Richard H. Rapp

Bio: Richard H. Rapp is an academic researcher from Ohio State University. The author has contributed to research in topics: Geoid & Gravity anomaly. The author has an hindex of 27, co-authored 81 publications receiving 3711 citations.

The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96

Abstract: The NASA Goddard Space Flight Center (GSFC), the National Imagery and Mapping Agency (NIMA), and The Ohio State University (OSU) have collaborated to develop an improved spherical harmonic model of the Earth's gravitational potential to degree 360. The new model, Earth Gravitational Model 1996 (EGM96), incorporates improved surface gravity data, altimeter-derived gravity anomalies from ERS-1 and from the GEOSAT Geodetic Mission (GM), extensive satellite tracking data-including new data from Satellite Laser Ranging (SLR), the Global Postioning System (GPS), NASA's Tracking and Data Relay Satellite System (TDRSS), the French DORIS system, and the US Navy TRANET Doppler tracking system-as well as direct altimeter ranges from TOPEX/POSEIDON (T/P), ERS-1, and GEOSAT. The final solution blends a low-degree combination model to degree 70, a block-diagonal solution from degree 71 to 359, and a quadrature solution at degree 360. The model was used to compute geoid undulations accurate to better than one meter (with the exception of areas void of dense and accurate surface gravity data) and realize WGS84 as a true three-dimensional reference system. Additional results from the EGM96 solution include models of the dynamic ocean topography to degree 20 from T/P and ERS-1 together, and GEOSAT separately, and improved orbit determination for Earth-orbiting satellites.

The Development of the NASA GSFC and NIMA Joint Geopotential Model

Abstract: The NASA Goddard Space Flight Center, the National Imagery and Mapping Agency (NIMA; formerly the Defense Mapping Agency or DMA) and The Ohio State University have collaborated to produce EGM96, an improved degree 360 spherical harmonic model representing the Earth’s gravitational potential. This model was developed using: (1) satellite tracking data from more than 20 satellites, including new data from GPS and TDRSS, as well as altimeter data from TOPEX, GEOSAT and ERS-1. (2) 30’ x 30’ terrestrial gravity data from NIMA’s comprehensive archives, including new measurements from areas such as the former Soviet Union, South America, Africa, Greenland, and elsewhere. (3) 30’ x 30’ gravity anomalies derived from the GEOSAT Geodetic Mission altimeter data, as well as altimeter derived anomalies derived from ERS-1 by KMS (Kort and Matrikelstyrelsen, Denmark) in regions outside the GEOSAT coverage. The high degree solutions were developed using two different model estimation techniques: quadrature, and block diagonal. The final model is a composite solution consisting a combination solution to degree 70, a block diagonal solution to degree 359, and the quadrature model at degree 360. This new model will be used to define an undulation model that will be the basis for an update of the WGS-84 geoid. In addition, the model will contribute to oceanographic studies by improving the modeling of the ocean geoid and to geodetic positioning using the Global Positioning System (GPS).

The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models

Abstract: The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.

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

Abstract: Two new geopotential coefficient models to spherical harmonic degree 360 are developed using recent advances made in theoretical modeling methods, satellite gravitational models, and expanded and improved terrestrial data. The new models are based on the combination of a satellite potential coefficient model (GEM-T2) to degree 50 with 30-arc mean gravity anomalies, yielding an adjusted set of coefficients and gravity anomalies, which were then harmonically analyzed to yield a set of potential coefficients to degree 360. The models were verified in several ways including satellite orbit residual analysis, demonstrating a substantial improvement over previous high-degree expansions.

Gravity model development for TOPEX/POSEIDON: Joint gravity models 1 and 2

Abstract: The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model-1 (JGM-1) and the postlaunch JGM-2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM-2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being +/- 25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3-4 cm root mean square (RMS), a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.

The Shuttle Radar Topography Mission

Abstract: [1] The Shuttle Radar Topography Mission produced the most complete, highest-resolution digital elevation model of the Earth. The project was a joint endeavor of NASA, the National Geospatial-Intelligence Agency, and the German and Italian Space Agencies and flew in February 2000. It used dual radar antennas to acquire interferometric radar data, processed to digital topographic data at 1 arc sec resolution. Details of the development, flight operations, data processing, and products are provided for users of this revolutionary data set.

The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)

Abstract: [1] EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG-GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area-mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid This grid was formed by merging terrestrial, altimetry-derived, and airborne gravity data Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159 Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of ±5 to ±10 cm EGM2008 vertical deflections over USA and Australia are within ±11 to ±13 arc-seconds of independent astrogeodetic values These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models EGM2008 performs equally well with other GRACE-based gravitational models in orbit computations Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, asingle global model may satisfy the requirements of a very wide range of applications

Marine gravity anomaly from Geosat and ERS 1 satellite altimetry

Abstract: Closely spaced satellite altimeter profiles collected during the Geosat Geodetic Mission (-6 km) and the ERS 1 Geodetic Phase (8 km) are easily converted to grids of vertical gravity gradient and gravity anomaly. The long-wavelength radial orbit error is suppressed below the noise level of the altimeter by taking the along-track derivative of each profile. Ascending and descending slope profiles are then interpolated onto separate uniform grids. These four grids are combined to form comparable grids of east and north vertical deflection using an iteration scheme that interpolates data gaps with minimum curvature. The vertical gravity gradient is calculated directly from the derivatives of the vertical deflection grids, while Fourier analysis is required to construct gravity anomalies from the two vertical deflection grids. These techniques are applied to a combination of high-density data from the dense mapping phases of Geosat and ERS 1 along with lower-density but higher-accuracy profiles from their repeat orbit phases. A comparison with shipboard gravity data shows the accuracy of the satellite- derived gravity anomaly is about 4-7 mGal for random ship tracks. The accuracy improves to 3 mGal when the ship track follows a Geosat Exact Repeat Mission track line. These data provide the first view of the ocean floor structures in many remote areas of the Earth. Some applications include inertial navigation, prediction of seafloor depth, planning shipboard surveys, plate tectonics, isostasy of volcanoes and spreading ridges, and petroleum exploration.

The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96

Abstract: The NASA Goddard Space Flight Center (GSFC), the National Imagery and Mapping Agency (NIMA), and The Ohio State University (OSU) have collaborated to develop an improved spherical harmonic model of the Earth's gravitational potential to degree 360. The new model, Earth Gravitational Model 1996 (EGM96), incorporates improved surface gravity data, altimeter-derived gravity anomalies from ERS-1 and from the GEOSAT Geodetic Mission (GM), extensive satellite tracking data-including new data from Satellite Laser Ranging (SLR), the Global Postioning System (GPS), NASA's Tracking and Data Relay Satellite System (TDRSS), the French DORIS system, and the US Navy TRANET Doppler tracking system-as well as direct altimeter ranges from TOPEX/POSEIDON (T/P), ERS-1, and GEOSAT. The final solution blends a low-degree combination model to degree 70, a block-diagonal solution from degree 71 to 359, and a quadrature solution at degree 360. The model was used to compute geoid undulations accurate to better than one meter (with the exception of areas void of dense and accurate surface gravity data) and realize WGS84 as a true three-dimensional reference system. Additional results from the EGM96 solution include models of the dynamic ocean topography to degree 20 from T/P and ERS-1 together, and GEOSAT separately, and improved orbit determination for Earth-orbiting satellites.