It is well know that GNSS permanent networks for real-time positioning with stations spaced at few tens of kilometers in the average were mainly designed to generate and transmit products for RTK (or Network-RTK) positioning. In this context, RTK products are restricted to users equipped with geodetic-class receivers which are continuously linked to the network processing center through Internet plus mobile phone. This work is a first step toward using a local network of permanent GNSS stations to generate and make available products devoted to ionospheric delay correction that could remarkably improve positioning accuracy for C/A receiver users, without forcing them to keep a continuous link with the network. A simple experiment was carried out based on data from the RESNAP-GPS network (

w3.uniroma1.it/resnap-gps

), located in the Lazio Region (Central Italy) and managed by DITS-Area di Geodesia e Geomatica, University of Rome “Sapienza”. C/A raw observations were processed with Bernese 5.0 CODSPP module (single point positioning based on code measurements) using IGS precise ephemeris and clocks. Further, the RINEX files were corrected for the Differential Code Biases (DCBs) according to IGS recommendations. One position per epoch (every 30 s) was estimated from C/A code; the vertical coordinate errors showed a typical signature due to the ionospheric activity: higher errors for day-time (up to 5 m) and smaller ones for night-time (around 1.5 m). In order to improve the accuracy of the solution, ionospheric corrections were estimated using the La Plata Ionospheric Model, based on the dual-frequency observations from the RESNAP-GPS network. This procedure allowed to reduce horizontal and vertical errors within 0.5 m (CE95) and 1 m (LE95) respectively. Finally, the possibility to predict the ionospheric model for few hours was preliminary checked. Our approach shows the possibility of a novel use of the measurements collected by GNSS permanent networks designed for real-time positioning services, which can assist and remarkably improve the C/A code real-time positioning supplying off-line predicted ionospheric corrections, acting as a local Ground Based Augmentation System.

During the first decades of ionospheric research, the physical description of the ionospheric free electron vertical density was mainly given by the Chapman theory in which the main driving parameters were the solar irradiance level and the solar zenith distance from the observation point. Any new observed phenomenon that could not be explained by the Chapman theory was considered an ‘anomaly’. After more than 50 years of continuous aeronomic research, many of these phenomena then called ‘anomalies’ were physically explained but some of them are still open to discussions, like the so-called Semi-annual Anomaly that produces global mean TEC values larger for equinoxes than for solstices; and the Annual Asymmetry that causes larger mean global TEC during the December than the June solstice (far larger than the 7% that would be expected from the change on the Sun–Earth relative distance). Using the high-precision TEC 13-year data series provided by the TOPEX/Poseidon mission, the main finding of this work is the characterization of the annual variation of the ionospheric daily mean TEC that reflects the combined effects of the both mentioned anomalies. The analysis of this annual pattern allows a precise quantification of the level of the effects of both anomalies, and suggests that the semi-annual anomaly does not have a half-year period, instead might be considered as another annual anomaly with two maxima separated by 220 days.

The remote sensing problem of poly-dispersed aerosols in the single scattering approximation is a classical example of the first kind Fredholm integral equation. Assuming that the prediction errors due to arbitrarily small perturbations in the complex aerosol refractive index or the upper radius bounds are negligible, one can form the signal-to-noise ratio (SNR) of the kernel matrix in terms of the singular value of the kernel matrix and the number of measurement wavelengths. The smoothness of the kernel matrix and the information potentialities vary, depending on the choice of a combination of sounding channels. The optimal choice is the one that provides the largest SNR. A numerical simulation with 11 samples of possible combinations is conducted in order to demonstrate that the prediction of aerosol extinction measurements using singular value decomposition is comparable with reference values. If two similar prediction results (e.g. one with SNR 2.019 and the other 2.132) are obtained, the higher value is apparently better, however, a drawback in this case is that the prediction errors increase with the increasing number of sounding channels used. In conclusion, it is noted that the information on the smoothness and potentialities of the kernel matrix has to be factorized in order to increase the success rate of the prediction. Fortran source code is available by its authors upon request.

We have been developing a state-of-art tool to estimate the atmospheric path delays by ray-tracing through meso-scale analysis (MANAL data) data, which is operationally used for numerical weather prediction by Japan Meteorological Agency (JMA). The tools, which we have named “KAshima RAytracing Tools (KARAT)”, are capable of calculating total slant delays and ray-bending angles considering real atmospheric phenomena. The KARAT can estimate atmospheric slant delays by an analytical 2-D ray-propagation model by Thayer and a 3-D Eikonal solver. The biases of slant delay estimates between the Thayer model and the modern mapping functions, which are ranging from 18 to 90 mm, are considered to be a deficiency of the mapping functions. We compared PPP solutions using KARAT with that using the Global Mapping Function (GMF) and Vienna Mapping Function 1 (VMF1) for GPS sites of the GEONET (GPS Earth Observation Network System) operated by Geographical Survey Institute (GSI). In our comparison 57 stations of GEONET during the year of 2008 were processed. The KARAT solutions are slightly better than the solutions using VMF1 and GMF with linear gradient model for horizontal and height positions. Our results imply that KARAT is a useful tool for an efficient reduction of atmospheric path delays in radio based space geodetic techniques such as GNSS and VLBI.

The tropospheric zenith delay (ZTD) of GPS observations is closely related to the integrated water vapour (IWV) content of the atmosphere. The scale factor between the IWV and the ZWD is a function of the mean temperature of the water vapour, which can be computed by a linear regression equation based on the surface temperature. A similar linear regression can be used to compute the IWV from surface water vapour density. In this paper we show a formula derived from more than 10,000 radiosonde observations in Hungary. Using this relation, it is possible to estimate the IWV content of the atmosphere, which could be scaled down to tropospheric zenith wet delay. Two time intervals are used for the validation of the results. The first one was a stormy summer period, while the other was a dry winter period. The results show that this approach provides slightly better coordinate RMS than the Niell or the Hopfield model. Moreover the coordinate solutions are relatively stable during the summer period as well, when a heavy storm caused unstable weather conditions. Studying the performance of the local regression model, the Hopfield and the Niell (Saastamoinen+Niell mapping function) model it could be seen that the local regression model gave the best a priori tropospheric delays for the processing.

Water vapor measurements from a Raman lidar developed conjointly by the IGN and the LATMOS/CNRS are used for documenting the water vapor heterogeneities and correcting GPS signal propagation delays in clear sky conditions. We use data from four 6 h-observing sessions during the VAPIC experiment (15 May–15 June 2004). The retrieval of zenith wet delays (ZWDs) from our Raman lidar is shown to agree well with radiosonde (0.6 ± 2.5 mm) and microwave radiometers (−6.6 ± 1.2 and 6.0 ± 3.8 mm) retrievals.

ZWDs estimated from GPS data present a good consistency too (−2.0 ± 2.7 mm) but they are still shown to not represent properly the fast evolutions with high frequency variations correlation about 0.12. Part of the errors is also due to multipath and antenna phase center variations. Within this framework, methodologies for integrating of zenith lidar observations into the GPS processing are described. They include also a correction for multipath and antenna phase center variation. The best results are obtained when the lidar ZWDs are used for a priori correcting the GPS phase observations: discrepancies between lidar and GPS estimates are then reduced to −1.1 ± 1.4 mm. It is shown also that mapping function derived from the lidar vertical profiles performs nearly as well as the VMF1 mapping function.

GNSS phase observations are well suited to study atmospheric refraction effects and to contribute to weather prediction. Current research activities focus on real time determination of slant tropospheric wet delays in order to determine the water vapor content. The long periodic variations of these delays are mainly caused by the steady state component of the refractive index field. In contrast, short periodic variations of the slant delays are induced by refractivity fluctuations along the signal’s path from the transmitter to the receiver. Focusing on higher temporal resolution of water vapor variations, this second component will be of special interest.

Based on turbulence theory, Schön and Brunner (J Geodes 82(1): 47–57) developed a formulation of the variances and covariances of GNSS phase observations induced by refractivity fluctuations in the troposphere. In this paper, we will use this model to investigate the generation of slant delay time series based on a spectral decomposition of the simulated turbulence theory-based variance–covariance matrices. Using an exemplary GPS configuration, the impact of the model parameters (as e.g. the refractivity structure constant, the outer scale length, the effective tropospheric height, and the wind direction and magnitude) on the covariance matrix and the generated time series is analysed.

In this paper we investigate the fitting of ray-tracing results to closed-form expressions. We focus on the variation of the delay with elevation angle and azimuth. For the elevation angle-dependence we compare the continued fraction form of Yan and Ping (Astron J 110(2):934–993, 1995) with that of Marini (Radio 11 Sci 7(2):223–231, 1972) (normalized to yield unity at zenith and found negligible differences between the two functional formulations for the hydrostatic case, while for the non-hydrostatic case, the Yan and Ping model performed marginally better. Since the ray-tracing results do not necessarily assume azimuthal symmetry, we have to account for the azimuth-dependence. For that we compare the linear gradient model of Davis et al. (Radio Sci 28(6):1003–1018, 1993) with the inclusion of second order terms (Seko et al., J Meteorol Soc Jpn 82(1B):339–350, 2004) and arbitrary spherical harmonics. These functional forms performed very well for the hydrostatic case, although for the non-hydrostatic case there were some large biases, particularly in the spherical harmonics of order 1, degree 1 and the 2nd order polynomial case.

This paper studies the estimation of integrated water vapour (IWV) from the zenith tropospheric delay (ZTD). In order to evaluate the technique, six mathematical models are compared using a stormy summer period and a calm and dry winter period. The mathematical models include locally derived models using more than 10,000 radiosonde observations. The GPS derived IWV values are compared to radiosonde observations and a linear regression prediction of IWV using surface observations, too. Moreover the computations were carried out during a heavy storm in the summer period, when the estimated IWV distribution is compared to radar observations, too.

The results show that the IWV values derived from GPS observations had an agreement with the radiosonde observations at the level of better than 2–3 mm in term of standard deviations. The results also show that GPS observations provide additional information to the estimation of IWV. Moreover the Hungarian Active GNSS Network was proved to be useful to monitor the water vapour content of the atmosphere during weather fronts as well.

The Global Navigation Satellite System (GNSS) provides a continuous, high precision, global, real-time, and all weather navigation and positioning, which powerfully contributes to all scientific questions related to precise positioning on Earth’s surface. Recently, the reflected and refracted signals from GNSS satellites resulted in many new applications in environmental remote sensing. The GNSS refracted signals from Radio Occultation satellites together with ground GNSS observations have produced wide applications in atmospheric remote sensing, including global monitoring of tropospheric water vapour, temperature and pressure, tropopause parameters and ionospheric parameters as well as ionospheric irregularities. The GNSS reflected signals from the ocean and land surface could determine the wave height, wind speed and wind direction of ocean surface and land surface conditions. In this paper, GNSS remote sensing applications in the atmosphere, oceans, land and hydrology are presented as well as recent results. With more and more GNSS satellite constellations in coming years, it is expected more and wider applications in various environment remote sensing.

Usually mean sea surface (MSS) is calculated by averaging altimetric measurements of sea surface height (SSH) over a given region and over a given time period. However, in the case of the Caspian Sea this represents a certain challenge and existing MSS models are unacceptable.

One of the possible solutions is to analyse the Caspian Sea MSS as task of investigation of space-time variability of equipotential sea surface or SSH without seasonal and synoptic variability. Regional MSS model of the Caspian Sea (GCRAS08 MSS) was calculated according to the following scheme.

For satellite altimetry data processing dry tropospheric corrections was calculated on atmospheric pressure from nearest weather stations located along the Caspian Sea costal line. From the TOPEX/Poseidon (T/P) and Jason-1 (J1) satellite altimetry data, the SSH synoptic and seasonal variations for all passes of each repeat cycle were eliminated. In last phase, the GCRAS08 MSS was constructed as a SSH function of latitude, longitude, and time with correction on climatic dynamic topography. For specified time interval SSH was interpolated on grid by radial basis function method.

For the first time GCRAS08 MSS model allow to investigate space–time variability of the Caspian Sea level. According to the received results spatial variability of rate of the Caspian Sea level change well correlate with EGM96 gravity anomalies field and the greatest variability is observed in the zone of gravity anomalies gradient maximum.

The SIRGAS reference frame is given by more than 200 continuously operating stations (SIRGAS-CON network), which are classified in four sub-networks: a continental one (SIRGAS-CON-C) with about 100 stations homogeneously distributed over Latin America and the Caribbean, and three densification sub-networks (SIRGAS-CON-D) covering the northern part, the middle part, and the southern part of the SIRGAS region. Each sub-network is processed by one of the SIRGAS Processing Centres: DGFI (Germany) is responsible for the SIRGAS-CON-C network, IGAC (Colombia) for the northern densification sub-network, IBGE (Brazil) for the middle one, and CIMA (Argentina) for the southern one. These Processing Centres deliver loosely constrained weekly solutions, which are integrated in a unified solution by the SIRGAS Combination Centres operating at DGFI and IBGE. The DGFI (i.e. IGS RNAAC SIR) weekly combinations are delivered to the IGS Data Centres for the global polyhedron, and are made available for users as official SIRGAS weekly reference frame solution. The IBGE weekly combinations provide control and redundancy. This paper describes the combination strategy applied by DGFI, emphasizing the evaluation of the individual solutions and the quality control of the final weekly combinations. The reliability of the resulting coordinates is estimated by comparing them with those produced by IBGE and the weekly combinations of the IGS global network.

Since the last SIRGAS meeting in May, 2008, IBGE has been playing a role as Processing and Combination Center of SIRGAS-CON network, in order to provide support to the SIRGAS reference frame. The SIRGAS-CON densification network is composed now by 150 continuously operating GNSS permanent stations and this number is increasing continuously. In the same SIRGAS meeting some aspects related to the network coordination were discussed in order to correct several factors that were affecting the quality of solutions, e.g. equipment changes, which may cause a discontinuity in the coordinate time series.

One of the tasks of the IBGE Analysis Center is the combination of weekly solutions computed by each SIRGAS-CON Processing Center and to generate a cumulative solution aligned to the IGS05 reference frame. In this paper four combination strategies were explored using the minimum constraints approach, preserving the original characteristics of the weekly solutions and providing the alignment to the IGS05 reference frame. The procedures adopted for the combination and statistical analysis of results are presented in this paper.

IBGE – The Brazilian Institute of Geography and Statistics became an Analysis Center for the SIRGAS-CON (Geocentric Reference System for the Americas), permanent GNSS network after getting experience as a Pilot Processing Center for 2 years. In the beginning, about 30 stations were processed. With the growing number of GNSS stations on the American continent, there are now about 100 stations being processed every week. Since week 1,495, IBGE officially shares the processing task of SIRGAS-CON network with three more Analysis Centers: Instituto Geográfico Agustín Codazzi – IGAC (Colômbia), Instituto de Geodésia y Geodinâmica de la Universidad Nacional del Cuyo, IGG-CIMA (Argentina) and Deutsches Geodätisches Forschungsinstitut-DGFI (Germany). Each center is responsible for the processing of a group of stations. The purpose of this effort is to contribute to the IGS Regional Network Associate Analysis Center for SIRGAS (IGS RNAAC SIR) solution, with a densified network. We present the current status and efforts of IBGE as an official Processing Center for SIRGAS. The perspective is to increase the number of stations in 2009, with the inclusion of new stations from the Brazilian GNSS Permanent Network, RBMC – Rede Brasileira de Monitoramento Contínuo dos Sistemas GNSS. The processing strategy applied using the Bernese GNSS Software is presented, as well as relevant information for the development of activities. Results are evaluated and compared to the solutions provided by other institutions (DGFI, IGG-CIMA and IGS) and discrepancies are analyzed. Some important issues related to the maintenance of the national permanent GPS networks are shown in the coordinate time series.

Brazil adopted SIRGAS2000 in 2005. This adoption called for the provision of the relationships between SIRGAS2000 and the previous reference frames used for positioning, mapping and GIS, namely, the Córrego Alegre (CA) and the South American Datum of 1969 (SAD 69). Two programs were designed for this purpose. The first one, TCGeo, provided the relationships based on three-translation Similarity Transformation parameters. TCGeo was replaced in December 2008, by ProGriD. ProGriD offers, besides the same similarity transformation as TCGeo, a set of transformations based on modelling the distortions of the networks used in the various realizations of CA and SAD 69. The distortion models are represented by a grid in which each node contains a transformation value in terms of difference in latitude and in longitude. The grid follows the same specifications of the NTv2 grid, which has been used in other countries, such as Canada, USA and Australia. This paper presents ProGriD and its main functionalities and capabilities.

The Deutsches Geodätisches Forschungsinstitut (DGFI) acts as the IGS Regional Network Associate Analysis Centre for SIRGAS (IGS RNAAC SIR) since June 1996. Each week a loosely constrained position solution including all available observations of the SIRGAS Continuously Operating Network (SIRGAS-CON) is generated and delivered to the IGS Data Centres to be integrated into the IGS polyhedron. Based on these weekly solutions, DGFI also computes multi-annual solutions for station positions and velocities to estimate the kinematics of the SIRGAS reference frame. These multi-annual solutions are updated yearly and include those stations operating more than 2 years continuously. This paper describes the computation of the latest multi-annual solution of the SIRGAS-CON network. Identified as SIR09P01, it was released in June 2009 and contains all the weekly solutions provided by the SIRGAS Analysis Centres from January 2, 2000 (GPS week 1,043) to January 3, 2009 (GPS week 1,512). It refers to the IGS05 frame at the epoch 2005.0 and provides positions and velocities for 128 SIRGAS-CON stations. The accuracy of its positions at the reference epoch is estimated to be better than ±0.5 mm in the horizontal component and ±0.9 mm in the vertical one. The accuracy of the linear velocities is about ±0.8 mm/a.

The analysis of the crust displacement in Amazon basin from the comparison between three data sources is the aim of this paper. The data involved are in-situ water level time series measured at ground-based hydrometric station of

Agência Nacional de Águas

(ANA), vertically-integrated water height deduced from GRACE geoid (height anomaly) and a continuous monitoring GPS station of

Instituto Brasileiro de Geografía e Estatística

(IBGE). Two analysis are carried out: the first comprehend the GPS vertical coordinate (UP) and in-situ daily data; the second is the 10-day interval of GRACE models, UP and in-situ data for a ~3-years period (January-2006 to December-2008). The GRACE models were computed by

Groupe de Recherce de Géodésie Spatiale

(CNES/GRGS) and the height anomaly was converted into Equivalent Water Height (EWH). The precise point positing (PPP) is the technique for absolute GPS processing. The Canadian Spatial Reference System (CSRS-PPP) service was used. The coordinate UP presents an annual cycle of vertical displacement with peak-to-peak amplitude of 80–100 mm. A correlation about 90% between in-situ and GRACE is detected. However, they have an inverse phase correlation with the vertical coordinate. This implies that the crust responds instantaneously to the hydrological loading cycle.

The efforts to compute the geoid model for South America, limited by 15° N and 57° S in latitude and 30° W and 95° W in longitude, are presented. The terrestrial gravity data for the continent have been updated with the most recent measurements in Argentina, Brazil, Chile, Ecuador and Paraguay. An attention was also addressed to DTM, on the basis of SRTM (Shuttle Radar Topography Mission). The complete Bouguer gravity anomaly; the direct, secondary and primary indirect topographic effects; and direct and primary indirect atmospheric effects have been derived through the Canadian package SHGEO (Stokes-Helmert Geoid software). The short wavelength component was estimated via FFT with Featherstone, Evans and Olliver (1998) modified kernel. The geopotential model EGM2008 represents an important contribution to the long and medium wavelength component knowledge of the gravitational field and it has been used as a reference field restricted to degree and order 150. The model has been validated over 1,411 GPS observations on Bench Marks of the spirit leveling network, where the geoidal height was derived from the association of the geodetic and the orthometric heights. The height anomaly derived from EGM2008 (degree and order 2,159 with additional coefficients to degree 2,190 and order 2,159), EIGEN_05c (degree and order 360) and MAPGEO2004 (official geoid model in Brazil since 2004) have also been compared with the GPS points.

The combination of global geopotential earth models with high resolution digital terrain models forms the main tool for geoid modelling and satisfies the requirements at a wide range of gravity field frequencies. The need for local and regional data can be reduced to minor areas around points of interest. The resolution gap between potential models and digital terrain models is narrowing – EGM08 and SRTM, for instance, going down to 5′- and 3″-spacing, respectively. The influence of regional gravity data or other field components is reduced to a limited area zone. This means a significant advantage particularly in the case of developing countries which normally demonstrate heterogeneous data quality, bad geographical distribution or complete lack of local data sources at all.

Using as test area the Maracaibo Lake and the Venezuelan Andes region – an area with a 4,000 m height variation and some major height changes caused by natural or human based environmental hazards–, a recent GPS project dedicated to precise satellite observations over points of the first order leveling network in the area was performed. Applying most rigorous processing techniques, ellipsoidal height determinations at the 1–3 cm level were achieved at the 2008 campaign. Agreement between GPS/Leveling measurements and modeled geoid values improved. Comparing the new data with GPS observations dating from 1993 to 1998 – which formed a crucial part of the previous national geoid determination –, showed the limitations of the applied technique, partly explainable by height changes occurring in the area. An increasing epoch difference between new data sets and the original observations of the leveling network contributes in the differences, too.

Least Squares Collocation (LSC) and kriging are the most used techniques to predict gravity values as well as gravity anomalies. The limitations of LSC technique are mainly related in obtaining an adequate co-variance function. Moreover, LSC and kriging predictions depend strongly on known data distribution. Artificial Neural Network (ANN) is a promising tool to be applied in the interpolation problems. Even though, far from the deterministic ones, these techniques are presented as alternatives for interpolating due their good adaptation to several data distribution and easy implementation for fusion of different kinds of data basis. To test the performance of ANN in face of interpolation problems with respect to LSC and kriging, an experiment was developed in a region in the Brazil–Argentina border. Interpolated gravity values were obtained by LSC and kriging and compared with values obtained by ANN considering different data distributions and by using the same test points where gravity values are known. Considering the need of consistency of datum for predicting gravity related values, only a Brazilian data set was used in the present analysis. The smallest number of reference data for training and the low dispersion reveals the ANN as an alternative for LSC and kriging techniques for the usual poor gravity data distribution in South America.

Currently, IBGE is working on providing new services together with the modernization of the RBMC, such as real-time services via Internet using NTRIP (Networked Transport of RTCM via Internet Protocol), called RBMC-IP and the computation of WADGPS (Wide Area Differential GPS) corrections. A NTRIP caster is in operation at IBGE and receives the streams of 26 stations established in the main cities of Brazil. It is expected to provide real-time data access to all users in the first half-year of 2009. In order to evaluate this new real-time service in terms of precision and accuracy, some tests were performed in Rio de Janeiro state using code and phase observables in static mode. Parameters like distance to the reference stations and the reliability of the connection in urban and rural areas were considered in this evaluation. Another test was performed by the Brazilian Navy during a bathymetric survey with the purpose to update the nautical cartography in an area south of the Brazilian coast, using RTK (Real-Time Kinematic) corrections in RTCM3.0 RTCM means Radio Technical Commission for Maritime Services. (Real-Time GNSS data Transmission Standard). A comparison between NTRIP solution and standard RTK solution using radio link was performed. This paper presents the results of these two experiments and provides an analysis of the advantages, disadvantages and potentialities of this new solution for kinematic and static real-time surveys.

Carrier phase measurements are extremely accurate but ambiguous. The reliability of integer ambiguity resolution is improving with Galileo which uses a Binary Offset Carrier (BOC) modulation, large signal bandwidths of up to 50 MHz and additional carrier frequencies.

In this paper, a group of multi-frequency mixed code carrier linear combinations is derived which preserves geometry, eliminates the ionospheric delay and maximizes the ratio between wavelength and noise standard deviation of the combination. Moreover, a partial integer decorrelation is suggested to improve the robustness of ambiguity resolution over biases due to orbital errors, satellite clock offsets, and multipath.

The proposed group of multi-frequency mixed code carrier linear combinations is characterized by a wavelength of more than 3 m, which makes this group of combinations an interesting candidate for both Wide Area Real Time Kinematics (RTK) and Precise Point Positioning.

Computing a position with Single Frequency Precise Point Positioning (SF-PPP) algorithms compels to the use of satellite clock corrections, and for use with

real-time

applications, only a limited set of sources for orbit and clock data is available, for example the predicted Ultra Rapid products of the International GNSS Service (IGS). Recently, real-time clock estimates have become available, for example the RETICLE clocks developed by GSOC/DLR. In this research, first a comparison is made in the satellite clock error domain as the real-time RETICLE and predicted Ultra Rapid corrections are compared to the Final IGS clock corrections. The empirical standard deviation of clock differences between Final and RETICLE clocks become less than 0.4 ns. Differences between Final and Ultra Rapid clocks lead to a standard deviation of around 2 ns. Secondly the single frequency precise point positioning position errors in the North, East and Up directions are investigated. With the use of the RETICLE clocks the empirical standard deviation of the position errors in the North and East directions are between 2 and 3 dm and in the Up direction around 5 dm. These results are comparable with the accuracies reached when using Final products.

GNSS Attitude Determination is a valuable technique for the estimation of platform orientation. To achieve high accuracies on the angular estimations, the GNSS carrier phase data has to be used. These data are known to be affected by integer ambiguities, which must be correctly resolved in order to exploit the higher precision of the phase observables with respect to the GNSS code data. For a set of GNSS antennae rigidly mounted on a platform, a number of nonlinear geometrical constraints can be exploited for the purpose of strengthening the underlying observation model and subsequently improving the capacity of fixing the correct set of integer ambiguities. A multivariate constrained version of the LAMBDA method is presented and tested here.

Personal navigation services usually rely on GNSS positioning and therefore their use is limited to open areas where enough satellite signals can be received. If the user moves in obstructed urban environment or indoors, alternative location methods are required to be able to locate the user continuously. In our approach GNSS positioning is combined with a MEMS-based Inertial Measurement Unit for continuous position determination. In addition, Radio Frequency Identification (RFID) Location Methods are employed.

In RFID positioning the location estimation can be based on signal strength measurements (i.e., received signal strength indication RSSI) which is a measurement of the power present in a received radio signal. Then the mobile receiver can compute its position using various methods based on RSSI. Three different methods have been developed and investigated, i.e., cell-based positioning, trilateration using ranges to the surrounding RFID transponders (so-called RFID tags) deduced from RSSI measurements, and RFID location fingerprinting.

In most common RFID applications positioning is performed using cell-based positioning. In this case, RFID tags can be installed as active landmarks with known location. The user is carrying a RFID reader and is positioned using Cell of Origin (CoO).

GNSS and RFID are then integrated with INS positioning for continuous position determination. INS measurements would be utilized to calculate the trajectory of the user based on the method of strap down mechanization. Since the INS components produce small measurement errors that accumulate over time and cause drift errors, the positions determined by RFID or GNSS are needed regularly to reduce the drift. All observations are integrated in a Kalman filter to estimate the user’s position and velocity.

By integrating the above mentioned measurements into an intelligent software package the developed personal navigator will enable to determine the mobile user’s position continuously, automatically and ubiquitously.

Navigation systems, such as the Global Positioning System (GPS) and inertial measurement units (IMUs) become miniaturized and cost effective, enabling their fusion in a portable, low-cost navigation device for individual users, supporting predominantly outdoor navigation. This paper presents an unconventional solution designed for indoor–outdoor navigation, based on integration of GPS, IMU, digital barometer, magnetometer compass, and human locomotion model handled by Artificial Intelligence (AI) techniques that form an adaptive knowledge-based system (KBS). KBS is trained during the GPS signal availability, and is used to support navigation under GPS-denied conditions. A complementary technique used in our solution, which supports indoor navigation, is the image-based technique that uses a Flash LADAR sensor. Navigation from 3D Flash LADAR scene reconstruction utilizes the range distance to static features common in images acquired from two separate locations, which allows for triangulating the user’s position. By combining Flash LADAR image with the IMU data, a linear feature-based algorithm that identifies common static features between two images, along with the error estimates, is facilitated. Since the algorithm is based on linear methodologies, it enables rapid processing while generating robust, accurate position and error estimation data. In this paper, system design, as well as a summary of the performance analysis in the mixed indoor–outdoor environments is presented.

The Brazilian Network for Continuous Monitoring of GNSS – RBMC is a national network of continuously operating reference GNSS stations. Since its establishment in December of 1996, it has been playing an essential role for the maintenance and user access of the fundamental geodetic frame in the country. In order to provide better services for RBMC, the Brazilian Institute of Geography and Statistics – IBGE and the National Institute of Colonization and Land Reform – INCRA are both partners involved in the National Geospatial Framework Project – PIGN. This paper provides an overview of the recent modernization phases the RBMC network has undergone highlighting its future steps. These steps involve the installation of new equipment, provide real time data from a group of “core” stations and compute real-time DGPS corrections, based on CDGPS (The real-time Canada-Wide DGPS Service) (The Real-Time Canada-Wide DGPS Service. http://www.cdgps.com/ 2009a). In addition to this, a post-mission Precise Point Positioning (PPP) service has been established based on the current Geodetic Survey Division of NRCan (CSRS-PPP) service. This service is operational since April 2009 and is in large use in the country. All activities mentioned before are based on a cooperation signed at the end of 2004 with the University of New Brunswick, supported by the Canadian International Development Agency and the Brazilian Cooperation Agency. The Geodetic Survey Division of NRCan is also participating in this modernization effort under the same project. This infrastructure of 66 GNSS stations, the real time, post processing services and the potentiality of providing Wide Area DGPS corrections in the future show that the RBMC system is comparable to those available in USA and Europe.

Before addressing GGOS issues we briefly introduce the modern understanding of geodesy and we review the development of geodesy as a science. This background is required to understand the motivation behind the development the International Association of Geodesy’s Global Geodetic Observing System (GGOS).

The article then reviews the development of GGOS since the 1998 IAG Section II Symposium in Munich, which may be viewed as the GGOS date of birth. It introduces the GGOS mission and summarizes the milestones of the GGOS establishment. The current state of GGOS implementation is presented and the next steps of the GGOS deployment are discussed.

The Global Geodetic Observing System (GGOS) is the contribution of the International Association of Geodesy (IAG) to the Global Earth Observing System of Systems (GEOSS). The implementation of common standards and conventions in all components of GGOS is of crucial importance to ensure highest accuracy of geodetic and geophysical products. Consistency with relevant external standards and conventions is mandatory to achieve interoperability with GEOSS.

The Bureau for Standards and Conventions (BSC) complements the already existing GGOS structure. Its tasks include keeping track of the strict observance of adopted geodetic standards and conventions applied by the different GGOS components and assuring consistency of data sets released by the services. Complementary tasks include the interaction with international bodies engaged with standards and conventions and the promotion of geodetic standards in the broader scientific and user community and society in general.

The International VLBI Service for Geodesy and Astrometry (IVS) is well on the way to fully defining a next generation VLBI system, called VLBI2010. The goals of the new system are to achieve 1-mm position accuracy over a 24-h observing session and to carry out continuous observations, with initial results to be delivered within 24 h after taking the data. These goals require a completely new technical and conceptual design of VLBI measurements. Based on extensive simulation studies, strategies have been developed by the IVS to significantly improve its product accuracy through the use of a network of small (~12-m) fast-slewing antennas, a new method for generating high precision delay measurements, and improved methods for handling biases related to system electronics, deformations of the antenna structures, and radio source structure. To test many of the proposed strategies, NASA is sponsoring a proof-of-concept development effort using IVS antennas near Washington, DC, and Boston, MA. Furthermore, as of Feb. 2009, the construction of ten new VLBI2010 sites has already been funded, which will improve the geographical distribution of geodetic VLBI sites and provide an important step towards a global VLBI2010 network.

New VLBI (Very Long Baseline Interferometry) data analysis software (called Vienna VLBI Software, VieVS) is being developed at the Institute of Geodesy and Geophysics in Vienna taking into consideration all present and future VLBI2010 requirements. The programming language MATLAB is used, which considerably eases the programming efforts because of many built-in functions and tools. MATLAB is the high-end programming language of the students at the Vienna University of Technology and at many other institutes worldwide. VieVS is equipped with the most recent models recommended by the IERS Conventions. The parameterization with piece-wise linear offsets at integer hours in the least-squares adjustment provides flexibility for the combination with other space geodetic techniques. First comparisons with other VLBI software packages show a very good agreement, and there are plans to add further features to VieVS, e.g. capabilities for Kalman filtering, phase delay solutions, and spacecraft tracking.

Estimating horizontal tropospheric gradients is a common practice in VLBI and GPS data analyses. We investigate here the possibility to do the same for DORIS. We reprocessed all 2007 DORIS data for all satellites, using exactly the same strategy as the latest ignwd08 solution (Willis et al., Adv Space Res 45(12):1470–1480, 2010) but adding two new parameters per day to account for any asymmetry of the tropospheric delays. When averaged over the full year the DORIS north gradient estimates show a significant correlation with GPS estimates at 33 co-located sites. The east gradient is loosely determined with DORIS due to the north-south orientation of the satellites passes in 2007. Typical values are below 1 mm and North component shows a latitude dependency, negative values in the Northern hemisphere and positive values in the Southern hemisphere.

The stacking of DORIS station weekly coordinates provides a more realistic value for a factor of unit weight when done using gradient estimation. Station coordinates also indicate a small improvement in internal consistency when compared to a 1-year position and velocity solution without estimating gradients. The DORIS-derived tropospheric gradients may still absorb other types of un-modeled errors, but estimation of such parameters should be investigated in more detail before reprocessing the entire DORIS data set in view of the next ITRF realization, following ITRF2008.

The Time, Frequency and Gravimetry Section of the International Bureau of Weights and Measures (BIPM) is charged with maintaining the conventional reference time scales on the basis of international coordination, and is responsible jointly with the U.S. Naval Observatory (USNO) for the Conventions Centre of the International Earth Rotation and Reference Systems Service (IERS). Another task of the Section relates to gravimetry; the gravity field is monitored both with gravimeters operated by the BIPM and with instruments from other institutes participating every 4 years in the International Comparisons of Absolute Gravimeters (ICAGs), organized jointly by the BIPM, the Consultative Committee for Mass and Related Quantities (CCM) and the International Association of Geodesy (IAG).

The BIPM Time, Frequency and Gravimetry (TFG) Section is a service of the IAG, and works in coordination with other IAG services, including the IERS and the International GNSS Service (IGS).

Observations from up to 51 GPS+GLONASS satellites are available as of September 2009. Mainly (near) real-time GNSS analyses, particularly navigation, warning systems or atmosphere monitoring, will benefit from the data from all these satellites. The International GNSS Service (IGS) has been providing precise GPS ultra-rapid orbits since 2000, but up to these days, due to a lack of contributing analysis centers, it does not provide GLONASS ultra-rapid orbit product. The Geodetic Observatory Pecný has been contributing to the IGS ultra-rapid orbits since 2004. In 2008/2009 an extension of the orbit determination procedure was prepared for the GLONASS system. Although the GLONASS global data coverage is far from optimal, we focused on a robust and satisfactory routine product already usable in (near) real-time GNSS analysis. We have tested the system for different schemes of processing – (1) common GNSS solution and (2) stand-alone GLONASS or GPS solutions. Resulting orbits and ERPs were evaluated with respect to the IGS final products. The use of the GLONASS ultra-rapid orbits was demonstrated in near real-time water vapor monitoring using the European network of 38 GNSS stations.

The steadily growing number of absolute gravimeters and absolute gravity measurements all over the world emphasizes the demand of an overview about existing locations, observations, instruments and institutions involved. As a contribution to the International Gravity Field Service (IGFS), a relational database was designed and implemented in a joint development of BKG and BGI and is in operational status now. Two objectives are aimed at: With freely available meta-data and contact details, the database should give an overview about existing stations and observations, serve as a platform for multidisciplinary cooperation and allow the coordination of forthcoming measurements. Among contributing groups or within international projects, an exchange of gravity values and processing details is possible. The database will function as a data inventory, assuring long term availability of the data. Prospectively, the database will be the foundation for a future international gravity reference system and will serve as a pool for geophysical interpretation of absolute gravity observations on a global scale.