Simulation of height anomaly precision obtainable from CHAMP-data
and from airborne gravity data in Bolivia.
by
C.C.Tscherning, Department of Geophysics, UCPH.
2004-06-27.
Using least-squares collocation (LSC, see Moritz, 1980) it is
possible to obtain error estimates of the quality of height
anomalies (quasi-geoid heights) from various combinations of data
and from various types of gravity field variations. It is only
necessary to know the position, type and error estimate of the
data and its statistical characteristice (covariance function).
The FORTRAN programs GEOCOL16, EMPCOV, COVFIT16 and TC from the
GRAVSOFT package (Tscherning et al., 1992) have been used to
execute the computations described below. Data, job-files and
output files are found in http://cct.gfy.ku.dk/bolivia/bolivia.htm
.
In this preliminary study we have computed error-estimates for
Bolivia, or more precisely for areas bounded by -24 deg. to -9
deg. in latitude and -70 deg. to -55 deg. in longitude, see
http://cct.gfy.ku.dk/bolivia/bolivia.pdf. The image shows the
topography as obtained from DTM2002, (Saleh and Pavlis, 2002).
CHAMP-data from one year of observations (Howe and Tscherning,
2004) http://cct.gfy.ku.dk/bolivia/bochamp.dat , were used to
generate gravity anomalies at an altitude of 300 m above the
terrain in order to simulate 32400 airborne gravity data, see
http://cct.gfy.ku.dk/bolivia/boliviag.dat . The creation of this
data-set was in principle not necessary since the simulations - as
mentioned above - may be carried out without using real data. Only
positions and error-estimates of the data are needed.
As a reference field EGM96 (Lemoine et al. 1998) to degree 24 was
used. The effect of the residual terrain was also subtracted from
the CHAMP data, see http://cct.gfy.ku.dk/bolivia/bochamp_tc.dat
These data were used to generate empirical covariance functions in
two sub-areas,(-24 deg. - -13 deg. in latitude and -70.0 deg. -63
deg. in longitude) one with high mountains and one in the lowland,
(-24 deg. to -13 deg. in latitude and -63 deg. to -55 deg. in
longitude), see http://cct.gfy.ku.dk/bolivia/bolivia.htm for input
and output-files.
The main result is that a gravity field variance of 413.5 mgal**2
and 1226.6 mgal**2 were found in the low and in the heigh area,
respectively, for data from which EGM96 to deg. 24 and residual
topographic effects have been subtracted. The value from the high
area is probably under-estimated. Real data are necessary in order
to obtain a better value.
These values were then used in the computation of simulated error-
estimates of height anomalies in two sub-areas within the two
areas, bounded by (-24.0 -13.0) in latitude and ( -63.0 -55.0) in
longitude, and (-24.0 -13.0) in latitude and (-70.0 -63.0) in
longitude.
About 3000 CHAMP height anomalies and 2000 gravity anomalies were
used in each case.
The subtraction of EGM96 to degree 24 from the data, results in a
height anomaly standard deviation of about 3 m. Using the CHAMP
data without topography then permits the prediction of height
anomalies with overall errors around 1 m. The error will be larger
in the high area and lower in the low area.
Using gravity data with a 5' spacing in the above mentioned sub-
areas, the error decreased to between 0.14 m and 0.43 m for the
low area and between 0.18 m and 0.56 for the high area, see
http://cct.gfy.ku.dk/bolivia/bochampgtclgeoid.pdf and
http://cct.gfy.ku.dk/bolivia/bochampgtchgeoid.pdf
Conclusion.
Using CHAMP data combined with airborne gravity data (with 2.0
mgal mean error) spaced 5' apart it is possible to obtain height
anomalies with mean errors of 0.14 m in low areas and 0.18 m in
high areas. Improvements may be obtained using a DTM of higher
resolution than the one used here and more dense gravity data. The
use of a complete higher order reference field like EGM96 to
degree 360 is not expected to give much improvement because the
regional data used to construct the model is not of high quality.
References:
Howe, E. and C.C.Tscherning: Gravity field model UCPH2004 from one
year of CHAMP data using energy conservation. Prepared for Porto
Meeting,2004.
Lemoine, F.G., S.C. Kenyon, J.K. Factor, R.G. Trimmer, N.K.
Pavlis, D.S. Chinn, C.M. Cox, S.M. Klosko, S.B. Luthcke, M.H.
Torrence, Y.M. Wang, R.G. Williamson, E.C. Pavlis, R.H. Rapp, and
T.R. Olson, The Development of the Joint NASA GSFC and the
National Imagery and
Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998-
206861, Goddard Space Flight Center, Greenbelt, MD, July, 1998.
Moritz, H.: Advanced Physical Geodesy. H.Wichmann Verlag,
Karlsruhe, 1980.
Saleh, J. and N.K. Pavlis, 2002). The Development and Evaluation
of the Global Digital Terrain Model DTM2002, 3rd Meeting of the
International Gravity and Geoid Commission, Thessaloniki, Greece.
Tscherning, C.C., R.Forsberg and P.Knudsen: The GRAVSOFT package
for geoid determination. Proc. 1. Continental Workshop on the
Geoid in Europe, Prague, May 1992, pp. 327-334, Research Institute
of Geodesy, Topography and Cartography, Prague, 1992.