Files and results from Auvergne test 2008-09.
Guidelines for tests.
Computation of covariance from GPS/lev - EIGEN.
The covariance function was computed from the
GPS/lev file minus EIGEN, see output from empcov.
It was fitted using covfit, see output and
showed a gravity (residual) anomaly variance of 431 mgal**2. Consequently it is
very unlikely that values smaller than -50 mgal belong to the correct
data population. (Note that the variance of the gravity residual
anomalies is below 300 mgal**2 as calculated from these anomalies).
A reason for this could very well be that the data used to
construct the free-air anomalies in reality were Bouger anomalies.
Result from test adding Bouger plate back.
Gravity data minus the global model (EIGEN) has been used.
The Bouger-plate effect have been added to values
which were smaller than -50 mgal. This resulted in a mean value
change from -73.18 to -18.71 mgal. However the standard-deviation increased.
Output from program reformatl.
The changed values are found in the file
where the columns are station-number, latitude, longitude, altitude,
original gravity anomaly, anomaly minus EIGEN, and anomaly minus EIGEN
but plus the Bouger-plate.
I think this shows that we maybe are dealing with data which have been derived from Bouger anomalies.
Analysis using RTM data with suspected errors removed.
In order to further check the data, also the effect an gravity of the
residual topograpy was removed using tc, job file.
The effect of removing the RTM can be seen from the followig table (units mgal):
Obs -5.58 16.37
Tc -4.07 7.40
Dif -1.51 12.10
An analysis of the data confirmed the suspicion of the errors in the data,
an the program reformatl was run again using the RTM-reduced gravity anomalies.
The gravity data with suspected errors all have station numbers starting with either
210 or 240. All data (totally 2219) from these sources were removed.
A subset of the data spaced 0.05 in latitude and 0.075 in longitude was
extraced using select.f ( Output ). This showes
very nicely the effect of using RTM. The standard deviation decreased
from 16 to 12 mgal, and the mean value decreased from -3.3 to 1.1 mgal.
Based on this a new covariance function was estimated an fitted using
covfit ( output )
The estimated covariance function parameters (depth to Bjerhammar-sphere,
variance of anomalies, scale-factor on error-degree-variances) were
merged into a lsc job-file
used to predict the height anomalies in the GPS/levelling points.
The RTM effect was removed from the GPS/level. data (minus EIGEN
contribution) using again tc ( job-file.)
The standard deviation was not lowered as expected. This is being
Last results, combining gravity and height-anomalies.
. Only empirical covariance function from gravity used to model the
analytic one. Result implies height anomalies have errors of 0.05 m +
a common bias.
Further analysis of the data
Search for duplicates.
The use of Least-Squares Collocation as implemented in GEOCOL requires
that the same data are not used twice, and the program gives out a warning
if two observations are located within a short distance. When a more dense
dataset was used in 2009 as described below, many warnings were received.
A Fortran program duplicates.f
was written to search for observations
which were closer than a given input parameter. Values which were
detected as duplicates were removed and output to a new data-set.
for a distance of 0.001 deg (approximately 110 m) 9094 values were
detected, with 235357 remaining. Some of the duplicates were just
different with respect to 0.2 m for the height, the latitude and longitude
beeing the same.
Comparison with EGM2008.
Analysys not yet completed.
Renewed tests 2009.
Restricted test with GEOCOL.
Data from a somewhat smaller area bounded by latitude 44.996 to 47.0049
and longitude 1.495 to 5.504 was selected and stored in a file gravi1.dat.
The file contains 18193 values.
From these data the contribution from the EGM and the topography was
subtracted resulting in a file gravi1-egm-tc.dat. The gravity data in this
area are much smoother than in the total area, having a standard
deviation of only 8 mgal, see the output file .
The gps-levelling data were again used, now with a slightly different
reference surface for TC made by R.Forsberg. This gave a dataset
The removal of the residual topography from the gravity data also
now gave good results, i.e. a standard deviation below 10 mgal.
The covariance function was also computed for
these data, giving a standard deviation of 0.13 m and a mean of -0.03 m.
The correlation distance is approximately 20 km.
First the gps_lev data were predicted from only the gravity data. This gave
a mean of the differences of -0.079 m and st.dev. of 0.064 m. The gps-lev
data were then addded and used with a standard deviation of the error of
0.01 m. A bias of 0.0311 m with standard deviation
of 0.014 m was estimated. The gps-lev data were
predicted (in the same points)
and the difference calculated. Obviously the mean of the differences is now
0.00 m, and the standard deviation fell to 0.0295 m.
Full area experiment
Experiment using GEOCOL.
This result gave a push to try for a larger data-set. Further gravity data
spaced 2 minutes apart were selected so that the total area bounded by
latitude 43 to 49 and longitude -1.0 7.0 were covered. This gave a total
of 69525 observations. Unfortunately the equations could not be solved due
to singularities in the normal-equations. It seemed that the cause
could be that some observations were very close (strongly correlated),
but I decided to change GEOCOL so that a large value will be put
in the diagonal if a singularity occurs.
In June experiments were repeated using the total data-set. The
job file is aulscfaa_all09zeta.job with input gravi1-egm-tc.dat,
GRAVI_V3_02_outer.dat and gps_lev_H-eigen-tc.dat.
One bias parameter was determined. Resulting in 69599 equations to be solved.
Here a comparison with the input gps_lev data gave mean 0.00 and standard
deviation 0.049 m. The mean of the error-estimates was 0.017 m, based on
a 0.01 m standard error for the input gps_lev data. (This value is
obviously too small).
The bias had a value of 0.084 m, with a standard error of 0.007 m.
Values in a grid were computed, initially at altitude 0.0, but later at
terrain altitude. They are stored in auvergne444806a-EGM-TCzeta.dat.
Giovanna then informed me, at only gravity anomalies should be used. A
new solution was made and stored in auvergne444806b-EGM-TCzeta.dat.
Both grids had then added RTM contributions and contributions fro the
EIGEN set of coefficients, resulting in two files delivered to Giovanna:
The agreement with gps_lev was now : mean difference= 0.084 and stdv. 0.081 m.
Experiment with FFT.
The full data-set from which had been subtracted the EGM and topographic
effects, GRAVI_V3-EIGEN-tc.dat, was gridded using GEOGRID with a
correlation distance of 12 km and a noice value of 0.5 mgal. The
result was stored in the file GRAVI_V3-EIGEN-tc.gri. This has the grid-lable
43.300000 48.700011 -0.700000 6.700015 0.01666670 0.01666670
so that it includes the test-area 44 to 48 deg lat. and 0 to 6 deg. longitude.
A height file with the same spacing had been made using
GEOIP . Then geofour was
used to convert the residual gravity grid to a residual height
anomaly grid, zeta-EIGEN-tc.gri. The gridded result was compared with the
observed residual gps-levelling. The result
x was an agreement with a standard deviation of 0.088 m.
The residuals were then fitted to the
FFT-grid of height anomalies, resulting in a new grid,zeta-EIGEN-tc_fit.gri.
The project is not very active. H.Yildiz has done several new investigations
and comparisons have been made. It has also been used to test GOCE results
in 2012. See http://cct.gfy.ku.dk/publ_cct/cct_publ.htm .
Last change 2012-11-15.