The development and analysis of geopotential coefficient models to spherical harmonic degree 360

Abstract

The GEM‐T2 potential coefficient model (incomplete to degree 50) has been combined, in a least squares sense, with 30 arc min mean anomalies, to obtain an adjusted set of coefficients and gravity anomalies. The adjusted anomalies were then harmonically analyzed to yield a set of potential coefficients to degree 360. The 30 arc min mean anomalies were estimated from terrestrial gravity data, from altimeter‐derived anomalies, and from 1°×1° terrestrial anomalies where such data were available. For areas devoid of gravity information, the anomalies were computed in two ways: (1) from the GEM‐T2 coefficients and (2) from the GEM‐T2 coefficients to degree 36 plus coefficients implied by a topographic/isostatic model. These “fill‐in” anomalies led to two potential coefficient models: OSU89A and OSU89B. The new models were checked in several ways including satellite orbit residual analysis, Geosat undulation comparisons, and Global Positioning System (GPS)/leveling undulation differences. The orbit fits (carried out by NASA) showed improvement over GEM‐T2. After correction for sea surface topography, orbit error, and permanent tidal effects, the geoid undulations from the OSU89B model have an RMS discrepancy with the Geosat‐implied undulation of ±59 cm over a complete 17‐day exact repeat cycle. The comparisons with GPS information indicate the accuracy of the computation of a relative undulation is of the order of 3–4 ppm of the distance between stations. The new models represent a substantial improvement over previous high‐degree expansions.

The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C

“…EIGEN-GRACE03S was used up to degree and order 150. Additionally, prior to the data evaluation, all data sets were transformed to a common reference ellipsoid, and the correction for the quadratic terms of the normal gravity gradient and ellipsoidal corrections were applied to those gravity anomalies that were given in spherical approximation (Rapp and Pavlis 1990). Finally, the coefficients for degree 360, which cannot be estimated with a 30' x 30' data grid in the block-diagonal approach, are computed through numerical quadrature, using the same data as used in the block-diagonal normal equation system.…”

Geodetic Coordinate Systems in Florida: GPS Contribution

“…However, in this approach it is mandatory to have geoidal heights or undulations. These were predicted using the recently released OSU89B 360 X 360 potential model (Rapp and Pavlis 1990). Although the estimated absolute accuracy of this type of model is generally quoted (for nonmountainous regions in the United States) on the order of 0.5-1 m, nevertheless, this figure may be slightly optimistic in Florida.…”

“…All indications point to the possibility that the true geoid in Florida is smoother than the model appears to indicate. We need to realize that the geoidal model may have an absolute accuracy of only about 1 m. However, as seen from the figure, this should not affect greatly the determination of relative geoidal heights between points that are not too far apart [3-4 ppm of the distance for the OSU89B (Rapp and Pavlis 1990)]. Therefore, the absolute accuracy of the geoid model OSU89B is still an open question that will require more comparisons to be answered conclusively.…”

On the Accuracy of EGM2008 with Measured Data Based on Strap-down Airborne Gravimetry

“…where fM = 3.986004415 × 1014 m 3 s -2 is the product of Newton's gravitational constant and Earth's mass, R= 6.3781363×10 6 m is the mean radius of Earth,  , θ and λ are the radial distance, colatitude, and longitude of the point, respectively, Under the condition of sphere approximate, the gravity disturbance ( or so-called gravity anomaly) on the surface has the relationship with gravitational potential as [7]: 2…”