The GRACE mission is designed to monitor mass flux on the Earth's surface at one month and high spatial resolution through the estimation of monthly gravity fields. Although this approach has been largely successful, information at submonthly time scales can be lost or even aliased through the estimation of static monthly parameters. Through an analysis of the GRACE data residuals, we show that the fundamental temporal and spatial resolution of the GRACE data is 10 days and 400 km. We present an approach similar in concept to altimetric methods that recovers submonthly mass flux at a high spatial resolution. Using 4°Â 4°blocks at 10-day intervals, we estimate the mass of surplus or deficit water over a 52°Â 60°grid centered on the Amazon basin for July 2003. We demonstrate that the recovered signals are coherent and correlate well with the expected hydrological signal. Citation: Rowlands, D. D., S. B.
Abstract. Over 20 global ocean tide models have been developed since 1994, primarily as a consequence of analysis of the precise altimetric measurements from TOPEX/POSEIDON and as a result of parallel developments in numerical tidal modeling and data assimilation. This paper provides an accuracy assessment of 10 such tide models and discusses their benefits in many fields including geodesy, oceanography, and geophysics. A variety of tests indicate that all these tide models agree within 2-3 cm in the deep ocean, and they represent a significant improvement over the classical Schwiderski 1980 model by approximately 5 cm rms. As a result, two tide models were selected for the reprocessing of TOPEX/POSEIDON Geophysical Data Records in late 1995. Current ocean tide models allow an improved observation of deep ocean surface dynamic topography using satellite altimetry. Other significant contributions include theft applications in an improved orbit computation for TOPEX/POSEIDON and other geodetic satellites, to yield accurate predictions of Earth rotation excitations and improved estimates of ocean loading corrections for geodetic observatories, and to allow better separation of astronomical tides from phenomena with meteorological and geophysical origins. The largest differences between these tide models occur in shallow waters, indicating that the current models are still problematic in these areas. Future improvement of global tide models is anticipated with additional high-quality altimeter data and with advances in numerical techniques to assimilate data into high-resolution hydrodynamic models.
 The differences between mass concentration (mascon) parameters and standard Stokes coefficient parameters in the recovery of gravity information from gravity recovery and climate experiment (GRACE) intersatellite K-band range rate data are investigated. First, mascons are decomposed into their Stokes coefficient representations to gauge the range of solutions available using each of the two types of parameters. Next, a direct comparison is made between two time series of unconstrained gravity solutions, one based on a set of global equal area mascon parameters (equivalent to 4°Â 4°at the equator), and the other based on standard Stokes coefficients with each time series using the same fundamental processing of the GRACE tracking data. It is shown that in unconstrained solutions, the type of gravity parameter being estimated does not qualitatively affect the estimated gravity field. It is also shown that many of the differences in mass flux derivations from GRACE gravity solutions arise from the type of smoothing being used and that the type of smoothing that can be embedded in mascon solutions has distinct advantages over postsolution smoothing. Finally, a 1 year time series based on global 2°equal area mascons estimated every 10 days is presented.
The spaceborne altimeter missions of Geos 3 (50‐cm accuracy) and the future Seasat (10‐cm accuracy) require precise knowledge of the radial position of the spacecraft to be most‐effective. Though errors in previous gravity models have produced large uncertainties in the orbital position of Geos 3, significant improvement has been obtained with new geopotential solutions, Goddard Earth Model (GEM) 9 and 10. The solution for GEM 9 was derived by combining laser data from Geos 3, Lageos, and Starlette; S band measurements on Landsat 1; and data from 26 other satellites used in previous solutions. GEM 10 is a combination solution containing a global set of surface gravity anomalies along with the data in GEM 9. Radial errors of Geos 3 for 5‐day arcs have been reduced from about 5 m to 1 m on the basis of orbital intercomparisons, station navigations, and analyses employing crossover points from passes of altimetry. The use of highly accurate laser data in a constrained least squares solution has permitted GEM 9 to be a larger field than previous derived satellite models, GEM 9 having harmonics complete to 20 × 20 with selected higher‐degree terms. The satellite data set has approximately 840,000 observations, of which 200,000 are laser ranges taken on nine satellites equipped with retroreflectors. GEM 10 is complete to 22 × 22 with selected higher‐degree terms out to degree and order 30 amounting to a total of 592 coefficients. Comparisons with surface gravity and altimeter data indicate a substantial improvement in GEM 9 over previous satellite solutions; GEM 9 is in even closer agreement with surface data than the previously published GEM 6 solution which contained surface gravity. In particular, the free air gravity anomalies calculated from GEM 9 and a surface gravity solution by Rapp (1977) are in excellent agreement for the high‐degree terms (13 ≤ l ≤ 22). From these terms an estimate is made of the gravity anomalies for the upper mantle. The mass constant of the earth, GM, has been estimated from the laser data as 398,600.64±0.02 km3/s2, a value which is principally determined from Lageos. The speed of light used was 299,792.5 km/s. Geocentric station positions were determined for approximately 150 stations in GEM 10. These station coordinates, their mean sea level heights, and altimetry data provide an estimate for the mean radius of the earth of ae = 6,378,139 ± 1 m. Accuracy estimates derived for the potential coefficients have been verified with independent data sets. These produce commission errors in geoid heights of 1.9 m and 1.5 m (global rms values), respectively, for GEM 9 and 10.
 New monthly estimates of the Earth's gravity field determined solely from GRACE inter-satellite range-rate measurements using an improved method of accelerometer calibration and the use of a baseline state parameterization are presented in this paper. Our methodology exploits the inherent power of the inter-satellite range-rate data at the expense of the GPS data, which are used solely for establishing an accurate orbital reference and for calibrating accelerometers. Resulting gravity solutions show significantly less error than previously published GRACE solutions, especially for spherical harmonic terms of degree 2 and terms of order 15,16. Citation:
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.
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.
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