Files, results and documents related to GOCE HPF WP3000.
GOCE HPF WP3000 Contribution from WP3220 and 3620 and 3810.
Development phase 1. WP3220. SGG External Calibration with
Terrestrial gravity data
D.Arabelos, Visiting professor from University of Thessaloniki has worked on
the project in all of September 2004.
Task 1: Determine size of required area(s) with terrestrial gravity data.
In order fulfill this task a sequence of Numerical experiments have been
initialized using data from:
(1) Canadian Plains.
Gravity data used in the CIGAR project and with results
published in (Arabelos & Tscherning, 1998) have been used,
and the contributions from EGM96 to degree 360 and GRACE GGM01C.GEO to
degree 200 have been subtracted.
Based in these differences empirical auto covariance functions were computed,
see job file and
EGM96 output file and
GRACE output file .
These covariance functions were used to determine parameters for an analytic
representation of the covariance functions, see
EGM96 output file and
GRACE output file .
Note, that the use of EGM96 to degree 360 - as expected - gives a slightly
lower signal variance than when GRACE is used to degree 200.
Based on the analytic parameters jobs to predict Tzz at satellite altitude
were set up. As data on the GOCE orbit IAG SC7 data were used. The positions
were originally given as cartesian-coordinates, but had been transformed to
geographical coordinates. The attitude was computed from the velocity vector.
A first run
was made with a subset of the data.
ep>This first result show that we in this area may predict Tzz at satellite altitude
from data in the selected area, where the gravity field is very smooth.
In fact the (residual) signal standard deviation at satellite altitude is only 5 mE.
More runs have been completed in order to see the influence of the
data-sampling area and the data density, see the report mentioned below.
(2) Other areas.
Similar experiments have been executed using Australian and Scandianvian data,
see Report on external calibration by D.Arabelos and
C.C.Tscherning, completed 2004-09-24. The main conclusion is that a 5'
sampling should be used for areas of size 10 deg. * 10 deg (/cos(latitude)).
Consequently areas bounded by 56 deg., 66 deg.,-121 deg. -109 deg.
for Canadian Plains, -33 deg., -23 deg., 124 deg., 136 deg. for
Australia and 54 deg., 64 deg., 18 deg., 30 deg. for Scandinavia
(minimum and maximum latitude, longitude).
Using EMPCOV empirical covariance functions were estimated for the 3
areas, and parameters defining an analytic models were determined using COVFIT.
The gravity anomalies minus the EGM96 or GRACE contribution were used n
the estimation procedure. Since the use of EGM96 gave the smalles residual
variances, these covariance function parameters were used, see
Task 2: Determine required resolution and accuracy of gravity data
The 3 above mentioned areas have been used in order to determine the
required resolution and size of the areas to be used for the calibration,
see the above mentioned report.
The data accuracy as associated with the collected data (generally 1 mgal)
has in the simulations been shown to be sufficient.
Task 3: Select areas that meet the requirements and assess whether gravity, topographic and DTM data is available to the HPF.
Besides the Canadian plains other areas are considered. One is the GOCINA
data area, one is a part of the European data-set used by University of Hannover,
a third is Japanese gravity data in the Kuroshio area and a fourth Australian
data and a fourth Australian data. Correspondence with the Japanese colleagues
showed that the data is not suitable. The Hannover data were not available
due to restrictions imposed by the data originator. Therefore the 3 othere areas
were selected, see above.
A 2' DTM (DTM2002.2) has been made available by N.Pavlis from NASA/GSFC.
It will not be necessary to use topographic data for this WP, since the
data in the areas which will be selected are as smooth as the data
in the Canadian plains.
Task 4: Aquire these data.
The Scandinavian data has been obtained from KMS. The Australian data were
obtained via Internet from Geoscience Australia.
Task 5: Evaluate terestrial data sources.
The data accuracy of data selected according to a 5' sampling
was initially verified by visual inspection of maps
of the gravity data, where EGM96 to degree 360 has been subtracted.
A possible outlier in the Baltic Sea was checked to be no outlier
by comparison with KMS gravity data determined from satellite altimetry.
A more detailed test has be executed of the 5' selected data,
using cross-validation (prediction
of all gravity values from the same values) using GEOCOL,
see Canadian data ,
Scandinavian data and
Australian Data . The
output files are named similarily, but with the suffix *.out.
A number of outliers were found. They were not deleted, but the
associated error-estimates were modified. A factor of 3.0 times the
error-estimate war used to identify suspected gross-errors.
Task 5: Update GEOCOL (output format, include scale factor in the
calibration parameters) and TC.
The update of GEOCOL, so that scale-facors may be computed, has been
completed. The new version is available via ftp.
In earlier investigations using CHAMP data bias, drift and scale-factor
parameters were determined "externally" using regression analysis. Here
it was faound that estimates of scale-factor and bias parameters were
nearly 100% correlated. This has been confirmed by numerical experiments
using the updated version of geocol, see
Job file and
and Output file .
The upgrade of TC is not needed, but will be made externally, i.e. so
that the frame transformation is made by a simple program.
In February and March 2005 numerical tests have been made in the
3 selected areas using the E2E test-data-sets,
Gravity gradients: syncro_ggt_idcal.mat
Quarternions: 30days_777_DAY.dat (noise-free).
Bias and tilt values (and error-estimates) have been determined for
various values of the error-correlation for the 3 diagonal components.
Noise standard deviations of 13 mE for Txx, 55 mE for Tyy and 56 mE for Tzz
were used. This implicitly presupposes that the calibration
in earlier steps of WP3000 have been succesfully completed.
The tests shows (as expected) that the estimation error increases
when the correlation distance increases.
The detailled results will be reported at the GOCINA workshop.
WP3620 and 3810
Work has not yet started on these packages.
Last update 2005-04-03 by cct.