Refinement of
the Current Observation Requirements
for GOCE.
ESTEC Contract 13229/98/NL/GD
Final Report.
November 1999.

Table of Content,

1. Introduction.
List of Authors
  1.1. Executive Summary.
  1.2. Project Management.

2.Monte Carlo Gravity Field Simulator .

3. Refined observation requirements.
  3.1 Oceanography
  3.2. Geodynamics
    3.3. Geodesy
    3.3.1. Height systems
    3.3.2. Influence on levelling by GPS
    3.3.3. Influence on inertial navigation
    3.3.4. Sea-level changes
    3.3.5. Influence on ice-mass balance
    3.3.6. Improvement in depth-estimation

4. Conclusion.

5. References.

Authors of this report are:

Professor C.Chr.Tscherning, University of Copenhagen, Denmark (Main contractor, Editor),

Senior Scientist Ole Andersen, Kort og Matrikelstyrelsen, Denmark, KMS,

Professor Demitris Arabelos, Aristotele University of Thessaloniki, Greece,

Dr. Eugenio Carminati, University of Miliano, Italy, (UM),

State Geodesist Rene Forsberg, (KMS),

Dr. Annalisa Gardi (UM),

State Geodesist Per Knudsen , (KMS),

Stud.scient. Jens Nykjśr Larsen, (KMS),

Professor Roberto Sabadini, (UM) and

Senior Scientist Gabriel Strykowski, KMS.

1. Introduction.

1.1. Executive Summary.

In this report is presented a study of the refinement of the current observation requirements of the European Space Agency (ESA) Gravity and Ocean Explorer Mission (GOCE). We have studied in more detail than already done (cf. ESA, 1996) the relationship between the precision of a gravity field model and the solution of different tasks, where the gravity field plays a major role.

The quality of a gravity field model can be expressed through a variance-covariance matrix of the spherical harmonic coefficients. From this matrix the precision of derived quantities like geoid undulation differences and gravity anomalies can found by covariance propagation. Information about such a matrix is available from earlier spherical harmonic models and recent simulations. However, the use of covariance propagation is only feasible if there exist a simple linear relationship between the coefficients and the quantity to be determined. Since this is not the case for most of cases we want to investigate, we have instead used the diagonal part of the matrix (the variances) to construct a Monte Carlo type gravity field simulator, which was used to generate N (typically 50) sets of geoid or gravity values for an area or for a set of points. The simulator also had the possibility of taking into account that the gravity field variation changes from area to area. Using this, we have calculated the result of solving typical tasks in three fields, oceanography, geodynamics (including glaciology) and geodesy, for each set of gravity and/or geoid heights. This gives (1) a lower bound for the observation requirements and (2) shows whether gravity field data may be used to discriminate between different hypotheses (especially in geodynamics).


In order to carry out these tasks a project team was formed of experts in these three fields, see Section 1.2 and the list of authors.

The first task (described in Chapter 2) was the creation of the Monte-Carlo type simulator of spherical harmonic coefficient induced errors in geoid or gravity anomalies. The spherical harmonic fields, EGM96 (complete to degree 360) (Lemoine et al., 1997) and GPM98 ( complete to degree and order 1800) (Wenzel, 1998) was used as the "true" gravity field, and the simulated fields were perturbations of these fields. A random number generator was used to generate perturbations with given standard deviation per spherical harmonic degree.

In Chapter 3 is described how the simulated fields have been used to solve a number of specific tasks. The result is expressed (as far as possible) as the ratio between what today is possible with EGM96 and what will be possible with results from the GOCE mission. However, the quality of EGM96 seems to be too optimistic in a number of areas such as the areas with major currents. But this does not influence the values of the results using simulated GOCE errors.

The Chapter is divided in 3 sections according to the above mentioned areas, and subdivided into specific tasks, where gravity and/or geoid heights are to be used:


It is investigated how an improved geoid ( + altimetry) can improve estimates of dynamic ocean topography. The improvement depends on to which extend a level of no motion (the geoid) can be defined. The relationship between the improvements of the geoid and the errors in current velocities obtained using the geostrophic assumption are calculated. Originally only three different areas were to be studied, where the current velocities are high, medium and low. However global computations have been done. Also results on improvements in estimates of volume transport are given.


Examples are given of typical tasks where improved gravity field information may improve the discrimination between different possible processes inside the Earth. An area covering Central Italy with good models of the rheology variations was selected. The important result is that gravity results from GOCE, but not e.g. EGM96, can be used to discriminate between the different hypotheses. Obviously the gravity field of Italy is well surveyed, so the results show how we in un-surveyed areas may be able to answer important questions related to possible earth-quake or land uplift/subsidence related for example to post-glacial rebound.


First the results of a study of the influence of the errors in spherical harmonic coefficients on the establishment of a world-wide height system are described. The geoid-height difference precision was calculated for various distances and in various scenarios (high, medium high and low gravity field variation). In general a factor between 5 and 10 improvement can be expected from GOCE as compared to EGM96.

The influence on levelling by GPS was studied in 3 scenarios: areas with small, medium and large gravity variations. An improvement similar to the one found for the height system connections were found.

The influence on inertial navigation was studied under various scenarios. The error due to velocity errors (which depend on the quality of the gravity field model) were integrated for various supposed tracks. Results for low-speed applications (ships, air planes), medium speed (commercial air crafts) and high speed applications (rockets, missiles) are given. The improvement is expressed in terms of the position error at the final destination.

The influence on the separation of steric from non steric sea-level fluctuations is studied. This was done by integration of longer-wavelength phenomena..

The influence on ice-mass balance is studied by evaluating the possible improvements in depth of ice estimates in Greenland.

An investigation not described in the original work-statement was defined during the study: Improvements on depth estimates of the ocean (bathymetry). Here depth estimates have earlier been made from ERS-1 geodetic mission data. However, these estimates are incorrect in areas with larger sea-surface topography variations. GOCE gravity may aid in improving the estimates in e.g. the areas of the large currents, where there typically also are large bathymetric variations.

The result are in general that a factor of between 2 and 10 can be obtained using GOCE as compared to EGM96. A number of important geodynamics investigations can only be made when GOCE results becomes available.

The low value of 2 occurs in situations where another ESA mission, ERS-1, has collected detailed sea surface heights, which subsequently were converted to gravity anomalies. These gravity anomalies are, however, erroneous in areas with larger currents or close to the coast. The global gravity model, EGM96, with which we have made our comparisons has error variances which only to a minor degree reflect this.

On the continents the existing gravity data is sparse or of bad quality as shown in the analysis

related to the construction of the Monte Carlo gravity Field simulator. This is here where we

maybe will have the most significant results from GOCE: a better understanding of earth-quake mechanisms and the tectonic origin of sea-level changes. And for geographical areas where many people are living.

The improvement in results in geodesy are spectacular. Often a probable ten-fold improvement is documented. This will make GPS-levelling possible in areas outside Europe and North America, where the existing geoid information is scarce. In Europe and North America the geoid determination will be improved.

'1.2. Project Management.

As described in the Request for Quotation, RFQ/3-9292/98/NL/GD ESA has requested a study of the refinement of the current observation requirements of the GOCE Mission to be executed. The Contract was awarded to a consortium lead by C.C.Tscherning, University of Copenhagen (UCPH). The partners in the consortium were: National Survey and Cadastre, (Denmark), (in Danish: Kort & Matrikelstyrelsen (KMS)) and the University of Milano.

Contract management was handled by Mrs. Henriette Hansen, Department of Geophysics, UCPH. The kick-off of the project took place on Nov. 1, 1998. Work on the task described in Chapter 2 started immediately afterwards. Progress reports were given at several GOCE Mission Advisory Group Meetings, notably on Dec. 14, 1998. E-mails were send out, as soon as new results became available stating the URL of the relevant documents.

The signed contract was received from ESA Jan. 25, 1999. Throughout the project a close contact has been maintained between the project manager and the ESA representative, J.Johannesen. A final presentation was given in ESTEC on June 23, 1999, where a draft report was presented. The present report is a revised version of this report.

A project home-page was established immediately after the kick off at (,

This page has been used as an important communication and coordination tool during the whole project.

Minutes of meetings have been posted on the home-page, together with progress reports and items for discussion. Nearly all documents have been available on electronic form throughout the project life-time.