R. J. Eanes

The Joint Gravity Model 3

An improved Earth geopotential model, complete to spherical harmonic degree and order 70, has been determined by combining the Joint Gravity Model 1 (JGM 1) geopotential coefficients, and their associated error covariance, with new information from SLR, DORIS, and GPS tracking of TOPEX/Poseidon, laser tracking of LAGEOS 1, LAGEOS 2, and Stella, and additional DORIS tracking of SPOT 2. The resulting field, JGM 3, which has been adopted for the TOPEX/Poseidon altimeter data rerelease, yields improved orbit accuracies as demonstrated by better fits to withheld tracking data and substantially reduced geographically correlated orbit error. Methods for analyzing the performance of the gravity field using high-precision tracking station positioning were applied. Geodetic results, including station coordinates and Earth orientation parameters, are significantly improved with the JGM 3 model. Sea surface topography solutions from TOPEX/Poseidon altimetry indicate that the ocean geoid has been improved. Subset solutions performed by withholding either the GPS data or the SLR/DORIS data were computed to demonstrate the effect of these particular data sets on the gravity model used for TOPEX/Poseidon orbit determination.

Geophysical interpretation of observed geocenter variations

Geocenter variations are caused by mass redistribution within the Earth system, especially the atmosphere, oceans, and continental water. Using surface pressure fields, and soil moisture and snow depth fields of the NCEP-NCAR Climate Data Assimilation System I (CDAS-I)1, we estimate contributions from variations in atmospheric surface pressure and continental water storage to the Earths geocenter (center of mass) variation. In addition, sea surface anomalies determined by the TOPEX/POSEIDON altimeter are used to investigate geocenter variations resulting from ocean mass redistribution. These sea surface height data were corrected using a simplified steric model. A comparison with observed geocenter variations derived from Lageos 1 and 2 satellite laser ranging data indicates that the atmosphere, oceans, and continental hydrological cycle all provide significant contributions at different frequencies. Geocenter variations estimated in this paper are in reasonably good agreement with results given by Dong et al. [1997] for atmospheric and ocean contributions, but not for the estimates of continental hydrological contributions.

Accuracy assessment of the large‐scale dynamic ocean topography from TOPEX/POSEIDON altimetry

The quality of TOPEX/POSEIDON determinations of the global scale dynamic ocean topography have been assessed by determining mean topography solutions for successive 10-day repeat cycles and by examining the temporal changes in the sea surface topography to identify known features. The assessment is based on the analysis of TOPEX altimeter data for cycles 1 through 36. Important errors in the tide model used to correct the altimeter data have been identified. The errors were reduced significantly by use of a new tide model derived with the TOPEX/POSEIDON measurements. Maps of the global 1-year mean topography, produced using four of the most accurate models of the marine geoid, show that the largest error in the dynamic ocean topography is now the uncertainty in the geoid. Temporal variations in the spatially smoothed maps of the annual sea surface topography show expected features, such as the known annual hemispherical sea surface rise and fall and the seasonal variability due to monsoon influence in the Indian Ocean. Changes in the sequence of 10-day topography maps show the development and propagation of an equatorial Kelvin wave in the Pacific beginning in December 1992 with a propagation velocity of approximately 3 m/s. The observations are consistent with observed changes in the equatorial trade winds, and with tide gauge and other in situ observations of the strengthening of the 1992 El Nino. Comparison of TOPEX-determined sea surface height at points near oceanic tide gauges shows agreement at the 4 cm RMS level over the tropical Pacific. The results show that the TOPEX altimeter data set can be used to map the ocean surface with a temporal resolution of 10 days and an accuracy which is consistent with traditional in situ methods for the determination of sea level variations.

Progress in the determination of the gravitational coefficient of the Earth

In most of the recent determinations of the geocentric gravitational coefficient (GM) of the Earth, the laser ranging data to the Lageos satellite have had the greatest influence on the solution. These data, however, have generally been processed with a small but significant error in one of the range corrections. In a new determination of GM using the corrected center-of-mass offset, a value of 398600.4415 km3/sec2 (including the mass of the atmosphere) has been obtained, with an estimated uncertainty (1 σ) of 0.0008 km3/sec2.

Determination of ocean tides from the first year of TOPEX/POSEIDON altimeter measurements

An improved geocentric global ocean tide model has been determined using 1 year of TOPEX/POSEIDON altimeter measurements to provide corrections to the Cartwright and Ray (1991) model (CR91). The corrections were determined on a 3°×3° grid using both the harmonic analysis method and the response method. The two approaches produce similar solutions. The effect on the tide solution of simultaneously adjusting radial orbit correction parameters using altimeter measurements was examined. Four semidiurnal (N2, M2, S2, and K2), four diurnal (Q1, O1, P1, and K1), and three long-period (Ssa, Mm, and Mƒ) constituents, along with the variation at the annual frequency, were included in the harmonic analysis solution. The observed annual variation represents the first global measurement describing accurate seasonal changes of the ocean during an El Nino year. The corrections to the M2 constituent have an RMS of 3.6 cm and display a clear banding pattern with regional highs and lows reaching 8 cm. The improved tide model reduces the weighted altimeter crossover residual from 9.8 cm RMS, when the CR91 tide model is used, to 8.2 cm RMS. Comparison of the improved model to pelagic tidal constants determined from 80 tide gauges gives RMS differences of 2.7 cm for M2 and 1.7 cm for K1. Comparable values when the CR91 model is used are 3.9 cm and 2.0 cm, respectively. Examination of TOPEX/POSEIDON sea level anomaly variations using the new tide model further confirms that the tide model has been improved.

Constraints on energy dissipation in the Earth's body tide from satellite tracking and altimetry

The phase lag by which the earths body tide follows the tidal potential is estimated for the principal lunar semidiurnal tide M(sub 2). The estimate results from combining recent tidal solutions from satellite tracking data and from Topex/Poseidon satellite altimeter data. Each data type is sensitive to the body-tide lag: gravitationally for the tracking data, geometrically for the altimetry. Allowance is made for the lunar atmospheric tide. For the tidal potential Love number kappa(sub 2) we obtain a lag epsilon of 0.20 deg +/- 0.05 deg, implying an effective body-tide Q of 280 and body-tide energy dissipation of 110 +/- 25 gigawatts.

Diurnal and semidiurnal variations in Earth orientation determined from LAGEOS laser ranging

The dynamical rotational equations of the solid Earth provide a useful global integrator of a variety of forcing functions of geophysical interest, including atmospheric mass and wind distribution, and oceanic mass and current distribution. Since the solid Earth/ocean/atmosphere is a coupled dynamical system, changes in these variables, which are frequently difficult to measure in a global sense, lead to changes in the more directly measurable quantity of the rotational axis position and rotation rate of the solid Earth. Satellite laser ranging (SLR) has demonstrated the ability to monitor variations in the both the orientation of the Earth’s spin axis and the rotation rate at the few centimeter level over the past decade (Eanes et al., 1989; Eanes and Watkins, 1990, 1991; IERS, 1989, 1992). The quality of the estimates of polar motion and UT1 have, naturally, improved with time to the current level of 0.5 mas, and the temporal resolution has likewise increased to the current 3-day length.

Comparison of VLBI and SLR geocentric site coordinates

The geocentric coordinates for 18 pairs of SLR and VLBI sites are compared. After a seven-parameter frame adjustment, the two coordinate sets have weighted rms differences of 15, 22, and 22 mm for X, Y, and Z, respectively, consistent with the formal errors being too small by a factor of about two.

Observations of annual variations of the Earth's gravitational field using satellite laser ranging and geophysical models

We have analyzed 6 years of satellite laser ranging (SLR) data to the Lageos 1 & 2 satellites to determine the annual variation of a set of spherical harmonic coefficients of the Earths gravity field complete to degree and order 4 (half-wavelength resolution of ∼5000 km). We have compared these results to a suite of geophysical models describing annual variations of the gravity field due to changes in the distribution of mass in the atmosphere, in the ocean, and continental hydrology (soil moisture and snow). We find that spherical harmonic coefficients derived from the satellite-observations and the aggregate of these geophysical models agree to about 1 mm RMS in geoid height, and have degree correlations that generally exceed the 90% confidence limit. We found that the SLR data could distinguish between two different hydrologic models, but were unable to distinguish between competing models of atmosphere and ocean mass variation, probably due to the small magnitude of the differences in these models (and the small total magnitude of the ocean signal) at the long wavelengths that can be observed by the satellite data. The satellite results should improve considerably in 2001 with the launch of the Gravity Recovery and Climate Experiment (GRACE), which will allow the determination of the time variations of the Earths gravity field with a spatial resolution of about 300 km.

Nongravitational effects and the LAGEOS eccentricity excitations

A model for explaining the anomalous eccentricity excitations of the orbit of the LAGEOS I satellite is considered. It is suggested that two phenomena are responsible for the major part of these residuals: (1) about 1.3% mismodeling of the LAGEOS I surface mean radiation pressure coefficient, and (2) the Yarkovsky-Schach thermal effect with a properly modeled evolution of the satellite spin axis. Minor influences are also attributed to the asymmetric reflectivity of the satellite surface and the asymmetric thermal emissivity of the Earth. For these cases we give a suitable and compact formulation for the long-term orbit analysis. It is argued that contrary to the case of the LAGEOS I along-track residuals adjustment, which does not allow the determination of a particular combination of the Yarkovsky-Schach effect parameters, the combined analysis of the along-track residuals and the eccentricity excitations allows for their decorrelation. The resulting value of the Yarkovsky-Schach amplitude is estimated to be approximately 241 pm/s2, more than twice as large as given in previous works. In view of the unexplained part of the eccentricity residuals, we discuss the possible importance of several other nongravitational effects (Yarkovsky thermal effects due to Earths heating, electromagnetic effects, mismodeling of the transitions through Earths penumbra), concluding that none of them is quantitatively a good candidate.