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Klosko, S. M.

Publications and source records attributed to Klosko, S. M..

At least 37 records · Page 2
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NASA NTRS1989

The GEM-T2 gravitational model

The GEM-T2 is the latest in a series of Goddard Earth Models of the terrestrial field. It was designed to bring modeling capabilities one step closer towards ultimately determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10-cm RMS (root mean square). It also improves models of the long wavelength geoid to support many oceanographic and geophysical applications. The GEM-T2 extends the spherical harmonic field to include more than 600 coefficients above degree 36 (which was the limit for its predecessor, GEM-T1). Like GEM-T1, it was produced entirely from satellite tracking data, but it now uses nearly twice as many satellites (31 vs. 17), contains four times the number of observations (2.4 million), has twice the number of data arcs (1132), and utilizes precise laser tracking from 11 satellites. The estimation technique for the solution has been augmented to include an optimum data weighting procedure with automatic error calibration for the gravitational parameters. Results for the GEM-T2 error calibration indicate significant improvement over previous satellite-only models. The error of commission in determining the geoid has been reduced from 155 cm in GEM-T1 to 105 cm for GEM-T2 for the 36 x 36 portion of the field, and 141 cm for the entire model. The orbital accuracies achieved using GEM-T2 are likewise improved. Also, the projected radial error on the TOPEX satellite orbit indicates 9.4 cm RMS for GEM-T2, compared to 24.1 cm for GEM-T1.

Marsh, J. G.↗
NASA NTRS1989

Gravitational model improvement at the Goddard Space Flight Center

Major new computations of terrestrial gravitational field models were performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). This development has incorporated the present state of the art results in satellite geodesy and have relied upon a more consistent set of reference constants than was heretofore utilized in GSFC's GEM models. The solutions are complete in spherical harmonic coefficients out to degree 50 for the gravity field parameters. These models include adjustment for a subset of 66 ocean tidal coefficients for the long wavelength components of 12 major ocean tides. This tidal adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor ocean tides and the Wahr frequency dependent solid earth tidal model. In addition 5-day averaged values for Earth rotation and polar motion were derived for the time period of 1980 onward. Two types of models were computed. These are satellite only models relying exclusively on tracking data and combination models which have incorporated satellite altimetry and surface gravity data. The satellite observational data base consists of over 1100 orbital arcs of data on 31 satellites. A large percentage of these observations were provided by third generation laser stations (less than 5 cm). A calibration of the model accuracy of the GEM-T2 satellite only solution indicated that it was a significant improvement over previous models based solely upon tracking data. The rms geoid error for this field is 110 cm to degree and order 36. This is a major advancement over GEM-T1 whose errors were estimated to be 160 cm. An error propagation using the covariances of the GEM-T2 model for the TOPEX radial orbit component indicates that the rms radial errors are expected to be 12 cm. The combination solution, PGS-3337, is a preliminary effort leading to the development of GEM-T3. PGS-3337 has incorporated global sets of surface gravity data and the Seasat altimetry to produce a model complete to (50,50). A solution for the dynamic ocean topography to degree and order 10 was included as part of this adjustment.

Marsh, J. G.↗
NASA NTRS1989

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the GEM-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient by coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment.

Lerch, F. J.↗
NASA NTRS1989

Dynamic sea surface topography, gravity and improved orbit accuracies from the direct evaluation of SEASAT altimeter data

A method for the simultaneous solution of dynamic ocean topography, gravity and orbits using satellite altimeter data is described. A GEM-T1 based gravitational model called PGS-3337 that incorporates Seasat altimetry, surface gravimetry and satellite tracking data has been determined complete to degree and order 50. The altimeter data is utilized as a dynamic observation of the satellite's height above the sea surface with a degree 10 model of dynamic topography being recovered simultaneously with the orbit parameters, gravity and tidal terms in this model. PGS-3337 has a geoid uncertainty of 60 cm root-mean-square (RMS) globally, with the uncertainty over the altimeter tracked ocean being in the 25 cm range. Doppler determined orbits for Seasat, show large improvements, with the sub-30 cm radial accuracies being achieved. When altimeter data is used in orbit determination, radial orbital accuracies of 20 cm are achieved. The RMS of fit to the altimeter data directly gives 30 cm fits for Seasat when using PGS-3337 and its geoid and dynamic topography model. This performance level is two to three times better than that achieved with earlier Goddard earth models (GEM) using the dynamic topography from long-term oceanographic averages. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 1500 km. The power in the dynamic topography recovery is now found to be closer to that of oceanographic studies than for previous satellite solutions. This is attributed primarily to the improved modeling of the geoid which has occurred. Study of the altimeter residuals reveals regions where tidal models are poor and sea state effects are major limitations.

Marsh, J. G.↗
NASA NTRS1988

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Lerch, F. J.↗
NASA NTRS1988

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.

Christodoulidis, D. C.↗
NASA NTRS1987

An improved model of the Earth's gravitational field: GEM-T1

Goddard Earth Model T1 (GEM-T1), which was developed from an analysis of direct satellite tracking observations, is the first in a new series of such models. GEM-T1 is complete to degree and order 36. It was developed using consistent reference parameters and extensive earth and ocean tidal models. It was simultaneously solved for gravitational and tidal terms, earth orientation parameters, and the orbital parameters of 580 individual satellite arcs. The solution used only satellite tracking data acquired on 17 different satellites and is predominantly based upon the precise laser data taken by third generation systems. In all, 800,000 observations were used. A major improvement in field accuracy was obtained. For marine geodetic applications, long wavelength geoidal modeling is twice as good as in earlier satellite-only GEM models. Orbit determination accuracy has also been substantially advanced over a wide range of satellites that have been tested.

Marsh, J. G.↗
NASA NTRS1987

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 x 10 to the minus 22 rad/second squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change of the earth's rotation rate of -4.69 + or - 0.36 x 10 to the minus 22 rad/second squared.

Christodoulidis, D. C.↗
NASA NTRS1986

Comments on Lambeck and Coleman - 'The earth's shape and gravity field: A report of progress from 1958 to 1982'

The accuracy and validation of global gravity models based on satellite data are discussed, responding to the statistical analysis of Lambeck and Coleman (1983) (LC). Included are an evaluation of the LC error spectra, a summary of independent-observation calibrations of the error estimates of the Goddard Earth Models (GEM) 9 and L2 (Lerch et al., 1977, 1979, 1982, 1983, and 1985), a comparison of GEM-L2 with GRIM-3B (Reigber et al., 1983), a comparison of recent models with LAGEOS laser ranging, and a summary of resonant-orbit model tests. It is concluded that the accuracy of GEMs 9, 10, and L2 is much higher than claimed by LC, that the GEMs are in good agreement with independent observations and with GRIM-3B, and that the GEM calibrations were adequate. In a reply by LC, a number of specific questions regarding the error estimates are addressed, and it is pointed out that the intermodel discrepancies of the greatest geophysical interest are those in the higher-order coefficients, not discussed in the present comment. It is argued that the differences among the geoid heights of even the most recent models are large enough to call for considerable improvements.

Lerch, F. J.↗
NASA NTRS1986

Contemporary plate motions from Lageos - A decade later

Progress made due to Lageos tracking and the participation of over 20 countries in the acquisition and analysis of precise range measurements is reviewed. Results of both the observed global and regional plate kinematics are presented. Mission accomplishments include the following: (1) laser technology advancements of more than an order of magnitude in single point range precision over the last ten years, (2) station positioning at the few centimeter accuracy level for annual solutions, and (3) the emergence of a global picture of plate kinematics.

Christodoulidis, D. C.↗
NASA NTRS1985

A global geodetic reference frame from Lageos ranging (SL5.1AP)

A summary of the results obtained for a new comprehensive geodetic parameter solution from the analysis of Lageos laser ranging data for the period May 1976 to the end of 1982 is presented. Estimates of each component of the polar motion and earth rotation, the station coordinates, the value of the earth's gravitational constant GM, and the elements of the Lageos orbit comprise this SL5.1AP solution. The results differ from previously published values primarily through incorporation of more rigorous dynamic models for the ocean and solid earth tides. The precision of the geodetic parameters are on average 5-marc sec polar motion, 0.2-ms length of day, better than 5-cm center-of-mass geodetic positioning, 3-cm global baselines, and 2-cm regional baselines. An assessment of the contribution of systematic errors in the interstation distance determination is presented.

Smith, D. E.↗
NASA NTRS1985

Observing tectonic plate motions and deformations from satellite laser ranging

The scope of geodesy has been greatly affected by the advent of artificial near-earth satellites. The present paper provides a description of the results obtained from the reduction of data collected with the aid of satellite laser ranging. It is pointed out that dynamic reduction of satellite laser ranging (SLR) data provides very precise positions in three dimensions for the laser tracking network. The vertical components of the stations, through the tracking geometry provided by the global network and the accurate knowledge of orbital dynamics, are uniquely related to the center of mass of the earth. Attention is given to the observations, the methodologies for reducing satellite observations to estimate station positions, Lageos-observed tectonic plate motions, an improved temporal resolution of SLR plate motions, and the SLR vertical datum.

Christodoulidis, D. C.↗
NASA NTRS1985

A gravity model for crustal dynamics (GEM-L2)

The Laser Geodynamics Satellite (Lageos) was the first NASA satellite which was placed into orbit exclusively for laser ranging applications. Lageos was designed to permit extremely accurate measurements of the earth's rotation and the movement of the tectonic plates. The Goddard earth model, GEM-L2, was derived mainly on the basis of the precise laser ranging data taken on many satellites. Douglas et al. (1984) have demonstrated the utility of GEM-L2 in detecting the broadest ocean circulations. As Lageos data constitute the most extensive set of satellite laser observations ever collected, the incorporation of 2-1/2 years of these data into the Goddard earth models (GEM) has substantially advanced the geodynamical objectives. The present paper discusses the products of the GEM-L2 solution.

Lerch, F. J.↗
NASA NTRS1985

On the accuracy of recent Goddard gravity models

The Goddard Space Flight Center (GSFC) has occupied a central position within NASA with respect to the development of earth gravity models. The gravity models at Goddard, which are referred to as the Goddard earth models (GEM's) have been under development for more than 15 years. The fields have increased in size and (apparent) accuracy with the inclusion of new tracking data, better nongravitational force modeling, and more orbits over a wide range of inclinations and mean motions. The usefulness of the considered models depends largely on accuracy estimates. The present paper is concerned with a reevaluation of earlier accuracy assessments, taking into account the accuracies of the GEM 9 and the GEM-L2 models. It is found that GEM 9 is about 30 percent more accurate than originally estimated in 1979 from older gravimetry data.

Lerch, F. J.↗
NASA NTRS1985

Geodetic and geophysical results from Lageos

Seven years of laser tracking of the Lageos spacecraft have been used to derive geodetic quantities describing the earth and its rotational motion. The dynamical motions of the solid-earth on its axis have been derived continuously since launch and changes in the length-of-day show very high correlation with variations in the atmospheric zonal winds between 1000 and 50 mbars. A significant improvement in the determination of the product of the earth's mass and the gravitational constant has been made. The high accuracy of the orbit determination of Lageos over the 7 years since launch has permitted the identification of a small deceleration in the nodal precession of the orbit. This deceleration is being caused by a small reduction in the flattening of the earth arising from the rebound of the earth after the last ice age. Measurements of the distances between the tracking stations over several years are showing changes consistent with tectonic plate motion and with general ideas of vertical movements.

Smith, D. E.↗
NASA NTRS1982

A refined gravity model from Lageos /GEM-L2/

Lageos satellite laser ranging (SLR) data taken over a 2.5 yr period were employed to develop the Goddard Earth Model GEM-L2, a refined gravity field model. Additional data was gathered with 30 other satellites, resulting in spherical harmonics through degree and order 20, based on over 600,000 measurements. The Lageos data was accurate down to 10 cm, after which the GEM 9 data were used to make adjustments past order 7. The resolution of long wavelength activity, through degree and order 4, was made possible by the Lageos data. The GEM-L2 model features a 20 x 20 geopotential, tracking station coordinates (20), 5-day polar motion and A1-UT1 values, and a GM value of 398,600.607 cu km/sq sec. The accuracy of station positioning has been raised to within 6 cm total position globally and within 1.8 cm in baselines. It is concluded that SLR is useful for measuring tectonic plate motions and inter-plate deformations.

Lerch, F. J.↗