European GOCE Gravity Consortium and GOCE HPF.
Activities of University of Copenhagen in support of the
European GOCE Gravity consortium .
SAGRADA - Satellite Gravity Data project.
Project supported by 1.5 M DKK by the Danish Natural Science
Research council (SNF) starting Sept. 1, 2001. The funding will be used
one PhD-student for 3 years and some running costs.
Parthers are Kort og Matrikelstyrelsen
and Terma A/S
Detailled project description (in Danish) .
ESA supported projects and current news.
GOCE: Preparation of the GOCE Level 1 to Level 2 data processing. .
University of Copenhagen is responsible for a number of work-packages,
and contribute to several others.
The main work will be realted to the use of Least-Squares Collocation
for the processing of the GOCE data. A close cooperation is expected
with Politecnico di Milano, University of Thessaloniki and Institut de
Staff working on the project are:
C.C.Tscherning, University of Copenhagen
D.Arabelos, University of Thessaloniki, email@example.com
Eva H. Ditlevsen (PhD-std.) University of Copenhagen,
Draft contributions to workpackages ("Slices"):
Slice 3, Task 3. (2001-09-29)
Slice 3, Task 5.3. (2001-09-28)
Draft Slice 4 PM2 report.(2001-10-03)
Polar gap investigation presented
Int. GOCE User Workshop, April 2001.
Aspects of GOCE calibration by R.Koop, P.Visser and
C.C.Tscherning, presented Int. GOCE User Workshop, April 2001.
Fast Spherical Collocation
Abstract of paper by F.Sanso' and C.C.Tscherning. Prepared for
IAG2001, Budapest, Sept. 2001.
Here many newer
publications are found.
1 deg. mean gravity anomalies - EGM96 to 72
1 deg. mean gravity anomalies - EGM96 to 72
In 2004 Martin L. Veicherts joined the project.
The design and implementation of the GOCE High level processing facility
started March 1, 2004 and is expected to end 2012.
UCPH contributes to two so-called Sub-processing facilities or
work packages, WP 3000 and
WP 7000 . Furthermore we contribute
to the evaluation of test-data
provided by ESA.
Check of GOCE products
Comparison of GOCE spherical harmonic solutions
using Norwegian test data.
Comparison of models using global data.
Prediction of gravity anomalies from Tzz and Tyy.
Differences from Tzz,
from Tyy. of gravity anomalies, EGM96 to 36 subtracted.
GOCE tracks in Fenno-Scandia.
Gravity anomaly prediction from GOCE Vzz data.
The following step is necessary in order to create Tzz anomalous gravity gradients.
Note that the calculation is done without using spherical approximation.
The used input file (GO_EGG_TRF_2009_2010.EDF) has been merged from
several ESA-GOCE files and records with outliers flagged have been removed.
Job to subtract EGM96 to deg. 36 from Vzz
and preserve error-estimates from GOCE gradient file.
New job with data from 2009-11., totally
28623 records. 2011-09-20.
Then the empirical covariance function
is estimated, followed by the estimation of the parameters defining an
The next step is done in spherical approximation. This is possible since we
work with anomalous quantities. Note, that the covariance parameters must be
determined separately using empcov and covfit16.
Jobfile to predict ground gravity from
Tzz reduced to deg. 36 and bias-adjusted per track.
Prediction of coefficients, 2011-06-06.
Program to create equal angular grid
Job to select gravity close to arctic 4/6 deg grid
Job to select gravity close to antarctic 4/6 deg grid
Job to predict arctic gravity at 15 km altitude
Job to predict antarctic gravity at 15 km altitude
Job to predict coefficients from 2.deg equal area
Tzz reduced to deg. 36.
Job to predict coefficients from Tzz reduced to deg.
36 and gravity at the poles upward continued to 15 km in order to avoid
problems with the Bjerhammar-sphere. The data are spaced close to 1.deg equal area.
Revised job with global covariance function. which
gave error-estimates agreeing with observed differences with respect to EGM96.
Results with error-estimates from 1-deg. prediction
and comparison with EGM96 from deg. 37. Legend: degree, stdv. predicted coefficients,
stdv. differences, mean of error-estimates, stdv. EGM96 coeff.
Results with error-estimates from 0.5 deg prediction
with global covariance function and gravity at the poles at 15 km altitude.
Check of collocation soultion included with prediciton "back" into gravity points.
Coefficients to be used in GEOCOL. Merged DIR_r2 to degree 36 and collocation solution from 37 to 200.
Summary of result
Prediction of dg and Tzz in grids at 10 km altitude.
Values of gravity anomalies and the vertical gravity gradient Tzz will
be predicted globally at 10 km altitude in 20 deg. x 20 deg. blocks
with 2.5 deg. overlap in a 0.1 deg grid.
POLIMI data at satellite altitude will be used, Tzz and Tyy or the
along-track second order gradient. At the poles ground gravist should be used.
Initially experiments with TRF data from 2009-11 provided by WP3000 was
conducted to get timing experience.
This dataset consist of 18447670 points. This is so large, at it will
not be possible to use all data. Subsets of 0.1666 and 0.125 deg
spacing was created from a data-set where the contribution from
ITG-Grace2010s.gfc to degree 36 was subtracted, resulting in
/home/gfy-goce/cct/cct1/dgravsoft/gozz0.166.dat, goyy0.166.dat and
The area bounded by -2.5 12.5 -2.5 12.5 was used and a dataset with
1 deg. spacing was used for prediction test derived from EGM2008 minus
ITG-Grace2010. 22 processors were used.
Using the 0.1666 spacing with one component (22464 obs.) took 5286
sek and two components (totally 44928 obs) 27715 sek. In both cases the
error-estimate for gravity anomalies was 6.8 mgal. The mean and standard
deviation of the difference with respect to the EPM2008 derived data-set
was -0.40, 9.65, compared to a data mean and stdv. of -2.0 , 19.4.
For the dataset with 0.125 deg. spacing the result was marginally better:
mean difference 0.50 and stdev. 9.16 (mgal). The LSC error estimate was
again 6.8 mgal. Totally 37972 points (of Tzz) was used, and the computation time was 17699 sek. (file: g_testz0.125.out, turn-around time 6 hours).
A comparison of the 411 values with DIR_r2 to deg. 240 gave mean of
differences of -0.73 and stdv. equal to 6.94 mgal.
D.Arabelos computed covariance function parameters for the 20 x 20 blocks,
(30x20 at the poles), see
Covariance parameters. using as theoretically correct the
ITG_Grace derived error-degree variances. They result in some
very large differences to the Bjerhammar-sphere.
An alternative may be to use the Tzz data for covariance estimation, see e.g.
covfit output .
A job was made (createjg.f90) to create a file lasallX.csh which
contained up to 162 input-files (lscXXX.inp) to create jobs for
gridding. Optionally the 20x20 grids were reduced by 9.5 deg. in all 4 directions.
This gave about 1200 obs per job. For the poles similar data-sets of ground
gravity were used. Each job takes about 50 s to run.
Gravity anomaly and Tzz grids at 10 km altitude were created, and the first
25 assembled by tar in dg4.tar.bz by the command tar -cjf dg4.tar.bz2 dg4/
where th grids had been put into a sub-directory denoted dg4. The file
has been made available by anonymous ftp, and Mirko has been asked to
check the file.
I created a 0.1666 deg. spaced gravity anomaly data-set at height 0 using EGM08 to 512.
Then I subtracted ITG to degree 36.
I also used the 0.1666 slected (not gridded) Tzz dataset with ITG subtracted.
Empirical covariance functions were estinated
http://cct.gfy.ku.dk/empcov_dg and http://cct.gfy.ku.dk/empcov_tzz.job
The two resulting covariance functions were used in covfit16
http://cct.gfy.ku.dk/covfit_dgzz.job with output: http://cct.gfy.ku.dk/covfit_dgzz.out
The result is similar to what DA has obtained.
I will try the same for some of the areas with very large Bjerhammar-sphere depths.
All the original data and results are in /home/gfy-gut/cct/cct1/dgravsoft.
On 2012-12-26 covariance functions for blocks 66,85,113 and 137 was computed fromgravity anomalies and Tzz. These four problematic blocks have problms, due to
a skew data-distribution as can be seen from the out-put histograms in the
It is uncertain what can be done about this. A brute-force use of covfit
n 2012-12-26 covariance functions for blocks 66,85,113 and 137 was computed from
gravity anomalies and Tzz. These four problematic blocks have problms, due to
a skew data-distribution as can be seen from the out-put histograms in the
A contouring of the dg and Tzz datasets reveals large differences for block
and compare with the gravity anomalies at 10 km from Tzz
dg from Tzz at 10 km.
The whole procedure is described here
Summary of results from 0.1666 deg. dat spacing:
Tzz at 10 km EGM08 (to 512) St.deviation
Tzz at 10 km st.deviation predicted - EGM08 values.
Tzz at 10 km mean error (E.U.)
dg at 10 km mean error (mgal)
EGM08 dg at 10 km st.deviation (mgal)
dg at 10 km difference predicted - EGM08 st.deviation (mgal)
CPU times for different block/
chunk sizes and number of data, and data noise st.dev..
A comparison og EGM08 at 10 km dg and Tzz with GODIR2 was made,
EGM08 -DIR2 dg at 10 km st.deviation (mgal)
EGM08 -DIR2 tz at 10 km st.deviation (mgal)
Total CPU-time for different servers and block and chunk-sizes.
And comparison of results for different Tz obs.error st.dev.
Block 73 with N observations Tzz
Source: /home/gfy-gut/cct/cct1/dgravsoft/lsc1073.out and lsc3073.out on
GUT. On IKOS: geocol/lsc3073.out, on GOCE lsc3073.out.
Time per Cunk-row for different block-sizes 22 processors block 73, 22464 obs:
Times for 05 block size.
Times for 10 block size.
Times for 15 block size.
Times for 20 block size.
Times for 25 block size.
Times for 30 block size.
was presented at HPH PM#26.
After the PM # 26 Oleg offered to make available the screened and interpolated
GRF data used when constructing the DIR4 solution.
The PSO_TRF_GRF and EGG_NOM_2 data was transferred on Feb. 11 and reformatted
using /home/gfy-gut/cct/cct1/dgravsoft/reformatg.f90 into two different
files on GRAVSOFT format:
GO_GRF_20091101-20100111_0101.DAR with time, positions and gradients and
GO_QUA_20091101-20100111_0101.DAT with time and quarternions.
The quarternions gave the rotation from GRF to a TRF in cartesian coordinates
so a new input mode (6) was defined in geocol19 to tage care of
this and to multiply with the rotation between the two TRF systems
(ENU and XYZ).
The data were compared to ITG-Grace2010 to degree 36 with satisfactory
results. A further check with prediction of the quantities from
Canadian ground gravity has been performed.
A check with prediction of one GRF quantity from the other was not succesful.
It seems to be a problem in the subroutine PRED. (2013-03-17). In order
to identify the problem a dataset was generaled for all gradients in the
altitude of 100 m from EGM2008 to deg. 512 in block 073. The data are
in /home/gfy-gut/cct/cct1/dgravsoft and named tvv073.dat, vv=zz,xz,xy,yy,xx,yz.
The error was identified as being related to the transfer of the program from f77 to f90, where EQUIVALENCE must be avoided. Then the prediction of all
6 quantities from all 6 was satisfactoty, except xz -> yy which seems biased.
The job-file is lsc_trf_073.job with output lsc_trf_073vvW.out.
Another error was identified, caused by the use of OMP. The array covx
was in a "use" statement, and was therefore not updated after rotation
to the GRF-frame.
A detailled test was then performed using noise-free data generated by the
DIR3 EGM to deg. 240, see
The program reformatg.f90 was changed, so that more GRF and QUAT files could be
reformatted simultaneously. This was used to reformat the first dataset received from Oleh,
5 # number of input file pairs
GO_GRF_20091101-20100324.DAT # output file name on the form time, lat., long., h., Tij,
error(Tij), totaly 8 data-elements
GO_QUA_20091101-20100324.DAT # output file with quarternions.
../../EGG_NOM_2__20100305-20100319_0101.DAT # 4 more pairs of data.
From the 2 out-put files 4 new files were created after subtraction of ITG-Grace to 36:
GO_GRF-ITG_TTTb.dat, with TT=xx,yy,zz,xz.
From these data-sets were selected values in block 073 spaced 0.16666 deg. The files are named
go_grfTTb073.dat with TT=xx,yy,zz or xz.
These data were used to predict gravity and Tzz at 10 km using the job-file
Also data from the larger time-span: 2009-1101 - 2012-0801 were prepared
and the contribution fro ITGGrace subtracted. The Tzz data were also used
to predict gravity anmalies and Tzz at 10 km in block 073. In the
latter case 2800 more data-points were used.
For gravity anomaly prediction the following results were obtained:
Data used________ mean____st.dev.___mean estimation error (mgal)
Number of data:_19707___________________________________22505
xx_______________ -1.06___ 8.03_____8.63_____-2.29___9.96___8.83
yy_______________ -1.01___ 8.43_____8.64_____-1.28___9.06___8.81
zz_______________ -0.35___ 7.49_____7.29_____-0.09___7.37___7.32
xz_______________ -0.36___ 7.88_____7.97_____-0.41___9.76___8.14
zz,_xx___________ -0.58___ 7.45_____7.08
zz,_yy___________ -0.53___ 7.43_____7.09
zz,_xz___________ -0.54___ 7.79_____7.01
This indicates that not much is to be gained by using GRF data instead of TRF data.
Due to the uniform distribution of the gradient data used for prediction of
gravity and Tzz at 10 km, the error estimates are very similar in a block.
However if one compares the error estimates to the data standard deviation,
there is a strong correlation.
If we look at block 044, it is especially significant as seen from the following
Predicted gravity anomalies
EGM2008 to 512 values
Tzz standard deviations in 1 deg. squares.
Scaled error estimates
These error estimates are much more reflecting the real error.
See program output.
The full signal shows many interesting features,
so we can use either the standard deviation or the rms for a global scaling.
A similar scaling has been tried globally using the mean standard-deviations
of the used 25 deg. blocks, see
the mean error-estimates. .
It will be based on global st.dev. of 1 deg. blocks.
Global table of Tzz
variation. r,s in last column.
The scaled error-estimates
tHE Blockwise scaled error-estimates
A presentation is in preparation
Paper submitted to proceedings, 2013-07-25.
Another aspect is that the same problem of uniform error-estimates also exist
for other modelling methods, e.g. for gravity anomalies computed from an EGM.
Here a similar scaling could also BE USED.
Prediction of coefficients from a 0.25 deg. equal area data-set.
Preparations for the computation of a new spherical harmonic model has started.
A data-set of TRF data for the full period 2009-20013 was prepared by Matija Herceg, and is
found at /home/gfy-gut/csh961/GOCEextract/TRF_2_2009_11-2013_09f.EDF.
The Trr values were extracted and the contribution from a model to deg. 36 was subtracted, see
of equal-area points with spacing 0.25 deg. was created using eqarea.f on goce.
The program selecgr had to be modified since the
number of data was too large. It is used to extract values in an 0.25 deg. eq. area grid.
Last update 2014-09-14 by CCT , e-mail: firstname.lastname@example.org