C. M. Cox

Bio: C. M. Cox is an academic researcher from STX Corporation. The author has contributed to research in topics: Geopotential & EGM96. The author has an hindex of 4, co-authored 5 publications receiving 1211 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).

Gravity Field Improvement Activities at NASA GSFC

Abstract: Since the completion of the EGM96 geopotential model, additional satellite tracking data has been added to the satellite-only geopotential model solution. The new data include, TRANET Doppler tracking data from the GEOSAT Geodetic Mission, TDRSS tracking of the Gamma Ray Observatory (GRO), the X-Ray Timing Explorer (XTE), the Earth Radiation Budget Satellite (ERBS), as well as additional data from the Extreme Ultraviolet Explorer (EUVE). The new data from the TDRSS tracked satellites make an important contribution to the satellite-only geopotential solution. Comparisons with independent 30′ × 30′ altimeter derived anomalies from the GEOSAT Geodetic Mission provided by NIMA show that the ERBS data contribute by reducing the residual at degree 70 by 0.47 mGal2. The data from XTE are valuable because of their unique inclination of 23°. Data from low inclination satellites is sparse in most satellite-only derived geopotential models, although substantial amounts of tracking data from EUVE (at an inclination of 28.5°) were included in EGM96. The performance of permutations and subsets of the EGM96 model are also shown to highlight different aspects of the model’s performance.

Further analyses towards the introduction of ocean circulation model information into geopotential solutions

Abstract: Two representation methods for the Dynamic Ocean Topography (DOT) are compared. One uses surface spherical harmonics, the other Proudman functions, which form an ocean domain-specific orthonormal basis. The DOT implied by the temporally averaged output of the POCM―4B ocean circulation model, provided the data for the implementation and testing of the two methods. Using these data a spherical harmonic representation was developed, to degree 30, and a Proudman function decomposition employing 961 basis vectors, so that both representations involve an equal number of parameters. The input DOT field had an rms value of ±66.6 cm. The recovered rms DOT was ±66.1 cm for the spherical harmonic case, ±66.3 cm for the Proudman function case, while the rms difference between the two cases was ±4.2 cm. Although in an overall sense the two representations (with equal number of parameters) yield similar results, in the proximity of the ocean domain boundary the Proudman functions approximate the input DOT field better than the surface spherical harmonics.

Intercomparison and evaluation of some contemporary global geopotential models

Abstract: The performance of five global Earth gravitational models, published after 1995, was examined through tests with data (mostly) withheld from the development of these models. We considered the models: JGM-3 (Tapley et al., 1996), GRIM4-C4 (Schwintzer et al., 1997), TEG-3 (Tapley et al., 1997), EGM96 (Lemoine et al., 1998) and GPM98A (Wenzel, 1998). The test data that we used for model evaluations include satellite tracking measurements acquired over several spacecraft at various inclinations and altitudes, geoid undulations (or height anomalies) determined from GPS positioning and leveling observations, Dynamic Ocean Topography (DOT) information implied by an ocean circulation model, as well as hydrographic estimates of (relative) DOT. Over 9307 GPS/leveling geoid undulation values distributed over North America, Europe and Australia, EGM96 (to degree 360) outperforms all other models tested, yielding a standard deviation of the undulation differences of ±37.2 cm. Considering that the available GPS/leveling data are located over some of the best surveyed areas (gravimetrically), this value is consistent with the predicted (commission plus omission) geoid error of EGM96, whose global rms value equals ±45.3 cm. Over the ocean, the performance of EGM96 is superior to that of all other models tested, as judged by the results of comparisons with both the POCM―4B circulation model DOT output and with the hydrographic DOT estimates. GPM98A was found to be inaccurate over medium wavelengths, and is not considered suitable for orbit determination applications.

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

Time-variable gravity from GRACE: First results

Abstract: Eleven monthly GRACE gravity field solutions are now available for analyses. We show those fields can be used to recover monthly changes in water storage, both on land and in the ocean, to accuracies of 1.5 cm of water thickness when smoothed over 1000 km. The amplitude of the annually varying signal can be determined to 1.0 cm. Results are 30% better for a 1500 km smoothing radius, and 40% worse for a 750 km radius. We estimate the annually varying component of water storage for three large drainage basins (the Mississippi, the Amazon, and a region draining into the Bay of Bengal), to accuracies of 1.0–1.5 cm.

Global marine gravity from retracked Geosat and ERS‐1 altimetry: Ridge segmentation versus spreading rate

Abstract: [1] Three approaches are used to reduce the error in the satellite-derived marine gravity anomalies. First, we have retracked the raw waveforms from the ERS-1 and Geosat/GM missions resulting in improvements in range precision of 40% and 27%, respectively. Second, we have used the recently published EGM2008 global gravity model as a reference field to provide a seamless gravity transition from land to ocean. Third, we have used a biharmonic spline interpolation method to construct residual vertical deflection grids. Comparisons between shipboard gravity and the global gravity grid show errors ranging from 2.0 mGal in the Gulf of Mexico to 4.0 mGal in areas with rugged seafloor topography. The largest errors of up to 20 mGal occur on the crests of narrow large seamounts. The global spreading ridges are well resolved and show variations in ridge axis morphology and segmentation with spreading rate. For rates less than about 60 mm/a the typical ridge segment is 50–80 km long while it increases dramatically at higher rates (100–1000 km). This transition spreading rate of 60 mm/a also marks the transition from axial valley to axial high. We speculate that a single mechanism controls both transitions; candidates include both lithospheric and asthenospheric processes.

Short Note: A global model of pressure and temperature for geodetic applications

Abstract: The empirical model GPT (Global Pressure and Temperature), which is based on spherical harmonics up to degree and order nine, provides pressure and temperature at any site in the vicinity of the Earth’s surface. It can be used for geodetic applications such as the determination of a priori hydrostatic zenith delays, reference pressure values for atmospheric loading, or thermal deformation of Very Long Baseline Interferometry (VLBI) radio telescopes. Input parameters of GPT are the station coordinates and the day of the year, thus also allowing one to model the annual variations of the parameters. As an improvement compared with previous models, it reproduces the large pressure anomaly over Antarctica, which can cause station height errors in the analysis of space-geodetic data of up to 1 cm if not considered properly in troposphere modelling. First tests at selected geodetic observing stations show that the pressure biases considerably decrease when using GPT instead of the very simple approaches applied to various Global Navigation Satellite Systems (GNSS) software packages so far. GPT also provides an appropriate model for the annual variability of global temperature.