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):
Mean Stdv.
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 investigated..

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 gps_lev_H-eigen-tcx.dat.
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 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 .

Last change 2012-11-15.