The GEM‐T2 potential coefficient model (incomplete to degree 50) has been combined, in a least squares sense, with 30 arc min mean anomalies, to obtain an adjusted set of coefficients and gravity anomalies. The adjusted anomalies were then harmonically analyzed to yield a set of potential coefficients to degree 360. The 30 arc min mean anomalies were estimated from terrestrial gravity data, from altimeter‐derived anomalies, and from 1°×1° terrestrial anomalies where such data were available. For areas devoid of gravity information, the anomalies were computed in two ways: (1) from the GEM‐T2 coefficients and (2) from the GEM‐T2 coefficients to degree 36 plus coefficients implied by a topographic/isostatic model. These “fill‐in” anomalies led to two potential coefficient models: OSU89A and OSU89B. The new models were checked in several ways including satellite orbit residual analysis, Geosat undulation comparisons, and Global Positioning System (GPS)/leveling undulation differences. The orbit fits (carried out by NASA) showed improvement over GEM‐T2. After correction for sea surface topography, orbit error, and permanent tidal effects, the geoid undulations from the OSU89B model have an RMS discrepancy with the Geosat‐implied undulation of ±59 cm over a complete 17‐day exact repeat cycle. The comparisons with GPS information indicate the accuracy of the computation of a relative undulation is of the order of 3–4 ppm of the distance between stations. The new models represent a substantial improvement over previous high‐degree expansions.
The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model‐1 (JGM‐I) and the postlaunch JGM‐2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM‐2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being ±25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3–4 cm RMS, a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed, geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.
The global SEASAT altimeter data set has been edited and adjusted using a crossing arc procedure fixing one long arc to provide control. In doing this a set of 168 master arcs were formed from repeat and near repeat arcs. The adjustment, carried out by D. Rowlands, was done in a global net, and four regional areas. The average crossover discrepancy before the adjustment was ±1.5 m, while after the adjustment (solving for a bias and trend) it was ±28 cm. The examination of the crossover discrepancies by area indicated larger than normal discrepancies in certain areas such as the Hudson Bay, the Mediterranean, and the North and Baltic seas. Some of these discrepancies are caused by invalid tide values applied to the altimeter data in these areas. The adjusted SEASAT sea surface heights were used to predict point values at 1° × 1° intersections in 10 different geographic regions for comparison with corresponding GEOS 3 values. A mean difference (GEOS 3 minus SEASAT) of 1.3±0.67 m was found, the mean difference being caused by different ellipsoid parameters. The adjusted data were also used to determine mean surface heights and gravity anomalies in 37,9051°×1°and 1178 5° equal‐area blocks with some of these values being on land. These estimations were done using least squares collocation using covariances functions scaled to each 5° region. The average predicted standard deviation of the 1°×1° anomalies was ±5.1 mGal, and ±2.7 mGal for the 5° blocks. SEASAT values were compared to the GEOS 3 values, finding a difference of ±7.8 mGal and ±0.87 m for the 1°×1° data, and ±2.2 mGal and ±0.76 m for the 5° data. Comparisons with terrestrial data showed no significant difference between the GEOS 3/SEASAT implied anomalies, although a number of significant discrepancies have been resolved with the SEASAT data.
The determination of high-degree geopotential models currently requires accurate terrestrial gravity information on a global basis. For the regions where such information is unavailable or poor, it is important to develop procedures for the estimation of gravity anomalies, based on existing data sources. This paper examines the possibility of combining low-degree satellite-derived geopotential models with the harmonic coefficients of the topographic-isostatic potential implied by the Airy/Heiskanen isostatic hypothesis.The compilation of a new global topographic database that provides additional information pertaining to terrain type classification, ice coverage etc. , is discussed first. Then the rigorous formulation for the determination of harmonic coefficients of the topographic-isostatic potential is extended to account for the various terrain types. This formulation, and a series expansion approach are implemented to determine topographic-isostatic coefficient sets complete to degree and order 360. These coefficients are then combined with satellite-derived models (GEM-TlIT2) to estimate 1" x 1" mean gravity anomalies. Comparisons of the estimated anomalies with observed values, as well as with anomalies derived from satellite altimetry, indicated the following. (a) Optimum results are obtained when the satellite models are used to degree 36 and the topographic-isostatic coefficients from 37 onwards. For example, when GEM-T2 to degree 36 is combined with the topographic-isostatic coefficients from 37 to 180, the root mean square (rms) anomaly difference with 6237 1" x 1" terrestrial values having a standard aeviation less than 10 mgals, was f18 mgals, which should be compared to the rms value of the terrestrial anomalies which was about f27mgals. The use of GEM-T2 alone up to degree 36 yields an rms discrepancy with the same terrestrial values of the order of f22mgal. (b) The effect of ice is significant and improves the quality of the estimated anomalies in polar regions where very limited gravity material exists. (c) The overall accuracy of the estimated anomalies is about equal to the overall accuracy of existing geophysically predicted anomalies. However, the use of the satellite model for the low degrees in the current procedure, may resolve problems associated with regional biases detected in the geophysical anomalies.
Gravity anomalies and sea surface heights have been computed on a 0.125° grid in the ocean areas from a combined GEOS 3/Seasat altimeter data set. The basic estimation procedure used least squares collocation where model covariance functions are tailored to individual areas through altimeter residual variance scaling. Preliminary tests led to production prediction procedures using a reference model defined by a set of potential coefficients complete to degree 180. Comparisons of the predicted anomalies with ship‐derived values showed agreement varying from ±9 to ±30 mGal. No correction to the altimeter‐implied sea surface heights was made for sea surface topography effects. The maximum anomaly predicted is 396 mGal near Hawaii and the most negative anomaly is −361 mGal over the Puerto Rican Trench. The actual resolution of the predicted quantities was estimated to be about 0.19° based on a power spectrum analysis. The resolution is limited by our data selection process which uses 300 data points from a thinned altimeter data set for the prediction of the 0.125° in a 3° × 3° block with one data selection and matrix inversion. The predicted data are used to compute 104 potential coefficient spectrums using flat earth approximations developed by Forsberg. The spectra were classified in terms of smooth, mild, or rough areas. The great majority (78) of the spectra were in the smooth classification. Good agreement was found from spectra computed from topographically reduced land data and the mean ocean data, up to degree 800. We found that the spectra decayed as l−3.6 as compared to the decay of l−3 implied by the Kaula model. The gridded data was used to compute 1° × 1° and 0.5° × 0.5° mean values. The 1° mean anomalies were compared to terrestrial data where an rms difference of ±7 mGal was found in comparing 10,139 values. These new values have allowed us to identify 1° mean anomalies (based on terrestrial estimates) that are in substantial error.
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