Gravity Field Determination by Satellite Gravity Gradiometry
Karl Heinz Ilk
Institut of Theoretical Geodesy
University Bonn

1 Objectives

The necessity of a high-resolution satellite borne gravity field mission was defined already in 1969 in the so-called Williamstown Report by the leading geo-scientists at that time. The idea was to derive the gravity field and positions at the earth’s surface and in space consistently at the same level of precision. For various technological as well as political reasons such a mission could not be realized within the last thirty years despite the intensive work of many individual scientists and scientific groups and the International Association of Geodesy (IAG) as a whole.

Occasionally the IAG General Assembly in Boulder, USA, in 1995 a Special Commission SC7 to Section II - Advanced Space Technology - had been established to create a forum that integrates all international activities related to gravity field determination by satellite gravity gradiometry and to prepare the conditions for a future mission. In detail, the Special Commission shall
represent IAG interests in such a mission on a political level,
support a gravity gradiometry mission by scientific studies,
investigate scientific and commercial applications of a very precise high resolution gravity field,
assist in coordination and definition of national and international concepts related to gravity gradiometry,
act as advisor to national and international bodies responsible for such a misssion,
inform the geodetic community about all these activities.
2 Activities

To make the work of the Special Commission as effective as possible and to integrate all interests to meet these ojectives a steering and advisory committee and various task groups have been created, as
Ad hoc group "Scientific objectives",
CIGAR-IV Study Group,
STEP-Geodesy Working Group,
Working Group "Application of Boundary Value Techniques to Satellite Gradiometry".
To inform the geodetic community about the relevant activities, a homepage has been created, accessible from the IAG homepage and via the homepage of the University Bonn „http://www.geod.uni-bonn.de".

There were various reasons that the work of the Special Commission was not as effective than formerly expected. The main reason is that it turned out to be very difficult for a group with only advicing function to influence national organizations to support a certain satellite borne gravity mission. Around the year 1995 the common opinion was that only a dedicated satellite gravity gradiometry mission could provide a gravity field which meets the demands of the community. In the following years since 1995 the situation changed in so far as the cheaper satellite-to-satellite tracking concept was more succesful in being realized. In the next section the development during the past four years is sketched.

3 The past years

End of the eighties a mission concept, based on the French GRADIO instrument, the so-called ARISTOTELES mission, was discussed in detail. In 1995 it was decided GPS/ ARISTOTELES not to follow up further on. The next realistic chance to place a geodetic gravity field mission emerged with the definition of a proposal to test the equivalence principle, fundamental for Einstein’s Gravitational Theory. This so-called STEP mission was proposed as a candidate for the Medium Size Programme M2 as a joint ESA/NASA project. It was proposed again for M3 as a sole ESA project. The STEP geodesy experiment was designed to consist of a one-axis superconducting gravity gradiometer with an expected accuracy of . The experiment was finally planned to be combined with multi high-low SST. In spring 1996 STEP was not recommended as M3-mission - only a so-called MiniSTEP or GeoSTEP should be realized, most probably as a joint NASA/ESA project.

After the year 1992 a number of „intermediate" mission concepts were proposed. They should „bridge" the past and future in gravity field research - and they should be cheaper than the mission proposals before. This is the programmatic idea behind the French mini-satellite concept BRIDGE. It was a CNES project and was considered to be based on SST/GPS or DORIS. Improved technology, in the main parts already available as existing sensors and commercial spacecraft components, and therefore cheaper than expected before gave a new fresh impulse to the idea of a future satellite gravity mission. These are the main criteria of the so-called „small satellite mission" concepts. Additional cost-reducing actions are the decision to reduce quality standards and test efforts. A further cost reducing factor is the availability of the Global Positioning System (GPS) or any other precise satellite navigation system as GLONASS. By these systems the high altitude component of a high-low SST configuration is provided - and a relatively cheap possibility to determine precise orbits.

The high-low mission concept based on GPS and a LEO (Low Earth Orbiter) were applied in the past for Topex/Poseidon, GPS/Met and the Explorer platform. Consequently, the high-low SST links are generally integrated in current mission concepts. Furthermore, it can be shown that SST and SGG are complementary techniques for detecting the gravity field: the long wavelength part can be improved by (high-low but also low-low) SST and the high-frequent part can be detected best by SGG. Therefore, current promising mission concepts consist of a combination of both, high-low SST and SGG or high-low SST and low-low SST. In the former case a low platform carries a gravity gradiometer (preferably a full tensor component gradiometer) and a system of high altitude satellites observes the low earth orbiter. In the latter case the low-low SST configuration is linked to the high altitude satellites of a precise satellite navigation system (GPS and/or GLONASS). Even if the small satellite mission concepts are not able to provide the very high accuracies and resolutions necessary for some applications in the geo-sciences they could decisively contribute to a gravity field improvement.

During the last years, a series of concepts were proposed; some of them were considered as low cost missions, e.g., the American proposals GRACE, COLIBRI or HUMMINGBIRD, or the German project CHAMP. Typically, the gravity field sensitive spacecraft were planned to be equipped with GPS receivers and accelerometers. A recent proposal is SAGE (Satellite Accelerometry for Gravity field Exploration). It is an Italian mission concept aiming at determining the gravity field of the earth by the high-low SST mode based on very accurate acceleration and position measurements. In case of the mission concepts GRACE and TIDES the relative motion of two small free-flying spacecrafts is planned to be measured. TIDES (Tidal Interferometric Detector in Space) is based on laser doppler interferometry using ultra-stable lasers. The concept consists of two small free-flying spacecraft in tandem formation about 500km apart and in near-circular orbit. The surface forces are considered to be compensated or measured and taken into account afterwards. Other mission concepts were based on satellite gravity gradiometry for deriving the high frequency part, eventually equipped with GPS receivers to enable satellite-to-satellite tracking to improve also the long wavelength part of the gravity field, as e.g. the American mission concept GEOID or ESA’s Earth Explorer Mission candidate GOCE. GEOID (Gravity for Earth, Ocean, and Ice Dynamics) was a spaceflight mission proposed by GSFC and based on the University of Maryland’s superconducting gravity gradiometer. These concepts can be considered as dedicated gravity missions. They have the potential to improve high frequent features of the static part of the gravity field up to a degree of 200 of a spherical harmonics expansion or even more - but they are expected to be more expensive and do not fulfill the criteria of small satellite missions.


4. The present situation

After careful selection procedures two mission concepts were successful and will be realized in the coming years: CHAMP, a German multi-sensor satellite mission with international contributions and GRACE, a combined high-low/low-low SST mission as a joint American-German mission. The European SGG - mission concept GOCE has a realistic chance for realisation and is under intensive preparation.

In early 2000, the German geoscientific small satellite CHAMP (Challenging Mini-Satellite Payload for Geophysical Research and Application) will be brought into a nearly circular orbit with an inclination of  at an altitude of about 400km. In a five years mission the observation system will provide earth system related data with yet unattained accuracy. The following main tasks are envisaged:
measurement of the stationary and time variable part of the global gravity field in the medium and long wavelength frequency range,
measurement of the global magnetic field and its temporal variations,
sounding of the atmosphere and the ionosphere.
The satellite mission will be carried out by DLR (German Space Agency) and GFZ (GeoForschungsZentrum) Potsdam. Of special importance of this mission is the fact that the first time in the history of satellite geodesy important earth related data will be collected at the same time for a time span of five years on a low altitude platform:
precise intersatellite measurements between the low satellite CHAMP and the high GPS satellites (high-low SST with a range accuracy of ),
accelerations along three axis to determine the surface and inertial forces of CHAMP (accuracy of acceleration: ),
orientation measurements by star sensors and by various GPS antennas,
radio occultation measurements between CHAMP and the GPS satellites,
measurement of scalar and vector magnetic field strengths,
measurement of the electrical field by ion drift meter,
precise earth bound (two-color) laser ranging,
altimeter measurements between CHAMP and the sea/ice surface by nadir oriented GPS antenna.
The measurement accuracy of the GPS receivers and the altitude of CHAMP between 300 to 500km enables a spatial resolution of the gravity field of approximately 500km. The expected accuracy of the corresponding spectral range is by a factor ten higher than realized in the present gravity field models. That means that the geoid can be determined with an accuracy of one centimeter for wavelengths down to 1000km.

The American-German mission GRACE (Gravity Recovery and Climate Experiment) will open the door to a further improvement of the gravity field with respect to accuracy and resolution. GRACE is a follow-on mission to CHAMP. The mission will consist of two identical CHAMP satellites without the boom where the magnetometers are placed in case of CHAMP. The intersatellite range-rates in along-track direction between the low satellites (at an altitude of about 400km) will be measured with -accuracy. The high-low links to the GPS satellites will have a comparable accuracy as planned for the CHAMP mission. With these measurement accuracies it will be possible to determine the medium and long wavelength part of the geoid down to 500km wavelengths with an accuracy of about . These are two orders better than in case of CHAMP. The launch of GRACE is planned for the year 2001. CHAMP and GRACE will have a parallel mission period of approximately two years. The parallel missions with different orbits will enable additional experiments which will lead to a synergetic effect of both missions. The tasks of GRACE are directed to the:
determination of the static part of the global gravity field with unattained accuracy in the medium spectral range; geoid accuracies of  for a resolution of  and of for a resolution of can be expected,
determination of the time variability of the gravity field in two to four weeks temporal resolution; the accuracy of the change of the geoid in the size of  can be expected,
sounding of the atmosphere and the ionosphere.
The GRACE low-low SST mission and the GPS-GRACE high-low SST test system will provide valuable earth related observables over a mission period of five years:
precise along-track intersatellite measurements between the low satellites of GRACE (low-low SST) in the size of few  and a mutual distance of both satellites between 200 and ,
precise relative measurements between the GRACE satellites and the GPS satellites,
accelerations along three axis to determine the surface and inertial forces of CHAMP (accuracy of acceleration: ),
radio occultation measurements between the low satellites of GRACE and the high GPS satellites at the setting and rising phase,
GOCE (Gravity Field and Steady-State Ocean Circulation Explorer Misson) is one of the candidates to become the first Earth Explorer core mission. It is a high resolution gravity field mission concept and will open a completely new range of spatial scales of the earth’s gravitational field spectrum down to 100km wavelength. GOCE is planned to be launched in a nearly circular sun-synchronous orbit with an inclination of  at an altitude of around 250 km, carrying a
dual frequency combined GPS and GLONASS receiver called GRAS (for its utilisation as GNSS receiver for atmospheric sounding), and a
three-axis gravity gradiometer, either an ambient temperature instrument with a precision of about  for the diagonal components of the gravity tensor, or a cryogenic gradiometer with a performance raughly one order of magnitude better, furthermore a
star tracker to control the orientation of the gradiometer with an accuracy of about , and an
equipment to keep the satellite motion drag-free.
The excellent evaluation of this mission concept under nine mission proposals of ESA’s Earth Explorer Mission programme justifies the hope that also this mission will be realized within the coming decade.

5 The future

CHAMP, GRACE and GOCE have the potential to revolutionize the knowledge of the system earth. Not only the static part of the gravity field can be determined with unattained accuracy also an eventual time dependency can be derived. Despite the fact that all three missions have the potential to measure the gravity field by sort of relative measurements between free falling sensors, they are not redundant. Indeed, the characteristics of high-low SST, low-low SST and SGG are rather complementary than competitive SST is superior in the lower harmonics below degree and order 50 to 60. A mission like GRACE, therefore, is optimal for studying time-varying gravity effects at moderate wavelengths. The static part of the gravity field up to approximately degree 50 can be expected with high accuracy. A condition to detect temporal effects is a corresponding mission duration of several years. Satellite gradiometry is superior for obtaining high spatial resolution from a moderate mission length. A recent study by ESA showed that increase of measurement precision or decrease of altitude results in a clear gain of spatial resolution in case of SGG, while this effect is very moderate in case of SST. A SGG mission like GOCE is superior in the short wavelengths parts of the gravity field up to a spherical harmonics degree of 250. The results of a mission like GOCE start to be better than those of a low-low SST mission from degree 60 to 80 on. A high-low SST mission like CHAMP can provide an improvement in the knowledge of the gravity field of approximately one order of magnitude over present models for wavelengths between 400 to 2000km.

One should be aware of the fact that the coming years will represent an enormous challenge for the geo-sciences. First of all with respect to the measurement and the processing procedures. Typical for the future satellite missions is the fact that they are not just point masses moving free within the gravity field as in the past. Instead they are multi-purpose observation and test systems on low flying platforms. Various different observables are collected parallel over years providing valuable information of the system earth. The first time in history it is possible to investigate the interactions of the potential fields of the earth. Challenging questions are related to the
formulation of balance equations for the various model parameters of the static and temporal parts of the gravity field,
development of models to take into account the fact that the three-dimensional orbits are measured together with atmospheric data, atitude control data (by star sensors) and accelerations in three directions to eliminate the surface forces,
data verfication, calibration and combination procedures based on existing terrestrial measurements and available models, and
tackling the inverse geophysical/geodetic models based on time series of the gravity field and the ionosphere, collected over a time span of severeal years.
Satellite measurements can provide unprecedented views of the earth's gravity field and its changes with time. Together with complementary geophysical data, satellite gravity data represent a "new frontier" in studies of the system earth. It can be expected that the work of Special Commission 7 can be more successful in the coming years than in the past. Indeed, the data available in the next future will attract many groups with different analysis concepts. In that case SC7 might have the chance to support the international exchange of ideas and to draw the greatest possible benefit out of these data.

6 Selected Literature ASI: SAGE, Phase A Final Report, International Geoid Service, Milano, Nov. 1998

Bills, B.G. and Paik, H.J.: GEOID mission: Gradiometer Views of Static and Dynamic Gravity Signals, presented at: AGU Spring Meeting, Baltimore, May 1996

Canavan, E.R. and M. Vol Moody: GEOID Mission: Instrument and Error Budget, presented at: AGU Spring Meeting, Baltimore, May 1996

Chao, B.F., Colombo, O.L. and P.L. Bender: Global Gravitational Changes and The Mission Concept of TIDES, presented at: AGU Spring Meeting, Baltimore, May 1996

Clark, T.A., Skillman, D.R., Bauer, F.H., O’Donnell, J.R., Pavlis, E.C., Liberman, D.I. and F. Bisiacci: COLIBRI: A Low-cost Spacecraft Design for Gravity Change Studies, presented at: AGU Spring Meeting, Baltimore, May 1996

Davis, E.S., Melbourne, W.G., Reigber, Ch., Tapley, B.D. and M.M. Watkins: GRACE: An SST Mission for Gravity Mapping, presented at: AGU Spring Meeting, Baltimore, May 1996

ESA: Geophysical Interpretation of High Resolution Gravity Field Information, Final report, 1991

ESA: Gravity Field and Stead-State Ocean Circulation Mission, Reports for Assessment: The Nine Candidate Earth Explorer Missions, ESA SP-1196(1), ESA Publications Division, ESTEC, Noordwijk, 1996

ESA: European Views on Dedicated Gravity Field Missions: GRACE and GOCE, European Space Agency, ESD-MAG-REP-CON-001, May 1998

GOCE: Gravity Field and Steady-State Ocean Circulation Mission. Reports for Assessment, The Nine Candidate Earth Explorer Missions, ESA SP-1196(1), 1996

Müller, J., Sneeuw, N., and R. Rummel: Problems and Prospects of the Planned Gravity Missions GOCE and CHAMP, this volume, Oct. 1996

NASA: Geophysical and Geodetic Requirements of Global Gravity Field Measurements (1987-2000). Report of a Gravity Workshop at Colorado Springs, Geodynamics Branch, 1987

NRC: NRC (National Research Council): Satellite Gravity and the Geosphere. National Academy Press, Washington D.C., 1997

Paik, H.J.: Superconducting Gravity Gradiometers on STEP, in: R. Rummel and P. Schwintzer (eds.), A Major STEP For Geodesy, Report 1994 of the STEP Geodesy Working Group, Munich, Potsdam, Nov. 1994

Pavlis, E.C., Clark, T.A. and B. Bills: Gravity Modelling With the Hummingbird Constellation, presented at: AGU Spring Meeting, Baltimore, May 1996

Pavlis, E.C., Lemoine, F.G., Olson, T.R., Rowlands, D.D. and J.C. Chan: Earth Gravity Model Improvement From GPS Tracking of Topex/Poseidon, GPS/Met and Explorer Platform, presented at: AGU Spring Meeting, Baltimore, May 1996

Reigber, Ch., Kang, Z., König, R. and P. Schwintzer: CHAMP - A Minisatellite Mission for Geopotential and Atmospheric Research, presented at: AGU Spring Meeting, Baltimore, May 1996a

Reigber, Ch., Bock, R., Förste, Ch., Grunwaldt, L., Jakowski, N., Lühr, H., Schwintzer, P. and C. Tilgner: CHAMP Phase B, Executive Summary, Scientific Technical Report STR96/13, GeoForschungsZentrum Potsdam, Potsdam, Nov. 1996b

Rim, H.J., Schutz, B.E., Abusali, P.A.M., Nam, Y.S., Poole, S.R., Ries, J.C., Shum, C.K. and B.D. Tapley: The Contribution of GPS Data to Modern Gravity Model Improvement, presented at: AGU Spring Meeting, Baltimore, May 1996

Rummel, R., Sneeuw, N. and J. Müller: Geodetic Requirements and Prospects Study of Gravity Explorer Mission Requirements (A Simulation Study), Technical Note, prepared for DASA, Dornier Satellitensysteme GmbH, München, Sept. 1995

Shirron, P., DiPirro, M., and S. Castles: GEOID Mission: Spacecraft and Dewar Design, presented at: AGU Spring Meeting, Baltimore, May 1996

Sneeuw, N.: Global Gravity Field Error Simulations for STEP-Geodesy, in: R. Rummel and P. Schwintzer (eds.), A Major STEP For Geodesy, Report 1994 of the STEP Geodesy Working Group, Munich, Potsdam, Nov. 1994

Sneeuw, N., Rummel, R., and J. Müller: The Earth’s Gravity Field from the STEP Mission, Class. Quantum Grav. 13, A113-A117, 1996

Sneeuw, N. and K. H. Ilk: The Status of Spaceborne gravity field mission consepts: a comparative simulation study, in J. Segawa, etal. (eds): Gravity, Geoid and Marine Geodesy, IAG Symposia Vol. 117, Springer, Berlin, etc., 1997

Williamstown Report: The Terrestrial Environment. Solid-Earth and Ocean Physics, Application of Space and Astronomic Techniques. Report of a Study at Willliamstown, Mass, to the NASA, 1969.