Progress in the following areas is described: refining altimeter and altimeter crossover measurement models for precise orbit determination and for the solution of the earth's gravity field; performing experiments using altimeter data for the improvement of precise satellite ephemerides; and analyzing an optimal relative data weighting algorithm to combine various data types in the solution of the gravity field

Schutz, B. E.

Shum, C. K.

Tapley, B. D.

English

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ALTIMETER MEASUREMENTS FOR THE DETERMINATION
OF THE EARTH'S GRAVITY FIELD
NASA GRANT NAG5-746
Semiannual Research Progress/Status Report
for the period
March 18, 1986 - September 14,1986
Submitted to
Ms. G. Wiseman
NASA Goddard Space Flight Center
Mail Code 200
Greenbelt, MD 20771
\
by the
Center for Space Research
The University of Texas at Austin
Austin, Texas 78712
(512)471-1356
Principal Investigator:
Dr. B. D. Tapley
Co-Principal Investigators:
Dr. B. E. Schutz
Dr. C. K. Shum
September 25,1986
(HAS A-CB-176 8 93) ALTIMETEE HEASUBEHENTS FOB N86-32912
TEE DETEBHIMA1IOH OF SHE E f l B T B ' S G R A V I T Y
FIELD Semiannual Eesearch Frogress/Status
Report, 18 Max.,- 14. .Sep. ,1986 (Texas Oniv.)., Unclas
^ ^ . CSCI 08N 63/46 44644
https://ntrs.nasa.gov/search.jsp?R=19860023440 2020-03-20T13:16:40+00:00Z
ALTIMETER MEASUREMENTS FOR THE DETERMINATION
OF THE EARTH'S GRAVITY FIELD
NASA Grant NAG5-746
INTRODUCTION
The University of Texas Center for Space Research (UT/CSR) research efforts under NASA
Grant NAG5-746 during the time period from March 18, 1986, to September 14, 1986, have
concentrated on the following areas:
• Refining altimeter and altimeter crossover measurement models for precise orbit determination
and for the solution of the earth's gravity field,
• Performing experiments using altimeter data for the improvement of precise satellite
ephemerides,
• Analyzing an optimal relative data weighting algorithm to combine various data types in the
solution of the gravity field.
ALTIMETER MODEL REFINEMENT
A model of the quasi-stationary sea surface topography (SST) was implemented in the University
.of Texas Orbit Processor (UTOPIA). The model uses a surface spherical harmonics representation
of the Levitus model of the SST, and it includes the capability to estimate the SST model in terms of
spherical harmonics coefficients using altimeter data. The model of SST is part of the dynamically
consistent altimeter measurement model which includes the modeling of the dynamical effect of the
global ocean surface on the satellite orbit
Software development efforts are underway to implement the capability for the computation and
generation of altimeter crossover measurements for the general case of two altimetric satellites.
ALTIMETER CROSSOVER EXPERIMENTS
Orbit determination experiments using altimeter crossover observations were performed.
Altimeter crossover and ground-based tracking data were used to determine SEAS AT 12-day arc
with orbit epoch beginning at July 7, 1978. When resonant coefficients and 10x10 gravity field
coefficients were solved using crossovers and tracking data, the SEASAT orbit was computed with a
better accuracy. A simulation experiment was then performed to confirm the above results. In
conclusion, the use of crossover measurements significantly improves the radial component of the
estimated orbit. The improvements in the geopotential gained from processing crossover
measurements will reduce the geographically correlated orbit error.
Further experiments using both direct altimeter and altimeter crossover data will be performed to
assess the ability of these data types in the role of orbit determination and mapping of geophysical
parameters.
APPLICATION OF ALTIMETER DATA
A new technique was developed to interpolate unevenly spaced GEOS-3 and SEASAT altimeter
data to generate the mean sea surface, or marine geoid, with high resolution. Green functions of the
biharmonic operator, in any number of dimensions, are used for minimum curvature interpolation of
irregularly spaced data ponts. The interpolating curve (or surface) is a linear combination of Green
functions centered at each data pont. In one (or two) dimensions, this technique is equivalent to
cubic spline (or bicubic spline) interpolation, while in three dimensions, it corresponds to
multiquadratic interpolation. Although this new technique is relatively slow, it is more flexible than
the spline method since both slopes and values can e used to find a surface. Moreover, noisy data
can be fit in a least-squares sense by reducing the number of model parameters. These properties are
well suited for interpolating irregularly spaced satellite altimeter profiles. The long wavelength
radial orbit error is suppressed by differentiating each profile. The shorter wavelength noise is
reduced by the least-squares fit to nearby profiles. Using this technique with 0.5 million GEOS-3
and SEASAT data points, it was found that the marine geoid of the areas covering the Gulf of
Mexico and the Caribbean are highly correlated with the sea floor topography. This suggests that
similar applications in more remote areas may reveal new features of the sea floor. Future plans
include application of altimeter data to produce a high resolution global ocean surface map.
GEOSAT altimeter data, if available, will be included.
RELATIVE DATA WEIGHTING
An optimal relative data weighting algorithm was developed to combine various data types for
the solution of the earth's gravity field. The algorithm minimizes the error introduced by the
observation noise and scales the a priori variances for an optimal solution. Evaluations and
experiments are underway to examine the ability of the data weighting algorithm for the optimal
solution of the earth's gravity field.
PUBLICATIONS/CONFERENCES
The following is a list of publications and conference presentations pertinent to the research
activities under NASA Grant NAG5-746:
• Altimeter Crossover Experiments, R. S. Nerem, C. K. Shum, and J. R. Ries. Presented at the
Sixth UT/GSFC TOPEX Gravity Model Development Meeting held at The University of Texas
at Austin, April 8-10, 1986.
• Altimeter Crossover Methods for Precision Orbit Determination, C. K. Shum, B. E. Schutz, B.
D. Tapley, B. H. Zhang, and R. S. Nerem. Abstract submitted to the Fall Meeting of the
American Geophysical Union, San Francisco, California, December 1986. A copy of the abstract
is included in Appendix A.
• Biharmonic Spline Interpolation of GEOS-3 and SEASAT Altimeter Data, D. T. Sandwell.
Submitted to EOS for publication. Abstract submitted to the Fall Meeting of the American
Geophysical Union, San Francisco, California, December 1986. A copy of the abstract is
included in Appendix B.
APPENDIX A
ALTIMETER CROSSOVER METHODS FOR PRECISION
ORBIT DETERMINATION
C. K. Shum, B. E. Schutz, B. D. Tapley, B. H Zhang, and R. S. Nerem
(Center for Space Research, The University of Texas at Austin, Austin,
Texas 78712)
The ability of satellite-borne radar altimeter data to measure the global
ocean surface with sub-centimeter accuracy provides a unique data set
to aid precision orbit determination as well as to map the earth's gravity
Geld and its geoid. Although satellite altimetry has a distinct advantage
in its global distribution of data, consideration of possible error sources
when altimeter data are directly used for orbit determination and
geophysical mapping suggests several disadvantages. In particular, long
wavelength oceanographic features and nontemporal ocean topography
can be absorbed into the orbit when altimeter data are directly used.
Altimeter crossover data, which eliminate the dependence on the
nontemporal ocean topography, provide a valuable data set in its global
coverage. In this investigation, techniques to employ altimeter
crossover data to perform precision orbit determination and to recover
geophysical parameters have been developed. New techniques of using
dual or multiple satellite crossover data for precision orbit determination
and geodetic parameter mapping have been investigated.
Acknowledgment: This research was supported by NASA under
Contract No. NAG 5-746.
1. 1986 Fall Meeting
2. SHUMOOOOOO
3. Dr. C. K. Shum
Center for Space Research
The University of Texas at Austin
Austin, TX 78712
(512)471-5573
4. G
5.
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8. Ms. Susie Y. Thorn
Center for Space Research
The University of Texas at Austin
Austin, TX 78712
9. C
APPENDIX B
BIHARMONIC SPLINE INTERPOLATION OF GEOS-3
AND SEASAT ALTIMETER DATA
ABSTRACT
Green functions of the biharmonic operator, in any number of dimensions, are used for minimum
curvature interpolation of irregularly spaced data ponts. The interpolating curve (or surface) is a
linear combination of Green functions centered at each data pont. In one (or two) dimensions, this
technique is equivalent to cubic spline (or bicubic spline) interpolation, while in three dimensions, it
corresponds to multiquadratic interpolation. Although this new technique is relatively slow, it is
more flexible than the spline method since both slopes and values can e used to find a surface.
Moreover, noisy data can be fit in a least-squares sense by reducing the number of model parameters.
These properties are well suited for interpolating irregularly spaced satellite altimeter profiles. The
long wavelength radial orbit error is suppressed by differentiating each profile. The shorter
wavelength noise is reduced by the least-squares fit to nearby profiles. Using this technique with 0.5
million GEOS-3 and SEASAT data points, it was found that the marine geoid of the Caribbean area
is highly correlated with the sea floor topography. This suggests that similar applications in more
remote areas may reveal new features of the sea floor.


Altimeter measurements for the determination of the Earth's gravity field

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