Gerhard Beutler

Earth Gravity Field from Space — From Sensors to Earth Sciences

Foreword. How to Climb the Gravity Wall R. Rummel. I: Precise Orbit Determination and Gravity Field Modelling. Strategies for Precise Orbit Determination of Low Earth Orbiters Using the GPS U. Hugentobler, G. Beutler. Aiming at a 1 cm Orbit for Low Earth Orbiters: Reduced-Dynamic and Kinematic Precise Orbit Determination P.N.A.M. Visser, J.van den IJssel. Space-Wise, Time-Wise, Torus and Rosborough Representations in Gravity Field Modelling N. Sneeuw. Gravity Field Recovery from GRACE: Unique Aspects of the High Precision Inter-Satellite Data and Analysis Methods G. Balmino. Global Gravity Field Recovery Using Solely GPS Tracking and Accelerometer Data from CHAMP C. Reigber, et al. The Processing of Band-Limited Measurements: Filtering Techniques in the Least Squares Context and in the Presence of Data Gaps W.-D. Schuh. II: Solid Earth Physics. Long Wavelength Sea Level and Solis Surface Perturbations Driven by Polar Ice Mass Variations: Fingerprinting Greenland and Antarctic Ice Sheet Flux M.E. Tamisiea, et al. Benefits from GOCE within Solid Earth Geophysics A.M. Marotta. The Potential of GOCE in Constraining the Structure of the Crust and Lithosphere from Post-Glacial Rebound L.L.A. Vermeersen. Deep and Shallow Solid-Earth Structures Reconstructed with Sequential Integrated Inversion (SII) of Seismic and Gravity Data R. Tondi, et al. Present-Day Sea Level Change: Observations and Causes A. Cazenave, et al. III: Ocean Circulation. Global Ocean Data Assimilation and Geoid Measurements C. Wunsch, D. Stammer. Resolution Needed for an Adequate Determination of the Mean Ocean Circulation from Altimetry and an Improved Geoid C. Le Provost, M. Bremond. Error Characteristics Esimated from CHAMP, GRACE and GOCE Derived Geoids and from Satellite Altimetry Derived Mean Dynamic Topography E.J.O. Schrama. Estimating the High-Resolution Mean Sea-Surface Velocity Field by Combined Use of Altimeter and Drifter Data for Geoid Model Improvement S. Imawaki, et al. Combined Use of Altimetry and In Situ Gravity Data for Coastal Dynamics Studies K. Haines, et al. Feasibility and Contribution to Ocean Circulation Studies of Ocean Bottom Pressure Determination C.W. Hughes, V. Stepanov. Impact of Geoid Improvement on Ocean Mass and Heat Transport Estimates P. Le Grand. How Operational Oceanography can Benefit from Dynamic Topography Esimates as Derived from Altimetry and Improved Geoid P.Y. Le Traon, et al. IV: Geodesy. Remarks on the Role of Height Datum in Altimetry-Gravity Boundary-Value Problems F. Sacerdote, F. Sanso. Ocean Tides in GRACE Monthly Averaged Gravity Fields P. Knudsen. Tidal Models in a New Era of Satellite Gravimetry R.D. Ray, et al. The Elusive Stationary Geoid M. Vermeer. Geodetic Methods for Calibration of GRACE and GOCE J. Bouman, R. Koop. V: Sea Level. Benefits of GRACE and GOCE to Sea Level Studies P. Woodworth, J.M. Gregory. What Might GRACE Contribute to Studies of Post Glacial Rebound? J. Wahr, I. Velicogna. Measuring the Distribution of Ocean Mass Using GRACE R.S. Nerem, et al. Monitoring Changes in Continental Water Storage with GRACE S. Swenson, J. Wahr. VI: Future Concepts. Attitude and Drag Control: An Application to the GOCE Satellite E. Canuto, et al. On Superconductive Gravity Gradiometry in Space S. Zarembinski. Satellite-Satellite Laser Links for Future Gravity Missions P.L. Bender, et al. Possible Future Use of Laser Gravity Gradiometers P.L. Bender, et al. MI

High‐frequency variations in Earth rotation from Global Positioning System data

Using the data of the global, dense Global Positioning System (GPS) network established by the International GPS Service a continuous, uninterrupted series of subdaily Earth rotation parameters (ERPs) with a time resolution of 2 hours has been generated at the Center for Orbit Determination in Europe. The series starts in January 1995 and has a length of more than 3 years. Starting from the 2-hour ERP values of this, to our knowledge, unique time series, the high-frequency variations in Universal Time (UT1) and polar motion (PM) due to ocean tides are studied and a set of sine and cosine coefficients is estimated for all the major tidal terms at nearly diurnal and semidiurnal frequencies. The GPS series is not very homogeneous (various processing changes during the 3 years) and still short compared to the length of very long baseline interferometry (VLBI) and satellite laser ranging (SLR) data sets. However, the results derived from this series are already of the same quality as the results from VLBI and SLR. A comparison of the tidal coefficients stemming from all three space-geodetic techniques shows an agreement on the 1 μs level for UT1 and 10 microarc seconds (μas) for PM, respectively. The RMS difference between the ocean tide amplitudes estimated from GPS data and from TOPEX/Poseidon altimeter data amounts to 0.7–0.9 μs in UT1 and 9–13 μas in PM. The residual spectrum that remains after the removal of all tidal terms has a noise level of ∼5–10 μas in PM and 0.5–1 μs in UT1 and contains nontidal signals (up to 55 μas in PM and 3 μs in UT1) that might be due to the impact of the satellite orbit modeling (12-hour revolution period of the satellites) or, alternatively, due to atmospheric or oceanic normal modes.

Combining the orbits of the IGS Analysis Centers

Currently seven Analysis Centers of the International GPS Service for Geodynamics (IGS) are producing daily precise orbits and the corresponding Earth Orientation Parameters (EOP). These individual products are available at several IGS Data Centers (e.g. CDDIS, IGN, SIO, etc.). During 1993 no official IGS orbits were produced, but the routine orbit comparisons by IGS indicated that, after small orientation and scale alignments, the orbit consistency was approaching the 20 cm level (a coordinate RMS), and that some orbit combination should be possible and feasible. An IGS combined orbit could provide a precise and efficient extension of the IERS Terrestrial Reference Frame (ITRF). Another advantage of such a combined orbit would be reliability and precision.Two schemes of orbit combinations are considered here: (a) the first method consists of a weighted averaging process of the earth-fixed satellite positions as produced by the individual Centers; (b) the second method uses the individual IGS orbit files as pseudo-observations in an orbit determination process, where in addition to the initial conditions, different parameter sets may be estimated. Both orbit combination methods have been tested on the January 1993 orbit data sets (GPS weeks 680 and 681) with an impressive agreement at the 5 cm level (coordinate RMS). The quality of the combined orbits is checked by processing a set of continental baselines in two different regions of the globe using different processing softwares. Both types of combined orbits gave similar baseline repeatability of a few ppb in both regions which compared favorably to the best individual orbits in the region.

CODE’s five-system orbit and clock solution—the challenges of multi-GNSS data analysis

This article describes the processing strategy and the validation results of CODE’s MGEX (COM) orbit and satellite clock solution, including the satellite systems GPS, GLONASS, Galileo, BeiDou, and QZSS. The validation with orbit misclosures and SLR residuals shows that the orbits of the new systems Galileo, BeiDou, and QZSS are affected by modelling deficiencies with impact on the orbit scale (e.g., antenna calibration, Earth albedo, and transmitter antenna thrust). Another weakness is the attitude and solar radiation pressure (SRP) modelling of satellites moving in the orbit normal mode—which is not yet correctly considered in the COM solution. Due to these issues, we consider the current state COM solution as preliminary. We, however, use the long-time series of COM products for identifying the challenges and for the assessment of model-improvements. The latter is demonstrated on the example of the solar radiation pressure (SRP) model, which has been replaced by a more generalized model. The SLR validation shows that the new SRP model significantly improves the orbit determination of Galileo and QZSS satellites at times when the satellite’s attitude is maintained by yaw-steering. The impact of this orbit improvement is also visible in the estimated satellite clocks—demonstrating the potential use of the new generation satellite clocks for orbit validation. Finally, we point out further challenges and open issues affecting multi-GNSS data processing that deserves dedicated studies.

The role of GPS in the study of global change

Abstract The Global Positioning System (GPS) may be used today as a mature technique in geodesy and geodynamics. Thanks to the orbits, the Earth orientation parameters, and the coordinates and velocities of about 100 IGS (International GPS Service for Geodynamics) stations, which are made available to the scientific community on a daily basis, GPS is a very powerful and serious contributor to all scientific questions related to high accuracy positioning on and near the Earths surface. In this article we first give a short characterization of the GPS (as compared to other space-geodetic techniques like VLBI and SLR). The difficulties related to GPS-determined station heights are subsequently discussed, in particular in view of the necessity to model tropospheric refraction. In studies related to Global Change as, e.g., sea level monitoring, and postglacial rebound, station heights and their development in time are of particular interest. It is known for a long time, however, that GPS-derived station heights are not of the same quality as GPS-derived horizontal positions. It is thus much more delicate to extract vertical (as opposed to horizontal) movements from GPS time series. When looking at station heights on a global scale, the motion of the Earths crust, defined by the tracking sites, relative to the center of mass of the Earth has to be taken into consideration in order to correctly interpret the relative movement of the crust and the sea level. This “motion of the geocenter” may have a size of up to a few centimeters. Solar radiation pressure acting on the GPS satellites is difficult to model due to the complicated shape of the spacecrafts and may affect the geocenter estimates derived from GPS data. GPS may contribute, however, to monitoring the time variations of the geocenter. The influence of the troposphere on the GPS signals is not just a nuisance, it may be used as a signal, too. GPS may be used as an accurate instrument to measure the integrated water vapor above the GPS sites. Long time series of water vapor values from a dense global network may eventually reveal trends in the water vapor content of the atmosphere. Last but not least, we discuss the importance of the IGS, its global products and the densification project, for Global Change investigations.

Integrated scientific and societal user requirements and functional specifications for the GGOS

As discussed in the previous chapters, the terrestrial reference frame is the foundation for virtually all space-based and ground-based Earth observations. Through its tie to the celestial reference frame by the time-dependent Earth rotation parameters it is also fundamentally important for interplanetary spacecraft tracking and navigation. Providing an accurate, stable, homogeneous, and maintainable terrestrial reference frame, celestial reference frame, and the Earth rotation parameters linking them together is one of the essential goals of GGOS. In recent decades, the geodetic techniques also contribute to the database of Earth observations in particular related to mass transport, dynamics, and ionosphere and troposphere parameters. Observations of changes in the Earth’s geometry (solid Earth surface, sea surface, lake surfaces, and ice surfaces) are an important contribution to the Earth observation database serving a wide range of applications. In this chapter, the requirements of the diverse set of scientific and societal users concerning the terrestrial and celestial reference frames, the associated Earth rotation parameters, and the complementary gravity measurements are first summarized. Subsequently, the requirements in terms of a number of quantities observed by geodetic techniques or determined in geodetic analysis are compiled. The tasks, products, and specifications of the GGOS that are needed in order to meet the most demanding requirements of the users are then presented.

AIUB-GRACE02S: Status of GRACE Gravity Field Recovery Using the Celestial Mechanics Approach

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

Integrated Global Geodetic Observing System (IGGOS): A Candidate IAG Project

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.

A new solar radiation pressure model for GPS

Abstract The largest error source in GPS orbits is due to the effects of the solar radiation pressure. Over the last few years many improvements were made in modeling the orbits of GPS satellites within the IGS. However, most improvements were achieved by increasing the number of estimated orbit and/or solar radiation pressure parameters. This increased number of estimated satellite parameters weakens the solutions of all estimated parameters. Due to correlations, the additional parameters may cause biases in other estimated quantities like, e.g., the length of day. In this paper we present a recently developed solar radiation pressure model for the GPS satellites. This model is based on experiences and results acquired at the Center of Orbit Determination in Europe (CODE) in the context of its IGS activities since June 1992. The new solar radiation pressure model outperforms the existing ROCK models by almost an order of magnitude. It also allows a reduction of the number of orbit parameters that have to be estimated.

Combining consecutive short arcs into long arcs for precise and efficient GPS Orbit Determination

AbstractThe final products of theCODE Analysis Center (Center for Orbit Determination in Europe) of theInternational GPS Service for Geodynamics (IGS) stem fromoverlapping 3-day-arcs. Until 31 December, 1994 these long arcs were computedfrom scratch, i.e. by processing three days of observations of about 40 stations (by mid 1995 about 60 stations were used) of the IGS Global Network in our parameter estimation program GPSEST. Becauseone-day-arcs have to be produced first (for the purpose of error detection etc.) the actual procedure was rather time-consuming.In the present article we develop the mathematical tools necessary to form long arcs based on the normal equation systems of consecutive short arcs (one-day-solutions in the case of CODE). The procedure in its simplest version is as follows:Each short arc is described bysix initial conditions and a number of dynamical orbit parameters (e.g. radiation pressure parameters). The resulting long arc in turn shall be based onn consecutive short arcs and described bysix initial conditions and again the same number of dynamical parameters as in the short arcs..By asking position and velocity to be continuous at the boundaries of the short arcs we obtain a long arc which is actually defined by one set of initial conditions andn sets of dynamical parameters (ifn short arcs are combined)..By asking the dynamical parameters to be identical in consecutive short arcs, the resulting long arc is characterized by exactly the same number of orbit parameters as each of the short arcs.This procedure isnot yet optimized becauseformally all n sets of orbit parameters have to be set up and solved for in the long arc solution (although they are not independent).In order to allow for an optimized solution we derive all necessary relations to eliminate the unnecessary parameters in the combination. Each long arc is characterized by the actual number of independent orbit parameters. The resulting procedure isvery efficient. From the point of view of the result the new procedure iscompletely equivalent to an actual re-evaluation of all observations pertaining to the long arc. It is much more efficient and flexible, however because it allows us to construct 2-day-arcs, 3-day-arcs, etc. based on the previously stored daily normal equation systems without requiring much additional CPU time.The theory is developed in the first four sections. Technical aspects are dealt with in appendices A and B. The actual implementation into the Bernese GPS Software system and test results are given in section 5.