University of Copenhagen
Department of Geophysics.
C.C.Tscherning. 16 April 1999
Contribution to: WP 1 progress report "Overall scientific data strategy".
Definition of the full framework of scientific product extraction as a preparation for the
use of the space-wise approach.
1. Definition of the full set of COCE observations.
1.1. Satellite-to-satellite tracking (SST).
The basic observations are pseudo-ranges and phases of the L1 and L2 signals received from
the GPS and GLONAS satellites. A 1 s sampling is assumed. The mean precision of the
pseudo-ranges must be given. (They will probably be constant).
To this comes the precise position of the satellites (from IGS), as well as of GOCE itself.
The positions must be given in an earth fixed conventional system (CTS), or a similar Earth
fixed system valid for a given time period. The positions should be given as Cartesian
coordinates (X, Y, Z) with associated standard deviations. The velocity vector of the
satellites is also needed.
The mean error of the quantities must be given.
The data should be tested by forming range rate rates and comparing these rates with
directional derivatives of a reference potential, such as EGM96.
1.2. Satellite Gravity Gradiometry. SGG.
We will expect to obtain derivatives Vij of the gravity potential (V). The derivatives will not
be point values, but will be filtered mean values along the orbit in a fixed period. The
characteristics of the filter must be given (e.g. as weights associated with a time difference).
The values must be given in E.U. with 3 significant digits.
The derivatives must be given in a satellite fixed frame, and the standard error of the filtered
values must be given. Along-track correlations must be known or estimated, see Arabelos &
If all the diagonal terms are known (Vii, i=1,3), it is possible to check immediately if the data
are consistent. The data should also be tested by computing anomalous values (i.e. Tij = Vij -
Uij, where Uij is a reference potential, such as EGM96).
The standard errors of the random signal must be given as calculated from ground based
The attitude of the SGG instrument must be given as observed by the star-trackers with a precision better than 10". The actual mean error must be given. The attitude should make it possible to relate a satellite fixed frame to an earth fixed.
Instrument drifts and rotations must be given, or estimated using ground gravity.
2. Definition of the full set of external information.
2.1. Global digital terrain models.
In order to improve the reference potential used to compute anomalous values, digital terrain
models (DTM) can be used. The global models, however, contain very large errors, which
makes them very difficult to use. For regional modelling, however, a regional remove-restore
procedure can be used, see Arabelos and Tscherning (1990, 1995).
Such models should be given as mean heights of blocks of size 15' or smaller. (A 5' DTM is
The use of a DTM can be enhanced using actual densities and depths of compensation. If this
information is available, it should be used.
However, another consideration is to use a first calculated GOCE potential function as a
reference function. This would enable a self consistent pre-smoothing of the gravity
2.2 Ground or airborne gravity data.
The gravity data will be used in combination with the satellite data in refined regional
solutions and for the calibration by upward continuation as described in Arabelos &
The ground data must be on the GRAVSOFT-standard form (Tscherning et. al., 1994), i.e.
Identifying number, latitude, longitude (in decimal degrees), altitude (or depth of ocean),
free-air anomaly or gravity disturbance, standard error of the anomaly or disturbance. The
coordinates must be given in WGS84. The height, however, must be the height above mean
sea level for gravity anomalies and ellipsoidal heights for gravity disturbances. The gravity
anomaly or disturbance must refer to the IGSN71 system. The error estimate should include
the effect of both the coordinate uncertainty and the gravity measurement.
For the airborne data additional information is needed:
Azimuth of flight direction, and the characteristics of the filter used on the raw data, see e.g.
Tscherning et al. (1998).
2.3. Data from sister missions.
Data from CHAMP or GRACE are basically SST data, and must be treated as such.
2.4. Tidal information.
The tidal forces, which are above instrument noise level must be calculated. In general we
expect the tidal effects originating from the Earth will be below noise level.
3. Frames and interfaces for the treatment of the data.
The measurements will be converted to anomalous quantities by linearisation. They may then
be represented as the result of a linear functional applied on the anomalous gravity signal,
plus systematic effects and random noise. The systematic effects will generally be a bias,
plus a quantity linear in time. (If not, we are faced with very difficult problems).
The noise will be modelled as having a normal distribution with known variance, but with a
spatial correlation, along track. This is very important, see Arabelos and Tscherning, 1999.
The error correlation has either to be estimated as described in the referenced paper, or
calculated based on the observation equations. SST data, for example, will have an
alongtrack correlation if represented as range rate rates.
In the least square collocation method (LSC) the data can be used directly as described above
in section 2. We will, however, have to calculate certain kinds of normal point or "normal
area" (means over blocks) values. This is necessary in order to reduce the amount of data
(which otherwise can not be handled globally by LSC). The latter kind of data may readily be
used in integration procedures, if for example the normal area values are means of vertical
gravity gradients, Tzz.
4. Quality control.
Different procedures of quality control are possible, and some are already implemented in
existing software, such as the GRAVSOFT program GEOCOL.
The simplest control can be made by comparing the satellite data with values calculated from
a spherical harmonic model like EGM96. Such a comparison will easily reveal large errors in
regions with a smooth gravity field. In montaneous, it will be more difficult. But here the
existence of a DTM can help to identify high frequency type of errors.
An effective method used on the ground is based on LSC. Each observation is "predicted"
from all other data in a certain range. This is already an operational procedure used on
airborne gradiometer data (Arabelos and Tscherning, 1999), and it will be tested on
simulated satellite data in WP 3.
The identification of systematic errors is also possible using LSC as demonstrated in
Arabelos & Tscherning (1998).
5. WP 1 report.
A technical note, including the above material, is in preparation.
Arabelos,D. and C.C.Tscherning: Simulation of regional gravity field recovery from satellite gravity gradiometer data using collocation and FFT. Bulletin Geodesique, Vol. 64, pp. 363-382, 1990.
Arabelos, D. and C.C.Tscherning: Regional recovery of the gravity field from SGG and Gravity Vector data using collocation. J.Geophys. Res., Vol. 100, No. B11, pp. 22009-22015, 1995.
Arabelos, D. & C.C.Tscherning: Calibration of satellite gradiometer data aided by ground gravity data. Journal of Geodesy, Vol. 12, no. 11, pp . 617 - 625, 1998.
Arabelos, D. & C.C.Tscherning: Gravity field recovery from airborne gravity gradiometer data using collocation and taking into account correlated errors. Phys. Chem. Earth (A), Vol. 24, No. 1, pp. 19-25, 1999.
Tscherning, C.C., P.Knudsen and R.Forsberg: Description of the GRAVSOFT package. Geophysical Institute, University of Copenhagen, Technical Report, 1991, 2. Ed. 1992, 3. Ed. 1993, 4. ed, 1994.
Tscherning, C.C., F.Rubek and R.Forsberg: Combining Airborne and ground Gravity using Collocation. In: Forsberg,R., M.Feissel, R.Dietrich (Eds): Geodesy on the Move. Proceeding IAG Scientific Assembly, Rio de Janeiro, Sept. 1997 ,IAG Symp. Vol. 119, pp. 18-23, Springer V.,1998 .
Last update 1999-04-16 by cct.