Report to IAG SSG 3.136: High Resolution Geoid Modeling and Evaluation
Dennis G. Milbert
National Geodetic Survey
National Ocean Survey, NOAA
Silver Spring, MD 20910
Jan 30, 1995
During this period, a new high-resolution geoid model, GEOID93, was released by the National Geodetic Survey (NGS). This model incorporated new terrain corrections, improved quality gravity data, the second order term of the normal gravity gradient, and the OSU91A model. Two deflection of the vertical models, DEFLEC90, and DEFLEC93 were also released by NGS. These models use cubic spline models of the geoid to develop deflections at the geoid. The deflections are then upward continued by the normal curvature of the plumbline correction. However, with the new deflection model for Alaska, the actual curvature of the plumbline is modeled by a variant of Eq (5.32), pg. 195 of Heiskanen and Moritz (1967).
The application of the integrated geodesy formulation in a rugged, high-altitude setting by Milbert and Dewhurst (1992) showed a requirement to use isostatic anomalies, and a need to develop an empirical cross-covariance function between gravity anomalies and anomalous geopotential.
In work leading to his doctorate, Yuki Kuroishi, spent one year of study at the National Geodetic Survey. In collaboration with Dennis Milbert, Dr. Kuroishi computed several 3'x3' models of the geoid for Japan. The JGEOID93 model was found to have 8.6 cm error in a 400x600 km area, when comparing GPS/leveling data sets. This figure is comparable to the error levels seen in the United States for the GEOID93 model.
As reported at various meetings of the American Geophysical Union, national geoid model comparisons with over 1400 GPS/leveling points now show 23.7 cm RMS. The error is long wavelength, with a decaying exponential-type empirical covariance function model of L=450 km. When the geoid model is augmented by a long-wavelength correction computed with collocation, the residual error is 6.2 cm RMS. This error is mostly white, with a correlated part of 2.6 cm. This shows remarkable short wavelength fidelity of national models on 3' grids.
Parks and Milbert (1994) study the effect additional gravity in the mountainous San Diego County region of the United States. Of particular note, they found a geoid error/gravity error ratio of 3 to 4 mm/milligal.
Milbert, D. G. 1991: A family of covariance functions based on degree variance models and expressible by elliptic integrals. Manuscripta Geodetica, 16(3), pp. 155-167.
Milbert, D. G., 1991: An accuracy assessment of the GEOID90 geoid height model for the Commonwealth of Virginia. National Geodetic Survey Report (unnumbered series), June 1991, 52 pp.
Milbert, D. G., 1991: GEOID90: A high-resolution geoid height model for the conterminous United States. Proceedings of U.S. Army Corps of Engineers 1991 Surveying Conference, Lousiville, July 16-18, pp. 8C1-8C7.
Milbert, D. G., 1991: DEFLEC90. Software for PC compatible computers. National Geodetic Survey, NOAA, Silver Spring, MD, 7 disks.
Milbert, D. G., 1991: Computing GPS-derived orthometric heights with the GEOID90 geoid
height model. Technical papers of the 1991 ACSM-ASPRS Fall Convention, Atlanta, October
28-November 1, pp. A46-55.
Milbert, D. G., 1991: GEOID90: A high-resolution geoid for the United States. Eos Trans, AGU, 72(49), pp. 545-554.
Milbert, D. G., W. T. Dewhurst, 1992: The Yellowstone-Hebgen Lake geoid obtained through the integrated geodesy approach. Journal of Geophysical Research, 97(B1), pp. 545-558.
Milbert, D. G., 1992: GPS and GEOID90 -- The new level rod. GPS World, 3(2), pp. 38-43.
Milbert, D. G. and D. G. Schultz, 1993: GEOID93. Software for PC compatible computers. National Geodetic Survey, NOAA, Silver Spring, MD, 5 disks.
Milbert, D. G. and D. G. Schultz, 1993: DEFLEC93. Software for PC compatible computers. National Geodetic Survey, NOAA, Silver Spring, MD, 9 disks.
Kuroishi, Y., D. G. Milbert, and D. G. Schultz, 1993: A Gravimetric Geoid of Japan: Importance on Sea Level Change Detection by Satellite Altimetry. Proceedings of the CRCM'93, Kobe, December 6-11, pp. 363-367.
Parks, W., and D. G. Milbert, 1994: A Geoid Height Model for San Diego County, California, to Test the Effect of Densifying Gravity Measurements on Accuracy of GPS-Estimated Orthometric Height. Surveying and Land Information Systems, 54(4), in press.