The GEM‐T2 Gravitational Model

Abstract

GEM‐T2 is the latest in a series of Goddard Earth models of the terrestrial gravitational field. It is the second in a planned sequence of gravity models designed to improve both the modeling capabilities for determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10‐cm RMS and for defining the long‐wavelength geoid to support many oceanographic and geophysical applications. GEM‐T2 includes more than 6OU coefficients above degree 36, the limit for GEM‐T1, and provides a dynamically determined model of the major tidal components which contains 90 terms. Like GEM‐T1, it was produced entirely from satellite tracking data. GEM‐T2 however, now uses nearly twice as many satellites (31 versus 17), contains 3 times the number of observations (2.4 million), and has twice the number of data arcs (1130). GEM‐T2 utilizes laser tracking from 11 satellites, Doppler data from four satellites, two‐ and three‐way range rate data from Landsat‐1, satellite‐to‐satellite tracking data between the geosynchronous ATS 6 and GEOS 3, and optical observations on 20 different orbits. This observation set effectively exhausts the inclination distribution available for gravitational field development from our historical data base. The recovery of the higher degree and order coefficients in GEM‐T2 was made possible through the application of a constrained least squares technique using the known spectrum of the Earth's gravity field as a priori information. The error calibration of the model was performed concurrently with its generation by comparing the complete model against test solutions which omit each individually identifiable data set in turn. The differences between the solutions isolate the contribution of a given data set, and the magnitudes of these differences are compared for consistency against their expected values from the respective solution covariances. The process yields near optimal data weights and assures that the model will be both self‐consistent and well calibrated. GEM‐T2 has benefitted by its application as demonstrated through comparisons using independently derived gravity anomalies from altimelry. Results for the GEM‐T2 error calibration indicate significant improvement over previous satellite‐only GEM models. The accuracy assessment of the lower degree and order coefficients of GEM‐T2 shows that their uncertainties have been reduced by 20% compared to GEM‐T1. The commission error of the geoid has been reduced from 160 cm for GEM‐T1 to 130 cm for GEM‐T2 for the 36 × 36 portion of the field. The orbital accuracies achieved using GEM‐T2 are likewise improved. This is especially true for the Starlette and GEOS 3 orbits where higher‐order resonance terms not present in GEM‐T1 (e.g., terms with m = 42,43) are now well represented in GEM‐T2. The improvement in orbital accuracy of GEM‐T2 over GEM‐T1 extends across all orbit inclinations. This confirms our conclusion that GEM‐T2 offers a significant advance in knowledge of the Earth's gravity field.

Tides—a modern perspective

“…Following the pioneering work by Spencer Jones (1939), who estimated a value for tidal dissipation of 2.76 TW from lunar occultations, more recent and reliable estimates by Morrison (1978) from 250-year data on Mercury's passage yield a value of 3.17 TW, again remarkably close to other recent estimates. Finally, tidal perturbations of the ephemerides of artificial satellites can also be used to estimate the tidal dissipation rates, and recent estimates applying this method to over 30 satellites (Marsh et al, 1990) also yield a value of 3.17 TW. The fourth method, lunar laser ranging, yields a value of 3.07 TW (Dickey et al, 1994), which is a slight underestimate, probably because of the short record length available at present.…”

“…Recent analysis of laminated tidal sedimentary records from Utah, Indiana, Alabama, and Australia (Sonett, 1996), produced by the semimonthly spring and neap tides during the Proterozoic era 900 million years ago, indicates that the year consisted then of 481 days each about 18 hours long, equivalent to an average LOD increase of 2.4 ms cy~'. Advances, mostly Downloaded by [Northeastern University] at 05:19 07 October 2014 in this decade, such as more accurate analyses of pretelescopic (Ciyuan & Yau, 1990) and telescopic (Morrison, 1978) astronomical observations, precise tracking of artificial satellites (Marsh et al, 1990), and lunar laser ranging of the Moon (Dickey et al,I994), have enabled for the very first time a precise quantification of the amount of dissipation of the lunar tidal energy in the global oceans, even though the precise mechanisms and regions of dissipation appear to be still elusive and problematic (see Munk, 1997, andKagan &Sundermann, 1996, for detailed discussions of tidal energetics). According to Munk (1997), after about 80 years of strenuous attempts, the convergence of tidal dissipation estimates by many diverse methods may very well be one of the triumphs of twentieth-century science.…”

Global surface heat flux anomalies from seismic tomography‐based models of mantle flow: Implications for mantle convection

“…The excellent theoretical description of all largest-scale features of the observation is typical of optimal results that obtain when the global tomographic model SFIK is employed to define the three-dimensional field of mantle heterogeneity. We inferred the viscosity profile of Figure 2a on the basis of a series of forward modeling calculations which minimized the squared misfit between prediction and the GEM-T2 field [Marsh et al, 1990]. It leads to an 83% variance reduction of the geoid data and 77% variance reduction of the free-air gravity data.…”

A combined theory for zonal harmonic and resonance perturbations of a near-circular orbit with applications to COSMOS 1603 (1984-106A)

“…Furthermore the residuals are significantly larger than the observed accuracites which varied between 2 x 10 -6 and 16 x 10 -6 (Paper 1). Apparently, although the simplistic modelling for the zonal variation is adequate qualitatively, the neglect of higher order terms in Equation (5) (Marsh et al, 1988), GEM-T2 (Marsh et al, 1989) and PGS-3337 (Marsh et al, 1990). 46960 when the eccentricity was close to its minimum value.…”