Vistas for Geodesy in the New Millennium

Natural Resources Canada’s (NRCan) Geodetic Survey Division (GSD), on behalf of the International GPS Service (IGS) and its Reference Frame Working Group, combines sets of station coordinates, velocities, Earth Rotation Parameters (ERP) and apparent geocenter positions to produce the IGS official station position/ERP solutions in the Software Independent Exchange (SINEX) format. The weekly combination includes solutions from the Analysis Centers (AC), while the Global Network Associate Analysis Centers (GNAAC) provide quality control.The weekly AC solutions include estimates of weekly station coordinates, apparent geocenter positions and daily ERPs. The ACs also provide separately, satellite orbit and clock estimates as part of their daily products, which are independently but consistently combined by the IGS AC Coordinator to produce the IGS orbit/clock products. All the AC products are required to be in a consistent reference frame. The combination of station coordinates originating from different ACs involves removing all available constraints and re-scaling the covariance information. The weekly combined station coordinates are accumulated in a cumulative solution containing estimated station coordinates and velocities at a reference epoch.

The Earth Rotation phenomena can be mathematically described through the EulerLiouville equations, which are originally nonlinear.In the present work, the Extended Kalman Filtering (EKF) algorithm for nonlinear dynamical system is applied to Earth Rotation Parameters (ERP) in order to produce a combined time series.The behavior of the resultant series is analyzed in comparison to IERS C04 solution, obtained using linear approximation algorithms.

Terrestrial reference frames realized by diverse satellite techniques and estimated through various Analyzing Centers show systematic differences in scale, origin, direction and rate of rotation axis, which are at the cm-level. One of the error sources is the uncertainty in the gravity field, including the adopted gravitational constant GM value. The sensitivity of the scale of an SLR frame to the relative error in GM is about 0.62, when tracking data to LAGEOS are used. If the frame is estimated from SLR measurements to GPS satellites, the sensitivity factor would have been increased to about 1.4, since the scale effect increases with the altitude of the satellite. But for GPS microwave-tracking data the scale sensitivity to the GM error is reduced to about 0.07 ! The reason is that the GPS is an one-way tracking technique, no reflector is needed, but two clocks are required. The errors in GM and the gravity model are largely absorbed in the double differences, or in the clock estimates. GM and gravity model errors are important for SLR, DORIS and PRARE techniques, but not for GPS. The ppb-level scale error in the GPS reference frame could result from the errors in the satellite antenna phase center offsets.

The unique radio astronomical technique of Space Very Long Baseline Interferometry (SVLBI) is an extension of the ground-based VLBI into the space. It has some important potential applications in geodesy and geodynamics, including the definition, practical realization, and interconnection of different reference frames, determining the geocentric positions of VLBI stations, estimation of the gravity field of the Earth, and satellite orbit determination using the delay and delay rate observables. With the launching of the first SVLBI satellite of the VLBI Space Observatory Programme (VSOP) of Japan, in February 1997, this technique has become a reality. An international team of scientists, working under the auspices of the FÖMI Satellite Geodetic Observatory, Hungary, has designed the GEDEX, for the purpose of exploring the feasibility of the geodetic applications of SVLBI.A brief description of the SVLBI technique and references to the significant theoretical developments in the field of geodetic SVLBI are provided, followed by an overview of salient features of the Highly Advanced Laboratory for Communications and Astronomy (HALCA), the orbital component of the VSOP mission. The state of the art and the projected developments in this field are summarised. The various aspects of GEDEX, including the objectives, the tasks involved, the scope of the experiment, the software development, the data formats and recent results of data pre-processing and test data analysis are discussed. A test VSOP data set has been pre-processed and analysed. Preliminary results show that the SVLBI delay residuals are at the level of a few meters.Conclusions drawn, based upon the experience gained in this project, and recommendations for future work are presented. The major practical problems with HALCA data for geodetic use include the single observing frequency, the limited bandwidth and sensitivity, the unreliable instrumental phase-cal data, the poor sky coverage and the sparse co-observing array of ground-based VLBI telescopes.

The recently developed method of ‘combined smoothing’ is shortly introduced and its main philosophy presented. The method is tested with simulated data in order to demonstrate that the method is capable of removing both long-term and stepwise systematic errors in time derivatives of certain Earth Orientation Parameters measured by satellite methods.It is then applied to combine the observations by VLBI (universal time, celestial pole offsets) with the time derivatives of the same quantities (length-of-day, celestial pole offset rate) measured by GPS. The input data are typically given in weekly (VLBI) and daily (GPS) intervals, both resulting curves (mutually consistent function values and time derivative values) are defined at all original epochs with any observation, i.e. at least in daily intervals.It is shown that the result of such combination is practically free of long-term systematic errors of GPS observations. It takes over the long-term stability of VLBI results, provides automatically the necessary calibration of GPS results against VLBI, and fills in the gaps in less dense VLBI measurements by more frequent and short-term stable GPS observations.

This paper deals with the estimation of geocenter variations on the basis of SLR data to LAGEOS 1 and 2. The paper describes the SLR data analysis with the DGFI software DOGS. We computed a combined LAGEOS 1 & 2 solution, and in addition two separate solutions using the data of both satellites independently. For the estimation of geocenter variations we applied a geometric and an analytic method. The results obtained from these different approaches were used to assess the accuracy and consistency of the geocenter determination. Finally we compared our estimates with other space geodetic and geophysically derived results. We found a good agreement for the annual amplitudes and phases, whereas the semiannual signals differ significantly.

Satellite laser ranging (SLR) has monitored for a long time the continuous redistribution of mass within the Earth system through concomitant changes in the Stokes’ coefficients of the terrestrial gravity field. JCET’s latest analysis of the 1993-present SLR data set from LAGEOS and LAGEOS 2 data for the IERS (International Earth Rotation Service) Terrestrial Reference Frame (ITRF) includes the weekly monitoring of such compound changes in the low degree and order harmonics. Along with the static parameters of the TRF we have determined a time series of variations of its origin with respect to the center of mass of the Earth system (geocenter). These estimates provide a measure of the total motion due to all unaccounted sources of mass transport within the Earth system and can be used to either complement the estimates from the future missions or to validate them through comparisons with their estimates for the same quantities. The data were reduced using NASA Goddard’s GEODYN and SOLVE II software, resulting to a final RMS error of ~8 mm.

The purpose of EUREF, the SubCommission for Europe of IAG’s (International Association of Geodesy) Commission X on Global and Regional Geodetic Networks, is the establishment and maintenance of the European Reference Frame.This is being achieved by means of a number of space geodetic reference stations (SLR and VLBI), an array of GPS permanent sites the EUREF Permanent Network (EPN), a network of highprecision geodetic reference sites determined by GPS campaigns, and the combination of the Unified European Levelling Network (UELN) and the European Vertical GPS Reference Network (EUVN).The ETRS89 (European Terrestrial Reference System 1989) is being adopted by several countries and organisations in Europe as the official system for geo-referencing. The European Community will use ETRS89 as conventional reference system as well.This paper describes the status of the different EUREF components and projects (GPS campaigns, EPN, UELN, EUVN), as well as some organisational aspects (the rebuilding of the homepage www.euref-iag.org, absolutely necessary for a better distribution of the information), and the relationship with other organisations.

The EUREF Permanent Network (EPN), established in 1996, consists currently of more than 120 GPS stations from 30 European countries. A significant portion of the network has more than 3 years of observation history, which provides the potential for reliable velocity estimation relevant for geophysical interpretation.This paper addresses the main error sources degrading the quality of the velocity estimation, illustrated with examples taken from the EPN. At the observation level, we demonstrate that changes in the station equipment and tracking performance can cause discontinuities and non-periodic signals, while monumentation commonly introduces annual signals in the coordinate time series. In addition, the RMS of the estimated coordinates and velocities can also be increased. At the processing level we demonstrate the importance of the appropriate reference frame fixing to avoid systematic biases in the estimated velocities.The derived residual (intraplate) velocities confirm the stability of the EPN at the level of a few mm/year. Velocities contradictory to the tectonic expectations are found only for stations with short observation history.

The CERGOP Project of the Central European Countries initiated six GPS observation campaigns from 1994 to 2001. By the high standards set within this project for site selection, observation and analysis a consistent set of epoch solutions with a precision in the 3–5 mm range was created. The network contains about 19 permanent and 38 epoch stations. In this paper a first combination solution over the seven years with a velocity field in the ITRF2000 is presented. It is based on the IGS and EUREF permanent sites and is analyzed in view of its consistency with ITRF2000 for common sites, with respect to time series for the individual stations and for the difficulties stemming from eccentricities required at some sites. Estimated velocities are at or below the 1 mm/yr accuracy level for the main sites and are consistent with the EUREF Permanent Network results. The final velocity field is to be published at the end of this year and will be used for the densification of the ITRF in Central Europe and for the analysis of geokinematics in that area.

We develop the theoretical background for generating artificial observations for a virtual reference receiver in post processing mode. We use double difference information from network solutions to correct zero difference observations in a preprocessing clock estimation process and find that the observations can be adjusted on the level of about 4 mm. Using simple ionosphere and troposphere modeling techniques we show how phase observations can be calculated for any location within the network. Full use is made of the ambiguity and ionosphere information from double difference network solutions in order to keep full consistency of the artificial phase observations on the double difference level. The effect of such observations is demonstrated with data from a GPS network in Switzerland. We find that baseline solutions are more precisely determined (e.g. ambiguity resolution) using a virtual receiver at one end with observations constructed with the proposed approach.

GPS precise point positioning (PPP) can provide high precision 3-D coordinates. Combined pseudorange and carrier phase observables, precise ephemeris and satellite clock corrections, together with data from dual frequency receivers, are the key factors for providing such levels of precision (few centimeters). In general, results obtained from PPP are referenced to an arbitrary reference frame, realized from a previous free network adjustment, in which satellite state vectors, station coordinates and other biases are estimated together. In order to obtain consistent results, the coordinates have to be transformed to the relevant reference frame and the appropriate daily transformation parameters must be available. Furthermore, the coordinates have to be mapped to a chosen reference epoch. If a velocity field is not available, an appropriated model, such as NNR-NUVEL-1A, has to be used. The quality of the results provided by this approach was evaluated using data from the Brazilian Network for Continuous Monitoring of the Global Positioning System (RBMC), which was processed using GIPSY-OASIS II software. The results obtained were compared to SIRGAS 1995.4 and ITRF2000, and reached precision better than 2cm. A description of the fundamentals of the PPP approach and its application in the integration of regional GPS networks with ITRF is the main purpose of this paper.

The modernization of the Hungarian Gravity Base Network was carried out in the framework of the establishment of the unified gravity network of the Central-European countries. The objective of former networks and the necessity of development are reviewed. The scale of the new network is guaranteed in SI system by the numerous absolute gravity measurements carried out of late years. The applied observation methods, data processing and adjustment procedures are presented. The results of the comparison of Unified European Gravity Network’94 (UEGN-94), Czech, Slovakian and Austrian networks with the Hungarian network (MGH-2000) are discussed.

The Technical Working Group of the IAG Subcornmission for Europe (EUREF) was asked by the European Commission to define a common height reference system for the exchange of geoinformation in Europe and to describe its realization on the basis of the European height projects United European Levelling Network (UELN) and European Vertical Reference Network (EUVN). EUREF decided to define an European Vertical Reference System (EVRS) as world height system (WHS) (http://evrs.leipzig.ifag.de/). EUREF endorsed UELN95/98 and EUVN as realizations of EVRS using the name EVRF2000, characterized by: the datum of ‘Normaal Amsterdams Peil’ (NAP)gravity potential differences with respect to NAP or equivalent normal heights.

At present, the classical height systems in S o uth America are realized by first order leveling networks, which refer to the mean sea level determined at local tide gauges. The sea surface variations and the neglect of the gravity effects in the height processing generate discrepancies between the different height systems. The connection of the leveling networks of Colombia, Ecuador and Venezuela performed on the occasion of the SIRGAS 2000 GPS campaign shows considerable discrepancies in the heights (exceeding 30 cm) of the three national classical reference systems. Since the principal requirement of a unified vertical reference system is a common reference surface, the gravimetric geoid/quasigeoid computation for Colombia (GEOCOL2001) was extended to the mentioned area. The resulting height anomalies are compared with the existing spirit leveling data and GPS heights. The discrepancies are -20 cm between Colombia and Ecuador, and they range from -53 cm to +49 cm along the Colombian-Venezuelan border.

The official height system of Switzerland LNO2 is based on levelling measurements only, without taking into account the gravity field. This causes inconsistencies for the surveyors who nowadays often determine heights out of GPS measurements and geoid information.A first step to overcome this problem is to introduce orthometric heights (LHN95) as the official national height system. This height system takes into account vertical movements and is based on a rigorous adjustment of all 1 st and 2nd order levelling measurements since 1902. The necessary mean gravity values along the plumbline are calculated out of a 25 meter DHM and associated density models. Besides of orthometric heights also normal heights are calculated. This allows us to compare the Swiss heights with the heights of our neighbouring countries and with the European height system. Furthermore it is a necessary prerequisite for the transformation between national height systems and the unification of national vertical datums.With the introduction of a new vertical system we have to provide a transformation method from LNO2 to LHN95. Our first approach for this transformation was to split the differences between a levelled and an orthometric system into several separate effects such as network distortions, vertical movements and the influence of the gravity field. These individual effects should be easier to interpolate than the differences as a whole.But even with the new orthometric height system full consistency between levelling and GPS measurements is not reached yet. We see systematic discrepancies between levelling, GPS and the geoid for which we have no explanation yet. The three data sets should be determined in one common adjustment process. This is not rigorously possible because, in general, the full variance-covariance information of all measurements is not available. In this paper a first approach and first results of a combined adjustment of GPS levelling and geoid are shown.

The integrity of the Australian Height Datum (AHD) has remained in some question ever since its adoption in 1971. Indeed, its creators commented that using 30 tide gauges ‘placed a strain’ on the least-squares network adjustment of the —97,230 km of spirit levelling used to realise the AHD. Although the AHD seems to have served Australians well, the question remains — can the AHD be improved? Of course, re-levelling an entire continent the size of Australia is prohibitively expensive, especially in the current climate of economic rationalism. Therefore, a proposal is made to enhance and redefine the AHD using the additional levelling data collected since 1971, mean sea level observations made at new tide gauges, models of the sea-surface topography, nation-wide GPS height networks and a regionally refined gravimetric geoid model. This proposal is balanced against the arguments in favour of retaining the existing AHD, coupled with a geoid model that has been warped to fit the existing AHD using nation-wide GPS networks co-located with AHD benchmarks.

Nowadays, determining the topography of Mean Sea Level (Sea Surface Topography — SST) at the tide gauge station and its temporal variation is one of the most important aspects of defining a vertical Datum. Different approaches are used for this purpose: Oceanographic approach; Satellite altimetry associated with geostrophic levelling; Gravity associated with satellite positioning; Geodetic boundary-value problem approach (GBVP). In this sense, time series for observing tide gauge geocentric position permits to fix its geometric position and to detect local dynamic effects on the crust and in the SST. The main purpose of Work Group III in SIRGAS project (Geocentric System for the Americas) is to establish the link of all vertical reference systems in South America. In general, each national vertical network in that region was established under three particular conditions: local vertical datum; height system without physical meaning; and different spirit levelling standards. The unification of South American vertical datums, is a fundamental step to understand the observed off set among the networks in the region. The achieved results of two multiparametric on the brazilian vertical datum and their analysis are presented in this paper.

Since IAU has adopted at its last General Assembly a fully relativistic new reference system the relativistic corrections and reductions to terrestrial fundamental parameters as evaluated by Kopejkin and others became more relevant to geodesy. IAU has decoupled TT from W0 so that basically IAG would be fi ee to introduce fully conventional new reference systems as advocated, e.g., by Rummel at the IAG-meeting at Banff. However, it should be carefully considered whether IAG should decouple itself from new developments where highprecision reference systems now are badly needed in various types of global geophysics. Purely conventional systems, based on „defining constants“, cannot replace high-precision frames based on well determined (± 10-99 and better) parameters and/or constants. Moreover, the update of WGS 84 by NIMA in ’97 reveals the interest of user communities in ellipsoidal systems. Even though WGS 84 is not a consistent system in the Somigliana-Pizetti sense it was recently adopted by FAA. M. Kumar and others have recently pointed out the discrepancy between IAG-resolution 16 and ITRF. This assumption is not quite correct. At the COSPARmeeting at Warsaw the incorporation of dynamic parameters in ITRF has been considered. By introducing W0 instead of the semi-major axis of the earth’s ellipsoid the problem of a triple-system of tidal regimes could be avoided which is never fully understood by non-experts. The transition from W0 to the semi-major axis of the earth ellipsoid is a well-known problem which was recently discussed within SC-3 of IAG.SC-3 of IAG has carefully considered tidal and non-tidal variations of fundamental parameters but before temporal changes have been carefully determined by GRACE etc. new systems should not be introduced. With GRACE, GOCE, JASON and ENVISAT together with new results from WOCE and GLOSS (incl. repeat GPS etc.) the evaluation of new high-precision reference systems becomes feasible. Pioneering work by Bursa et al. as well as by Grafarend et al. has clearly shown that new and efficient global vertical datums and SomiglianaPizzetti reference systems, respectively, can become available soon. If IAG wants to play its role in determnining and defining global terrestrial reference systems it will soon be able to introduce new systems corresponding to the new IAU systems. If not,others will do it as IAPSO and other user groups obviously need up-to-date high precision reference frames and systems. Consistent ellipsoidal systems of Somigliana-Pizzetti type are needed even though the evaluation of really independent four-parametersets is now difficult and problematic.

Four fundamental geodetic parameters, namely % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaai4EaiaadE % eacaWGnbGaaiilaiaadEfadaWgaaWcbaGaaGimaaqabaGccaGGSaGa % euyQdCLaaiilaiaadQeadaWgaaWcbaGaaGOmaaqabaGccaGG9baaaa!40BB! $$\{ GM,{W_0},\Omega ,{J_2}\} $$ , determine a world geodetic datum. With respect to the Somigliana-Pizzetti Level Ellipsoid I International Reference Ellipsoid these fundamental parameters from best estimates at a reference epoch determine its semi-major axis a as well as its semi-minor axis b (or equivalently the linear eccentricity % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTduMaey % ypa0ZaaOaaaeaacaWGHbWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIa % amOyamaaCaaaleqabaGaaGOmaaaaaeqaaaaa!3D3A! $$\varepsilon = \sqrt {{a^2} + {b^2}} $$ . Satellite orbit analysis as well as sea level projects have indicated that the four fundamental geodetic parameters are time-dependent, described for instance by % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaai4EaiaacI % cacaWGdbGaamytaiqacMcagaGaaiaacYcaceWGxbGbaiaadaWgaaWc % baGaaGimaaqabaGccaGGSaGafuyQdCLbaiaacaGGSaGabmOsayaaca % WaaSbaaSqaaiaaikdaaeqaaOGaaiyFaaaa!4234! $$\{ (CM\dot ),{\dot W},\dot \Omega ,{\dot J_2}\} $$ . Here we have % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaai4EaiaacI % cacaWGhbGaamytaiqacMcagaGaaiaacYcaceWGxbGbaiaadaWgaaWc % baGaaGimaaqabaGccaGGSaGafuyQdCLbaiaacaGGSaGabmOsayaaca % WaaSbaaSqaaiaaikdaaeqaaOGaaiyFaaaa!4238! $$\{ (GM\dot ),{\dot W_0},\dot \Omega ,{\dot J_2}\} $$ . Here we have analyzed the impact of best estimates of % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaai4EaiqadE % fagaGaamaaBaaaleaacaaIWaaabeaakiaacYcaceWGkbGbaiaadaWg % aaWcbaGaaGOmaaqabaGccaGG9baaaa!3C41! $$\{ {\dot W_0},{\dot J_2}\} $$ on shape and size parameters, i.e., {ȧ,ḃ} and (ȧ±̇,), of the World Geodetic Datum 2000 (WGD2000). Based on the best estimate of time variations of % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaai4EaiqadE % fagaGaamaaBaaaleaacaaIWaaabeaakiaacYcaceWGkbGbaiaadaWg % aaWcbaGaaGOmaaqabaGccaGG9baaaa!3C41! $$\{ {\dot W_0},{\dot J_2}\} $$ we have computed the best estimates ȧ = (0.3 ± 0.02) mm / year, ḃ= (-0.0002 ± 0.00008) mm/ year, and ɛ- = (3.7 ± 0.3) mm / year as the time variation of the shape and size parameters of the WGD 2000. The new results give a scientific basis for answering the question: Is there a need for a Geodetic Datum 2000?

“The geodesist [and the geophysicist] needs a permanent reference surface, whereas the astronomer [and apparently some geodesists] wants the best approximation of the Earth by an ellipsoid.” “It is much better to use a fixed reference ellipsoid with rigidly assumed parameters … but from time to time to compute the ‘best’ corrections to [them].” (Italic text quoted from Heiskanen & Moritz, 1967.) Geodesy now plays a key role in detecting and monitoring global change. This needs a datum that does not change with time, either in discontinuous jumps through adopting new parameters or continuously through adopting time-varying ones. I review the logical sequence connecting Reference System to the task of finding out how the Earth works. The Reference System is an adopted model of the Earth, which need not be a good fit to the real Earth and there is no case for changing the GRS80 parameters. Even the 1924 Ellipsoid satisfies the condition that anomalies can be approximated linearly.The weakness of GRS80 is imprecise or inappropriate physics, not the value of its parameters. The 1983 Hamburg amendment corresponds to defining the ellipsoid as a gravitational equipotential of the Earth’s internal density distribution (core, solid, oceans and atmosphere). The geodetic terminology for this — ‘zero frequency tide’ is not self-explanatory. Any other treatment of tides corrupts observations by empirical and inexact assumptions. I also discuss the relation of GRS80 to the vertical datum and see a misunderstanding over the primacy of a and W ₀ : both are arbitrary because neither corresponds to an inherent property of the real Earth. The present drift towards adopting a 5 parameter reference system is misconceived. I make the case for adopting a (which is independent of tidal conventions!) and then defining W ₀ = (U ₀ )_GRS80. I compare this with alternatives.

Spherical harmonic analysis of gridded (and noisy) data on a sphere (with uniform error for a fixed latitude) gives rise to simple systems of equations. This has for the method of least-squares collocation (using an isotropic covariance function or reproducing kernel) been implemented with as much generality as the theory allows. The data only needs to be at the same altitude and of the same kind for each latitude. This permits for example the combination of gravity data at the surface of the Earth and data at satellite altitude.Suppose that data are associated with the points of a grid with N values in latitude and M values in longitude. The latitudes do not need to be spaced uniformly. Also suppose we want to determine the spherical harmonic coefficients to a maximal degree and order K. Then the method will require that we solve K systems of equations each having a symmetric positive definite matrix of size N * N, only.Results of three simulation studies using the method are described.

The Earth’s principal axes and principal moments of inertia were determined from the 2nd degree harmonic coefficients of recent Earth gravity field models and several values of the dynamical ellipticity. Closed exact formulae for the estimation of these parameters are developed based upon the exact analytical solution of eigenvalue-eigenvector problem and error propagation. These formulae are applied to determine (a) the “time-independent” components at epoch of the Earth’s tensor of inertia and their accuracies and (b) the time-dependent components of the tensor of inertia, which are based on satellite solutions for the secular variation in the degree 2 zonal coefficient and periodic variations in the degree 2 tesseral coefficients resolved from the IERS 0.05-yr polar motion data. Special attention was given to the evolution with time of the polar axis C of inertia in view of the creation of a dynamical reference frame. The time evolution of the Earth mechanical and geometrical parameters can be compared with their accuracy estimates at epoch.

Helmert’s methods of condensation are generalized, considering a variable depth of the condensation layer below the geoid. Expressing the respective formulae for the combined topographic-condensation reduction both in space and frequency domain for a spherical approximation of the Earth, some drawbacks of Helmert’s second method of condensation become visible. It is shown by theoretical arguments that the residual gravity field is very rough after applying Helmert’s second model of reduction; this property, well-known from practical calculations, makes this procedure unsuitable for downward continuation. It is concluded that for precise geoid and quasigeoid determination Helmert’s second condensation method should be replaced by the generalized model in order to provide reasonable results in rugged terrain.

Using GEOSAT GM altimetry data, shipborne gravity, land gravity and GPS/leveling data, a numerical solution for the fixed altimetry-gravimetry boundary value problem (AGBVP) II is evaluated and tested. Two types of solutions are applied — with and without smoothness conditions along the coastline. Data available in the area of Newfoundland, eastern coastal region of Canada, are used. A comparison with a standard estimation method for the efficient combination of heterogeneous data, namely multiple input, multiple output system theory (MIMOST), is carried out. Conclusions for the combination of different data types and smoothness conditions along the coastline are drawn.

An analysis is made on the feasibility of using in-situ GRACE measurements for geoid determination. The method investigated consists of local downward continuation using integral inversion. The observables considered are potential differences (DT) and gravity disturbance differences (DGD). The regularization of this ill-posed problem is studied using the Tikhonov, damped singular value decomposition, and conjugate gradient methods.In the search for the best regularization parameter (α), the L-curve method is found to succeed when only random errors in the measurements corrupt the solution. However, with model errors, the method does not produce satisfactory results. An empirical method is formulated to find a near optimum a. Simulations show that the Tikhonov regularization yields best results. Combined with B-spline smoothing and applied to simulated data for 30 days of gravity mapping, the method produces local geoid (20-degree harmonic model removed) errors of about 12 cm and 11 cm for 1.2 degree resolution using DT and DGD, respectively. All simulations are made using the geopotential model EGM96.

CHAMP (Challenging Mini-Satellite Pay-load for Geophysical Research and Application) has opened a new era of global gravity field determination by satellites. Satellite platform, accelerometer, star tracker and actuators are modeled using a simulation tool in which orbit dynamics, satellite control systems, sensor and error characteristics are taken into account. The results of the simulations are compared with real CHAMP data obtained during the commissioning phase. From this comparison, insight is gained into the actual performance of these instruments as an integrated gravity sensing system. A possible cross-fertilization of star tracker and accelerometer data is discussed in some detail.

The GOCE level lb data products consist, among others, of time lines of calibrated and corrected gravity gradient data and SST data. The calibration for GOCE can be described as a multi-step procedure consisting of a pre-flight, on-ground calibration, an in-flight internal calibration and a so-called external (or absolute) calibration step. The latter consists of checking and correcting the data by comparison with external data, models or other external gravity field knowledge in order to improve absolute calibration parameters determined earlier and to correct for known or unknown errors in the data which have not been corrected for before. Obvious choices for external calibration are to compare the GOCE data with ground based gravity data, with existing global gravity field models or to intercompare different GOCE data products, like the accelerometer common mode observations with the GPS data. The latter two methods are studied in more detail here. It appears that for the gradiometer observations, the use of existing global gravity field models may help the calibration for the low frequencies below the measurement bandwidth. The calibration of the common mode observations using GPS data depends heavily on the quality of prior conservative force models. In addition, we consider here the problem of in flight performance monitoring of the GOCE measurements using a collinear track technique in analogy to satellite altimetry. We discuss the results of a new algorithm designed for a sun-synchronous frozen repeat orbit and treat two extreme scenarios. For the best case scenario our conclusion is that it is possible to monitor the stability of the instrument within the measurement band to around (MATH) whereas for our worst case scenario this is a factor of 10 less accurate.

The determination of the Earth’s exterior gravity field from noisy satellite gravity gradient (SGG) data lacks stability due to the polar gaps and the downward continuation process. After discretization, this property translates into an illconditioned system of normal equations, which has to be regularized in order to obtain a physically meaningful solution. Regularization requires the selection of (1) a regularization method and (2) a parameter choice rule. Important selection criteria are that the regularization strategy is applicable to the largescale problem of GO CE data analysis, characterized by millions of observations and ten thousands of unknowns, and that the parameter choice rule is independent of some prior information such as the total error power or the smoothness of the solution. We have investigated Tikhonovtype regularization with the Generalized Cross Validation (GCV) parameter choice method and an ‘adjustable’ regularization matrix, including Kaula stabilization as well as derivative-constraining regularization as special cases. The method has been modified allowing for coloured noise observations to be taken into account, and for fast computation of the traceterm in GCV by using a randomized traceestimator. Results from a detailed numerical study following the baseline of the GOCE mission are presented. We can show that significant improvements with respect to the Kaula stabilization method are possible.

The effects of aliasing and polar data gap have been investigated analytically and numerically for the upcoming dedicated gravity satellite missions. It is verified that they could cause more significant systematic error in the solution via least-squares estimation than the effect from the instrument’s noise. Both effects produce similar error trends in the geoid height estimation, while they corrupt coefficients corresponding to different spectral domains.This paper develops possible methods to reduce the errors caused by them. A new scheme is proposed to decrease the aliasing error and a combination solution is suggested to reduce the corruption due to the polar data gap. Numerical results are computed through GOCE and GRACE simulation studies. It is shown that the geoid error due to the aliasing is reduced near the poles from 11cm to less than 1cm by estimating 20% more coefficients beyond the Nyquist limit and the geoid error due to the polar data gap in the GOCE mission is reduced to less than 1cm by including GRACE measurements in the polar areas.

The Gravity Recovery And Climate Experience (GRACE) satellite will detect seasonal variations of gravity with very high accuracy. A prospective follow-on of the GRACE would be the Satellite-to-Satellite laser Interferometry (SSI). To make use of the highly accurate measurements of seasonal gravity expected from these satellites, beyond the measurement errors it is important to consider the error sources affecting particularly the seasonal frequency. In this study two errors were attempted to be modeled: the short-period aliasing effect and the effect of the oceanic response to atmosphere. The results show that these phenomena should notably affect the ability of the satellites.

Two test areas with different characteristics of the terrain were selected in Hungary to model the gravity field. We have used point gravity gradients, their terrain effects and geopotential information to model geoid heights by numerical integration using kernel functions for specific gradient and curvature combinations which arise from the solution of the corresponding overdetermined geodetic boundary value problem. The truncation characteristics of these kernel functions were also taken into account. We have compared our results with the collocation solution as well

In the past five years, considerable progress has been made in improving the accuracy of scalar gravimetry by integrated INS/DGPS sys- tems, both of the strapdown and the stable platform system type. Less attention has been given to vec- tor gravimetry and the results that have been pub- lished are much poorer in comparison. If the attitude components of the gravity disturbance vector could be determined with the same accuracy as its magni- tude, deflections of the vertical could be estimated with a standard deviation of about 0.3 arc seconds for a mimimum half-wavelength resolution of 1.5–2.0 km. This is not be possible at the moment. In this paper the reasons for the accuracy difference have been studied by analysing airborne gravity data taken over a well-determined reference field in the Canadian Rocky Mountains. Two different methods have been applied to determine the horizontal components of the gravity disturbance vector, i.e. the deflections of the vertical. In the first one, the standard method-direct deflection determination along individual profiles — has been used. In the second one, deflections have been estimated from gravity disturbances at flight level, using a modified Vening-Meinesz approach. The differences in results between the two methods clearly point to the large influence of gyro drifts in the direct deflection determination method.

Experiences from recent airborne gravity campaigns undertaken by National Survey and Cadastre — Denmark (KMS) in cooperation with different partners are described in this paper. Data from surveys over Great Barrier Reef Australia, in the Baltic Sea and in Greenland are analyzed with emphasis on system performance, data validation and especially error sources. All campaigns employed a LaCoste and Romberg air/sea gravimeter.Both internal crossover analysis and comparison to existing surface data indicate a noise level around 1.5 to 2 mGal at 6 km resolution. Examples from a sedimentary basin in the northeast Greenland shelf region show that the resolution and accuracy of the system are sufficient for mapping of geological structures of interest to hydrocarbon exploration. Salt structures were recognized in an earlier marine seismic survey and the related negative gravity anomalies are clearly mapped by the airborne gravity system.Due to its good drift characteristics the LaCoste and Romberg gravimeter has proven to be a reliable and operational tool for geodetic purposes, e.g. provide bias free data for local geoid models. Consequently data from adjacent tracks can be mixed directly in the filtering stage of the processing.Processing algorithms that ensure an unbiased recovery of the longest wavelength components are described in some detail.

As airborne gravimetry matures as a technology, the major challenge remaining is to improve the accuracy and resolution of the measured gravity field. Errors in DGPS derived accelerations used for motion compensation are one of the main limitations. The standard method of determining aircraft acceleration is time differentiation of DGPS positions. In an effort to improve the quality of aircraft accelerations, an alternative method of deriving accelerations from DGPS is evaluated. The method, which was first presented by Jekeli (1994), estimates acceleration directly from GPS carrier phase measurements. It is revisited, with modification, and results in the gravity domain are presented for the first time.The carrier phase method is modified to utilize a least squares solution with a covariance model, to include all satellites available for a flight line.Using data from a strapdown airborne gravimetry campaign, gravity disturbance are estimated for the same input data with both the standard and modified carrier phase approaches. The results are compared and the effect of the carrier phase derived accelerations is shown.To assess the accuracy, results are compared to an upward continued reference field. The modified carrier method is shown to improve the estimated gravity disturbances, especially under turbulent flying conditions and during times of higher atmospheric activity. The results are discussed with respect to the requirements of exploration geophysics.

Gravity disturbances obtained from an airborne system are low-pass filtered with a certain cut-off frequency to minimize the high frequency errors. To use the filtered disturbances in geoid determination, the gravity signal coming from the topography should also be filtered to the same frequency. The cut-off frequencies that are used here are: 1/30, 1/60, and 1/90 Hz. The first purpose of this study is to investigate whether all the filtering frequencies can be used for geoid determination. Although filtering is essential for consistent treatment of the data, our second objective is to study the effect of not filtering the topographic gravity signal in a way that it is consistent with the filtering of the gravity disturbances. The last goal will be to evaluate the DTM resolution needed for computing a precise geoid from airborne gravity. To study the above objectives, we worked with data obtained from a strapdown INS/GPS gravimeter in September 1996 over the Canadian Rocky Mountains. Different DTM resolutions were tested. Geoid solutions from the three filtering frequencies and the geoid solution without filtering of the topographic signal were computed and intercompared. By comparing all solutions to an existing gravimetric geoid in the area, conclusions were drawn and recommendations were made on the appropriate use of filtering frequencies and DTM resolutions.

Regarding the rapidly growing airborne gravimetric database worldwide, an investigation to study efficient and stable geoid computations based on this type of data was assessed to be important. The efficiency and quality of results for different approaches and combinations with surface data are discussed. The data sets used are: 1) Airborne gravimetry in the Skagerrak acquired during the AGMASCO EU-project (MAS3-CT95–0014), 2) Marine gravity data in the Skagerrak extracted from the BGI database, 3) UEGN94 absolute gravimetric network data. The methods applied on these data sets to compute a regional geoid are: 1) collocation; 2) collocation with regularization; 3) approximation by radial multipole potentials, including point mass potentials. The concluding results of the investigation are: 1) collocation with regularization provides more accurate results than the standard collocation method using the same reproducing kernel, 2) higher stability of solutions is achieved by including absolute gravimetric network data, 3) the approximation by radial multipole potentials is recommended especially for fast computations of the geoid from airborne data without loss of accuracy. Comparisons of all achieved solutions of this study with the geoid model for the European Nordic countries show a good agreement (mean deviation ~ 0.5 cm; rms 5 – 6 cm). This noise level corresponds to an estimated geoid accuracy of better than 10 cm for the Skagerrak.

Airborne remote sensing provides a m potentially efficient way to monitor and map the ar cryosphere of the earth, especially in selected areas for pl climate-related change studies or ground truth for cl space missions such as IceSat or CryoSat. In this paper d we will describe a Twin-Otter based airborne gravity s and laser altimetry/scanning system being developed ai at KMS, and its use for mapping the ice sheet margins n of Greenland, as well as initial tests for mapping of fc sea-ice freeboard and thickness in the Arctic Ocean. v The laser system is based on a Riegl laser scanner and pl Optech laser altimeters, with roll and pitch from a fi Honeywell INS or a Greenwood IMU. The la performance of the system is evaluated against GPS in runway surveys and known surface heights, showing fc fits at the few-dm level in general. The system is also ar to be used for general detailed DEM determination v and evaluation in more temporate climates.Sea-ice freeboard surveys have been performed as piggy-back activities on airborne gravity surveys of the Greenland continental shelf regions, with derived geoid information providing an enhanced mean sea surface for ice freeboard estimation. The changing thickness of the Arctic Ocean ice pack is the major driver for ESA’s CryoSat mission, planned for launch in early 2004. Over land ice, the emphasis of surveys has been to provide reference DEMs for glaciological studies and evaluation of airborne SAR interferometry. Experiments in East Greenland show that airborne SAR interferometry, as implemented in the DTU-EMISAR system, has the potential to provide ice sheet DEM’s at accuracies approaching the 1 m-level r.m.s. in different types of snow facies zones, but with significant radar penetration in the dry-snow zone on the higher levels of the ice sheet.

The series of satellite missions flown over the past decade, together with the recently flown Shuttle Radar Topographic Mission (SRTM), has led to the creation of large databases of information, which are currently being transformed, into detailed Digital Elevation Models (DEMs) for relatively small areas, using both stereo and interferometric techniques. Whilst the high frequency information content means that these techniques can provide extremely detailed models of the topographic surface, distortions and vertical shifts can occur due to various combinations of instrument limitations, orbit mismodelling, shadowing and layover problems, incoherence effects, and the use of incorrect ground control points. Independent validation and assessment of these DEMs can be problematic over remote areas where the availability of public domain DEM data is extremely limited. Mosaicing of adjacent DEMs to create larger-scale coverage can also be complicated by the presence of distortions in the DEM data, even where the same technique has been used to generate the input models. This paper presents the results of a case study using land altimeter derived heights to assess and error correct stereo SAR and InSAR DEM data, as a first step towards creating an operational facility for validation of InSAR, stereo SAR and SRTM derived DEMs. The input DEM has been selected over varying terrain types to explore the potential and limitations of this technique.It is shown that a rule-based expert system can be used to both optimize the calculation of range to surface for different echo shapes, and to select the `best’ echoes for comparison. This allows the generation of an altimeter validation dataset of sufficient accuracy to enable the detailed assessment of stereo SAR and InSAR DEM data, over a variety of terrain types. The comparison between the Altimeter and DEM height datasets shows that both datasets agree at the 8–9m level. This level of agreement is obtained when comparison data over extreme terrain is excluded and the Altimeter dataset is optimized. This paper investigates the potential of altimetry for determining InSAR DEM errors.

The continuous downward continuation of the gravity field has been classified as an inverse, ill-posed problem. The practical evaluation of the harmonic Poisson downward continuation integral requires, however, the reformulation of the problem into discrete summations or convolution forms. Although this can be considered as regularization by discretization, it is not sufficient for practical downward continuation with current airborne data, because round-off errors and noise in the data are amplified. Sophisticated regularization, filtering or iteration methods have to be applied, which act on the signal to noise ratio and take the property of large sparse linear equation system into account during the downward continuation process.The numerical comparison of direct and indirect methods for solving the discrete, inverse Poisson integral is the topic of this paper. Using high-frequency synthetic data sets at a typical flight height and with a characteristic noise level, the performance of the different methods is evaluated with respect to the reference gravity field generated at the reference sphere. The result is a detailed characterization of the behaviour of the algorithms for large sparse systems and includes the investigation of their behaviour for different applications, such as geoid determination and resource exploration. The methods that showed the most promising results for the synthetic data set were also used on a real data set.

The determination of the earth’s exterior gravity field from noisy satellite observations lacks stability, due to the downward continuation process and due to data gaps. This property translates into an ill-conditioned least-squares problem. It is routinely solved after forming the normal equations and adding a constraint or covariance matrix which reflects the prior knowledge about the gravity field and accounts for regularization. In this contribution we investigate a modification: the use of Lanczos methods for the iterative solution of the problem, and, by controlled stopping and in combination with Tikhonov regularization, for suppressing the amplification of data noise. There are essentially two regularization parameters to be chosen properly: the Tikhonov parameter, and the number of iterations. Our simulations show that this can be done effiiciently by applying a cross-validation procedure on the satellite gravity data. However, further investigations are needed.

The development of procedures for the estimation of the gravity field from satellite gravity gradients is one of key problems in preparation of the GOCE mission to be launched in 2005. Different strategies are currently being developed and implemented. Standard least-squares estimation requires sophisticated algorithms in order to handle the huge number of observations and unknowns, the ill-conditioning of the normal matrix and the colored observation noise, just to mention some of the numerous challenging problems. Therefore, an approximation to the least-squares estimator has been developed, which significantly reduces the numerical costs but is non-optimal in the least-squares sense. This approach is known as time-wise semianalytical method. It has been used extensively for error propagation in mission design studies, and, in the course of the last years, has been extended to allow for the estimation of potential coefficients from measured gravity gradients. The objective of this research is to investigate the performance of the time-wise semi-analytical method. This question has become increasingly important since the time-wise semi-analytical method may also be used as quicklook analysis tool during the GOCE mission. As a quick-look tool it should be very fast compared to exact least-squares solutions but should also be sufficiently accurate. Results from very extensive and realistic simulations are presented and compared with the exact least-squares solution. The analysis shows that the semi-analytical solution does not differ much from the exact least-squares solution, but is a factor 2 – 3 faster. A further improvement by a factor 10 is achieved if the time-wise synthesis step is replaced by a combination of classical spherical harmonic synthesis using Legendre functions and 3D-interpolation.

Spherical harmonic expansions form partial sums of fully normalised associated Legendre functions [ALFs], which, for ultra-high degree and order (eg.~2700), range over thousands of orders of magnitude towards the poles. This causes existing recursion techniques for computing values of individual ALFs and their derivatives to fail. Alternatively, high degree synthesis is possible using Clenshaw’s (1955) method. Straightforward numerical principles govern the stability of this technique. Suprisingly, existing algorithms for computing ALFs and their first and second derivatives are easily modified to incorporate these same numerical principles. These modified recursions yield scaled ALFs and derivatives, which are then rescaled during final synthesis in Horner’s scheme. This new approach matched Clenshaw’s method for precision and effiiciency in numerical tests. Moreover, the new techniques have the benefit of simplicity, and thus ease of programming and v ersiati lity.

In general, large systems of linear equations cannot be solved directly. An iterative solver has to be applied instead. Unfortunately, iterative solvers have a notouriously slow convergence rate, which in the worst case can prevent convergence at all, due to the inavoidable rounding errors.Multi-grid iteration schemes are meant to guarantee a sufficiently high convergence rate, independent from the dimension of the linear system. The idea behind the multi-grid solvers is that the traditional iterative solvers eliminate only the short-wavelength error constituents in the initial guess for the solution. For the elimination of the remaining long-wavelength error constituents a much coarser grid is sufficient. On the coarse grid the dimension of the problem is much smaller so that the elimination can be done by a direct solver.The paper shows that wavelet techniques successfully can be applied for the following steps of a multi-grid procedure: Generation of an approximation of the proplem on a coarse grid from a given approximation on the fine grid.Restriction of a signal on a fine grid to its approximation on a coarse grid.Uplift of a signal from the coarse to the fine grid.The paper starts with a theoretical explanation of the links between wavelets and multi-grid solvers. Based on this investigation the class of operators, which are suitable for a multi-grid solution strategy can be characterized. Two numerical examples will demonstrate the efficiency of wavelet based multi-grid solvers for the planar Stokes problem and for satellite gravity gradiometry.

The GPS (Global Positioning System) radio occultation experiment onboard the German CHAMP (CHAllenging Microsatellite payload) satellite was successfully started on February 11, 2001. By the end of July 2001 about 16,000 occultations were recorded. More than 80% of the measurements could be processed to derive vertical profiles of atmospheric temperature and specific humidity. Throughout the measurement period GPS anti-spoofing mode was enabled. On average, about 230 globally distributed occultations per day were recorded. Their distribution shows a characteristic latitudinal dependence with maximum occultation density at polar regions and minimum density in the equatorial region. A statistical comparison of dry temperature profiles, derived from CHAMP measurements, and corresponding meteorological analyses shows excellent agreement between 8 and 30 km altitude. For the Northern hemisphere the mean deviation is <0.5 K with a standard deviation of <1 K between 12 and 25 km.A single difference technique was applied to the data analysis. The temperature difference for an individual profiile compared to the corresponding data, retrieved by double differencing, is <0.1 K below 20 km and <0.5 K below 35 km altitude.

The FOURIER mission (Adriani et al. 2001) has been selected by the Italian Space Agency, together with other 4 projects, for a feasibility study. Within the current year one of these will be selected to fly within the next 4 years. The primary goal of FOURIER is the development of a systematic and objective observational test of the predictive capabilities of climate models, as proposed by Goody (1998). This requires long-term climate benchmark observations that differ from those presently available. High accuracy, demonstrable with respect to international standards, is the primary requirement. Other important features follow from this requirement. At least two types of space measurement satisfy these criteria: refractivity retrieved by GPS microwave occultation data; and calibrated, resolved, thermal radiances. In Fourier mission it is foreseen to put on board both a GPS-GLONASS receiver and a spectral radiometer (the Planetary Fourier Spectrometer —PFS-) to perform just such a test. In the paper will be discussed how to compare and validate data which will be obtained with both instruments for the future mission. Essentially the “main drawback” is that: while the PFS points to nadir direction, GNSS occultations are retrieved just along Earth grazing directions. So only the occultations that occur along the spacecraft velocity direction are selected and benchmarking for calibration purposes.

The Zenith Total Delay (ZTD) parameters estimated in the GPS analyses are rather sensitive to the applied processing strategy.In this paper, we are focusing on the specific aspects of the post-processed (PP) and near real-time (NRT) GPS ZTD monitoring. We are studying the sensitivity of estimated ZTD to the network design, to the ambiguity handling and to the use of Earth Rotation Parameters (ERP) for the orbit modelling.The results were obtained using the NRT and PP analyses at the Geodetic Observatory Pecný (GOP) in the frame of COST-716 action (the European Co-operation in the Field of Scientific and Technical Research, http://www.oso.chalmers.se/geo/cost716.html).

GPS measurements from the EPN (EUREF Permanent Network) were used to monitor the ionospheric effects of a geomagnetic storm. A series of ionosphere maps were produced to present the spatial distribution of TEC. The dense network of GPS stations in Europe allows to obtain high spatial and temporal resolution of TEC. Our estimation technique provided TEC maps with 15min interval and with a spatial resolution of 150–350 km. As an example we analysed geomagnetic disturbances, which occurred during the month of September 1999. It was found that the storm essentially modified the ionosphere.Large and medium-scale structures were detected in auroral and subauroral ionosphere as well as at middle latitudes. The deep spatial TEC changes were caused by the occurrence of the main ionospheric trough, which during the storm moved in the direction of the Equator. During most of the disturbed period the ionospheric trough moved down to a latitude of about 50°N. Under these conditions horizontal gradients in the ionosphere essentially increased, what we attribute to the occurrence of the trough. Also we detected medium-scale structures, which decreased the spatial correlation of the ionosphere.

The operational potential of ground-based GPS data to the fields of climate and Numerical Weather Prediction (NWP) is demonstrated in the European COST-716 action. The best way hitherto for NWP is to assimilate Zenith Total Delay (ZTD), but in order to be useful the estimates must arrive within 1 hour and 45 minutes.To demonstrate this a trial was started in March 2001 involving several analysis centres, each processing a GPS network and delivering estimates of ZTD to a gateway at the UK Met Office in a standard meteorological data format. The network consists of 120 GPS stations in Europe, of which several are processed by more than one analysis centre. The algorithms, dataflow, formats and assimilation into Numerical Weather Prediction (NWP) models have been tested on 15 days of GPS data which were processed off-line, but to near-real time quality, for the period of June 9–23, 2000.In this paper we will focus on the achievements of COST-716, give an overview of the demonstration experiments and provide an outlook to future implementation of GPS data usage within operational meteorology and climate research.

Kinematic point positioning of a Low Earth Orbiter (LEO) using GPS data is one possibility to get precise orbit information. This approach is followed at the Astronomical Institute of the University of Bern (AIUB) as an alternative to the dynamical orbit determination. Kinematic point positioning allows to recover the trajectory of the LEO without making use of any a priori gravity field information. This may be very useful for gravity field recovery, in particular in view of present and upcoming satellite missions like CHAMP, GRACE and GOCE which all have an accelerometer on board.The emphasis of this paper is to study the effect of different data screening options on the quality of the kinematic orbit for a LEO. The impact of observations at low elevations in conjunction with elevationdependent weighting is investigated. The tests are carried out using data from SAC-C and CHAMP. Comparison with dynamic orbits of the satellites indicate that a kinematic LEO orbit at the decimeter accuracy level is feasible provided good code and phase GPS data is available.

The aim is to present and to examine an algorithm for the orbit analysis of a low-Earthorbiting GPS-tracked satellite to determine the spherical harmonic coefficients of the Earth’s gravitational field. By means of Newton’s interpolation scheme the accelerations acting on the satellite are derived from the satellite’s GPSpositions x(t _k ), y(t _k ), z(t _k ) or position differences Δx,(t _k-1 k), Δy(t _k-1 k), Δz(t _k-1 k). This is done in a quasiInertial Reference Frame to avoid frame accelerations. The acceleration vector is balanced due to Newton’s equation of motion by the gravitational force vector, namely the gradient of the gravitational potential. The coordinates of the gradient of the gravitational potential, which are given in a Cartesian representation, also have to be transformed to the quasi-Inertial Reference Frame. The resulting equation system is then solved by means of a Gauss-Markov model. In order to get a more stable solution for higher resolutions a regularization method (Tikhonov, Kaula) can be applied.

GPS meteorology has a potential of seamless sounding of refractivity from LEO (low earth orbit) orbit altitude to near Earth surface, and vertically above the land-based receivers. In GPS occultation technique, the LEO position and velocity are required with accuracy of 10 cm and 0.1 mm/s RMS, respectively [Rocken et al., 1997; Zhao, 1998] to retrieve temperature profile with accuracy of 1 K or better for higher altitudes. Even more stringent, from the operational standpoint, might be the need for nearreal time retrieval of atmospheric profiles for potential contribution of GPS/LEO data to operational weather forecasting.The Ohio State University is an IGS LEO/GPS Associate Analysis Center participating in the IGS LEO Pilot Study Project, studying the orbit determination in near real-time, to support atmospheric data retrieval from GPS/LEO occultations. In addition, the Center is a part of the NSF/UCAR SuomiNet GPS network, also supported by NOAA and Natural Resources Canada. This is a 16-station network, currently under implementation, located primarily along the shoreline of the Great Lakes, including Lake Erie shorelines bordering the State of Ohio. The stations, equipped with dual frequency GPS receivers and meteorological sensors, will be collocated with the NOAA tide gauges, and will support not only the atmospheric research but also the accuracy improvement of the International Great Lakes Datum (IGLD).The primary objective of this paper is to present the proposed procedures and techniques for the Center’s operations that will support the experiments in orbit determination, occultation data processing, as well as atmospheric data retrieval from LEO. In particular, we will focus on GPS/LEO precise orbit determination (POD) with special emphasis on triple difference (TD) kinematic approach. The triple difference technique, successfully applied to GPS POD, has already been presented by GrejnerBrzezinska [ 1995], Goad et al. [ 1996] and Kwon [ 1997]; we have now extended this method to LEO POD. Preliminary results of kinematic POD for the CHAMP satellite, and the atmospheric parameter retrieval using GPS/MET data are also discussed.

A method for kinematic precise orbit determination (POD) based on double-difference algorithms including ambiguity resolution has been developed and first results for the CHAMP satellite are presented here. We show that MelbourneWiibbena wide-laning together with a bootstrapping strategy for the narrow-lane ambiguity resolution is a promising method in double-difference kinematic POD of low Earth orbiters (LEO) using the ground IGS network and LEO spaceborne GPS receiver. The ambiguity resolution strategy has been checked by comparing the ambiguities of a kinematic with a reduced-dynamic narrow-lane bootstrapping based on a reduced-dynamic orbit parameterization. Moreover, results from simulated and real CHAMP SST data have been analyzed concerning the impact of ambiguity resolution.

Abstract. The interval approach is used to describe remaining sytematic errors in geodetic observations after several correction steps which are preceding the network adjustment. The interval extension of the least-squares estimator enables to propagate such effects to the estimated parameters, i.e. the coordinates of a geodetic network.In this paper an interval-based optimization concept with respect to the systematic effects is proposed. Following the classic network optimization strategies, concepts for a configuration and a weighting optimization are developed. In addition, variation of the interval radii themselves allows to reduce the impact of systematics on the coordinates. The resulting optimal networks are less sensitive to remaining systematic errors of the observations. An exemplary monitoring network is used to discuss the concept and to show numerical results.

The Ohio State University currently is developing a GPS/INS/CCD integrated system1 for precise (centimeter level) monitoring of highway center and edge lines. The positioning component of the system is based on a tightly integrated GPS/INS system, and the imaging component comprises a single down-looking, highperformance digital color camera. The high image rate provides sufficient overlap of the subsequent images at highway speed; therefore, stereo data processing is expected to be performed in real-time with the support of on-the-fly navigation solution.From the navigation standpoint, post processing of GPS/INS data provides more accurate orientation, a benefit of forward and backward trajectory processing, and precisely synchronized timing information. However, approximate navigation data available in real-time (e.g., the estimates of the motion between epochs, when consecutive images are taken, can provide camera orientation and especially the relative orientation estimates) can be used to support image matching on-the-fly, necessitating extracting and storing only the needed information, as opposed to the entire image (we are only concerned with simple linear features). Besides the motion, the attitude change between two image captures is of interest, since the quality of these estimates has a very strong impact on the search space, allowing for short computation times and making the whole concept feasible in real-time. Obviously, additional post-processing will further refine the positioning and orientation data extracted in real-time and will provide precise geo-referencing of the features. The technique of using navigation data to support OTF image processing adds more robustness to the system, allowing faster and more automatic data processing and saves storage space and processing time, because data acquisition is combined with the image pre-processing.

In a continuous GPS deformation monitoring scheme, any action taken generally relies on a description of the state of the process or events as given by GPS measurements. Timely and correct interpretation of the GPS data is essential to improved quality control, safer system operations, and reduction in the number of false alarms. Unfortunately, GPS data are contaminated by both random and systematic errors of unknown sources. Instrument failure, poor or uncalibrated instrumentation, receiver noise and multipath, all can contribute to data problems. Without proper pretreatment, the necessary interpretation is difficult, if not impossible. Data contaminated by outliers must be eliminated and noise levels reduced. In many cases, critical information occurs over a short duration, and hence is difficult to detect. Wavelets can be used to pre-process data in order to better locate and identify significant events. Combining this type of data pre-processing with multivariate statistics can generate useful insights into the problems of deformation monitoring, data analysis and data interpretation.Multivariate techniques can be used to identify process variability and to develop models for online monitoring and control. By comparing new observations with a reference model that describes normal variability, simple control charts can be constructed to detect data inconsistencies and processing problems. This paper extends these concepts by demonstrating that correlated output of multiple sensors such as GPS receivers, accelerometers, anemometers or temperature sensors can be significantly improved with pre-filtering of the time series signals using a median filter, and a time-scale decomposition using a multi-resolution wavelet function. After the data are filtered and decomposed, the multivariate statistical method of Principal Component Analysis is used to develop a deformation monitoring model.

The regular monitoring of structures often requires measurement of relative displacements, which may, in turn, be used to assess the structure’s stress and drift conditions during, for example, seismic events. The instruments most commonly used to monitor structural systems during earthquakes are accelerometers. However, accelerometers do not directly measure structural displacements. Recent advances in Global Positioning System (GPS) technology can provide a supplementary sensor which can directly provide displacement information in real time.The paper discusses the suitability of GPS for monitoring the dynamic response of the cablestayed bridge on Evripos Channel, in the island of Evia, Greece. The GPS technology applied to the monitoring of the Evripos bridge is discussed and issues regarding data collection are examined. A discussion on the GPS data processing strategies employed in this project is given and results regarding the dynamic characteristics and behaviour of the bridge in high frequency vibrating events are presented.

A multi-antenna GPS system was designed and applied mainly to the so-called ‘tideindependent’ bathymetric measurements. It aimed at improving the accuracy achieved by the traditional technique, in which the tidal observations required were made at the tide gauges along the coast. The attitude parameters of the vessel, estimated by the GPS system, can also be introduced to the corrections for the bathymetric measurements. The assessment using different correction modes, based on GPS solutions and applied to the bathymetric measurements, indicated that the measurement quality has been significantly improved by the tide-independent technique. The accuracy of bathymetric measurements has shown the improvement of up to 47%, and fully satisfied to the first-order standard of the international hydrographic survey. The offshore tidal observations, relied on the vessel-based GPS system, were also effectively made by the vertical component of the GPS solutions. The average agreement between the observations from the GPS solutions and tide gauge records has found to be better than 3 cm, based on the field tests carried out nearby the Hsinchu Harbor located at the northwestern coast of Taiwan.

The purpose of this paper is to expose some unresolved problems that were not encountered in the geodetic, operational research and/or statistical literature so far, were only recently brought out by the space geodetic techniques, GPS and (In)SAR, for example, and should be solved in order to rigorously assess the quality of precise positioning products. We first summarize the major features of GPS mixed integer observational models, which are essentially different from conventional geodetic observational models and demand different solution approaches. We then discuss three major classes of methods for GPS ambiguity decorrelation, and show a dilemma of it. Finally, we briefly outline some new questions in connection of GPS precise positioning.

The determination of a realistic variance model is still an important issue in GPS data processing. An a-priori model of the variances of the double differenced phase observations is set up using their measured signal-to-noise ratios (C/N₀). We present an adaptive variance model for GPS carrier phase observations (SIGMA-F) to be used with least squares estimation (LS). It is based on a fuzzy system which combines robust estimation and data quality assessment.The processing results obtained are more stable than the purely robust estimates, and they are more reliable than LS estimates using purely C/N₀-based weights. We present results using actually measured GPS data from two different projects. We show that SIGMA-F successfully mitigates biases with kinematic processing of short baselines.

Geographical Information System (GIS) is nowadays a key technology to handle spatial data (Burrough and McDonnell (1998)). Pattern recognition and image processing methods based on raster data are relevant to acquire spatial information belonging to GIS. Tough analyzing raster data is often time-consuming, template matching techniques are still indispensable in raster data processing. Applications in automatically detecting benchmarks or targets (photogrammetry, surveying) of cartographic and topographical images show its importance. By means of new approaches presented in this paper, template matching methods become more efficient and less processing time-consuming. Templates, well known from common matching techniques, will be completed with a knowledge base, which contains more information than only the geometric one. Fuzzy techniques like separating regions of different significance or the introduction of structural points, further a knowledge-based strategy to keep similar templates efficiently separate by means of alternative search are newly developed methods, which will be proposed here. For obtaining information we intend to use query languages. All these strategies are implemented in a software module of the ETH Zurich whose practical experiences can be presented.

Adjustment of geodetic data using coordinate-based formulations leads to rank-deficient Gauss-Markov models depending on the observation type. Among alternatives, minimum norm least squares solution (equivalently BLUMBE) is used to overcome this deficiency. In this study we examine further extensions of the minimum norm solution in the least-squares solution space, such as partial MINOLESS, which make use of a selection matrix. We derive Best Linear Minimum Partial Bias Estimation (BLIMPBE) via bias minimization from which partial MINOLESS can be obtained as a special case. We show, through an example, that BLIMPBE can be used effectively to control the contribution of the various parameters to the overall solution in the presence of model or observation biases.

During the evaluation of the observations in geodetic networks, detectability of a possible error in any observation and its effect on the unknown parameters of the so-called network is one of the most important measures of the reliability of that network.It is well known that the outliers in geodetic observations have bad effects on the unknown parameters to be estimated, and they cause artificial correlations between the entire data set. For this reason, before geodetic computations, all the outlying observations have to be detected and their effects on other observations and the unknown parameters have to be removed. However, for this goal, there are some different procedures currently performed, such as conventional outlier detection, robust estimation and last of all fuzzy theory.In this paper, conventional outlier testing, robust estimation and fuzzy techniques have been used to detect the outliers within a geodetic network and the results have been compared.

We have computed GPS time series of different resolutions in the Finnish permanent GPS network FinnRef. In the Lomb periodigrams we can distinguish an annual period (Mäkinen et al. 2000) but also a diurnal period. The annual period is visible in all components, including the computed baseline length between two stations. The amplitude of a period is a function of the baseline length, thus behaving like a scale error.The annual periods, which can be seen in almost all baseline lengths of the FinnRef network, are in phase for each baseline. It may indicate that some modelling error exists in the GPS computation. However, we cannot exclude a physical reason, i.e. an unmodelled crustal deformation that causes a network scale error. Therefore, a geophysical interpretation of annual variations in the height component of GPS time series must be attempted, though with caution.The annual period in the baseline lengths between the FinnRef stations can be found also in the GPS solutions made by the EUREF computing centre.We discuss on the etfect and possible reasons for periods, and tests made for studying and removing the periodicity.

In GPS data processing it is not uncommon to eliminate the presence of ionospheric delays by taking certain linear combinations of the carrier phase data. This approach is in fact equivalent to the processing of the original, not combined, L₁ and L₂ phase observations in which the ionospheric delays are modelled as unknown parameters. When using phase data only, the presence of the unknown ionospheric delays produces a rank defect in the model of observation equations. Eliminating this rank defect leads to the conclusion that not all of the original L₁ and L₂ ambiguities can be estimated as integers, but only a certain linear combination of them. In this contribution, it is investigated how this situation changes when triple-frequency, phase-only data of modernised GPS are used. We identify the integer rank defects, show which integer ambiguity combinations are estimable and determine their corresponding ambiguitv success-rates.

Multipath remains a major error source in both static and kinematic positioning. For example, it takes a toll in the carrier phase, causing the receiver to measure a distorted phase. Various improvements in receiver and antenna technologies, as well as modelling strategies, have resulted in better ways of coping with this error source. Multipath has been shown to be highly correlated for an array of closely spaced antennas. This fact has allowed various investigations using different antenna/receiver array configurations. In our investigation, we have used a configuration based on two closely spaced antennas linked to a single GPS receiver. Our methodology introduces a temporal factor in the measurements, with the assumption that multipath parameters and satellite geometry have a slow variation in time and space. This paper presents a spectral analysis, which intends to evaluate the performance of the multipath parameters estimation process. The analysis compares estimated multipath signal with the original input data that feeds the estimation process.

GPS systematic errors, such as multipath, ionospheric and tropospheric errors (or residual ionospheric and tropospheric errors after correction using some techniques) are the main error sources for high precision positioning applications. Efficient detection, identification and mitigation of systematic errors is the key to successful and reliable resolution of ambiguities and estimation of site coordinates.In this paper, an automatic test procedure, comprising detection and identification of GPS systematic errors is developed. Firstly, the Durbin-Watson test procedure is extended for the detection of GPS systematic errors. An approximate method to calculate the percentage points of the lower and upper bounds of the test statistic is then given for the identification of GPS systematic errors after significant systematic errors have been detected. Two GPS data sets are used to demonstrate the potential of this automatic test procedure.

Since its introduction to civilian users in the early 1980s, the Global Positioning System (GPS) has been playing an increasingly important role in high precision surveying and geodetic applications. Like traditional geodetic network adjustment, data processing for precise GPS static positioning is invariably performed using the least squares method, which requires both functional and stochastic models. A double-differencing technique is commonly used for constructing the functional model in order to account for systematic errors in the observations. In current stochastic models, it is usually assumed that all the one-way measurements have equal variance, and that they are statistically independent. The above functional and stochastic models have therefore been used in standard GPS data processing algorithms.However, with the use of such GPS data processing algorithms, systematic errors in GPS measurements cannot be eliminated completely, or accounted for satisfactorily. These residual systematic errors (remaining after double-differencing the observations) can have a significant effect on both the ambiguity resolution process and the GPS positioning results. This is a potentially critical problem for high precision GPS positioning applications. It is therefore necessary to develop an appropriate data processing algorithm, which can effectively deal with systematic errors in a non-deterministic manner. Recently, several approaches have been suggested to mitigate the impact of systematic errors on GPS positioning results: the semi-parametric model, the use of wavelets and new stochastic modelling methodologies. These approaches use different bases and have different implications for data processing. This paper aims to numerically compare the above three methods.

The length of day (LOD) values deduced from fossils and tidal deposits strongly suggest that the Earth’s despinning rate was on average about five times smaller in the Proterozoic than in the Phanerozoic. Moreover, these data indicate that between 250 and 100 million years ago, i.e. during Mesozoic there was a non-linear variation superimposed on the overall linear trend of the Earth’s rotation rate as a function of time. In order to understand these observations within a geodynamical framework, we investigated the variations throughout geological time of the oceanic tides, of tectonic plate speeds, and of geomagnetic paleointensities. In agreement with other authors, we found that in the Mesozoic, the geomagnetic moment underwent a minimum, but no statistically significant change could be inferred for the Proterozoic and the Archean. On the other hand, during the Mesozoic, concomitantly with the geomagnetic paleointensity minimum, the average oceanic tidal torque and the average lithospheric plate speeds, were significantly smaller than before and after this epoch.We partly ascribe the difference of the despinning rate in the Proterozoic and Phanerozoic to a more intensive mass redistribution within the Earth remote geological past. Less deep oceans and/or the exsistence of a supercontinent during most of the Proterozoic could also account for the observed LOD data. As far as the Mesozoic data are concerned, we show that they can almost certainly be explained by the tectonic regime of the epoch and the exsistence of the supercontinent Pangea. In any case, our work suggests that there exsists a complex interplay between geomagnetic, tectonic and rotational processes.

The effect of the superficial fluid layers (atmosphere and ocean) on the Earth rotation occurs by means of three torques: the pressure torque (or mountain torque) arising from a difference of pressure on the two sides of a mountain, the gravitational torque, due to the interaction between the Earth masses and the fluid masses, and the friction torque. For the equatorial component, the Earth bulge plays a very important role: there is a pressure torque acting on the equatorial bulge and a gravitational torque associated with the attraction of the Earth dynamical flattening (degree 2 order 0 form factor) by the fluid mass. Due to the large scale and the size of the bulge, this effect is dominant for the equatorial components of the torque. In all the atmospheric and oceanic Global Circulation Models (GCMs), the ellipticity of the Earth (and of its gravitational potential) does not appear explicitly in the equation/boundary conditions. It was already known from previous studies that the part of this torque due to the interaction of the fluid with the solid Earth is, nevertheless, to be accounted for in the angular momentum budget. In this paper, we extend this study to the additional atmospheric pressure torque due to the fact that the ocean surface is ellipsoidal, and show that this part is fully compensated by the Earth reaction to the associated ocean forcing. In the case of the ocean, we also discuss the source of this ellipsoidal torque geographically, using the output of the CLIO model.

Recently, Gross (2000) demonstrated that the Chandler wobble may be excited by a combination of oceanic and atmospheric processes during 1985–1996 using observational records and a general ocean circulation model. Aoyama and Naito (2001) suggest that the atmospheric wind and pressure variations by themselves maintain a major part of the observed Chandler wobble during the period 1983–1998. A coupled climate system model provides a synthetic climate record with temporal and spatial coverage not attainable with historical observational data, allowing for the evaluation of climate excitation of polar motion at longer timescales (such as the 30-year Markowitz wobble) and over a longer period. The U.S. Department of Energy’s Parallel Climate Model (PCM) has simulated the climate for 1870–1999 using historical atmospheric conditions. The ten historical simulations have been produced by varying the length of the spin-up. We present results of polar motion excitation from PCM oceanic, atmospheric, and hydrologie processes.

A 50-year time series of ocean angular momentum (OAM) is used to estimate the oceanic contribution to the excitation of the Chandler wobble. Our estimate of the oceanic excitation power, 18 mas2/cpy, is in good agreement with the residual excitation derived from a simultaneous use of polar motion and atmospheric angular momentum data, 21 mas2/cpy. Direct comparison of the OAM series and the inferred non-atmospheric excitation yields lower correlation and lower coherence at the Chandler frequency than in the study of Brzeziński and Nastula (2001) based on the shorter OAM series of Ponte et al. (1998). Differences in coherence levels are partly related to significant differences found in the two OAM series, indicating substantial dependence of OAM results on model and data assimilation procedures.

Time series of Earth Orientation Parameters (EOP) have been obtained from independent parallel Very Long Baseline Interferometry (VLBI) networks NEOS-A and CORE-A using OCCAM 5.0 software.This paper presents the results and their detailed consideration. The EOP time series are approximated by linear functions so offset and rate of the differences between the networks (NEOS — CORE) for the same epoch can be estimated. It appears that biases between two EOP systems are negligibly small in 1996–1997 years, but are increasing in time. The study is important to make up an accurate International Celestial Reference Frame (ICRF) and International Terrestrial Reference Frame.

Accurate Earth Rotation Parameter (ERP) series, determined from GPS solutions, allow the study of rapid variations in polar motion, including the detection of oscillations with periods shorter than 12 hours. In this paper, the GPS (CODE) polar motion series in the period 1997.5 through 2001.0 with a resolution of two hours is studied using Fourier Transform Spectral Analysis. The resulting spectra display clear oscillations with periods of 12, 8 and 5–6 hours and have somewhat variable amplitudes throughout the 3.5 years under consideration.To check any association between such high frequency polar motion oscillations and atmospheric forcing a temporally dense set of equatorial Atmospheric Angular Momentum (AAM) functions with a resolution of three hours is analysed for the year 1995. In this series oscillations at a period around 8 and 12 hours were detected in the computed spectra as well.

Nutation theory of the Earth with an atmosphere, an elastic mantle, a liquid outer and a solid inner core (SIC) is developed. The results are compared with the new IAU theory MHB2000. It is shown that disagreements of both theories with observations are less then 1 mas. New normal modes of the Earth are calculated. To complete the model, the theory accounts for the super-rotation of the SIC.

Global warming, by definition, changes the atmospheric temperature field . This temperature change is not expected to be uniform, either geographically, or with height in the atmosphere. By the thermal wind equation, changes in the poleto-equator temperature gradient will cause changes in the atmospheric zonal winds. Numerous previous studies have shown that observed length-of-day (LOD) variations on time scales of a few days to a few years are largely caused by atmospheric zonal wind fluctuations. In particular, seasonal variations in LOD have been previously shown to be dominantly caused by seasonal variations in the atmospheric zonal winds. Here, observed changes in the strength of seasonal LOD and wind-driven atmospheric angular momentum signals during 1962 to 2000 are analyzed and shown to be significantly correlated with each other and with the Southern Oscillation Index. This demonstrates that the observed seasonal LOD signal can be used as a proxy measurement for changes in the angular momentum of the seasonal zonal winds, thereby allowing changes in the seasonal zonal winds to be studied even when wind measurements are not available. In addition, the approach of studying decadal-scale changes in the strength of the seasonal cycle allows LOD measurements to be used in climate change studies, studies that cannot be undertaken directly due to uncertainties in modeling the dominant decadal-scale changes in LOD caused by core-mantle boundary processes.

The rotation of the Earth is affected by redistributions of masses in the atmosphere, the oceans and the Earth’s interior. In order to investigate its reaction on the combined effect of mass redistributions in these components a new gyroscopic model is being developed. The model is based on the balance of angular momentum, which can be described by the non-linear Liouville differential equation. Time-dependent circulation processes in atmosphere and oceans yield variations of the Earth’s tensor of inertia and relative angular momenta. The respective values are derived from both reanalysis data and model simulations. Some refinements concerning the shape of the Earth’s body and back-coupling mechanisms like rotational deformation are considered in the model. The results are derived numerically since the solution can not be given in analytical terms. Four different numerical solvers are tested to assess the reliability of the results. First results for polar motion and length of day variation are compared with the geodetic observations published in the series C04 by the International Earth Rotation Service (IERS).

As Very Long Baseline interferometry (VLBI) is the geodetic space technique which directly links terrestrial and celestial reference frames, it is particularly suitable to determine the Earth orientation parameters (EOP). Efforts have been made from several groups to derive the EOP with subdiurnal resolution. To avoid misleading interpretations it is worthwhile to study the quality of such highly resolved parameters from a statistical point of view focussing on standard VLBI observations and processing. Main subject of interest is the role of the observation configuration and of the chosen temporal resolution.The respective normal equations of the leastsquares parameter estimation are analyzed to illustrate the precision of the estimated EOP for different input scenarios. The correlations between individual EOP or parameter groups with influence on the EOP are studied. Eigenvalue decompositions are performed to check for structures in the precision of the parameters. The significance of the highly resolved EOP is tested using statistical methods. In the numerical part of the study, two representative VLBI networks (NEOS-A, CORE-A) are treated in detail. The VLBI data are processed using the software package OCCAM 5.0 LSM.

The Bulgarian tide gauges in the towns of Varna and Burgas have started working since 1928. The location of the two installations is described and a short analysis of the data is presented. The monthly and annual mean sea levels are revised using available benchmark datum history information.Data sets of atmospheric pressure and sea surface temperature during the same time span are also used to find the possible links between the sea-level variations in the two local regions and processes. The basic features of sea-level variations in the regions of the two tide gauges are analysed. A spectral analysis of the monthly tide records is performed both in time and frequency domain. The contributions of periodic components ranging between 8 and 19 years are attenuated using symmetric low-pass filters. The filtered series are subjected to spectral analysis through the Fast Fourier Transform method. The annual and semi-annual cycle and the longer-term variability are analysed and they show to be consistent over the area. The results indicate that the sea level of Varna and Burgas has linear trend of 1.4 ± 0.3 mm/year and 1.6 ± 0.4 respectively. No significant trends were found in the meteorological records. The effects of the local atmospheric pressure variations on the amplitudes of the annual sea-level changes are about 7% for Varna and 5% for Burgas of the amplitudes obtained after the effects are corrected. It is mentioned that the interannual variations in the sea level are related to river discharge of the Danube.

Seasonal and low-frequency variations in basin-scale mean sea level are studied for the period 1950 to 2000 by interpolating sparse tide gauge data to a global grid using empirical orthogonal functions (EOFs) of sea level variability determined from TOPEX/Poseidon (T/P) altimeter data. Results are based on data and with no long term trends. The fact that the results do not have secular trends is an artifact of the analysis, and should not be interpreted as an indication that sea level is not rising. Reconstructions using global EOF modes compare better with T/P for basin-scale averages than reconstructions based on basin EOF modes. An analysis of mean sea level in the North Pacific and North Atlantic suggests both basins have a significant trend in the mean annual amplitude over time and that the North Atlantic has a significant trend in the mean annual phase. It is also demonstrated that volume changes of the upper layer thickness in the tropical Pacific can be calculated from the reconstructed data with an accuracy comparable to other methods.

Variations in mean sea level are considered as an indicator for global as well as regional environmental change. The spatial distribution of sea level variations can be observed by satellite altimeters with a high precision. The sea level variations in the North Atlantic are studied in this paper by using eight years of sea level data derived from the TOPEX/Poseidon altimeter mission. The mean sea level change for this time period shows regionally remarkable differences and does agree only partly with the mean sea surface temperature change. The annual oscillation has a dominant contribution to the total sea level variability, but within the central Gulf Stream, eddy activity contributes even more strongly to the overall variability. After removing the annual and semi-annual oscillation and an alias period of the altimeter with the M2 tide, the residuals are smoothed by a moving 90 day mean filter and examined by Principal Component Analysis. A low frequency variation with an approximate period of 6-7 years as well as an anomalous sea level change at the end of 1995 have been detected. The analysis of sea surface temperature data also shows a similar long periodic and anomalous behaviour.

Altimetric sea-surface heights from the ERS-1, ERS-2 and TOPEX/Poseidon missions as well as tide gauge observations in the Baltic Sea area were used for comparisons with the output of a high resolution oceanographic model. The general agreement of the in-situ sealevel measurements and the sea-surface heights obtained from the model was investigated. Special attention was paid to the analysis of the temporal and spatial sea-level variability as well as sea-level extrema (high/low fill level, extreme sea-surface slopes).The observed and modelled sea-surface heights show a high correlation (above 0.8) . Extreme situations appear also as extremes in the model, yet the magnitudes of the variations are slightly underestimated by the model.Another aspect to be considered is the stationary sea surface. The mean sea-surface topography determined from satellite altimetry in combination with a regional geoid model was cornpared to the mean sea-surface topography that was derived from the oceanographic model. The well-known general behaviour of the Baltic Sea mean sea-surface is reflected in both solutions. However, a detailed comparison and the determination of features of small dimensions demands further investigations.

Unless accounted for, annual signals in geodetic data can significantly bias estimation of site velocities. For high accuracy applications, annual and semi-annual sinusoidal signals should be estimated simultaneously with site velocity and initial position. Minimum velocity bias is theoretically predicted at integer-plus-half years, as confirmed by tests with real data. Below 2.5 years, the velocity bias can bècome unacceptably large, and simultaneous estimation does not necessarily improve velocity estimates.

Results from GPS network of 42 stations measured in 1996, 1997, 1998 and 2000 and our geological studies indicate that Bulgaria can be separated into four major velocity “domains”: an Eastern Domain that does not move relative to Eurasia, a North-central Domain that moves to the NE, a South-central Domain that moves to the SSE, and a Western Domain that is the transition zone between the North-central and South-central domains. The boundary between the North-central and Eastern domains is a poorly defined zone of NW-trending shortening. The boundary between the North-central and South-central domains is a broad zone of N-S to NNE-SSW extension, with a total differential motion of 3-5 mm/yr. The extensional boundary follows the E-W trending Sub-Balkan graben system and Thracian basin of central Bulgaria. The zone of extension appears to continue into the Sofia graben and through a topographically low part of the Stara Planina Mountains. Both the GPS results and geological interpretation of active tectonics indicate that either N-S extension does not continue eastward to the Black Sea, or if it does continue eastward it has a very slow rate. The zone of extension in central and western Bulgaria marks the northern boundary of the Aegean extensional region. Velocities of 3-4 inm/yr to the south and 3 mm/yr to the ESE in south central Bulgaria, south of the extensional zone express a transition to the Aegean extensional region farther south.

Geodetic measurements in the Imperial Valley, southern California, show high strain rates and evidence of fault creep. In May of 1999 and 2000, we surveyed 46 GPS stations in a dense grid (half-mile spacing) along the Imperial Fault using rapid-static mode (15–20 minute occupations). Results indicate the Iimperial Fault is creeping at a rate of 9 mm/yr. The velocity field is asymmetrical across the fault and indicates a dipping fault plane to the northeast. Combining our results with far-field velocities from the Southern California Earthquake Center, we fit the data to a simple elastic dislocation model with 45 mm/yr of rightlateral slip below 10 km and creep from 200–800 m on a dipping plane (85°) to the northeast.North of the Salton Sea, where there is sparse GPS coverage, we used interferometric Synthetic Aperture Radar (InSAR) to determine the interseismic creep signature. Since the landscape over the cropland changes over short time intervals, forming useful interferograms can be challenging. We used permanent scatterers to improve coherence. These permanent scatterers are stable locations that provide estimates of phase, modulo 2πt, and serve to mask poorly correlated areas. Correlation estimates improved for shortbaseline (<100 m), long-timespan (3–8 years) interferograms in this region when using the Permanent Scatterers weighting technique.Results from 69 interferograms revealed a diffuse secular strain buildup, punctuated by two episodes of localized creep. These episodes coincide with the 1992 Landers and 1999 Hector Mine earthquakes and imply triggered slip from these two events. Profiles across this section of the fault show peak-to-trough amplitude ranging from 20 to 50 mm and the deformation pattern is consistent with a model where free slip occurs to a depth of 2 km.

This work analyzes recent crustal deformation and strain accumulations in continental China based on GPS and seismicity data. Since the early 1990s, several regional GPS networks for active tectonic studies were established in continental China. All of these networks were surveyed in campaign mode at one to two year intervals and have been conducted on a scale ranging from several hundred kilometers to a few of thousands kilometers. Each individual network was originally designed to address local problems without attempting to measure the large-scale deformation of continental China, and therefore can’t be merged together seamlessly, due to different data analysis strategies involved, to yield a uniform velocity field (Bannette, et al., 1999). The only realistic approach for a large-scale GPS solution to date is to merge the original observations from different regional networks into a coherent solution. According this strategy, a uniform velocity field in 1TRF97 frame on continental China scale was obtained (Wang, et al., 2001). It appears that Tibetan Plateau itself absorbs most of the deformation caused by collision and penetration between India and Eurasia. More than 80% of the relative motion is accommodated by convergence within the Plateau. The North China and South China blocks, east of the Tibetan Plateau move coherently at a rates of 10 to 14 mm/yr with respect to the stable EurasiaWe perform a joint inversion of seismicity data and 338 GPS velocities in continental China for a self-consistent velocity field, strain rate field. The model velocity field is expanded as bi-cubic spline interpolation functions defined within a 2° × 2° grid that covers the country and extends into the assumed rigid India and Eurasian plates to south and north. The inversion jointly minimizes the magnitudes of fitted strain rates and the misfit to the observed velocity data. The spline technique allows high spatial resolution of strain rate variations, especially in regions with spatially dense GPS data. Our results show that the maximum strain rate is located along the South-North tectonic zone, Chuan-Dian block, these are the most intensive neotectonic deformation areas in continental China.

The KSP network of the Communications Research Laboratory, a regional VLBI network around Tokyo, detected significant displacements from volcanic and seismic activities in the Izu islands, located 100-300 km from the network. A 13 0km baseline revealed a gradual shortening of 4.5 cm over two months. Of particular importance is that the real-time VLBI monitoring has been operational on a daily basis, which enables us to investigate the development of source activity. The finding also raises interesting questions. Can we model the far-field deformation in terms of dislocations buried in a homogeneous half-space ? May we safely neglect the earth's sphericity, stratification and self-gravitation? The Izu islands event provides us with a rare opportunity to answer these questions because it includes both tensile dislocation and shear dislocations. We compute horizontal displacements for several cases: (1) an elastic homogenous half-space, and (2) a radially stratified perfectly elastic earth. The two models give remarkably different results for tensile dislocation. The result clearly indicates that far-field displacement should be analyzed in the framework of spherical earth theory.

Altimeter data from the tandem mission of the European Remote sensing Satellites, ERS-1 and ERS-2, are used to study the validity of the Inverse Barometer (IB) correction on a near-global spatial-scale, and at time-scales as short as 2 days (Nyquist period) . IB regression coefficients calculated from differences between corresponding pairs of Sea Surface Height (SSH) anomalies and calculated Air Pressures (AP) from the two satellites yield departures up to -0.6 cm/mbar in the tropics. This magnitude of departure has previously been shown in an analysis of tide gauge data. In the tropics a clear trend is apparent, from the largest departures at short time-scales, to IB-like results at periods around 20–30 days. Outside the tropics the response behaves largely like an inverted barometer. Use was also made of a next pass analysis technique performed separately for ERS-1 and ERS-2, using data only during the tandem mission phase. The approximate sampling interval, is 16 days (32 days Nyquist period) for the ERS 35-day repeat cycle. Results also compare well to previous studies using tide gauge and numerical model data at these time-scales. Departures in the Southern Ocean are apparent in the ERS analyses though are not as large as results from TOPEX data.

The possibility of improving the estimation of the bottom topography of the Earth’s oceans using gravity data is investigated in two extended test areas. The first area is located in the Mediterranean Sea southwest of the island of Gavdos, Greece and bounded by 33° ≤ ø ≤c 35° and 15 ° ≤ λ 25°. The other one is across the Mid Atlantic Ridge bounded by 40° ≤ ø ≤ 50° and 330° ≤ λ ≤ 340°. The integrated inversion method of gravity data proposed by Knudsen is used in an attempt to improve our knowledge of the ocean bathyrnetry and its gravity response. The KMS99 satellite altimetry-derived global marine gravity field is used with a-priori statistical characteristics of depths in a least squares collocation procedure to produce new depths. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V9, are used to derive the depth apriori statistical information and to test how the gravity data can improve the depth estimation. Two- and threelayer models are used to represent the Earth’s structure. The improvement in the estimation of the bottom topography is investigated through an RTM reduction of shipbome gravity data and ERS l-GM satellite altimetry SSHs. Throughout this study, the EGM96 geopotential model complete to degree and order 360 is used as a reference field to model the low frequency part of the gravity field spectrum.

Reasonable estimates of altimetry regional accuracies can contribute to a better understanding of both geodesy and oceanography. The National Imagery and Mapping Agency (NIMA) has historically used its best marine gravity anomalies as ‘truth’ data to estimate the accuracy of altimetry gravity anomalies (Δgs). Altimetry gravity anomalies are not of uniform quality. A procedure is described for assigning regional accuracies to a set of altimetry 5’x5’ mean gravity anomalies. The method can be adapted to a wide range of quantities.A two source set of altimetry 5’x5’ mean anomalies is used to illustrate the procedure. It was computed from a combination of the Kort & Matrikelstyrelsen (KMS) KMS99 2’ Ags and the Goddard Space Flight Center (GSFC) GSFC00JDG 2’ Ags. The combination means matched the trut’h’ data more closely than means derived from either single source.Regions are characterized by using four factors strongly correlated to altimetry accuracy. Estimates based on comparisons with the ‘truth’ data are generalized to all such regions. The ‘truth’ set, computed from NIMA’s best marine gravity anomalies, is large and diverse. It should provide an adequate assessment for most types of regions.Depth is used to define areas of degraded quality such as shallow water, near-shore areas, and deep trench areas. The Litton/TASC “Gravity Field Roughness Map” is used to define regions of roughness defined by their spectral characteristics.The KMS99 “err” values and the GSFC mean sea surface height standard deviations are used to identify the regions where the altimetry quality is degraded by currents.Extensions and improvements are discussed.

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1,1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W₀ and the geopotential scale factor R₀= GM/W₀ (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W₀ = (62 636 856.160 ±0.002) m2·s_-2, R₀ = (6 363 672.544 8 ±0.000 2) m. The actual accuracy is limited by the altimeter calibration error (2–3cm) and it is conservatively estimated to be about ±0.5m2·s-2 (±5cm). The differences between the yearly mean sea surface (MSS) levels, came out as follows: 1993–1994: -(1.2 ±0.7) mm, 1994–1995: (0.5 ±0.7) mm, 1995–1990: (0.5 ±0.7) mm, 1996–1997: (0.1 ±0.7) mm, 1997–1998: -(0.5 ±0.7) mm, 1998–1999: (0.0 ±0.7) mm and 1999–2000 (0.6 ±0.7) mm. The corresponding rate of change in the MSS level (or R₀) during the whole period of 1993–2000 is (0.02±0.07) mm/y. The value W₀ was found to be quite stable (see table), it depends only on the adopted GM, ω and the volume enclosed by surface W = W₀. W₀ can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W₀ is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W₀ provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W₀, the semi-major axis a of the Earth’s general ellipsoid can easily be derived. However, an apriori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W₀ in the least squares sense and an ellipsoid which has the global geopotential average equal to W₀. It is demonstrated that both α-valwes are practically equal to the value obtained by the Pizzetti’s theory of the level ellipsoid: a = (6 378 136.7±0.05) m.

This study investigates the behaviour of satellite altimeter data in coastal regions in order to estimate a boundary around Australia’s coasts in which the altimeter range may be poorly estimated by on-board tracking software. These contaminated data are then retracked to give a preliminary improved result. Over one million ERS-2 (March to April 1999) and Poseidon (January 1998 to January 1999) radar altimeter waveform data were used in an area of 350 km off Australia’s shoreline. Using the 50% retracking point as the estimate of the expected tracker point, the ERS-2 and Poseidon missions do not exactly track at the ‘tracker point/gate’ in areas within 10 km off the shoreline. Using the standard deviation of the mean power of the returned waveforms as an indication of the general variability shows obvious coastal contamination out to ~4 km, and less obvious contamination out to ~8-10 km. The preliminary results from an iterative least squares retracking procedure show that retracking can extend the altimeter-derived sea surface height profile shoreward along ground tracks. Therefore, retracking appears necessary to correct the on-board estimates of the range measurements in coastal regions.

Long-term sea level change is important for a variety of environmental and socio-economic reasons, especially for the large portion of the world’s population who lives in coastal zones. Satellite altimetry now offers a unique opportunity for improving our knowledge about global and regional sea level change.TOPEX/POSEIDON (T/P) sea level observations and Reynolds AVHRR sea surface temperature observations over the most recent 8 years have qualitatively been used to study regional correlations between long-term changes in sea level and sea surface temperature. Long-term is here taken to be linear signals in the 8-year time period.Consistent increases in both sea level and sea surface temperatures are found in most parts of the Atlantic Ocean over this period. In the Indian Ocean and particularly the Pacific Ocean, the trends in both sea level and temperature are still dominated by the large changes associated with the El Nino Southern Oscillation (ENSO).Sea level changes over the most recent 8 years detected by T/P sea level observations are correlated with changes in the Reynolds AVHRR sea surface temperature observations with a global averaged correlation of 0.62. On regional scales this number becomes higher. Specifically, in the tropical part of the Pacific and Atlantic Ocean where the correlation computed over 20° latitude bands increases to 0.89.

The paper includes concise information on recent geodetic and geodynamic projects that are realised in international cooperation of the European countries in the frame of the scientific programme of seventeen countries assembled in the CEI (Central European Initiative) WG Science and Technology Section C “Geodesy”. The main achievements of the first phase of the international geodynamic project CERGOP (Central Europe Regional Geodynamics Project) are outlined. First phase of the Project CERGOP was concluded in June 1998. The establishment and maintenance of the Central European GPS Reference Network (CEGRN) consisting of 31 sites on the territory of 11 countries was performed with an accuracy of 2–4 mm in horizontal coordinates and 4–8 mm in vertical coordinates. The second phase of the Project CERGOP-2, now being realised, includes new member countries; the extension of the CEGRN results in accepting in total more than 60 CEGRN sites. Since 1994 six epoch five-day monitoring satellite GPS CEGRN campaigns were carried out in yearly intervals in 1994, 1995, 1996, 1997 (CERGOP-1) and 1999, 2001 (CERGOP-2). Another CEI project UNIGRACE (Unification of gravity networks in Central and Eastern Europe) consists in establishing seventeen absolute gravity stations covering the area from the Baltic Sea to Adriatic and the Black Sea forming the excellent frame for connection of all national gravimetric networks and providing the unified precise gravity frame in Central and Eastern Europe.The programme of activities of the Section C Working Group on Satellite Navigation Systems and actions realised by the Working Group on University Education Standards are summarised. The cooperation links between CEI WGST Section C “Geodesy” and EGS (European Geophysical Society) as well as IAG (International Association of Geodesy) are outlined.

This paper describes the evolution of the scientific cooperation in the field of geodesy in Central and Eastern Europe from 1956 to 1990 and attempts an evaluation of the effect and some result. The cooperation was performed multilaterally, since the sixties coordinated by the commission “KAPG” of the academies of sciences and within the program “Interkosmos”. It promoted the scientific activities of the geodesists in the context of geophysics and space research. Main fields were: investigations on recent crustal movements, absolute and relative gravity measurements, research on earth tides, polar motion and time variations, use of satellites for geodesy and geody-namics. Enormous effort was devoted to the standardization and the modernization of the equipment. Remarkable results could be achieved in the field of theory. The cooperation promoted the interdisciplinary work. The geodynamic aspects became early one of the main themes of the geodetic research. The most outstanding person in the cooperation was Yu.D. Boulanger, Corr. Member of the USSR Academy of Sciences and also President and Honorary President of IAG; he deceased in 1996. Prof. Dr. A.G. Massevitch, Astronomical Council of the USSR Academy of Sciences, deserves deep appreciation of her great part to use satellite tracking for geodesy and geophysics.

After the second World War the Hungarian geodetic and land survey basis (control nets, map systems) were incomplete. The possible frames for geodetic activity and for development were limited by the formation of the socialistic regimes in East European Countries.In the fifties the Hungarian National Survey was required to take part in conversion of the Hungarian agriculture and in the arrangements of constructions for socialistic industry. Later, the formation of Warsaw Pact brought the opportunity (and necessity) for establisment of new geodetic control nets (both triangulation and levelling as well as gravimetric nets).Because surveying activity (triangulation, levelling and gravimetry) spreaded over the hole territory of European socialist countries, and because of necessity of unified technology (mainly because of the military interest) there has been established in Sofia (1952) the Co-operational Organization of National Surveys of the participant countries (CONS). At the beginning the range of duties of CONS was the coordination of the works and preparation of plans; after that technology development and development of new up-to-date instruments had also role in the co-operation.Some years later the academies of sciences of the participant countries established astronomical, then geophysical—geodesical comissions for research (1NTERCOSMOS, KAPG).

The epoch GPS observations performed in the framework of the Central Europe Regional Geodynamics Project are used for estimation of coordinates and velocities of monitored sites. The coordinate estimates and their covariance matrices from individual campaigns performed from 1994 to 1999 are combined in the complex model enabling to estimate besides the coordinates, velocities and transformation parameters also systematical parameters, as site eccentricities and antenna phase center positions. The horizontal velocities of selected reliable 24 sites are used for deformation analysis of Earth’s crust in Central European region. We apply the analytical surface deformation theory for evaluation of surface dilatation (or depression) and orientation and magnitude of maximum elongation (compression). The results obtained show the stability of northern part of Central Europe (deformations up to 2mm/100km/year) and structured distribution of horizontal deformations in the southern parts of the region with both dilatation and depression up to 4mm/100km/year.

What will be the scientific issues of geodesy in the coming decade? Naturally, it is impossible to give an accurate answer to this question. However, an attempt can be made to look into the future based on some trends of the past. During the past three decades geodesy underwent fundamental changes, mainly due to the potential that became available through modern space techniques. As a result, geodesy is today able to provide a whole range of novel results of immediate importance to earth sciences; in some sense, due to this development, geodesy itself became a discipline of earth sciences. In the following, it is tried to provide a sketch of future challenges for geodesy based on an analysis of these changes of the recent past. The main challenge is the realisation of an integrated global geodetic observing system. It requires the connection in one well defined terrestrial reference frame of the three fundamental pillars of geodesy — geometry, earth rotation and gravity/geoid — with a relative precision of I part per billion and consistent over decades. To meet this objective a series of theoretical and practical problems is still to be solved. However, with such a system geodesy would take a very central position in earth system sciences.

The sphere of influence of space geodesy is ever enlarging, with impressive achievements in the last few decades in many diverse areas (such as geodynamics, planetary and atmospheric sciences, oceanography, tectonics, and ice studies). Earth system studies have made major advances with the advent of accurate space geodetic techniques with high temporal resolution and the increasing availability of complementary geophysical data. Examples include positioning at the millimeter level, enabling determination of crustal deformation and strain with unprecedented accuracy at high time resolution; water vapor monitoring via GPS; and improved gravity modeling and orbit determination, permitting an unparalleled view of the 1997–1998 ENSO event. The new millennium holds even more promise, with many planned developments, such as GOCE, GRACE, and ICESAT missions, densification of GPS networks, and the development of new technologies. This paper will highlight recent geodetic advances and their interdisciplinary impact with a vision towards the future.

In the first paragraph an attempt is made to clarify what is the meaning of theoretical geodesy by comparing it with theoretical physics. In the second paragraph an analysis is performed to identify the specific character of theoretical geodesy, culminating in the definition of a standard model of geodetic data analysis. In the third paragraph five examples are presented of unsolved theoretical geodetic problems. A short conclusion follows.

This document describes the IAG Review after the completion of the work of the IAG Review Committee. It should be viewed as the Explanatory Supplement for the new International Association of Geodesy’s (IAG’s) Statutes and ByLaws, which were adopted by the IAG Council at the 2001 Scientific Assembly in Budapest on September 7, 2001. The motivation for the review is developed in section 2. The essential steps of the Review process are summarized in section 3, the key elements of the new Statutes and ByLaws are contained in section 4. The continuation of the review process is briefly addressed in section 5.

IAG projects are a key element of the proposed new structure of the International Association of Geodesy (IAG). IAG projects should be of broad scope and of highest interest and importance for the entire field of geodesy.